diff --git a/test/extract_questions.py b/test/extract_questions.py new file mode 100644 index 0000000..40739de --- /dev/null +++ b/test/extract_questions.py @@ -0,0 +1,49 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Fri Jul 26 15:03:02 2019 + +@author: domonique_hodge +""" +import pickle +import json +import nltk +from sklearn.feature_extraction.text import TfidfVectorizer +from summa.summarizer import summarize + +import pynlp +from pynlp import StanfordCoreNLP + +#Extract questions from papers +papers = json.load( open( "/Users/domonique_hodge/Documents/External Clients/DARPA/cleanedArticles-03042019.json", "rb" ) ) + +all_questions = [] + + +for i in papers.keys(): + print(i) + + + all_text = papers[i]['text'] + + try: + sentence = sent_tokenize(all_text) + sentence_index = [i for i, x in enumerate(sentence) if x[-1:] == "?"] + + num_quest = len(sentence_index) + + if num_quest >0: + for j in range(0,num_quest): + question = sentence[[i for i, x in enumerate(sentence) if x[-1:] == "?"][j]] + all_questions.append(question) + except: + print('Error occured with tokenizing article') + +no_duplicate_quest = list(dict.fromkeys(all_questions)) + +#write to txt file + +with open('/Users/domonique_hodge/Documents/External Clients/DARPA/QG Net update/questions_v2.txt', 'w') as f: + for item in no_duplicate_quest: + f.write("%s\n" % item) + diff --git a/test/input_subset_used.txt b/test/input_subset_used.txt new file mode 100644 index 0000000..8781e47 --- /dev/null +++ b/test/input_subset_used.txt @@ -0,0 +1,3201 @@ +Information￨U￨NN￨O￨- on￨L￨IN￨O￨- sapovirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- or￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- in￨L￨IN￨O￨- free-ranging￨L￨JJ￨O￨- wildlife￨L￨NN￨O￨A is￨L￨VBZ￨O￨- scant￨L￨JJ￨O￨- and￨L￨CC￨O￨- long-term￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- any￨L￨DT￨O￨- wildlife￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- lacking￨L￨VBG￨O￨- .￨L￨.￨O￨- +Its￨U￨PRP$￨O￨- wild￨L￨JJ￨O￨A carnivore￨L￨NN￨O￨- guild￨L￨NN￨O￨- of￨L￨IN￨O￨- 26￨L￨CD￨NUMBER￨- species￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- multi-host￨L￨JJ￨O￨- landscape￨L￨NN￨O￨- for￨L￨IN￨O￨- viral￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 34￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 36￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- spotted￨L￨JJ￨O￨- hyena￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Crocuta￨U￨NN￨O￨- crocuta￨L￨NN￨O￨- ,￨L￨,￨O￨- family￨L￨NN￨O￨- Hyaenidae￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- abundant￨L￨JJ￨O￨- large￨L￨JJ￨O￨- carnivore￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A —￨L￨:￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- PI-SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- online￨L￨JJ￨O￨- TV￨U￨NN￨O￨- series￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- and￨L￨CC￨O￨- test￨L￨NN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- using￨L￨VBG￨O￨- three￨L￨CD￨NUMBER￨- popular￨L￨JJ￨O￨- South￨U￨JJ￨NATIONALITY￨- Korean￨U￨JJ￨NATIONALITY￨- TV￨U￨NN￨O￨- series￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- finds￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A stimulation￨L￨NN￨O￨- would￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- online￨L￨JJ￨O￨- streaming￨L￨NN￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- TV￨U￨NN￨O￨- series￨L￨NN￨O￨- audience￨L￨NN￨O￨- significantly￨L￨RB￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- lock-in￨L￨NN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +TV￨U￨NN￨O￨- series￨L￨NN￨O￨- update￨L￨VBP￨O￨- periods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- fixed￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- viewed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A stimulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- audiences￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- impulsive￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- suppresses￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- TV￨U￨NN￨O￨- series￨L￨NN￨O￨- updates￨L￨NNS￨O￨- stimulate￨L￨VBP￨O￨- diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- major￨L￨JJ￨O￨- online￨L￨JJ￨O￨- video-streaming￨L￨JJ￨O￨- service￨L￨NN￨O￨- suppliers￨L￨NNS￨O￨- buy￨L￨VBP￨O￨- the￨L￨DT￨O￨- broadcast￨L￨NN￨O￨- rights￨L￨NNS￨O￨- of￨L￨IN￨O￨- TV￨U￨NN￨O￨- series￨L￨NN￨O￨A and￨L￨CC￨O￨- sell￨L￨VB￨O￨- inserted￨L￨VBN￨O￨- commercial￨L￨JJ￨O￨- advertisements￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- audiences￨L￨NNS￨O￨- must￨L￨MD￨O￨- view￨L￨VB￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- perform￨L￨VB￨O￨- the￨L￨DT￨O￨- isolated￨L￨VBN￨O￨- contingency￨L￨NN￨O￨- analysis￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨A called￨L￨VBN￨O￨- “￨L￨``￨O￨- temporal￨L￨JJ￨O￨- knockout￨L￨NN￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- TKO￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- super-spreader￨L￨JJ￨O￨- and￨L￨CC￨O￨- immunization￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- measure￨L￨VB￨O￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨- ’s￨L￨POS￨O￨- influence/impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨A called￨L￨VBN￨O￨- “￨L￨``￨O￨- temporal￨L￨JJ￨O￨- knockout￨L￨NN￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- TKO￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- super-spreader￨L￨JJ￨O￨- and￨L￨CC￨O￨- immunization￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- measure￨L￨VB￨O￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨- ’s￨L￨POS￨O￨- influence/impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +TKO￨U￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- network￨L￨NN￨O￨- measure￨L￨NN￨O￨A for￨L￨IN￨O￨- approximating￨L￨VBG￨O￨- influence￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- rather￨L￨RB￨O￨- an￨L￨DT￨O￨- all-things-considered￨L￨JJ￨O￨- empirical￨L￨JJ￨O￨- measurement￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨- ’s￨L￨POS￨O￨- time-dependent￨L￨JJ￨O￨- potential￨L￨NN￨O￨- to￨L￨TO￨O￨- change￨L￨VB￨O￨- propagation￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- for￨L￨IN￨O￨- use￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- benchmark￨L￨NN￨O￨- in￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- network￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- generated￨L￨VBN￨O￨- or￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- used￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- placement￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- these￨L￨DT￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- identified￨L￨VBN￨O￨- best￨L￨JJS￨O￨- measure￨L￨NN￨O￨A of￨L￨IN￨O￨- influence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Danon13￨U￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- extensive￨L￨JJ￨O￨- review￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Identical￨U￨JJ￨MISC￨- synchronization￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- non-autonomous￨L￨JJ￨O￨- unified￨L￨JJ￨O￨- chaotic￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- switchBehnaz￨L￨NN￨O￨- Koocheck￨U￨NNP￨O￨- Shooshtari￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- AbdolMohammad￨U￨NNP￨O￨- Forouzanfar￨U￨NNP￨O￨- †￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- MohammadReza￨U￨NNP￨O￨- Molaei￨U￨NNP￨O￨- †￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- †￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- 5:1667￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- a￨L￨DT￨O￨- non-autonomous￨L￨JJ￨O￨- unified￨L￨JJ￨O￨- chaotic￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- switch￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- Chen￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Lorenz￨U￨NNP￨PERSON￨- systems￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- identical￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- complete￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- synchronization￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- bi-directionally￨L￨RB￨O￨- coupled￨L￨VBN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- identical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- analyze￨L￨VB￨O￨- its￨L￨PRP$￨O￨- stability￨L￨NN￨O￨- by￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- Lyapunov￨U￨NNP￨PERSON￨- characteristic￨L￨JJ￨O￨- exponent￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- seems￨L￨VBZ￨O￨- that￨L￨IN￨O￨- Chaotic￨U￨JJ￨O￨- systems￨L￨NNS￨O￨- oppose￨L￨VBP￨O￨- with￨L￨IN￨O￨- synchronization￨L￨NN￨O￨A ,￨L￨,￨O￨- because￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- identical￨L￨JJ￨O￨- chaotic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- nearly￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- trajectories￨L￨NNS￨O￨- in￨L￨IN￨O￨- phase￨L￨NN￨O￨- space￨L￨NN￨O￨- which￨L￨WDT￨O￨- diverge￨L￨VBP￨O￨- quickly￨L￨RB￨O￨- .￨L￨.￨O￨- +Synchronization￨U￨NN￨O￨- of￨L￨IN￨O￨- chaos￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- happen￨L￨VB￨O￨- when￨L￨WRB￨O￨- some￨L￨DT￨O￨- dissipative￨L￨JJ￨O￨- chaotic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨A are￨L￨VBP￨O￨- coupled￨L￨VBN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- realized￨L￨VBN￨O￨- that￨L￨IN￨O￨- chaotic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- synchronized￨L￨VBN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- address￨L￨VB￨O￨- this￨L￨DT￨O￨- gap￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- multidisciplinary￨L￨JJ￨O￨- dialog￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- established￨L￨VBN￨O￨- virtual￨L￨JJ￨O￨- “￨L￨``￨O￨- Community￨U￨NN￨O￨- of￨L￨IN￨O￨- Practice￨U￨NNP￨O￨- ,￨L￨,￨O￨- ”￨L￨''￨O￨- called￨L￨VBN￨O￨- mod4PH￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Modeling￨U￨VBG￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- enhance￨L￨VB￨O￨- the￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- applications￨L￨NNS￨O￨- for￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- clinical￨L￨JJ￨O￨- decision-making￨L￨JJ￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- such￨L￨JJ￨O￨- glossaries￨L￨NNS￨O￨- define￨L￨VBP￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- terms￨L￨NNS￨O￨- and￨L￨CC￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vocabulary￨L￨NN￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A modeling￨L￨NN￨O￨A literature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- aim￨L￨VB￨O￨- at￨L￨IN￨O￨- standardizing￨L￨VBG￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- lexicon￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- terminology￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mod4PH￨L￨NN￨O￨- group￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- glossary￨L￨NN￨O￨- of￨L￨IN￨O￨- terms￨L￨NNS￨O￨- ,￨L￨,￨O￨- ”￨L￨''￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- use￨L￨NN￨O￨- and￨L￨CC￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A modeling￨L￨NN￨O￨A terms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- glossary￨L￨NN￨O￨- was￨L￨VBD￨O￨- created￨L￨VBN￨O￨- and￨L￨CC￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- summary￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- online￨L￨NN￨O￨- forum￨L￨NN￨O￨- discussions￨L￨NNS￨O￨- surrounding￨L￨VBG￨O￨- the￨L￨DT￨O￨- usage￨L￨NN￨O￨- and￨L￨CC￨O￨- definition￨L￨NN￨O￨A of￨L￨IN￨O￨- key￨L￨JJ￨O￨- terms￨L￨NNS￨O￨- in￨L￨IN￨O￨- modeling￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mod4PH￨L￨NN￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- LinkedIn￨U￨NNP￨O￨- forum￨L￨NN￨O￨- ,￨L￨,￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- from￨L￨IN￨O￨- different￨L￨JJ￨O￨- disciplines￨L￨NNS￨O￨- including￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A modeling￨L￨NN￨O￨A ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- policy￨L￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- disagreement￨L￨NN￨O￨- between￨L￨IN￨O￨- phylogeny￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- history￨L￨NN￨O￨- are￨L￨VBP￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Incomplete￨U￨JJ￨O￨- transmission￨L￨NN￨O￨- bottlenecks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- within-host￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨A variation￨L￨NN￨O￨A is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- from￨L￨IN￨O￨- donor￨L￨NN￨O￨- to￨L￨TO￨O￨- recipient￨L￨JJ￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- non-negligibly￨L￨JJ￨O￨- small￨L￨JJ￨O￨- inoculum￨L￨NN￨O￨- ;￨L￨:￨O￨- this￨L￨DT￨O￨- means￨L￨VBZ￨O￨- lineages￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- shared￨L￨VBN￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- ancestor￨L￨NN￨O￨- since￨L￨IN￨O￨- long￨L￨JJ￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Non-sampled￨U￨JJ￨MISC￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- sampled￨L￨VBN￨O￨A patient￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- linked￨L￨VBN￨O￨- by￨L￨IN￨O￨- direct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- most￨L￨RBS￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- sampled￨L￨VBN￨O￨- patient￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- non-sampled￨L￨JJ￨O￨- intermediate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Multiply￨U￨RB￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- patients￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- erroneously￨L￨RB￨O￨- excluded￨L￨VBN￨O￨- from￨L￨IN￨O￨- some￨L￨DT￨O￨- transmission￨L￨NN￨O￨- chains￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- if￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- patient￨L￨NN￨O￨A are￨L￨VBP￨O￨- not￨L￨RB￨O￨- collected￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1D￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- A￨U￨NNP￨O￨- spatial￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Wild￨U￨NNP￨O￨- Poliovirus￨U￨NNP￨O￨- Type￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- Kano￨U￨NNP￨CITY￨- State￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Nigeria￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- calibration￨L￨NN￨O￨- and￨L￨CC￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- elimination￨L￨NN￨O￨- probabilityKevin￨L￨NN￨O￨- A.￨U￨NN￨O￨- 2016Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Since￨U￨IN￨O￨- the￨L￨DT￨O￨- launch￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Global￨U￨JJ￨O￨- Polio￨U￨NNP￨O￨- Eradication￨U￨NN￨O￨- Initiative￨U￨NNP￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- but￨L￨CC￨O￨- three￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Nigeria￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Pakistan￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Afghanistan￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- apparently￨L￨RB￨O￨- interrupted￨L￨JJ￨O￨- all￨L￨DT￨O￨- wild￨L￨JJ￨O￨A poliovirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- WPV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- article￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- calibration￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨A poliovirus￨L￨NN￨O￨- Type￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- Kano￨U￨NNP￨CITY￨- State￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Nigeria￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- WPV1￨U￨NN￨O￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- 5￨L￨CD￨NUMBER￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- 6￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- WPV1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- drive￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- development￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- susceptible-exposed-infective-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A featuring￨L￨VBG￨O￨- seasonal￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- and￨L￨CC￨O￨- age-dependent￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- calibrated￨L￨VBN￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- resampled￨L￨JJ￨O￨- ,￨L￨,￨O￨- projected￨L￨VBD￨O￨- forward￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- recent￨L￨JJ￨O￨- case￨L￨NN￨O￨- counts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- Type￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- poliovirus￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- eliminated￨L￨VBN￨O￨- in￨L￨IN￨O￨- Kano￨U￨NNP￨CITY￨- state￨L￨NN￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Burkina￨U￨NNP￨PERSON￨- Faso￨U￨NNP￨PERSON￨- experienced￨L￨VBD￨O￨- a￨L￨DT￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨- that￨L￨WDT￨O￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- 54,111￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- high￨L￨JJ￨O￨- estimated￨L￨VBN￨O￨- administrative￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- several￨L￨JJ￨O￨- supplemental￨L￨JJ￨O￨- campaigns￨L￨NNS￨O￨- ;￨L￨:￨O￨- many￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- children￨L￨NNS￨O￨- who￨L￨WP￨O￨- missed￨L￨VBD￨O￨- vaccinations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- locally￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- during￨L￨IN￨O￨- campaigns￨L￨NNS￨O￨- and￨L￨CC￨O￨- contributed￨L￨VBD￨O￨- significantly￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- outbreak9￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- immunized￨L￨VBN￨O￨- to￨L￨TO￨O￨- interrupt￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- scales￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- highly￨L￨RB￨O￨- transmissible￨L￨JJ￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- that￨L￨IN￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- remain￨L￨VBP￨O￨- above￨L￨IN￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- local￨L￨JJ￨O￨- elimination1213￨L￨NN￨O￨- ,￨L￨,￨O￨- emphasizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- accurate￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- measurements￨L￨NNS￨O￨- established￨L￨VBD￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- ,￨L￨,￨O￨- positive￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- largest￨L￨JJS￨O￨- cities￨L￨NNS￨O￨- in￨L￨IN￨O￨- Niger￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- drove￨L￨VBD￨O￨- local￨L￨JJ￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- both￨L￨CC￨O￨- across￨L￨IN￨O￨- cities￨L￨NNS￨O￨- and￨L￨CC￨O￨- within￨L￨IN￨O￨- them￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- Figs￨U￨NNS￨O￨- 1A￨L￨NN￨O￨- and￨L￨CC￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 172728￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Twenty-three￨U￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- response￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- was￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨- by￨L￨IN￨O￨- immunizing￨L￨VBG￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- children￨L￨NNS￨O￨- younger￨L￨JJR￨O￨- than￨L￨IN￨O￨- 60￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- satellite-derived￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- refine￨L￨VB￨O￨- our￨L￨PRP$￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- immunization￨L￨NN￨O￨- campaign￨L￨NN￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- eight￨L￨CD￨NUMBER￨- cities￨L￨NNS￨O￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- finds￨L￨VBZ￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- Delhi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- 48￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- households￨L￨NNS￨O￨A in￨L￨IN￨O￨- slums￨L￨NNS￨O￨- have￨L￨VBP￨O￨- five￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- people￨L￨NNS￨O￨- sleeping￨L￨VBG￨O￨- per￨L￨IN￨O￨- room￨L￨NN￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- 19￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- non-slum￨L￨JJ￨O￨- households￨L￨NNS￨O￨- .5￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- overcrowded￨L￨JJ￨O￨- living￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- facilitate￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- airborne￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .6￨L￨NN￨NUMBER￨- 7￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- high-density￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- developed￨L￨VBN￨O￨- and￨L￨CC￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- poverty￨L￨NN￨O￨- and￨L￨CC￨O￨- higher￨L￨JJR￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- no￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- ,￨L￨,￨O￨- large￨L￨JJ￨O￨- urban￨L￨JJ￨O￨A areas￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- eg￨L￨FW￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- several￨L￨JJ￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- slums￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- their￨L￨PRP$￨O￨- geographic￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- ,￨L￨,￨O￨- compositions￨L￨NNS￨O￨- ,￨L￨,￨O￨- unique￨L￨JJ￨O￨- home￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- agent-resolved￨L￨JJ￨O￨- activity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- differ￨L￨VBP￨O￨A between￨L￨IN￨O￨- slum￨L￨NN￨O￨- and￨L￨CC￨O￨- non-slum￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- from￨L￨IN￨O￨- those￨L￨DT￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- networked￨L￨JJ￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- ignores￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- slums￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- later￨L￨RB￨O￨- use￨L￨VB￨O￨- this￨L￨DT￨O￨- understanding￨L￨VBG￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- appropriate￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- detailed￨L￨VBN￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- slums￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- larger￨L￨JJR￨O￨- urban￨L￨JJ￨O￨A population￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- reside￨L￨VBP￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨A models￨L￨NNS￨O￨A previously￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- are￨L￨VBP￨O￨- compartmental￨L￨JJ￨O￨- constructs￨L￨NNS￨O￨- that￨L￨WDT￨O￨- divide￨L￨VBP￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- chain￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- constructs￨L￨NNS￨O￨- additionally￨L￨RB￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- partial￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- exposure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SEIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Accurate￨U￨JJ￨O￨- forecasts￨L￨NNS￨O￨A of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- incidence￨L￨NN￨O￨- could￨L￨MD￨O￨- thus￨L￨RB￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- management￨L￨NN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- data-driven￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- and￨L￨CC￨O￨- better￨L￨RBR￨O￨- timed￨L￨VBN￨O￨- for￨L￨IN￨O￨- patient￨L￨NN￨O￨- demand￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- validation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- model-inference￨L￨NN￨O￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- forecasting￨L￨VBG￨O￨A the￨L￨DT￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- model-inference￨L￨NN￨O￨- system￨L￨NN￨O￨- developed￨L￨VBD￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- forecasts￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- critical￨L￨JJ￨O￨- RSV￨U￨NN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- core￨L￨NN￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- forecasting￨L￨NN￨O￨A system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- refined￨L￨JJ￨O￨- SOSa-SPSa￨U￨NN￨MISC￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- depicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- sentiment￨L￨NN￨O￨- contagion￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- possibility￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- when￨L￨WRB￨O￨- coming￨L￨VBG￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- pessimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- comes￨L￨VBZ￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- optimistic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- become￨L￨VBP￨O￨- optimistic￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- β￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- whom￨L￨WP￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- come￨L￨VBP￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- spontaneously￨L￨RB￨O￨- become￨L￨VBP￨O￨- optimistic￨L￨JJ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- α￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- whom￨L￨WP￨O￨- the￨L￨DT￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- come￨L￨VBP￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- g￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- become￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- exists￨L￨VBZ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- first￨L￨RB￨ORDINAL￨- extended￨L￨VBD￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- uninfected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨A spontaneously￨L￨RB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- whom￨L￨WP￨O￨- the￨L￨DT￨O￨- uninfected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- come￨L￨VBN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- limitation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SOSa-SPSa￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- only￨L￨RB￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- optimists￨L￨NNS￨O￨- and￨L￨CC￨O￨- pessimists￨L￨NNS￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- transform￨L￨VB￨O￨- into￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨A but￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- interact￨L￨VB￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- directly￨L￨RB￨O￨- .￨L￨.￨O￨- +Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- presents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- sentiment￨L￨NN￨O￨- contagion￨L￨NN￨O￨- process￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- pessimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- divided￨L￨VBN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- status￨L￨NN￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- O￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- pessimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SISa￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- against￨L￨IN￨O￨- our￨L￨PRP$￨O￨- expectations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- can￨L￨MD￨O￨- decrease￨L￨VB￨O￨- significantly￨L￨RB￨O￨- with￨L￨IN￨O￨- population￨L￨NN￨O￨A density￨L￨NN￨O￨A ,￨L￨,￨O￨- possibly￨L￨RB￨O￨- because￨L￨IN￨O￨- higher￨L￨JJR￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- areas￨L￨NNS￨O￨- are￨L￨VBP￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- attributes￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- better￨L￨JJR￨O￨- healthcare￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- work￨L￨NN￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- location-specific￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- better￨L￨JJR￨O￨A model￨L￨NN￨TITLE￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- reason￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- topic￨L￨NN￨O￨- of￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- research￨L￨NN￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- have￨L￨VBP￨O￨- often￨L￨RB￨O￨- been￨L￨VBN￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- homogenously￨L￨RB￨O￨- mix￨L￨VB￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- recent￨L￨JJ￨O￨- EVD￨U￨NN￨O￨- models34567￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- recent￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- migration￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases8￨L￨NN￨O￨- ,￨L￨,￨O￨- homogeneous￨L￨JJ￨O￨A mixing￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- especially￨L￨RB￨O￨- poor￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- for￨L￨IN￨O￨- EVD￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨A understand￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- test￨L￨VB￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- leading￨L￨VBG￨O￨- EVD￨U￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- West￨U￨NNP￨O￨- Africa￨U￨NNP￨O￨- Ebola￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- have￨L￨VBP￨O￨- often￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- via￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨A mixing34567￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- major￨L￨JJ￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- control￨L￨VBP￨O￨- activities￨L￨NNS￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- routine￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- are￨L￨VBP￨O￨- supplemental￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIAs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- periodic￨L￨JJ￨O￨- national￨L￨JJ￨O￨- or￨L￨CC￨O￨- regional￨L￨JJ￨O￨- campaigns￨L￨NNS￨O￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- providing￨L￨VBG￨O￨- vaccine￨L￨NN￨O￨- to￨L￨TO￨O￨- everyone￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- defined￨L￨VBN￨O￨- age￨L￨NN￨O￨- range￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- scatter￨L￨NN￨O￨- in￨L￨IN￨O￨- relative￨L￨JJ￨O￨- fatalities￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- healthcare￨L￨NN￨O￨- measures￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- pulse￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Removed￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinations￨L￨NNS￨O￨- .￨L￨.￨O￨- +QV￨U￨NN￨O￨- =￨L￨JJ￨O￨- ΔV/ΔT￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- pulse￨L￨NN￨O￨A and￨L￨CC￨O￨- a￨L￨DT￨O￨- negative￨L￨JJ￨O￨- or￨L￨CC￨O￨- small￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- value￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- on-time￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- timing￨L￨NN￨O￨A goes￨L￨VBZ￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- but￨L￨CC￨O￨- presumably￨L￨RB￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- rate￨L￨NN￨O￨- drops￨L￨VBZ￨O￨- towards￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- percentage￨L￨NN￨O￨- saturates￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- coverage￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Mereckiene￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 's￨L￨POS￨O￨- NumericCitation￨U￨NNP￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- values￨L￨NNS￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- t￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- denote￨L￨VBP￨O￨- the￨L￨DT￨DURATION￨- weeks￨L￨NNS￨DURATION￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- vaccination￨L￨NN￨O￨A starts￨L￨VBZ￨O￨- and￨L￨CC￨O￨- ends￨L￨VBZ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- being￨L￨VBG￨O￨- counted￨L￨VBN￨O￨- cumulatively￨L￨RB￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- schools￨L￨NNS￨O￨A were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- calibrate￨L￨VB￨O￨- a￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- grades￨L￨NNS￨O￨- and￨L￨CC￨O￨- schools￨L￨NNS￨O￨- using￨L￨VBG￨O￨- Markov￨U￨NNP￨PERSON￨- Chain￨U￨NNP￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- MCMC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- median￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- schools￨L￨NNS￨O￨A of￨L￨IN￨O￨- 1.16￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 1.40￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- students￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- school￨L￨NN￨O￨- case￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 0.85￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 1.09￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- schools￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- A/H1N1pdm09￨U￨NNP￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- has￨L￨VBZ￨O￨- made￨L￨VBN￨O￨- it￨L￨PRP￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- collect￨L￨VB￨O￨- detailed￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- symptoms￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- primary￨L￨JJ￨O￨- schools￨L￨NNS￨O￨A of￨L￨IN￨O￨- Trento￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- The￨U￨DT￨O￨- discrepancy￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- within-school￨L￨NN￨O￨- transmission￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- household￨L￨NN￨O￨- and￨L￨CC￨O￨- community￨L￨NN￨O￨- transmission￨L￨NN￨O￨- played￨L￨VBD￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- sustaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- school￨L￨NN￨O￨A epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- high￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- students￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- class￨L￨NN￨O￨- confirms￨L￨VBZ￨O￨- that￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- within-class￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- key￨L￨JJ￨O￨- to￨L￨TO￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- school￨L￨NN￨O￨A settings￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Theoretically￨U￨RB￨O￨- ,￨L￨,￨O￨- influence￨L￨NN￨O￨A maximization￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- problem￨L￨NN￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- effectively￨L￨RB￨O￨- identify￨L￨VB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- maximize￨L￨VB￨O￨- their￨L￨PRP$￨O￨- spreading￨L￨NN￨O￨- influence￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- much￨L￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- on￨L￨IN￨O￨- measuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- node￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- effectively￨L￨RB￨O￨- identify￨L￨VB￨O￨- multiple￨L￨JJ￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨A are￨L￨VBP￨O￨- still￨L￨RB￨O￨- lacking￨L￨VBG￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- researches￨L￨VBZ￨O￨- in￨L￨IN￨O￨- sociology￨L￨NN￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- selecting￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- degree￨L￨NN￨O￨- as￨L￨IN￨O￨- spreaders￨L￨NNS￨O￨A can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- better￨L￨JJR￨O￨- spreading￨L￨NN￨O￨- influence￨L￨NN￨O￨- than￨L￨IN￨O￨- many￨L￨JJ￨O￨- other￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- attempted￨L￨VBD￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- effective￨L￨JJ￨O￨- multiple￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨A by￨L￨IN￨O￨- generalizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- idea￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coloring￨L￨VBG￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- graph￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Experiments￨U￨NNS￨O￨- are￨L￨VBP￨O￨- performed￨L￨VBN￨O￨- on￨L￨IN￨O￨- several￨L￨JJ￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- outperform￨L￨VB￨O￨- some￨L￨DT￨O￨- centrality-based￨L￨JJ￨O￨- methods￨L￨NNS￨O￨A .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- average￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- become￨L￨VB￨O￨- Then￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- after￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- dengue￨L￨NN￨O￨A should￨L￨MD￨O￨- be￨L￨VB￨O￨- Comparing￨U￨VBG￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- see￨L￨VB￨O￨- that￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- I￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- decrease￨L￨VBP￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- increases￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- we￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- inoculate￨L￨VB￨O￨- against￨L￨IN￨O￨- dengue￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- three￨L￨CD￨NUMBER￨- routes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨- as￨L￨IN￨O￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- Now￨U￨RB￨DATE￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- P￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- P0￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- start￨L￨VBP￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- intuitive￨L￨JJ￨O￨- view￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- dengue￨L￨NN￨O￨A among￨L￨IN￨O￨- humans￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- simple￨L￨JJ￨O￨- static￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- illustrated￨L￨VBD￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- purpose￨L￨NN￨O￨- here￨L￨RB￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- propose￨L￨VB￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- co-infection￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨A and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- with￨L￨IN￨O￨- particular￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- and￨L￨CC￨O￨- implication￨L￨NN￨O￨- for￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- dengue￨L￨NN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- diagram￨L￨NN￨O￨- of￨L￨IN￨O￨- co-infection￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨A and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- among￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- mosquitos￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- adopt￨L￨VBP￨O￨- a￨L￨DT￨O￨- computational￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- step￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- possible￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- :￨L￨:￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- binding￨L￨NN￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- receptor￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- binding￨L￨NN￨O￨- protein￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- receptor￨L￨NN￨O￨- protein￨L￨NN￨O￨- expression￨L￨NN￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- gene￨L￨NN￨O￨- regulatory￨L￨JJ￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- receptor￨L￨NN￨O￨- binding￨L￨NN￨O￨- complexity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- understood￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- amino￨L￨NN￨O￨- acids￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- entry￨L￨NN￨O￨- protein￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- receptor￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- increases￨L￨VBZ￨O￨- ,￨L￨,￨O￨- viruses￨L￨NNS￨O￨- tend￨L￨VBP￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- specialists￨L￨NNS￨O￨- and￨L￨CC￨O￨- target￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- specific￨L￨JJ￨O￨- receptor￨L￨NN￨O￨- .￨L￨.￨O￨- +Commonly￨U￨RB￨O￨- ,￨L￨,￨O￨- viruses￨L￨NNS￨O￨- enter￨L￨VBP￨O￨- host￨L￨NN￨TITLE￨- cells￨L￨NNS￨O￨- by￨L￨IN￨O￨- binding￨L￨NN￨O￨- cell￨L￨NN￨O￨- surface￨L￨NN￨O￨A receptors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Almost￨U￨RB￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- assume￨L￨VB￨O￨- ,￨L￨,￨O￨- first￨L￨RB￨ORDINAL￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- dt￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- dt￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- once￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- any￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computer￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- latency￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- computers￨L￨NNS￨O￨- become￨L￨VBP￨O￨- the￨L￨DT￨O￨- E￨U￨NN￨O￨- ones￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- secondly￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- anti-virus￨L￨JJ￨O￨- software￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- affected￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- completely￨L￨RB￨O￨- and￨L￨CC￨O￨- immediately￨L￨RB￨O￨- eliminated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Next￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- admits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- virus-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- that￨L￨IN￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- virus￨L￨NN￨O￨A eradication￨L￨NN￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- admits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- equilibrium￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- whereas￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A disappears￨L￨VBZ￨O￨- completely￨L￨RB￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- find￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨- models￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨- in￨L￨IN￨O￨- Ref￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- virus￨L￨NN￨O￨A equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- propelled￨L￨VBN￨O￨- by￨L￨IN￨O￨- decisions￨L￨NNS￨O￨- made￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- consume￨L￨VB￨O￨- and￨L￨CC￨O￨- share￨L￨VB￨O￨A the￨L￨DT￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- identified￨L￨VBN￨O￨- by￨L￨IN￨O￨- Christakis￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Fowler￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- outcome￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- structural￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- reflects￨L￨VBZ￨O￨- volition￨L￨NN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- individual￨L￨JJ￨O￨- decisions￨L￨NNS￨O￨- to￨L￨TO￨O￨- consume￨L￨VB￨O￨- ,￨L￨,￨O￨- modify￨L￨VB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- share￨L￨NN￨O￨A information￨L￨NN￨O￨- and￨L￨CC￨O￨- seeks￨L￨VBZ￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- emergent￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- local￨L￨JJ￨O￨- preferences￨L￨NNS￨O￨- with￨L￨IN￨O￨- special￨L￨JJ￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- tie￨L￨JJ￨O￨- strength￨L￨NN￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- the￨L￨DT￨O￨- Diffusion￨U￨NNP￨MISC￨- of￨L￨IN￨MISC￨- Innovations￨U￨NNPS￨MISC￨- we￨L￨PRP￨O￨- adopt￨L￨VBP￨O￨- the￨L￨DT￨O￨- concepts￨L￨NNS￨O￨- communication￨L￨NN￨O￨- channels￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- directionality￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- communication￨L￨NN￨O￨- proximity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- tie￨L￨JJ￨O￨- strength￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- individual￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- modification￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- inflection￨L￨NN￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +Reinvention￨U￨NNP￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- modification￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- levels￨L￨NNS￨O￨- :￨L￨:￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- attribute￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- itself￨L￨PRP￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- an￨L￨DT￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- whether￨L￨IN￨O￨- it￨L￨PRP￨O￨- enhances￨L￨VBZ￨O￨- or￨L￨CC￨O￨- diminishes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- spreads￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- behavior￨L￨NN￨O￨- performed￨L￨VBN￨O￨- by￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- modification￨L￨NN￨O￨- activity￨L￨NN￨O￨- shed￨L￨VBD￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- act￨L￨NN￨O￨- of￨L￨IN￨O￨- modifying￨L￨VBG￨O￨- information￨L￨NN￨O￨A has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- accelerating￨L￨VBG￨O￨- or￨L￨CC￨O￨- decelerating￨L￨VBG￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- conceptually￨L￨RB￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- relatively￨L￨RB￨O￨- well-studied￨L￨JJ￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- locating￨L￨VBG￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- cascade￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- –￨L￨:￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- information￨L￨NN￨O￨- cascade￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- challenging￨L￨JJ￨O￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- because￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- perturbed￨L￨VBN￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨A to￨L￨TO￨O￨- having￨L￨VBG￨O￨- observations￨L￨NNS￨O￨- at￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- times￨L￨NNS￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- having￨L￨VBG￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- “￨L￨``￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- ”￨L￨''￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- –￨L￨:￨O￨- ,￨L￨,￨O￨- –￨L￨:￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- having￨L￨VBG￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- sparse￨L￨JJ￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- perturbed￨L￨VBN￨O￨- and￨L￨CC￨O￨- unperturbed￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- situations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- complete￨L￨JJ￨O￨- or￨L￨CC￨O￨- almost￨L￨RB￨O￨- complete￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- perturbed￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- lack￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- spreads￨L￨VBZ￨O￨- [￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- situations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- alone￨L￨RB￨O￨- reasonable￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- an￨L￨DT￨O￨- abstract￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- situations￨L￨NNS￨O￨- above￨L￨IN￨O￨- are￨L￨VBP￨O￨- analogous￨L￨JJ￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- aspects￨L￨NNS￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- perturbation￨L￨NN￨O￨A spread￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- whose￨L￨WP$￨O￨- elements￨L￨NNS￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- known￨L￨VBN￨O￨- complex￨L￨NN￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- wish￨L￨VBP￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- path￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- observation￨L￨NN￨O￨- that￨L￨IN￨O￨- provides￨L￨VBZ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- perturbed￨L￨VBN￨O￨- or￨L￨CC￨O￨- unperturbed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- to￨L￨TO￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- color￨L￨NN￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- the￨L￨DT￨O￨- ranking￨L￨JJ￨O￨- assigned￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨A paths￨L￨NNS￨O￨- approach￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- label￨L￨NN￨O￨- propagation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- exposure￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- larger￨L￨JJR￨O￨- red￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- deemed￨L￨VBN￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- perturbed￨L￨VBN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- darker￨L￨JJR￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- deemed￨L￨VBN￨O￨- less￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- By￨U￨IN￨O￨- using￨L￨VBG￨O￨- shortest￨L￨JJS￨O￨A paths￨L￨NNS￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- propagation￨L￨NN￨O￨- path￨L￨NN￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 11￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 14￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- assigned￨L￨VBN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- perturbed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- because￨L￨IN￨O￨- both￨L￨DT￨O￨- paths￨L￨NNS￨O￨- connecting￨L￨VBG￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 6￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- equally￨L￨RB￨O￨- short￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- all￨L￨DT￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- deemed￨L￨VBN￨O￨- equally￨L￨RB￨O￨- unlikely￨L￨JJ￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- perturbed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- because￨L￨IN￨O￨- no￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- path￨L￨NN￨O￨- traverses￨L￨VBZ￨O￨- them￨L￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Label￨U￨NN￨O￨- propagation￨L￨NN￨O￨- assigns￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- perturbed￨L￨VBN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- to￨L￨TO￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 2-to-5￨L￨JJ￨O￨- path￨L￨NN￨O￨A but￨L￨CC￨O￨- also￨L￨RB￨O￨- to￨L￨TO￨O￨- nodes￨L￨NNS￨O￨- 7￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- no￨L￨DT￨O￨- observed￨L￨VBN￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unperturbed￨L￨JJ￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- formally￨L￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- D￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- on￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- θ￨L￨VBP￨O￨- is￨L￨VBZ￨O￨- replaced￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- of￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨A by￨L￨IN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- ρ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- distance￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- dataset￨L￨NN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ϵ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- tolerance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2011￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- estimated￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- similarity￨L￨NN￨O￨- and￨L￨CC￨O￨- estimated￨L￨VBN￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- relating￨L￨VBG￨O￨- 60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- HIV-infected￨U￨JJ￨O￨- men￨L￨NNS￨O￨A who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MSM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- Kingdom￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- sophisticated￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- complex￨L￨JJ￨O￨- population￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- phylogenies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- inference￨L￨NN￨O￨A of￨L￨IN￨O￨- structural￨L￨JJ￨O￨- network￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- been￨L￨VBN￨O￨- limited￨L￨VBN￨O￨- .￨L￨.￨O￨- +Unfortunately￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- explicitly￨L￨RB￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- tree￨L￨NN￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- normalizing￨L￨VBG￨O￨- constant￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- using￨L￨VBG￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A models￨L￨NNS￨O￨- from￨L￨IN￨O￨- observed￨L￨VBN￨O￨- phylogenetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- better￨L￨RBR￨O￨- relate￨L￨VB￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- major￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- a￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- term￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- acquisition￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- outside￨L￨IN￨O￨A the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- simulation￨L￨NN￨O￨- :￨L￨:￨O￨- rate￨L￨NN￨O￨A of￨L￨IN￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.001￨L￨CD￨DURATION￨- yr￨L￨NN￨DURATION￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- initial￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1000￨L￨CD￨DATE￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 365/14￨L￨CD￨NUMBER￨- yr￨L￨NN￨DURATION￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- 14￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- spontaneous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- ξ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.00067￨L￨CD￨DURATION￨- yr￨L￨NN￨DURATION￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- birth￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/60￨L￨CD￨NUMBER￨- yr￨L￨NN￨DURATION￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- example￨L￨NN￨O￨- contains￨L￨VBZ￨O￨- multiple￨L￨JJ￨O￨- ‘￨L￨``￨O￨- sparks￨L￨VBZ￨O￨- ’￨L￨''￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨A to￨L￨TO￨O￨- supercriticality￨L￨NN￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- demonstrating￨L￨VBG￨O￨- that￨L￨IN￨O￨- bifurcation￨L￨NN￨O￨- delay￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- simply￨L￨RB￨O￨- the￨L￨DT￨O￨- waiting￨L￨VBG￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- spark￨L￨VB￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- after￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- pure￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨A and￨L￨CC￨O￨- prevalence￨L￨NN￨O￨- are￨L￨VBP￨O￨- potentially￨L￨RB￨O￨- of￨L￨IN￨O￨- use￨L￨NN￨O￨- for￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- and￨L￨CC￨O￨- tracking￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- typical￨L￨JJ￨O￨- criticisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- ‘￨L￨``￨O￨- big￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ’￨L￨POS￨O￨- analyses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- as￨L￨IN￨O￨- containing￨L￨VBG￨O￨- biases￨L￨NNS￨O￨- and￨L￨CC￨O￨- tending￨L￨VBG￨O￨- towards￨L￨IN￨O￨- overfitting￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- behavioural￨L￨JJ￨O￨- change￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- media￨L￨NNS￨O￨A by￨L￨IN￨O￨- explicitly￨L￨RB￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- compartment￨L￨NN￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- mass￨L￨NN￨O￨- media￨L￨NNS￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR-type￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- incorporating￨L￨VBG￨O￨- effects￨L￨NNS￨O￨- like￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- criteria￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- media￨L￨NNS￨O￨A function￨L￨NN￨O￨- proposed￨L￨VBN￨O￨- here￨L￨RB￨O￨- fits￨L￨VBZ￨O￨- historical￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- other￨L￨JJ￨O￨- media￨L￨NNS￨O￨- functions￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- become￨L￨VBN￨O￨- popular￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- data￨L￨NNS￨O￨- streams￨L￨NNS￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- Internet￨U￨NN￨MISC￨- and￨L￨CC￨O￨- online￨L￨NN￨O￨- social￨L￨JJ￨O￨- media￨L￨NNS￨O￨A usage￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- data-driven￨L￨JJ￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- couples￨L￨VBZ￨O￨- these￨L￨DT￨O￨- existing￨L￨VBG￨O￨- paradigms￨L￨NNS￨O￨- :￨L￨:￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- media￨L￨NNS￨O￨A engagement￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- behaviour￨L￨NN￨O￨- change￨L￨NN￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- then￨L￨RB￨O￨- be￨L￨VB￨O￨- validated￨L￨VBN￨O￨- against￨L￨IN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- demography￨L￨NN￨O￨A and￨L￨CC￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- strongly￨L￨RB￨O￨- between￨L￨IN￨O￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨DATE￨- may￨L￨MD￨DATE￨- impact￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- limit￨L￨VB￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- conclusions￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- observations￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- country￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- generalized￨L￨VBN￨O￨- to￨L￨TO￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- non-outbreak￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- hospitals￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- outside￨L￨IN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- official￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- zone￨L￨NN￨O￨- ,￨L￨,￨O￨- nosocomial￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- might￨L￨MD￨O￨- arise￨L￨VB￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- patient￨L￨NN￨O￨- or￨L￨CC￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- HCW￨U￨NN￨O￨- is￨L￨VBZ￨O￨- transferred￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- care￨L￨NN￨O￨- center8￨L￨NN￨O￨- or￨L￨CC￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- patient￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- at￨L￨IN￨O￨- hospital￨L￨NN￨O￨- with￨L￨IN￨O￨- nonspecific￨L￨JJ￨O￨- EVD￨U￨NN￨O￨- symptoms￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- hospitals￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- differ￨L￨VB￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- contact￨L￨VB￨O￨- patterns￨L￨NNS￨O￨- between￨L￨IN￨O￨- HCW￨U￨NN￨O￨- and￨L￨CC￨O￨- patients￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- outbreak￨L￨NN￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- symptomatic￨L￨JJ￨O￨- patients￨L￨NNS￨O￨A are￨L￨VBP￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- HCW12￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- facilitated￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- dry￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- patients￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- exhibit￨L￨VB￨O￨- specific￨L￨JJ￨O￨- signs￨L￨NNS￨O￨- of￨L￨IN￨O￨- EVD67￨U￨NN￨O￨- .￨L￨.￨O￨- +Contact￨U￨NN￨O￨- between￨L￨IN￨O￨- EVD￨U￨NN￨O￨- patients￨L￨NNS￨O￨A and￨L￨CC￨O￨- healthcare￨L￨NN￨O￨- workers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- HCW￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- contributes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- hospital￨L￨NN￨O￨- spread5￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- complex￨L￨JJ￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- being￨L￨VBG￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- quickly￨L￨RB￨O￨A and￨L￨CC￨O￨- reliably￨L￨RB￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host-vector-pathogen￨L￨NN￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- perturbations￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- controls￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- connecting￨L￨VBG￨O￨- strategic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- more￨L￨RBR￨O￨- closely￨L￨RB￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨A to￨L￨TO￨O￨- make￨L￨VB￨O￨- qualitative￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- and￨L￨CC￨O￨- yet￨L￨RB￨O￨- retain￨L￨VB￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- what￨L￨WP￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- elements￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- —￨L￨:￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- specific￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- many￨L￨JJ￨O￨- possible￨L￨JJ￨O￨- intervention￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A ,￨L￨,￨O￨- compare￨L￨VBP￨O￨- them￨L￨PRP￨O￨- cost-effectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- do￨L￨VBP￨O￨- so￨L￨RB￨O￨- quickly￨L￨RB￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- lone￨L￨JJ￨O￨- and￨L￨CC￨O￨- combined￨L￨JJ￨O￨- intervention￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A faster￨L￨RBR￨O￨- than￨L￨IN￨O￨- almost￨L￨RB￨O￨- any￨L￨DT￨O￨- other￨L￨JJ￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- argue￨L￨VBP￨O￨- that￨L￨IN￨O￨- collaborations￨L￨NNS￨O￨- between￨L￨IN￨O￨- empiricists￨L￨NNS￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- modelers￨L￨NNS￨O￨- can￨L￨MD￨O￨- more￨L￨RBR￨O￨- efficiently￨L￨RB￨O￨- identify￨L￨VB￨O￨- effective￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨A for￨L￨IN￨O￨- HLB￨U￨NN￨ORGANIZATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- SPIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- planning￨L￨NN￨O￨- horizon￨L￨NN￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- over￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- calculate￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- utilities￨L￨NNS￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- a￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨A decision￨L￨NN￨O￨- —￨L￨:￨O￨- affects￨L￨VBZ￨O￨- behavioral￨L￨JJ￨O￨- change￨L￨NN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- that￨L￨DT￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SPIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Prophylactic￨U￨JJ￨O￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨O￨- ,￨L￨,￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- developed￨L￨VBN￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- couples￨L￨VBZ￨O￨- individual￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨A decisions￨L￨NNS￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SPIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- couples￨L￨NNS￨O￨- two￨L￨CD￨NUMBER￨- sub-models￨L￨NNS￨O￨- :￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Disease￨U￨NNP￨CAUSE_OF_DEATH￨- Dynamics￨U￨NNP￨MISC￨- Model￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- reproducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- another￨L￨DT￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Behavioral￨U￨NNP￨O￨- Decision￨U￨NNP￨O￨- Model￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- agents￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- make￨L￨VBP￨O￨- the￨L￨DT￨O￨- decision￨L￨NN￨O￨- to￨L￨TO￨O￨- engage￨L￨VB￨O￨- in￨L￨IN￨O￨- prophylactic￨L￨NN￨O￨A or￨L￨CC￨O￨- non-prophylactic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +Agents￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- engage￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- status￨L￨NN￨O￨- quo￨L￨NN￨O￨- behavior￨L￨NN￨O￨- while￨L￨IN￨O￨- agents￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- prophylactic￨L￨JJ￨O￨A state￨L￨NN￨O￨- employ￨L￨VBP￨O￨- preventative￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reduce￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- agents￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- vulnerable￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- or￨L￨CC￨O￨- prophylactic￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- statistics￨L￨NNS￨O￨- ,￨L￨,￨O￨- season￨L￨NN￨O￨- exponent￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3,4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- reflects￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stable￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- newly￨L￨RB￨O￨A acute￨L￨JJ￨O￨- human￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- total￨L￨JJ￨O￨- newly￨L￨RB￨O￨- acute￨L￨JJ￨O￨- human￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- we￨L￨PRP￨O￨- all￨L￨DT￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- brucellosis￨L￨NN￨O￨- has￨L￨VBZ￨O￨- seasonal￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- ,￨L￨,￨O￨- hence￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- human￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- significantly￨L￨RB￨O￨- increasing￨L￨VBG￨O￨- annually￨L￨RB￨SET￨- in￨L￨IN￨SET￨- summer￨L￨NN￨DATE￨- and￨L￨CC￨O￨- autumn￨L￨NN￨DATE￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- in￨L￨IN￨O￨- spring￨L￨NN￨DATE￨- and￨L￨CC￨O￨- winter￨L￨NN￨DATE￨A are￨L￨VBP￨O￨- relatively￨L￨RB￨O￨- decreasing￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Eventually￨U￨RB￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Figure￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- conclude￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- newly￨L￨RB￨O￨A acute￨L￨JJ￨O￨- human￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- spring￨L￨NN￨DATE￨- and￨L￨CC￨O￨- winter￨L￨NN￨DATE￨- are￨L￨VBP￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- those￨L￨DT￨O￨- in￨L￨IN￨O￨- summer￨L￨NN￨DATE￨- and￨L￨CC￨O￨- autumn￨L￨NN￨DATE￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- confirmed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨A acute￨L￨JJ￨O￨- human￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Bayingolin￨U￨NNP￨LOCATION￨- Mongol￨U￨NNP￨LOCATION￨- Autonomous￨U￨NNP￨LOCATION￨- Prefecture￨U￨NNP￨LOCATION￨- show￨L￨VBP￨O￨- a￨L￨DT￨O￨- pronounced￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- fluctuation￨L￨NN￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- brucellosis￨L￨NN￨O￨- among￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- ,￨L￨,￨O￨- sheep￨L￨NN￨O￨- ,￨L￨,￨O￨- elk￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨A [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Date￨U￨NN￨O￨- of￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- infected￨L￨JJ￨O￨- case￨L￨NN￨O￨- for￨L￨IN￨O￨- administrative￨L￨JJ￨O￨- units￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- countries￨L￨NNS￨O￨- of￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Guinea￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- surrounding￨L￨VBG￨O￨- nations￨L￨NNS￨O￨- of￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- openly￨L￨RB￨O￨- accessible￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- 16￨L￨CD￨NUMBER￨- spatial￨L￨JJ￨O￨- models￨L￨NNS￨O￨- reflecting￨L￨VBG￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨A density￨L￨NN￨O￨A ,￨L￨,￨O￨- border￨L￨NN￨O￨- closure￨L￨NN￨O￨- ,￨L￨,￨O￨- long-distance￨L￨JJ￨O￨- dispersal￨L￨NN￨O￨- and￨L￨CC￨O￨- individual￨L￨JJ￨O￨- movement￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- electronic￨L￨JJ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- Methods￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- daily￨L￨JJ￨SET￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- locations￨L￨NNS￨O￨- depended￨L￨VBD￨O￨- on￨L￨IN￨O￨- distance￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨A density￨L￨NN￨O￨A and￨L￨CC￨O￨- international￨L￨JJ￨O￨- border￨L￨NN￨O￨- closures￨L￨NNS￨O￨- between￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- neighbouring￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- available￨L￨JJ￨O￨- proxies￨L￨NNS￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- from￨L￨IN￨O￨- individual￨L￨JJ￨O￨- cell￨L￨NN￨O￨- phone￨L￨NN￨O￨- records￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- were￨L￨VBD￨O￨- a￨L￨DT￨O￨- poor￨L￨JJ￨O￨- predictor￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Blue￨U￨JJ￨O￨- lines￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- best-fit￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- distance￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨A density￨L￨NN￨O￨A and￨L￨CC￨O￨- whether￨L￨IN￨O￨- links￨L￨NNS￨O￨- cross￨L￨VBP￨O￨- the￨L￨DT￨O￨- border￨L￨NN￨O￨- surrounding￨L￨VBG￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- fitted￨L￨VBD￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- beginning￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- ending￨L￨VBG￨O￨- on￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- electronic￨L￨JJ￨O￨A supplementary￨L￨JJ￨O￨A material￨L￨NN￨O￨- ,￨L￨,￨O￨- table￨L￨NN￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Administrative￨U￨JJ￨O￨- units￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨A the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- coloured￨L￨VBN￨O￨- by￨L￨IN￨O￨- date￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 34￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NNP￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 1299￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1308￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asCost-Utility￨L￨NN￨O￨- of￨L￨IN￨O￨- Quadrivalent￨U￨JJ￨O￨- Versus￨U￨NNP￨O￨- Trivalent￨U￨NNP￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- Vaccine￨U￨NNP￨O￨- in￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Using￨U￨VBG￨O￨- an￨L￨DT￨O￨- Individual-Based￨U￨JJ￨MISC￨- Dynamic￨U￨NNP￨MISC￨- Transmission￨U￨NNP￨MISC￨- ModelAuthorsAuthors￨U￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsChristiaan￨L￨NNP￨O￨- DolkMartin￨U￨NNP￨PERSON￨- EichnerRobert￨U￨NNP￨PERSON￨- WelteAnastassia￨U￨NNP￨PERSON￨- AnastassopoulouLaure-Anne￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- BellinghenBarbara￨U￨NNP￨PERSON￨- Poulsen￨U￨NNP￨PERSON￨- NautrupIlse￨U￨NNP￨O￨- Van￨U￨NNP￨O￨- VlaenderenRuprecht￨U￨NNP￨O￨- Schmidt-OttMarkus￨U￨NNP￨O￨- SchwehmMaarten￨U￨NNP￨O￨- PostmaOpen￨U￨NNP￨O￨- AccessOriginal￨U￨NNP￨O￨- Research￨U￨NNP￨O￨- ArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1.7￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 10￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractBackgroundSeasonal￨U￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- primarily￨L￨RB￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨DT￨O￨- strain￨L￨NN￨O￨- subtypes￨L￨NNS￨O￨- and￨L￨CC￨O￨- strains￨L￨NNS￨O￨- from￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- B￨U￨NN￨O￨- lineages￨L￨NNS￨O￨- that￨L￨WDT￨O￨- vary￨L￨VBP￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- .￨L￨.￨O￨- +Quadrivalent￨U￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- QIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- includes￨L￨VBZ￨O￨- both￨L￨DT￨O￨- B-lineage￨U￨JJ￨MISC￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- works￨L￨NNS￨O￨- have￨L￨VBP￨O￨- exploited￨L￨VBN￨O￨- the￨L￨DT￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- awareness￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- none￨L￨NN￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- explored￨L￨VBN￨O￨- the￨L￨DT￨O￨- realistic￨L￨JJ￨O￨- coevolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- layers￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- explored16￨L￨NN￨O￨- ,￨L￨,￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- suited￨L￨VBN￨O￨- underlying￨L￨VBG￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- taking￨L￨VBG￨O￨- place￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨- networks1718192021￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- more￨L￨RBR￨O￨- realistically￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- coevolution￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- awareness￨L￨NN￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨A network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- linked￨L￨VBN￨O￨- with￨L￨IN￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- socioeconomic￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- awareness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- susceptibility35￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- preventive￨L￨JJ￨O￨A isolation￨L￨NN￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- keep￨L￨VB￨O￨- under￨L￨IN￨O￨- control￨L￨NN￨O￨- properly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- specific￨L￨JJ￨O￨- social￨L￨JJ￨O￨- categories￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- with￨L￨IN￨O￨- regards￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- less￨L￨RBR￨O￨- aware￨L￨JJ￨O￨- and￨L￨CC￨O￨- economically￨L￨RB￨O￨- disadvantaged￨L￨JJ￨O￨- other￨L￨JJ￨O￨- than￨L￨IN￨O￨- being￨L￨VBG￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- central￨L￨JJ￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- work￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- propose￨L￨VB￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- introducing￨L￨VBG￨O￨- an￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- preventive￨L￨JJ￨O￨A isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- skill￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- systems￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- and￨L￨CC￨O￨- richness￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- observational￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- should￨L￨MD￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- be￨L￨VB￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- forecast￨L￨NN￨O￨A system￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- method￨L￨NN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- data￨L￨NN￨O￨- and/or￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- epidemic￨L￨JJ￨O￨- features￨L￨NNS￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- forecast￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- either￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- or￨L￨CC￨O￨- optimized￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- state-space￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- address￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- questions￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- what￨L￨WP￨O￨- spatial￨L￨JJ￨O￨- scale￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- granularity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- simulation￨L￨NN￨O￨- does￨L￨VBZ￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- connection￨L￨NN￨O￨- improve￨L￨VB￨O￨- forecast￨L￨NN￨O￨A performance￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- whether￨L￨IN￨O￨- forecast￨L￨NN￨O￨- performance￨L￨NN￨O￨- differs￨L￨VBZ￨O￨- between￨L￨IN￨O￨- interpandemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- pandemic￨L￨JJ￨O￨- seasons￨L￨NNS￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- differing￨L￨VBG￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Addressing￨U￨VBG￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- factor￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- compared￨L￨VBD￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- —￨L￨:￨O￨- three￨L￨CD￨NUMBER￨- ensemble￨L￨NN￨O￨- filters￨L￨NNS￨O￨- and￨L￨CC￨O￨- three￨L￨CD￨NUMBER￨- particle￨L￨NN￨O￨- type￨L￨NN￨O￨- filters￨L￨NNS￨O￨- —￨L￨:￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- forecast￨L￨NN￨O￨A of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- revealed￨L￨VBD￨O￨- key￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- among￨L￨IN￨O￨- those￨L￨DT￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- test￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- network￨L￨NN￨O￨- forecast￨L￨NN￨O￨A system￨L￨NN￨O￨- at￨L￨IN￨O￨- borough￨L￨NN￨O￨- and￨L￨CC￨O￨- neighborhood￨L￨NN￨O￨- spatial￨L￨JJ￨O￨- resolutions￨L￨NNS￨O￨- using￨L￨VBG￨O￨- ILI￨U￨NN￨O￨- +￨L￨CC￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- virulence-transmission￨L￨NN￨O￨- trade-off￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- promising￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- virulence￨L￨NN￨O￨A of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- predictions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- been￨L￨VBN￨O￨- approached￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- piecemeal￨L￨RB￨O￨- manner￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- combining￨L￨VBG￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- ,￨L￨,￨O￨- AIDS-free￨U￨JJ￨O￨- survival￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- SPVL￨U￨NN￨O￨- from￨L￨IN￨O￨- very￨L￨RB￨O￨- different￨L￨JJ￨O￨- cohorts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- functions￨L￨NNS￨O￨- fitted￨L￨VBD￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- well￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- shown￨L￨VBN￨O￨- by￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- non-parametric￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- stratified￨L￨VBN￨O￨- by￨L￨IN￨O￨- SPVL￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1a￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- Kaplan-Meier￨U￨NNP￨O￨- plot￨L￨NN￨O￨- comparing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- prediction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- best￨L￨JJS￨O￨- model￨L￨NN￨TITLE￨- fit￨L￨NN￨O￨- was￨L￨VBD￨O￨- one￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- increases￨L￨VBZ￨O￨- from￨L￨IN￨O￨- 0.019￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- year￨L￨NN￨DURATION￨- to￨L￨TO￨O￨- 0.14￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- year￨L￨NN￨DURATION￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- stepwise￨L￨JJ￨O￨- fashion￨L￨NN￨O￨- as￨L￨IN￨O￨- SPVL￨U￨NN￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- plateaus￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1a￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- ΔAIC￨U￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- 75.96￨L￨CD￨NUMBER￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- null￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 817￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- HIV-1￨U￨NN￨MISC￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- set-point￨L￨JJ￨O￨- viral￨L￨JJ￨O￨A load￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- SPVL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- stable￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptomatic￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- trait￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- both￨L￨DT￨O￨- variable￨L￨JJ￨O￨- and￨L￨CC￨O￨- heritable￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- current￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- USRT￨U￨NNP￨ORGANIZATION￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨RB￨ORDINAL￨- comprehensive￨L￨JJ￨O￨- dose￨L￨NN￨O￨- –￨L￨:￨O￨- response￨L￨NN￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A risk￨L￨NN￨O￨- among￨L￨IN￨O￨- medical￨L￨JJ￨O￨- radiation￨L￨NN￨O￨- workers￨L￨NNS￨O￨- using￨L￨VBG￨O￨- individualised￨L￨JJ￨O￨- annual￨L￨JJ￨SET￨- dose￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- badge￨L￨NN￨O￨- dose￨L￨NN￨O￨- measurements￨L￨NNS￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- more￨L￨JJR￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- covering￨L￨VBG￨O￨- ∼￨L￨SYM￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- worker￨L￨NN￨O￨- total￨L￨JJ￨O￨- doses￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- work￨L￨NN￨O￨- history￨L￨NN￨O￨- and￨L￨CC￨O￨- practices￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dose￨L￨NN￨O￨- –￨L￨:￨O￨- response￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- using￨L￨VBG￨O￨- internal￨L￨JJ￨O￨- comparisons￨L￨NNS￨O￨- of￨L￨IN￨O￨- excess￨L￨JJ￨O￨- relative￨L￨JJ￨O￨- risk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ERR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- stratified￨L￨VBN￨O￨- by￨L￨IN￨O￨- birth￨L￨NN￨O￨- cohort￨L￨NN￨O￨- and￨L￨CC￨O￨- year￨L￨NN￨DURATION￨- first￨L￨RB￨ORDINAL￨- worked￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- findings￨L￨NNS￨O￨- from￨L￨IN￨O￨- our￨L￨PRP$￨O￨- earlier￨L￨JJR￨O￨- work-history￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Hormonal￨U￨JJ￨O￨- ,￨L￨,￨O￨- reproductive￨L￨JJ￨O￨- ,￨L￨,￨O￨- lifestyle￨L￨NN￨O￨- ,￨L￨,￨O￨- anthropometric￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- known￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- ∼￨L￨CD￨PERCENT￨- 40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Madigan￨U￨NN￨PERSON￨- ;￨L￨:￨O￨- Sprague￨U￨NNP￨LOCATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- our￨L￨PRP$￨O￨- earlier￨L￨JJR￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- USRT￨U￨NNP￨MISC￨- Cohort￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- Mohan￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Doody￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- WeCare￨U￨NNP￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- second￨L￨JJ￨ORDINAL￨- breast￨L￨NN￨O￨- cancers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Langholz￨U￨NN￨LOCATION￨- ;￨L￨:￨O￨- Bernstein￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- examined￨L￨VBD￨O￨- individual￨L￨JJ￨O￨- radiation￨L￨NN￨O￨- exposure￨L￨NN￨O￨- and￨L￨CC￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- risks￨L￨NNS￨O￨- adjusting￨L￨VBG￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- known￨L￨JJ￨O￨- lifestyle￨L￨NN￨O￨- and￨L￨CC￨O￨- reproductive￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- self-reported￨L￨JJ￨O￨- work￨L￨NN￨O￨- history￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- Radiologic￨U￨NNP￨O￨- Technologists￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- USRT￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- experienced￨L￨VBD￨O￨- elevated￨L￨JJ￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Doody￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Mohan￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- moderate￨L￨JJ￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- ionising￨L￨VBG￨O￨- radiation￨L￨NN￨O￨- doses￨L￨NNS￨O￨- in￨L￨IN￨O￨- atomic￨L￨JJ￨O￨- bomb￨L￨NN￨O￨- survivors￨L￨NNS￨O￨- and￨L￨CC￨O￨- radiotherapy￨L￨NN￨O￨- patients￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simulation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A that￨L￨WDT￨O￨- fits￨L￨VBZ￨O￨- historical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- trends￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- deaths￨L￨NNS￨O￨- and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- capturing￨L￨VBG￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- behavioral￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- with￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- various￨L￨JJ￨O￨- policy￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- implementation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- decrease￨L￨VB￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- unintended￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- .￨L￨.￨O￨- +Later￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- causal￨L￨JJ￨O￨A loop￨L￨NN￨O￨- diagram￨L￨NN￨O￨- is￨L￨VBZ￨O￨- provided￨L￨VBN￨O￨- that￨L￨IN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- causal￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- key￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- public￨L￨NN￨O￨- ’s￨L￨POS￨O￨- situational￨L￨JJ￨O￨- awareness￨L￨NN￨O￨- and￨L￨CC￨O￨- attention￨L￨NN￨O￨- towards￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- consequently￨L￨RB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A to￨L￨TO￨O￨- test￨L￨VB￨O￨- various￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- and￨L￨CC￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- adverse￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- sociocultural￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- may￨L￨MD￨O￨- rise￨L￨VB￨O￨- up￨L￨RP￨O￨- to￨L￨TO￨O￨- 4.6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- sociocultural￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- discussed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Rowell￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fatal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- wise￨L￨JJ￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- public￨L￨JJ￨O￨- fear￨L￨NN￨O￨- ;￨L￨:￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contrary￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- author￨L￨NN￨TITLE￨- explains￨L￨VBZ￨O￨- that￨L￨IN￨O￨- fear￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- leveraged￨L￨VBN￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- public￨L￨JJ￨O￨- awareness￨L￨NN￨O￨A about￨L￨IN￨O￨- the￨L￨DT￨O￨- proper￨L￨JJ￨O￨- steps￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- extremely￨L￨RB￨O￨- helpful￨L￨JJ￨O￨- for￨L￨IN￨O￨- testing￨L￨VBG￨O￨- different￨L￨JJ￨O￨- policy￨L￨NN￨O￨A scenarios￨L￨NNS￨O￨- during￨L￨IN￨O￨- such￨L￨JJ￨O￨- crises￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- 7￨L￨CD￨NUMBER￨- by￨L￨IN￨O￨- saving￨L￨VBG￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- management￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- mitigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- event￨L￨NN￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- PRRS￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- field￨L￨NN￨O￨- virus￨L￨NN￨O￨- re-introduction￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- farrow-to-wean￨L￨JJ￨O￨- swine￨L￨NNS￨O￨- herd￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- developed￨L￨VBD￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- included￨L￨VBD￨O￨- herd￨L￨NN￨O￨A closure￨L￨NN￨O￨- with￨L￨IN￨O￨- or￨L￨CC￨O￨- without￨L￨IN￨O￨- gilt￨L￨JJ￨O￨- acclimation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- single￨L￨JJ￨O￨- or￨L￨CC￨O￨- repeated￨L￨VBN￨O￨- mass￨L￨NN￨O￨- immunization￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- modified-live￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- Midwestern￨U￨NN￨LOCATION￨- US￨U￨NNP￨COUNTRY￨- farrow-to-wean￨L￨JJ￨O￨- herd￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- different￨L￨JJ￨O￨- PRRS￨U￨NN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- PRRS￨U￨NN￨O￨- sites￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- 1,000-sow￨L￨JJ￨MISC￨- farrow-to-wean￨L￨JJ￨MISC￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- herd￨L￨NN￨O￨A as￨L￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- used￨L￨VBN￨O￨- stochastic￨L￨JJ￨O￨- “￨L￨``￨O￨- SIR￨U￨NN￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- ,￨L￨,￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- compartments￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stratified￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- PRRS￨U￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PRRSV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- time-to-extinction￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- 115-sow￨L￨JJ￨O￨- breeding￨L￨NN￨O￨- herd￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +Secondary￨U￨JJ￨O￨- objectives￨L￨NNS￨O￨- were￨L￨VBD￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- immunization￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- would￨L￨MD￨O￨- change￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- swine￨L￨NNS￨O￨- farm￨L￨NN￨O￨- .￨L￨.￨O￨- +Subjects￨U￨NNS￨O￨- were￨L￨VBD￨O￨- included￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- inclusion￨L￨NN￨O￨- criteria￨L￨NNS￨O￨- were￨L￨VBD￨O￨- met￨L￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- emergency￨L￨NN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- incidents￨L￨NNS￨O￨- with￨L￨IN￨O￨- ≥￨L￨NN￨O￨- 30￨L￨CD￨NUMBER￨- patients￨L￨NNS￨O￨- ;￨L￨:￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- incidents￨L￨NNS￨O￨- with￨L￨IN￨O￨- specific￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- subtypes￨L￨NNS￨O￨A verified￨L￨VBN￨O￨- by￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- examinations￨L￨NNS￨O￨- including￨L￨VBG￨O￨- virus￨L￨NN￨O￨- isolation￨L￨NN￨O￨- and/or￨L￨CC￨O￨- nucleic￨L￨JJ￨O￨- acid￨L￨NN￨O￨- detection￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- healthcare￨L￨NN￨O￨- authority￨L￨NN￨O￨- intervention￨L￨NN￨O￨- of￨L￨IN￨O￨- ≥￨L￨CD￨NUMBER￨- 5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- criteria￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- ≥￨L￨NN￨O￨- 30￨L￨CD￨NUMBER￨- ILIs￨U￨NNS￨O￨- occurring￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- preschool￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- collective￨L￨JJ￨O￨- organization￨L￨NN￨O￨- within￨L￨IN￨O￨- 1￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- laboratory-confirmed￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A viruses￨L￨NNS￨O￨A through￨L￨IN￨O￨- virus￨L￨NN￨O￨- isolation￨L￨NN￨O￨- or￨L￨CC￨O￨- real-time￨L￨JJ￨O￨- reverse￨L￨JJ￨O￨- transcriptase￨L￨NN￨O￨- polymerase￨L￨NN￨O￨- chain￨L￨NN￨O￨- reaction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RT-PCR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mixed￨L￨JJ￨O￨- type￨L￨NN￨O￨- refers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- mixture￨L￨NN￨O￨- of￨L￨IN￨O￨- ≥￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- virus￨L￨NN￨O￨- types￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- case￨L￨NN￨O￨- sample￨L￨NN￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- ;￨L￨:￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- include￨L￨VB￨O￨- ≥￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- subtypes￨L￨NNS￨O￨- of￨L￨IN￨O￨- type￨L￨NN￨O￨- A￨U￨NN￨O￨- or￨L￨CC￨O￨- ≥￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- subtype￨L￨NN￨O￨- of￨L￨IN￨O￨- type￨L￨NN￨O￨- A￨U￨NN￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- type￨L￨NN￨O￨- B￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A viruses￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- addressed￨L￨VBD￨O￨- this￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- parameterized￨L￨VBN￨O￨- stochastic￨L￨JJ￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- ,￨L￨,￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- SEIBM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- designed￨L￨VBN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- landscape-scale￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 47￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 50￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- multi-species￨L￨NNS￨O￨- wildlife￨L￨NN￨O￨A hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 51￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 52￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- claim￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- adequate￨L￨JJ￨O￨A predictions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- management￨L￨NN￨O￨- activities￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- mitigation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- contingency￨L￨NN￨O￨- planning￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- driving￨L￨VBG￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- adequate￨L￨JJ￨O￨A representation￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- of￨L￨IN￨O￨- crucial￨L￨JJ￨O￨- importance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Summarizing￨U￨VBG￨O￨- transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- hence￨L￨RB￨O￨- ,￨L￨,￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- allow￨L￨VB￨O￨- inferences￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- stages￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- persist￨L￨VB￨O￨- outside￨L￨IN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- whether￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- IT￨U￨PRP￨O￨- may￨L￨MD￨O￨- require￨L￨VB￨O￨- different￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- mitigation￨L￨NN￨O￨A efforts￨L￨NNS￨O￨- than￨L￨IN￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- DT￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- explanatory￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- assessed￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- included￨L￨VBD￨O￨- susceptible￨L￨JJ￨O￨- animal￨L￨NN￨O￨A densities￨L￨NNS￨O￨- ,￨L￨,￨O￨- weather￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- detection￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- IPs￨U￨NNS￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- 7￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- under￨L￨IN￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- AUC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- 7￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- convex￨L￨NN￨O￨- hull￨L￨NN￨O￨- calculation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Modeling￨U￨NN￨O￨- studies￨L￨NNS￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- in￨L￨IN￨O￨- Australia￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- overseas￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- and/or￨L￨CC￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- FMD￨U￨NN￨ORGANIZATION￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- situations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- widespread￨L￨JJ￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- resources￨L￨NNS￨O￨A for￨L￨IN￨O￨- stamping￨L￨VBG￨O￨- out￨L￨RP￨O￨- are￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- .￨L￨.￨O￨- +Sarandopoulos￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- conducted￨L￨VBD￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- 125￨L￨CD￨NUMBER￨- FMD￨U￨NN￨ORGANIZATION￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- non-endemic￨L￨JJ￨O￨- temperate￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- reported￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- OIE￨U￨NN￨O￨- between￨L￨IN￨O￨- January￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2005￨L￨CD￨DATE￨- and￨L￨CC￨O￨- December￨U￨NNP￨DATE￨- 31￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2013￨L￨CD￨DATE￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- associations￨L￨NNS￨O￨- between￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- size/duration￨L￨NN￨O￨- and￨L￨CC￨O￨- early￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- explanatory￨L￨JJ￨O￨- variables￨L￨NNS￨O￨A .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- New￨U￨NNP￨COUNTRY￨- Zealand￨U￨NNP￨COUNTRY￨- invest￨L￨VB￨O￨- considerable￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- in￨L￨IN￨O￨- preparedness￨L￨NN￨O￨- and￨L￨CC￨O￨- planning￨L￨NN￨O￨- for￨L￨IN￨O￨- emergency￨L￨NN￨O￨- animal￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- maintaining￨L￨VBG￨O￨- vaccine￨L￨NN￨O￨- banks￨L￨NNS￨O￨- for￨L￨IN￨O￨- FMD￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- HCV￨U￨NN￨O￨- incidence￨L￨NN￨O￨- stabilized￨L￨VBD￨O￨- among￨L￨IN￨O￨- heterosexuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- decreased￨L￨VBD￨O￨- among￨L￨IN￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- inject￨L￨VBP￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- .3￨L￨NN￨NUMBER￨- An￨U￨DT￨O￨- international￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- HCV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- HIV‐infected￨U￨JJ￨O￨- MSM￨U￨NN￨ORGANIZATION￨- was￨L￨VBD￨O￨- revealed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨- study￨L￨NN￨O￨- .11￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- high‐risk￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- including￨L￨VBG￨O￨- condomless￨L￨JJ￨O￨- traumatic￨L￨JJ￨O￨- anal￨L￨JJ￨O￨- intercourse￨L￨NN￨O￨- ,￨L￨,￨O￨- fisting￨L￨VBG￨O￨- ,￨L￨,￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- recreational￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- group￨L￨NN￨O￨- sex￨L￨NN￨O￨A .1￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 13￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- SHCS￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- HCV￨U￨NN￨O￨- incidence￨L￨NN￨O￨- coincided￨L￨VBD￨O￨- with￨L￨IN￨O￨- reduced￨L￨VBN￨O￨- self‐reported￨L￨JJ￨O￨- condom￨L￨NN￨O￨- use￨L￨NN￨O￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨O￨- on￨L￨IN￨O￨- antiretroviral￨L￨JJ￨O￨- therapy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ART￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .14￨L￨CD￨NUMBER￨- Effective￨U￨JJ￨O￨- interventions￨L￨NNS￨O￨- to￨L￨TO￨O￨- curb￨L￨VB￨O￨- the￨L￨DT￨O￨- HCV￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- among￨L￨IN￨O￨- HIV‐infected￨U￨JJ￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- remain￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- established￨L￨VBN￨O￨- .￨L￨.￨O￨- +antiretroviral￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- confidence￨L￨NN￨O￨- interval￨L￨NN￨O￨- direct‐acting￨L￨VBG￨O￨- antiviral￨L￨JJ￨O￨- agent￨L￨NN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨- C￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- interquartile￨L￨JJ￨O￨- range￨L￨NN￨O￨- men￨L￨NNS￨O￨A who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- person‐years￨L￨NNS￨O￨- Swiss￨U￨JJ￨NATIONALITY￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- Cohort￨U￨NN￨O￨- Study￨U￨NN￨O￨- The￨U￨DT￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨- C￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HCV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ‐￨L￨RB￨O￨- infected￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- evolved￨L￨VBN￨O￨- quickly￨L￨RB￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- few￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- .1￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- Western￨U￨JJ￨MISC￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- HCV￨U￨NN￨O￨- is￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- among￨L￨IN￨O￨- HIV‐infected￨U￨JJ￨O￨- men￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MSM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .1￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- observed￨L￨VBD￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Swiss￨U￨JJ￨NATIONALITY￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- Cohort￨U￨NN￨MISC￨- Study￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- SHCS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,10￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- steep￨L￨JJ￨O￨- rise￨L￨NN￨O￨- in￨L￨IN￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- HCV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨O￨- without￨L￨IN￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- injection￨L￨NN￨O￨- drug￨L￨NN￨O￨- use￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- without￨L￨IN￨O￨- bias￨L￨NN￨O￨- in￨L￨IN￨O￨- heterogenous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- scholars￨L￨NNS￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- precise￨L￨JJ￨O￨- hierarchical￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- hubs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- firstly￨L￨RB￨O￨- informed￨L￨VBN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- pervades￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- progressive￨L￨JJ￨IDEOLOGY￨- cascade￨L￨NN￨O￨- across￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- degree￨L￨NN￨O￨- classes41￨L￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- results￨L￨NNS￨O￨- have￨L￨VBP￨O￨- manifested￨L￨VBN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- uncorrelated￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- designing￨L￨VBG￨O￨- a￨L￨DT￨O￨- proper￨L￨JJ￨O￨- contact￨L￨NN￨O￨- strategy￨L￨NN￨O￨- can￨L￨MD￨O￨- effectively￨L￨RB￨O￨- promote￨L￨VB￨O￨A the￨L￨DT￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- preferential￨L￨JJ￨O￨- contact￨L￨NN￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PCS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- information￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- informed￨L￨VBN￨O￨A nodes￨L￨NNS￨O￨- densities￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- plant￨L￨NN￨O￨- pathogenic￨L￨JJ￨O￨- fungi￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- genus￨L￨NN￨O￨- Fusarium￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- putative￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- effector￨L￨NN￨O￨- genes￨L￨NNS￨O￨A and/or￨L￨CC￨O￨- secondary￨L￨JJ￨O￨- metabolite￨L￨NN￨O￨- gene￨L￨NN￨O￨- clusters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- regulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- ortholog￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- transcription￨L￨NN￨O￨- factor￨L￨NN￨O￨- :￨L￨:￨O￨- F.￨U￨NNP￨O￨- Also￨U￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- plant￨L￨NN￨O￨- pathogenic￨L￨JJ￨O￨- fungi￨L￨NNS￨O￨- Botrytis￨U￨NNP￨O￨- cinerea￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Reg1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Verticillium￨U￨NNP￨O￨- dahliae￨L￨NNP￨O￨- (￨L￨-LRB-￨O￨- VdSge1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Cladosporium￨U￨NN￨O￨- fulvum￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CfWor1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Zymoseptoria￨U￨NN￨O￨- tritici￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZtWor1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Ustilago￨U￨NNP￨O￨- maydis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- UmRos1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Magnaporthe￨U￨NN￨O￨- oryzae￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MoGti1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- deletion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- gene￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- transcription￨L￨NN￨O￨- factor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- partially￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- perturbs￨L￨VBZ￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- effector￨L￨NN￨O￨- genes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 32￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Ustilago￨U￨NNP￨O￨- maydis￨L￨VBZ￨O￨- the￨L￨DT￨O￨- heterodimer￨L￨NN￨O￨- bE/bW￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- forkhead￨L￨NN￨O￨- transcription￨L￨NN￨O￨- factor￨L￨NN￨O￨- Fox1￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- zinc￨L￨NN￨O￨- finger￨L￨NN￨O￨- transcription￨L￨NN￨O￨- factors￨L￨NNS￨O￨- Rbf1￨U￨NN￨O￨- and￨L￨CC￨O￨- Mzr1￨U￨NN￨O￨- are￨L￨VBP￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- transcriptional￨L￨JJ￨O￨- regulation￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogenicity-related￨L￨JJ￨O￨- genes￨L￨NNS￨O￨A and/or￨L￨CC￨O￨- effector￨L￨NN￨O￨- genes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Leptosphaeria￨U￨NNP￨LOCATION￨- maculans￨L￨NNS￨O￨- and￨L￨CC￨O￨- Stagnospora￨U￨NN￨O￨- nodorum￨L￨NN￨O￨- ,￨L￨,￨O￨- homologs￨L￨NNS￨O￨- of￨L￨IN￨O￨- StuA￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- bHLH￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- basic￨L￨JJ￨O￨- helix-loop-helix￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- transcription￨L￨NN￨O￨- factor￨L￨NN￨O￨- ,￨L￨,￨O￨- regulate￨L￨VBP￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- effector￨L￨NN￨O￨- genes￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- works￨L￨NNS￨O￨- on￨L￨IN￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- have￨L￨VBP￨O￨- greatly￨L￨RB￨O￨- deepened￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- level￨L￨NN￨O￨- and￨L￨CC￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- useful￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- overlooked￨L￨VBN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- what￨L￨WP￨O￨- would￨L￨MD￨O￨- happen￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- aim￨L￨VB￨O￨- for￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- but￨L￨CC￨O￨- only￨L￨RB￨O￨- suppose￨L￨VBP￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- localized￨L￨JJ￨O￨A target￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mixed￨L￨JJ￨O￨- degree￨L￨NN￨O￨- decomposition￨L￨NN￨O￨- method￨L￨NN￨O￨- consider￨L￨VBP￨O￨- both￨L￨DT￨O￨- the￨L￨DT￨O￨- residual￨L￨JJ￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- exhausted￨L￨VBN￨O￨- degree￨L￨NN￨O￨- when￨L￨WRB￨O￨- decomposing￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- rank￨L￨VB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- accordingly27￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- iterative￨L￨JJ￨O￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- method￨L￨NN￨O￨- incorporates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- centrality￨L￨NN￨O￨- information￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- in￨L￨IN￨O￨- ranking￨L￨JJ￨O￨A spreaders28￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- diversity￨L￨NN￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- the￨L￨DT￨O￨- ranking￨L￨JJ￨O￨- method29￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- hiring￨L￨VBG￨O￨- committee￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- know￨L￨VB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- these￨L￨DT￨O￨- PhD￨U￨NN￨O￨- students￨L￨NNS￨O￨A but￨L￨CC￨O￨- the￨L￨DT￨O￨- email￨L￨NN￨O￨- address￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- collaborators￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- published￨L￨VBN￨O￨- papers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- author￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- paper￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- essentially￨L￨RB￨O￨- a￨L￨DT￨O￨- target￨L￨NN￨O￨- spreading￨L￨NN￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- collaboration￨L￨NN￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- one￨L￨PRP￨NUMBER￨- has￨L￨VBZ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- node￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- propagate￨L￨VB￨O￨- such￨L￨JJ￨O￨- information￨L￨NN￨O￨- to￨L￨TO￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- PhD￨U￨NN￨O￨- students￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- towards￨L￨IN￨O￨- localized￨L￨JJ￨O￨A targets￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- attention￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- perceive￨L￨VB￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- govern￨L￨VBP￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨A size￨L￨NN￨O￨A in￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- clarify￨L￨VB￨O￨- how￨L￨WRB￨O￨- each￨L￨DT￨O￨- key￨L￨JJ￨O￨- factor￨L￨NN￨O￨- contributes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- various￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- issue￨L￨NN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨A size￨L￨NN￨O￨A is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- system￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- composite￨L￨NN￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- non-human￨L￨JJ￨O￨- primates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- primates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- generally￨L￨RB￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- sylvatic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- viruses￨L￨NNS￨O￨A ,￨L￨,￨O￨- this￨L￨DT￨O￨- paradigm￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- scant￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- and￨L￨CC￨O￨- researchers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- have￨L￨VBP￨O￨- repeatedly￨L￨RB￨O￨- cautioned￨L￨VBN￨O￨- that￨L￨IN￨O￨- other￨L￨JJ￨O￨- animal￨L￨JJ￨O￨- species￨L￨NNS￨O￨- may￨L￨MD￨O￨- play￨L￨VB￨O￨- key￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Dengue￨U￨JJ￨O￨- virus￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- DENV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- chikungunya￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- and￨L￨CC￨O￨- spread￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- and￨L￨CC￨O￨- rapidly￨L￨RB￨O￨- across￨L￨IN￨O￨- both￨L￨DT￨O￨- Central￨U￨NNP￨O￨- and￨L￨CC￨O￨- South￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- reaching￨L￨VBG￨O￨- dozens￨L￨NNS￨O￨- of￨L￨IN￨O￨- countries￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- year￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- introduction￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- ZIKV￨U￨NNP￨O￨- was￨L￨VBD￨O￨- first￨L￨JJ￨ORDINAL￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ancestral￨L￨JJ￨O￨- sylvatic￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- of￨L￨IN￨O￨- YFV￨U￨NN￨O￨- ,￨L￨,￨O￨- CHIKV￨U￨NN￨O￨- and￨L￨CC￨O￨- ZIKV￨U￨NN￨O￨- occur￨L￨VBP￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- DENV￨U￨NN￨O￨- ancestral￨L￨JJ￨O￨- cycle￨L￨NN￨O￨A occurs￨L￨VBZ￨O￨- in￨L￨IN￨O￨- Southeast￨U￨NNP￨LOCATION￨- Asia￨U￨NNP￨CITY￨- with￨L￨IN￨O￨- later￨L￨JJ￨O￨- transport￨L￨NN￨O￨- to￨L￨TO￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- enzootic￨L￨JJ￨O￨- establishment￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- invasion￨L￨NN￨O￨- of￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- by￨L￨IN￨O￨- Zika￨U￨NNP￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- latest￨L￨JJS￨O￨- upheaval￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- decade-long￨L￨JJ￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- viruses￨L￨NNS￨O￨A transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- Aedes￨U￨VBZ￨O￨- aegypti￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- predicted￨L￨VBN￨O￨- well￨L￨RB￨O￨- in￨L￨IN￨O￨- advance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- association￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- neuropathology￨L￨NN￨O￨- and￨L￨CC￨O￨- teratogenicity￨L￨NN￨O￨- were￨L￨VBD￨O￨- only￨L￨RB￨O￨- revealed￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A through￨L￨IN￨O￨- the￨L￨DT￨O￨- Pacific￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- into￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- whether￨L￨IN￨O￨- this￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- difference￨L￨NN￨O￨- alone￨L￨RB￨O￨- can￨L￨MD￨O￨- drive￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- sex-specific￨L￨JJ￨O￨- virulence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen.We￨L￨NN￨O￨- advance￨L￨NN￨O￨- evolutionary￨L￨JJ￨O￨- theory￨L￨NN￨O￨- by￨L￨IN￨O￨- formulating￨L￨VBG￨O￨- and￨L￨CC￨O￨- solving￨L￨VBG￨O￨- analytically￨L￨RB￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model23￨L￨NN￨O￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- vertical￨L￨JJ￨O￨- and￨L￨CC￨O￨- horizontal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- male￨L￨JJ￨O￨A and￨L￨CC￨O￨- female￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- will￨L￨MD￨O￨- explore￨L￨VB￨O￨- which￨L￨WDT￨O￨- factors￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- selection￨L￨NN￨O￨- for￨L￨IN￨O￨- differential￨L￨JJ￨O￨- exploitation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- residing￨L￨VBG￨O￨- in￨L￨IN￨O￨- female￨L￨JJ￨O￨- and￨L￨CC￨O￨- male￨L￨JJ￨O￨A hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- each￨L￨DT￨O￨- sex￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogens￨L￨NNS￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- host￨L￨VBP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- that￨L￨IN￨O￨- natural￨L￨JJ￨O￨- selection￨L￨NN￨O￨- acting￨L￨VBG￨O￨- differently￨L￨RB￨O￨- on￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- in￨L￨IN￨O￨- male￨L￨NN￨O￨A and￨L￨CC￨O￨- female￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- pathogens￨L￨NNS￨O￨- exhibiting￨L￨VBG￨O￨- different￨L￨JJ￨O￨- virulence￨L￨NN￨O￨- in￨L￨IN￨O￨- men￨L￨NNS￨O￨- and￨L￨CC￨O￨- women￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- progression￨L￨NN￨O￨- and￨L￨CC￨O￨- fatality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- virulence￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- affect￨L￨VB￨O￨- sex-specific￨L￨JJ￨O￨- organs￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- substantially￨L￨RB￨O￨- between￨L￨IN￨O￨- men￨L￨NNS￨O￨- and￨L￨CC￨O￨- women12￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- solve￨L￨VBP￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- allowing￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- to￨L￨TO￨O￨- exhibit￨L￨VB￨O￨- different￨L￨JJ￨O￨- virulence￨L￨NN￨O￨A in￨L￨IN￨O￨- men￨L￨NNS￨O￨- and￨L￨CC￨O￨- women￨L￨NNS￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- April￨U￨NNP￨DATE￨- 15￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2016￨L￨CD￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨ORGANIZATION￨- Strategic￨U￨NNP￨ORGANIZATION￨- Advisory￨U￨NNP￨ORGANIZATION￨- Group￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨O￨- Experts￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- SAGE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- immunisation￨L￨NN￨O￨- recommended￨L￨VBD￨O￨- Dengvaxia￨U￨NNP￨PERSON￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- regions￨L￨NNS￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- endemicity￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- indicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- seroprevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- or￨L￨CC￨O￨- greater￨L￨JJR￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- modeled￨L￨VBN￨O￨- reduced￨L￨VBN￨O￨- dengue￨L￨JJ￨O￨A hospitalizations￨L￨NNS￨O￨- by￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- over￨L￨IN￨O￨- 30￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- vaccinating￨L￨VBG￨O￨- yearly￨L￨JJ￨SET￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- 9￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- children￨L￨NNS￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- was￨L￨VBD￨O￨- revisited￨L￨VBN￨O￨- and￨L￨CC￨O￨- published￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- concluding￨L￨VBG￨O￨- that￨L￨IN￨O￨- Dengvaxia￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- given￨L￨VBN￨O￨- ,￨L￨,￨O￨- every￨L￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- 9￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- children￨L￨NNS￨O￨- living￨L￨VBG￨O￨- in￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A endemic￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- reduce￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- significantly￨L￨RB￨O￨- over￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- introduction￨L￨NN￨O￨- and￨L￨CC￨O￨- beyond￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- 21￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- to￨L￨TO￨O￨- 29￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- over￨L￨IN￨O￨- 20￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- modellers￨L￨NNS￨O￨- from￨L￨IN￨O￨- Sanofi￨U￨NNP￨ORGANIZATION￨- Pasteur￨U￨NNP￨ORGANIZATION￨- have￨L￨VBP￨O￨- predicted￨L￨VBN￨O￨- that￨L￨IN￨O￨- Dengvaxia￨U￨NNP￨PERSON￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- by￨L￨IN￨O￨- about￨L￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- within￨L￨IN￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- country￨L￨NN￨O￨- ’s￨L￨POS￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- vaccinated￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- achieving￨L￨VBG￨O￨- a￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- dengue￨L￨JJ￨O￨- prevention￨L￨NN￨O￨- goal￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- 3￨L￨CD￨NUMBER￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- phase￨L￨NN￨O￨- III￨U￨CD￨NUMBER￨- trials￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- high￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- partial￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A immunes￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- high￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- hospitalizations￨L￨NNS￨O￨- during￨L￨IN￨O￨- breakthrough￨L￨NN￨O￨- dengue￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- persons￨L￨NNS￨O￨- who￨L￨WP￨O￨- were￨L￨VBD￨O￨- vaccinated￨L￨VBN￨O￨- when￨L￨WRB￨O￨- seronegative￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- manufacturer￨L￨NN￨TITLE￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- has￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- 25￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- Phase￨U￨NN￨O￨- III￨U￨CD￨NUMBER￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- 66￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- olds￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- outline￨L￨VBP￨O￨- 3￨L￨CD￨NUMBER￨- components￨L￨NNS￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- building￨L￨VBG￨O￨- a￨L￨DT￨O￨- predictive￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- researchers￨L￨NNS￨O￨- and￨L￨CC￨O￨- managers￨L￨NNS￨O￨- should￨L￨MD￨O￨- consider￨L￨VB￨O￨- early￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- wildlife￨L￨NN￨O￨A pathogen￨L￨NN￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- modeling￨L￨NN￨O￨- frame￨L￨NN￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- appropriate￨L￨JJ￨O￨- ,￨L￨,￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- parameters￨L￨NNS￨O￨- or￨L￨CC￨O￨- factors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- making￨L￨VBG￨O￨- preliminary￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- collate￨L￨VB￨O￨- existing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- parameterize￨L￨VB￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- quickly￨L￨RB￨O￨- ,￨L￨,￨O￨- rigorously￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- effectively￨L￨RB￨O￨- synthesizes￨L￨VBZ￨O￨- relevant￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- a￨L￨DT￨O￨- wildlife￨L￨NN￨O￨A pathogen￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- emergence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- essential￨L￨JJ￨O￨- for￨L￨IN￨O￨- informing￨L￨VBG￨O￨- management￨L￨NN￨O￨- at￨L￨IN￨O￨- critical￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- and￨L￨CC￨O￨- ultimately￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- livestock￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- wildlife￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- reluctant￨L￨JJ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- forecasting￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- management￨L￨NN￨O￨A actions￨L￨NNS￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- parameters￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- essential￨L￨JJ￨O￨- component￨L￨NN￨O￨- for￨L￨IN￨O￨- applying￨L￨VBG￨O￨- decision￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- emerging￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- predictive￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- trade-offs￨L￨NNS￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- management￨L￨NN￨O￨A actions￨L￨NNS￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- consequences￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- this￨L￨DT￨O￨- 4-5-3￨L￨CD￨NUMBER￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- can￨L￨MD￨O￨- work￨L￨VB￨O￨- with￨L￨IN￨O￨- managers￨L￨NNS￨O￨- to￨L￨TO￨O￨- rapidly￨L￨RB￨O￨- develop￨L￨VB￨O￨- useful￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- with￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- and￨L￨CC￨O￨- prioritize￨L￨VB￨O￨- information￨L￨NN￨O￨- gathering￨L￨NN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- management￨L￨NN￨O￨A of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- accumulated￨L￨VBN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- temporal￨L￨JJ￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- ,￨L￨,￨O￨- clinical￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- information￨L￨NN￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- valuable￨L￨JJ￨O￨- information￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- exploited￨L￨VBN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- and￨L￨CC￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- One￨U￨CD￨NUMBER￨- feasible￨L￨JJ￨O￨- means￨L￨NNS￨O￨- to￨L￨TO￨O￨- promptly￨L￨RB￨O￨- detect￨L￨VB￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- track￨L￨VB￨O￨- the￨L￨DT￨O￨- progress￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- regional￨L￨JJ￨O￨- or￨L￨CC￨O￨- national￨L￨JJ￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- medical￨L￨JJ￨O￨- centres￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stochastic￨U￨NNP￨MISC￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- populationsRui-Xing￨L￨JJ￨O￨- Ming1￨U￨NN￨O￨- ,￨L￨,￨O￨- Jiming￨U￨VBG￨PERSON￨- Liu2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- William￨U￨NNP￨PERSON￨- K.￨U￨NNP￨PERSON￨- Recent￨U￨JJ￨PERSON￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- stressed￨L￨VBN￨O￨- the￨L￨DT￨O￨- urgency￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- when￨L￨WRB￨O￨- and￨L￨CC￨O￨- where￨L￨WRB￨O￨- outbreaks￨L￨NNS￨O￨- may￨L￨MD￨O￨- emerge￨L￨VB￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A spread￨L￨VBN￨O￨- because￨L￨RB￨O￨- many￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- unknown￨L￨JJ￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- quantitatively￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- such￨L￨JJ￨O￨- information￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- passengers￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- flight￨L￨NN￨O￨- or￨L￨CC￨O￨- number￨L￨NN￨O￨- co-authorship￨L￨NN￨O￨- papers￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- bind￨L￨VBP￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- weight￨L￨NN￨O￨- value￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- edge10￨L￨NN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨A based￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- that￨L￨WDT￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- essence￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨A computes￨L￨VBZ￨O￨- ranking￨L￨JJ￨O￨- score￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- connectivity￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- some￨L￨DT￨O￨- consensus￨L￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- terms￨L￨NNS￨O￨- ,￨L￨,￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- traits￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- essential￨L￨JJ￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- ,￨L￨,￨O￨- cause￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- within￨L￨IN￨O￨- human￨L￨JJ￨O￨A populations￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- Citation￨U￨NNP￨MISC￨- Ebola￨U￨NNP￨MISC￨- virus￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- EVD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- continuing￨L￨VBG￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- underlined￨L￨VBN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- better￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- emerge￨L￨VB￨O￨- and￨L￨CC￨O￨- cause￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- traits￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- human￨L￨JJ￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- by￨L￨IN￨O￨- any￨L￨DT￨O￨- transmission￨L￨NN￨O￨- route￨L￨NN￨O￨- other￨L￨JJ￨O￨- than￨L￨IN￨O￨- deliberate￨L￨JJ￨O￨- laboratory￨L￨NN￨O￨- exposure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +Level￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- indicates￨L￨VBZ￨O￨- viruses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- infect￨L￨VB￨O￨- humans￨L￨NNS￨O￨A but￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- from￨L￨IN￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +Level￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- indicates￨L￨VBZ￨O￨- viruses￨L￨NNS￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- humans￨L￨NNS￨O￨A are￨L￨VBP￨O￨- exposed￨L￨VBN￨O￨- but￨L￨CC￨O￨- which￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- infect￨L￨VB￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- placement￨L￨NN￨O￨- position￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- function￨L￨NN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- immunizing￨L￨VBG￨O￨- those￨L￨DT￨O￨- candidate￨L￨NN￨TITLE￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- introduces￨L￨VBZ￨O￨- Dancing￨U￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DWPV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨A placement￨L￨NN￨O￨- strategy￨L￨NN￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- division￨L￨NN￨O￨- into￨L￨IN￨O￨- our￨L￨PRP$￨O￨- solution￨L￨NN￨O￨- .￨L￨.￨O￨- +Researchers￨U￨NNS￨O￨- try￨L￨VBP￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- protection￨L￨NN￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- algorithm￨L￨NN￨O￨- by￨L￨IN￨O￨- modifying￨L￨VBG￨O￨- heuristic￨L￨NN￨O￨- idea￨L￨NN￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- NP-hard￨U￨JJ￨MISC￨- NumericCitation￨U￨NN￨MISC￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- computing￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨A between￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- #￨L￨#￨O￨- p￨L￨NN￨O￨- problem￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- immunization￨L￨NN￨O￨- strategy￨L￨NN￨O￨A should￨L￨MD￨O￨- take￨L￨VB￨O￨- the￨L￨DT￨O￨- benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- time￨L￨NN￨O￨- slot￨L￨NN￨O￨- into￨L￨IN￨O￨- consideration￨L￨NN￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- utilization￨L￨NN￨O￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- typical￨L￨JJ￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- which￨L￨WDT￨O￨- quantify￨L￨VBP￨O￨- how￨L￨WRB￨O￨- much￨L￨RB￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- centrally￨L￨RB￨O￨- positioned￨L￨JJ￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- betweenness￨L￨NN￨O￨- ,￨L￨,￨O￨- closeness￨L￨NN￨O￨- ,￨L￨,￨O￨- local￨L￨JJ￨O￨- rank￨L￨NN￨O￨- ,￨L￨,￨O￨- h-index￨L￨NN￨O￨- ,￨L￨,￨O￨- Katz￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- eigenvector￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- k-shell￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- k-truss￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- percolation￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- accessibility￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- influence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- expected￨L￨VBN￨O￨- force￨L￨NN￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨A the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- quickly￨L￨RB￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Those￨U￨DT￨O￨- interacting￨L￨VBG￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- affecting￨L￨VBG￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- ’s￨L￨POS￨O￨- states￨L￨NNS￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- vertices￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- representing￨L￨VBG￨O￨A the￨L￨DT￨O￨- objects￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- edges￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- representing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- relations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Not￨U￨RB￨O￨- any￨L￨DT￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- important￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- various￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨A importance￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- Darwinian￨U￨JJ￨MISC￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- linked￨L￨VBD￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- genotype￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- frequencies￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- alleles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- surviving￨L￨VBG￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- genotypes￨L￨NNS￨O￨- could￨L￨MD￨O￨- change￨L￨VB￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- selection￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- agent￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- could￨L￨MD￨O￨- occur￨L￨VB￨O￨- if￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- adults￨L￨NNS￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- between￨L￨IN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- exposure￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- the￨L￨DT￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- unnecessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- invoke￨L￨VB￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- allele￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- Darwinian￨U￨JJ￨MISC￨- evolution￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- observed￨L￨VBN￨O￨- mortality￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- plausible￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- mortality￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- mortality￨L￨NN￨O￨- feedbacks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- identify￨L￨VBP￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen-specific￨L￨JJ￨O￨- mortality￨L￨NN￨O￨A rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- starting￨L￨VBG￨O￨- frequencies￨L￨NNS￨O￨- of￨L￨IN￨O￨- protective￨L￨JJ￨O￨- alleles￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 19th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- mortality￨L￨NN￨O￨- transition￨L￨NN￨O￨- of￨L￨IN￨O￨- Pacific￨U￨NNP￨ORGANIZATION￨- Islanders￨U￨NNPS￨ORGANIZATION￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- non-zero￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- individuals￨L￨NNS￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- the￨L￨DT￨O￨- mortality￨L￨NN￨O￨A rate￨L￨NN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- that￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- detecting￨L￨VBG￨O￨- subpopulations￨L￨NNS￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨A may￨L￨MD￨O￨- potentially￨L￨RB￨O￨- facilitate￨L￨VB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- impactful￨L￨JJ￨O￨- and￨L￨CC￨O￨- cost-effective￨L￨JJ￨O￨- deployment￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- resources￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- point-of-care￨L￨JJ￨O￨- testing￨L￨NN￨O￨- or￨L￨CC￨O￨- pre-exposure￨L￨JJ￨O￨- prophylaxis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Historically￨U￨NNP￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A has￨L￨VBZ￨O￨- often￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- partition￨L￨NN￨O￨- the￨L￨DT￨O￨- sequence￨L￨NN￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- into￨L￨IN￨O￨- clades￨L￨NNS￨O￨- or￨L￨CC￨O￨- subtypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- different￨L￨JJ￨O￨- investigators￨L￨NNS￨O￨- can￨L￨MD￨O￨- refer￨L￨VB￨O￨- to￨L￨TO￨O￨- similar￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- nomenclature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- seldom￨L￨RB￨O￨- been￨L￨VBN￨O￨- validated￨L￨VBN￨O￨- on￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- where￨L￨WRB￨O￨- actual￨L￨JJ￨O￨- clusters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- different￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A methods￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- empirical￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- .￨L￨.￨O￨- +Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨A methods￨L￨NNS￨O￨- play￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- extensive￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- that￨L￨WDT￨O￨- accumulates￨L￨VBZ￨O￨- in￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Genetic￨U￨JJ￨O￨- clustering￨L￨NN￨O￨A methods￨L￨NNS￨O￨- operate￨L￨VBP￨O￨- on￨L￨IN￨O￨- variation￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- nucleotide￨L￨NN￨O￨- sequencing￨L￨NN￨O￨- or￨L￨CC￨O￨- nucleic￨L￨JJ￨O￨- acid￨L￨NN￨O￨- profiling￨L￨NN￨O￨- of￨L￨IN￨O￨- conspicuous￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- features￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- restriction￨L￨NN￨O￨- fragment￨L￨NN￨O￨- length￨L￨NN￨O￨- polymorphisms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- RFLPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- three￨L￨CD￨NUMBER￨- generations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- iterative￨L￨JJ￨O￨- fitting￨L￨JJ￨O￨A procedure￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- d￨L￨NN￨O￨- had￨L￨VBD￨O￨- stabilized￨L￨VBN￨O￨- sufficiently￨L￨RB￨O￨- to￨L￨TO￨O￨- project￨L￨VB￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- with￨L￨IN￨O￨- reasonable￨L￨JJ￨O￨- accuracy￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- porcine￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- diarrhea￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PEDV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- outbreak￨L￨NN￨O￨A in￨L￨IN￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- decay￨L￨NN￨O￨- and￨L￨CC￨O￨- exponential￨L￨JJ￨O￨- adjustment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IDEA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- modelAmy￨L￨NNP￨O￨- L.￨U￨NNP￨O￨- Using￨U￨VBG￨O￨- our￨L￨PRP$￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- 2-parameter￨L￨JJ￨O￨- IDEA￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- PEDV￨U￨NN￨O￨- on￨L￨IN￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- swine￨L￨NNS￨O￨- farms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- best-fit￨L￨JJS￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- between￨L￨IN￨O￨- farm￨L￨NN￨O￨- transmission￨L￨NN￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨A the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- publically￨L￨RB￨O￨- available￨L￨JJ￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- IDEA￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- projections￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- excellent￨L￨JJ￨O￨A agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- 7-day￨L￨JJ￨DURATION￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- estimate￨L￨NN￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- strongly￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- ambient￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- precipitation￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- predicted￨L￨VBD￨O￨- future￨L￨JJ￨DATE￨- climate￨L￨NN￨O￨- changes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- altered￨L￨JJ￨O￨- rainfall￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- ,￨L￨,￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- Hawaiian￨U￨JJ￨O￨- forest￨L￨NN￨O￨A birds￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- altitudinal￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- on￨L￨IN￨O￨- avian￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- Hawaiian￨U￨JJ￨LOCATION￨- forest￨L￨NN￨O￨A birds￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- previously￨L￨RB￨DATE￨- NumericCitation￨U￨NNP￨O￨- linked￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- climate￨L￨NN￨O￨- projections￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- warm￨L￨JJ￨O￨- and￨L￨CC￨O￨- dry￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- RCP￨U￨NN￨O￨- 4.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- warm￨L￨JJ￨O￨- and￨L￨CC￨O￨- wet￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- A1B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hot￨L￨JJ￨O￨- and￨L￨CC￨O￨- dry￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- RCP￨U￨NN￨O￨- 8.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- futures￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- our￨L￨PRP$￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- mosquito￨L￨NN￨O￨- abundance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- bird￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- until￨L￨IN￨O￨- the￨L￨DT￨DATE￨- end￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- 21st￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- .￨L￨.￨O￨- +Malaria￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- recently￨L￨RB￨DATE￨- increased￨L￨VBN￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- at￨L￨IN￨O￨- high￨L￨JJ￨O￨- elevations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Hawai’i￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- constitute￨L￨VBP￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- remaining￨L￨VBG￨O￨- refugia￨L￨NN￨O￨- for￨L￨IN￨O￨- native￨L￨JJ￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- supporting￨L￨VBG￨O￨- the￨L￨DT￨O￨- concern￨L￨NN￨O￨- that￨L￨IN￨O￨- native￨L￨JJ￨O￨- Hawaiian￨U￨JJ￨MISC￨- forest￨L￨NN￨O￨A birds￨L￨NNS￨O￨- may￨L￨MD￨O￨- suffer￨L￨VB￨O￨- further￨L￨JJ￨O￨- population￨L￨NN￨O￨- declines￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- species￨L￨NNS￨O￨- extinction￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- climate-induced￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 8,11,13,14,22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- comprehensive￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Hawaiian￨U￨JJ￨O￨- forest￨L￨NN￨O￨A bird-malaria￨L￨NN￨O￨- system￨L￨NN￨O￨- illustrates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- transmission￨L￨NN￨O￨- varies￨L￨VBZ￨O￨- across￨L￨IN￨O￨- altitudes￨L￨NNS￨O￨- on￨L￨IN￨O￨- Hawai’i￨U￨NNP￨LOCATION￨- Island￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- from￨L￨IN￨O￨- high￨L￨JJ￨O￨- year-round￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- warm￨L￨JJ￨O￨- lowland￨L￨JJ￨O￨- forests￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- episodic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- at￨L￨IN￨O￨- mid￨L￨JJ￨O￨- elevation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infrequent￨L￨JJ￨O￨- summer￨L￨NN￨DATE￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- cool￨L￨JJ￨O￨- high￨L￨JJ￨O￨- elevations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Even￨U￨RB￨O￨- though￨L￨IN￨O￨- these￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- not￨L￨RB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- life￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- multitude￨L￨NN￨O￨- of￨L￨IN￨O￨- BCMs￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- setting￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- still￨L￨RB￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- game-theoretical￨L￨JJ￨O￨- foundation￨L￨NN￨O￨- that￨L￨WDT￨O￨- caused￨L￨VBD￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- ‘￨L￨``￨O￨- vaccination￨L￨NN￨O￨- games￨L￨NNS￨O￨A ’￨L￨POS￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- ‘￨L￨``￨O￨- epidemic￨L￨JJ￨O￨- games￨L￨NNS￨O￨- with￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨- ’￨L￨''￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- incorporating￨L￨VBG￨O￨- behavioural￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- as￨L￨IN￨O￨- ‘￨L￨``￨O￨- behavioural￨L￨JJ￨O￨- change￨L￨NN￨O￨- models￨L￨NNS￨O￨- ’￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- BCMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- typically￨L￨RB￨O￨- complement￨L￨VBP￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- attempt￨L￨NN￨O￨- to￨L￨TO￨O￨- mimic￨L￨VB￨O￨- real￨L￨JJ￨O￨A life￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- A/H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- has￨L￨VBZ￨O￨- triggered￨L￨VBN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- to￨L￨TO￨O￨- adapt￨L￨VB￨O￨- their￨L￨PRP$￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- take￨L￨VB￨O￨- preventive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- interest￨L￨NN￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- behaviour￨L￨NN￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- disease-related￨L￨JJ￨O￨- information￨L￨NN￨O￨- into￨L￨IN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- essence￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- BCM￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- responsive￨L￨JJ￨O￨- to￨L￨TO￨O￨- external￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- take￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- preventive￨L￨JJ￨O￨A measures￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- contracting￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- HAT￨U￨NN￨O￨- ,￨L￨,￨O￨- multiple￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- including￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- trypanosomes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- scale￨L￨NN￨O￨- migrations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- activity-related￨L￨JJ￨O￨- movements￨L￨NNS￨O￨A through￨L￨IN￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- exposure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- key￨L￨JJ￨O￨- to￨L￨TO￨O￨- HAT￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- agent-based￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- movements￨L￨NNS￨O￨A that￨L￨WDT￨O￨- expose￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- hazards￨L￨NNS￨O￨- that￨L￨WDT￨O￨- vary￨L￨VBP￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨- has￨L￨VBZ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- risk-mitigation￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- feed￨L￨VB￨O￨- into￨L￨IN￨O￨- policy￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- the￨L￨DT￨O￨- ABM￨U￨NNP￨MISC￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨A activities￨L￨NNS￨O￨- that￨L￨WDT￨O￨- generate￨L￨VBP￨O￨- large￨L￨JJ￨O￨- amounts￨L￨NNS￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- results￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- explored￨L￨VBN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- depth￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- emergent￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +African￨U￨JJ￨NATIONALITY￨- animal￨L￨NN￨O￨- trypanosomiasis￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- AAT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- as￨L￨IN￨O￨- being￨L￨VBG￨O￨- “￨L￨``￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- factors￨L￨NNS￨O￨A restricting￨L￨VBG￨O￨- economic￨L￨JJ￨O￨- development￨L￨NN￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- today￨L￨NN￨DATE￨- ”￨L￨''￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- widespread￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- overstocking￨L￨NN￨O￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- in￨L￨IN￨O￨- tsetse-free￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Important￨U￨JJ￨O￨- research￨L￨NN￨O￨- questions￨L￨NNS￨O￨- explored￨L￨VBN￨O￨- were￨L￨VBD￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- spatial￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- parasite￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pressure￨L￨NN￨O￨A related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- urbanization￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- temporal￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- parasite￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pressure￨L￨NN￨O￨- in￨L￨IN￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- year￨L￨NN￨DATE￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- or￨L￨CC￨O￨- an￨L￨DT￨O￨- age-dependent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pressure￨L￨NN￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- parasite￨L￨NN￨O￨- abundance￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- assuming￨L￨VBG￨O￨- E.￨U￨NNP￨O￨- Methods￨U￨NNS￨O￨- By￨U￨IN￨O￨- developing￨L￨VBG￨O￨- and￨L￨CC￨O￨- comparing￨L￨VBG￨O￨- different￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- we￨L￨PRP￨O￨- characterised￨L￨VBD￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pressure￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨- that￨L￨WDT￨O￨- foxes￨L￨NNS￨O￨- acquired￨L￨VBN￨O￨- after￨L￨IN￨O￨- exposure￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- foxes￨L￨NNS￨O￨- in￨L￨IN￨O￨- Zurich￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- included￨L￨VBD￨O￨- the￨L￨DT￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pressure￨L￨NN￨O￨A with￨L￨IN￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- fox￨L￨NN￨O￨- and￨L￨CC￨O￨- season￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- regulating￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- on￨L￨IN￨O￨- parasite￨L￨NN￨O￨- abundance￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- zoonotic￨L￨JJ￨O￨- parasite￨L￨NN￨O￨A among￨L￨IN￨O￨- the￨L￨DT￨O￨- fox￨L￨NN￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- remarkably￨L￨RB￨O￨- aggregated￨L￨VBN￨O￨- with￨L￨IN￨O￨- few￨L￨JJ￨O￨- heavily￨L￨RB￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- harbouring￨L￨VBG￨O￨- much￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨NN￨O￨- burdens￨L￨NNS￨O￨- and￨L￨CC￨O￨- being￨L￨VBG￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- parasitic￨L￨JJ￨O￨- egg￨L￨NN￨O￨- contamination￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Mathematical￨U￨JJ￨MISC￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- Echinococcus￨U￨NN￨O￨- multilocularis￨L￨NNS￨O￨- abundance￨L￨NN￨O￨A in￨L￨IN￨O￨- foxes￨L￨NNS￨O￨- in￨L￨IN￨O￨- Zurich￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- SwitzerlandBelen￨U￨NNP￨MISC￨- Otero-Abad1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- Simon￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- alleviate￨L￨VB￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- various￨L￨JJ￨O￨- rumor￨L￨NN￨O￨A theories￨L￨NNS￨O￨- from￨L￨IN￨O￨- social￨L￨JJ￨O￨- ,￨L￨,￨O￨- psychological￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- CMC￨U￨NNP￨ORGANIZATION￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- used￨L￨VBD￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- features￨L￨NNS￨O￨- .￨L￨.￨O￨- +Second￨U￨NNP￨ORDINAL￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- report￨L￨VBP￨O￨- findings￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- snapshot￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- identified￨L￨VBN￨O￨- features￨L￨NNS￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A propagation￨L￨NN￨O￨- phases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Rumor-related￨U￨JJ￨O￨- tweets￨L￨NNS￨O￨- were￨L￨VBD￨O￨- extracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- examined￨L￨VBN￨O￨- over￨L￨IN￨O￨- different￨L￨JJ￨O￨- time￨L￨NN￨O￨- windows￨L￨NNS￨O￨- ,￨L￨,￨O￨- form￨L￨VBP￨O￨- the￨L￨DT￨DURATION￨- initial￨L￨JJ￨DURATION￨- 3￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨A to￨L￨TO￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨DURATION￨- 56￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- circulation￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- features￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- rumor￨L￨NN￨O￨A classification￨L￨NN￨O￨- .￨L￨.￨O￨- +Public￨U￨NNP￨O￨- health￨L￨NN￨O￨- decision￨L￨NN￨O￨- makers￨L￨NNS￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- require￨L￨VBP￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- inference￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- fundamental￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- using￨L￨VBG￨O￨- observations￨L￨NNS￨O￨A that￨L￨WDT￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- imperfectly￨L￨RB￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- reported￨L￨VBD￨O￨- disease-related￨L￨JJ￨O￨- illnesses￨L￨NNS￨O￨- serve￨L￨VBP￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- imperfect￨L￨JJ￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- incident￨L￨NN￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- methods￨L￨NNS￨O￨- make￨L￨VBP￨O￨A use￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- involve￨L￨VB￨O￨- Markov￨U￨NNP￨PERSON￨- Chain￨U￨NNP￨O￨- Monte￨U￨NNP￨O￨- Carlo￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- filtering￨L￨VBG￨O￨- techniques￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 32￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- sample￨L￨NN￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨- states￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- individual-level￨L￨JJ￨O￨- data￨L￨NNS￨O￨- required￨L￨VBN￨O￨- by￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- network￨L￨NN￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- compartmental￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- projecting￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- trajectory￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- calibration￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- Multiple￨U￨JJ￨O￨- Shooting￨U￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- Stochastic￨U￨NNP￨O￨- systems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MSS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- utilizes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- noise￨L￨NN￨O￨- approximation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LNA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- state-updating￨L￨JJ￨O￨- procedure￨L￨NN￨O￨- to￨L￨TO￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- observations￨L￨NNS￨O￨A while￨L￨IN￨O￨- explicitly￨L￨RB￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- interdependency￨L￨NN￨O￨- between￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- wide￨L￨JJ￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- to￨L￨TO￨O￨- calibrate￨L￨VB￨O￨- these￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- differ￨L￨VBP￨O￨- based￨L￨VBN￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- observations￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- delay￨L￨NN￨O￨- is￨L￨VBZ￨O￨- primarily￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- replication￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- competing￨L￨VBG￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- activation￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨A compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- from￨L￨IN￨O￨- published￨L￨VBN￨O￨- data￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1,22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- between￨L￨IN￨O￨- 0.06￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 3.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- cells￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- proliferate￨L￨VBP￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- predicted￨L￨VBN￨O￨- that￨L￨IN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- recombination￨L￨NN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- circulating￨L￨VBG￨O￨- viral￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- fragments￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- genome￨L￨NN￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- latent￨L￨JJ￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- time￨L￨NN￨O￨- during￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- quasispecies￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- evolutionary￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- active￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- actively￨L￨RB￨O￨- replicating￨L￨VBG￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨A represents￨L￨VBZ￨O￨- long-lived￨L￨JJ￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- growing￨L￨VBG￨O￨- fascination￨L￨NN￨O￨- with￨L￨IN￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- high-dimensional￨L￨JJ￨O￨- complex￨L￨NN￨O￨- system123456￨L￨NN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- huge￨L￨JJ￨O￨- components￨L￨NNS￨O￨A interacting￨L￨VBG￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- usually￨L￨RB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- coupled￨L￨VBN￨O￨- dynamical￨L￨JJ￨O￨- units￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- spreading7￨L￨NN￨O￨- ,￨L￨,￨O￨- neuronal￨L￨JJ￨O￨- networks8￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Kuramoto￨U￨NNP￨O￨- model9￨L￨NN￨O￨- ,￨L￨,￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- self-driven￨L￨JJ￨O￨- particles10￨L￨NN￨O￨- ,￨L￨,￨O￨- percolation￨L￨NN￨O￨- or￨L￨CC￨O￨- cascading￨L￨VBG￨O￨- procedure11121314151617￨L￨NN￨O￨- ,￨L￨,￨O￨- Ising￨U￨JJ￨O￨- model181920212223￨L￨NN￨O￨- and￨L￨CC￨O￨- ecosystems242526￨L￨NN￨O￨- etc￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- Gao￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- proposed￨L￨VBD￨O￨- an￨L￨DT￨O￨- elaborate￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- coding￨L￨VBG￨O￨- the￨L￨DT￨O￨- microcosmic￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- information￨L￨NN￨O￨- between￨L￨IN￨O￨- components￨L￨NNS￨O￨A into￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- the￨L￨DT￨O￨- multi-dimensional￨L￨JJ￨O￨- coupled￨L￨VBN￨O￨- nonlinear￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- simply￨L￨RB￨O￨- reduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- 1D￨L￨NN￨O￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- universal￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- theories￨L￨NNS￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- too￨L￨RB￨O￨- complicated￨L￨VBN￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- accurate￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- coupled￨L￨VBN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- interacting￨L￨VBG￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- highly￨L￨RB￨O￨- heterogenous￨L￨JJ￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- inhomogeneous￨L￨JJ￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- components￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- achievements￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- these￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- structure28￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- heterogenous￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- centrality￨L￨NN￨O￨- and￨L￨CC￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- usually￨L￨RB￨O￨A varies￨L￨VBZ￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- since￨L￨IN￨O￨- permutation￨L￨NN￨O￨- symmetry￨L￨NN￨O￨- breaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- therefore￨L￨RB￨O￨- could￨L￨MD￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- this￨L￨DT￨O￨- distinctiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- as￨L￨IN￨O￨- w￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- difficulty￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- activity￨L￨NN￨O￨- x￨L￨CC￨O￨- converted￨L￨VBN￨O￨- by￨L￨IN￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- resembling￨L￨VBG￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- in￨L￨IN￨O￨- Newtonian￨U￨JJ￨O￨- mechanics￨L￨NNS￨O￨- as￨L￨IN￨O￨- intrinsic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- promote￨L￨VB￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- generalized￨L￨VBN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- other￨L￨JJ￨O￨- than￨L￨IN￨O￨- resilience￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- to￨L￨TO￨O￨- figure￨L￨VB￨O￨- out￨L￨RP￨O￨- the￨L￨DT￨O￨- applicability￨L￨NN￨O￨- and￨L￨CC￨O￨- limitation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reduced￨L￨VBN￨O￨A 1D￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- equation￨L￨NN￨O￨- .￨L￨.￨O￨- +Adding￨U￨VBG￨O￨- another￨L￨DT￨O￨- layer￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- detail￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- agents￨L￨NNS￨O￨A depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- connections￨L￨NNS￨O￨- ,￨L￨,￨O￨- introducing￨L￨VBG￨O￨- time￨L￨NN￨O￨- fluctuations￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- agent￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- relevant￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- either￨L￨CC￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- agents￨L￨NNS￨O￨A are￨L￨VBP￨O￨- well-described￨L￨JJ￨O￨- by￨L￨IN￨O￨- averages￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- result￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- random-mixing￨L￨JJ￨O￨- hypothesis56￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- scheme￨L￨NN￨O￨- ,￨L￨,￨O￨- agents￨L￨NNS￨O￨A are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- connections￨L￨NNS￨O￨- are￨L￨VBP￨O￨- distributed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- A￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- assigned￨L￨VBN￨O￨- network￨L￨NN￨O￨- configuration11￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- satisfies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- 〈￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- 〉￨L￨NN￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- β/γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number7￨L￨NN￨DATE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- formed￨L￨VBN￨O￨- by￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- chickens￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- σ1￨L￨NN￨O￨- and￨L￨CC￨O￨- σ2￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- wild‐type￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- barn￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- mutant￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- barn￨L￨NN￨O￨- at￨L￨IN￨O￨- that￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- individual‐based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- in￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- an￨L￨DT￨O￨- expression￨L￨NN￨O￨- for￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- fitness￨L￨NN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- it￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- reduced￨L￨VBN￨O￨A lifespan￨L￨NN￨O￨- of￨L￨IN￨O￨- poultry￨L￨NN￨O￨- on￨L￨IN￨O￨- industrial￨L￨JJ￨O￨- farms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- reduced￨L￨VBN￨O￨- cohort￨L￨NN￨O￨- duration￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- virulence￨L￨NN￨O￨- .￨L￨.￨O￨- +Chickens￨U￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- wild‐type￨L￨JJ￨O￨- strain￨L￨NN￨O￨- shed￨L￨VBD￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨A at￨L￨IN￨O￨- rate￨L￨NN￨O￨- κ1￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- chickens￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- mutant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- shed￨L￨VBD￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- κ2￨L￨NN￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- a￨L￨DT￨O￨- chicken￨L￨NN￨O￨- perishes￨L￨VBZ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- occurs￨L￨VBZ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- v￨L￨LS￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- chickens￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- wild‐type￨L￨JJ￨O￨- strain￨L￨NN￨O￨- and￨L￨CC￨O￨- v￨L￨LS￨O￨- 2￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- chickens￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- mutant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- ω1￨L￨NN￨O￨- or￨L￨CC￨O￨- ω2￨L￨NN￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨A are￨L￨VBP￨O￨- released￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- barn￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Ing￨U￨NNP￨O￨- process￨L￨NN￨O￨- has￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- denotes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- well￨L￨RB￨O￨- defined￨L￨VBN￨O￨- linear￨L￨JJ￨O￨- transformation￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- automatically￨L￨RB￨O￨- gather￨L￨VB￨O￨- neighbour￨L￨NN￨O￨A ’s￨L￨POS￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- information￨L￨NN￨O￨- or￨L￨CC￨O￨- called￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- score￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- n￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- gathering￨L￨NN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- properly￨L￨RB￨O￨A chosen￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Ing￨U￨NNP￨O￨- process￨L￨NN￨O￨- will￨L￨MD￨O￨- obtain￨L￨VB￨O￨- more￨L￨RBR￨O￨- exact￨L￨JJ￨O￨- rankings￨L￨NNS￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- H-index28￨U￨NN￨O￨- ,￨L￨,￨O￨- coreness10￨L￨NN￨O￨- ,￨L￨,￨O￨- closeness32￨L￨NN￨O￨- ,￨L￨,￨O￨- betweenness33￨L￨NN￨O￨- ,￨L￨,￨O￨- LeaderRank￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- LR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 34￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- weighted￨L￨JJ￨O￨- LeaderRank￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- WLR￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- 35￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- CR30￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- evaluate￨L￨VB￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- Ing￨U￨NNP￨O￨- score￨L￨NN￨O￨- can￨L￨MD￨O￨- estimate￨L￨VB￨O￨- node￨L￨NN￨O￨A importance￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model31￨L￨NN￨O￨- on￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- representative￨L￨JJ￨TITLE￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- random￨L￨JJ￨O￨- contact￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- between￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- direct￨L￨JJ￨O￨- from￨L￨IN￨O￨- man￨L￨NN￨O￨- to￨L￨TO￨O￨- pig￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- infected￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A have￨L￨VBP￨O￨- equal￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- man￨L￨NN￨O￨- after￨L￨IN￨O￨- slaughter￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- fixed￨L￨VBN￨O￨- at￨L￨IN￨O￨- 1000￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- include￨L￨VBP￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- taeniosis￨L￨NN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- ,￨L￨,￨O￨- health￨L￨NN￨O￨- education￨L￨NN￨O￨- ,￨L￨,￨O￨- improved￨L￨VBD￨O￨- meat￨L￨NN￨O￨- inspection￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- improved￨L￨VBD￨O￨- hygiene￨L￨NN￨O￨- and￨L￨CC￨O￨- sanitation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Gabriël￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Included￨U￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- assessment￨L￨NN￨O￨- should￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- affected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- and￨L￨CC￨O￨- pig￨L￨NN￨O￨- owners￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- lose￨L￨VBP￨O￨- 50￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- pigs￨L￨NNS￨O￨A if￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Trevisan￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- also￨L￨RB￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- confined￨L￨VBN￨O￨- pigs￨L￨NNS￨O￨A had￨L￨VBD￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- free-roaming￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- –￨L￨:￨O￨- control￨L￨JJ￨O￨- study￨L￨NN￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- confirmed￨L￨VBN￨O￨- that￨L￨IN￨O￨- feeding￨L￨VBG￨O￨- potato￨L￨NN￨O￨- peels￨L￨VBZ￨O￨- to￨L￨TO￨O￨- pigs￨L￨NNS￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- risk￨L￨NN￨O￨- in￨L￨IN￨O￨- getting￨L￨VBG￨O￨- porcine￨L￨NN￨O￨- cysticercosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +WHO￨U￨WP￨O￨- considers￨L￨VBZ￨O￨- Taenia￨U￨NNP￨LOCATION￨- solium￨L￨NN￨O￨- taeniosis/cysticercosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TSTC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- an￨L￨DT￨O￨- eradicable￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- its￨L￨PRP$￨O￨- simple￨L￨JJ￨O￨- life￨L￨NN￨O￨- cycle￨L￨NN￨O￨- and￨L￨CC￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- powerful￨L￨JJ￨O￨- and￨L￨CC￨O￨- inexpensive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- tools￨L￨NNS￨O￨A .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- kernel￨L￨NN￨O￨- functions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- unable￨L￨JJ￨O￨- to￨L￨TO￨O￨- tease￨L￨VB￨O￨- apart￨L￨RB￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- indirect￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- those￨L￨DT￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- farm￨L￨NN￨O￨A operators￨L￨NNS￨O￨- .￨L￨.￨O￨- +Statistical￨U￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- long￨L￨RB￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- many￨L￨JJ￨O￨- complex￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- written￨L￨VBN￨O￨- texts￨L￨NNS￨O￨- and￨L￨CC￨O￨- language￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- now￨L￨RB￨DATE￨- include￨L￨VBP￨O￨- network￨L￨NN￨O￨- representations￨L￨NNS￨O￨- of￨L￨IN￨O￨- text￨L￨NN￨O￨A to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- linguistic￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- from￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- physics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- authorship￨L￨NN￨O￨- recognition￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- included￨L￨VBD￨O￨- text￨L￨NN￨O￨A modeling￨L￨NN￨O￨- with￨L￨IN￨O￨- co-occurrence￨L￨NN￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 42￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 47￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Networks￨U￨NNP￨O￨- generated￨L￨VBD￨O￨- from￨L￨IN￨O￨- text￨L￨NN￨O￨A share￨L￨NN￨O￨- several￨L￨JJ￨O￨- features￨L￨NNS￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- complex￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- transportation￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- biological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- co-occurrence￨L￨NN￨O￨- representation￨L￨NN￨O￨- to￨L￨TO￨O￨- probe￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- along￨L￨IN￨O￨- a￨L￨DT￨O￨- text￨L￨NN￨O￨A is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- author￨L￨NN￨TITLE￨- ’s￨L￨POS￨O￨- style￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- GBFP￨U￨NN￨O￨- identifies￨L￨VBZ￨O￨- multiple￨L￨JJ￨O￨- main￨L￨JJ￨O￨- paths￨L￨NNS￨O￨A for￨L￨IN￨O￨- each￨L￨DT￨O￨- case￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- easily￨L￨RB￨O￨- recognizable￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- all￨L￨DT￨O￨- high-persistence￨L￨JJ￨O￨- patents￨L￨NNS￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- approach￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- identify￨L￨VB￨O￨- some￨L￨DT￨O￨- dominantly￨L￨RB￨O￨- important￨L￨JJ￨O￨- patents￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- identified￨L￨VBN￨O￨- main￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- yields￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- network￨L￨NN￨O￨- complexity￨L￨NN￨O￨- that￨L￨WDT￨O￨- makes￨L￨VBZ￨O￨- qualitatively￨L￨RB￨O￨- tracing￨L￨VBG￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- problematic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- method￨L￨NN￨O￨- searches￨L￨NNS￨O￨- backward￨L￨RB￨O￨- and￨L￨CC￨O￨- forward￨L￨RB￨O￨- paths￨L￨NNS￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- genetically￨L￨RB￨O￨- dominant￨L￨JJ￨O￨- patents￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- generate￨L￨VB￨O￨- multiple￨L￨JJ￨O￨- interconnected￨L￨JJ￨O￨- main￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- without￨L￨IN￨O￨- missing￨L￨VBG￨O￨- any￨L￨DT￨O￨- dominantly￨L￨RB￨O￨- important￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- domain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- we￨L￨PRP￨O￨- label￨L￨VBP￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- method￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- backward-forward￨L￨JJ￨O￨- path￨L￨NN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- acronym￨L￨NN￨O￨- GBFP￨U￨NN￨O￨- throughout￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- adopt￨L￨VBP￨O￨- the￨L￨DT￨O￨- genetic￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- persistence￨L￨NN￨O￨- measurement￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GKPM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- suggested￨L￨VBN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- differently￨L￨RB￨O￨- from￨L￨IN￨O￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- paths￨L￨NNS￨O￨A by￨L￨IN￨O￨- forward￨L￨RB￨O￨- and￨L￨CC￨O￨- backward￨L￨RB￨O￨- tracing￨L￨VBG￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- citation-based￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- significant￨L￨JJ￨O￨- trajectories￨L￨NNS￨O￨- ,￨L￨,￨O￨- Hummon￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Doreian￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- first￨L￨RB￨ORDINAL￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- main￨L￨JJ￨O￨A path￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- and￨L￨CC￨O￨- much￨L￨JJ￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- applied￨L￨VBN￨O￨- main￨L￨JJ￨O￨- path￨L￨NN￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- technologies￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- technological￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Phylodynamic￨U￨JJ￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV-1￨U￨NN￨MISC￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- asymmetry￨L￨NN￨O￨- in￨L￨IN￨O￨- viral￨L￨JJ￨O￨- phylogenies￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- indicative￨L￨JJ￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- transmissions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- heterogeneous￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- yield￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨- with￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- mean￨L￨NN￨O￨- cluster￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- shorter￨L￨JJR￨O￨- mean￨L￨VB￨O￨- branch￨L￨NN￨O￨- lengths￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- somewhat￨L￨RB￨O￨- higher￨L￨JJR￨O￨- tree￨L￨NN￨O￨A imbalance￨L￨NN￨O￨- than￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- relatively￨L￨RB￨O￨- homogeneous￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Phylodynamics￨U￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- linking￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- with￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- fast￨L￨RB￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- histories￨L￨NNS￨O￨- become￨L￨VBP￨O￨- “￨L￨``￨O￨- recorded￨L￨VBN￨O￨- ”￨L￨''￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- between-host￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- phylogeny￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- phylogenetic￨L￨JJ￨O￨- tree￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Keeping￨U￨VBG￨O￨- track￨L￨NN￨O￨- of￨L￨IN￨O￨- who￨L￨WP￨O￨- transmits￨L￨VBZ￨O￨- to￨L￨TO￨O￨- whom￨L￨WP￨O￨- and￨L￨CC￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- every￨L￨DT￨O￨- individual￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- only￨L￨RB￨O￨- once￨L￨RB￨DATE￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- other￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- history￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- rooted￨L￨JJ￨O￨- tree￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- transmission￨L￨NN￨O￨- tree￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Previously￨U￨RB￨DATE￨- ,￨L￨,￨O￨- Britton￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- O’Neill￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- Erdős-Rényi￨U￨JJ￨MISC￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- it￨L￨PRP￨O￨- using￨L￨VBG￨O￨- recovery￨L￨NN￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- Groendyke￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- changed￨L￨VBN￨O￨- by￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- βf￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- us￨L￨PRP￨O￨- suppose￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- are￨L￨VBP￨O￨- different￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- general￨L￨JJ￨TITLE￨- deterministic￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨A equation￨L￨NN￨O￨A :￨L￨:￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- randomly￨L￨RB￨O￨- fluctuating￨L￨VBG￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- will￨L￨MD￨O￨- manifest￨L￨VB￨O￨- themselves￨L￨PRP￨O￨- mainly￨L￨RB￨O￨- as￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- β￨L￨RB￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- d￨L￨NN￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- change￨L￨NN￨O￨- to￨L￨TO￨O￨- random￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomesBy￨L￨NN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- limit￨L￨NN￨O￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- error￨L￨NN￨O￨A term￨L￨NN￨O￨- error￨L￨NN￨O￨- dt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- i￨L￨FW￨O￨- ≤￨L￨FW￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- normal￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- with￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- mean￨L￨NN￨O￨- and￨L￨CC￨O￨- variance￨L￨NN￨O￨- σ2dt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- i￨L￨FW￨O￨- ≤￨L￨FW￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- Itô￨U￨NN￨O￨- stochastic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- Model￨U￨NNP￨TITLE￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨A case￨L￨NN￨O￨A where￨L￨WRB￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- q￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- by￨L￨IN￨O￨- Yang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Mao￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- σ1￨L￨NN￨O￨- =￨L￨JJ￨O￨- σ2￨L￨NN￨O￨- =￨L￨JJ￨O￨- σ3￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- j￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- l￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- q￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- also￨L￨RB￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Assume￨U￨VB￨O￨- that￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- H1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- H2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- hold￨L￨VBP￨O￨- ;￨L￨:￨O￨- then￨L￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- +3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- solution￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- will￨L￨MD￨O￨- remain￨L￨VB￨O￨- in￨L￨IN￨O￨- R￨U￨NN￨O￨- +3￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨A the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- fully￨L￨RB￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- requires￨L￨VBZ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- partnership￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- arise￨L￨VBP￨O￨- from￨L￨IN￨O￨- reinfection￨L￨NN￨O￨A that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- SIS-type￨U￨JJ￨MISC￨- behaviour￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- inherently￨L￨RB￨O￨- lower-dimensional￨L￨JJ￨O￨- than￨L￨IN￨O￨- their￨L￨PRP$￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- counterparts￨L￨NNS￨O￨- ,￨L￨,￨O￨- potential￨L￨JJ￨O￨- reinfection￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- multiple￨L￨JJ￨O￨- times￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- between￨L￨IN￨O￨- neighbouring￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- makes￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- more￨L￨RBR￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- tractable￨L￨JJ￨O￨- results￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- utilise￨L￨VB￨O￨- such￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- techniques￨L￨NNS￨O￨A to￨L￨TO￨O￨- gain￨L￨VB￨O￨- a￨L￨DT￨O￨- clear￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- STIs￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- other￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- short-duration￨L￨NN￨O￨- immunity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- on￨L￨IN￨O￨- understanding￨L￨NN￨O￨- when￨L￨WRB￨O￨- simple￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- fail￨L￨VBP￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨- or￨L￨CC￨O￨- related￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- discussed￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- exact￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- marginal￨L￨JJ￨O￨A probabilities￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- finite￨L￨JJ￨O￨- explicitly￨L￨RB￨O￨- known￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Much￨U￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- focussed￨L￨VBN￨O￨- on￨L￨IN￨O￨- extending￨L￨VBG￨O￨- such￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- weighted￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- duration￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 35￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 37￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- denominator￨L￨NN￨O￨- that￨L￨WDT￨O￨- on￨L￨IN￨O￨- clustered￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- results￨L￨VBZ￨O￨- from￨L￨IN￨O￨- all￨L￨DT￨O￨- approaches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- approximate￨L￨JJ￨O￨- .￨L￨.￨O￨- +Consider￨U￨VB￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- population￨L￨NN￨O￨- patch￨L￨NN￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- admixture￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- refractory￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- initial￨L￨JJ￨O￨- fractions￨L￨NNS￨O￨- S0￨U￨NN￨O￨- ,￨L￨,￨O￨- I0￨U￨NN￨O￨- and￨L￨CC￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- scenario￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- sub-population￨L￨NN￨O￨- of￨L￨IN￨O￨- refractory￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- cycle￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- entirely￨L￨RB￨O￨- reflected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- S0￨U￨NN￨O￨- ,￨L￨,￨O￨- I0￨U￨NN￨O￨- and￨L￨CC￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- again￨L￨RB￨O￨- ,￨L￨,￨O￨- right￨L￨RB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- prone￨L￨JJ￨O￨- to￨L￨TO￨O￨- spreading￨L￨VBG￨O￨- and￨L￨CC￨O￨- persistance￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- becomes￨L￨VBZ￨O￨- persistent￨L￨JJ￨O￨A in￨L￨IN￨O￨- time7￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- state￨L￨NN￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immediate￨L￨JJ￨O￨- neighbourhood￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- stochastic￨L￨JJ￨O￨- in￨L￨IN￨O￨- nature￨L￨NN￨O￨- and￨L￨CC￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨A states￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- refractory￨L￨JJ￨O￨A stage￨L￨NN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- becomes￨L￨VBZ￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- infect￨L￨VB￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +Liu￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 17￨L￨CD￨NUMBER￨- gave￨L￨VBD￨O￨- a￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- centrality￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Dynamics-Sensitive￨U￨JJ￨O￨- centrality￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- while￨L￨IN￨O￨- only￨L￨RB￨O￨- use￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- influence￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- performs￨L￨VBZ￨O￨- much￨L￨RB￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- some￨L￨DT￨O￨- topological￨L￨JJ￨O￨- structural￨L￨JJ￨O￨- centralities￨L￨NNS￨O￨- like￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- k-shell￨L￨NN￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- comparable￨L￨JJ￨O￨- with￨L￨IN￨O￨- eigenvector￨L￨NN￨O￨- centrality￨L￨NN￨O￨- .￨L￨.￨O￨- +suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvector￨L￨NN￨O￨- centrality￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- dynamical￨L￨JJ￨O￨- influences￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- spreading￨L￨NN￨O￨- model34￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- proof￨L￨NN￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- given￨L￨VBN￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- exist￨L￨VBP￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- scale￨L￨NN￨O￨- and￨L￨CC￨O￨- eigenvector￨L￨NN￨O￨- centrality￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks35￨L￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- of￨L￨IN￨O￨- conventional￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- combine￨L￨VBP￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- centrality￨L￨NN￨O￨A closely￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- topological￨L￨JJ￨O￨- structure13141516￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- emphasize￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- closeness￨L￨NN￨O￨- ,￨L￨,￨O￨- betweenness￨L￨NN￨O￨- ,￨L￨,￨O￨- k-shell15￨L￨NN￨O￨- ,￨L￨,￨O￨- H-index16￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- real￨L￨JJ￨O￨- life￨L￨NN￨O￨- many￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- temporal3637383940414243￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- topological￨L￨JJ￨O￨A structure￨L￨NN￨O￨- evolving￨L￨VBG￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- time-order￨L￨NN￨O￨- have￨L￨VBP￨O￨- great￨L￨JJ￨O￨- influence￨L￨NN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- networks414445￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- centrality￨L￨NN￨O￨A which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes44464748￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- only￨L￨RB￨O￨- take￨L￨VBP￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- an￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- sized￨L￨VBN￨O￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- ILI￨U￨NN￨O￨- seek￨L￨VBP￨O￨- medical￨L￨JJ￨O￨- care￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- sample￨L￨NN￨O￨- can￨L￨MD￨O￨- change￨L￨VB￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- circulating￨L￨VBG￨O￨- virus￨L￨NN￨O￨- subtype￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- season￨L￨NN￨O￨A to￨L￨TO￨O￨- season￨L￨NN￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- country￨L￨NN￨O￨- to￨L￨TO￨O￨- country￨L￨NN￨O￨- ;￨L￨:￨O￨- second￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- medical￨L￨JJ￨O￨- professionals￨L￨NNS￨O￨- participating￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sentinel￨L￨NN￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- physicians￨L￨NNS￨O￨- working￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- or￨L￨CC￨O￨- region￨L￨NN￨O￨- NumericCitation￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- low￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- and￨L￨CC￨O￨- unpredictability￨L￨NN￨O￨- ;￨L￨:￨O￨- third￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- consultations￨L￨NNS￨O￨- happened￨L￨VBD￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- delay￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- available￨L￨JJ￨O￨- at￨L￨IN￨O￨- best￨L￨JJS￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- lag￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨A by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- EISN-ILI￨U￨NN￨MISC￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- modified￨L￨VBN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- MSIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- research￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- mainly￨L￨RB￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- the￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨A ’s￨L￨POS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- ’s￨L￨POS￨O￨- timing￨L￨NN￨O￨- ,￨L￨,￨O￨- neglecting￨L￨VBG￨O￨- timely￨L￨JJ￨O￨- onset￨L￨NN￨O￨- identification￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- few￨L￨JJ￨O￨- other￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- develop￨L￨VBP￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- different￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- it￨L￨PRP￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- with￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- or￨L￨CC￨O￨- just￨L￨RB￨O￨- by￨L￨IN￨O￨- testing￨L￨VBG￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- particularly￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- sensor￨L￨NN￨O￨- worm￨L￨NN￨O￨A by￨L￨IN￨O￨- several￨L￨JJ￨O￨- iterative￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- security￨L￨NN￨O￨- states￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- propagation￨L￨NN￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- provide￨L￨VB￨O￨- macroscopic￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨- sensor￨L￨NN￨O￨- worm￨L￨NN￨O￨A ’s￨L￨POS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- scale￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- accurately￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- follows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- transition￨L￨NN￨O￨- scheme￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S-I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- microscopically￨L￨RB￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- prior￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- sensor￨L￨NN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- worm￨L￨NN￨O￨A .￨L￨.￨O￨- +Worm￨U￨NN￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- always￨L￨RB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- imminent￨L￨JJ￨O￨- and￨L￨CC￨O￨- effective￨L￨JJ￨O￨- threats￨L￨NNS￨O￨- against￨L￨IN￨O￨- energy￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- confidentiality￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- service￨L￨NN￨O￨- availability￨L￨NN￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- WSNs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- defending￨L￨VBG￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- worm￨L￨NN￨O￨A carrier￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- research￨L￨NN￨O￨- modeled￨L￨VBD￨O￨- the￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- attributable￨L￨JJ￨O￨- to￨L￨TO￨O￨- iNTS￨L￨NN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- programmatic￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- NTS￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- utilizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- Expanded￨U￨NNP￨O￨- Program￨U￨NN￨O￨- on￨L￨IN￨O￨- Immunization￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- EPI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- infrastructure￨L￨NN￨O￨- that￨L￨IN￨O￨- successfully￨L￨RB￨O￨- delivered￨L￨VBN￨O￨- Hib￨U￨NN￨O￨- and￨L￨CC￨O￨- pneumococcal￨L￨JJ￨O￨- conjugate￨L￨NN￨O￨A vaccines￨L￨NNS￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- drastically￨L￨RB￨O￨- reduced￨L￨VBN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- invasive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- those￨L￨DT￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- burdens￨L￨NNS￨O￨- of￨L￨IN￨O￨- invasive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- Haemophilus￨U￨JJ￨O￨- influenzae￨L￨NNS￨O￨- type￨L￨NN￨O￨- b￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Hib￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Streptococcus￨U￨NN￨O￨- pneumoniae￨L￨FW￨O￨- have￨L￨VBP￨O￨- plummeted￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- Hib￨U￨NN￨O￨- conjugate￨L￨NN￨O￨A and￨L￨CC￨O￨- multivalent￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨- conjugate￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- recognition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- iNTS￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Numbers￨U￨NNS￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- within￨L￨IN￨O￨- specific￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- pooled￨L￨VBD￨O￨- across￨L￨IN￨O￨- even￨L￨RB￨O￨- years￨L￨NNS￨DURATION￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- HGT￨U￨NNP￨O￨- surveillance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- 2002￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2004￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2006￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2008￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2010￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- with￨L￨IN￨O￨- denominators￨L￨NNS￨O￨- from￨L￨IN￨O￨- INSTAT￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- group-specific￨L￨JJ￨O￨- hospitalization￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- iNTS￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- then￨L￨RB￨O￨- validated￨L￨VBN￨O￨- by￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- iNTS￨L￨NN￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- estimated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- odd￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨A of￨L￨IN￨O￨- HGT￨U￨NN￨O￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infinite￨L￨JJ￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- vanishes￨L￨VBZ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- percolates￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- non-zero￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- levels￨L￨NNS￨O￨- via￨L￨IN￨O￨- hierarchical￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- from￨L￨IN￨O￨- hub￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- lower￨L￨JJR￨O￨- degree￨L￨NN￨O￨- nodes12￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- SIS￨U￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- maximum￨L￨NN￨O￨- degree￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- cutoff￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- hub￨L￨NN￨O￨A node￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- act￨L￨VBP￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- incessant￨L￨JJ￨O￨- source￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state89￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemics￨U￨NNS￨O￨- on￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- exhibit￨L￨VB￨O￨- complex￨L￨JJ￨O￨- emergent￨L￨JJ￨O￨- dynamics3235363738￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- sustained￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨- ,￨L￨,￨O￨- bistability￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hysteresis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- emergent￨L￨JJ￨O￨- topological￨L￨JJ￨O￨- properties32353940￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- heterogeneous￨L￨JJ￨O￨- degree￨L￨NN￨O￨A distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- assortative￨L￨JJ￨O￨- degree￨L￨NN￨O￨- correlations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- SIR￨U￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- differently￨L￨RB￨O￨- from￨L￨IN￨O￨- SIS￨U￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts81011￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- vanishes￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨- limit￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- degree￨L￨NN￨O￨A increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- true￨L￨JJ￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- unless￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- restriction￨L￨NN￨O￨- on￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- cognitive￨L￨JJ￨O￨- limitations7￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- transition￨L￨NN￨O￨- point￨L￨NN￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- excitation￨L￨NN￨O￨- propagation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- input￨L￨NN￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- excitation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- injected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- distant￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- output￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨A in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model111213￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- note￨L￨NN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- excitation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- contribution￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- fold￨L￨NN￨COUNTRY￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- a￨L￨DT￨O￨- relative￨L￨JJ￨O￨- excitation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- minimal￨L￨JJ￨O￨A fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- excited￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- excited￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- usage￨L￨NN￨O￨- of￨L￨IN￨O￨- structural￨L￨JJ￨O￨- components￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- cycles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- producing￨L￨VBG￨O￨- reentrant￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Inspired￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- self-sustained￨L￨JJ￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- neuroscience￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- here￨L￨RB￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- minimal￨L￨JJ￨O￨A discrete￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- excitable￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- relative￨L￨JJ￨O￨- excitation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- excitations￨L￨NNS￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Quantitatively￨U￨RB￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- smallest￨L￨JJS￨O￨- integer￨L￨NN￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- or￨L￨CC￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- κk￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- acts￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- barrier￨L￨NN￨O￨- for￨L￨IN￨O￨- propagation￨L￨NN￨O￨A ,￨L￨,￨O￨- by￨L￨IN￨O￨- requiring￨L￨VBG￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- n￨L￨NN￨O￨- incoming￨L￨JJ￨O￨- excitations￨L￨NNS￨O￨- to￨L￨TO￨O￨- switch￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- excited￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- work5￨L￨NN￨O￨- ;￨L￨:￨O￨- there￨L￨RB￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- neighboring￨L￨VBG￨O￨- excitation￨L￨NN￨O￨- was￨L￨VBD￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- trigger￨L￨VB￨O￨- transition￨L￨NN￨O￨A to￨L￨TO￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- κ￨L￨VB￨O￨- →￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- an￨L￨DT￨O￨- elementary￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- relatively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- how￨L￨WRB￨O￨- web￨L￨NN￨O￨A malware￨L￨NN￨O￨- spread￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨- ’￨L￨POS￨O￨- security￨L￨NN￨O￨- awareness￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- develop￨L￨VB￨O￨- proper￨L￨JJ￨O￨- prevention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- with￨L￨IN￨O￨- human￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +Hosts￨U￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- web￨L￨NN￨O￨A malware￨L￨NN￨O￨- can￨L￨MD￨O￨- suffer￨L￨VB￨O￨- from￨L￨IN￨O￨- modifications￨L￨NNS￨O￨- of￨L￨IN￨O￨- browser￨L￨NN￨O￨- settings￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- default￨L￨NN￨O￨- homepage￨L￨NN￨O￨- ,￨L￨,￨O￨- search￨L￨NN￨O￨- bars￨L￨NNS￨O￨- ,￨L￨,￨O￨- toolbars￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- cause￨L￨VB￨O￨- user￨L￨NN￨O￨- registry￨L￨NN￨O￨- modification￨L￨NN￨O￨- ,￨L￨,￨O￨- display￨L￨VBP￨O￨- intermittent￨L￨JJ￨O￨- advertising￨L￨NN￨O￨- pop-ups￨L￨NNS￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- transmit￨L￨VB￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- your￨L￨PRP$￨O￨- web-browsing￨L￨JJ￨O￨- habits￨L￨NNS￨O￨- to￨L￨TO￨O￨- advertisers￨L￨NNS￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- third￨L￨JJ￨ORDINAL￨- party￨L￨NN￨O￨- interests￨L￨NNS￨O￨- without￨L￨IN￨O￨- your￨L￨PRP$￨O￨- awareness￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- human￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- influences￨L￨VBZ￨O￨- on￨L￨IN￨O￨- web￨L￨NN￨O￨A malware￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- propagation￨L￨NN￨O￨- when￨L￨WRB￨O￨- user￨L￨NN￨O￨- ’s￨L￨POS￨O￨- security￨L￨NN￨O￨- awareness￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- hyperlinks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- addresses￨L￨NNS￨O￨- of￨L￨IN￨O￨- corresponding￨L￨JJ￨O￨- harmful￨L￨JJ￨O￨- websites￨L￨NNS￨O￨- purporting￨L￨VBG￨O￨- to￨L￨TO￨O￨- proliferate￨L￨VB￨O￨- malware￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- exist￨L￨VB￨O￨- in￨L￨IN￨O￨- short￨L￨JJ￨O￨- messages￨L￨NNS￨O￨- or￨L￨CC￨O￨- spam￨L￨NN￨O￨- emails￨L￨NNS￨O￨- that￨L￨WDT￨O￨- lure￨L￨VBP￨O￨- victims￨L￨NNS￨O￨- to￨L￨TO￨O￨- click￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- malicious￨L￨JJ￨O￨- URLs￨U￨NNS￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- redirect￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- false￨L￨JJ￨O￨- web￨L￨NN￨O￨A page￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- inject￨L￨VB￨O￨- malware￨L￨NN￨O￨- into￨L￨IN￨O￨- their￨L￨PRP$￨O￨- devices￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- recent￨L￨JJ￨O￨- reviews￨L￨NNS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- determinants￨L￨NNS￨O￨- of￨L￨IN￨O￨- spillover￨L￨NN￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- knowledge-gap￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- exists￨L￨VBZ￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- lack￨L￨VBP￨O￨- empirically￨L￨RB￨O￨- validated￨L￨VBN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ecological￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- wildlife￨L￨NN￨O￨A reservoirs￨L￨NNS￨O￨- and￨L￨CC￨O￨- key￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- hantavirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- climate￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- condition￨L￨NN￨O￨- and/or￨L￨CC￨O￨- agricultural￨L￨JJ￨O￨- activity￨L￨NN￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- via￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- reservoir￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- exposure￨L￨NN￨O￨- risk￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- virus￨L￨NN￨O￨- stability￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- untangle￨L￨VB￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- ,￨L￨,￨O￨- combined￨L￨JJ￨O￨- field￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- that￨L￨WDT￨O￨- link￨L￨VBP￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- wildlife￨L￨NN￨O￨A with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- wildlife￨L￨NN￨O￨- reservoir￨L￨NN￨O￨- are￨L￨VBP￨O￨- essential￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- in￨L￨IN￨O￨- question￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- cause￨L￨VB￨O￨- hantavirus￨L￨NN￨O￨- pulmonary￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- HPS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- hemorrhagic￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- renal￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HFRS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- range￨L￨VBP￨O￨- between￨L￨IN￨O￨- 0.5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Hantavirus￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- numerous￨L￨JJ￨O￨- significant￨L￨JJ￨O￨- zoonotic￨L￨JJ￨O￨A outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- HFRS￨U￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- Hantaan￨U￨JJ￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HTNV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- Korean￨U￨NNP￨NATIONALITY￨- War￨U￨NNP￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- HPS￨U￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- Sin￨U￨NNP￨O￨- Nombre￨U￨NNP￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SNV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- group-based￨L￨JJ￨O￨- metric￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- R0￨U￨NN￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- high￨L￨JJ￨O￨- within-group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- within￨L￨IN￨O￨- farm￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- only￨L￨RB￨O￨- low￨L￨JJ￨O￨- between-group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- between￨L￨IN￨O￨- farm￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- R0￨U￨NN￨O￨- can￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- poor￨L￨JJ￨O￨- at￨L￨IN￨O￨- describing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- metapopulations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- farm￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- to￨L￨TO￨O￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- via￨L￨IN￨O￨- livestock￨L￨NN￨O￨- movements￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- technique￨L￨NN￨O￨A ,￨L￨,￨O￨- consider￨L￨VB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- SEIR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- born￨L￨VBN￨O￨- into￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- following￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- they￨L￨PRP￨O￨- enter￨L￨VBP￨O￨- exposed￨L￨VBN￨O￨- state￨L￨NN￨O￨- E￨U￨NN￨O￨- and￨L￨CC￨O￨- incubate￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- progress￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- state￨L￨NN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- recover￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- state￨L￨NN￨O￨- R.￨U￨NNP￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- *￨L￨SYM￨O￨- takes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- intuitive￨L￨JJ￨O￨- form￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨A rate￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- within-herd￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- within-herd￨L￨JJ￨O￨- persistent￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- R￨U￨NN￨O￨- *￨L￨SYM￨O￨- peaks￨L￨VBZ￨O￨- at￨L￨IN￨O￨- intermediate￨L￨JJ￨O￨- movement￨L￨NN￨O￨A rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- revealing￨L￨VBG￨O￨- ranges￨L￨NNS￨O￨- of￨L￨IN￨O￨- movement￨L￨NN￨O￨- rates￨L￨NNS￨O￨- where￨L￨WRB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- intervention￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- most￨L￨RBS￨O￨- difficult￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨A of￨L￨IN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- related￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- normalization￨L￨NN￨O￨- condition￨L￨NN￨O￨- The￨U￨DT￨O￨- following￨L￨VBG￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obeyed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- :￨L￨:￨O￨- These￨U￨DT￨O￨- equations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- become￨L￨VBP￨O￨- recovered￨L￨VBN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- available￨L￨JJ￨O￨A data￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- newly￨L￨RB￨O￨- infected￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- and￨L￨CC￨O￨- total￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- cumulative￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- agent￨L￨NN￨O￨- based￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- Euclidean￨U￨JJ￨MISC￨- network20￨L￨NN￨O￨- ,￨L￨,￨O￨- mentioned￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- paragraph￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- analysed￨L￨VBN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- data￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- extended￨L￨VBD￨O￨- over￨L￨IN￨O￨- approximately￨L￨RB￨O￨- two￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨A data￨L￨NNS￨O￨A for￨L￨IN￨O￨- total￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- cumulative￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- extracted￨L￨VBN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨A reach￨L￨VBP￨O￨- a￨L￨DT￨O￨- saturation￨L￨NN￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- conclude￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- existed￨L￨VBN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- longer￨L￨JJR￨O￨- period￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Guinea￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- list￨L￨VBP￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- traits￨L￨NNS￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A that￨L￨WDT￨O￨- could￨L￨MD￨O￨- amplify￨L￨VB￨O￨- their￨L￨PRP$￨O￨- vulnerability￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- under￨L￨IN￨O￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- to￨L￨TO￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- parasite￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- various￨L￨JJ￨O￨- mitigation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- both￨L￨CC￨O￨- parasites￨L￨NNS￨O￨- and￨L￨CC￨O￨- hosts￨L￨NNS￨O￨- adapting￨L￨VBG￨O￨- to￨L￨TO￨O￨- disrupted￨L￨VBN￨O￨- climates￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- 54￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- free-living￨L￨JJ￨O￨- species￨L￨NNS￨O￨- eventually￨L￨RB￨O￨- committed￨L￨VBN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fate￨L￨NN￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A remains￨L￨VBZ￨O￨- uncertain￨L￨JJ￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- significant￨L￨JJ￨O￨- research￨L￨NN￨O￨- profiling￨L￨VBG￨O￨- climate-driven￨L￨JJ￨O￨- biodiversity￨L￨NN￨O￨- loss￨L￨NN￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- turn￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- century￨L￨NN￨DATE￨- .￨L￨.￨O￨- +Identifying￨U￨VBG￨O￨- traits￨L￨NNS￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- predispose￨L￨VB￨O￨- parasites￨L￨NNS￨O￨A to￨L￨TO￨O￨- climate-driven￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- ,￨L￨,￨O￨- separate￨L￨JJ￨O￨- from￨L￨IN￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- would￨L￨MD￨O￨- provide￨L￨VB￨O￨- conservation￨L￨NN￨O￨- a￨L￨DT￨O￨- much￨L￨JJ￨O￨- needed￨L￨VBN￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- risk￨L￨NN￨O￨- assessment￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- robust￨L￨JJ￨O￨- and￨L￨CC￨O￨- applicable￨L￨JJ￨O￨- across￨L￨IN￨O￨- major￨L￨JJ￨O￨- parasitic￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Macroparasites￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- already￨L￨RB￨O￨- uniquely￨L￨RB￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- secondary￨L￨JJ￨O￨- extinctions￨L￨NNS￨O￨- ;￨L￨:￨O￨- theoretical￨L￨JJ￨O￨- work￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- parasite￨L￨NN￨O￨- vulnerability￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- 10￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- extinction￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- and￨L￨CC￨O￨- tertiary￨L￨JJ￨O￨- extinctions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- highlighted￨L￨VBN￨O￨- that￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A can￨L￨MD￨O￨- dilute￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- counterintuitive￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- observe￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- age-specific￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- computationally￨L￨RB￨O￨- expensive￨L￨JJ￨O￨- but￨L￨CC￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- fast￨L￨JJ￨O￨- but￨L￨CC￨O￨- more￨L￨RBR￨O￨- stylized￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- different￨L￨JJ￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- both￨L￨DT￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- calibrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- similar￨L￨JJ￨O￨- results￨L￨NNS￨O￨- under￨L￨IN￨O￨- no￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- goal￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- possible￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- performances￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- agent-based￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- may￨L￨MD￨O￨- differ￨L￨VB￨O￨- significantly￨L￨RB￨O￨- in￨L￨IN￨O￨- practical￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- total￨L￨JJ￨O￨- cost￨L￨NN￨O￨- and￨L￨CC￨O￨- 34￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- strategies￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- each￨L￨DT￨O￨- iteration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- optimization￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- performances￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨- generated￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- experiments￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- mesh-adaptive￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- effective￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- objective￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Λ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ;￨L￨:￨O￨- μ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- μ2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- disease-induced￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- β1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- β2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- or￨L￨CC￨O￨- infected￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- to￨L￨TO￨O￨- mosquito￨L￨NN￨O￨- ;￨L￨:￨O￨- α1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- saturation￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ;￨L￨:￨O￨- υ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ;￨L￨:￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- K￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- environment￨L￨NN￨O￨- for￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- above￨L￨JJ￨O￨- works￨L￨NNS￨O￨- and￨L￨CC￨O￨- [￨L￨-LRB-￨O￨- 29￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 34￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- lymphatic￨L￨JJ￨O￨- filariasis￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- environment￨L￨NN￨O￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- background￨L￨NN￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- initial￨L￨JJ￨O￨- valueswhere￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- separately￨L￨RB￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ;￨L￨:￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- for￨L￨IN￨O￨- mosquito￨L￨NN￨O￨A population￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Nonautonomous￨U￨JJ￨O￨- phenomenon￨L￨NN￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- often￨L￨RB￨O￨- occurs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨A systems￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- operator￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- globally￨L￨RB￨O￨- asymptotical￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- and￨L￨CC￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incursion￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- relate￨L￨VBP￨O￨- to￨L￨TO￨O￨- farm￨L￨NN￨O￨A density￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- movements￨L￨NNS￨O￨- to￨L￨TO￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- area789￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- strain￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus7￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- incursions10￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- human￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- compliance￨L￨NN￨O￨- with￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- movement￨L￨NN￨O￨- restrictions1112￨L￨NN￨O￨- have￨L￨VBP￨O￨- all￨L￨DT￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- farm￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- strict￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- implemented￨L￨VBN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- depopulating￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- premises￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- IPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- tracing￨L￨VBG￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- premises￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- strict￨L￨JJ￨O￨- movement￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨- for￨L￨IN￨O￨- farms￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vicinity￨L￨NN￨O￨- of￨L￨IN￨O￨- IPs￨U￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- line￨L￨NN￨O￨- with￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- and￨L￨CC￨O￨- European￨U￨JJ￨NATIONALITY￨- level￨L￨NN￨O￨- legislation￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- generated￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- vary￨L￨VBP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- taken￨L￨VBN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- an￨L￨DT￨O￨- incursion￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- geographical￨L￨JJ￨O￨- location￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- producer￨L￨NN￨TITLE￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- explore￨L￨VB￨O￨- which￨L￨WDT￨O￨- other￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- would￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- generated￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- incorporates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- premises￨L￨NNS￨O￨A to￨L￨TO￨O￨- premises￨L￨NNS￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- through￨L￨IN￨O￨- local￨L￨JJ￨O￨- spread￨L￨NN￨O￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- randomly￨L￨RB￨O￨- selected￨L￨VBN￨O￨- farm￨L￨NN￨O￨- in￨L￨IN￨O￨- GB￨U￨NN￨O￨- .￨L￨.￨O￨- +tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- genomes￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- deposited￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- European￨U￨JJ￨NATIONALITY￨- Nucleotide￨U￨NN￨MISC￨- Archive￨U￨NNP￨MISC￨- ;￨L￨:￨O￨- accession￨L￨NN￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- PRJEB12764￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- url￨L￨NN￨O￨- -￨L￨:￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- commands￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- reference￨L￨NN￨O￨- alignment￨L￨NN￨O￨- and￨L￨CC￨O￨- variant￨L￨JJ￨O￨- calling￨L￨VBG￨O￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- text￨L￨NN￨O￨- file￨L￨NN￨O￨- from￨L￨IN￨O￨- Figshare￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.6084￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- m9.figshare￨L￨JJ￨O￨- .3153280￨L￨NN￨NUMBER￨- (￨L￨-LRB-￨O￨- url￨L￨NN￨O￨- -￨L￨:￨O￨- emiology/3153280￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- final￨L￨JJ￨O￨- dataset￨L￨NN￨O￨- of￨L￨IN￨O￨- variants￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- fasta￨L￨NN￨O￨- file￨L￨NN￨O￨- from￨L￨IN￨O￨- Figshare￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.6084￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- m9.figshare￨L￨JJ￨O￨- .3153280￨L￨NN￨NUMBER￨- (￨L￨-LRB-￨O￨- url￨L￨NN￨O￨- -￨L￨:￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- TransPhylo￨U￨NNP￨MISC￨- code￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- update￨L￨VBP￨O￨- written￨L￨VBN￨O￨- specifically￨L￨RB￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- from￨L￨IN￨O￨- GitHub￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- url￨L￨NN￨O￨- -￨L￨:￨O￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- described￨L￨VBN￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- person-to-person￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- from￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- genome￨L￨NN￨O￨- data￨L￨NNS￨O￨- ;￨L￨:￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- an￨L￨DT￨O￨- improvement￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- ’s￨L￨POS￨O￨- underlying￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- time￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- person￨L￨NN￨O￨A was￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- previously￨L￨RB￨DATE￨- developed￨L￨VBD￨O￨- TransPhylo￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Didelot￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- transmissions￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- timing￨L￨NN￨O￨- given￨L￨VBN￨O￨- mutational￨L￨JJ￨O￨- events￨L￨NNS￨O￨- captured￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- time-labelled￨L￨JJ￨O￨- phylogeny￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- used￨L￨VBD￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨- transmissions￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- 33￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2011￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Transmission￨U￨NNP￨O￨- inference￨L￨NN￨O￨- from￨L￨IN￨O￨- genomic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- uses￨L￨VBZ￨O￨- mutations￨L￨NNS￨O￨- –￨L￨:￨O￨- fixed￨L￨JJ￨O￨- or￨L￨CC￨O￨- minor￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Worby￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Poon￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- shared￨L￨VBN￨O￨- across￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- isolates￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- putative￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- events￨L￨NNS￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- request￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Medical￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- Officer￨U￨NNP￨O￨- leading￨L￨VBG￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- response￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analysed￨L￨VBD￨O￨- Mycobacterium￨U￨NN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨A genomes￨L￨NNS￨O￨- from￨L￨IN￨O￨- 48￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 52￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- decline￨L￨NN￨O￨- in￨L￨IN￨O￨- newly￨L￨RB￨O￨- diagnosed￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- truly￨L￨RB￨O￨- signaled￨L￨VBD￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- In￨U￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- travel￨L￨NN￨O￨- data￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- arrival￨L￨NN￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- seeded￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- originating￨L￨VBG￨O￨A country￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- connecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- originating￨L￨VBG￨O￨- country￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +KeywordsBasic￨U￨JJ￨O￨- reproduction￨L￨NN￨O￨- numberEpidemic￨L￨JJ￨O￨- modelsTravel￨L￨NN￨O￨- dataSIR￨L￨NN￨O￨- modelInfluenza￨L￨NN￨O￨- pandemic￨L￨JJ￨O￨- BackgroundIn￨U￨NN￨O￨- responding￨L￨VBG￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 21st￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- reliable￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- phases￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A pandemic￨L￨NN￨O￨A is￨L￨VBZ￨O￨- critical￨L￨JJ￨O￨- .￨L￨.￨O￨- +Method￨U￨NN￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- likelihood-based￨L￨JJ￨O￨- method￨L￨NN￨O￨- using￨L￨VBG￨O￨- arrival￨L￨NN￨O￨A times￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- and￨L￨CC￨O￨- timely￨L￨JJ￨O￨- source￨L￨NN￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmissibility￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- statistically￨L￨RB￨O￨- fit￨L￨VBP￨O￨- each￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- cross-sectional￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- load￨L￨NN￨O￨A ,￨L￨,￨O￨- PCR￨U￨NN￨O￨- and￨L￨CC￨O￨- TF￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- for￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- on￨L￨IN￨O￨- age-specific￨L￨JJ￨O￨- bacterial￨L￨JJ￨O￨- load￨L￨NN￨O￨A ,￨L￨,￨O￨- PCR￨U￨NN￨O￨- and￨L￨CC￨O￨- TF￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- evaluated￨L￨VBN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- trachoma￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Susceptible￨U￨NNP￨O￨- ,￨L￨,￨O￨- Infected￨U￨JJ￨O￨- ,￨L￨,￨O￨- Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- has￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- state￨L￨NN￨O￨A are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- I￨U￨PRP￨O￨- state￨L￨VBP￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- PCR￨U￨NN￨O￨- detectable￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- Model￨U￨NNP￨TITLE￨- 2￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨A the￨L￨DT￨O￨- same￨L￨JJ￨O￨- structure￨L￨NN￨O￨- as￨L￨IN￨O￨- Model￨U￨NNP￨TITLE￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- we￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- assume￨L￨VB￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- D￨U￨NN￨O￨- state￨L￨NN￨O￨- are￨L￨VBP￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- re-infection￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- human￨L￨JJ￨O￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- combined￨L￨JJ￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- poultry￨L￨NN￨O￨A and￨L￨CC￨O￨- generate￨L￨VB￨O￨- retrospective￨L￨NN￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- incidence￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- poultry￨L￨NN￨O￨- and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- eastern￨L￨JJ￨O￨- and￨L￨CC￨O￨- southern￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- estimate￨L￨NN￨O￨- critical￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- generate￨L￨VB￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- and￨L￨CC￨O￨- pandemic￨L￨JJ￨O￨- human￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- H1N1￨U￨NN￨O￨- ,￨L￨,￨O￨- H3N2￨U￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- temperate￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 18-20￨L￨CD￨DATE￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- subtropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- limited￨L￨JJ￨O￨- ,￨L￨,￨O￨- partial￨L￨JJ￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨A poses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenge￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- and￨L￨CC￨O￨- quantification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- H7N9￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- spillover￨L￨JJR￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- poultry￨L￨NN￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- link￨L￨NN￨O￨- between￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨A and￨L￨CC￨O￨- human￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- LBMs￨U￨NNS￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- because￨L￨IN￨O￨- human￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- cases￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- well￨L￨RB￨O￨- documented￨L￨VBN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- human￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- serve￨L￨VBP￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- sentinel￨L￨NN￨O￨- proxy￨L￨NN￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- among￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- .￨L￨.￨O￨- +Outbreaks￨U￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- cases￨L￨NNS￨O￨- peak￨L￨NN￨O￨- in￨L￨IN￨O￨- winter￨L￨NN￨DATE￨- months￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- geographical￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- eastern￨L￨JJ￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- southern￨L￨JJ￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Finding￨U￨VBG￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- forest￨L￨NN￨O￨A when￨L￨WRB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- present￨L￨JJ￨DATE￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- economically￨L￨RB￨O￨- important￨L￨JJ￨O￨- decision￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- forest￨L￨NN￨O￨- manager￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- arrival￨L￨NN￨O￨- of￨L￨IN￨O￨- pests￨L￨NNS￨O￨- and￨L￨CC￨O￨- pathogens￨L￨NNS￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- losses￨L￨NNS￨O￨- in￨L￨IN￨O￨- market￨L￨NN￨O￨- values￨L￨NNS￨O￨- through￨L￨IN￨O￨- :￨L￨:￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- tree￨L￨NN￨O￨- growth￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- D.￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2016￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- even-aged￨L￨JJ￨O￨- forest￨L￨NN￨O￨- by￨L￨IN￨O￨- creating￨L￨VBG￨O￨- a￨L￨DT￨O￨- generalisable￨L￨JJ￨O￨- ,￨L￨,￨O￨- bioeconomic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- ,￨L￨,￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single-rotation￨L￨JJ￨O￨- Faustmann￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- net￨L￨JJ￨O￨- present￨L￨JJ￨DATE￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- NPV￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- forest￨L￨NN￨O￨- by￨L￨IN￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- one-off￨L￨JJ￨O￨- establishment￨L￨NN￨O￨- cost￨L￨NN￨O￨- and￨L￨CC￨O￨- timber￨L￨NN￨O￨- revenue￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- then￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- non-timber￨L￨JJ￨O￨- benefits￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- cornerstone￨L￨NN￨O￨- of￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- studies￨L￨NNS￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- provision￨L￨NN￨O￨- of￨L￨IN￨O￨- recreational￨L￨JJ￨O￨- services￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- carbon￨L￨NN￨O￨- sequestration￨L￨NN￨O￨- ,￨L￨,￨O￨- taxes￨L￨NNS￨O￨- or￨L￨CC￨O￨- subsidies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- timber￨L￨NN￨O￨- and￨L￨CC￨O￨- carbon￨L￨NN￨O￨- sequestration￨L￨NN￨O￨- benefits￨L￨NNS￨O￨- while￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- biodiversity￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- forest￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- interdependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- provision￨L￨NN￨O￨- of￨L￨IN￨O￨- amenity￨L￨NN￨O￨- services￨L￨NNS￨O￨- from￨L￨IN￨O￨- adjacent￨L￨JJ￨O￨- forests￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- trade-off￨L￨NN￨O￨- between￨L￨IN￨O￨- waiting￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- timber￨L￨NN￨O￨- to￨L￨TO￨O￨- grow￨L￨VB￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- further￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- maximises￨L￨VBZ￨O￨- the￨L￨DT￨O￨- NPV￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- forest￨L￨NN￨O￨A ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- when￨L￨WRB￨O￨- timber￨L￨NN￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- no￨L￨DT￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- quickly￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- timber￨L￨NN￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- non-zero￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- to￨L￨TO￨O￨- wait￨L￨VB￨O￨- until￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- to￨L￨TO￨O￨- harvest￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- management￨L￨NN￨O￨- decision￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- clear-felling￨L￨JJ￨O￨- and￨L￨CC￨O￨- ask￨L￨VB￨O￨- :￨L￨:￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- multiple-benefit￨L￨JJ￨O￨- forest￨L￨NN￨O￨A ?￨L￨.￨O￨- +Over￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- Bayesian￨U￨JJ￨O￨- inferential￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- enable￨L￨VB￨O￨- statistically￨L￨RB￨O￨- rigorous￨L￨JJ￨O￨- parameterization￨L￨NN￨O￨- of￨L￨IN￨O￨- discrete￨L￨JJ￨O￨A state￨L￨NN￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- semi-Markov￨L￨JJ￨MISC￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- DCTMPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- noisy￨L￨JJ￨O￨- and￨L￨CC￨O￨- incomplete￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- typical￨L￨JJ￨O￨- of￨L￨IN￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- detections￨L￨NNS￨O￨- from￨L￨IN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Information￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- uncertainty￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- key￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨A is￨L￨VBZ￨O￨- encoded￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- posterior￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- joint￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- describing￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- missing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- transition￨L￨NN￨O￨- times￨L￨NNS￨O￨- conditional￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- modeling￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Their￨U￨PRP$￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- nature￨L￨NN￨O￨- enables￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- than￨L￨IN￨O￨- discrete￨L￨JJ￨O￨A time￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- discrete￨L￨JJ￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ideally￨L￨RB￨O￨- suited￨L￨VBN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- farms￨L￨NNS￨O￨- classified￨L￨VBN￨O￨- into￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- inference￨L￨NN￨O￨- tools￨L￨NNS￨O￨A for￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- make￨L￨VBP￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- data-augmentation￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- missing￨L￨VBG￨O￨- information￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- times￨L￨NNS￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- as￨L￨IN￨O￨- additional￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- inferred￨L￨VBN￨O￨- .￨L￨.￨O￨- +Subsequent￨U￨JJ￨O￨- risk￨L￨NN￨O￨- assessment￨L￨NN￨O￨- can￨L￨MD￨O￨- then￨L￨RB￨O￨- be￨L￨VB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- best￨L￨JJS￨O￨- fits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- suitably￨L￨RB￨O￨- weighted￨L￨JJ￨O￨- outputs￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- quantitatively￨L￨RB￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- disease-behaviour￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- fit￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- dueling￨L￨NN￨O￨- contagion￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- jointly￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +And￨U￨CC￨O￨- while￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- devoted￨L￨VBN￨O￨- considerable￨L￨JJ￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- incentives￨L￨NNS￨O￨- facing￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- deciding￨L￨VBG￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- threat￨L￨NN￨O￨- posed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- contagion￨L￨NN￨O￨A in￨L￨IN￨O￨- question￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- paid￨L￨VBN￨O￨- less￨L￨JJR￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- decisions￨L￨NNS￨O￨- on￨L￨IN￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- perceived￨L￨VBN￨O￨- risks￨L￨NNS￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨A influence￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- take￨L￨VB￨O￨- preventative￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- vaccination28￨L￨NN￨O￨- or￨L￨CC￨O￨- reduced￨L￨VBN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- others13￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- behavioural￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- modify￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection323334￨L￨NN￨O￨- .￨L￨.￨O￨- +Yet￨U￨RB￨O￨- ,￨L￨,￨O￨- accumulating￨L￨VBG￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A is￨L￨VBZ￨O￨- common242526￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- comes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- health￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- smoking￨L￨NN￨CAUSE_OF_DEATH￨- cessation27￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- adoption2829￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- reason￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- focus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- on￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- key￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dueling￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- how￨L￨WRB￨O￨- severe￨L￨JJ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- really￨L￨RB￨O￨- is￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- promptly￨L￨RB￨O￨- the￨L￨DT￨O￨- focal￨L￨JJ￨O￨- population￨L￨NN￨O￨- responds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Regional￨U￨NNP￨O￨- rainfall￨L￨NNS￨O￨- was￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- mediates￨L￨VBZ￨O￨- this￨L￨DT￨O￨- long-range￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- ENSO￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- monsoon￨L￨NN￨O￨- rains￨L￨NNS￨O￨- and￨L￨CC￨O￨- river￨L￨NN￨TITLE￨- discharge￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- levels￨L￨NNS￨O￨- in￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Both￨U￨CC￨O￨- statistical￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- and￨L￨CC￨O￨- process-based￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- ENSO￨U￨NNP￨ORGANIZATION￨- on￨L￨IN￨O￨- rural￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- of￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- For￨U￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨A of￨L￨IN￨O￨- Dhaka￨U￨NNP￨CITY￨- itself￨L￨PRP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- capital￨L￨NN￨O￨- of￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- mechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- incorporating￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- lacking￨L￨VBG￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- phenomenological￨L￨JJ￨O￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- thanas￨L￨FW￨O￨- ”￨L￨''￨O￨- or￨L￨CC￨O￨- districts￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- specifically￨L￨RB￨O￨- identified￨L￨VBD￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- within￨L￨IN￨O￨- Dhaka￨U￨NNP￨CITY￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- truly￨L￨RB￨O￨- urban￨L￨JJ￨O￨- core￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨A and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- more￨L￨JJR￨O￨- rural￨L￨JJ￨O￨- periphery￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- former￨L￨JJ￨O￨- exhibiting￨L￨VBG￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- stronger￨L￨JJR￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- ENSO￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +Climate￨U￨NN￨O￨- variability￨L￨NN￨O￨- ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- the￨L￨DT￨O￨- El￨U￨NNP￨MISC￨- Niño-Southern￨U￨NNP￨MISC￨- Oscillation￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- ENSO￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨A the￨L￨DT￨O￨- year-to-year￨L￨JJ￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- district￨L￨NN￨O￨A given￨L￨VBN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- ascertain￨L￨VB￨O￨- the￨L￨DT￨O￨- strengths￨L￨NNS￨O￨- and￨L￨CC￨O￨- weaknesses￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- TF￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- data￨L￨NNS￨O￨- contained￨L￨VBD￨O￨- district￨L￨NN￨O￨A level￨L￨NN￨O￨- TF￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- at￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2010￨L￨CD￨DATE￨- .￨L￨.￨O￨- +Available￨U￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- IRS￨U￨NNP￨ORGANIZATION￨- on￨L￨IN￨O￨- VL￨U￨NNP￨O￨- incidence￨L￨NN￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- accurate￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- variant￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- asymptomatic￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- contributors￨L￨NNS￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- annual￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- 10,000￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- was￨L￨VBD￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- feasible￨L￨JJ￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- settings￨L￨NNS￨O￨- that￨L￨WDT￨O￨- experience￨L￨VBP￨O￨- optimal￨L￨JJ￨O￨- IRS￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- onwards￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- baseline￨L￨NN￨O￨- endemicity￨L￨NN￨O￨- of￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- VL￨U￨NN￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- 10,000￨L￨CD￨NUMBER￨- capita￨L￨NN￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- estimated￨L￨VBN￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- VL￨U￨NNP￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- develop￨L￨VBP￨O￨- clinical￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- fitting￨L￨NN￨O￨- a￨L￨DT￨O￨- multi-state￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- to￨L￨TO￨O￨- serological￨L￨JJ￨O￨- and￨L￨CC￨O￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- endemic￨L￨JJ￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Symptomatic￨U￨JJ￨O￨- cases￨L￨NNS￨O￨- can￨L￨MD￨O￨- receive￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- VL￨U￨NN￨O￨- treatments￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- E0￨U￨NN￨O￨- and￨L￨CC￨O￨- E1￨U￨NN￨O￨- treated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- develop￨L￨VB￨O￨A PKDL￨U￨NN￨ORGANIZATION￨- after￨L￨IN￨O￨- some￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- apparent￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- absolute￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- this￨L￨DT￨O￨- putatively￨L￨RB￨O￨- recovered￨L￨VBN￨O￨- stage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- included￨L￨VBN￨O￨- because￨L￨IN￨O￨- some￨L￨DT￨O￨- VL￨U￨NN￨O￨- cases￨L￨NNS￨O￨- seem￨L￨VBP￨O￨- to￨L￨TO￨O￨- harbor￨L￨VB￨O￨- dormant￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- after￨L￨IN￨O￨- treatment￨L￨NN￨O￨- which￨L￨WDT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- late￨L￨JJ￨O￨- post-treatment￨L￨JJ￨O￨- dermatological￨L￨JJ￨O￨- complication￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Warwick￨U￨NNP￨ORGANIZATION￨- developed￨L￨VBD￨O￨- model￨L￨NN￨TITLE￨- W￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- converts￨L￨VBZ￨O￨- their￨L￨PRP$￨O￨- recent￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vector￨L￨NN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- asymptomatic￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- contributors￨L￨NNS￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Erasmus￨U￨NNP￨O￨- MC￨U￨NNP￨O￨- developed￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- VL￨U￨NNP￨O￨- models￨L￨NNS￨O￨- :￨L￨:￨O￨- model￨L￨NN￨TITLE￨- E0￨U￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- symptomatic￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- sole￨L￨JJ￨O￨- contributors￨L￨NNS￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- E1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- best-performing￨L￨JJS￨O￨- model￨L￨NN￨TITLE￨- from￨L￨IN￨O￨- their￨L￨PRP$￨O￨- recent￨L￨JJ￨O￨- study￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- contributors￨L￨NNS￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- asymptomatic￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- groups￨L￨NNS￨O￨- have￨L￨VBP￨O￨- approached￨L￨VBN￨O￨- modelling￨L￨VBG￨O￨- systematic￨L￨JJ￨O￨A non-adherence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- shall￨L￨MD￨O￨- use￨L￨VB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- catch-all￨L￨JJ￨O￨- term￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- when￨L￨WRB￨O￨- some￨L￨DT￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- repeatedly￨L￨RB￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- receive￨L￨VB￨O￨- treatments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- these￨L￨DT￨O￨- different￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- never￨L￨RB￨O￨- been￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- simulated￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- predicted￨L￨VBN￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Early￨U￨RB￨O￨- modelling￨L￨VBG￨O￨- work￨L￨NN￨O￨- for￨L￨IN￨O￨- lymphatic￨L￨JJ￨O￨- filariasis￨L￨NN￨O￨- highlighted￨L￨VBD￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- systematic￨L￨JJ￨O￨A non-adherence￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- program￨L￨NN￨O￨- can￨L￨MD￨O￨- undermine￨L￨VB￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- program￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- untreated￨L￨JJ￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- act￨L￨VBP￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- onward￨L￨RB￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- setting￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- systematic￨L￨JJ￨O￨A non-adherence￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- helminth￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- for￨L￨IN￨O￨- systematic￨L￨JJ￨O￨A non-adherence￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- helminth￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- into￨L￨IN￨O￨- treatment￨L￨NN￨O￨- campaign￨L￨NN￨O￨- coverage￨L￨NN￨O￨- highlight￨L￨VBP￨O￨- the￨L￨DT￨O￨- unreliability￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- coverage￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- further￨L￨RB￨O￨- complicating￨L￨VBG￨O￨- modelling￨L￨NN￨O￨A efforts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- pathogens￨L￨NNS￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- threshold￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- dose￨L￨NN￨O￨A of￨L￨IN￨O￨- childhood￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- ;￨L￨:￨O￨- even￨L￨RB￨O￨- where￨L￨WRB￨O￨- routine￨L￨JJ￨O￨- first￨L￨JJ￨ORDINAL￨- dose￨L￨NN￨O￨- coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- ,￨L￨,￨O￨- primary￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- failure￨L￨NN￨O￨- ,￨L￨,￨O￨- ∼￨L￨SYM￨O￨- 14￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- at￨L￨IN￨O￨- 9￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- interactions￨L￨NNS￨O￨- with￨L￨IN￨O￨- maternal￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- can￨L￨MD￨O￨- limit￨L￨VB￨O￨- immunization￨L￨NN￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- p￨L￨NN￨O￨- threshold￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- where￨L￨WRB￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- remains￨L￨VBZ￨O￨- endemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- maintained￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- routine￨L￨JJ￨O￨- childhood￨L￨NN￨O￨- dose￨L￨NN￨O￨A and￨L￨CC￨O￨- periodic￨L￨JJ￨O￨- ,￨L￨,￨O￨- age-targeted￨L￨JJ￨O￨- supplemental￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIAs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Though￨U￨IN￨O￨- the￨L￨DT￨O￨- intent￨L￨NN￨O￨- of￨L￨IN￨O￨- campaigns￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- age￨L￨NN￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- immunized￨L￨VBN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- campaigns￨L￨NNS￨O￨- may￨L￨MD￨O￨- differ￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- logistical￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- in￨L￨IN￨O￨- implementation￨L￨NN￨O￨- ,￨L￨,￨O￨- under-estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- vaccination￨L￨NN￨O￨- services￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- illustrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- while￨L￨IN￨O￨- broader￨L￨JJR￨O￨- age￨L￨NN￨O￨- target￨L￨NN￨O￨- SIAs￨U￨NNS￨O￨- necessarily￨L￨RB￨O￨- reduce￨L￨VB￨O￨- R￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- marginal￨L￨JJ￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- campaigns￨L￨NNS￨O￨A depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- context￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- that￨L￨WDT￨O￨- was￨L￨VBD￨O￨- immunized￨L￨VBN￨O￨- by￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- using￨L￨VBG￨O￨- UNICEF￨U￨NNP￨ORGANIZATION￨- /￨L￨:￨O￨- Citation￨U￨NNP￨O￨- for￨L￨IN￨O￨- routine￨L￨JJ￨O￨A and￨L￨CC￨O￨- SIAs￨U￨NNS￨O￨- ,￨L￨,￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Supplementary￨U￨NNP￨O￨- Material￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- propose￨L￨VBP￨O￨- effective￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A into￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- scholars￨L￨NNS￨O￨- used￨L￨VBN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +applied￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- daily￨L￨JJ￨SET￨- contact￨L￨NN￨O￨A activity￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- even￨L￨RB￨O￨- gradual￨L￨JJ￨O￨- and￨L￨CC￨O￨- mild￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- changes￨L￨NNS￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- dramatic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- slowing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- determine￨L￨VB￨O￨- who￨L￨WP￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- greatly￨L￨RB￨O￨- affect￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- spread￨L￨VBN￨O￨- through￨L￨IN￨O￨- physical￨L￨JJ￨O￨- contact￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- follows￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- people￨L￨NNS￨O￨- .￨L￨.￨O￨- +Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- surge￨L￨NN￨O￨- in￨L￨IN￨O￨- interest￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A models￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual101112131415￨L￨NN￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- individual￨L￨JJ￨O￨- preemptive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- have￨L￨VBP￨O￨- on￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A over￨L￨IN￨O￨- networks17181920￨L￨NN￨O￨- .￨L￨.￨O￨- +Beyond￨U￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- meet￨L￨VBP￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- contacts￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- preemptive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨A taken￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease16￨L￨NN￨O￨- .￨L￨.￨O￨- +That￨U￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- preemptive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- which￨L￨WDT￨O￨- then￨L￨RB￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A .￨L￨.￨O￨- +These￨U￨DT￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- can￨L￨MD￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- preempt￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨VBN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Keeping￨U￨VBG￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- precision￨L￨NN￨O￨A public￨L￨JJ￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- geospatial￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- in￨L￨IN￨O￨- mind￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨- simulation￨L￨NN￨O￨- based￨L￨VBN￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- hypothetical￨L￨JJ￨O￨- EVD￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- undertaken￨L￨VBN￨O￨- with￨L￨IN￨O￨- following￨L￨VBG￨O￨- objectives￨L￨NNS￨O￨- :￨L￨:￨O￨- To￨U￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- on￨L￨IN￨O￨- 01.01.2017￨L￨CD￨DATE￨- at￨L￨IN￨O￨- New￨U￨NNP￨CITY￨- Delhi￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- EVD￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- span￨L￨NN￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- precision￨L￨NN￨O￨A public￨L￨JJ￨O￨- health￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- simply￨L￨RB￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- improving￨L￨VBG￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- promote￨L￨VBP￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reduce￨L￨VB￨O￨- health￨L￨NN￨O￨- disparities￨L￨NNS￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- emerging￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- technologies￨L￨NNS￨O￨- for￨L￨IN￨O￨- measuring￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- exposures￨L￨NNS￨O￨- ,￨L￨,￨O￨- behaviours￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- developing￨L￨VBG￨O￨- interventional￨L￨JJ￨O￨- policies￨L￨NNS￨O￨- for￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- programs￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- health￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- emergent￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- of￨L￨IN￨O￨- precession￨L￨NN￨O￨- public￨L￨JJ￨O￨A health￨L￨NN￨O￨A are￨L￨VBP￨O￨- improving￨L￨VBG￨O￨- methodologies￨L￨NNS￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- modernizing￨L￨VBG￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- targeting￨L￨VBG￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- prevent￨L￨VB￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Geospatial￨U￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- geographic￨L￨JJ￨O￨- information￨L￨NN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- tool￨L￨NN￨O￨- of￨L￨IN￨O￨- precision￨L￨NN￨O￨A public￨L￨JJ￨O￨- health￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- .￨L￨.￨O￨- +Systematic￨U￨JJ￨O￨- computations￨L￨NNS￨O￨- revealed￨L￨VBD￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- interdependent￨L￨JJ￨O￨- links￨L￨NNS￨O￨A so￨L￨IN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- failure￨L￨NN￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- node￨L￨NN￨O￨- causes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- immediate￨L￨JJ￨O￨- failures￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- it￨L￨PRP￨O￨- by￨L￨IN￨O￨- such￨L￨JJ￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- first-and￨L￨JJ￨O￨- second-order￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- crossover￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- arise￨L￨VB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- strength￨L￨NN￨O￨- is￨L￨VBZ￨O￨- changed23￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- vary￨L￨VBP￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- dependency￨L￨NN￨O￨- links￨L￨NNS￨O￨A and￨L￨CC￨O￨- find￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- final￨L￨JJ￨O￨- recovered￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- increases￨L￨VBZ￨O￨- greatly￨L￨RB￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dependency￨L￨NN￨O￨- links￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- .￨L￨.￨O￨- +Concretely￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- increase￨L￨VBP￨O￨- ρ0￨L￨VB￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- change￨L￨VB￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- dependency￨L￨NN￨O￨- links￨L￨NNS￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- changes￨L￨NNS￨O￨- from￨L￨IN￨O￨- first-order￨L￨JJ￨O￨- to￨L￨TO￨O￨- second-order￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- dependency￨L￨NN￨O￨- links￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- node￨L￨NN￨O￨- adopts￨L￨VBZ￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- pieces￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- received￨L￨VBN￨O￨- from￨L￨IN￨O￨- adopted￨L￨VBN￨O￨A neighbors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- exceeds￨L￨VBZ￨O￨- an￨L￨DT￨O￨- adoption￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- if￨L￨IN￨O￨- its￨L￨PRP$￨O￨- dependency￨L￨NN￨O￨- node￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- adopted￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Canada￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- wildlife￨L￨NN￨O￨- species￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- reservoirs￨L￨NNS￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A because￨L￨IN￨O￨- of￨L￨IN￨O￨- successful￨L￨JJ￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨- in￨L￨IN￨O￨- dogs￨L￨NNS￨O￨- through￨L￨IN￨O￨- widespread￨L￨JJ￨O￨- availability￨L￨NN￨O￨- and￨L￨CC￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- parenteral￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- ,￨L￨,￨O￨- restricted￨L￨JJ￨O￨- animal￨L￨NN￨O￨- movements￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- public￨L￨JJ￨O￨- awareness￨L￨NN￨O￨- and￨L￨CC￨O￨- responsible￨L￨JJ￨O￨- pet￨L￨NN￨O￨- ownership￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- threats￨L￨NNS￨O￨- to￨L￨TO￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- agriculture￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- free-ranging￨L￨JJ￨O￨- wildlife￨L￨NN￨O￨- populations￨L￨NNS￨O￨- posed￨L￨VBN￨O￨- by￨L￨IN￨O￨- RABV￨U￨NN￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A control￨L￨NN￨O￨- targeting￨L￨VBG￨O￨- animal￨L￨NN￨O￨- populations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- implemented￨L￨VBN￨O￨- worldwide￨L￨RB￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- local￨L￨JJ￨O￨- population￨L￨NN￨O￨- reduction￨L￨NN￨O￨- ,￨L￨,￨O￨- parenteral￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- oral￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- 6,000￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- rabies￨L￨NNP￨O￨A are￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- diagnosed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- raccoon￨L￨NN￨O￨- variant￨L￨NN￨O￨- of￨L￨IN￨O￨- RABV￨U￨NN￨O￨- is￨L￨VBZ￨O￨- enzootic￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- trend￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- partly￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- elevated￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- spillover￨L￨NN￨O￨- of￨L￨IN￨O￨- raccoon￨L￨NN￨O￨- variants￨L￨NNS￨O￨- into￨L￨IN￨O￨- other￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- peridomestic￨L￨JJ￨O￨- habits￨L￨NNS￨O￨- ,￨L￨,￨O￨- importance￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- rabies￨L￨NNP￨O￨A reservoir￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- movement￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- understanding￨L￨VBG￨O￨- raccoon￨L￨NN￨O￨- movement￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- study￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- human￨L￨JJ￨O￨- desire￨L￨NN￨O￨- for￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- wildlife￨L￨NN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- concern￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- species￨L￨NNS￨O￨- impacted￨L￨VBN￨O￨- by￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- seasonality￨L￨NN￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨A population￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- decision￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Studying￨U￨VBG￨O￨- financing￨L￨NN￨O￨- issues￨L￨NNS￨O￨- of￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- companies￨L￨NNS￨O￨- and￨L￨CC￨O￨- analyzing￨L￨VBG￨O￨- financing￨L￨NN￨O￨- difference￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- governance￨L￨NN￨O￨- structure￨L￨NN￨O￨- can￨L￨MD￨O￨- effectively￨L￨RB￨O￨- circumvent￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- corporate￨L￨JJ￨O￨- financing￨L￨NN￨O￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- promote￨L￨VB￨O￨- the￨L￨DT￨O￨- improvement￨L￨NN￨O￨- of￨L￨IN￨O￨- legal￨L￨JJ￨O￨- regulations￨L￨NNS￨O￨- specific￨L￨JJ￨O￨- to￨L￨TO￨O￨- listed￨L￨VBN￨O￨A companies￨L￨NNS￨O￨- ’￨L￨POS￨O￨- financing￨L￨NN￨O￨- .￨L￨.￨O￨- +Distinguished￨U￨VBN￨O￨- from￨L￨IN￨O￨- other￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- utilities￨L￨NNS￨O￨- complex￨L￨JJ￨O￨A network￨L￨NN￨O￨A to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- scientific￨L￨JJ￨O￨- companies￨L￨NNS￨O￨- ’￨L￨POS￨O￨- financing￨L￨NN￨O￨- preference￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- governance￨L￨NN￨O￨- structure￨L￨NN￨O￨- on￨L￨IN￨O￨- financing￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- proposes￨L￨VBZ￨O￨- practical￨L￨JJ￨O￨- suggestions￨L￨NNS￨O￨- to￨L￨TO￨O￨- legal￨L￨JJ￨O￨- regulations￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- aspect￨L￨NN￨O￨- of￨L￨IN￨O￨- regulating￨L￨VBG￨O￨- financing￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- and￨L￨CC￨O￨- optimizing￨L￨VBG￨O￨- governance￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- listed￨L￨VBN￨O￨A companies￨L￨NNS￨O￨- ’￨L￨POS￨O￨- financing￨L￨NN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- characteristics￨L￨NNS￨O￨- :￨L￨:￨O￨- first￨L￨RB￨ORDINAL￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- ,￨L￨,￨O￨- internal￨L￨JJ￨O￨- capital￨L￨NN￨O￨- accumulation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- insufficient￨L￨JJ￨O￨- so￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- internal￨L￨JJ￨O￨- financing￨L￨NN￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- governance￨L￨NN￨O￨- structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- taken￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- indicator￨L￨NN￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- among￨L￨IN￨O￨- selected￨L￨VBN￨O￨- listed￨L￨VBN￨O￨A companies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Governance￨U￨NN￨O￨- structure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- affect￨L￨VBP￨O￨- financing￨L￨VBG￨O￨- decision￨L￨NN￨O￨- making￨L￨NN￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- extent￨L￨NN￨O￨- ,￨L￨,￨O￨- different￨L￨JJ￨O￨- governance￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- companies￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- various￨L￨JJ￨O￨- financing￨L￨NN￨O￨- decision￨L￨NN￨O￨- .￨L￨.￨O￨- +Pioneer￨U￨NNP￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- expression￨L￨NN￨O￨A profiles￨L￨NNS￨O￨- of￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- animal￨L￨NN￨O￨- pathogens￨L￨NNS￨O￨- in￨L￨IN￨O￨- infected￨L￨JJ￨O￨- tissues￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- genes￨L￨NNS￨O￨- induced￨L￨VBD￨O￨- more￨L￨RBR￨O￨- strongly￨L￨RB￨O￨- contributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- bacterial￨L￨JJ￨O￨- virulence￨L￨NN￨O￨- and/or￨L￨CC￨O￨- survival￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- gene￨L￨NN￨O￨A expression￨L￨NN￨O￨A in￨L￨IN￨O￨- planta￨L￨NN￨O￨- using￨L￨VBG￨O￨- quantitative￨L￨JJ￨O￨- reporters￨L￨NNS￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- R.￨U￨NNP￨MISC￨- solanacearum￨L￨NN￨O￨- virulence￨L￨NN￨O￨- genes￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- unexpected￨L￨JJ￨O￨- expression￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Changes￨U￨NNS￨O￨- in￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- gene￨L￨NN￨O￨A expression￨L￨NN￨O￨A control￨L￨VBP￨O￨- the￨L￨DT￨O￨- switch￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- commensal￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- parasitic￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- subvert￨L￨VB￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- metabolism￨L￨NN￨O￨- or￨L￨CC￨O￨- development￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- 's￨L￨POS￨O￨- benefit￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +solanacearum￨L￨NN￨O￨- virulence￨L￨NN￨O￨- gene￨L￨NN￨O￨A expression￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- discovery￨L￨NN￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- regulatory￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Epidemiological￨U￨JJ￨O￨- dynamics￨L￨NNS￨O￨- were￨L￨VBD￨O￨- first￨L￨JJ￨ORDINAL￨- captured￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tree￨L￨NN￨O￨- prior￨L￨RB￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- coalescent￨L￨JJ￨O￨A theory￨L￨NN￨O￨- and￨L￨CC￨O￨- assuming￨L￨VBG￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- flexible￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- effective￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- combining￨L￨VBG￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- estimate￨L￨VB￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- most￨L￨JJS￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- inferred￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- framework￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- observing￨L￨VBG￨O￨- a￨L￨DT￨O￨- phylogeny￨L￨NN￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- managed￨L￨VBD￨O￨- to￨L￨TO￨O￨- express￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- “￨L￨``￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- “￨L￨``￨O￨- Susceptible-Infected-Removed￨U￨JJ￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A using￨L￨VBG￨O￨- coalescent￨L￨JJ￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- was￨L￨VBD￨O￨- then￨L￨RB￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A and￨L￨CC￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- average￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- 10-year￨L￨JJ￨DURATION￨- time￨L￨NN￨O￨- horizon￨L￨NN￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- IIV4￨U￨NN￨O￨- versus￨L￨CC￨O￨A IIV3￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- vaccinating￨L￨VBG￨O￨- equal￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- discounted￨L￨JJ￨O￨- annual￨L￨JJ￨SET￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- type￨L￨NN￨O￨- B￨U￨NN￨O￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- 1,973,849￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- undiscounted￨L￨JJ￨O￨- 2,325,644￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- fewer￨L￨JJR￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- influenza-related￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- therefore￨L￨RB￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- projected￨L￨VBN￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- IIV4￨U￨NN￨O￨- versus￨L￨CC￨O￨A IIV3￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- prevention￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨JJR￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- societal￨L￨JJ￨O￨- value￨L￨NN￨O￨- and￨L￨CC￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- IIV4￨U￨NN￨O￨- .￨L￨.￨O￨- +Costs￨U￨NNS￨O￨- for￨L￨IN￨O￨- patient￨L￨NN￨O￨- time￨L￨NN￨O￨- lost￨L￨VBD￨O￨- for￨L￨IN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- for￨L￨IN￨O￨- influenza-related￨L￨JJ￨O￨- death￨L￨NN￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- numerator￨L￨NN￨O￨- as￨L￨IN￨O￨- these￨L￨DT￨O￨- time￨L￨NN￨O￨- losses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- captured￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- QALY￨U￨NNP￨O￨- loss￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- ;￨L￨:￨O￨- it￨L￨PRP￨O￨- would￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- double￨L￨JJ￨O￨- counting￨L￨VBG￨O￨- to￨L￨TO￨O￨- also￨L￨RB￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- patient￨L￨NN￨O￨- time￨L￨NN￨O￨- lost￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- numerator￨L￨NN￨O￨- .￨L￨.￨O￨- +AE￨U￨NN￨O￨- ,￨L￨,￨O￨- adverse￨L￨JJ￨O￨- event￨L￨NN￨O￨- ;￨L￨:￨O￨- ICER￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- incremental￨L￨JJ￨O￨- cost-effectiveness￨L￨NN￨O￨- ratio￨L￨NN￨O￨- ;￨L￨:￨O￨- IIV3￨U￨NN￨O￨- ,￨L￨,￨O￨- trivalent￨L￨JJ￨O￨- inactivated￨L￨VBN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨A ;￨L￨:￨O￨- IIV4￨U￨NN￨O￨- ,￨L￨,￨O￨- quadrivalent￨L￨NN￨O￨- inactivated￨L￨VBD￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- ;￨L￨:￨O￨- QALY￨U￨NNP￨O￨- ,￨L￨,￨O￨- quality-adjusted￨L￨JJ￨O￨- life￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +Annual￨U￨JJ￨SET￨- vaccine-related￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- by￨L￨IN￨O￨- $￨L￨$￨MONEY￨- 599￨L￨CD￨MONEY￨- million￨L￨CD￨MONEY￨- (￨L￨-LRB-￨O￨- 5.7￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- IIV4￨U￨NN￨O￨- versus￨L￨CC￨O￨A IIV3￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- these￨L￨DT￨O￨- recent￨L￨JJ￨O￨- progresses￨L￨VBZ￨O￨- in￨L￨IN￨O￨- searching￨L￨VBG￨O￨- for￨L￨IN￨O￨- optimal￨L￨JJ￨O￨A influencers￨L￨NNS￨O￨- in￨L￨IN￨O￨- LTM￨U￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenging￨L￨JJ￨O￨- task￨L￨NN￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- massively￨L￨RB￨O￨- large-scale￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- tens￨L￨NNS￨O￨- of￨L￨IN￨O￨- millions￨L￨NNS￨O￨- nodes￨L￨NNS￨O￨- encountered￨L￨VBN￨O￨- in￨L￨IN￨O￨- modern￨L￨JJ￨O￨- big-data￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- subcritical￨L￨JJ￨O￨- paths￨L￨NNS￨O￨A are￨L￨VBP￨O￨- such￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- along￨L￨IN￨O￨- which￨L￨WDT￨O￨- cascades￨L￨NNS￨O￨- can￨L￨MD￨O￨- propagate￨L￨VB￨O￨- ,￨L￨,￨O￨- CI-TM￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- reliable￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- seeds￨L￨NNS￨O￨- ’￨L￨POS￨O￨- structural￨L￨JJ￨O￨- importance￨L￨NN￨O￨- in￨L￨IN￨O￨- LTM￨U￨NN￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- seed￨L￨NN￨O￨- ’s￨L￨POS￨O￨- contribution￨L￨NN￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- collective￨L￨JJ￨O￨- influence￨L￨NN￨O￨- in￨L￨IN￨O￨- threshold￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- CI-TM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- subcritical￨L￨JJ￨O￨- paths￨L￨NNS￨O￨A emanating￨L￨VBG￨O￨- from￨L￨IN￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- enable￨L￨VBP￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- and￨L￨CC￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- guide￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- planning￨L￨NN￨O￨- and￨L￨CC￨O￨- response￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 32￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 34￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- relatively￨L￨RB￨O￨- few￨L￨JJ￨O￨- validated￨L￨VBN￨O￨A CHIKV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- fewer￨L￨JJR￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- validated￨L￨VBN￨O￨- Ae￨U￨NN￨O￨- .￨L￨.￨O￨- +albopictus￨L￨NN￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- environmental￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- temperature￨L￨NN￨O￨- significantly￨L￨RB￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- developmental￨L￨JJ￨O￨- and￨L￨CC￨O￨- metabolic￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- thought￨L￨VBN￨O￨- to￨L￨TO￨O￨- also￨L￨RB￨O￨- influence￨L￨VB￨O￨- egg￨L￨NN￨O￨- production￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- blood￨L￨NN￨O￨- meals￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- extreme￨L￨JJ￨O￨- temperatures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- >￨L￨JJR￨O￨- 40￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- having￨L￨VBG￨O￨- damaging￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +albopictus￨L￨JJ￨O￨- population￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- reliable￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- about￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- programs￨L￨NNS￨O￨- at￨L￨IN￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- challenging￨L￨VBG￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- a￨L￨DT￨O￨- CHIKV-infected￨U￨JJ￨MISC￨- vector￨L￨NN￨O￨- bites￨L￨VBZ￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- transmits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- asymptomatic￨L￨JJ￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- begins￨L￨VBZ￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- twelve￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨A with￨L￨IN￨O￨- an￨L￨DT￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- four￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Differences￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- H7N9￨U￨NN￨O￨- and￨L￨CC￨O￨- H5N1￨U￨NN￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- :￨L￨:￨O￨- human￨L￨JJ￨O￨- H5N1￨U￨NN￨O￨- cases￨L￨NNS￨O￨- report￨L￨VBP￨O￨- higher￨L￨JJR￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- higher￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- sick￨L￨JJ￨O￨- or￨L￨CC￨O￨- dead￨L￨JJ￨O￨- birds￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- H7N9￨U￨NN￨O￨- is￨L￨VBZ￨O￨- asymptomatic￨L￨JJ￨O￨- in￨L￨IN￨O￨- birds￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- found￨L￨VBN￨O￨- at￨L￨IN￨O￨- lower￨L￨JJR￨O￨- prevalence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- comparable￨L￨JJ￨O￨- time￨L￨NN￨O￨- frame￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considerably￨L￨RB￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- H7N9￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- aimed￨L￨VBN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- upon￨L￨IN￨O￨- our￨L￨PRP$￨O￨- current￨L￨JJ￨DATE￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- behind￨L￨IN￨O￨- H7N9￨U￨NN￨O￨- and￨L￨CC￨O￨- H5N1￨U￨NN￨O￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- risk￨L￨NN￨O￨A profile￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- virus￨L￨NN￨O￨- subtypes￨L￨NNS￨O￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- mainland￨L￨NN￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- highlight￨L￨VB￨O￨- the￨L￨DT￨O￨- regions￨L￨NNS￨O￨- at￨L￨IN￨O￨- greatest￨L￨JJS￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- experiencing￨L￨VBG￨O￨- AIV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +SDMs￨U￨NNS￨O￨- can￨L￨MD￨O￨- aid￨L￨VB￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- spatial￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- help￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- risk￨L￨NN￨O￨A factors￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- occurrence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reveal￨L￨VBP￨O￨- specific￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- at￨L￨IN￨O￨- highest￨L￨JJS￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- targeted￨L￨VBN￨O￨- for￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- small￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- SDMs￨U￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨A areas￨L￨NNS￨O￨- to￨L￨TO￨O￨- target￨L￨VB￨O￨- for￨L￨IN￨O￨- control￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- H5N1￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- H7N9￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- 24￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- species￨L￨NNS￨O￨- distribution￨L￨NN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SDMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- geographic￨L￨JJ￨O￨- risk￨L￨NN￨O￨A profiles￨L￨NNS￨O￨- for￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- and￨L￨CC￨O￨- H7N9￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- great￨L￨JJ￨O￨- gap￨L￨NN￨O￨- in￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- has￨L￨VBZ￨O￨- however￨L￨RB￨O￨- been￨L￨VBN￨O￨- identified￨L￨VBN￨O￨- for￨L￨IN￨O￨- enzootic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- daily￨L￨JJ￨SET￨- impacting￨L￨VBG￨O￨- the￨L￨DT￨O￨- swine￨L￨NNS￨O￨- sector￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- variation￨L￨NN￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- as￨L￨IN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- assessments￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- conditions.KeywordsVacccinationInfectious￨L￨JJ￨O￨- disesasesReproduction￨L￨NN￨O￨- numberHerd￨L￨NN￨O￨- immunityPig￨L￨NN￨O￨- populations￨L￨NNS￨O￨- BackgroundThe￨U￨NNP￨O￨- main￨L￨JJ￨O￨- pursued￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- pig￨L￨NN￨O￨- production￨L￨NN￨O￨- and￨L￨CC￨O￨- generally￨L￨RB￨O￨- in￨L￨IN￨O￨- animal￨L￨NN￨O￨- production￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- direct￨L￨JJ￨O￨- protection￨L￨NN￨O￨A .￨L￨.￨O￨- +Beyond￨U￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- protection￨L￨NN￨O￨A conferred￨L￨VBN￨O￨- by￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- indirect￨L￨JJ￨O￨- protection￨L￨NN￨O￨- of￨L￨IN￨O￨- non-immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- ones￨L￨NNS￨O￨- also￨L￨RB￨O￨- contributes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- controlling￨L￨VBG￨O￨- pathogen￨L￨NN￨O￨- spread￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- scale￨L￨NN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity.Pathogen￨L￨NN￨O￨- spread￨L￨NN￨O￨- within￨L￨IN￨O￨- pig￨L￨NN￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- strongly￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- required￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- pathogen￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- several￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- pathogen￨L￨NN￨O￨A shedding￨L￨VBG￨O￨- in￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- animals￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- documented￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- collective￨L￨JJ￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- vaccinations￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- generally￨L￨RB￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- wider￨L￨JJR￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- pathogen￨L￨NN￨O￨A diffusion￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- scale￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- induces￨L￨VBZ￨O￨- an￨L￨DT￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- potentially￨L￨RB￨O￨- decreasing￨L￨VBG￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- immunologically￨L￨RB￨O￨- naïve￨L￨JJ￨O￨- animals￨L￨NNS￨O￨A .￨L￨.￨O￨- +Still￨U￨RB￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- yet-to-be￨L￨JJ￨O￨- elucidated￨L￨VBN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- what￨L￨WP￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- economically￨L￨RB￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- farm￨L￨NN￨O￨- and￨L￨CC￨O￨- regional￨L￨JJ￨O￨A level￨L￨NN￨O￨- ,￨L￨,￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- voluntary￨L￨JJ￨O￨- regional￨L￨JJ￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- may￨L￨MD￨O￨- play￨L￨VB￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- optimize￨L￨VB￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- monitoring￨L￨NN￨O￨- in￨L￨IN￨O￨- infected￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- farm￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- routes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- PRRSv￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Those￨U￨DT￨O￨- unknowns￨L￨NNS￨O￨- include￨L￨VBP￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- updated￨L￨VBN￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- regional￨L￨JJ￨O￨A PRRSv￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- endemically￨L￨RB￨O￨- infected￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- full￨L￨JJ￨O￨- quantification￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- production￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- subclinically￨L￨RB￨O￨- affected￨L￨VBN￨O￨- herds￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- improved￨L￨VBN￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- PRRSv￨U￨NN￨O￨- strains￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- close￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- relatedness￨L￨NN￨O￨- and￨L￨CC￨O￨- linked￨L￨VBN￨O￨- epidemiologically￨L￨RB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- presented￨L￨VBD￨O￨- demonstrate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- quantitative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- routinely￨L￨RB￨O￨- collected￨L￨VBN￨O￨- data￨L￨NNS￨O￨- may￨L￨MD￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- regional￨L￨JJ￨O￨A epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- PRRSv￨U￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- its￨L￨PRP$￨O￨- full￨L￨JJ￨O￨- impact￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- integration￨L￨NN￨O￨- of￨L￨IN￨O￨- phylodynamic￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- of￨L￨IN￨O￨- PRRSv￨U￨NN￨O￨- might￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- prevention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- high-risk￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Novel￨U￨JJ￨MISC￨- analytic￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- porcine￨L￨NN￨O￨- reproductive￨L￨JJ￨O￨- and￨L￨CC￨O￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨A virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PRRSv￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- :￨L￨:￨O￨- lessons￨L￨NNS￨O￨- learned￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- U.S.Julio￨U￨NNP￨O￨- Alvarez1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Pablo￨U￨NNP￨O￨- Valdes-Donoso1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Steven￨U￨NNP￨PERSON￨- Tousignant1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Mohammad￨U￨NNP￨PERSON￨- Alkhamis1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Robert￨U￨NNP￨PERSON￨- Morrison1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Andres￨U￨NNP￨O￨- Perez1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2:3￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ’s￨L￨POS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- porcine￨L￨NN￨O￨- reproductive￨L￨JJ￨O￨- and￨L￨CC￨O￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PRRSv￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- posed￨L￨VBN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pig￨L￨NN￨O￨- industry￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- porcine￨L￨NN￨O￨- reproductive￨L￨JJ￨O￨- and￨L￨CC￨O￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨A virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PRRSv￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- posed￨L￨VBN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pig￨L￨NN￨O￨- industry￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- persistence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- ecological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- like￨L￨IN￨O￨- seasonality￨L￨NN￨O￨- ,￨L￨,￨O￨- interaction￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- circulating￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨A .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- mix￨L￨VBP￨O￨- homogeneously￨L￨RB￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- called￨L￨VBN￨O￨- sub-populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- patches￨L￨NNS￨O￨A or￨L￨CC￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- system￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- level￨L￨NN￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- sub-populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- travel￨L￨VBP￨O￨- along￨L￨IN￨O￨- mobility￨L￨NN￨O￨- connections￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- measles￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- may￨L￨MD￨O￨- impact￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- persistence￨L￨NN￨O￨A and￨L￨CC￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- community￨L￨NN￨O￨- size￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- threshold￨L￨NN￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spatial￨L￨JJ￨O￨A structure￨L￨NN￨O￨A of￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- important￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-trivial￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- also￨L￨RB￨O￨- when￨L￨WRB￨O￨- waning￨L￨VBG￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- regimes￨L￨NNS￨O￨- following￨L￨VBG￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- considered￨L￨VBD￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- V￨U￨NN￨O￨- patches￨L￨NNS￨O￨A ,￨L￨,￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- that￨L￨WDT￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sub-populations￨L￨NNS￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- linked￨L￨VBN￨O￨- via￨L￨IN￨O￨- mobility￨L￨NN￨O￨- connections￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- :￨L￨:￨O￨- how￨L￨WRB￨O￨- does￨L￨VBZ￨O￨- the￨L￨DT￨O￨- arrival￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- and￨L￨CC￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- planting￨L￨NN￨O￨- strategy￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- tree￨L￨NN￨O￨- species￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- mixture￨L￨NN￨O￨- ?￨L￨.￨O￨- +Bioeconomic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- useful￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- pests￨L￨NNS￨O￨- and￨L￨CC￨O￨- pathogens￨L￨NNS￨O￨- on￨L￨IN￨O￨- forest￨L￨NN￨O￨- management￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- species￨L￨NNS￨O￨A diversification￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- literature￨L￨NN￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- area￨L￨NN￨O￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- optimisation￨L￨NN￨O￨- problem￨L￨NN￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- objective￨L￨JJ￨O￨- function￨L￨NN￨O￨- that￨L￨WDT￨O￨- calculates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- present￨L￨JJ￨DATE￨- value￨L￨NN￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- planting￨L￨VBG￨O￨- both￨L￨CC￨O￨- species￨L￨NNS￨O￨A ,￨L￨,￨O￨- when￨L￨WRB￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- ideal￨L￨JJ￨O￨- situation￨L￨NN￨O￨- ’￨L￨''￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- monoculture￨L￨NN￨O￨- of￨L￨IN￨O￨- trees￨L￨NNS￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- A￨U￨DT￨O￨- remaining￨L￨VBG￨O￨- un-infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- forest￨L￨NN￨O￨- manager￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- option￨L￨NN￨O￨- of￨L￨IN￨O￨- planting￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- tree￨L￨NN￨O￨- species￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- species￨L￨NNS￨O￨- A￨U￨DT￨O￨- or￨L￨CC￨O￨- species￨L￨NNS￨O￨- B￨U￨NN￨O￨- or￨L￨CC￨O￨- both￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- rotation￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- note￨L￨NN￨O￨- :￨L￨:￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- create￨L￨VBP￨O￨- a￨L￨DT￨O￨- bioeconomic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- finds￨L￨VBZ￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- planting￨L￨NN￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- tree￨L￨NN￨O￨- species￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- k-shell￨L￨NN￨O￨- decomposition￨L￨NN￨O￨- decomposes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- into￨L￨IN￨O￨- hierarchically￨L￨RB￨O￨- ordered￨L￨VBN￨O￨- shells￨L￨NNS￨O￨- by￨L￨IN￨O￨- recursively￨L￨RB￨O￨- pruning￨L￨NN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- less￨L￨RBR￨O￨- than￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- shell￨L￨NN￨O￨A index￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Methods￨U￨NNS￨O￨- for￨L￨IN￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- built￨L￨VBN￨O￨- upon￨L￨IN￨O￨- German￨U￨JJ￨NATIONALITY￨- population￨L￨NN￨O￨- counts￨L￨NNS￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨A history￨L￨NN￨O￨- and￨L￨CC￨O￨- was￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- influenza-attributable￨L￨JJ￨O￨- medically￨L￨RB￨O￨- attended￨L￨VBD￨O￨- acute￨L￨JJ￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- I-MAARI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- strain￨L￨NN￨O￨- distribution￨L￨NN￨O￨- using￨L￨VBG￨O￨- Bayesian￨U￨JJ￨MISC￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Is￨U￨VBZ￨MISC￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- modelling￨L￨NN￨O￨- studyFelix￨L￨NN￨O￨- Weidemann1￨U￨NN￨O￨- ,￨L￨,￨O￨- Cornelius￨U￨NNP￨PERSON￨- Remschmidt1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Silke￨U￨NNP￨PERSON￨- Buda2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Udo￨U￨NNP￨PERSON￨- Buchholz2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Bernhard￨U￨NNP￨PERSON￨- Ultsch1￨U￨NN￨O￨- and￨L￨CC￨O￨- Ole￨U￨JJ￨MISC￨- Wichmann1Email￨U￨NN￨MISC￨- authorBMC￨L￨NN￨MISC￨- Infectious￨U￨JJ￨MISC￨- DiseasesBMC￨U￨NN￨MISC￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 17:258￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- children￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- countries￨L￨NNS￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- implemented￨L￨VBN￨O￨- childhood￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- programs￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- overall￨L￨JJ￨O￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- thereby￨L￨RB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- also￨L￨RB￨O￨- challenging￨L￨VBG￨O￨- established￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- the￨L￨DT￨O￨- significant￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- established￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- ask￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- questions￨L￨NNS￨O￨A core￨L￨NN￨O￨- to￨L￨TO￨O￨- understanding￨L￨VBG￨O￨- group￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- for￨L￨IN￨O￨- learning￨L￨VBG￨O￨- in￨L￨IN￨O￨- MOOCs￨U￨NNS￨O￨- :￨L￨:￨O￨- What￨U￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- communication￨L￨NN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- forums￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- does￨L￨VBZ￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- forums￨L￨NNS￨O￨- ?￨L￨.￨O￨- +By￨U￨IN￨O￨- considering￨L￨VBG￨O￨- phylogenies￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- coalescent￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- also￨L￨RB￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- phylogeny￨L￨NN￨O￨- evolving￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- defined￨L￨VBN￨O￨- statistical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- phylogenies￨L￨NNS￨O￨- using￨L￨VBG￨O￨- likelihood-based￨L￨JJ￨O￨- inference￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- pairwise￨L￨JJ￨O￨- coalescent￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- naturally￨L￨RB￨O￨- takes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- incomplete￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- to￨L￨TO￨O￨- shape￨L￨VB￨O￨- pathogen￨L￨NN￨O￨- phylogenies￨L￨NNS￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- samples￨L￨NNS￨O￨- together￨L￨RB￨O￨- in￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨A trees￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- previously￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- indicate￨L￨VB￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- phylogenetic￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- can￨L￨MD￨O￨- arise￨L￨VB￨O￨- naturally￨L￨RB￨O￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- no￨L￨DT￨O￨- measurable￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- clustering￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Analogously￨U￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- shifting￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- focus￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- coalescent￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ’s￨L￨POS￨O￨- phylogenetic￨L￨JJ￨O￨- history￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- backwards-time￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- use￨L￨VBP￨O￨- pairwise￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 31￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 33￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- specified￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- evaluate￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Latin￨U￨JJ￨O￨- hypercube￨L￨NN￨O￨- design￨L￨NN￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- run￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compute￨L￨VBP￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- metrics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- summarize￨L￨VBP￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨A trajectory￨L￨NN￨O￨- of￨L￨IN￨O￨- SPVL￨U￨NN￨ORGANIZATION￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- the￨L￨DT￨O￨- within-couple￨L￨NN￨O￨- transmission￨L￨NN￨O￨A rate￨L￨NN￨O￨A ,￨L￨,￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- “￨L￨``￨O￨- Contact￨U￨NN￨O￨- Structure￨U￨NN￨O￨- ”￨L￨''￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- and￨L￨CC￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Primary￨U￨JJ￨O￨- and￨L￨CC￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ’s￨L￨POS￨O￨- SPVL￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- gives￨L￨VBZ￨O￨- definitions￨L￨NNS￨O￨- ,￨L￨,￨O￨- units￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- models￨L￨NNS￨O￨- explicitly￨L￨RB￨O￨- track￨L￨VBP￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- log10￨L￨NN￨O￨- SPVL￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- denote￨L￨VBP￨O￨A as￨L￨IN￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- progression￨L￨NN￨O￨- to￨L￨TO￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- itself￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- “￨L￨``￨O￨- virulence￨L￨NN￨O￨- ”￨L￨''￨O￨- to￨L￨TO￨O￨- denote￨L￨VB￨O￨- log10￨L￨NN￨O￨- SPVL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Shirreff￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ’s￨L￨POS￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A rate￨L￨NN￨O￨A and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- duration￨L￨NN￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- virus￨L￨NN￨O￨- load￨L￨NN￨O￨- only￨L￨RB￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptomatic￨L￨JJ￨O￨- stage￨L￨NN￨O￨- .￨L￨.￨O￨- +Experiences￨U￨NNS￨O￨- in￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- Marburg￨U￨NNP￨O￨- virus￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Angola￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- EVD￨U￨NNP￨O￨- in￨L￨IN￨O￨- Uganda￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- outbreak￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- emphasize￨L￨VBP￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- promotion￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- context￨L￨NN￨O￨- and￨L￨CC￨O￨- culture￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- work￨L￨NN￨O￨- closely￨L￨RB￨O￨- with￨L￨IN￨O￨- community￨L￨NN￨O￨- leaders￨L￨NNS￨O￨- to￨L￨TO￨O￨- adapt￨L￨VB￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- setting￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Beyond￨U￨IN￨O￨- its￨L￨PRP$￨O￨- humanitarian￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- provision￨L￨NN￨O￨- of￨L￨IN￨O￨- appropriate￨L￨JJ￨O￨- care￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- greater￨L￨JJR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- beds￨L￨NNS￨O￨- can￨L￨MD￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- curbing￨L￨VBG￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- by￨L￨IN￨O￨- removing￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨A and￨L￨CC￨O￨- isolating￨L￨VBG￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- preventing￨L￨VBG￨O￨- further￨L￨JJ￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- this￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- small￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- early￨L￨JJ￨DATE￨A June￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Lofa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- growth￨L￨NN￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- between￨L￨IN￨O￨- early￨L￨JJ￨DATE￨- July￨U￨NNP￨DATE￨- and￨L￨CC￨O￨- late￨L￨JJ￨DATE￨- August￨U￨NNP￨DATE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- EVD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- writing￨L￨VBG￨O￨- ,￨L￨,￨O￨- caused￨L￨VBD￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 11￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- reported￨L￨VBN￨O￨- from￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 28￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- confronted￨L￨VBN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨A ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- typically￨L￨RB￨O￨- work￨L￨VBP￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- by￨L￨IN￨O￨- performing￨L￨VBG￨O￨- assessments￨L￨NNS￨O￨- ,￨L￨,￨O￨- analyzing￨L￨VBG￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- identifying￨L￨VBG￨O￨- resources￨L￨NNS￨O￨- and￨L￨CC￨O￨- interacting￨L￨VBG￨O￨- with￨L￨IN￨O￨- subject￨L￨JJ￨O￨- mater￨L￨NN￨O￨- experts234￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- used￨L￨VBN￨O￨- compartmental￨L￨JJ￨O￨A models￨L￨NNS￨O￨A with￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- like￨L￨IN￨O￨- quarantine￨L￨NN￨O￨- or￨L￨CC￨O￨- isolation￨L￨NN￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- hospitals￨L￨NNS￨O￨- or￨L￨CC￨O￨- cities￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- interventions6789￨L￨NN￨O￨- .￨L￨.￨O￨- +Modeling￨U￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- attractive￨L￨JJ￨O￨- supplemental￨L￨JJ￨O￨- method￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ’s￨L￨POS￨O￨- trajectory￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- control￨L￨NN￨O￨A measures￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- timely￨L￨JJ￨O￨- manner￨L￨NN￨O￨- .￨L￨.￨O￨- +Compartmental￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- historically￨L￨RB￨O￨- common￨L￨JJ￨O￨- ;￨L￨:￨O￨- they￨L￨PRP￨O￨- divide￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- categories￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- hospitalization￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- established￨L￨VBN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- A￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨VB￨O￨- the￨L￨DT￨O￨- per￨L￨FW￨O￨- capita￨L￨NN￨O￨- disease-induced￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨A .￨L￨.￨O￨- +They￨U￨PRP￨O￨- chose￨L￨VBD￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- discovered￨L￨VBD￨O￨- the￨L￨DT￨O￨- complicated￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- including￨L￨VBG￨O￨- Saddle-Node￨U￨NNP￨MISC￨- bifurcation￨L￨NN￨O￨A ,￨L￨,￨O￨- Backward￨U￨RB￨O￨- bifurcation￨L￨NN￨O￨- and￨L￨CC￨O￨- Bogdanov-Takens￨U￨NNS￨O￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- codimension￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- contributes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rich￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- hospital￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- respectively￨L￨RB￨O￨A ,￨L￨,￨O￨- Liu￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Cui￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- used￨L￨VBD￨O￨- βe￨L￨NN￨O￨- −￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- c1￨L￨NN￨O￨- −￨L￨SYM￨O￨- c2￨L￨FW￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- coverage￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- section￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- looking￨L￨VBG￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- backward￨L￨RB￨O￨- bifurcation￨L￨NN￨O￨A of￨L￨IN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- much￨L￨JJ￨O￨- complicated￨L￨JJ￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcation￨L￨NN￨O￨- and￨L￨CC￨O￨- Bogdanov-Takens￨U￨NNS￨MISC￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- codimension￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 3￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- discovered￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- undergoes￨L￨VBZ￨O￨- Saddle-Node￨U￨NNP￨MISC￨- bifurcation￨L￨NN￨O￨A ,￨L￨,￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcation￨L￨NN￨O￨- and￨L￨CC￨O￨- Bogdanov-Takens￨U￨NNS￨MISC￨- bifurcation￨L￨NN￨O￨- ,￨L￨,￨O￨- standing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- collision￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- equilibria￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existance￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- varying￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Serological￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- level￨L￨NN￨O￨- increases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- immunity￨L￨NN￨O￨- wanes￨L￨VBZ￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A increases￨L￨NNS￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- antibody￨L￨NN￨O￨- threshold￨L￨NN￨O￨- defining￨L￨VBG￨O￨- the￨L￨DT￨O￨- protective￨L￨JJ￨O￨- level￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- well￨L￨RB￨O￨- specified￨L￨VBN￨O￨- for￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- debunked￨L￨VBN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- at￨L￨IN￨O￨- 75￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 86￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- mumps￨L￨NNS￨O￨- vaccination￨L￨NN￨O￨A levels￨L￨NNS￨O￨- have￨L￨VBP￨O￨- stayed￨L￨VBN￨O￨- above￨L￨IN￨O￨- that￨L￨DT￨O￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- Scotland￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- 87￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 94￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 2005￨L￨CD￨DATE￨- saw￨L￨VBD￨O￨- a￨L￨DT￨O￨- sudden￨L￨JJ￨O￨- high￨L￨JJ￨O￨- resurgence￨L￨NN￨O￨- in￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- with￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 4500￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- 8￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- after￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- second￨L￨JJ￨DATE￨- dose￨L￨NN￨O￨- of￨L￨IN￨O￨- MMR￨U￨NN￨ORGANIZATION￨- was￨L￨VBD￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨A program￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- vaccination￨L￨NN￨O￨A and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- added￨L￨VBN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- 67￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- infected￨L￨VBN￨O￨- in￨L￨IN￨O￨- Scotland￨U￨NNP￨COUNTRY￨- were￨L￨VBD￨O￨- fully￨L￨RB￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- doses￨L￨NNS￨O￨A confounded￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- analysis￨L￨NN￨O￨- consisted￨L￨VBD￨O￨- of￨L￨IN￨O￨- interlinked￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- same-sex￨L￨JJ￨O￨- HPV￨U￨NN￨O￨- 6/11/16￨L￨CD￨DATE￨- /￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- population￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- anogenital￨L￨JJ￨O￨- warts￨L￨NNS￨O￨- ,￨L￨,￨O￨- anal￨L￨JJ￨O￨- ,￨L￨,￨O￨- penile￨L￨JJ￨O￨- ,￨L￨,￨O￨- oropharyngeal￨L￨NN￨O￨- ,￨L￨,￨O￨- oral￨L￨JJ￨O￨- cavity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- laryngeal￨L￨NN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- quality-adjusted￨L￨JJ￨O￨- life￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- (￨L￨-LRB-￨O￨- QALY￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outcomes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Rates￨U￨NNP￨O￨- governing￨L￨VBG￨O￨- transitions￨L￨NNS￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- stages￨L￨NNS￨O￨- were￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- to￨L￨TO￨O￨- age-standardized￨L￨JJ￨O￨- anal￨L￨JJ￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- English￨U￨NNP￨NATIONALITY￨- MSM￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- age-specific￨L￨JJ￨O￨- anal￨L￨JJ￨O￨- HPV￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- 511￨L￨CD￨NUMBER￨- MSM￨U￨NN￨O￨- attending￨L￨VBG￨O￨- a￨L￨DT￨O￨- London-based￨U￨JJ￨O￨- GUM￨U￨NN￨O￨- clinic￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- both￨L￨DT￨O￨- stratified￨L￨VBN￨O￨- by￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- initiation￨L￨NN￨O￨- of￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proportionate￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- anal￨L￨JJ￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- HPV￨U￨NN￨O￨- type￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- pre-vaccination￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- cancers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Summary￨U￨NN￨O￨- of￨L￨IN￨O￨- Demographic￨U￨JJ￨MISC￨- ,￨L￨,￨O￨- Epidemiological￨U￨JJ￨O￨- ,￨L￨,￨O￨- Sexual￨U￨JJ￨O￨- Behavior￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Clinic￨U￨NNP￨O￨- Attendance￨U￨NNP￨O￨- Parameters￨U￨NNP￨O￨- Used￨U￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Models￨U￨NNS￨O￨- Abbreviations￨U￨NNS￨O￨- :￨L￨:￨O￨- CI￨U￨NN￨O￨- ,￨L￨,￨O￨- confidence￨L￨NN￨O￨- interval￨L￨NN￨O￨- ;￨L￨:￨O￨- GUM￨U￨NNP￨O￨- ,￨L￨,￨O￨- genitourinary￨L￨JJ￨O￨- clinic￨L￨NN￨O￨- ;￨L￨:￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- ;￨L￨:￨O￨- HPV￨U￨NNP￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- papillomavirus￨L￨NN￨O￨- ;￨L￨:￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- men￨L￨NNS￨O￨A who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- ;￨L￨:￨O￨- py￨L￨NN￨O￨- ,￨L￨,￨O￨- person-years￨L￨NNS￨O￨- ;￨L￨:￨O￨- RR￨U￨NNP￨O￨- ,￨L￨,￨O￨- relative￨L￨JJ￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +Abbreviations￨U￨NNS￨O￨- :￨L￨:￨O￨- AGW￨U￨NN￨O￨- ,￨L￨,￨O￨- anogenital￨L￨JJ￨O￨- warts￨L￨NNS￨O￨- ;￨L￨:￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- ;￨L￨:￨O￨- HPV￨U￨NNP￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- papillomavirus￨L￨NN￨O￨- ;￨L￨:￨O￨- GUM￨U￨NNP￨O￨- ,￨L￨,￨O￨- genitourinary￨L￨JJ￨O￨- clinic￨L￨NN￨O￨- ;￨L￨:￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- men￨L￨NNS￨O￨A who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- ;￨L￨:￨O￨- QALY￨U￨NNP￨O￨- ,￨L￨,￨O￨- quality-adjusted￨L￨JJ￨O￨- life￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- quantify￨L￨VBP￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Susceptible-Infected-Recovered-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- simulation￨L￨NN￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- sophisticated￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- tool￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- demography￨L￨NN￨O￨- and￨L￨CC￨O￨- age-dependent￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- results￨L￨VBZ￨O￨- for￨L￨IN￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- live￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- old￨L￨JJ￨DURATION￨- children￨L￨NNS￨O￨- in￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- averaged￨L￨VBD￨O￨- over￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- confirm￨L￨VBP￨O￨- this￨L￨DT￨O￨- result￨L￨NN￨O￨- :￨L￨:￨O￨- four￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- seven￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- as￨L￨IN￨O￨- many￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- prevented￨L￨VBN￨O￨- among￨L￨IN￨O￨- non-vaccinated￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- as￨L￨IN￨O￨- among￨L￨IN￨O￨- vaccinees￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- death￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- occur￨L￨VBP￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- frequently￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- unvaccinated￨L￨JJ￨O￨- elderly￨L￨JJ￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- target￨L￨NN￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- ,￨L￨,￨O￨- indirect￨L￨JJ￨O￨A benefits￨L￨NNS￨O￨- can￨L￨MD￨O￨- surpass￨L￨VB￨O￨- direct￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- 20￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 30￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- As￨U￨IN￨O￨- shown￨L￨VBN￨O￨- analytically￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIRS￨U￨NN￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- indirect￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- effects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- bigger￨L￨JJR￨O￨- than￨L￨IN￨O￨- direct￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- indirect￨L￨JJ￨O￨A effect￨L￨NN￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- “￨L￨``￨O￨- herd￨L￨NN￨O￨- protection￨L￨NN￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- everybody￨L￨NN￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- to￨L￨TO￨O￨- choose￨L￨VB￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- of￨L￨IN￨O￨- unobserved￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- T￨U￨NN￨O￨- :￨L￨:￨O￨- random￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- :￨L￨:￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- incomplete￨L￨JJ￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- of￨L￨IN￨O￨- unobserved￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- T￨U￨NN￨O￨- are￨L￨VBP￨O￨- drawn￨L￨VBN￨O￨- randomly￨L￨RB￨O￨- ,￨L￨,￨O￨- independently￨L￨RB￨O￨- and￨L￨CC￨O￨- uniformly￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- probability￨L￨NN￨O￨- 1/3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- direct￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- performed￨L￨VBN￨O￨- with￨L￨IN￨O￨- such￨L￨JJ￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- .￨L￨.￨O￨- +density￨L￨NN￨O￨- sampling￨L￨NN￨O￨- :￨L￨:￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- incomplete￨L￨JJ￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- X￨U￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- T￨U￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- probability￨L￨NN￨O￨- to￨L￨TO￨O￨- assign￨L￨VB￨O￨- ,￨L￨,￨O￨- independently￨L￨RB￨O￨- and￨L￨CC￨O￨- uniformly￨L￨RB￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Similarity￨U￨NN￨O￨- Sampling￨U￨NN￨O￨- method￨L￨NN￨O￨- consists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- |￨L￨CD￨NUMBER￨- x0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- computing￨L￨VBG￨O￨- an￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- histogram￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- realizations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- contributing￨L￨VBG￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- weight￨L￨NN￨O￨- that￨L￨WDT￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- similarity￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- actually￨L￨RB￨O￨- observed￨L￨VBN￨O￨- states￨L￨NNS￨O￨- at￨L￨IN￨O￨- T.￨U￨NNP￨O￨- +Among￨U￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Belief￨U￨NNP￨O￨- Propagation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- BP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- very￨L￨RB￨O￨- reliable￨L￨JJ￨O￨- and￨L￨CC￨O￨- efficient￨L￨JJ￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- also￨L￨RB￨O￨- makes￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- easily￨L￨RB￨O￨- reconstruct￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- marginals￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- states￨L￨NNS￨O￨A at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- exploiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- causality￨L￨NN￨O￨- relations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- generated￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- after￨L￨IN￨O￨- T￨U￨NN￨O￨- requires￨L￨VBZ￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- joint￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- |￨L￨CD￨NUMBER￨- x0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨A time￨L￨NN￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- some￨L￨DT￨O￨- later￨L￨JJR￨O￨- time￨L￨NN￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- .￨L￨.￨O￨- +Examples￨U￨NNS￨O￨- include￨L￨VBP￨O￨- algorithms￨L￨NNS￨O￨- in￨L￨IN￨O￨- implantable￨L￨JJ￨O￨- defibrillators￨L￨NNS￨O￨- and￨L￨CC￨O￨- pacemakers￨L￨NNS￨O￨- to￨L￨TO￨O￨- cope￨L￨VB￨O￨- with￨L￨IN￨O￨- irregular￨L￨JJ￨O￨- heartbeats￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- construction￨L￨NN￨O￨- and￨L￨CC￨O￨- fitting￨L￨NN￨O￨- for￨L￨IN￨O￨- prostate￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- treatment￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- epidemiology￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- artificial￨L￨JJ￨O￨- beta-cell￨L￨NN￨O￨- or￨L￨CC￨O￨- pancreas￨L￨NN￨O￨- project￨L￨NN￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- manage￨L￨VB￨O￨- insulin￨L￨NN￨O￨- and￨L￨CC￨O￨- glucose￨L￨NN￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- type￨L￨NN￨O￨A 1￨L￨CD￨NUMBER￨- diabetes￨L￨NN￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- online￨L￨JJ￨O￨- search￨L￨NN￨O￨- engines￨L￨NNS￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- and￨L￨CC￨O￨- forecast￨L￨VB￨O￨A dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- actively￨L￨RB￨O￨- developing￨L￨VBG￨O￨- research￨L￨NN￨O￨- areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- data￨L￨NNS￨O￨- sciences￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- just￨L￨RB￨O￨- to￨L￨TO￨O￨- name￨L￨VB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- forecasting￨L￨NN￨O￨- with￨L￨IN￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Wikipedia￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- UptoDate￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Correlate￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- approaches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- some￨L￨DT￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- linear￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- generalized￨L￨VBN￨O￨- linear￨L￨JJ￨O￨- regression￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- GLM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- is￨L￨VBZ￨O￨- performed￨L￨VBN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- least￨L￨JJS￨O￨- absolute￨L￨JJ￨O￨- shrinkage￨L￨NN￨O￨- and￨L￨CC￨O￨- selection￨L￨NN￨O￨- operator￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- LASSO￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- penalized￨L￨VBN￨O￨- regression￨L￨NN￨O￨- NumericCitation￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- used￨L￨VBD￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- filters￨L￨NNS￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨A ILI￨U￨NNP￨O￨- +￨L￨CC￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- calculated￨L￨VBN￨O￨- by￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- streams￨L￨NNS￨O￨- of￨L￨IN￨O￨- ILI￨U￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- viral￨L￨JJ￨O￨- detection￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- forecast￨L￨NN￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- related￨L￨JJ￨O￨- deaths￨L￨NNS￨O￨- using￨L￨VBG￨O￨- search￨L￨NN￨O￨- query￨L￨NN￨O￨- from￨L￨IN￨O￨- Yahoo￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- Yuan￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- practical￨L￨JJ￨O￨- and￨L￨CC￨O￨- extremely￨L￨RB￨O￨- challenging￨L￨JJ￨O￨- issue￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- a￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- be￨L￨VB￨O￨- identified￨L￨VBN￨O￨- which￨L￨WDT￨O￨- produce￨L￨VBP￨O￨- sufficient￨L￨JJ￨O￨- observation￨L￨NN￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- sources￨L￨NNS￨O￨A at￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- actually￨L￨RB￨O￨- be￨L￨VB￨O￨- located￨L￨VBN￨O￨- ?￨L￨.￨O￨- +All￨U￨DT￨O￨- these￨L￨DT￨O￨- call￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- efficient￨L￨JJ￨O￨- methodologies￨L￨NNS￨O￨- to￨L￨TO￨O￨- locate￨L￨VB￨O￨- diffusion￨L￨NN￨O￨- sources￨L￨NNS￨O￨A based￨L￨VBN￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- limited￨L￨JJ￨O￨- ,￨L￨,￨O￨- practically￨L￨RB￨O￨- available￨L￨JJ￨O￨- information￨L￨NN￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- of￨L￨IN￨O￨- acquiring￨L￨VBG￨O￨- global￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- output￨L￨NN￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- messenger/sensor￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- as￨L￨IN￨O￨- Nm￨U￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- fully￨L￨RB￨O￨- locate￨L￨VB￨O￨- any￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sources￨L￨NNS￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- way￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- focus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- issue￨L￨NN￨O￨- of￨L￨IN￨O￨- locatability￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- limited￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- sparse￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- observation￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- diffusion￨L￨JJ￨O￨- sources￨L￨NNS￨O￨A locatable￨L￨JJ￨O￨- ?￨L￨.￨O￨- +The￨U￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- Nm￨U￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- nm￨L￨NN￨O￨- ≡￨L￨NN￨O￨- Nm/N￨U￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- characterizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- locatability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- that￨L￨WDT￨O￨- networks￨L￨NNS￨O￨- requiring￨L￨VBG￨O￨- smaller￨L￨JJR￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- nm￨L￨NN￨O￨- are￨L￨VBP￨O￨- deemed￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- stronger￨L￨JJR￨O￨- locatability￨L￨NN￨O￨- of￨L￨IN￨O￨- sources￨L￨NNS￨O￨A .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- ZIKV￨U￨NN￨O￨- ’s￨L￨POS￨O￨- low￨L￨JJ￨O￨- reporting￨L￨NN￨O￨A rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- suitable￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- may￨L￨MD￨O￨- reflect￨L￨VB￨O￨- diverse￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- introductions￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- self-sustaining￨L￨JJ￨O￨- local￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Confirmed￨U￨VBD￨O￨- local￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NNP￨O￨- Virus￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- Texas￨U￨NNP￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- Florida￨U￨NNP￨STATE_OR_PROVINCE￨- have￨L￨VBP￨O￨- heightened￨L￨VBN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- and￨L￨CC￨O￨- accurate￨L￨JJ￨O￨- indicators￨L￨NNS￨O￨- of￨L￨IN￨O￨- self-sustaining￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- areas￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- southern￨L￨JJ￨O￨A United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- 268￨L￨CD￨NUMBER￨- reported￨L￨VBD￨O￨- mosquito-borne￨L￨JJ￨O￨- autochthonous￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- local￨L￨JJ￨O￨A )￨L￨-RRB-￨O￨- ZIKV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- occurred￨L￨VBD￨O￨- in￨L￨IN￨O￨- Southern￨U￨NNP￨LOCATION￨- Florida￨U￨NNP￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- Texas￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨- ZIKV￨U￨NN￨O￨- vector￨L￨NN￨O￨- ,￨L￨,￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- over￨L￨IN￨O￨- 30￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- ZIKV￨U￨NN￨O￨- risk￨L￨NN￨O￨- assessment￨L￨NN￨O￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- reporting￨L￨NN￨O￨A ,￨L￨,￨O￨- importations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vector-human￨L￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- importation￨L￨NN￨O￨- risk￨L￨NN￨O￨A was￨L￨VBD￨O￨- concentrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- metropolitan￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- sustained￨L￨JJ￨O￨- ZIKV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- is￨L￨VBZ￨O￨- concentrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- southeastern￨L￨JJ￨O￨- counties￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- Houston￨U￨NNP￨CITY￨- metropolitan￨L￨JJ￨O￨- region￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Texas-Mexico￨U￨NNP￨MISC￨- border￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Numerically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- policy￨L￨NN￨O￨A exhibits￨L￨VBZ￨O￨- switch￨L￨NN￨O￨- points￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- paths￨L￨NNS￨O￨- to￨L￨TO￨O￨- coexistence￨L￨NN￨O￨- equilibria￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- spirals￨L￨NNS￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- coexistence￨L￨NN￨O￨- equilibria￨L￨NNS￨O￨- are￨L￨VBP￨O￨- never￨L￨RB￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- paths.KeywordsMultiple￨L￨NN￨O￨- strain￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- Economic￨U￨JJ￨O￨- epidemiology￨L￨NN￨O￨- Treatment￨U￨NN￨O￨- Optimal￨U￨JJ￨O￨- control￨L￨NN￨O￨- The￨U￨DT￨O￨- authors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- grateful￨L￨JJ￨O￨- to￨L￨TO￨O￨- seminar￨L￨NN￨O￨- participants￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Cambridge￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- Royal￨U￨NNP￨ORGANIZATION￨- Economic￨U￨NNP￨ORGANIZATION￨- Society￨U￨NNP￨ORGANIZATION￨- Conference￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Cambridge￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- valuable￨L￨JJ￨O￨- comments.Mathematics￨L￨NNS￨O￨- Subject￨U￨JJ￨O￨- Classification91B55￨U￨NN￨O￨- 91B76￨L￨NN￨O￨- 93C15￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSeveral￨U￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- pose￨L￨VBP￨O￨- a￨L￨DT￨O￨- pressing￨L￨VBG￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- in￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Lyme￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Human￨U￨JJ￨O￨- Papillomavirus￨U￨NN￨O￨- ,￨L￨,￨O￨- Helicobacter￨U￨NNP￨PERSON￨- pylori￨L￨NNP￨PERSON￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- chlamydia￨L￨NN￨O￨- trachomatis￨L￨NN￨O￨- satisfies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- analysed￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- guidance￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- causes.We￨L￨NN￨O￨- analyse￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- policy￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- two-strain￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- analytically￨L￨RB￨O￨- and￨L￨CC￨O￨- numerically￨L￨RB￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- results￨L￨NNS￨O￨- lie￨L￨VBP￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- intervention￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- less￨L￨JJR￨O￨- infectious￨L￨JJ￨O￨- strain￨L￨NN￨O￨- dies￨L￨VBZ￨O￨- out.We￨L￨NN￨O￨- provide￨L￨VB￨O￨- numerical￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- look￨L￨VB￨O￨- for￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- policy￨L￨NN￨O￨A along￨L￨IN￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +Optimal￨U￨JJ￨O￨- policy￨L￨NN￨O￨A determines￨L￨VBZ￨O￨- what￨L￨WP￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- social￨L￨JJ￨IDEOLOGY￨- welfare￨L￨NN￨IDEOLOGY￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- chlamydia￨L￨NN￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Traditional￨U￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- influenza-like￨L￨JJ￨O￨- illnesses￨L￨NNS￨O￨- reports￨L￨NNS￨O￨- ,￨L￨,￨O￨- lag￨L￨NN￨O￨- behind￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- 2￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- information￨L￨NN￨O￨- contained￨L￨VBD￨O￨- in￨L￨IN￨O￨- cloud-based￨L￨JJ￨O￨- electronic￨L￨JJ￨O￨- health￨L￨NN￨O￨- records￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- EHR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- Internet￨U￨NNP￨MISC￨- users￨L￨NNS￨O￨- ’￨L￨POS￨O￨- search￨L￨NN￨O￨- activity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- near￨L￨JJ￨O￨- real-time￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- with￨L￨IN￨O￨- historical￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A activity￨L￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- national￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- forecasts￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- up￨L￨RP￨DURATION￨- to￨L￨TO￨DURATION￨- 4￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- ahead￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- publication￨L￨NN￨O￨- of￨L￨IN￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- reports￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- extend￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- originally￨L￨RB￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- track￨L￨VB￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A using￨L￨VBG￨O￨- Google￨U￨NNP￨ORGANIZATION￨- searches￨L￨NNS￨O￨- ,￨L￨,￨O￨- named￨L￨VBN￨O￨- ARGO￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- combine￨L￨VB￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- EHR￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- Internet￨U￨NN￨MISC￨- searches￨L￨NNS￨O￨- with￨L￨IN￨O￨- historical￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- activities￨L￨NNS￨O￨- .￨L￨.￨O￨- +spumarius￨L￨NN￨O￨- by￨L￨IN￨O￨- half￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- 500￨L￨CD￨NUMBER￨- m.Using￨L￨NN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- map￨L￨NN￨O￨- of￨L￨IN￨O￨- olive￨L￨JJ￨O￨- orchards￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- generated￨L￨VBD￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- X.￨U￨NNP￨O￨- fastidiosa￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pathways￨L￨NNS￨O￨- in￨L￨IN￨O￨- Puglia￨U￨NNP￨LOCATION￨- by￨L￨IN￨O￨- connecting￨L￨VBG￨O￨- all￨L￨DT￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- olive￨L￨JJ￨O￨- orchards￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- ’s￨L￨POS￨O￨- reach￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- km￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- apart￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- measured￨L￨VBN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- closest￨L￨JJS￨O￨- sides￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- orchards￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Network￨U￨NNP￨O￨- analysis￨L￨NN￨O￨- reveals￨L￨VBZ￨O￨- why￨L￨WRB￨O￨- Xylella￨U￨NNP￨ORGANIZATION￨- fastidiosa￨L￨NNP￨ORGANIZATION￨- will￨L￨MD￨O￨- persist￨L￨VB￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- Giovanni￨U￨NNP￨PERSON￨- Strona￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Corrie￨U￨NNP￨PERSON￨- Jacobien￨U￨NNP￨PERSON￨- Carstens￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Pieter￨U￨NNP￨PERSON￨- S.￨U￨NNP￨PERSON￨- Here￨U￨RB￨PERSON￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- much￨L￨RB￨O￨- the￨L￨DT￨O￨- landscape￨L￨NN￨O￨- layout￨L￨NN￨O￨- in￨L￨IN￨O￨- Puglia￨U￨NNP￨LOCATION￨- contributed￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Xylella￨U￨NNP￨O￨- fastidiosa￨L￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- what￨L￨WP￨O￨- clues￨L￨NNS￨O￨- it￨L￨PRP￨O￨- holds￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- options￨L￨NNS￨O￨A for￨L￨IN￨O￨- eradicating￨L￨VBG￨O￨- or￨L￨CC￨O￨- containing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic.The￨L￨NN￨O￨- list￨L￨NN￨O￨- of￨L￨IN￨O￨- insects￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- theoretically￨L￨RB￨O￨- serve￨L￨VB￨O￨- as￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- for￨L￨IN￨O￨- X.￨U￨NNP￨O￨- fastidiosa￨L￨NNP￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- olive￨L￨JJ￨O￨- orchards￨L￨NNS￨O￨- of￨L￨IN￨O￨- Southern￨U￨NNP￨LOCATION￨- Italy￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- meadow￨L￨NN￨O￨- splittlebug￨L￨NN￨O￨- ,￨L￨,￨O￨- Philaenus￨U￨NN￨O￨- spumarius￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Linnaeus￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 1758￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- abundant￨L￨JJ￨O￨- xylem-fluid￨L￨JJ￨O￨- feeding￨L￨NN￨O￨- hemipteran￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- area6￨L￨NN￨O￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Impact￨U￨NN￨O￨- of￨L￨IN￨O￨- Hepatitis￨U￨NNP￨CAUSE_OF_DEATH￨- C￨U￨NNP￨CAUSE_OF_DEATH￨- Treatment￨U￨NN￨O￨- as￨L￨IN￨O￨- Prevention￨U￨NNP￨O￨- for￨L￨IN￨O￨- People￨U￨NNS￨O￨- Who￨U￨WP￨O￨- Inject￨U￨VB￨O￨- Drugs￨U￨NNS￨CRIMINAL_CHARGE￨- is￨L￨VBZ￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- contact￨L￨VB￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- Cornelia￨U￨NNP￨PERSON￨- Metzig￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Julian￨U￨NNP￨PERSON￨- Surey3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marie￨U￨NNP￨PERSON￨- Francis3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jim￨U￨NNP￨PERSON￨- Conneely4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ibrahim￨U￨NNP￨PERSON￨- Abubakar3￨U￨NN￨O￨- ,5,6￨L￨CD￨NUMBER￨- &￨L￨CC￨O￨- Peter￨U￨NNP￨PERSON￨- J.￨U￨NNP￨PERSON￨- White￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,7￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 1833￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNS￨O￨- EpidemiologyViral￨U￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- AbstractTreatment￨U￨NN￨O￨- as￨L￨IN￨O￨- Prevention￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- TasP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- using￨L￨VBG￨O￨- directly-acting￨L￨JJ￨O￨- antivirals￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- advocated￨L￨VBN￨O￨- for￨L￨IN￨O￨- Hepatitis￨U￨NNP￨CAUSE_OF_DEATH￨- C￨U￨NNP￨CAUSE_OF_DEATH￨- Virus￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- HCV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- inject￨L￨VBP￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨A (￨L￨-LRB-￨O￨- PWID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- treatment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- expensive￨L￨JJ￨O￨- and￨L￨CC￨O￨- TasP￨U￨NN￨ORGANIZATION￨- ’s￨L￨POS￨O￨- effectiveness￨L￨NN￨O￨- is￨L￨VBZ￨O￨- uncertain￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- all￨L￨DT￨O￨- network￨L￨NN￨O￨- types￨L￨NNS￨O￨- TasP￨U￨NN￨O￨- ’s￨L￨POS￨O￨- effectiveness￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- treated￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- change￨L￨VBP￨O￨- risk￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- treatment￨L￨NN￨O￨A coverage￨L￨NN￨O￨- :￨L￨:￨O￨- higher￨L￨JJR￨O￨- coverage￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- fewer￨L￨JJR￨O￨- total￨L￨NN￨O￨- treatments￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- health￨L￨NN￨O￨- gain￨L￨NN￨O￨- .￨L￨.￨O￨- +IntroductionHepatitis￨U￨NN￨MISC￨- C￨U￨NN￨MISC￨- Virus￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- HCV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- inject￨L￨VBP￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨A (￨L￨-LRB-￨O￨- PWID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- priority￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- London￨U￨NNP￨CITY￨- being￨L￨VBG￨O￨- around￨L￨IN￨O￨- 43￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +[￨L￨-LRB-￨O￨- Aldridge￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- summarizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- project￨L￨NN￨O￨- that￨L￨WDT￨O￨- evaluated￨L￨VBD￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- centrally￨L￨RB￨O￨- organized￨L￨VBN￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- for￨L￨IN￨O￨- footrot￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Swiss￨U￨JJ￨NATIONALITY￨- sheep￨L￨NN￨O￨A population￨L￨NN￨O￨- .￨L￨.￨O￨- +Outline￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- research￨L￨NN￨O￨- project￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- –￨L￨:￨O￨- benefit￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- centrally￨L￨RB￨O￨- organized￨L￨VBN￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- for￨L￨IN￨O￨- footrot￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Swiss￨U￨JJ￨NATIONALITY￨- sheep￨L￨NN￨O￨A population￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- regions￨L￨NNS￨O￨- also￨L￨RB￨O￨- served￨L￨VBD￨O￨- as￨L￨IN￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- regionalization￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- entropy￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- MEM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- –￨L￨:￨O￨- benefit￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- varying￨L￨VBG￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- questionnaire￨L￨NN￨O￨- was￨L￨VBD￨O￨- sent￨L￨VBN￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- sheep￨L￨NN￨O￨A farmers￨L￨NNS￨O￨- of￨L￨IN￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- revealing￨L￨VBG￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- perceived￨L￨VBN￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- footrot￨L￨NN￨O￨- in￨L￨IN￨O￨- Swiss￨U￨JJ￨NATIONALITY￨- sheep￨L￨NN￨O￨- premises￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- epidemiologic￨L￨JJ￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- management￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- footrot￨L￨NN￨O￨- prevalence￨L￨NN￨O￨A in￨L￨IN￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Methodology￨U￨NNP￨O￨- Article￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Clone￨U￨NN￨O￨- temporal￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- sequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- graph￨L￨NN￨O￨- snapshotsMoritz￨L￨NN￨O￨- Hanke1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- and￨L￨CC￨O￨- Ronja￨U￨NN￨O￨- Foraita1BMC￨U￨NN￨O￨- BioinformaticsBMC￨U￨NN￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18:261￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Different￨U￨NNP￨O￨- phenomena￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- genes￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- thought￨L￨VBN￨O￨- of￨L￨IN￨O￨- as￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Focusing￨U￨VBG￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨A as￨L￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- simulated￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- of￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- graph￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- that￨L￨WDT￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- improves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- important￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- in￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- graph￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- ,￨L￨,￨O￨- classical￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- like￨L￨IN￨O￨- closeness￨L￨NN￨O￨- and￨L￨CC￨O￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- single￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Incompletely￨U￨RB￨O￨- observed￨L￨VBN￨O￨- graph￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- lack￨L￨VBP￨O￨- important￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- duration￨L￨NN￨O￨- or￨L￨CC￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- biased￨L￨VBN￨O￨- temporal￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A values￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- implicit￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- sequence￨L￨NN￨O￨- contains￨L￨VBZ￨O￨- all￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- recently￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- do￨L￨VBP￨O￨- allow￨L￨VB￨O￨- mutations￨L￨NNS￨O￨A to￨L￨TO￨O￨- occur￨L￨VB￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- make￨L￨VBP￨O￨- other￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- not￨L￨RB￨O￨- fully￨L￨RB￨O￨- reflecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- above-described￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- phenomenological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- distances￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- dominant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- mutations￨L￨NNS￨O￨- can￨L￨MD￨O￨- accumulate￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- clearly￨L￨RB￨O￨- defined￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Much￨U￨JJ￨O￨- progress￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- made￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- development￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- existing￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- either￨L￨CC￨O￨- include￨L￨VBP￨O￨- assumptions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- take￨L￨VB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- process￨L￨NN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- designed￨L￨VBN￨O￨- for￨L￨IN￨O￨- specific￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- fit-for-purpose￨L￨JJ￨O￨- code￨L￨NN￨O￨- for￨L￨IN￨O￨- data￨L￨NN￨O￨- analysis￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- make￨L￨VB￨O￨- limiting￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- sampling￨L￨NN￨O￨A times￨L￨NNS￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- publications￨L￨NNS￨O￨- by￨L￨IN￨O￨- Didelot￨U￨NNP￨PERSON￨- et￨L￨NNP￨O￨- al￨L￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- Ypma￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- revealed￨L￨VBD￨O￨- that￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- relate￨L￨VB￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- is￨L￨VBZ￨O￨- illustrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨O￨- 1A￨L￨NN￨O￨- :￨L￨:￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- four￨L￨CD￨NUMBER￨- unobserved￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- sampling￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- within￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- mutation￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- four￨L￨CD￨NUMBER￨- processes￨L￨NNS￨O￨- indicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- 1￨L￨CD￨NUMBER￨- infecting￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- sampled￨L￨VBN￨O￨- sequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- sampling￨L￨NN￨O￨A ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- coalescence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- mutation￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- most￨L￨JJS￨O￨- or￨L￨CC￨O￨- all￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- are￨L￨VBP￨O￨- sampled￨L￨VBN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- nucleotides￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- single-nucleotide￨L￨JJ￨O￨- polymorphisms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SNPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- resolve￨L￨VB￨O￨- transmission￨L￨NN￨O￨- clusters￨L￨NNS￨O￨- ,￨L￨,￨O￨- individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- complete￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- considered￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- scenarios￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- baseline￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- no￨L￨DT￨O￨- intervention￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- scenario￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- school-based￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- all￨L￨DT￨O￨- students￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- school￨L￨NN￨O￨A were￨L￨VBD￨O￨- vaccinated￨L￨VBN￨O￨- once￨L￨RB￨DATE￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- beyond￨L￨IN￨O￨- a￨L￨DT￨O￨- stated￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- surveillance￨L￨NN￨O￨- study￨L￨NN￨O￨- were￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- at￨L￨IN￨O￨- elementary￨L￨JJ￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- found￨L￨VBD￨O￨- school￨L￨NN￨TITLE￨A nurse￨L￨NN￨TITLE￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- tracking￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- lowering￨L￨VBG￨O￨- annual￨L￨JJ￨SET￨- varicella￨L￨NN￨O￨- incident￨L￨NN￨O￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- primarily￨L￨RB￨O￨- used￨L￨VBN￨O￨- empirical￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- European￨U￨JJ￨NATIONALITY￨- populations￨L￨NNS￨O￨- but￨L￨CC￨O￨- failed￨L￨VBD￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- class￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨A structure￨L￨NN￨O￨- of￨L￨IN￨O￨- student￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +developed￨L￨VBN￨O￨- two￨L￨CD￨NUMBER￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A holidays￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- 22￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- to￨L￨TO￨O￨- 31￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- student￨L￨NN￨TITLE￨- contacts￨L￨NNS￨O￨- during￨L￨IN￨O￨- summer￨L￨NN￨DATE￨- holidays￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Information￨U￨NN￨O￨- includes￨L￨VBZ￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- primary￨L￨JJ￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- secondary￨L￨JJ￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- college￨L￨NN￨O￨- or￨L￨CC￨O￨- university￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- reporting￨L￨VBG￨O￨- date￨L￨NN￨O￨- of￨L￨IN￨O￨- H1N1￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- dates￨L￨NNS￨O￨- of￨L￨IN￨O￨- symptom￨L￨NN￨O￨- onset￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DO￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- interventions￨L￨NNS￨O￨- including￨L￨VBG￨O￨- case￨L￨NN￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- symptomatic￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- environment￨L￨NN￨O￨- disinfection￨L￨NN￨O￨- ,￨L￨,￨O￨- health￨L￨NN￨O￨- education￨L￨NN￨O￨- ,￨L￨,￨O￨- antivirals￨L￨NNS￨O￨- for￨L￨IN￨O￨- treatment￨L￨NN￨O￨- or￨L￨CC￨O￨- prophylaxis￨L￨NN￨O￨- use￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- grade￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- collected￨L￨VBD￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- small-scale￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- at￨L￨IN￨O￨- schools￨L￨NNS￨O￨- in￨L￨IN￨O￨- Changsha￨U￨NNP￨LOCATION￨- city￨L￨NN￨O￨- from￨L￨IN￨O￨- January￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2009￨L￨CD￨DATE￨- to￨L￨TO￨O￨- December￨U￨NNP￨DATE￨- 31￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2013￨L￨CD￨DATE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- common￨L￨JJ￨O￨- countermeasures￨L￨NNS￨O￨- in￨L￨IN￨O￨- school￨L￨NN￨O￨A outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- antivirus￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- .￨L￨.￨O￨- +Typically￨U￨RB￨O￨- ,￨L￨,￨O￨- school￨L￨NN￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- directly￨L￨RB￨O￨- to￨L￨TO￨O￨- county￨L￨NN￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- by￨L￨IN￨O￨- primary￨L￨JJ￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- center￨L￨NN￨O￨- ,￨L￨,￨O￨- school￨L￨NN￨O￨- clinics￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- clinics￨L￨NNS￨O￨- and￨L￨CC￨O￨- hospitals￨L￨NNS￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- school￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- practice￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- countermeasures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- taken￨L￨VBN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- at￨L￨IN￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- pharmaceutical￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- typically￨L￨RB￨O￨- antivirus￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- non-pharmaceutical￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- isolation￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Influenza￨U￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- spreads￨L￨VBZ￨O￨- fast￨L￨RB￨O￨- at￨L￨IN￨O￨- school￨L￨NN￨O￨A and￨L￨CC￨O￨- often￨L￨RB￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- small-scale￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- Se￨U￨NNP￨O￨- estimates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- methods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- sample￨L￨NN￨O￨- matrix￨L￨NN￨O￨- ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- samples￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- sampling￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- herd￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- output￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- concludes￨L￨VBZ￨O￨- by￨L￨IN￨O￨- discussing￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- specific￨L￨JJ￨O￨- preclinical￨L￨JJ￨O￨- samples￨L￨NNS￨O￨A to￨L￨TO￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- aid￨L￨VB￨O￨- in￨L￨IN￨O￨- reactive￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- comments￨L￨NNS￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- performance￨L￨NN￨O￨- as￨L￨IN￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- transmission￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Se￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- sample￨L￨NN￨O￨- matrices￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨A of￨L￨IN￨O￨- FMDV-infected￨U￨JJ￨O￨- cattle￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- inoculated￨L￨VBN￨O￨- and￨L￨CC￨O￨- contact-infected￨L￨JJ￨O￨- calves￨L￨NNS￨O￨- started￨L￨VBD￨O￨- shedding￨L￨VBG￨O￨A virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- detected￨L￨VBN￨O￨- by￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- quantitative￨L￨JJ￨O￨- reverse￨L￨NN￨O￨- transcription-PCR￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- qPCR￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- 1￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- postinoculation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dpi￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- at￨L￨IN￨O￨- 1￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- postchallenge￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- nasal￨L￨JJ￨O￨- samples￨L￨NNS￨O￨A in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- shedding￨L￨VBG￨O￨- was￨L￨VBD￨O￨- significantly￨L￨RB￨O￨- higher￨L￨JJR￨O￨- (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- <￨L￨JJR￨O￨- 0.05￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- during￨L￨IN￨O￨- this￨L￨DT￨O￨- phase￨L￨NN￨O￨- than￨L￨IN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- preclinical￨L￨JJ￨O￨- or￨L￨CC￨O￨- early￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- phase￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- ants￨L￨NNS￨O￨- display￨L￨VBP￨O￨- a￨L￨DT￨O￨- remarkable￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- synchronization￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- activity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- quasi-periodic￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- physical￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- nestmates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- S1￨U￨NN￨O￨- Video￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- roughly￨L￨RB￨O￨- three￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- four￨L￨CD￨NUMBER￨- peaks￨L￨NNS￨O￨- per￨L￨IN￨O￨- hour￨L￨NN￨DURATION￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- test￨L￨VB￨O￨- whether￨L￨IN￨O￨- STACs￨U￨NNS￨O￨- could￨L￨MD￨O￨- potentially￨L￨RB￨O￨- influence￨L￨VB￨O￨- information￨L￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- automated￨L￨VBN￨O￨- tracking￨L￨NN￨O￨- system￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- barcode￨L￨NN￨O￨- tag￨L￨NN￨O￨- is￨L￨VBZ￨O￨- attached￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- thorax￨L￨NN￨O￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- ant￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- colony￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1a￨L￨NN￨O￨- and￨L￨CC￨O￨- 1b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- acquire￨L￨VB￨O￨- 15￨L￨CD￨NUMBER￨- three-day-long￨L￨JJ￨DURATION￨- records￨L￨NNS￨O￨A of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- physical￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- nests￨L￨NNS￨O￨- of￨L￨IN￨O￨- L￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- colony￨L￨NN￨O￨- exhibits￨L￨VBZ￨O￨- short-term￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨A in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- movement￨L￨NN￨O￨- activity￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- g￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- time-ordered￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Both￨U￨CC￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- activity￨L￨NN￨O￨A and￨L￨CC￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- time-series￨L￨NNS￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- λ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 960￨L￨CD￨DURATION￨- seconds￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Synchronized￨U￨NNP￨O￨- and￨L￨CC￨O￨- mixed￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- coupled￨L￨VBN￨O￨A recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- Muhua￨U￨NNP￨PERSON￨- Zheng1￨U￨NN￨PERSON￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ming￨U￨VBG￨PERSON￨- Zhao3￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Byungjoon￨U￨NNP￨O￨- Min2￨U￨NNP￨O￨- &￨L￨CC￨O￨- Zonghua￨U￨NNP￨O￨- Liu1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2424￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- scienceInfluenza￨L￨NN￨O￨- virus￨L￨NN￨O￨- AbstractEpidemic￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- are￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- growing￨L￨VBG￨O￨- aspect￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- here￨L￨RB￨O￨- report￨L￨VBP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- coupled￨L￨VBN￨O￨A regions￨L￨NNS￨O￨- or￨L￨CC￨O￨- cities￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- coupled￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- show￨L￨VB￨O￨- either￨L￨CC￨O￨- synchronized￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- pattern￨L￨NN￨O￨- where￨L￨WRB￨O￨- outbreaks￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- simultaneously￨L￨RB￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- networks￨L￨NNS￨O￨- or￨L￨CC￨O￨- mixed￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- pattern￨L￨NN￨O￨- where￨L￨WRB￨O￨- outbreaks￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- network￨L￨NN￨O￨- but￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- in￨L￨IN￨O￨- another￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- reveal￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- mechanism￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- two-layered￨L￨JJ￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- coupled￨L￨VBN￨O￨A recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- synchronized￨L￨VBN￨O￨- and￨L￨CC￨O￨- mixed￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- synchronized￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- pattern￨L￨NN￨O￨- is￨L￨VBZ￨O￨- preferred￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- triggered￨L￨VBN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- coupled￨L￨VBN￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- mixed￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- pattern￨L￨NN￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- average￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- features￨L￨NNS￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- seed￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- best￨L￨JJS￨O￨- correlate￨L￨VBP￨O￨- the￨L￨DT￨O￨- similarity￨L￨NN￨O￨- between￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- discuss￨L￨VB￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- results￨L￨NNS￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- adequacy￨L￨NN￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨A data￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- recurrent￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- aim￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- originating￨L￨VBG￨O￨- from￨L￨IN￨O￨- every￨L￨DT￨O￨- possible￨L￨JJ￨O￨- seed￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- quantify￨L￨VB￨O￨- their￨L￨PRP$￨O￨- similarity￨L￨NN￨O￨A in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- invasion￨L￨NN￨O￨- tree￨L￨NN￨O￨- and￨L￨CC￨O￨- arrival￨L￨NN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- extensive￨L￨JJ￨O￨- side-by-side￨L￨RB￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- France￨U￨NNP￨COUNTRY￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- commuting￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- :￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- extracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- official￨L￨JJ￨O￨- census￨L￨NN￨O￨- survey￨L￨NN￨O￨- and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨A dataset￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- detailed￨L￨JJ￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨A is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- characterizing￨L￨VBG￨O￨- and￨L￨CC￨O￨- forecasting￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- an￨L￨DT￨O￨- essential￨L￨JJ￨O￨- ingredient￨L￨NN￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- at￨L￨IN￨O￨- global￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- national￨L￨JJ￨O￨- or￨L￨CC￨O￨- continental￨L￨JJ￨O￨- scale￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- thoroughly￨L￨RB￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- adequacy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨A network￨L￨NN￨O￨- to￨L￨TO￨O￨- match￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- census￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- With￨U￨IN￨O￨- incorporating￨L￨VBG￨O￨- hospital￨L￨NN￨O￨A isolation￨L￨NN￨O￨- and￨L￨CC￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- medication￨L￨NN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- analyzing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- resisting￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- 10,029￨L￨CD￨NUMBER￨- total￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- 23￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- expect￨L￨VBP￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- EVD￨U￨NN￨O￨- in￨L￨IN￨O￨- 285￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- devising￨L￨VBG￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A eradicationShuo￨L￨NN￨O￨- Jiang￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kaiqin￨U￨NNP￨PERSON￨- Wang￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Chaoqun￨U￨NNP￨PERSON￨- Li￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Guangbin￨U￨NNP￨PERSON￨- Hong￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Xuan￨U￨NNP￨PERSON￨- Zhang1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Menglin￨U￨NNP￨O￨- Shan1￨U￨NN￨O￨- ,￨L￨,￨O￨- Hongbin￨U￨NNP￨PERSON￨- Li3￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Jin￨U￨NN￨O￨- Wang1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- †￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 15:124￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2015￨L￨CD￨DATE￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- EVD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- defines￨L￨VBZ￨O￨- an￨L￨DT￨O￨- unprecedented￨L￨JJ￨O￨- health￨L￨NN￨O￨- threat￨L￨NN￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- regional￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- with￨L￨IN￨O￨- our￨L￨PRP$￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- paths￨L￨NNS￨O￨- including￨L￨VBG￨O￨- household￨L￨NN￨O￨- ,￨L￨,￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- hospital￨L￨NN￨O￨A and￨L￨CC￨O￨- unsafe￨L￨JJ￨O￨- funeral￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- and￨L￨CC￨O￨- eradication￨L￨NN￨O￨A pathways￨L￨NNS￨O￨- ,￨L￨,￨O￨- further￨L￨RB￨O￨- fit￨L￨VB￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- total￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- calculated￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- as￨L￨IN￨O￨- 1.754￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- construct￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- devise￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A eradication￨L￨NN￨O￨- plan￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 01￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Voluntary￨U￨NNP￨O￨- Vaccination￨U￨NN￨O￨- through￨L￨IN￨O￨- Self-organizing￨U￨JJ￨O￨- Behaviors￨U￨NNS￨O￨- on￨L￨IN￨O￨- Locally-mixed￨U￨JJ￨MISC￨- Social￨U￨NNP￨MISC￨- Networks￨U￨NNP￨MISC￨- Benyun￨U￨NNP￨MISC￨- Shi1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Hongjun￨U￨NNP￨PERSON￨- Qiu1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Wenfang￨U￨NNP￨O￨- Niu1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yizhi￨U￨NNP￨O￨- Ren1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Hong￨U￨NNP￨O￨- Ding1￨U￨NNP￨O￨- ,2￨L￨NNP￨O￨- &￨L￨CC￨O￨- Dan￨U￨NNP￨O￨- Chen1￨U￨NNP￨O￨- ,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2665￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- science￨L￨NN￨O￨- AbstractVoluntary￨U￨NNP￨O￨- vaccination￨L￨NN￨O￨A reflects￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- weigh￨L￨VBP￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine-preventable￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- carry￨L￨VBP￨O￨- out￨L￨RP￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- locally-mixed￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- voluntary￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- studying￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- self-organizing￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- circumstance￨L￨NN￨O￨- of￨L￨IN￨O￨- voluntary￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccinating￨L￨VBG￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- weigh￨L￨VBP￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- financial￨L￨JJ￨O￨- cost8￨L￨NN￨O￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- side￨L￨NN￨O￨- effects10￨L￨NN￨O￨- ,11,12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- homogeneously￨L￨RB￨O￨- mixing￨L￨VBG￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- depends￨L￨VBZ￨O￨- largely￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- best￨L￨JJS￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- and￨L￨CC￨O￨- incorporate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- externalities￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨A when￨L￨WRB￨O￨- making￨L￨VBG￨O￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- aimed￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- within￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- facilities￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- reviewed￨L￨VBD￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- publications￨L￨NNS￨O￨- which￨L￨WDT￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- described￨L￨VBD￨O￨- the￨L￨DT￨O￨- externalities￨L￨NNS￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- described￨L￨VBN￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- externalities￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- or￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- described￨L￨VBN￨O￨- macro-level￨L￨JJ￨O￨- policy￨L￨NN￨O￨- options￨L￨NNS￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- externalities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- How￨U￨WRB￨MISC￨- externalities￨L￨NNS￨O￨- impact￨L￨VBP￨O￨- an￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨A in￨L￨IN￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- organizationsJenine￨L￨NN￨O￨- R.￨U￨NNP￨O￨- Few￨U￨JJ￨O￨- resources￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- allocated￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- on￨L￨IN￨O￨- global￨L￨JJ￨O￨- ,￨L￨,￨O￨- national￨L￨JJ￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- part￨L￨NN￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- broader￨L￨JJR￨O￨- economic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- externality￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- fully￨L￨RB￨O￨- considered￨L￨VBN￨O￨- when￨L￨WRB￨O￨- determining￨L￨VBG￨O￨- how￨L￨WRB￨O￨- much￨L￨JJ￨O￨- to￨L￨TO￨O￨- invest￨L￨VB￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- AROs￨U￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- stewardship￨L￨NN￨O￨- programs￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- Based￨U￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- findings￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- methodology￨L￨NN￨O￨- that￨L￨WDT￨O￨- healthcare￨L￨NN￨O￨- organizations￨L￨NNS￨O￨- can￨L￨MD￨O￨- use￨L￨VB￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- negative￨L￨JJ￨O￨- externalities￨L￨NNS￨O￨- when￨L￨WRB￨O￨- making￨L￨VBG￨O￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- on￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨A AROs￨U￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- justify￨L￨VB￨O￨- expenditures￨L￨NNS￨O￨- on￨L￨IN￨O￨- programs￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reduce￨L￨VBP￨O￨- AROs￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- to￨L￨TO￨O￨- formally￨L￨RB￨O￨- incorporate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- negative￨L￨JJ￨O￨- externality￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨A associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- use￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- quantifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- externalities￨L￨NNS￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- use￨L￨NN￨O￨- ,￨L￨,￨O￨- combining￨L￨VBG￨O￨- the￨L￨DT￨O￨- attributable￨L￨JJ￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- AROs￨U￨NNS￨O￨- with￨L￨IN￨O￨- time-series￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- showing￨L￨VBG￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- utilization￨L￨NN￨O￨- and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- AROs￨U￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- absolute￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A for￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- week￨L￨NN￨DURATION￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- calculated￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- follow-up￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- plus￨L￨CC￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- older￨L￨JJR￨O￨- than￨L￨IN￨O￨- 6￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- to￨L￨TO￨O￨- week￨L￨NN￨DURATION￨- t￨L￨NN￨O￨- subtracted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- to￨L￨TO￨O￨- week￨L￨NN￨DURATION￨- t￨L￨NN￨O￨- We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- S0￨U￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨NN￨O￨- expected￨L￨VBD￨O￨- duration￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- discussed￨L￨VBN￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- calculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- rotavirus￨L￨NN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- made￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- assumptions￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- represented￨L￨VBN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- reported￨L￨VBN￨O￨- rotavirus￨L￨NN￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- of￨L￨IN￨O￨- primary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- removed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- severe￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- after￨L￨IN￨O￨- their￨L￨PRP$￨O￨- primary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- adjusted￨L￨VBD￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- for￨L￨IN￨O￨- under-ascertainment￨L￨NN￨O￨- to￨L￨TO￨O￨- arrive￨L￨VB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- balance￨L￨NN￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A :￨L￨:￨O￨- Because￨U￨IN￨O￨- all￨L￨DT￨O￨- children￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- once￨L￨RB￨DATE￨- before￨L￨IN￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- set￨L￨VBD￨O￨- the￨L￨DT￨O￨- time-dependent￨L￨JJ￨O￨- denominator￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- births￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- previous￨L￨JJ￨DURATION￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- infected￨L￨JJ￨O￨- per￨L￨IN￨O￨- primary￨L￨JJ￨O￨- case￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨A as￨L￨IN￨O￨- where￨L￨WRB￨O￨- Î￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- u￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rotavirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- u￨L￨NN￨O￨- and￨L￨CC￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- u￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- interval￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- u￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- calculated￨L￨VBD￨O￨- in￨L￨IN￨O￨- eAppendix￨L￨NN￨O￨- B￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- set￨L￨VBD￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- disentangle￨L￨VB￨O￨- possible￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- weather￨L￨NN￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- factors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- outcome￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- here￨L￨RB￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- modern￨L￨JJ￨O￨- transportation￨L￨NN￨O￨A networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- made￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- integrated￨L￨VBN￨O￨- with￨L￨IN￨O￨- established￨L￨JJ￨O￨- software￨L￨NN￨O￨- packages￨L￨NNS￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- testing￨L￨NN￨O￨- and￨L￨CC￨O￨- deployment￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- data￨L￨NNS￨O￨- generator￨L￨NN￨O￨- that￨L￨WDT￨O￨- models￨L￨NNS￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- contagion￨L￨NN￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- cities￨L￨NNS￨O￨A connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- airline￨L￨NN￨O￨- routes￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- counts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- then￨L￨RB￨O￨- added￨L￨VBN￨O￨- onto￨L￨IN￨O￨- statically￨L￨RB￨O￨- generated￨L￨VBN￨O￨- baseline￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- city￨L￨NN￨O￨A to￨L￨TO￨O￨- produce￨L￨VB￨O￨- a￨L￨DT￨O￨- full￨L￨JJ￨O￨- synthetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- set￨L￨VBN￨O￨- .￨L￨.￨O￨- +Values￨U￨NNS￨O￨- are￨L￨VBP￨O￨- then￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- PMF￨U￨NN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- an￨L￨DT￨O￨- expected￨L￨VBN￨O￨- degree￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- connected￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- city￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- generate￨L￨VBP￨O￨- a￨L￨DT￨O￨- transportation￨L￨NN￨O￨A network￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- Chung-Lu￨U￨NN￨MISC￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- that￨L￨WDT￨O￨- preserves￨L￨VBZ￨O￨- these￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- morbidity￨L￨NN￨O￨- by￨L￨IN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- tradition￨L￨NN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- expansion￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- fitted￨L￨VBD￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- detailed￨L￨JJ￨O￨- local￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- nasopharyngeal￨L￨JJ￨O￨- carriage￨L￨NN￨O￨- and￨L￨CC￨O￨- invasive￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- IPD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- marginal￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- PCV￨U￨NN￨O￨- catch-up￨L￨NN￨O￨- campaign￨L￨NN￨O￨- over￨L￨IN￨O￨- hypothetical￨L￨JJ￨O￨- routine￨L￨JJ￨O￨- cohort￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- setting￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- campaigns￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- dose￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Assessing￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- catch-up￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨A conjugate￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- modelling￨L￨NN￨O￨- study￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- PCV10￨U￨NN￨O￨- introduction￨L￨NN￨O￨- in￨L￨IN￨O￨- Kilifi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- KenyaStefan￨U￨NNP￨O￨- Flasche1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- John￨U￨NNP￨PERSON￨- Ojal1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Olivier￨U￨NNP￨PERSON￨- Le￨U￨NNP￨PERSON￨- Polain￨U￨NNP￨PERSON￨- de￨L￨IN￨O￨- Waroux1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Mark￨U￨NNP￨PERSON￨- Otiende2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Katherine￨U￨NNP￨PERSON￨- L.￨U￨NNP￨PERSON￨- 2017Received￨L￨NNP￨PERSON￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organisation￨U￨NNP￨ORGANIZATION￨- recommends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- catch-up￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨- conjugate￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PCVs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- accelerate￨L￨VB￨O￨- herd￨L￨NN￨O￨- protection￨L￨NN￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- PCV￨U￨NN￨O￨- impact￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- within￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- introduction￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- catch-up￨L￨NN￨O￨- campaign￨L￨NN￨O￨A among￨L￨IN￨O￨- children￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- prevents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- 65￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 48￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 84￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- IPD￨U￨NN￨O￨- cases￨L￨NNS￨O￨- across￨L￨IN￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- PCV￨U￨NN￨O￨- cohort￨L￨NN￨O￨- introduction￨L￨NN￨O￨- alone￨L￨RB￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- In￨U￨IN￨O￨- Kilifi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Kenya￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- PCV10￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- three-dose￨L￨JJ￨O￨- Expanded￨U￨NNP￨O￨- Programme￨U￨NNP￨O￨- on￨L￨IN￨O￨- Immunisation￨U￨NNP￨O￨- infant￨L￨NN￨O￨- schedule￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- catch-up￨L￨NN￨O￨- campaign￨L￨NN￨O￨A in￨L￨IN￨O￨- children￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bat￨L￨NN￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- EV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- birth￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- death￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- competition￨L￨NN￨O￨- for￨L￨IN￨O￨- resources￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- EV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- retrieval￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- recovery￨L￨NN￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- Methods￨U￨NNS￨O￨- section￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- and￨L￨CC￨O￨- characterize￨L￨VBP￨O￨- theoretically￨L￨RB￨O￨A an￨L￨DT￨O￨- Ebola￨U￨NN￨MISC￨- zoonotic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bat￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- bats￨L￨NNS￨O￨- population￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- resources￨L￨NNS￨O￨A represented￨L￨VBD￨O￨- effectively￨L￨RB￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- K￨U￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- likewise￨L￨RB￨O￨- ,￨L￨,￨O￨- those￨L￨DT￨O￨- resources￨L￨NNS￨O￨- conditions￨L￨NNS￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bats￨L￨NNS￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- hypothesis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- filovirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- bats￨L￨NNS￨O￨- :￨L￨:￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- older￨L￨JJR￨O￨- juveniles￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- bats￨L￨NNS￨O￨- can￨L￨MD￨O￨- survive￨L￨VB￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- has￨L￨VBZ￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- immunization￨L￨NN￨O￨- with￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨A conjugate￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- which￨L￨WDT￨O￨- protection￨L￨NN￨O￨- applies￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- to￨L￨TO￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity.The￨L￨NN￨O￨- first￨L￨JJ￨ORDINAL￨- licensed￨L￨JJ￨O￨- multivalent￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨- conjugate￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PCV7￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- confers￨L￨VBZ￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- 7￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- >￨L￨JJR￨O￨- 90￨L￨CD￨NUMBER￨- pneumococcal￨L￨JJ￨O￨- capsular￨L￨JJ￨O￨- serotypes3￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- against￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6B￨L￨NN￨O￨- ,￨L￨,￨O￨- 9V￨L￨NN￨O￨- ,￨L￨,￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 18C￨L￨NN￨O￨- ,￨L￨,￨O￨- 19F￨L￨NN￨O￨- and￨L￨CC￨O￨- 23F￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- eliciting￨L￨VBG￨O￨- anti-capsular￨L￨JJ￨O￨- antibodies4￨L￨NN￨O￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Geographic￨U￨NNP￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨A vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- post-PCV7￨L￨JJ￨O￨- Erida￨U￨NNP￨O￨- Gjini￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 3049￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- Bacterial￨U￨JJ￨O￨- infectionStatistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- AbstractAlthough￨U￨NNP￨O￨- mean￨L￨VB￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- multivalent￨L￨JJ￨O￨- pneumococcus￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- intensively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- ,￨L￨,￨O￨- variance￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- VE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- overlooked￨L￨VBN￨O￨- .￨L￨.￨O￨- +Model￨U￨NNP￨TITLE￨- fitting￨L￨JJ￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- dataset￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- site-specific￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- against￨L￨IN￨O￨- acquisition￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- pneumococcal￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- early￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- PCV77￨U￨NN￨O￨- ,8,9,10￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- protective￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- became￨L￨VBD￨O￨- clear￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- colonization￨L￨NN￨O￨- by￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- serotypes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- VT￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- their￨L￨PRP$￨O￨- associated￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- An￨U￨DT￨O￨- Immunization￨U￨NN￨O￨- Strategy￨U￨NN￨O￨- for￨L￨IN￨O￨- Hidden￨U￨NNP￨O￨- Populations￨U￨NNP￨O￨- Saran￨U￨NNP￨O￨- Chen1￨U￨NN￨O￨- na1￨L￨NN￨O￨- &￨L￨CC￨O￨- Xin￨U￨NNP￨O￨- Lu1￨U￨NN￨O￨- ,2,3,4￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 3268￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksEpidemiology￨L￨NN￨O￨- AbstractHidden￨U￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- injecting￨L￨VBG￨O￨- drug￨L￨NN￨O￨- users￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IDUs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- sex￨L￨NN￨O￨- workers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SWs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- men￨L￨NNS￨O￨A who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MSM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- at￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- contracting￨L￨NN￨O￨- and￨L￨CC￨O￨- transmitting￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- gonorrhea￨L￨NN￨O￨- ,￨L￨,￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- etc￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- RDS￨U￨NN￨O￨- sampling￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- cost-efficient￨L￨JJ￨O￨- and￨L￨CC￨O￨- feasible￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- intervention￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- for￨L￨IN￨O￨- hidden￨L￨JJ￨O￨A populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- an￨L￨DT￨O￨- innovative￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- sampling￨L￨NN￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- hidden￨L￨JJ￨O￨A populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- Respondent-driven￨U￨JJ￨O￨- Sampling￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- RDS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- RDS￨U￨NN￨O￨- strategy￨L￨NN￨O￨A is￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- steps￨L￨NNS￨O￨- :￨L￨:￨O￨- First￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- RDS￨U￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- personal￨L￨JJ￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- sample￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- on￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- reveal￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- RDS￨U￨NN￨O￨- strategy￨L￨NN￨O￨A is￨L￨VBZ￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- There￨U￨EX￨O￨- was￨L￨VBD￨O￨- no￨L￨DT￨O￨- intervention￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- used￨L￨VBN￨O￨- here￨L￨RB￨O￨- provide￨L￨VBP￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- conditions￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- MERS￨U￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Estimation￨U￨NN￨MISC￨- of￨L￨IN￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Middle￨U￨NNP￨LOCATION￨- East￨U￨NNP￨LOCATION￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨A coronavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MERS-CoV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- Hyuk-Jun￨U￨NNP￨O￨- Chang1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 16:79￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- In￨U￨IN￨O￨- South￨U￨NNP￨COUNTRY￨- Korea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- Middle￨U￨NNP￨LOCATION￨- East￨U￨NNP￨LOCATION￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MERS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- estimates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- MERS￨U￨NN￨O￨- coronavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CoV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- MERS￨U￨NNS￨O￨- in￨L￨IN￨O￨- South￨U￨NNP￨COUNTRY￨- Korea￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- South￨U￨NNP￨COUNTRY￨- Korea￨U￨NNP￨COUNTRY￨- MERS￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- uses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ODEs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- fit￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- South￨U￨NNP￨COUNTRY￨- Korea￨U￨NNP￨COUNTRY￨- outbreak￨L￨NN￨O￨A minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- squared￨L￨VBN￨O￨- errors￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Economic￨U￨NNP￨O￨- evaluations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- conducted￨L￨VBN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- ways￨L￨NNS￨O￨- :￨L￨:￨O￨- by￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- burden￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- by￨L￨IN￨O￨- aggregating￨L￨VBG￨O￨- influenza-and￨L￨JJ￨O￨- intervention-associated￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- calculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- intervention￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A .￨L￨.￨O￨- +Emphasizing￨U￨VBG￨O￨- the￨L￨DT￨O￨- adequacy￨L￨NN￨O￨- of￨L￨IN￨O￨- hospital-resource￨L￨NN￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- allows￨L￨VBZ￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- community￨L￨NN￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨- pandemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- ensure￨L￨VB￨O￨- hospital￨L￨NN￨O￨A resource￨L￨NN￨O￨- adequacy￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- estimates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- upon￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- representative￨L￨JJ￨TITLE￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- municipality￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- closely￨L￨RB￨O￨- resemble￨L￨VBP￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- from￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- cities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +InFluNet￨U￨NNP￨O￨- combines￨L￨VBZ￨O￨- demographic￨L￨JJ￨O￨- ,￨L￨,￨O￨- hospital￨L￨NN￨O￨A and￨L￨CC￨O￨- intervention￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- under￨L￨IN￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- suggest￨L￨VBP￨O￨- new￨L￨JJ￨O￨- marker￨L￨NN￨TITLE￨- VRTP￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- on￨L￨IN￨O￨- turning￨L￨VBG￨O￨- point￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Scale-free￨U￨JJ￨MISC￨- (￨L￨-LRB-￨O￨- SF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- observe￨L￨VBP￨O￨- the￨L￨DT￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- effects￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Volume￨U￨NN￨O￨- 18￨L￨CD￨NUMBER￨A Supplement￨U￨NN￨O￨- 7￨L￨CD￨NUMBER￨- Proceedings￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Tenth￨U￨NNP￨ORDINAL￨- International￨U￨NNP￨O￨- Workshop￨U￨NNP￨O￨- on￨L￨IN￨O￨- Data￨U￨NNP￨O￨- and￨L￨CC￨O￨- Text￨U￨VB￨O￨- Mining￨U￨NN￨O￨- in￨L￨IN￨O￨- Biomedical￨U￨NNP￨MISC￨- Informatics￨U￨NNP￨MISC￨- Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Coupling￨U￨NN￨MISC￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- turning￨L￨VBG￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networksKiseong￨L￨NN￨O￨- Kim1￨U￨NN￨O￨- ,￨L￨,￨O￨- Sangyeon￨U￨NN￨O￨- Lee1￨U￨NN￨O￨- ,￨L￨,￨O￨- Doheon￨U￨NN￨O￨- Lee1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Kwang￨U￨NNP￨PERSON￨- Hyung￨U￨NNP￨PERSON￨- Lee1Email￨U￨NN￨O￨- authorBMC￨L￨NN￨O￨- BioinformaticsBMC￨U￨NN￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Suppl￨U￨NN￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- 250￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- spreading￨L￨NN￨O￨A phenomenon￨L￨NN￨O￨- simulator￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- input￨L￨NN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- performed￨L￨VBD￨O￨- the￨L￨DT￨O￨- experiment￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Susceptible-Infective-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- spreading￨L￨VBG￨O￨A phenomena￨L￨NNS￨O￨- using￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- spreading￨L￨VBG￨O￨- factors￨L￨NNS￨O￨- ;￨L￨:￨O￨- contagiousness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- induced￨L￨VBD￨O￨- the￨L￨DT￨O￨- VRTP￨U￨NNP￨O￨- formula￨L￨NN￨O￨A for￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- exploiting￨L￨VBG￨O￨- such￨L￨JJ￨O￨- time-of-arrival￨L￨JJ￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- taking￨L￨VBG￨O￨- place￨L￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- partially￨L￨RB￨O￨- because￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨A interactions￨L￨NNS￨O￨- serve￨L￨VBP￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- for￨L￨IN￨O￨- material￨L￨NN￨O￨- or￨L￨CC￨O￨- information￨L￨NN￨O￨- exchange￨L￨NN￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- cultural￨L￨JJ￨O￨- fads￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proliferation￨L￨NN￨O￨- of￨L￨IN￨O￨- innovative￨L￨JJ￨O￨- ideas￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- review28￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Towards￨U￨IN￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- null￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- procedure￨L￨NN￨O￨- for￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- data-driven￨L￨JJ￨O￨- fashion￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- conceive￨L￨VBP￨O￨- the￨L￨DT￨O￨- STN￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- convenient￨L￨JJ￨O￨- descriptive￨L￨JJ￨O￨- device￨L￨NN￨O￨- for￨L￨IN￨O￨- explaining￨L￨VBG￨O￨- time-course￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- diffusion￨L￨NN￨O￨- processes￨L￨NNS￨O￨- thereon￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- carry￨L￨VBP￨O￨- out￨L￨RP￨O￨- extensive￨L￨JJ￨O￨- benchmark￨L￨NN￨O￨- tests￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- validate￨L￨VB￨O￨- the￨L￨DT￨O￨- reconstruction￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- restrict￨L￨VBP￨O￨- on￨L￨IN￨O￨- reconstructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- STNs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- —￨L￨:￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- generally￨L￨RB￨O￨- taken￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- null￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- preserving￨L￨VBG￨O￨- temporal￨L￨JJ￨O￨- statistics￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- dyads￨L￨NNS￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- but￨L￨CC￨O￨- ignoring￨L￨VBG￨O￨- higher-order￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- across￨L￨IN￨O￨- them15￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- STN￨U￨NN￨O￨- builds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- time-aggregated￨L￨JJ￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- extra￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨A dimension￨L￨NN￨O￨- by￨L￨IN￨O￨- assigning￨L￨VBG￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- link￨L￨NN￨O￨- a￨L￨DT￨O￨- mutually￨L￨RB￨O￨- independent￨L￨JJ￨RELIGION￨- random￨L￨JJ￨O￨- IET￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- denoting￨L￨VBG￨O￨- the￨L￨DT￨O￨- interval￨L￨NN￨O￨- of￨L￨IN￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- events￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- renewal￨L￨NN￨O￨- manner29￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- later￨L￨RB￨O￨- on￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- fundamentally￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- learn￨L￨VB￨O￨- latent￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- discovering￨L￨VBG￨O￨- both￨L￨CC￨O￨- structural￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨A regularities￨L￨NNS￨O￨- in￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- prominence￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- fields￨L￨NNS￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- biology￨L￨NN￨O￨- to￨L￨TO￨O￨- smart￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- ,￨L￨,￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- challenging￨L￨JJ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- these￨L￨DT￨O￨- are￨L￨VBP￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- discrete￨L￨JJ￨O￨- state￨L￨NN￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- potentially￨L￨RB￨O￨- infinite￨L￨JJ￨O￨A state-space￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- pseudo-marginal￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- algorithms￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- truncation￨L￨NN￨O￨- method￨L￨NN￨O￨- which￨L￨WDT￨O￨- enables￨L￨VBZ￨O￨- a￨L￨DT￨O￨- principled￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- infinite￨L￨JJ￨O￨A state￨L￨NN￨O￨- spaces￨L￨NNS￨O￨- .￨L￨.￨O￨- +Of￨U￨IN￨O￨- particular￨L￨JJ￨O￨- relevance￨L￨NN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- are￨L￨VBP￨O￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- state-space￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organised￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- population￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- Jump￨U￨NNP￨O￨- Processes￨U￨NNP￨O￨- ,￨L￨,￨O￨- pMJP￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨A label￨L￨NN￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- counts￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- entities￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- species￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- efficient￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- joint￨L￨JJ￨O￨- state/parameter￨L￨NN￨O￨- posterior￨L￨NN￨O￨- sampling￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- Jump￨U￨NNP￨O￨- processes￨L￨NNS￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Capasso￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Serio12￨U￨NN￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- into￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- saturation￨L￨NN￨O￨- level￨L￨NN￨O￨- when￨L￨WRB￨O￨- I￨U￨PRP￨O￨- gets￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- Equality￨U￨FW￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- alpha￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- βI￨L￨NN￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- tfrac￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- alpha￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- inhibition￨L￨NN￨O￨- effect￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- when￨L￨WRB￨O￨- their￨L￨PRP$￨O￨- number￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- crowding￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- note￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨- Qixing￨U￨VBG￨O￨- Han1￨U￨NN￨O￨- ,￨L￨,￨O￨- Liang￨U￨NNP￨PERSON￨- Chen2￨U￨NNP￨O￨- &￨L￨CC￨O￨- Daqing￨U￨NNP￨O￨- Jiang3￨U￨NN￨O￨- ,4￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 3996￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsInfectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- AbstractThe￨U￨NNP￨O￨- stochastic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- and￨L￨CC￨O￨- summarized￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- Define￨U￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨A is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- SEIR￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-infected-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- SEIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- investigated￨L￨VBN￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- researchers7￨L￨JJ￨O￨- ,8,9￨L￨NN￨O￨- .￨L￨.￨O￨- +Investigating￨U￨VBG￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- weather￨L￨NN￨O￨- and￨L￨CC￨O￨- climate￨L￨NN￨O￨A on￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- requires￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- disentangle￨L￨VB￨O￨- concurrent￨L￨JJ￨O￨- modes￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmissions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- environmental￨L￨JJ￨O￨- from￨L￨IN￨O￨- human-to-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- tease￨L￨VB￨O￨- apart￨L￨RB￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- exposures￨L￨NNS￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- ;￨L￨:￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- identify￨L￨VB￨O￨- and￨L￨CC￨O￨- separate￨L￨JJ￨O￨- socio-economic￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- and￨L￨CC￨O￨- behavioural￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- ;￨L￨:￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- integrate￨L￨VB￨O￨- all￨L￨PDT￨O￨- these￨L￨DT￨O￨- different￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- unified￨L￨VBN￨O￨- perspective￨L￨NN￨O￨- ;￨L￨:￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- attribute￨L￨NN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- observed￨L￨VBN￨O￨- environmental￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- vi￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- quantify￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- social￨L￨JJ￨O￨- ,￨L￨,￨O￨- economic￨L￨JJ￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- project￨L￨VB￨O￨- the￨L￨DT￨DATE￨- future￨L￨JJ￨DATE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- changes￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exposure￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- directly￨L￨RB￨O￨- or￨L￨CC￨O￨- indirectly￨L￨RB￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- meteorological/climate￨L￨NN￨O￨- variables￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- high￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- drinking￨L￨NN￨O￨- contaminated￨L￨VBN￨O￨- water￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- poor￨L￨JJ￨O￨- water￨L￨NN￨O￨- drainage￨L￨NN￨O￨- management￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- land￨L￨VB￨O￨- use￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- behavioural￨L￨NN￨O￨- and/or￨L￨CC￨O￨- socio-economic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- recreational￨L￨JJ￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- unclean￨L￨JJ￨O￨- water￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Infectious￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- water￨L￨NN￨O￨A are￨L￨VBP￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- “￨L￨``￨O￨- water-system-related￨L￨JJ￨O￨- ”￨L￨''￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- via￨L￨IN￨O￨- aerosols￨L￨NNS￨O￨- from￨L￨IN￨O￨- poorly￨L￨RB￨O￨- managed￨L￨VBN￨O￨- cooling￨L￨VBG￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- Legionellosis￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- water-based￨L￨JJ￨O￨- ”￨L￨''￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- via￨L￨IN￨O￨- aquatic￨L￨JJ￨O￨- vectors￨L￨NNS￨O￨- or￨L￨CC￨O￨- intermediate￨L￨JJ￨O￨- in￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- Schistosomiasis￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- water-borne￨L￨JJ￨O￨- ”￨L￨''￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- via￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- ,￨L￨,￨O￨- parasitic￨L￨JJ￨O￨- and￨L￨CC￨O￨- viral￨L￨JJ￨O￨- oral-faecal￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- ingestion￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- “￨L￨``￨O￨- water-washed￨L￨JJ￨O￨- ”￨L￨''￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- poor￨L￨JJ￨O￨- hygiene￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- insufficient￨L￨JJ￨O￨- water￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- include￨L￨VB￨O￨- oral-faecal￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- hookworm￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- particularly￨L￨RB￨O￨- important￨L￨JJ￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- water￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- those￨L￨DT￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- neglected￨L￨VBN￨O￨- tropical￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- NTD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organisation￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨ORGANIZATION￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- journal￨L￨NN￨O￨- Plos￨U￨NNP￨O￨- NTD￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- recently￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- estimated￨L￨VBD￨O￨- that￨L￨IN￨O￨- leptospirosis￨L￨NN￨O￨- causes￨L￨VBZ￨O￨A 1.03￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- 58,900￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- placing￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- leading￨L￨VBG￨O￨- zoonotic￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- of￨L￨IN￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- in￨L￨IN￨O￨- Central￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- have￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- environmental￨L￨JJ￨O￨- and￨L￨CC￨O￨- socioeconomic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- increase￨L￨VBP￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- leptospirosis￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- volcanic￨L￨JJ￨O￨- origin￨L￨NN￨O￨- soil￨L￨NN￨O￨- ,￨L￨,￨O￨- precipitation￨L￨NN￨O￨- ,￨L￨,￨O￨- higher￨L￨JJR￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- rural￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- greater￨L￨JJR￨O￨- unsatisfied￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- needs￨L￨NNS￨O￨- for￨L￨IN￨O￨- improved￨L￨JJ￨O￨- housing￨L￨NN￨O￨- and￨L￨CC￨O￨- sanitary￨L￨JJ￨O￨- services￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- extreme￨L￨JJ￨O￨A poverty￨L￨NN￨O￨- and￨L￨CC￨O￨- higher￨L￨JJR￨O￨- illiteracy￨L￨NN￨O￨- rates￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Mass￨U￨JJ￨STATE_OR_PROVINCE￨- chemoprophylaxis￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- after￨L￨IN￨O￨- leptospirosis￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- following￨L￨VBG￨O￨- floods￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- or￨L￨CC￨O￨- during￨L￨IN￨O￨- water-sports￨L￨JJ￨O￨- events￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- Latin￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- preventive￨L￨JJ￨O￨- measure￨L￨NN￨O￨- in￨L￨IN￨O￨- high-risk￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- facilities￨L￨NNS￨O￨- was￨L￨VBD￨O￨- difficult￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Rain￨U￨NN￨O￨- and￨L￨CC￨O￨- floods￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- primary￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- for￨L￨IN￨O￨- leptospirosis￨L￨NN￨O￨- and￨L￨CC￨O￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- reported￨L￨VBN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- following￨L￨VBG￨O￨- extreme￨L￨JJ￨O￨A weather￨L￨NN￨O￨- events￨L￨NNS￨O￨- in￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- locales￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Guyana￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- New￨U￨NNP￨LOCATION￨- Caledonia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Nicaragua￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Philippines￨U￨NNPS￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- Central￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- have￨L￨VB￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- leptospirosis￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- being￨L￨VBG￨O￨- developing￨L￨VBG￨O￨- activities￨L￨NNS￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- and￨L￨CC￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- highlights￨L￨VBZ￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- antibody￨L￨NN￨O￨A loss￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- bias￨L￨NN￨O￨- our￨L￨PRP$￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- critical￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- management￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- serological￨L￨JJ￨O￨- data.KeywordsAntibody￨L￨JJ￨O￨- loss￨L￨NN￨O￨- Approximate￨U￨NNP￨O￨- Bayesian￨U￨NNP￨O￨- computation￨L￨NN￨O￨- Brucellosis￨U￨NNP￨O￨- Greater￨U￨NNP￨O￨- Yellowstone￨U￨NNP￨O￨- Ecosystem￨U￨NNP￨O￨- Basic￨U￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Serology￨U￨NNP￨O￨- Electronic￨U￨NNP￨O￨- supplementary￨L￨JJ￨O￨- materialThe￨L￨NN￨O￨- online￨L￨NN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- doi￨L￨FW￨O￨- :￨L￨:￨O￨- 10.1007￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- s10393-017-1235-z￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- contains￨L￨VBZ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- authorized￨L￨VBN￨O￨- users.IntroductionMany￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- monitoring￨L￨NN￨O￨- programs￨L￨NNS￨O￨- in￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- rely￨L￨VBP￨O￨- on￨L￨IN￨O￨- serology￨L￨NN￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- analyses￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- played￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- 's￨L￨POS￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- Network￨U￨NNP￨O￨- analysis￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- potential￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- identifying￨L￨VBG￨O￨- central￨L￨JJ￨O￨- and/or￨L￨CC￨O￨- highly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- holdings￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨A movements￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- arcs￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- herd￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- inter-herd￨L￨JJ￨O￨- spread￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- area￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- primarily￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- animal￨L￨JJ￨O￨A contacts￨L￨NNS￨O￨- at￨L￨IN￨O￨- pastures￨L￨NNS￨O￨- or￨L￨CC￨O￨- through￨L￨IN￨O￨- animal￨L￨NN￨O￨- movements￨L￨NNS￨O￨- between￨L￨IN￨O￨- herds￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- planning￨L￨VBG￨O￨- and￨L￨CC￨O￨- defining￨L￨VBG￨O￨- prevention￨L￨NN￨O￨- activities￨L￨NNS￨O￨- but￨L￨CC￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- of￨L￨IN￨O￨- limited￨L￨JJ￨O￨- or￨L￨CC￨O￨- no￨L￨DT￨O￨- value￨L￨NN￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- already￨L￨RB￨O￨- spread￨L￨VBN￨O￨A ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- that￨L￨DT￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- scenario￨L￨NN￨O￨- of￨L￨IN￨O￨- brucellosis￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- grouped￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- are￨L￨VBP￨O￨- embedded￨L￨VBN￨O￨- in￨L￨IN￨O￨- animal￨L￨NN￨O￨A movement￨L￨NN￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 15,16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- classical￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vital￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨A I￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- N￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- above￨L￨IN￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- inflow￨L￨NN￨O￨- of￨L￨IN￨O￨- newborns￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- μN￨L￨NN￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- classes￨L￨NNS￨O￨- at￨L￨IN￨O￨- rates￨L￨NNS￨O￨- μN￨L￨NN￨O￨- ,￨L￨,￨O￨- μI￨L￨NN￨O￨- and￨L￨CC￨O￨- μR￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- continuous-time￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Schröding-prey￨U￨JJ￨MISC￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨A I￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Equality￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨A mu￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- times￨L￨NNS￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- death-adjusted￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Guckenheimer￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Holmes￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- examined￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- non-monotonic￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- also￨L￨RB￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- derived￨L￨VBD￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +Robinson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Holmes￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- discussed￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Schrödinger-prey￨U￨JJ￨MISC￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- undergoes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- flip￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨A and￨L￨CC￨O￨- a￨L￨DT￨O￨- Hopf￨U￨NNP￨O￨- bifurcation￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- center￨L￨NN￨O￨- manifold￨L￨NN￨O￨- theorem￨L￨NN￨O￨- and￨L￨CC￨O￨- bifurcation￨L￨NN￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- present￨L￨VB￨DATE￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- integrated￨L￨VBN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- electronically￨L￨RB￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- in￨L￨IN￨O￨- local￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Western￨U￨JJ￨MISC￨- hemisphere￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- its￨L￨PRP$￨O￨- performance￨L￨NN￨O￨- by￨L￨IN￨O￨- retrospective￨L￨JJ￨O￨- application￨L￨NN￨O￨- on￨L￨IN￨O￨- authentic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- Swedish￨U￨JJ￨NATIONALITY￨- county￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- need￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- adapted￨L￨VBD￨O￨- to￨L￨TO￨O￨- extensive￨L￨JJ￨O￨- but￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- extends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- algorithms￨L￨NNS￨O￨- for￨L￨IN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- winter￨L￨NN￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- seasons￨L￨NNS￨O￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- novel￨L￨JJ￨O￨- method￨L￨NN￨O￨- was￨L￨VBD￨O￨- formally￨L￨RB￨O￨- defined￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- design￨L￨NN￨O￨- rationale￨L￨NN￨O￨- for￨L￨IN￨O￨- integrated￨L￨VBN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨A methods￨L￨NNS￨O￨- specifically￨L￨RB￨O￨- adapted￨L￨VBD￨O￨- for￨L￨IN￨O￨- application￨L￨NN￨O￨- in￨L￨IN￨O￨- local￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- presentation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- integrated￨L￨VBN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨A method￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- summary￨L￨NN￨O￨- label￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- winter￨L￨NN￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- seasons￨L￨NNS￨O￨- and￨L￨CC￨O￨- pandemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- knowledge￨L￨NN￨O￨- need￨L￨NN￨O￨- presently￨L￨RB￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- immediate￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- at￨L￨IN￨O￨- local￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Newborn￨U￨JJ￨O￨- infants￨L￨NNS￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- protected￨L￨VBN￨O￨- from￨L￨IN￨O￨- RSV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- maternal￨L￨JJ￨O￨- antibodies￨L￨NNS￨O￨- until￨L￨IN￨O￨- about￨L￨IN￨DURATION￨- six￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨A of￨L￨IN￨O￨- age￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- RSV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- six￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- six￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Few￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- vaccination￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- RSV￨U￨NN￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- have￨L￨VBP￨O￨- generally￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- RSV￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- perspective￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- newborn￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Spanish￨U￨JJ￨NATIONALITY￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- Valencia￨U￨NNP￨CITY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- RSV￨U￨NN￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- entering￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- temporarily￨L￨RB￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- currently￨L￨RB￨DATE￨- no￨L￨DT￨O￨- licensed￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- RSV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- about￨L￨IN￨DURATION￨- 50￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- research￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨MISC￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- age￨L￨NN￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨O￨- A￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- SNPs￨U￨NNS￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseaseFloor￨L￨NN￨O￨- Biemans1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Mart￨U￨NNP￨ORGANIZATION￨- C.￨U￨NNP￨ORGANIZATION￨- Selection￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- breeding￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- desirable￨L￨JJ￨O￨- traits￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- fight￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- genetic￨L￨JJ￨O￨A )￨L￨-RRB-￨O￨- traits￨L￨NNS￨O￨- :￨L￨:￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +Quantitative￨U￨JJ￨O￨- genetic￨L￨JJ￨O￨A studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- generally￨L￨RB￨O￨- connect￨L￨VBP￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- genotype￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- capture￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- set￨L￨VBD￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- single￨L￨JJ￨O￨- nucleotide￨L￨NN￨O￨- polymorphisms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SNPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- usually￨L￨RB￨O￨- ignore￨L￨VBP￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- herd￨L￨NN￨O￨- mates￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- limit￨L￨VB￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Optimizing￨U￨NNP￨O￨- sentinel￨L￨NN￨O￨- surveillance￨L￨NN￨O￨A in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- Yuan￨U￨NN￨O￨- Bai1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Bo￨U￨NNP￨PERSON￨- Yang￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Lijuan￨U￨NNP￨PERSON￨- Lin1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jose￨U￨NNP￨PERSON￨- L.￨U￨NNP￨PERSON￨- Herrera3￨U￨NNP￨PERSON￨- ,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Zhanwei￨U￨NNP￨ORGANIZATION￨- Du3￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Petter￨U￨NNP￨ORGANIZATION￨- Holme5￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 4804￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksNetwork￨L￨NN￨O￨- topology￨L￨NN￨O￨- AbstractTo￨U￨NN￨O￨- help￨L￨NN￨O￨- health￨L￨NN￨O￨- policy￨L￨NN￨O￨- makers￨L￨NNS￨O￨- gain￨L￨NN￨O￨- response￨L￨NN￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- threats￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- early￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- calculate￨L￨VBP￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- difference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- lead￨L￨NN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- surveillance￨L￨NN￨O￨A set￨L￨NN￨O￨- and￨L￨CC￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- reaching￨L￨VBG￨O￨- 1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- have￨L￨VBP￨O￨- addressed￨L￨VBN￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- designing￨L￨VBG￨O￨- surveillance￨L￨NN￨O￨A systems￨L￨NNS￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- common￨L￨JJ￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨A is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- carefully￨L￨RB￨O￨- select￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- sentinels￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- sensors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- report￨L￨VB￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- coupled￨L￨JJ￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- unifies￨L￨VBZ￨O￨- both￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- enabling￨L￨VBG￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vector￨L￨NN￨O￨A population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Agent-based￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- take￨L￨VBP￨O￨- almost￨L￨RB￨O￨- the￨L￨DT￨O￨- opposite￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- generalisations￨L￨NNS￨O￨- mentioned￨L￨VBN￨O￨- above￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- ‘￨L￨``￨O￨- agent￨L￨NN￨O￨- ’￨L￨''￨O￨- -￨L￨:￨O￨- )￨L￨-RRB-￨O￨- level￨L￨NN￨O￨- processes￨L￨VBZ￨O￨- occurring￨L￨VBG￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- try￨L￨VB￨O￨- to￨L￨TO￨O￨- calibrate￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- matching￨L￨VBG￨O￨- the￨L￨DT￨O￨- aggregate￨L￨NN￨O￨- behaviour￨L￨NN￨O￨A to￨L￨TO￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- behaviour￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- infectious￨L￨JJ￨O￨- ’￨L￨''￨O￨- compartment￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- individuals￨L￨NNS￨O￨- taking￨L￨VBG￨O￨- part￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- it￨L￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ‘￨L￨``￨O￨- recovered￨L￨VBN￨O￨- ’￨L￨''￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- no￨L￨RB￨O￨- longer￨L￨RB￨O￨- influencing￨L￨VBG￨O￨- others￨L￨NNS￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- part￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨A modify￨L￨VB￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- changing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- move￨L￨VBP￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- .￨L￨.￨O￨- +established￨L￨VBN￨O￨A a￨L￨DT￨O￨- Susceptible-Exposed-Infectious-Quarantined-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIQR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- R0￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- HFMD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- mainland￨L￨NN￨O￨- China￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +established￨L￨VBN￨O￨A a￨L￨DT￨O￨- Susceptible-Exposed-Infectious-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- among￨L￨IN￨O￨- young￨L￨JJ￨O￨- children￨L￨NNS￨O￨- in￨L￨IN￨O￨- Khulna￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Also￨U￨RB￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- threshold￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HIT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- needed￨L￨VBD￨O￨- to￨L￨TO￨O￨- stop￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- communicable￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Dynamic￨U￨NNP￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- contributed￨L￨VBN￨O￨A greatly￨L￨RB￨O￨- to￨L￨TO￨O￨- estimating￨L￨VBG￨O￨- R0￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- expected￨L￨VBN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨A case￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- The￨U￨DT￨O￨- switch￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- nine-valent￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- in￨L￨IN￨O￨- Italy￨U￨NNP￨COUNTRY￨- can￨L￨MD￨O￨- further￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- HPV-related￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- cost-effective￨L￨JJ￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Compared￨U￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- with￨L￨IN￨O￨- quadrivalent￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- nine-valent￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- programme￨L￨NN￨O￨- including￨L￨VBG￨O￨- girls￨L￨NNS￨O￨- and￨L￨CC￨O￨- boys￨L￨NNS￨O￨- shows￨L￨VBZ￨O￨- further￨L￨RB￨O￨- reductions￨L￨NNS￨O￨- of￨L￨IN￨O￨- 17￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- 35￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 14￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- anal￨L￨JJ￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- males￨L￨NNS￨O￨- and￨L￨CC￨O￨- females￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- million￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- genital￨L￨JJ￨O￨- warts￨L￨NNS￨O￨- avoided￨L￨VBN￨O￨- after￨L￨IN￨O￨- 100￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Cost-effectiveness￨U￨NN￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nine-valent￨L￨JJ￨O￨- HPV￨U￨NN￨O￨- vaccine￨L￨NN￨O￨A in￨L￨IN￨O￨- ItalyFrancesco￨U￨NNP￨O￨- Saverio￨U￨NNP￨O￨- Mennini1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Paolo￨U￨NNP￨PERSON￨- Bonanni3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Florence￨U￨NNP￨CITY￨- Bianic4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Chiara￨U￨NNP￨PERSON￨- de￨L￨IN￨PERSON￨- Waure5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Gianluca￨U￨NNP￨PERSON￨- Baio6￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Giacomo￨U￨NNP￨PERSON￨- Plazzotta7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Mathieu￨U￨NNP￨PERSON￨- Uhart8Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Alessandro￨U￨NNP￨PERSON￨- Rinaldi9￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Nathalie￨U￨NNP￨PERSON￨- Largeron8￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 15:11￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- In￨U￨IN￨O￨- Italy￨U￨NNP￨COUNTRY￨- HPV￨U￨NNP￨O￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- quadrivalent￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Gardasil￨U￨NNP￨ORGANIZATION￨- ®￨L￨NNP￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- offered￨L￨VBN￨O￨- actively￨L￨RB￨O￨- and￨L￨CC￨O￨- free￨L￨JJ￨O￨- of￨L￨IN￨O￨- charge￨L￨NN￨O￨- to￨L￨TO￨O￨- girls￨L￨NNS￨O￨- aged￨L￨VBN￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- illustration￨L￨NN￨O￨- is￨L￨VBZ￨O￨- from￨L￨IN￨O￨- Castillo-Chavez￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Yakubu￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- built￨L￨VBD￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dispersal￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- among￨L￨IN￨O￨- patches￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- answer￨L￨VB￨O￨A questions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- used￨L￨VBD￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- on￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ODEs￨U￨NNS￨O￨- :￨L￨:￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- sanitation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- provision￨L￨NN￨O￨- of￨L￨IN￨O￨- clean￨L￨JJ￨O￨- water￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- analysed￨L￨VBN￨O￨- ,￨L￨,￨O￨- comparing￨L￨VBG￨O￨- preemptive￨L￨JJ￨O￨- to￨L￨TO￨O￨- responsive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Vaccinations￨U￨NNS￨O￨- are￨L￨VBP￨O￨- currently￨L￨RB￨DATE￨- being￨L￨VBG￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- intervention￨L￨NN￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- in￨L￨IN￨O￨- Haiti￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- extended￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Tien￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Earn￨U￨VB￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- a￨L￨DT￨O￨- multi-patch￨L￨JJ￨O￨- structure￨L￨NN￨O￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨A movement￨L￨NN￨O￨A .￨L￨.￨O￨- +Prior￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- from￨L￨IN￨O￨- Yapp￨U￨NNP￨LOCATION￨- Island￨U￨NNP￨LOCATION￨- suggest￨L￨VBP￨O￨A that￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- asymptomatic￨L￨JJ￨O￨- or￨L￨CC￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- mild￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- initial￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- from￨L￨IN￨O￨- Latin￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- ZIKV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- less￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- and￨L￨CC￨O￨- less￨L￨RBR￨O￨- febrile￨L￨JJ￨O￨- than￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- dengue￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DENV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- described￨L￨VBD￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨A response￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Power￨U￨NN￨O￨- function￨L￨NN￨O￨- which￨L￨WDT￨O￨- described￨L￨VBD￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- said￨L￨VBD￨O￨- response￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- waves￨L￨NNS￨O￨- of￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- and￨L￨CC￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- human￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨A changes￨L￨NNS￨O￨- responding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- ,￨L￨,￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Bootsma￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ferguson￨U￨NNP￨PERSON￨- modelled￨L￨VBD￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨A responses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Hill￨U￨NNP￨O￨- function￨L￨NN￨O￨- which￨L￨WDT￨O￨- described￨L￨VBD￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- also￨L￨RB￨O￨- lacked￨L￨VBD￨O￨- a￨L￨DT￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- functions￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- behavioral￨L￨JJ￨O￨A responses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- which￨L￨WDT￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- included￨L￨VBD￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- did￨L￨VBD￨O￨A not￨L￨RB￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- fit￨L￨NN￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- gathers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- descriptive￨L￨JJ￨O￨- statistics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transportation￨L￨NN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- rail￨L￨NN￨O￨- transit￨L￨NN￨O￨- stations￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- rail￨L￨NN￨O￨- transit￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- median￨L￨NN￨O￨- of￨L￨IN￨O￨- in-degrees￨L￨NNS￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- out-degrees￨L￨JJ￨O￨- O￨U￨NN￨O￨- ,￨L￨,￨O￨- averaged￨L￨VBD￨O￨- shortest￨L￨JJS￨O￨- path￨L￨NN￨O￨- distance￨L￨NN￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- c￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- assortativity￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- r￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- public￨L￨JJ￨O￨- transport￨L￨NN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- Beijing￨U￨NNP￨CITY￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- naturally￨L￨RB￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- unweighted￨L￨JJ￨O￨- directed￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- stations￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- directed￨L￨VBN￨O￨- edge￨L￨NN￨O￨- from￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- node￨L￨NN￨O￨- j￨L￨NN￨O￨- means￨L￨VBZ￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- route￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- station￨L￨NN￨O￨- j￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- successor￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- station￨L￨NN￨O￨- i￨L￨FW￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 250￨L￨CD￨NUMBER￨- meters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- for￨L￨IN￨O￨- short￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- Beijing￨U￨NNP￨CITY￨- public￨L￨JJ￨O￨- transport￨L￨NN￨O￨- system￨L￨NN￨O￨- ;￨L￨:￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- without￨L￨IN￨O￨- rail￨L￨NN￨O￨- transit￨L￨NN￨O￨- stations￨L￨NNS￨O￨A ;￨L￨:￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rail￨L￨NN￨O￨- transit￨L￨NN￨O￨- network￨L￨NN￨O￨- ;￨L￨:￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- randomized￨L￨VBN￨O￨- degree-preserving￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aimed￨L￨VBD￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- technique￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible￨U￨NNP￨O￨- –￨L￨:￨O￨- Infected￨U￨JJ￨O￨- –￨L￨:￨O￨- Recovered￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- elementary￨L￨JJ￨O￨A school￨L￨NN￨O￨- students￨L￨NNS￨O￨- in￨L￨IN￨O￨- Oita￨U￨NNP￨LOCATION￨- City￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- absentee￨L￨NN￨O￨- survey￨L￨NN￨O￨- was￨L￨VBD￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- decision-making￨L￨NN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨- or￨L￨CC￨O￨- school￨L￨NN￨O￨- events￨L￨NNS￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- performed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- as￨L￨IN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- A/H1N1pdm￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- elementary￨L￨JJ￨O￨A schools￨L￨NNS￨O￨- of￨L￨IN￨O￨- Oita￨U￨NNP￨LOCATION￨- City￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- aimed￨L￨VBD￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- A/H1N1pdm￨U￨NN￨O￨- pandemic￨L￨NN￨O￨- among￨L￨IN￨O￨- elementary￨L￨JJ￨O￨A school￨L￨NN￨O￨- students￨L￨NNS￨O￨- in￨L￨IN￨O￨- Oita￨U￨NNP￨LOCATION￨- City￨U￨NNP￨LOCATION￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- absentee￨L￨NN￨O￨- survey￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- survey￨L￨NN￨O￨- ,￨L￨,￨O￨- every￨L￨DT￨O￨- public￨L￨JJ￨O￨- elementary￨L￨JJ￨O￨A school￨L￨NN￨O￨- was￨L￨VBD￨O￨- obligated￨L￨VBN￨O￨- to￨L￨TO￨O￨- report￨L￨VB￨O￨- the￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- absentees￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- A/H1N1pdm￨U￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Oita￨U￨NNP￨ORGANIZATION￨- City￨U￨NNP￨ORGANIZATION￨- Board￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Education￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +KeywordsMulti-group￨U￨JJ￨O￨- SVIRI￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelRelapseBasic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A numberGlobal￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stabilityHerpes￨L￨NNS￨O￨- Simplex￨U￨NNP￨O￨- Virus￨U￨NN￨O￨- Type￨U￨NN￨O￨- 2Vaccination￨L￨NN￨O￨- BackgroundHerpes￨U￨NNS￨O￨- Simplex￨U￨NNP￨O￨- Virus￨U￨NN￨O￨- Type￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- HSV-2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- about￨L￨IN￨O￨- 417￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- 15-49￨L￨CD￨DATE￨- worldwide￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- ℜ0￨U￨NN￨O￨- and￨L￨CC￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- ℜ0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- if￨L￨IN￨O￨- ℜ0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- so￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- compartmental￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- for￨L￨IN￨O￨- HSV-2￨U￨NN￨MISC￨- were￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- was￨L￨VBD￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- connection￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- ℜ0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- through￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A result￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- ℜ0￨U￨NN￨O￨- for￨L￨IN￨O￨- HSV-2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Clustering￨U￨NN￨O￨- provides￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- advantages￨L￨NNS￨O￨- over￨L￨IN￨O￨- flat￨L￨JJ￨O￨- architecture￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- inter-node￨L￨JJ￨O￨- communication￨L￨NN￨O￨- ,￨L￨,￨O￨- network￨L￨NN￨O￨- scalability￨L￨NN￨O￨- ,￨L￨,￨O￨- bandwidth￨L￨NN￨O￨- management￨L￨NN￨O￨- and￨L￨CC￨O￨- allowing￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- sleep￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- energy￨L￨NN￨O￨A savings￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +CH￨U￨NN￨COUNTRY￨- selection￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- single￨L￨JJ￨O￨- criteria￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- residual￨L￨JJ￨O￨- energy￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- poor￨L￨JJ￨O￨- performance￨L￨NN￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- selected￨L￨VBN￨O￨- CH￨U￨NN￨COUNTRY￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- choice￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- current￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- extended￨L￨VBN￨O￨- cluster￨L￨NN￨O￨A head￨L￨NN￨O￨- selection￨L￨NN￨O￨- criteria￨L￨NNS￨O￨- to￨L￨TO￨O￨- five￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- selected￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- cluster￨L￨NN￨O￨- head￨L￨NN￨O￨- using￨L￨VBG￨O￨- ANP￨U￨NN￨ORGANIZATION￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- cluster￨L￨NN￨O￨A has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- cluster￨L￨NN￨O￨- head￨L￨NN￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- forwarding￨L￨NN￨O￨- aggregated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- member￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- base￨L￨NN￨O￨- station￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- directly￨L￨RB￨O￨- or￨L￨CC￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- CHs￨U￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- those￨L￨DT￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- links￨L￨NNS￨O￨- are￨L￨VBP￨O￨- removed￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- above￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- giant￨L￨JJ￨O￨A component￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- continuously￨L￨RB￨O￨- ,￨L￨,￨O￨- approaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nonzero￨L￨NN￨O￨- value￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- way￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- it￨L￨PRP￨O￨- finally￨L￨RB￨O￨- collapses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- HPT￨U￨NN￨O￨- occurs￨L￨VBZ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- giant￨L￨JJ￨O￨A cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- transition￨L￨NN￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- susceptible/infective/removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model2￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- percolating￨L￨VBG￨O￨- clusters￨L￨NNS￨O￨- grown￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- CB￨U￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨A the￨L￨DT￨O￨- CB￨U￨NN￨O￨- process￨L￨NN￨O￨- persists￨L￨VBZ￨O￨- for￨L￨IN￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- 1/3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- become￨L￨VBP￨O￨- vulnerable￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- then￨L￨RB￨O￨- activated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- short￨L￨JJ￨O￨- SC￨U￨NN￨STATE_OR_PROVINCE￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- observing￨L￨VBG￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- wave￨L￨NN￨O￨A ,￨L￨,￨O￨- while￨L￨IN￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- its￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- increases￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- wave￨L￨NN￨O￨A is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- varies￨L￨VBZ￨O￨A between￨L￨IN￨O￨- 1.9￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 2.8￨L￨CD￨NUMBER￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- Antioquia￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Colombia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- varies￨L￨VBZ￨O￨- between￨L￨IN￨O￨- 4￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- 26￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- below￨L￨IN￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- in￨L￨IN￨O￨- blunting￨L￨VBG￨O￨- the￨L￨DT￨O￨- ZIKV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- to￨L￨TO￨O￨- mosquitoes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Asymptomatic￨U￨NNP￨O￨- Transmission￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Dynamics￨U￨NNPS￨MISC￨- of￨L￨IN￨MISC￨- Zika￨U￨NNP￨MISC￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- Seyed￨U￨NNP￨O￨- M.￨U￨NNP￨O￨- Pereira2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Fatima￨U￨NNP￨PERSON￨- Abdirizak3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marek￨U￨NN￨PERSON￨- Laskowski1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Cecile￨U￨NNP￨PERSON￨- Viboud4￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Gerardo￨U￨NNP￨PERSON￨- Chowell￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,4￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 5829￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- French￨U￨JJ￨NATIONALITY￨- Polynesia￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Zika￨U￨NNP￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- widely￨L￨RB￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- where￨L￨WRB￨O￨- Aedes￨U￨NNP￨O￨- Aegypti￨U￨NNP￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- transmitting￨L￨VBG￨O￨A vector￨L￨NN￨O￨- is￨L￨VBZ￨O￨- endemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- now￨L￨RB￨DATE￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- scholars￨L￨NNS￨O￨A have￨L￨VBP￨O￨- paid￨L￨VBN￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- delay￨L￨NN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- partial￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- constructed￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- attention￨L￨NN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- involving￨L￨VBG￨O￨- vertical￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- was￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- removed￨L￨VBN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- members￨L￨NNS￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- decades￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observed￨L￨VBD￨O￨- that￨L￨IN￨O￨- scholars￨L￨NNS￨O￨- published￨L￨VBN￨O￨- few￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- in￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- journals￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- mathematics￨L￨NNS￨O￨- considering￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- vertical￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- transmitted￨L￨VBN￨O￨- from￨L￨IN￨O￨- parents￨L￨NNS￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- offspring￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 24￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- σ2￨L￨NN￨O￨- >￨L￨JJR￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- easily￨L￨RB￨O￨- see￨L￨VB￨O￨- from￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- thatDividing￨L￨VBG￨O￨- both￨L￨DT￨O￨- sides￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- haveSince￨L￨VBP￨O￨- lim￨L￨NN￨O￨- sup￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 〈￨L￨CD￨NUMBER￨- M￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 〉￨L￨SYM￨O￨- /￨L￨:￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- <￨L￨JJR￨O￨- σ2￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- ∞￨L￨CD￨NUMBER￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨A number￨L￨NN￨O￨A theorem￨L￨NN￨O￨- for￨L￨IN￨O￨- martingales￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- obtain￨L￨VB￨O￨- that￨L￨IN￨O￨- Then￨U￨RB￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- superior￨L￨JJ￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- sides￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- when￨L￨WRB￨O￨- σ2￨L￨NN￨O￨- >￨L￨JJR￨O￨- β2/2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- pb￨L￨NN￨O￨- ′￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- implies￨L￨VBZ￨O￨- limI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- σ2￨L￨NN￨O￨- >￨L￨JJR￨O￨- max￨L￨NN￨O￨A {￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- β2/2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- pb￨L￨NN￨O￨- ′￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- σ2￨L￨NN￨O￨- <￨L￨JJR￨O￨- β￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- investigates￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- proposes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- four￨L￨CD￨NUMBER￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- restrain￨L￨VB￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A process￨L￨NN￨O￨- :￨L￨:￨O￨- blocking￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- blocking￨L￨VBG￨O￨- edges￨L￨NNS￨O￨- ,￨L￨,￨O￨- distracting￨L￨VBG￨O￨- node￨L￨NN￨O￨- attention￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- propagating￨L￨VBG￨O￨- opposite￨L￨JJ￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Effective￨U￨NNP￨O￨- Methods￨U￨NNS￨O￨- of￨L￨IN￨O￨- Restraining￨U￨VBG￨O￨- Diffusion￨U￨NNP￨O￨- in￨L￨IN￨O￨- Terms￨U￨NNS￨O￨- of￨L￨IN￨O￨- Epidemic￨U￨NNP￨O￨- Dynamics￨U￨NNP￨O￨- Fei￨U￨NNP￨O￨- Xiong1￨U￨NN￨O￨- ,2￨L￨NN￨O￨- &￨L￨CC￨O￨- Zhao-Yi￨U￨NN￨O￨- Li1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 6013￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComplex￨L￨NNP￨O￨- networksStatistical￨L￨JJ￨O￨- physics￨L￨NNS￨O￨- AbstractRemoving￨U￨VBG￨O￨- influential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- shortcuts￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- restrains￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- destroys￨L￨VBZ￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- changes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Propagating￨U￨VBG￨O￨- opposite￨L￨JJ￨O￨- information￨L￨NN￨O￨- can￨L￨MD￨O￨- effectively￨L￨RB￨O￨- prevent￨L￨VB￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- target￨L￨NN￨O￨- information￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- distracting￨L￨VBG￨O￨- node￨L￨NN￨O￨- attention￨L￨NN￨O￨- only￨L￨RB￨O￨- takes￨L￨VBZ￨O￨- effect￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- an￨L￨DT￨O￨- alternative￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- field￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- imposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- node￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- and￨L￨CC￨O￨- slow￨L￨VB￨O￨- down￨L￨RP￨O￨- diffusion￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Information￨U￨NN￨O￨- diffusion￨L￨NN￨O￨A in￨L￨IN￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- was￨L￨VBD￨O￨- explored￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reposting￨L￨VBG￨O￨- behaviors￨L￨NNS￨O￨- were￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- among￨L￨IN￨O￨- node￨L￨NN￨O￨- interactions18￨L￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- very￨L￨RB￨O￨- useful￨L￨JJ￨O￨- to￨L￨TO￨O￨- tailor￨L￨VB￨O￨- mitigation￨L￨NN￨O￨- strategies3.The￨L￨NN￨O￨- San￨U￨NNP￨ORGANIZATION￨- Francisco￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- SFDPH￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- maintains￨L￨VBZ￨O￨- legally￨L￨RB￨O￨- mandated￨L￨VBN￨O￨- case-based￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- collected￨L￨VBN￨O￨- sociodemographic￨L￨JJ￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- reported￨L￨VBN￨O￨- and￨L￨CC￨O￨- investigated￨L￨VBN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Clients￨U￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- largest￨L￨JJS￨O￨- component￨L￨NN￨O￨- were￨L￨VBD￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- HIV-positive￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- <￨L￨JJR￨O￨- 0.001￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- Chi-square￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- had￨L￨VBN￨O￨- more￨L￨RBR￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- <￨L￨JJR￨O￨- 0.0001￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- ANOVA￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- than￨L￨IN￨O￨- clients￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- smaller￨L￨JJR￨O￨- connected￨L￨JJ￨O￨- components4.A￨L￨NN￨O￨- partner￨L￨NN￨O￨- notification￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PN￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- called￨L￨VBN￨O￨- an￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- notifies￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- directly￨L￨RB￨O￨- or￨L￨CC￨O￨- indirectly￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- his￨L￨PRP$￨O￨- partners￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- neighbors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sexual￨L￨JJ￨O￨A network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- his￨L￨PRP$￨O￨- infectious￨L￨JJ￨O￨- state5￨L￨NN￨O￨- .￨L￨.￨O￨- +4￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨A network￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- community￨L￨NN￨O￨- of￨L￨IN￨O￨- San￨U￨NNP￨CITY￨- Francisco￨U￨NNP￨CITY￨- from￨L￨IN￨O￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- routinely￨L￨RB￨O￨- collected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- SFDPH￨U￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- possible￨L￨JJ￨O￨- new￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Individual-based￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- successful￨L￨JJ￨O￨- in￨L￨IN￨O￨- relating￨L￨VBG￨O￨- critical￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A network10￨L￨NN￨O￨- ,11,12,13,14￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- brief￨L￨NN￨O￨- ,￨L￨,￨O￨- previously￨L￨RB￨DATE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- presented￨L￨VBD￨O￨- controlled￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- 6-to￨L￨JJ￨O￨- 8-week-old￨L￨JJ￨DURATION￨- puppy￨L￨NN￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Puppy￨U￨NNP￨O￨- Profiling￨U￨NNP￨O￨- Assessment￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- PPA￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- three￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- stroking￨L￨VBG￨O￨- ,￨L￨,￨O￨- fake￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- ramp￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- stimuli￨L￨NNS￨O￨- presented￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- including￨L￨VBG￨O￨- following￨L￨VBG￨O￨- ,￨L￨,￨O￨- retrieve￨L￨VB￨O￨- ,￨L￨,￨O￨- gentle￨L￨JJ￨O￨- restraint￨L￨NN￨O￨- ,￨L￨,￨O￨- noise￨L￨NN￨O￨- ,￨L￨,￨O￨- tunnel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- usefully￨L￨RB￨O￨- combined￨L￨VBN￨O￨- and￨L￨CC￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- whether￨L￨IN￨O￨- dogs￨L￨NNS￨O￨A completed￨L￨VBN￨O￨- guide￨L￨NN￨TITLE￨- dogs￨L￨NNS￨O￨- training￨L￨VBG￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- a￨L￨DT￨O￨- working￨L￨VBG￨O￨- guide￨L￨NN￨TITLE￨- dog￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- success￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- epidemiological￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- animal￨L￨NN￨O￨- behavior￨L￨NN￨O￨A research￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- survival￨L￨NN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- MSM￨U￨NN￨ORGANIZATION￨- to￨L￨TO￨O￨- Guide￨U￨NNP￨ORGANIZATION￨- Dogs￨U￨NNP￨ORGANIZATION￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- dog￨L￨NN￨O￨- qualifying￨L￨VBG￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- ,￨L￨,￨O￨- movements￨L￨NNS￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- training￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- this￨L￨DT￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- popular￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- survival￨L￨NN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- multistate￨L￨NN￨O￨- modeling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MSM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- guide￨L￨NN￨TITLE￨A dog￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- Guide￨U￨NNP￨ORGANIZATION￨- Dogs￨U￨NNP￨ORGANIZATION￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- prospectively￨L￨RB￨O￨- collecting￨L￨VBG￨O￨- more￨L￨JJR￨O￨- detailed￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- dogs￨L￨NNS￨O￨A during￨L￨IN￨O￨- training￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- and￨L￨CC￨O￨- record￨L￨VB￨O￨- behavior￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- behavior￨L￨NN￨O￨A data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- previously￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- datasets￨L￨NNS￨O￨- from￨L￨IN￨O￨- Guide￨U￨NNP￨ORGANIZATION￨- Dogs￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +Pearson￨U￨NNP￨PERSON￨- method￨L￨NN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- weekly￨L￨JJ￨SET￨- A/H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨- isolation￨L￨NN￨O￨- rate￨L￨NN￨O￨- curve￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2009￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- effective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- succeeding￨L￨VBG￨O￨- A/H1N1￨U￨NN￨O￨- clade￨L￨NN￨O￨- 2B-2￨L￨NN￨O￨- ,￨L￨,￨O￨- carrying￨L￨VBG￨O￨- H275Y￨U￨NN￨O￨- mutation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- neuraminidase￨L￨NN￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- around￨L￨IN￨O￨- 1.65￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- ran￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- A/H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- isolation￨L￨NN￨O￨- rate￨L￨NN￨O￨- through￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2008￨L￨CD￨DATE￨- single-clade￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A and￨L￨CC￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- clade-based￨L￨JJ￨O￨- A/H1N1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2009￨L￨CD￨DATE￨- two-clade￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- viral￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- in￨L￨IN￨O￨- immunocompromised￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A may￨L￨MD￨O￨- impact￨L￨VB￨O￨- larger-scale￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- emergence￨L￨NN￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- categorization￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- importantly￨L￨RB￨O￨- ,￨L￨,￨O￨- incorporates￨L￨VBZ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- evolution￨L￨NN￨O￨- to￨L￨TO￨O￨- reveal￨L￨VB￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- immunocompromised￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- evolution￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- NoV￨U￨NN￨DATE￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- apparent￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- for￨L￨IN￨O￨- immunocompromised￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A to￨L￨TO￨O￨- generate￨L￨VB￨O￨- significant￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- during￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- isolation￨L￨NN￨O￨- and￨L￨CC￨O￨- rarity￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- limits￨L￨VBZ￨O￨- their￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- NoV￨U￨NN￨DATE￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- rapidly￨L￨RB￨O￨- evolving￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- in￨L￨IN￨O￨- chronically￨L￨RB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- immunocompromised￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- components￨L￨NNS￨O￨- .￨L￨.￨O￨- +Importantly￨U￨RB￨O￨- ,￨L￨,￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- ‘￨L￨``￨O￨- immunocompromised￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A ’￨L￨POS￨O￨- as￨L￨IN￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- more￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- immunodeficienies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- that￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- chronic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- typically￨L￨RB￨O￨- acute￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- constant￨L￨JJ￨O￨- size￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- immunocompromised￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- births￨L￨NNS￨O￨- or￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- kill￨L￨VB￨O￨- hosts￨L￨NNS￨O￨A so￨L￨IN￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- cases￨L￨NNS￨O￨- recover￨L￨VB￨O￨- ,￨L￨,￨O￨- become￨L￨VB￨O￨- immune￨L￨JJ￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- reinfection￨L￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- RVF￨U￨NN￨O￨- emergence￨L￨NN￨O￨- conducted￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Horn￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Africa￨U￨NNP￨ORGANIZATION￨- using￨L￨VBG￨O￨- ecological￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- above-average￨L￨JJ￨O￨- rainfall￨L￨NNS￨O￨- and￨L￨CC￨O￨- vegetation￨L￨NN￨O￨- density￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Normalized￨U￨JJ￨MISC￨- Vegetation￨U￨NNP￨MISC￨- Difference￨U￨NNP￨MISC￨- Index￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- NDVI￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- over￨L￨IN￨O￨- 3￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- 4￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- could￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- RVF￨U￨NN￨O￨- re-emergence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- seem￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- always￨L￨RB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- Madagascar￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Southern￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- other￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- livestock￨L￨NN￨O￨A susceptibility￨L￨NN￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- play￨L￨VB￨O￨- a￨L￨DT￨O￨- role￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- RVF￨U￨NN￨O￨- emergence￨L￨NN￨O￨- that￨L￨WDT￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- livestock￨L￨NN￨O￨A susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- climate￨L￨NN￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- import￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- serological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- livestock￨L￨NN￨O￨A population￨L￨NN￨O￨- was￨L￨VBD￨O￨- purposively￨L￨RB￨O￨- stratified￨L￨VBN￨O￨- in￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- yearly￨L￨JJ￨SET￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- a￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- ∊￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- age-specific￨L￨JJ￨O￨- IgG￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- fitting￨L￨JJ￨O￨- paragraph￨L￨NN￨O￨- and￨L￨CC￨O￨- S1￨U￨NN￨O￨- Text￨U￨VBP￨O￨- for￨L￨IN￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Subsequent￨U￨JJ￨O￨- serological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- in￨L￨IN￨O￨- Mayotte￨U￨NNP￨LOCATION￨- in￨L￨IN￨O￨- livestock￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 2004￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2016￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- no￨L￨DT￨O￨- symptoms￨L￨NNS￨O￨- in￨L￨IN￨O￨- animals￨L￨NNS￨O￨- being￨L￨VBG￨O￨- detected￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨A to￨L￨TO￨O￨- study￨L￨VB￨O￨- RVF￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- looked￨L￨VBD￨O￨- mainly￨L￨RB￨O￨- at￨L￨IN￨O￨- RVF￨U￨NN￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- once￨L￨RB￨DATE￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- they￨L￨PRP￨O￨- assessed￨L￨VBD￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- few￨L￨JJ￨O￨- were￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Early￨U￨NNP￨MISC￨- rigorous￨L￨JJ￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A can￨L￨MD￨O￨- largely￨L￨RB￨O￨- reduce￨L￨VB￨O￨- dengue￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- magnitude￨L￨NN￨O￨- :￨L￨:￨O￨- experience￨L￨NN￨O￨- from￨L￨IN￨O￨- Chaozhou￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- ChinaTao￨U￨NNP￨PERSON￨- Liu￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Guanghu￨U￨NNP￨PERSON￨- Zhu￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jianfeng￨U￨NNP￨PERSON￨- He2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Tie￨U￨NNP￨O￨- Song2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Meng￨U￨NNP￨PERSON￨- Zhang2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hualiang￨U￨NNP￨O￨- Lin1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Jianpeng￨U￨NNP￨PERSON￨- Xiao1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Weilin￨U￨NNP￨PERSON￨- Zeng1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Xing￨U￨NNP￨PERSON￨- Li1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Zhihao￨U￨NNP￨PERSON￨- Li1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Runsheng￨U￨NNP￨O￨- Xie1￨U￨NN￨O￨- ,￨L￨,￨O￨- Haojie￨U￨NN￨O￨- Zhong2￨U￨NN￨O￨- ,￨L￨,￨O￨- Xiaocheng￨U￨NN￨O￨- Wu2￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Wenbiao￨U￨NNP￨O￨- Hu4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Yonghui￨U￨NNP￨O￨- Zhang2Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Wenjun￨U￨NNP￨O￨- Ma1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- †￨L￨CD￨NUMBER￨- Contributed￨U￨VBD￨O￨- equallyBMC￨L￨NNP￨O￨- Public￨U￨NNP￨O￨- HealthBMC￨U￨NNP￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18:90￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- SEIR￨U￨NN￨O￨- modeling￨L￨NN￨O￨- using￨L￨VBG￨O￨- BI￨U￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- actual￨L￨JJ￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A showed￨L￨VBD￨O￨- a￨L￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 1255￨L￨CD￨DATE￨- dengue￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1250￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- intensified￨L￨VBD￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- reduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- should￨L￨MD￨O￨- such￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- be￨L￨VB￨O￨- initiated￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A outbreaks￨L￨NNS￨O￨- developing￨L￨VBG￨O￨- ?￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Exposed￨U￨VBN￨O￨- ,￨L￨,￨O￨- Infected￨U￨JJ￨O￨- and￨L￨CC￨O￨- Removed￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- timing￨L￨NN￨O￨- on￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- This￨U￨DT￨O￨- study￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- early￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- rigorous￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A interventions￨L￨NNS￨O￨- can￨L￨MD￨O￨- effectively￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- shorten￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- duration￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Role￨U￨NN￨MISC￨- of￨L￨IN￨O￨- meteorological￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- in￨L￨IN￨O￨- reported￨L￨VBN￨O￨- chickenpox￨L￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- ChinaBanghua￨U￨NNP￨O￨- Chen1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Ayako￨U￨NNP￨PERSON￨- Sumi2Email￨U￨NNP￨O￨- authorView￨L￨NNP￨O￨- ORCID￨U￨NNP￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Lei￨U￨NN￨O￨- Wang3￨U￨NN￨O￨- ,￨L￨,￨O￨- Wang￨U￨NNP￨O￨- Zhou4Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Nobumichi￨U￨JJ￨MISC￨- Kobayashi2BMC￨U￨NN￨MISC￨- Infectious￨U￨JJ￨MISC￨- DiseasesBMC￨U￨NN￨MISC￨- series￨L￨NN￨O￨A –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 17:538￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Q￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- were￨L￨VBD￨O￨- positively￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- mean￨L￨NN￨O￨- temperature￨L￨NN￨O￨A and￨L￨CC￨O￨- rainfall￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- city￨L￨NN￨O￨- .￨L￨.￨O￨- +Conversely￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Q￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- were￨L￨VBD￨O￨- negatively￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- mean￨L￨NN￨O￨- temperature￨L￨NN￨O￨A and￨L￨CC￨O￨- rainfall￨L￨NNS￨O￨- of￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨A data￨L￨NNS￨O￨- of￨L￨IN￨O￨- chickenpox￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- Wuhan￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- have￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- peaks￨L￨NNS￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- winter￨L￨NN￨DATE￨- and￨L￨CC￨O￨- another￨L￨DT￨O￨- in￨L￨IN￨O￨- spring￨L￨NN￨DATE￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- a￨L￨DT￨O￨- bimodal￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Impact￨U￨NN￨O￨- of￨L￨IN￨O￨- life￨L￨NN￨O￨- stage-dependent￨L￨JJ￨O￨- dispersal￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- colonization￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- patches￨L￨NNS￨O￨- by￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- and￨L￨CC￨O￨- tick-borne￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- agentsSarah￨L￨NN￨O￨- Kada1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Karen￨U￨NNP￨PERSON￨- D.￨U￨NNP￨O￨- 2017Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- When￨U￨WRB￨O￨- colonization￨L￨NN￨O￨- and￨L￨CC￨O￨- gene￨L￨NN￨O￨- flow￨L￨NN￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- host-mediated￨L￨JJ￨O￨- dispersal￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- factor￨L￨NN￨O￨- affecting￨L￨VBG￨O￨- vector￨L￨NN￨O￨- dispersal￨L￨JJ￨O￨- potential￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- spent￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- blood￨L￨NN￨O￨- meal￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- vary￨L￨VB￨O￨- strongly￨L￨RB￨O￨- among￨L￨IN￨O￨- life￨L￨NN￨O￨- history￨L￨NN￨O￨- stages￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- vector￨L￨NN￨O￨- life￨L￨NN￨O￨A history￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- blood￨L￨NN￨O￨- meal￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Allee￨U￨JJ￨O￨- effects￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- condition￨L￨NN￨O￨- the￨L￨DT￨O￨- colonization￨L￨NN￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- ;￨L￨:￨O￨- hard￨L￨JJ￨O￨- ticks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- take￨L￨VBP￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- ,￨L￨,￨O￨- long￨L￨JJ￨O￨- blood￨L￨NN￨O￨- meal￨L￨NN￨O￨- per￨L￨IN￨O￨- life￨L￨NN￨O￨- stage￨L￨NN￨O￨- ,￨L￨,￨O￨- should￨L￨MD￨O￨- have￨L￨VB￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- colonization￨L￨NN￨O￨- rates￨L￨NNS￨O￨- than￨L￨IN￨O￨- soft￨L￨JJ￨O￨- ticks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- take￨L￨VBP￨O￨- repeated￨L￨VBN￨O￨- short￨L￨JJ￨O￨- meals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- 2-patch￨L￨JJ￨O￨- vector-pathogen￨L￨JJ￨O￨- population￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- seabird￨L￨NN￨O￨- ticks￨L￨VBZ￨O￨- as￨L￨IN￨O￨- biological￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- how￨L￨WRB￨O￨- vector￨L￨NN￨O￨- colonization￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- shaped￨L￨VBN￨O￨- by￨L￨IN￨O￨- life￨L￨NN￨O￨- stage-dependent￨L￨JJ￨O￨- dispersal￨L￨NN￨O￨A .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- dispersal￨L￨JJ￨O￨A potential￨L￨NN￨O￨- has￨L￨VBZ￨O￨- direct￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- when￨L￨WRB￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- transovarial￨L￨JJ￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- anticipating￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨A has￨L￨VBZ￨O￨- predominantly￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- specific￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- attempt￨L￨NN￨O￨- at￨L￨IN￨O￨- applying￨L￨VBG￨O￨- EWS￨U￨NN￨O￨- to￨L￨TO￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- emergence￨L￨NN￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- –￨L￨:￨O￨- immigration￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- BDI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- viewed￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- possible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- direct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- modelling￨L￨VBG￨O￨- spillover￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- external￨L￨JJ￨O￨- source￨L￨NN￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- chains￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- fed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- pool￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- test￨L￨VBP￨O￨- the￨L￨DT￨O￨- robustness￨L￨NN￨O￨- of￨L￨IN￨O￨- measures￨L￨NNS￨O￨- to￨L￨TO￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- simulating￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨A using￨L￨VBG￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIRS￨U￨NN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- varying￨L￨VBG￨O￨- immunology￨L￨NN￨O￨- and￨L￨CC￨O￨- demographics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- exploring￨L￨VBG￨O￨- EWS￨U￨NN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- performance￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- direction￨L￨NN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- transition￨L￨NN￨O￨A is￨L￨VBZ￨O￨- traversed￨L￨VBN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- contrasting￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨ORGANIZATION￨- .￨L￨.￨O￨- +Dynamical￨U￨JJ￨O￨- systems￨L￨NNS￨O￨- theory￨L￨NN￨O￨- states￨L￨VBZ￨O￨- that￨L￨IN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- stable￨L￨JJ￨O￨- system￨L￨NN￨O￨- approaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- tipping￨L￨JJ￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- taken￨L￨VBN￨O￨- to￨L￨TO￨O￨- recover￨L￨VB￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- ;￨L￨:￨O￨- ultimately￨L￨RB￨O￨- diverging￨L￨VBG￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- spatially￨L￨RB￨O￨- and￨L￨CC￨O￨- temporally￨L￨RB￨O￨- clustered￨L￨VBN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A incidence￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- predominance￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- serotype￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨- by￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- aggregated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- limits￨L￨NNS￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- answer￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- research￨L￨NN￨O￨- questions￨L￨NNS￨O￨- :￨L￨:￨O￨- How￨U￨WRB￨O￨- does￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- of￨L￨IN￨O￨- buildings￨L￨NNS￨O￨- influence￨L￨VBP￨O￨- dengue￨L￨JJ￨O￨A incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ?￨L￨.￨O￨- +Interested￨U￨VBN￨O￨- in￨L￨IN￨O￨- addressing￨L￨VBG￨O￨- this￨L￨DT￨O￨- issue￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- objectives￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- are￨L￨VBP￨O￨- twofold￨L￨JJ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- of￨L￨IN￨O￨- residential￨L￨JJ￨O￨- buildings￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +How￨U￨WRB￨O￨- does￨L￨VBZ￨O￨- mosquito￨L￨NN￨O￨- population￨L￨NN￨O￨- distribution￨L￨NN￨O￨- influence￨L￨NN￨O￨- dengue￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- serotype-specific￨L￨JJ￨O￨- dominance￨L￨NN￨O￨- ?￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- four￨L￨CD￨NUMBER￨- environments￨L￨NNS￨O￨- were￨L￨VBD￨O￨- set￨L￨VBN￨O￨- up￨L￨RP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- mosquito￨L￨NN￨O￨A agents￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- in￨L￨IN￨O￨- specific￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- houses￨L￨NNS￨O￨- ,￨L￨,￨O￨- workplaces￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- schools￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Four￨U￨CD￨NUMBER￨- quantitative￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- risk￨L￨NN￨O￨- assessment￨L￨NN￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- monthly￨L￨JJ￨SET￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- ASF￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- CSF￨U￨NN￨O￨- introduction￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- live￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A and￨L￨CC￨O￨- products￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- of￨L￨IN￨O￨- origin￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- notification￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- addressed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- event￨L￨NN￨O￨- pathways￨L￨NNS￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- ASF￨U￨NN￨O￨- being￨L￨VBG￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- live￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A ,￨L￨,￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- ASF￨U￨NNP￨O￨- introduction￨L￨NN￨O￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- swine￨L￨NNS￨O￨- products￨L￨NNS￨O￨- ,￨L￨,￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- introduction￨L￨NN￨O￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- live￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- iv￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- being￨L￨VBG￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- swine￨L￨NNS￨O￨- products￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- ,￨L￨,￨O￨- ASF￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- CSF￨U￨NN￨O￨- introduction￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- at￨L￨IN￨O￨- state￨L￨NN￨O￨- level￨L￨NN￨O￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- live￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A and￨L￨CC￨O￨- swine￨L￨NNS￨O￨- products￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- monthly￨L￨JJ￨SET￨- basis￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- incorporated￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- online￨L￨JJ￨O￨- platform￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- BioPortal￨U￨JJ￨MISC￨- ™￨L￨NN￨O￨- accessible￨L￨JJ￨O￨- at￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- their￨L￨PRP$￨O￨- visualization￨L￨NN￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- developed￨L￨VBD￨O￨- here￨L￨RB￨O￨- will￨L￨MD￨O￨- serve￨L￨VB￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- template￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- introduction￨L￨NN￨O￨A of￨L￨IN￨O￨- other￨L￨JJ￨O￨- TADs￨U￨NNS￨O￨- .￨L￨.￨O￨- +ASF￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- CSF￨U￨NN￨O￨- represent￨L￨VBP￨O￨- a￨L￨DT￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- swine￨L￨NNS￨O￨A industry￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- important￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- if￨L￨IN￨O￨- they￨L￨PRP￨O￨- were￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- swine￨L￨NNS￨O￨- production￨L￨NN￨O￨- countries￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- previous￨L￨JJ￨O￨- health￨L￨NN￨O￨- economic￨L￨JJ￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- universal￨L￨JJ￨O￨- childhood￨L￨NN￨O￨- rotavirus￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- cost￨L￨VBN￨O￨- –￨L￨:￨O￨- effective￨L￨JJ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- societal￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- healthcare￨L￨NN￨O￨- perspective￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- limited￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- The￨U￨NNP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- largely￨L￨RB￨O￨- preventable￨L￨JJ￨O￨- through￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- rotavirus￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- of￨L￨IN￨O￨- 81￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- worldwide￨L￨RB￨O￨- ;￨L￨:￨O￨- eight￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- European￨U￨NNP￨ORGANIZATION￨- Union￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- Many￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- clearly￨L￨RB￨O￨- illustrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- whether￨L￨IN￨O￨- these￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- outweigh￨L￨VBP￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- country￨L￨NN￨O￨- –￨L￨:￨O￨- specific￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨- rotavirus￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A programme￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- –￨L￨:￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Norwegian￨U￨JJ￨NATIONALITY￨- setting￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- hospitalisation￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- RVGE￨U￨NN￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- at￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- 1000￨L￨CD￨DATE￨A children￨L￨NNS￨O￨- below￨L￨IN￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- primary￨L￨JJ￨O￨- care￨L￨NN￨O￨- consultations￨L￨NNS￨O￨- and￨L￨CC￨O￨- homecare￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- episodes￨L￨NNS￨O￨- was￨L￨VBD￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- hospitalisation￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Effects￨U￨NNS￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- Michele￨U￨NNP￨PERSON￨- Starnini1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Andrea￨U￨NNP￨PERSON￨- Baronchelli3￨U￨NNP￨O￨- &￨L￨CC￨O￨- Romualdo￨U￨NNP￨O￨- Pastor-Satorras4￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 8597￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksPhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractMulti-layered￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- advance￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- study￨L￨NN￨O￨- has￨L￨VBZ￨O￨- shed￨L￨VBN￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- new￨L￨JJ￨O￨- physical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- .￨L￨.￨O￨- +IntroductionRecently￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- science1￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- enriched￨L￨VBN￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- new￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨- :￨L￨:￨O￨- Multiplex￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- 2,3,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- edges￨L￨NNS￨O￨- belong￨L￨VBP￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- layers￨L￨NNS￨O￨A ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- edges￨L￨NNS￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- creation￨L￨NN￨O￨- and￨L￨CC￨O￨- annihilation￨L￨NN￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- interactions￨L￨NNS￨O￨- switching￨L￨VBG￨O￨- on￨L￨IN￨O￨- and￨L￨CC￨O￨- off￨L￨IN￨O￨- with￨L￨IN￨O￨- given￨L￨VBN￨O￨- characteristic￨L￨JJ￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨A representation￨L￨NN￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- observables￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- multilayer￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- ,￨L￨,￨O￨- degree￨L￨NN￨O￨- correlations￨L￨NNS￨O￨- or￨L￨CC￨O￨- layer￨L￨NN￨TITLE￨- overlap2￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- allowed￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- structural￨L￨JJ￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- networked￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- helped￨L￨VBD￨O￨- clarify￨L￨VB￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- them7￨L￨CD￨NUMBER￨- ,8,9,10,11￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨A are￨L￨VBP￨O￨- a￨L￨DT￨O￨- signature￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- ‘￨L￨``￨O￨- multitasking￨L￨VBG￨O￨- ’￨L￨''￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- switching￨L￨NN￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- social￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- uncorrelated￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- layers￨L￨NNS￨O￨- exhibited￨L￨VBN￨O￨- by￨L￨IN￨O￨- real￨L￨JJ￨O￨- social￨L￨JJ￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Egyptian￨U￨NNP￨NATIONALITY￨- rousette￨L￨NN￨O￨- bats￨L￨NNS￨O￨- maintain￨L￨VBP￨O￨- long-term￨L￨JJ￨O￨- protective￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- Marburg￨U￨NNP￨MISC￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- despite￨L￨IN￨O￨- diminished￨L￨JJ￨O￨- antibody￨L￨NN￨O￨- levels￨L￨NNS￨O￨- Amy￨U￨NNP￨PERSON￨- J.￨U￨NNP￨PERSON￨- Towner￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 8763￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Microbial￨U￨NNP￨O￨- ecologyViral￨L￨NNP￨O￨- reservoirsVirus￨L￨NNP￨O￨- –￨L￨:￨O￨- host￨L￨NN￨TITLE￨- interactions￨L￨NNS￨O￨- AbstractAlthough￨U￨NNP￨O￨- bats￨L￨NNS￨O￨- are￨L￨VBP￨O￨- natural￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- for￨L￨IN￨O￨- numerous￨L￨JJ￨O￨- zoonotic￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- following￨L￨VBG￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- maintained￨L￨VBN￨O￨- in￨L￨IN￨O￨- nature￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- reinfection￨L￨NN￨O￨- of￨L￨IN￨O￨- ERBs￨U￨NNS￨MISC￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- MARV￨U￨NNP￨O￨- maintenance￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- challenge￨L￨VBP￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- ERBs￨U￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- “￨L￨``￨O￨- naturally￨L￨RB￨O￨- ”￨L￨''￨O￨- or￨L￨CC￨O￨- experimentally￨L￨RB￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- MARV￨U￨NN￨ORGANIZATION￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨A prior￨L￨RB￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- ERBs￨U￨NNS￨O￨- with￨L￨IN￨O￨- MARV￨U￨NN￨O￨- ,￨L￨,￨O￨- virus-specific￨L￨JJ￨O￨- IgG￨U￨NN￨O￨- antibodies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- induced￨L￨VBN￨O￨- but￨L￨CC￨O￨- rapidly￨L￨RB￨O￨- wane￨L￨VB￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- 3￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨A post-infection￨L￨JJ￨O￨- the￨L￨DT￨O￨- bats￨L￨NNS￨O￨- are￨L￨VBP￨O￨- seronegative￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Egyptian￨U￨JJ￨NATIONALITY￨- rousette￨L￨NN￨O￨- bat￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ERB￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- known￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨A host￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- Marburg￨U￨NNP￨MISC￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MARV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- inference￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- building￨L￨NN￨O￨- on￨L￨IN￨O￨- core￨L￨NN￨O￨- biological￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- experiments￨L￨NNS￨O￨- indicating￨L￨VBG￨O￨- vector￨L￨NN￨O￨- or￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- survival￨L￨NN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- climatic￨L￨JJ￨O￨A variable￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- leveraging￨L￨VBG￨O￨- spatial￨L￨JJ￨O￨- variation￨L￨NN￨O￨- and￨L￨CC￨O￨- range￨L￨NN￨O￨- limits￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- climatic￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- building￨L￨NN￨O￨- mechanistic￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- from￨L￨IN￨O￨- shorter￨L￨JJR￨O￨- time-series￨L￨NNS￨O￨- of￨L￨IN￨O￨- climatic￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- which￨L￨WDT￨O￨- itself￨L￨PRP￨O￨- often￨L￨RB￨O￨- builds￨L￨VBZ￨O￨- on￨L￨IN￨O￨- biological￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- and/or￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- variation￨L￨NN￨O￨- .￨L￨.￨O￨- +Infectious￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- climatic￨L￨JJ￨O￨A conditions￨L￨NNS￨O￨- through￨L￨IN￨O￨- their￨L￨PRP$￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- and￨L￨CC￨O￨- ticks￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- pathogen￨L￨NN￨O￨- survival￨L￨NN￨O￨- outside￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- contamination￨L￨NN￨O￨- and￨L￨CC￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- water-borne￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- dampening￨L￨VBG￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- immunity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- disruptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- status￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- malnutrition￨L￨NN￨CAUSE_OF_DEATH￨- linked￨L￨VBN￨O￨- to￨L￨TO￨O￨- droughts￨L￨NNS￨O￨- or￨L￨CC￨O￨- floods￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- disruption￨L￨NN￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- systems￨L￨NNS￨O￨- by￨L￨IN￨O￨- disasters￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- floods￨L￨NNS￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- hurricanes￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- issue￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- while￨L￨IN￨O￨- climate￨L￨NN￨O￨A acts￨L￨VBZ￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- extrinsic￨L￨JJ￨O￨- driver￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- also￨L￨RB￨O￨- have￨L￨VBP￨O￨- intrinsic￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- population-level￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- increasing￨L￨VBG￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨- can￨L￨MD￨O￨- modify￨L￨VB￨O￨- previous￨L￨JJ￨O￨- geographical￨L￨JJ￨O￨- limits￨L￨NNS￨O￨- for￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Appropriately￨U￨RB￨O￨- attributing￨L￨VBG￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- climatic￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- quantifying￨L￨VBG￨O￨- this￨L￨DT￨O￨- relationship￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- step￨L￨NN￨O￨- in￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Disentangling￨U￨VBG￨O￨- these￨L￨DT￨O￨- drivers￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- careful￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- and￨L￨CC￨O￨- model-based￨L￨JJ￨O￨- partitioning￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- climate￨L￨NN￨O￨A and￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- while￨L￨IN￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- pathogen￨L￨NN￨O￨- biology￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- carriage￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- serotype￨L￨NN￨O￨A transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- serotype￨L￨NN￨O￨- co-circulation￨L￨NN￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- Brazilian￨U￨JJ￨NATIONALITY￨- multi-serotype￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- v￨L￨LS￨O￨- k￨L￨NN￨O￨- ∞￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- k￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- metastable￨L￨JJ￨O￨- state￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- τ￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨A of￨L￨IN￨O￨- node￨L￨NN￨O￨- k￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- equals￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- y￨L￨NN￨O￨- ∞￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- vulnerability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network.Researchers￨L￨NNPS￨O￨- have￨L￨VBP￨O￨- mainly￨L￨RB￨O￨- concentrated￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- y￨L￨NN￨O￨- ∞￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- metastable￨L￨JJ￨O￨- state￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- against￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- observation￨L￨NN￨O￨- points￨L￨VBZ￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- find￨L￨VB￨O￨- a￨L￨DT￨O￨- topological￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨A of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- rankings￨L￨NNS￨O￨- in￨L￨IN￨O￨- vulnerability￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- different￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- τ￨L￨NN￨O￨- varies￨L￨VBZ￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- a￨L￨DT￨O￨- topological￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- remains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- nodal￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A probability￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- network￨L￨NN￨O￨- topologies￨L￨NNS￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- τ￨L￨NN￨O￨- varies￨L￨VBZ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- metastable￨L￨JJ￨O￨- state￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- τ￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- non-vaccine￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- NVTs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- weak￨L￨JJ￨O￨- or￨L￨CC￨O￨- strong￨L￨JJ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- competition￨L￨NN￨O￨- and￨L￨CC￨O￨- carriage￨L￨NN￨O￨A incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- estimated￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- prior￨L￨JJ￨O￨- field￨L￨NN￨O￨- study￨L￨NN￨O￨- within￨L￨IN￨O￨- KHDSS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- post-vaccination￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- carriage￨L￨NN￨O￨A and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- five￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- for￨L￨IN￨O￨- validation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- predictions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Nasopharyngeal￨U￨JJ￨MISC￨- swabs￨L￨NNS￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- and￨L￨CC￨O￨- pneumococcal￨L￨JJ￨O￨- serotype-specific￨L￨JJ￨O￨- carriage￨L￨NN￨O￨A ascertained￨L￨VBD￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- pre-vaccination￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- serotype￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- carriage￨L￨NN￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- a￨L￨DT￨DURATION￨- few￨L￨JJ￨DURATION￨- months￨L￨NNS￨DURATION￨- post-vaccination￨L￨JJ￨O￨- vaccine-type￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨- carriage￨L￨NN￨O￨A and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- had￨L￨VBD￨O￨- dropped￨L￨VBN￨O￨- substantially￨L￨RB￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameterized￨L￨VBN￨O￨- with￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- KHDSS￨U￨NNP￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- pre-vaccination￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨A epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- PCV10￨U￨NN￨O￨- in￨L￨IN￨O￨- Kilifi￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Methods￨U￨NNS￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- :￨L￨:￨O￨- Evaluating￨U￨VBG￨O￨- the￨L￨DT￨O￨- precision￨L￨NN￨O￨- of￨L￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- regression￨L￨NN￨O￨A and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- novel￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- Carsten￨U￨NNP￨PERSON￨- Kirkeby￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Tariq￨U￨NNP￨PERSON￨- Halasa￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Maya￨U￨JJ￨PERSON￨- Gussmann1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Nils￨U￨NNP￨PERSON￨- Toft1￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Kaare￨U￨NNP￨O￨- Græsbøll1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 9496￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- Computational￨U￨JJ￨O￨- modelsData￨L￨NN￨O￨- processing￨L￨NN￨O￨- An￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- Correction￨U￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- was￨L￨VBD￨O￨- published￨L￨VBN￨O￨- on￨L￨IN￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- This￨U￨DT￨O￨- article￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- updated￨L￨VBN￨O￨- AbstractPrecise￨U￨NNP￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- critical￨L￨JJ￨O￨- for￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- most￨L￨JJS￨O￨- tested￨L￨VBN￨O￨- scenarios￨L￨NNS￨O￨- these￨L￨DT￨O￨- new￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- perform￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- or￨L￨CC￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- regression￨L￨NN￨O￨A ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- long￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- devise￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- new￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- these￨L￨DT￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- frequently￨L￨RB￨O￨- used￨L￨VBN￨O￨- Poisson￨U￨NNP￨PERSON￨- regression￨L￨NN￨O￨A method￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- easily￨L￨RB￨O￨- biased￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- when￨L￨WRB￨O￨- using￨L￨VBG￨O￨- these￨L￨DT￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- simulation￨L￨NN￨O￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A rate￨L￨NN￨O￨A .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- earliest￨L￨JJS￨O￨- models￨L￨NNS￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- population￨L￨NN￨O￨- being￨L￨VBG￨O￨- studied￨L￨VBN￨O￨- was￨L￨VBD￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- consisted￨L￨VBD￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- class￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- direct￨L￨JJ￨O￨A contact￨L￨NN￨O￨- with￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- recovered￨L￨VBN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- spread￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- again￨L￨RB￨O￨- .￨L￨.￨O￨- +Relaxing￨U￨VBG￨O￨- this￨L￨DT￨O￨- assumption￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- employ￨L￨VB￨O￨- a￨L￨DT￨O￨- stage-progression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- linear￨L￨JJ￨O￨- chain￨L￨NN￨O￨- trick￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- Dengue￨U￨JJ￨O￨- [￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨A of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- substages￨L￨NNS￨O￨- for￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- various￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- being￨L￨VBG￨O￨- analyzed￨L￨VBN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- exact￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨- final￨L￨JJ￨O￨A size￨L￨NN￨O￨A relations￨L￨NNS￨O￨- for￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- ℛ0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- individual￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- wholly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- humans￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- vectors￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- mosquitoes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- final￨L￨JJ￨O￨A size￨L￨NN￨O￨A relation￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- that￨L￨WDT￨O￨- also￨L￨RB￨O￨- included￨L￨VBD￨O￨- direct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- Zika￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- Zhao￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 17￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 18￨L￨CD￨NUMBER￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- susceptible-infected-hibernator-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIHR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- incorporated￨L￨VBD￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- memory￨L￨NN￨O￨- and￨L￨CC￨O￨- forgetting￨L￨VBG￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- Lü￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 19￨L￨CD￨NUMBER￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- strengthening￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- external￨L￨JJ￨O￨- social￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- established￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model.Research￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- opinion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- mutual￨L￨JJ￨O￨- relevance￨L￨NN￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- exchange￨L￨NN￨O￨- since￨L￨IN￨O￨- pieces￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- shared￨L￨VBN￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- people￨L￨NNS￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- thought￨L￨VBN￨O￨- of￨L￨IN￨O￨- like￨L￨IN￨O￨- opinions￨L￨NNS￨O￨A .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- information￨L￨NN￨O￨- entropy￨L￨NN￨O￨A Chao￨U￨NNP￨O￨- Wang1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Zong￨U￨NNP￨PERSON￨- Xuan￨U￨NNP￨PERSON￨- Tan2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ye￨U￨PRP￨PERSON￨- Ye1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Lu￨U￨NN￨PERSON￨- Wang1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Kang￨U￨NNP￨PERSON￨- Hao￨U￨NNP￨PERSON￨- Cheong3￨U￨NNP￨O￨- &￨L￨CC￨O￨- Neng-gang￨U￨NNP￨O￨- Xie1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 9615￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Evolutionary￨U￨NNP￨O￨- theoryInformation￨L￨NN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- computation￨L￨NN￨O￨- AbstractRumor￨U￨NN￨O￨- spreading￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- people￨L￨NNS￨O￨- ’s￨L￨POS￨O￨- lives￨L￨NNS￨O￨- ,￨L￨,￨O￨- distorting￨L￨VBG￨O￨- scientific￨L￨JJ￨O￨- facts￨L￨NNS￨O￨- and￨L￨CC￨O￨- influencing￨L￨VBG￨O￨- political￨L￨JJ￨O￨- opinions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- approaches￨L￨NNS￨O￨- include￨L￨VBP￨O￨- research￨L￨NN￨O￨- by￨L￨IN￨O￨- Martins￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 29￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- applied￨L￨VBD￨O￨- the￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- exchange￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- opinions￨L￨NNS￨O￨A and￨L￨CC￨O￨- Mare￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 31￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- studied￨L￨VBD￨O￨- an￨L￨DT￨O￨- opinion￨L￨NN￨O￨- persuasion￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- game￨L￨NN￨O￨- theory.It￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- distortion￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- distortions￨L￨NNS￨O￨- thus￨L￨RB￨O￨- produced￨L￨VBN￨O￨- are￨L￨VBP￨O￨- vital￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- rumors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- information￨L￨NN￨O￨- entropy￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- considerations￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- memory￨L￨NN￨O￨- ,￨L￨,￨O￨- conformity￨L￨NN￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- subjective￨L￨JJ￨O￨- propensity￨L￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- distortions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- trust￨L￨NN￨O￨- that￨L￨IN￨O￨- people￨L￨NNS￨O￨- place￨L￨VBP￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- K￨U￨NN￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- was￨L￨VBD￨O￨- subsequently￨L￨RB￨O￨- analyzed￨L￨VBN￨O￨- regarding￨L￨VBG￨O￨- average￨L￨JJ￨O￨- information￨L￨NN￨O￨- entropy￨L￨NN￨O￨A ,￨L￨,￨O￨- opinion￨L￨NN￨O￨- fragmentation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- linear￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨A models￨L￨NNS￨O￨A we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- section￨L￨NN￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- formwhere￨L￨NN￨O￨- X￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- state￨L￨NN￨O￨- variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- constant￨L￨JJ￨O￨- inflows￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- M￨U￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- n￨L￨NN￨O￨- ×￨L￨NN￨O￨- n￨L￨NN￨O￨- transition￨L￨NN￨O￨- rate￨L￨NN￨O￨- matrix￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- we￨L￨PRP￨O￨- began￨L￨VBD￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- states￨L￨NNS￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- ,￨L￨,￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- wished￨L￨VBD￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- product￨L￨NN￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- would￨L￨MD￨O￨- expect￨L￨VB￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- infectives￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- region￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- inflow￨L￨NN￨O￨- with￨L￨IN￨O￨- rate￨L￨NN￨O￨- Λ￨U￨NN￨O￨- and￨L￨CC￨O￨- outflow￨L￨NN￨O￨- with￨L￨IN￨O￨- rate￨L￨NN￨O￨- μN￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- immigration-death￨L￨JJ￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- elementary￨L￨JJ￨O￨- ordinary￨L￨JJ￨O￨A differential￨L￨JJ￨O￨A equation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- dN/dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- Λ￨U￨NN￨O￨- −￨L￨NN￨O￨- μN￨L￨NN￨O￨- .￨L￨.￨O￨- )￨L￨-RRB-￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- data￨L￨NNS￨O￨- incompleteness￨L￨NN￨O￨- or￨L￨CC￨O￨- limited￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- measured￨L￨VBN￨O￨- contact￨L￨NN￨O￨- network20￨L￨NN￨O￨- ,21,22,23￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- it￨L￨PRP￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- data-driven￨L￨JJ￨O￨- models￨L￨NNS￨O￨- using￨L￨VBG￨O￨- incomplete￨L￨JJ￨O￨A data20￨L￨NN￨O￨- ,￨L￨,￨O￨- 23,24,25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- importantly￨L￨RB￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- or￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- from￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- information26￨L￨NN￨O￨- ,27,28￨L￨CD￨NUMBER￨- and/or￨L￨CC￨O￨- to￨L￨TO￨O￨- devise￨L￨VB￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- correctly￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- risk￨L￨NN￨O￨- even￨L￨RB￨O￨- from￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- data23￨L￨NN￨O￨- ,￨L￨,￨O￨- 29￨L￨CD￨NUMBER￨- [￨L￨-LRB-￨O￨- Note￨U￨VB￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- wearable￨L￨JJ￨O￨- sensors￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- opposite￨L￨JJ￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- false￨L￨JJ￨O￨- positives￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- propagation￨L￨NN￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- arise￨L￨VB￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- similar￨L￨JJ￨O￨- method￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- work￨L￨VB￨O￨- well￨L￨RB￨O￨- also￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- diaries￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- wearable￨L￨JJ￨O￨- sensors29￨L￨NN￨O￨- :￨L￨:￨O￨- although￨L￨IN￨O￨- not￨L￨RB￨O￨- all￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- diaries￨L￨NNS￨O￨- ,￨L￨,￨O￨- building￨L￨VBG￨O￨- surrogate￨L￨JJ￨O￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- matrix￨L￨NN￨O￨- measured￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- diaries￨L￨NNS￨O￨- and￨L￨CC￨O￨- publicly￨L￨RB￨O￨- available￨L￨JJ￨O￨- statistics￨L￨NNS￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- durations￨L￨NNS￨O￨- made￨L￨VBD￨O￨- it￨L￨PRP￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- correctly￨L￨RB￨O￨A estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- using￨L￨VBG￨O￨- surrogate￨L￨JJ￨O￨- data￨L￨NNS￨O￨- built￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- uniform￨L￨JJ￨O￨- population￨L￨NN￨O￨- sampling￨L￨NN￨O￨- yields￨L￨VBZ￨O￨- an￨L￨DT￨O￨- improvement￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sampled￨L￨VBN￨O￨A data￨L￨NNS￨O￨- but￨L￨CC￨O￨- is￨L￨VBZ￨O￨- strongly￨L￨RB￨O￨- limited￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- underestimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- density￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sampled￨L￨VBN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Uniform￨U￨NN￨O￨- node￨L￨NN￨O￨- sampling￨L￨NN￨O￨A indeed￨L￨RB￨O￨- maintains￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- contact￨L￨NN￨O￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- densities￨L￨NNS￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- structured￨L￨VBN￨O￨- in￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- classes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- school￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- recent￨L￨JJ￨O￨- sparse￨L￨JJ￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SINDy￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- uses￨L￨VBZ￨O￨- sparse￨L￨JJ￨O￨- regression￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- Pareto￨U￨NNP￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- correctly￨L￨RB￨O￨A discover￨L￨VB￨O￨- parsimonious￨L￨JJ￨O￨- governing￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- combinatorially￨L￨RB￨O￨- large￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Schematic￨U￨JJ￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- generation￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- generation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- terms￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- relative￨L￨JJ￨O￨- Akaike￨U￨JJ￨MISC￨- information￨L￨NN￨O￨- criteria￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- AICc￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Section￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- shows￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- down-selected￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- combinatorially￨L￨RB￨O￨- large￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- space￨L￨NN￨O￨- using￨L￨VBG￨O￨- SINDy￨U￨NNP￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- further￨L￨JJ￨O￨- sub-selected￨L￨JJ￨O￨- and￨L￨CC￨O￨- ranked￨L￨VBD￨O￨- using￨L￨VBG￨O￨- information￨L￨NN￨O￨- criteria￨L￨NNS￨O￨A .￨L￨.￨O￨- +As￨U￨IN￨O￨- outlined￨L￨VBN￨O￨- in￨L￨IN￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- AIC￨U￨NNP￨ORGANIZATION￨- scores￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- correctly￨L￨RB￨O￨A infer￨L￨VB￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time-series￨L￨NNS￨O￨- dataset￨L￨VBP￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- combinatorially￨L￨RB￨O￨- large￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- manuscript￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Akaike￨U￨NNP￨O￨- information￨L￨NN￨O￨- criteria￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- AIC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- connected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- SINDy￨U￨NNP￨O￨- architecture￨L￨NN￨O￨- to￨L￨TO￨O￨- hierarchically￨L￨RB￨O￨- rank￨L￨VB￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Pareto￨U￨NNP￨O￨- front￨L￨NN￨O￨- for￨L￨IN￨O￨- automatic￨L￨JJ￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- informative￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Based￨U￨VBD￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- simulating￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- associated￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- cervical￨L￨JJ￨O￨- intraepithelial￨L￨JJ￨O￨- neoplasia￨L￨NN￨O￨- ,￨L￨,￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- genital￨L￨JJ￨O￨- warts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- quadrivalent￨L￨NN￨O￨- and￨L￨CC￨O￨- bivalent￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- .￨L￨.￨O￨- +Kaufmann7￨U￨NN￨O￨- ,￨L￨,￨O￨- Yvonne￨U￨NNP￨PERSON￨- Deleré8￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Bernhard￨U￨NNP￨PERSON￨- Ultsch9￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ole￨U￨JJ￨O￨- Wichmann9￨U￨NN￨O￨- ,￨L￨,￨O￨- Alexander￨U￨NNP￨PERSON￨- Krämer10￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wolfgang￨U￨NNP￨PERSON￨- Greiner1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 15:18￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- papillomavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HPV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A screening￨L￨NN￨O￨- programme￨L￨NN￨O￨- in￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Forecasting￨U￨NN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- subject￨L￨NN￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- forcingPaige￨L￨NNP￨O￨- B.￨U￨NNP￨O￨- Forecasting￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- using￨L￨VBG￨O￨- early￨L￨JJ￨O￨- warning￨L￨NN￨O￨- signals￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- EWS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- in￨L￨IN￨O￨- non-seasonal￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- proposed￨L￨VBD￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- new￨L￨JJ￨O￨- early￨L￨JJ￨O￨- warning￨L￨NN￨O￨- signals￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- wavelet￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assessed￨L￨VBD￨O￨- whether￨L￨IN￨O￨- EWS￨U￨NNP￨O￨- also￨L￨RB￨O￨- anticipate￨L￨VBP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨A in￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Large￨U￨JJ￨O￨- order￨L￨NN￨O￨- fluctuations￨L￨NNS￨O￨A ,￨L￨,￨O￨- switching￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Jason￨U￨NNP￨PERSON￨- Hindes1￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Ira￨U￨NNP￨O￨- B.￨U￨NNP￨O￨- Schwartz1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 10663￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksNonlinear￨L￨NN￨O￨- phenomenaStatistical￨L￨JJ￨O￨- physics￨L￨NN￨O￨- AbstractWe￨U￨NN￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- technique￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- large￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- and￨L￨CC￨O￨- switching￨L￨NN￨O￨- from￨L￨IN￨O￨- internal￨L￨JJ￨O￨- noise￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- switching￨L￨NN￨O￨- between￨L￨IN￨O￨- ordered￨L￨VBN￨O￨- states￨L￨NNS￨O￨- for￨L￨IN￨O￨- networks￨L￨NNS￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- mean-field￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- order-disorder￨L￨JJ￨O￨- kinetics￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- construct￨L￨VBP￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- probable￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- optimal￨L￨JJ￨O￨- path￨L￨NN￨O￨- of￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨A from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- ordered￨L￨VBN￨O￨- state￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- and￨L￨CC￨O￨- synthetic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- quantify￨L￨VBP￨O￨- how￨L￨WRB￨O￨- network￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- scaling￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- rainfall￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨A transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- this￨L￨DT￨O￨- condition￨L￨NN￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- to￨L￨TO￨O￨- lay￨L￨VB￨O￨- their￨L￨PRP$￨O￨- eggs￨L￨NNS￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- mosquito￨L￨NN￨O￨- to￨L￨TO￨O￨- come￨L￨VB￨O￨- into￨L￨IN￨O￨- contact￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨A transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- either￨L￨CC￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- vectors￨L￨NNS￨O￨- or￨L￨CC￨O￨- interrupt￨L￨VB￨O￨- the￨L￨DT￨O￨- human-vector￨L￨JJ￨O￨- contact￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- see￨L￨VB￨O￨- from￨L￨IN￨O￨- Figures￨U￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- rainfall￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- cosine￨L￨JJ￨O￨- function￨L￨NN￨O￨- dependence￨L￨NN￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- Stolwijk￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mosquitoes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Dengue￨U￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨A that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- bite￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- most￨L￨JJS￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- simulate￨L￨VBP￨O￨- curves￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- these￨L￨DT￨O￨- approaches￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- outbreak￨L￨NN￨O￨- curves￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- ODA￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- an￨L￨DT￨O￨- overall￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- trend￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- until￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- quality￨L￨NN￨O￨- forecasting￨L￨NN￨O￨- is￨L￨VBZ￨O￨- achieved￨L￨VBN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- realistic￨L￨JJ￨O￨- averaged￨L￨VBD￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- describing￨L￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- regard￨L￨NN￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- curves￨L￨NNS￨O￨A ,￨L￨,￨O￨- several￨L￨JJ￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- pointed￨L￨VBN￨O￨- out￨L￨RP￨O￨- NumericCitation￨U￨NNP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- signals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- hindered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- shortage￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- enough￨L￨RB￨O￨- clearly-defined￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- signals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- authors￨L￨NNS￨O￨- including￨L￨VBG￨O￨- Buckeridge￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Jackson￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- algorithm￨L￨NN￨O￨- evaluation￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨A curve￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- shape￨L￨NN￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- mean￨L￨NN￨O￨- and￨L￨CC￨O￨- variance￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- outbreak￨L￨NN￨O￨A detection￨L￨NN￨O￨- algorithms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ODA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- Chen￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- review￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- designers￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- laboratory￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- opt￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- suitable￨L￨JJ￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simpler￨L￨JJR￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- build￨L￨VB￨O￨- the￨L￨DT￨O￨- synthetic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨A curve￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- its￨L￨PRP$￨O￨- expected￨L￨JJ￨O￨- shape￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Lessons￨U￨NNPS￨MISC￨- from￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- decade￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- individual-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A :￨L￨:￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2006-2015￨L￨CD￨DURATION￨- )￨L￨-RRB-￨O￨- Lander￨U￨NNP￨O￨- Willem1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Frederik￨U￨NNP￨O￨- Verelst1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Joke￨U￨NNP￨O￨- Bilcke1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Niel￨U￨NNP￨PERSON￨- Hens1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Philippe￨U￨NNP￨PERSON￨- Beutels1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3BMC￨L￨NNP￨O￨- Infectious￨U￨JJ￨O￨- DiseasesBMC￨U￨NN￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 17:612￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Individual-based￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IBMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- useful￨L￨JJ￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- events￨L￨NNS￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- stochasticity￨L￨NN￨O￨- and/or￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- well￨L￨RB￨O￨- established￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- re￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- bioterrorism￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Individual￨U￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- level￨L￨NN￨O￨- is￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- documented￨L￨VBN￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- understood￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- elimination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- vaccine-preventable￨L￨JJ￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- polio￨L￨NNP￨O￨- ,￨L￨,￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- stochasticity￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extracted￨L￨VBD￨O￨- detailed￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- features￨L￨NNS￨O￨- from￨L￨IN￨O￨- papers￨L￨NNS￨O￨- on￨L￨IN￨O￨- established￨L￨JJ￨O￨- vaccine-preventable￨L￨JJ￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- full-text￨L￨JJ￨O￨- screening￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- identified￨L￨VBD￨O￨- 698￨L￨CD￨NUMBER￨- papers￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- applied￨L￨VBD￨O￨- an￨L￨DT￨O￨- IBM￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- listed￨L￨VBN￨O￨- these￨L￨DT￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- reference￨L￨NN￨O￨- database￨L￨NN￨O￨- ,￨L￨,￨O￨- describing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- general￨L￨JJ￨TITLE￨- characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- interacting￨L￨VBG￨O￨- components￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- circles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- multiple￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- shaded￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- surrounding￨L￨VBG￨O￨- the￨L￨DT￨O￨- components￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- above-mentioned￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- also￨L￨RB￨O￨- face￨L￨VBP￨O￨- with￨L￨IN￨O￨- new￨L￨JJ￨O￨- opportunities￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- data-centric￨L￨JJ￨O￨- era￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- enabled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- confluence￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- various￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- analytical￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- in￨L￨IN￨O￨- data￨L￨NNS￨O￨- science￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- interacting￨L￨VBG￨O￨- and￨L￨CC￨O￨- coupling￨L￨NN￨O￨- relationships￨L￨NNS￨O￨- among￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- impact￨L￨NN￨O￨- factors￨L￨NNS￨O￨A have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- temporally￨L￨RB￨O￨- ,￨L￨,￨O￨- spatially￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- socially￨L￨RB￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- exhibiting￨L￨VBG￨O￨- systems￨L￨NNS￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- feedback￨L￨NN￨O￨- ,￨L￨,￨O￨- saturation￨L￨NN￨O￨- ,￨L￨,￨O￨- bifurcation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- chaos￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- make￨L￨VBP￨O￨- it￨L￨PRP￨O￨- hardly￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- utilize￨L￨VB￨O￨- the￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- comprehensive￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- snail￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- observed￨L￨VBN￨O￨- to￨L￨TO￨O￨- follow￨L￨VB￨O￨- seasonal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Later￨U￨RBR￨O￨- works￨L￨VBZ￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- played￨L￨VBN￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- water￨L￨NN￨O￨A sources￨L￨NNS￨O￨- and￨L￨CC￨O￨- individual￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- site-specific￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- features￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- local-scale￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- coupling￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- schistosomiasis￨L￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- emphasis￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- integration￨L￨NN￨O￨- of￨L￨IN￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- water￨L￨NN￨O￨A bodies￨L￨NNS￨O￨- may￨L￨MD￨O￨- represent￨L￨VB￨O￨- habitats￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- quality￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- snail￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- schistosomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- thus￨L￨RB￨O￨- be￨L￨VB￨O￨- relatively￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- snail￨L￨NN￨O￨- population￨L￨NN￨O￨- abundance￨L￨NN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- e.g￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- communities￨L￨NNS￨O￨- with￨L￨IN￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- several￨L￨JJ￨O￨- water￨L￨NN￨O￨A sources￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- risk￨L￨NN￨O￨- group￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- endowed￨L￨VBN￨O￨- with￨L￨IN￨O￨- differential￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- specific￨L￨JJ￨O￨- water-contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- schistosomiasis￨L￨NN￨O￨- transmission￨L￨NN￨O￨- also￨L￨RB￨O￨- requires￨L￨VBZ￨O￨- an￨L￨DT￨O￨- account￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- preferences￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- water￨L￨NN￨O￨A contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g￨L￨FW￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- 214￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- clinical￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- 438,000￨L￨CD￨NUMBER￨- malaria-attributable￨L￨JJ￨O￨- deaths￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- occurred￨L￨VBD￨O￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- 88￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- deaths￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A a￨L￨DT￨O￨- leading￨L￨VBG￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- problem￨L￨NN￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- burden￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- geospatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- costing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- optimization￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- budgeted￨L￨VBN￨O￨- and￨L￨CC￨O￨- projected￨L￨VBN￨O￨- funds￨L￨NNS￨O￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A intervention￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Allocative￨U￨JJ￨O￨- efficiency￨L￨NN￨O￨- gains￨L￨NNS￨O￨- could￨L￨MD￨O￨- avert￨L￨VB￨O￨- approximately￨L￨RB￨O￨- 84,000￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- or￨L￨CC￨O￨- 15.7￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Nigeria￨U￨NNP￨COUNTRY￨- over￨L￨IN￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Wilson1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 16:368￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- high￨L￨JJ￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- limited￨L￨JJ￨O￨- funding￨L￨NN￨O￨- means￨L￨VBZ￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- necessity￨L￨NN￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- allocative￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Importantly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- modulating￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- reversion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- strongest￨L￨JJS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- biologically￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- case￨L￨NN￨O￨- when￨L￨WRB￨O￨- fitness￨L￨NN￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- in￨L￨IN￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- are￨L￨VBP￨O￨- small￨L￨JJ￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- treatment￨L￨NN￨O￨- guidelines￨L￨NNS￨O￨- typically￨L￨RB￨O￨- occur￨L￨VBP￨O￨- much￨L￨RB￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨A strain￨L￨NN￨O￨- has￨L￨VBZ￨O￨- fixed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- population￨L￨NN￨O￨- across￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- expect￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- crossing￨L￨VBG￨O￨- of￨L￨IN￨O￨- fitness￨L￨NN￨O￨- valleys￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- not￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- reversion￨L￨NN￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- sensitivity￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- study￨L￨NN￨O￨- reveals￨L￨VBZ￨O￨- that￨L￨IN￨O￨- large￨L￨JJ￨O￨- fitness￨L￨NN￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- non-trivial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- reversion￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- once￨L￨RB￨DATE￨- treatment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stopped￨L￨VBN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- resistant￨L￨JJ￨O￨A strain￨L￨NN￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- fitness￨L￨NN￨O￨- deficit￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- impacts￨L￨NNS￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- manner￨L￨NN￨O￨- largely￨L￨RB￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- de￨L￨FW￨O￨- novo￨L￨FW￨O￨- emergence￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 40￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 42￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- wild-type￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- strains￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- simultaneously￨L￨RB￨O￨- spreading￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Published￨U￨VBN￨O￨- literature￨L￨NN￨O￨- in￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- categories￨L￨NNS￨O￨- are￨L￨VBP￨O￨- reviewed￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- identifying￨L￨VBG￨O￨- non-traditional￨L￨JJ￨O￨- but￨L￨CC￨O￨- critical￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- for￨L￨IN￨O￨- VL￨U￨NNP￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- resource￨L￨NN￨O￨- limited￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- Leishmaniasis￨U￨NNP￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- related￨L￨JJ￨O￨- vector￨L￨NN￨O￨A borne￨L￨VBD￨O￨A infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- identified￨L￨VBN￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- its￨L￨PRP$￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Challenges￨U￨NNS￨MISC￨- in￨L￨IN￨O￨- modeling￨L￨NN￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- neglected￨L￨VBN￨O￨- tropical￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- visceral￨L￨JJ￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- resource￨L￨NN￨O￨- limited￨L￨JJ￨O￨- settingsSwati￨L￨NN￨O￨- DebRoy1￨U￨NN￨O￨- ,￨L￨,￨O￨- Olivia￨U￨JJ￨O￨- Prosper2￨U￨NN￨O￨- ,￨L￨,￨O￨- Austin￨U￨NNP￨CITY￨- Mishoe1￨U￨NNP￨O￨- and￨L￨CC￨O￨- Anuj￨U￨NNP￨PERSON￨- Mubayi3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 14:10￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Objectives￨U￨NNS￨O￨- Neglected￨U￨VBN￨O￨- tropical￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- NTD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- account￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- control￨L￨NN￨O￨- faces￨L￨VBZ￨O￨- several￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨A including￨L￨VBG￨O￨- diminishing￨L￨VBG￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- financial￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- for￨L￨IN￨O￨- those￨L￨DT￨O￨- distressed￨L￨JJ￨O￨- from￨L￨IN￨O￨- such￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- reviews￨L￨VBZ￨O￨- literature￨L￨NN￨O￨- on￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- collects￨L￨VBZ￨O￨- challenges￨L￨NNS￨O￨A and￨L￨CC￨O￨- successes￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- recommends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- MDA￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- elimination￨L￨NN￨O￨A of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- approaching￨L￨VBG￨O￨- interruption￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- good￨L￨JJ￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- effective￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- re-introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- models￨L￨NNS￨O￨- range￨L￨VBP￨O￨- from￨L￨IN￨O￨- simple￨L￨JJ￨O￨- conceptual￨L￨JJ￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- distinguishing￨L￨VBG￨O￨- between￨L￨IN￨O￨- infection-versus￨L￨JJ￨O￨- vaccination-induced￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- inclusion￨L￨NN￨O￨A of￨L￨IN￨O￨- primary￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- failure￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- leaky￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- age-dependent￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +Currently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- variable￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨A of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- has￨L￨VBZ￨O￨- had￨L￨VBN￨O￨- little￨L￨JJ￨O￨- attention￨L￨NN￨O￨- in￨L￨IN￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- cost-effectiveness￨L￨NN￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- annual￨L￨JJ￨SET￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨A of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- causes￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Importantly￨U￨RB￨O￨- ,￨L￨,￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨A of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- variable￨L￨JJ￨O￨- duration￨L￨NN￨O￨A of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- resistant￨L￨JJ￨O￨A and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- frog￨L￨NN￨O￨- species￨L￨NNS￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fungal￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- Batrachochytridium￨U￨NN￨O￨- dendrobatidis￨L￨VBZ￨O￨- upregulated￨L￨VBN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- experienced￨L￨VBD￨O￨- different￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outcomes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Characterizing￨U￨VBG￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- of￨L￨IN￨O￨- tolerant￨L￨JJ￨O￨- or￨L￨CC￨O￨- resistant￨L￨JJ￨O￨A vertebrate￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- fungal￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- identify￨L￨VB￨O￨- adaptive￨L￨JJ￨O￨- genes￨L￨NNS￨O￨- or￨L￨CC￨O￨- processes￨L￨NNS￨O￨- linked￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduced￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- or￨L￨CC￨O￨- occurrence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- can￨L￨MD￨O￨- then￨L￨RB￨O￨- inform￨L￨VB￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- species￨L￨NNS￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- species￨L￨NNS￨O￨- recently￨L￨RB￨DATE￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- insufficient￨L￨JJ￨O￨- time￨L￨NN￨O￨- has￨L￨VBZ￨O￨- elapsed￨L￨VBN￨O￨- for￨L￨IN￨O￨- selection￨L￨NN￨O￨- for￨L￨IN￨O￨- tolerance￨L￨NN￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- pathways￨L￨NNS￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- tolerant￨L￨JJ￨O￨- ,￨L￨,￨O￨- resistant￨L￨JJ￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- can￨L￨MD￨O￨- differ￨L￨VB￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- molecular￨L￨JJ￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +Few￨U￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- fungal￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- vertebrate￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- understood￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- often￨L￨RB￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- species￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- network￨L￨NN￨O￨- immunization￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- important￨L￨JJ￨O￨- in￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- for￨L￨IN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- links￨L￨NNS￨O￨A are￨L￨VBP￨O￨- evident￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- livestock￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- one￨L￨CD￨NUMBER￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- farm￨L￨NN￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- are￨L￨VBP￨O￨- connections￨L￨NNS￨O￨- by￨L￨IN￨O￨- transport￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- thus￨L￨RB￨O￨- three￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- an￨L￨DT￨O￨- endeavor￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- itself￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- as￨L￨IN￨O￨- our￨L￨PRP$￨O￨- base￨L￨NN￨O￨- unit￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- gathering￨L￨VBG￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- cinfo￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- units￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- person￨L￨NN￨O￨- getting￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- cvacc￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- carry￨L￨VB￨O￨- out￨L￨RP￨O￨- a￨L￨DT￨O￨- targeted￨L￨VBN￨O￨A vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- would￨L￨MD￨O￨- first￨L￨RB￨ORDINAL￨- need￨L￨VB￨O￨- to￨L￨TO￨O￨- gather￨L￨VB￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- use￨L￨VB￨O￨- this￨L￨DT￨O￨- information￨L￨NN￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- otherwise￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- strategy￨L￨NN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- works￨L￨VBZ￨O￨- by￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨A all￨L￨DT￨O￨- network￨L￨NN￨O￨- neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- person￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- premises￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- —￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- most￨L￨RBS￨O￨- active￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- being￨L￨VBG￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- exploit￨L￨VB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- targeted￨L￨VBN￨O￨A vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- non-rodent￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- cats￨L￨NNS￨O￨- and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- antibody-mediated￨L￨JJ￨O￨- immune￨L￨JJ￨O￨A responses￨L￨NNS￨O￨A to￨L￨TO￨O￨- persistent￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- appear￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- common￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- least￨L￨JJS￨O￨- twelve￨L￨CD￨NUMBER￨- known￨L￨JJ￨O￨- species￨L￨NNS￨O￨- or￨L￨CC￨O￨- subspecies￨L￨NNS￨O￨- of￨L￨IN￨O￨- Bartonella￨U￨NNP￨PERSON￨- bacteria￨L￨NNS￨O￨- are￨L￨VBP￨O￨- now￨L￨RB￨DATE￨- recognized￨L￨VBN￨O￨A zoonotic￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- B.￨U￨NNP￨PERSON￨- Among￨U￨IN￨PERSON￨- Bartonella￨U￨NNP￨PERSON￨- spp.￨L￨NNP￨O￨- ,￨L￨,￨O￨- B.￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- B.￨U￨NNP￨O￨- antigens￨L￨NNS￨O￨- in￨L￨IN￨O￨- rodent￨L￨JJ￨O￨- serum￨L￨NN￨O￨- samples￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- but￨L￨CC￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- Bartonella￨U￨NNP￨PERSON￨- spp￨L￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- projected￨L￨VBN￨O￨A age-specific￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- POLYMOD￨U￨NN￨LOCATION￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- validated￨L￨VBN￨O￨- approximations￨L￨NNS￨O￨- to￨L￨TO￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- when￨L￨WRB￨O￨- directly￨L￨RB￨O￨- measured￨L￨VBN￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- POLYMOD￨U￨NN￨O￨- survey￨L￨NN￨O￨- collected￨L￨VBN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- contact￨L￨NN￨O￨- occurred￨L￨VBD￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- refined￨L￨JJ￨O￨- projection￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- household￨L￨NN￨O￨- structures￨L￨NNS￨O￨- ,￨L￨,￨O￨- labor-force￨L￨JJ￨O￨- participation￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- enrolment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- separately￨L￨RB￨O￨- projecting￨L￨VBG￨O￨- contacts￨L￨NNS￨O￨A in￨L￨IN￨O￨- different￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- tailor￨L￨VB￨O￨- the￨L￨DT￨O￨- POLYMOD￨U￨NN￨O￨- estimates￨L￨VBZ￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- setting￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- to￨L￨TO￨O￨- adjust￨L￨VB￨O￨- them￨L￨PRP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- age-profiles￨L￨NNS￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- country￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- eight￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- EU￨U￨NNP￨LOCATION￨- that￨L￨WDT￨O￨- contributed￨L￨VBD￨O￨- to￨L￨TO￨O￨- POLYMOD￨U￨NN￨O￨- ,￨L￨,￨O￨- inflating￨L￨VBG￨O￨- the￨L￨DT￨O￨- projected￨L￨VBN￨O￨A number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- younger￨L￨JJR￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- country￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- young￨L￨JJ￨O￨- age-profile￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- concurrently￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- projected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- elderly￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨A structure￨L￨NN￨O￨A of￨L￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- socioeconomic￨L￨JJ￨O￨- development￨L￨NN￨O￨- ,￨L￨,￨O￨- family￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- transition￨L￨NN￨O￨- differ￨L￨VBP￨O￨- substantially￨L￨RB￨O￨- and￨L￨CC￨O￨- contact￨L￨VB￨O￨- patterns￨L￨NNS￨O￨- concomitantly￨L￨RB￨O￨- vary￨L￨VBP￨O￨- across￨L￨IN￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- measured￨L￨VBD￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨A structure￨L￨NN￨O￨A of￨L￨IN￨O￨- ~￨L￨NN￨O￨- 100￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- contacts￨L￨NNS￨O￨- across￨L￨IN￨O￨- eight￨L￨CD￨NUMBER￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- using￨L￨VBG￨O￨- paper￨L￨NN￨O￨- diaries￨L￨NNS￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- POLYMOD￨U￨NN￨O￨- project￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- a￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- suggest￨L￨VBP￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- transmission￨L￨NN￨O￨- have￨L￨VBP￨O￨- emerged￨L￨VBN￨O￨- as￨L￨RB￨O￨- important￨L￨JJ￨O￨- tool￨L￨NN￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨- classification￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ICD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- ICD-10￨U￨NN￨MISC￨- code￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- process￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- phases￨L￨NNS￨O￨- :￨L￨:￨O￨- acute￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- period￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- B23￨U￨NN￨O￨- .0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Z20￨U￨NN￨O￨- .6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Z21￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- typical￨L￨JJ￨O￨- of￨L￨IN￨O￨- AIDS￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- B20￨U￨NN￨O￨- ~￨L￨NN￨O￨- B24￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- modify￨L￨VBP￨O￨- the￨L￨DT￨O￨- SEI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- patients￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- stage￨L￨NN￨O￨- were￨L￨VBD￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- apply￨L￨VB￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- time￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- Global￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Observatory￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- GHO￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- World￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- Organization￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- almost￨L￨RB￨O￨- 78￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨A people￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- about￨L￨IN￨O￨- 39￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- have￨L￨VBP￨O￨- died￨L￨VBN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- about￨L￨RB￨O￨- 35.0￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- were￨L￨VBD￨O￨- living￨L￨VBG￨O￨- with￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- and￨L￨CC￨O￨- 1.5￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- died￨L￨VBD￨O￨- of￨L￨IN￨O￨- AIDS-related￨U￨JJ￨O￨- illnesses￨L￨NNS￨O￨- worldwide￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- direct￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- adverse￨L￨JJ￨O￨- health￨L￨NN￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- toxins￨L￨NNS￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- issue￨L￨NN￨O￨- of￨L￨IN￨O￨- combating￨L￨VBG￨O￨- the￨L￨DT￨O￨- concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- AFs￨U￨NNS￨O￨- in￨L￨IN￨O￨- foods￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- difficult￨L￨JJ￨O￨- task￨L￨NN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- cloud￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainties￨L￨NNS￨O￨- which￨L￨WDT￨O￨- might￨L￨MD￨O￨- arise￨L￨VB￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- exposure￨L￨NN￨O￨- ,￨L￨,￨O￨- constrains￨L￨VBZ￨O￨- inprocuring￨L￨VBG￨O￨- representative￨L￨JJ￨TITLE￨- samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- food￨L￨NN￨O￨A from￨L￨IN￨O￨- subsistence￨L￨NN￨O￨- farmers￨L￨NNS￨O￨- ,￨L￨,￨O￨- multiple￨L￨JJ￨O￨- vulnerable￨L￨JJ￨O￨- crops￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- relevant￨L￨JJ￨O￨- confounding￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- mask￨L￨NN￨O￨- or￨L￨CC￨O￨- otherwise￨L￨RB￨O￨- obscure￨L￨JJ￨O￨- any￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- putative￨L￨JJ￨O￨- causative￨L￨JJ￨O￨- agent￨L￨NN￨O￨- within￨L￨IN￨O￨- food￨L￨NN￨O￨- supply￨L￨NN￨O￨- chain￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- AFs￨U￨NNS￨O￨- contamination￨L￨NN￨O￨A is￨L￨VBZ￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- Aspergillus￨U￨JJ￨O￨- species￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- ,￨L￨,￨O￨- farming￨L￨VBG￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- handling￨L￨VBG￨O￨- and￨L￨CC￨O￨- storage￨L￨NN￨O￨- practices￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- several￨L￨JJ￨O￨- other￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- toxins￨L￨NNS￨O￨- humans￨L￨NNS￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- make-up￨L￨NN￨O￨- ,￨L￨,￨O￨- drying￨L￨VBG￨O￨- or￨L￨CC￨O￨- evapo-transpiration￨L￨NN￨O￨- ,￨L￨,￨O￨- soil￨L￨NN￨O￨- nature￨L￨NN￨O￨- ,￨L￨,￨O￨- moisture￨L￨NN￨O￨- deficit￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- insect￨L￨JJ￨O￨- infestations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- numerous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- conducted￨L￨VBN￨O￨- showing￨L￨VBG￨O￨- toxicological￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- contamination￨L￨NN￨O￨A and￨L￨CC￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- AFs￨U￨NNS￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- mycotoxins￨L￨NNS￨O￨- ,￨L￨,￨O￨- aflatoxins￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- AFs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- principal￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- challenging￨L￨JJ￨O￨- in￨L￨IN￨O￨- foods￨L￨NNS￨O￨- and￨L￨CC￨O￨- animal￨L￨NN￨O￨- feeds￨L￨VBZ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- associated￨L￨VBN￨O￨- toxicity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- mutagenicity￨L￨NN￨O￨- ,￨L￨,￨O￨- carcinogenicity￨L￨NN￨O￨- and￨L￨CC￨O￨- teratogenicity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- heat￨L￨NN￨O￨- resistance￨L￨NN￨O￨- during￨L￨IN￨O￨- food￨L￨NN￨O￨A processing￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- probable￨L￨JJ￨O￨- intermediary￨L￨JJ￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- transmitted￨L￨VBD￨O￨- proto-HSV2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- henceforth￨L￨NN￨O￨- HSV2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- anc-chimps￨L￨NNS￨O￨- to￨L￨TO￨O￨- modern￨L￨JJ￨O￨A humans￨L￨NNS￨O￨- involves￨L￨VBZ￨O￨- four￨L￨CD￨NUMBER￨- steps￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- acquisition￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- involves￨L￨VBZ￨O￨- collecting￨L￨VBG￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- fossil￨L￨NN￨O￨- records￨L￨NNS￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- intermediary￨L￨JJ￨O￨- hominins￨L￨NNS￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- geographical￨L￨JJ￨O￨- range￨L￨NN￨O￨- and￨L￨CC￨O￨- time-period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- tropical￨L￨JJ￨O￨- rainforest￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- generation￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- paths￨L￨NNS￨O￨- of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- from￨L￨IN￨O￨- anc-chimps￨L￨NNS￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- through￨L￨IN￨O￨- different￨L￨JJ￨O￨- hominins￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- created￨L￨VBN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- probabilistic￨L￨JJ￨O￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- involves￨L￨VBZ￨O￨- assigning￨L￨VBG￨O￨- weights￨L￨NNS￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- paths￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- network￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- optimal￨L￨JJ￨O￨- path￨L￨NN￨O￨- traversal￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- evaluates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- path￨L￨NN￨O￨- from￨L￨IN￨O￨- anc-chimps￨L￨NNS￨O￨- to￨L￨TO￨O￨- modern￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- weights￨L￨NNS￨O￨- assigned￨L￨VBN￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- hypothesise￨L￨VBP￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- combining￨L￨VBG￨O￨- fossil￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- when￨L￨WRB￨O￨- and￨L￨CC￨O￨- where￨L￨WRB￨O￨- different￨L￨JJ￨O￨- hominin￨L￨NN￨O￨- species￨L￨NNS￨O￨- were￨L￨VBD￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- geographical￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- modern￨L￨JJ￨O￨A chimpanzees￨L￨NNS￨O￨- and￨L￨CC￨O￨- bonobos￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- reconstructed￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- tropical￨L￨JJ￨O￨- rainforest￨L￨NN￨O￨- habitat￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- proxy￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- chimpanzee/bonobo￨L￨NN￨O￨- ancestor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- anc-chimps￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- it￨L￨PRP￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- statistically￨L￨RB￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- facilitated￨L￨VBD￨O￨- the￨L￨DT￨O￨- host-switch￨L￨NN￨O￨- of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- modern￨L￨JJ￨O￨- human￨L￨JJ￨O￨- lineage￨L￨NN￨O￨- defined￨L￨VBN￨O￨- here￨L￨RB￨O￨- as￨L￨IN￨O￨- beginning￨L￨VBG￨O￨- with￨L￨IN￨O￨- Homo￨U￨NN￨PERSON￨- erectus￨L￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- paths￨L￨NNS￨O￨A of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- from￨L￨IN￨O￨- anc-chimps￨L￨NNS￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- through￨L￨IN￨O￨- different￨L￨JJ￨O￨- hominins￨L￨NNS￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- directed￨L￨VBN￨O￨- acyclic￨L￨NN￨O￨- graph￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DAG￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- G￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- comprising￨L￨VBG￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- potential￨L￨JJ￨O￨- intermediary￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- connecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- species￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figs￨U￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- establish￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- probable￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- path￨L￨NN￨O￨- of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- from￨L￨IN￨O￨- anc-chimps￨L￨NNS￨O￨- to￨L￨TO￨O￨- modern￨L￨JJ￨O￨A humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- potential￨L￨JJ￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- intermediary￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- predicts￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- host-switch￨L￨NN￨O￨- of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- occurred￨L￨VBD￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨A anc-chimps￨L￨NNS￨O￨- -￨L￨:￨O￨- >￨L￨JJR￨O￨- P.boisei￨U￨NN￨O￨- -￨L￨:￨O￨- >￨L￨JJR￨O￨- H.erectus￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- highlighted￨L￨VBN￨O￨- in￨L￨IN￨O￨- bold￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- has￨L￨VBZ￨O￨- tried￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- causative￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- for￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- successive￨L￨JJ￨O￨A years￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +Cases￨U￨NNS￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- with￨L￨IN￨O￨- classical￨L￨JJ￨O￨- presentation￨L￨NN￨O￨- and￨L￨CC￨O￨- having￨L￨VBG￨O￨- active￨L￨JJ￨O￨- oral￨L￨JJ￨O￨- lesions￨L￨NNS￨O￨- were￨L￨VBD￨O￨- selected￨L￨VBN￨O￨- during￨L￨IN￨O￨- monsoon￨L￨NN￨O￨- and￨L￨CC￨O￨- postmonsoon￨L￨NN￨O￨- session￨L￨NN￨O￨- between￨L￨IN￨O￨- July￨U￨NNP￨DATE￨- and￨L￨CC￨DATE￨- November￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- successive￨L￨JJ￨O￨A years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 2013￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2014￨L￨CD￨DATE￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- document￨L￨VB￨O￨- clinicoepidemiological￨L￨JJ￨O￨- profile￨L￨NN￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- and￨L￨CC￨O￨- molecular￨L￨JJ￨O￨A detection￨L￨NN￨O￨- of￨L￨IN￨O￨- circulating￨L￨VBG￨O￨- enteroviruses￨L￨NNS￨O￨- causing￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- Virological￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨A of￨L￨IN￨O￨- HFMD￨U￨NN￨ORGANIZATION￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- infrequently￨L￨RB￨O￨- done￨L￨VBN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- HFMD￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- enteroviral￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- caused￨L￨VBD￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨A by￨L￨IN￨O￨- enterovirus￨L￨NN￨O￨- 71￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- EV71￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- coxsackievirus￨L￨NN￨O￨- A16￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- CVA16￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨A techniques￨L￨NNS￨O￨- allow￨L￨VBP￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- shedding￨L￨VBG￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- predicting￨L￨VBG￨O￨- future￨L￨JJ￨DATE￨- trends￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Access￨U￨NN￨O￨- to￨L￨TO￨O￨- big￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- unanswered￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- enable￨L￨VBP￨O￨- novel￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- connect￨L￨VB￨O￨- within-host￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨A level￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- between-host￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Immunoepidemiological￨U￨JJ￨O￨- models￨L￨NNS￨O￨- factor￨L￨IN￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨A level￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Within-host￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨A level￨L￨NN￨O￨A study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- target￨L￨NN￨O￨- immune￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- —￨L￨:￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- macrophages￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- dendritic￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- explicit￨L￨JJ￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨A mechanism￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- process￨L￨NN￨O￨- models￨L￨NNS￨O￨- ideal￨L￨JJ￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- population-level￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- arise￨L￨VBP￨O￨- from￨L￨IN￨O￨- individual-level￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- ways￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- anticipate￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- today￨L￨NN￨DATE￨- feed￨L￨NN￨O￨- into￨L￨IN￨O￨- generating￨L￨VBG￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- tomorrow￨L￨NN￨DATE￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ABMs￨U￨NNS￨O￨- ;￨L￨:￨O￨- also￨L￨RB￨O￨- referred￨L￨VBN￨O￨A to￨L￨TO￨O￨- as￨L￨IN￨O￨- individual-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- modelled￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- plus￨L￨CC￨O￨- all￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- progresses￨L￨VBZ￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- rules￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- becoming￨L￨VBG￨O￨- increasingly￨L￨RB￨O￨A popular￨L￨JJ￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- drive￨L￨VBP￨O￨- the￨L￨DT￨O￨- host-to-host￨L￨JJ￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- within-host￨L￨NN￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- and￨L￨CC￨O￨- applied￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- these￨L￨DT￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- ,￨L￨,￨O￨- often￨L￨RB￨O￨- referred￨L￨VBN￨O￨A to￨L￨TO￨O￨- as￨L￨IN￨O￨- mechanistic￨L￨JJ￨O￨- or￨L￨CC￨O￨- process￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- increasingly￨L￨RB￨O￨- common￨L￨JJ￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ecology￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- in￨L￨IN￨O￨- veterinary￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +Early￨U￨RB￨O￨- epidemiological￨L￨JJ￨O￨- process￨L￨NN￨O￨- models￨L￨NNS￨O￨- typically￨L￨RB￨O￨- took￨L￨VBD￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨A models￨L￨NNS￨O￨A representing￨L￨VBG￨O￨- susceptible-infectious-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- susceptible-infectious-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 03￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- geo-computational￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- exploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- progression￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨A Wei-Chien-Benny￨U￨NNP￨O￨- Chin￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Tzai-Hung￨U￨JJ￨O￨- Wen1￨U￨NN￨O￨- ,￨L￨,￨O￨- Clive￨U￨NNP￨PERSON￨- E.￨U￨NNP￨PERSON￨- Sabel2￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- I-Hsiang￨U￨NNP￨O￨- Wang1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 12565￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Environmental￨U￨NNP￨O￨- social￨L￨JJ￨O￨- sciencesInfectious￨L￨JJ￨O￨- diseasesScientific￨L￨JJ￨O￨- data￨L￨NNS￨O￨- AbstractA￨U￨NN￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- linked￨L￨VBN￨O￨- events￨L￨NNS￨O￨- through￨L￨IN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- data￨L￨NN￨O￨- exploration￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- TrAcking￨U￨VBG￨O￨- Progression￨U￨NN￨O￨- In￨U￨IN￨O￨- Time￨U￨NNP￨O￨- And￨U￨CC￨O￨- Space￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- TaPiTaS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- diffusion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨- load￨L￨NN￨O￨- of￨L￨IN￨O￨- respiratory￨L￨JJ￨O￨- material￨L￨NN￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- with￨L￨IN￨O￨- MDR/XDR-TB￨U￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- differ￨L￨VB￨O￨- from￨L￨IN￨O￨- that￨L￨DT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- drug￨L￨NN￨O￨- sensitivity￨L￨NN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- the￨L￨DT￨O￨- viability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- anti-TB￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- relatively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- uninfected￨L￨JJ￨O￨- ,￨L￨,￨O￨- latent￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- active￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- persons￨L￨NNS￨O￨- and￨L￨CC￨O￨- more￨L￨JJR￨O￨- detailed￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- subdivisions￨L￨NNS￨O￨- to￨L￨TO￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- :￨L￨:￨O￨- drug￨L￨NN￨O￨A sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- drug￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- allowing￨L￨VBG￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- different￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 3,5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Tuberculosis￨U￨NN￨CAUSE_OF_DEATH￨- remains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- main￨L￨JJ￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- multi-and￨L￨JJ￨O￨- extensively￨L￨RB￨O￨- drug￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- MDR￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- XDR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Mycobacterium￨U￨NN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- MbT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨A development￨L￨NN￨O￨- and￨L￨CC￨O￨- expansion￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- helpful￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- diagnosis￨L￨NN￨O￨- and￨L￨CC￨O￨- prognoses￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- treatment￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population-level￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- review￨L￨NN￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- an￨L￨DT￨O￨- approach￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- fitting￨L￨JJ￨O￨- by￨L￨IN￨O￨- logistic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- without￨L￨IN￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- detailed￨L￨JJ￨O￨A mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Article￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Control￨U￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- swine￨L￨NNS￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨A farms￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- modeling￨L￨NN￨O￨- assessmentCharlie￨L￨NN￨O￨- Cador1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Mathieu￨U￨NNP￨PERSON￨- Andraud1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Lander￨U￨NNP￨O￨- Willem2￨U￨NN￨O￨- and￨L￨CC￨O￨- Nicolas￨U￨NNP￨PERSON￨- Rose1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 48:58￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractSwine￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- viruses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- swIAVs￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- endemically￨L￨RB￨O￨- in￨L￨IN￨O￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨- farms￨L￨NNS￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- repeated￨L￨VBN￨O￨- swine￨L￨NNS￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- successive￨L￨JJ￨O￨- batches￨L￨NNS￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- mostly￨L￨RB￨O￨- around￨L￨IN￨O￨- 8￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- specific￨L￨JJ￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨A farms￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- animals￨L￨NNS￨O￨- at￨L￨IN￨O￨- infection-time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- co-circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- subtypes￨L￨NNS￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- consecutive￨L￨JJ￨O￨- or￨L￨CC￨O￨- concomitant￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- evidenced￨L￨VBN￨O￨- as￨L￨IN￨O￨- factors￨L￨NNS￨O￨- favouring￨L￨VBG￨O￨- swIAV￨L￨NN￨O￨- persistence￨L￨NN￨O￨- within￨L￨IN￨O￨- herds￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- some￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- batch-to-batch￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- beneficial￨L￨JJ￨O￨- effect￨L￨NN￨O￨- in￨L￨IN￨O￨- breeding￨L￨VBG￨O￨- sows￨L￨VBZ￨O￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- swIAVs￨L￨NNS￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨- ,￨L￨,￨O￨- none￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- achieved￨L￨VBD￨O￨- swIAVs￨L￨NNS￨O￨- fade-out￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨A herd￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- co-circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- swIAVs￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨A herd￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- reassortant￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- generation￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- co-infection￨L￨JJ￨O￨- events￨L￨NNS￨O￨- .￨L￨.￨O￨- +Zika￨U￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Flavivirus￨U￨NNP￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- dengue￨L￨VB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- primarily￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- bites￨L￨VBZ￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- female￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Aedes￨U￨NNP￨O￨- genus￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Lee￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Pietz￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- zika￨L￨NN￨O￨A transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- vector-host￨L￨JJ￨O￨- structure￨L￨NN￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- in￨L￨IN￨O￨- vector￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- presented￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- zika￨L￨NN￨O￨A virus￨L￨NN￨O￨- with￨L￨IN￨O￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- Sun￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- developed￨L￨VBD￨O￨A a￨L￨DT￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2013￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- H1N1￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- increased￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- short-term￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- waning￨L￨VBG￨O￨- after￨L￨IN￨O￨- jointly￨L￨RB￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- serological￨L￨JJ￨O￨A data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- widespread￨L￨JJ￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- serological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- many￨L￨JJ￨O￨- recent￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- serosurveillance￨L￨NN￨O￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- current￨L￨JJ￨DATE￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- thus￨L￨RB￨O￨- far￨L￨RB￨O￨- not￨L￨RB￨O￨- explicitly￨L￨RB￨O￨- represented￨L￨VBN￨O￨- individual￨L￨JJ￨O￨- antibody￨L￨NN￨O￨A titre￨L￨NN￨O￨- levels￨L￨NNS￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- correspondence￨L￨NN￨O￨- with￨L￨IN￨O￨- immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- coupling￨L￨NN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- serological￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- key￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- in￨L￨IN￨O￨- stratified￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- antibody￨L￨NN￨O￨A boosting￨L￨VBG￨O￨- and￨L￨CC￨O￨- protection￨L￨NN￨O￨- in￨L￨IN￨O￨- greater￨L￨JJR￨O￨- detail￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- antibody￨L￨NN￨O￨A boosting￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- antibody￨L￨NN￨O￨- titres￨L￨NNS￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- serological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- underestimation￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- because￨L￨RB￨O￨- low￨L￨JJ￨O￨- titres￨L￨NNS￨O￨- are￨L￨VBP￨O￨- ignored￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- multi-level￨L￨JJ￨O￨- susceptible-infected-recovered-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- all￨L￨DT￨O￨- antibody￨L￨NN￨O￨A titres￨L￨NNS￨O￨- were￨L￨VBD￨O￨- represented￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- here￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- titre￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- Methods￨U￨NNS￨O￨- and￨L￨CC￨O￨- Fig￨U￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨A in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- Francisco￨U￨NNP￨O￨- Herrerías-Azcué￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Tobias￨U￨NNP￨PERSON￨- Galla￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 13008￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsPopulation￨L￨NN￨O￨- dynamicsStatistical￨L￨JJ￨O￨- physics￨L￨NN￨O￨- AbstractModels￨U￨NNS￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- noise￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- cycles￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- population￨L￨NN￨O￨- averages￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptibilities￨L￨NNS￨O￨- and￨L￨CC￨O￨- infectivities￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- that￨L￨IN￨O￨- their￨L￨PRP$￨O￨- amplitude￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- higher-order￨L￨JJ￨O￨- moments￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨A ,￨L￨,￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- stochasticity￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- how￨L￨WRB￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptibilities￨L￨NNS￨O￨- and￨L￨CC￨O￨- propensities￨L￨NNS￨O￨- to￨L￨TO￨O￨- pass￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- affects￨L￨VBZ￨O￨- these￨L￨DT￨O￨- quasi-cycles￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- variant￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infective-recovered￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- both￨L￨DT￨O￨- agent-to-agent￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨A and￨L￨CC￨O￨- intrinsic￨L￨JJ￨O￨- noise￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- synchronisation￨L￨NN￨O￨- properties￨L￨NNS￨O￨- and￨L￨CC￨O￨- phase￨L￨NN￨O￨- lag￨L￨NN￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨A groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Counteracting￨U￨VBG￨O￨- structural￨L￨JJ￨O￨- errors￨L￨NNS￨O￨- in￨L￨IN￨O￨- ensemble￨L￨NN￨O￨- forecast￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- Sen￨U￨NNP￨O￨- Pei￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Jeffrey￨U￨NNP￨PERSON￨- Shaman1￨U￨NNP￨O￨- Nature￨U￨NNP￨O￨- Communicationsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 925￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Computational￨U￨JJ￨O￨- biology￨L￨NN￨O￨- and￨L￨CC￨O￨- bioinformaticsEpidemiologyInfectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- AbstractFor￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecasts￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- forecast￨L￨NN￨O￨- inaccuracy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- partly￨L￨RB￨O￨- attributable￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- error￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- retrospective￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- historical￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- for￨L￨IN￨O￨- 95￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- overall￨L￨JJ￨O￨- forecast￨L￨NN￨O￨A accuracy￨L￨NN￨O￨- for￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- peak￨L￨NN￨O￨- timing￨L￨NN￨O￨- ,￨L￨,￨O￨- peak￨L￨NN￨O￨- intensity￨L￨NN￨O￨- and￨L￨CC￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- substantially￨L￨RB￨O￨- improved￨L￨VBN￨O￨- for￨L￨IN￨O￨- predicted￨L￨VBN￨O￨- lead￨L￨JJ￨O￨- times￨L￨NNS￨O￨- up￨L￨IN￨DURATION￨- to￨L￨TO￨DURATION￨- 10￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- quantification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- error￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- forecast￨L￨NN￨O￨A models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- needed￨L￨VBN￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- growth￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- corrected￨L￨VBN￨O￨- and￨L￨CC￨O￨- forecast￨L￨VBN￨O￨- skill￨L￨NN￨O￨- improved￨L￨VBN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- counteracting￨L￨VBG￨O￨- these￨L￨DT￨O￨- structural￨L￨JJ￨O￨- errors￨L￨NNS￨O￨- ,￨L￨,￨O￨- diagnosed￨L￨VBD￨O￨- using￨L￨VBG￨O￨- error￨L￨NN￨O￨- breeding￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- forecast￨L￨NN￨O￨A approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- dynamical￨L￨JJ￨O￨- error￨L￨NN￨O￨- correction￨L￨NN￨O￨- and￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- filtering￨L￨VBG￨O￨- techniques￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- error￨L￨NN￨O￨- growth￨L￨NN￨O￨- correction￨L￨NN￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- generalized￨L￨VBN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- forecast￨L￨NN￨O￨A accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- latter￨L￨JJ￨O￨- gives￨L￨VBZ￨O￨- an￨L￨DT￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- perfect￨L￨JJ￨O￨- vaccination.As￨L￨NNS￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- correspondence￨L￨NN￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Wilkinson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Sharkey￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A system￨L￨NN￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- equivalent￨L￨JJ￨O￨- non-Markovian￨L￨JJ￨MISC￨- pairwise￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- Poisson￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Wilkinson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Sharkey￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- contact￨L￨NN￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- Poisson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- generalised￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A equations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- unifying￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- representations￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- convergence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- monotone￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- follows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- here￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- StrictGreaterThan￨U￨NN￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- Kermack￨U￨NNP￨O￨- –￨L￨:￨O￨- McKendrick￨U￨NNP￨PERSON￨- model.KeywordsStochastic￨L￨NNP￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- Kermack￨U￨NNP￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- -341￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- KJS.Mathematics￨U￨NNPS￨O￨- Subject￨U￨NNP￨O￨- Classification92D30￨U￨NN￨O￨- 91D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionOne￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- earliest￨L￨JJS￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- comprehensively￨L￨RB￨O￨- analysed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1927￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +2.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- Karrer￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Newman￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Wilkinson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Sharkey￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- more￨L￨JJR￨O￨- general￨L￨JJ￨TITLE￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A system￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- underestimate￨L￨VB￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- StrictGreaterThan￨U￨NN￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- during￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Theorem￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- Corollary￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +SharkeyOpen￨U￨NNP￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1.2￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 3￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractWe￨U￨NN￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- stochastic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- it￨L￨PRP￨O￨- takes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- contact￨L￨VB￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighbours￨L￨NNS￨O￨- after￨L￨IN￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- correlated￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨- events￨L￨NNS￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- as￨L￨IN￨O￨- unknowns￨L￨NNS￨O￨- to￨L￨TO￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- sampled￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- MCMC￨U￨NN￨O￨- routine￨L￨NN￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- these￨L￨DT￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- times￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- household￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- method￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- posteriors￨L￨NNS￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- compute￨L￨VBP￨O￨- show￨L￨VB￨O￨- good￨L￨JJ￨O￨- convergence￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- household￨L￨NN￨O￨A data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨A the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- dispersal￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Esteva￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Vargas￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- considering￨L￨VBG￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- variable￨L￨JJ￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Polwiang￨U￨NN￨PERSON￨- discussed￨L￨VBD￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨A and￨L￨CC￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- climate￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +So￨U￨RB￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- made￨L￨VBN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +used￨L￨VBN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- analysis￨L￨NN￨O￨- comparing￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- dengue￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- software￨L￨NN￨O￨- package￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- R￨U￨NN￨O￨- language￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- and￨L￨CC￨O￨- study￨L￨VB￨O￨- concepts￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- modern￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨- or￨L￨CC￨O￨- write￨L￨VB￨O￨- computer￨L￨NN￨O￨- code￨L￨NN￨O￨- .￨L￨.￨O￨- +New￨U￨NNP￨O￨- tools￨L￨NNS￨O￨- and￨L￨CC￨O￨- approaches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- reach￨L￨VB￨O￨- a￨L￨DT￨O￨- wider￨L￨JJR￨O￨- audience￨L￨NN￨O￨- and￨L￨CC￨O￨- allow￨L￨VB￨O￨- students￨L￨NNS￨O￨- to￨L￨TO￨O￨- learn￨L￨VB￨O￨- concepts￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- critical￨L￨JJ￨O￨- community￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- population-level￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- obstacles￨L￨NNS￨O￨- of￨L￨IN￨O￨- coding￨L￨VBG￨O￨- or￨L￨CC￨O￨- having￨L￨VBG￨O￨- to￨L￨TO￨O￨- formulate￨L￨VB￨O￨- and￨L￨CC￨O￨- analyze￨L￨VB￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- package￨L￨NN￨O￨A includes￨L￨VBZ￨O￨- documentation￨L￨NN￨O￨- and￨L￨CC￨O￨- material￨L￨NN￨O￨- to￨L￨TO￨O￨- serve￨L￨VB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- stand-alone￨L￨JJ￨O￨- tool￨L￨NN￨O￨- —￨L￨:￨O￨- supplemented￨L￨VBN￨O￨- as￨L￨IN￨O￨- needed￨L￨VBN￨O￨- with￨L￨IN￨O￨- provided￨L￨VBN￨O￨- references￨L￨NNS￨O￨- —￨L￨:￨O￨- for￨L￨IN￨O￨- students￨L￨NNS￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- an￨L￨DT￨O￨- introduction￨L￨NN￨O￨- to￨L￨TO￨O￨- important￨L￨JJ￨O￨- modern￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- concepts￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- textbooks￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- that￨L￨WDT￨O￨- teach￨L￨VBP￨O￨- a￨L￨DT￨O￨- model-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- exist￨L￨VBP￨O￨- ,￨L￨,￨O￨- almost￨L￨RB￨O￨- any￨L￨DT￨O￨- such￨L￨JJ￨O￨- teaching￨L￨NN￨O￨- material￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- students￨L￨NNS￨O￨A to￨L￨TO￨O￨- work￨L￨VB￨O￨- with￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- write￨L￨VB￨O￨- computer￨L￨NN￨O￨- code￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- package￨L￨NN￨O￨A is￨L￨VBZ￨O￨- built￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- modular￨L￨JJ￨O￨- way￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- student￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- seamlessly￨L￨RB￨O￨- continue￨L￨VB￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- journey￨L￨NN￨O￨- of￨L￨IN￨O￨- learning￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modeling￨L￨NN￨O￨- if￨L￨IN￨O￨- they￨L￨PRP￨O￨- choose￨L￨VBP￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- so￨L￨RB￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- characterize￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- and￨L￨CC￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨A events￨L￨NNS￨O￨- ,￨L￨,￨O￨- mediated￨L￨VBN￨O￨- by￨L￨IN￨O￨- transient￨L￨JJ￨O￨- heterosubtypic￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- following￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- integrate￨L￨VB￨O￨- environmental￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- on￨L￨IN￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- two-strain￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- heterosubtypic￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- new￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨A risk￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- expected￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨A declines￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- wake￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- does￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- early￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- preceded￨L￨VBN￨O￨- by￨L￨IN￨O￨- viral￨L￨JJ￨O￨- reassortment￨L￨NN￨O￨- in￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- co-infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- should￨L￨MD￨O￨- become￨L￨VB￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- increases￨L￨VBZ￨O￨- [￨L￨-LRB-￨O￨- 34￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 36￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- simulated￨L￨JJ￨O￨- thousands￨L￨NNS￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- virus￨L￨NN￨O￨- introductions￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- changing￨L￨VBG￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- Reff￨U￨NNP￨PERSON￨- upon￨L￨IN￨O￨- emergence￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- seasons￨L￨NNS￨O￨- unfold￨L￨VBP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- methods￨L￨NNS￨O￨- would￨L￨MD￨O￨- contribute￨L￨VB￨O￨- in￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- of￨L￨IN￨O￨- household￨L￨NN￨O￨A structures￨L￨NNS￨O￨- among￨L￨IN￨O￨- Indigenous￨U￨JJ￨O￨- communities￨L￨NNS￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- accurate￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- better￨L￨JJR￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- support￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- household￨L￨NN￨O￨A structures￨L￨NNS￨O￨- in￨L￨IN￨O￨- remote￨L￨JJ￨O￨- and￨L￨CC￨O￨- isolated￨L￨VBN￨O￨- communities￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- especially￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- them￨L￨PRP￨O￨- into￨L￨IN￨O￨- consideration￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Household￨U￨NNP￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- ages￨L￨NNS￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨A resident￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- per￨L￨IN￨O￨- room￨L￨NN￨O￨- ,￨L￨,￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- vary￨L￨VB￨O￨- across￨L￨IN￨O￨- subpopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- upon￨L￨IN￨O￨- fertility￨L￨NN￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- socioeconomic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- cultural￨L￨JJ￨O￨- norms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Transcriptional￨U￨JJ￨O￨- regulation￨L￨NN￨O￨- ,￨L￨,￨O￨- led￨L￨VBN￨O￨- by￨L￨IN￨O￨- transcription￨L￨NN￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- TFs￨U￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- regulation￨L￨NN￨O￨- proteins￨L￨NNS￨O￨- that￨L￨WDT￨O￨- link￨L￨VBP￨O￨- DNA￨U￨NN￨O￨- sequences￨L￨NNS￨O￨- in￨L￨IN￨O￨- specific￨L￨JJ￨O￨- promoter￨L￨NN￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- target￨L￨NN￨O￨- genes￨L￨NNS￨O￨A –￨L￨:￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- mechanism￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- activated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- organism￨L￨NN￨O￨- to￨L￨TO￨O￨- enhance￨L￨VB￨O￨- or￨L￨CC￨O￨- repress￨L￨VB￨O￨- gene￨L￨NN￨O￨- expression￨L￨NN￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- internal￨L￨JJ￨O￨- or￨L￨CC￨O￨- external￨L￨JJ￨O￨- stimuli￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- cacao￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Theobroma￨U￨NN￨O￨- cacao￨L￨NN￨O￨- L.￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- portion￨L￨NN￨O￨- of￨L￨IN￨O￨- WRKY￨U￨NN￨O￨- genes￨L￨NNS￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- identified￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- with￨L￨IN￨O￨- regards￨L￨VBZ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- expression￨L￨NN￨O￨- ,￨L￨,￨O￨- phylogeny￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- Malvaceae￨U￨NNP￨O￨- family￨L￨NN￨O￨- ,￨L￨,￨O￨- and/or￨L￨CC￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- marker￨L￨NN￨TITLE￨- assisted￨L￨VBN￨O￨- selection￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- no￨L￨DT￨O￨- exhaustive￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- TF￨U￨NN￨O￨- family￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- cacao￨L￨NN￨O￨- genome￨L￨NN￨O￨- data￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- WRKY￨U￨NN￨O￨- proteins￨L￨NNS￨O￨A contain￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- DNA￨U￨NN￨MISC￨- binding￨L￨NN￨O￨- domains￨L￨NNS￨O￨- of￨L￨IN￨O￨- 60￨L￨CD￨NUMBER￨- amino￨L￨NN￨O￨- acids￨L￨NNS￨O￨- containing￨L￨VBG￨O￨- the￨L￨DT￨O￨- conserved￨L￨VBN￨O￨- heptapeptide￨L￨NN￨O￨- WRKYGQK￨U￨NN￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- zinc-finger￨L￨JJ￨O￨- motif￨L￨NN￨O￨- C2H2￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- C-X4-5-C-X22-23-H-X-H￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- C2HC￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- C-X7-C-X23-24-H-X-C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- scheme￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- in￨L￨IN￨O￨- silico￨L￨JJ￨O￨- pipeline￨L￨NN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Theobroma￨U￨NN￨O￨- cacao￨L￨NN￨O￨- WRKY￨U￨NN￨O￨- protein￨L￨NN￨O￨A set￨L￨NN￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- S1￨U￨NN￨O￨- Fig￨U￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- expression￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- WRKY￨U￨NN￨O￨- genes￨L￨NNS￨O￨A in￨L￨IN￨O￨- cacao￨L￨NN￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogenic￨L￨JJ￨O￨- fungus￨L￨NN￨O￨- M￨U￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Targeted￨U￨VBN￨O￨- Recovery￨U￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- Effective￨U￨JJ￨O￨- Strategy￨U￨NN￨O￨- against￨L￨IN￨O￨- Epidemic￨U￨NNP￨O￨- Spreading￨U￨NNP￨O￨- L.￨U￨NNP￨O￨- J.￨U￨NNP￨O￨- Herrmann1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 14356￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComplex￨L￨NNP￨O￨- networksPhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractWe￨U￨NN￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- targeted￨L￨VBN￨O￨A intervention￨L￨NN￨O￨- protocol￨L￨NN￨O￨- where￨L￨WRB￨O￨- recovery￨L￨NN￨O￨- is￨L￨VBZ￨O￨- restricted￨L￨JJ￨O￨- to￨L￨TO￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- least￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- neighbours￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- targeted￨L￨VBN￨O￨A recovery￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- standard￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- constituents￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- spontaneously￨L￨RB￨O￨- recover￨L￨VB￨O￨- after￨L￨IN￨O￨- being￨L￨VBG￨O￨- infected19￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- spatially￨L￨RB￨O￨A embedded￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- stays￨L￨NNS￨O￨- strongly￨L￨RB￨O￨- spatially￨L￨RB￨O￨- confined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- length￨L￨NN￨O￨- scale￨L￨NN￨O￨- undergoing￨L￨VBG￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- targeted￨L￨VBN￨O￨A recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- would￨L￨MD￨O￨- recover￨L￨VB￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- boundary￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- first￨L￨RB￨ORDINAL￨- .￨L￨.￨O￨- +Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equation￨L￨NN￨O￨- at￨L￨IN￨O￨- criticality￨L￨NN￨O￨A demonstrates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- nonsymmetric￨L￨JJ￨O￨- average￨L￨JJ￨O￨- avalanche￨L￨NN￨O￨- shapes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- experiments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- occur￨L￨VBP￨O￨- for￨L￨IN￨O￨- certain￨L￨JJ￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +Avalanching￨U￨VBG￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- disciplines￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- average￨L￨JJ￨O￨- avalanche￨L￨NN￨O￨- shapes￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- profiles￨L￨NNS￨O￨A of￨L￨IN￨O￨- avalanches￨L￨NNS￨O￨- of￨L￨IN￨O￨- fixed￨L￨VBN￨O￨- duration￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- Markov￨U￨NNP￨PERSON￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- an￨L￨DT￨O￨- equation￨L￨NN￨O￨- governing￨L￨VBG￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨A avalanche￨L￨NN￨O￨- shape￨L￨NN￨O￨- for￨L￨IN￨O￨- cascade￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rescaled￨L￨VBN￨O￨- average￨L￨JJ￨O￨A avalanche￨L￨NN￨O￨- shapes￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- collapse￨L￨NN￨O￨- onto￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- universal￨L￨JJ￨O￨- curve￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- developed￨L￨VBD￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- trajectory￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- DOTS￨U￨NNS￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- maintained￨L￨VBN￨O￨- or￨L￨CC￨O￨- if￨L￨IN￨O￨- new￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- 8.6￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨A new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- 1.3￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- 320,000￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- a￨L￨DT￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- incorporated￨L￨VBD￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨A and￨L￨CC￨O￨- chemoprophylaxis￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- modified￨L￨VBN￨O￨- predator￨L￨NN￨O￨- –￨L￨:￨O￨- prey￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- transmissible￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨- and￨L￨CC￨O￨- prey￨L￨NN￨O￨- species￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- analysed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- police￨L￨NN￨O￨- as￨L￨IN￨O￨- predators￨L￨NNS￨O￨- and￨L￨CC￨O￨- gang￨L￨NN￨O￨- members￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- recruitment￨L￨NN￨O￨- into￨L￨IN￨O￨- gangs￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- manner￨L￨NN￨O￨A reminiscent￨L￨JJ￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- details￨L￨NNS￨O￨A the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- gang￨L￨NN￨O￨- territories￨L￨NNS￨O￨- and￨L￨CC￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- between-gang￨L￨JJ￨O￨- violence￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- studied￨L￨VBN￨O￨- using￨L￨VBG￨O￨- Lotka￨U￨NNP￨LOCATION￨- –￨L￨:￨O￨- Volterra￨U￨NNP￨CITY￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- gang￨L￨NN￨O￨- violence￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- crimes￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- carried￨L￨VBN￨O￨A out￨L￨RP￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- gaps￨L￨NNS￨O￨- identified￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- National￨U￨NNP￨ORGANIZATION￨- Malaria￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- Program￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- NMCP￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- rational￨L￨JJ￨O￨- deployment￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- and￨L￨CC￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- makes￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- further￨L￨RB￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- usefulness￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- support￨L￨VB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- This￨U￨DT￨O￨- paper￨L￨NN￨O￨- will￨L￨MD￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A situation￨L￨NN￨O￨- in￨L￨IN￨O￨- Ghana￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- brief￨L￨JJ￨O￨- account￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Ghanaian￨U￨JJ￨NATIONALITY￨- context￨L￨NN￨O￨- towards￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- informed￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- elimination￨L￨NN￨O￨- programme￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨ORGANIZATION￨- Development￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- successive￨L￨JJ￨O￨- strategic￨L￨JJ￨O￨- plans￨L￨NNS￨O￨- of￨L￨IN￨O￨- action￨L￨NN￨O￨- ,￨L￨,￨O￨- intervention￨L￨NN￨O￨- policies￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- boost￨L￨NN￨O￨- in￨L￨IN￨O￨- financial￨L￨JJ￨O￨- support￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- Ghana￨U￨NNP￨COUNTRY￨- have￨L￨VBP￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- coverage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A morbidity￨L￨NN￨O￨- in￨L￨IN￨O￨- Ghana￨U￨NNP￨COUNTRY￨- remains￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- high￨L￨JJ￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- If￨U￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- collaboration￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- National￨U￨NNP￨ORGANIZATION￨- Malaria￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Ministry￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Ghana￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Service￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- could￨L￨MD￨O￨- guide￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨A alone￨L￨RB￨O￨- or￨L￨CC￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Estimates￨U￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- trends￨L￨NNS￨O￨- are￨L￨VBP￨O￨- created￨L￨VBN￨O￨- by￨L￨IN￨O￨- statistically￨L￨RB￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- Estimation￨U￨NN￨O￨- and￨L￨CC￨O￨- Projection￨U￨NNP￨O￨- Package￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- EPP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- ‘￨L￨``￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- ’￨L￨''￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- sentinel￨L￨NN￨O￨A surveillance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ANC-SS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- prevalence￨L￨NN￨O￨- from￨L￨IN￨O￨- nationally￨L￨RB￨O￨- representative￨L￨JJ￨TITLE￨- household￨L￨NN￨O￨- surveys￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- national￨L￨JJ￨O￨- survey￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- for￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- settings￨L￨NNS￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- sites￨L￨NNS￨O￨- and￨L￨CC￨O￨- frequent￨L￨JJ￨O￨- sentinel￨L￨NN￨O￨A surveys￨L￨NNS￨O￨- ,￨L￨,￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- tend￨L￨VBP￨O￨- to￨L￨TO￨O￨- overwhelm￨L￨VB￨O￨- the￨L￨DT￨O￨- higher-quality￨L￨JJ￨O￨- national￨L￨JJ￨O￨- survey￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- trends￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- inconsistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- national￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- primary￨L￨JJ￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- are￨L￨VBP￨O￨- sentinel￨L￨JJ￨O￨A surveillance￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- among￨L￨IN￨O￨- pregnant￨L￨JJ￨O￨- women￨L￨NNS￨O￨- attending￨L￨VBG￨O￨- antenatal￨L￨JJ￨O￨- clinics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- linear￨L￨JJ￨O￨- mixed-effects￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- potentially￨L￨RB￨O￨- unbalanced￨L￨JJ￨O￨- repeated￨L￨VBN￨O￨- observations￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- when￨L￨WRB￨O￨- inferring￨L￨VBG￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- prevalence￨L￨NN￨O￨A trend￨L￨NN￨O￨- from￨L￨IN￨O￨- ANC-SS￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- assumption￨L￨NN￨O￨- underpinning￨L￨VBG￨O￨- this￨L￨DT￨O￨- estimation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- discrepancies￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- predictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- ANC-SS￨U￨NN￨O￨- prevalence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- error￨L￨NN￨O￨- expected￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- clinic￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +al￨L￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- and￨L￨CC￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- explains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- phenomena￨L￨NNS￨O￨- of￨L￨IN￨O￨- polarization￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- evolve￨L￨VBP￨O￨- under￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- implementing￨L￨VBG￨O￨- those￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- social￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- opinion￨L￨NN￨O￨A ’s￨L￨POS￨O￨- formation￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- compromise￨L￨NN￨O￨- and￨L￨CC￨O￨- persuasion￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨- may￨L￨MD￨O￨- change￨L￨VB￨O￨- its￨L￨PRP$￨O￨- decision￨L￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- pressure￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- switching￨L￨VBG￨O￨- his￨L￨PRP$￨O￨- present￨L￨JJ￨DATE￨- choice￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- non-linearly￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- opposite￨L￨JJ￨O￨- opinion￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- are￨L￨VBP￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- studying￨L￨VBG￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- opinion￨L￨NN￨O￨A formation￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- favor￨L￨NN￨O￨- or￨L￨CC￨O￨- against￨L￨IN￨O￨- of￨L￨IN￨O￨- getting￨L￨VBG￨O￨- vaccinated￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- contribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- opinion￨L￨NN￨O￨A formation￨L￨NN￨O￨- on￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- the￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- patch-level￨L￨JJ￨O￨- approach￨L￨NN￨O￨- conforms￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- desirable￨L￨JJ￨O￨- SEIR-type￨U￨JJ￨MISC￨- mechanistic￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- successful￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- unsuccessful￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- patch￨L￨NN￨O￨A level￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- aggregation￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- points￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- arbitrary￨L￨JJ￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- inevitably￨L￨RB￨O￨- degrades￨L￨VBZ￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- resolution￨L￨NN￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- individual-to-individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission-network-based￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- partial-likelihood￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- preserves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- point￨L￨NN￨O￨- nature￨L￨NN￨O￨- ’￨L￨''￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- but￨L￨CC￨O￨- fails￨L￨VBZ￨O￨- to￨L￨TO￨O￨- conform￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨A framework￨L￨NN￨O￨- by￨L￨IN￨O￨- completely￨L￨RB￨O￨- ignoring￨L￨VBG￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- growing￨L￨VBG￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- more￨L￨RBR￨O￨- precise￨L￨JJ￨O￨- spatio-temporal￨L￨JJ￨O￨- data￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- accompanied￨L￨VBN￨O￨- by￨L￨IN￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- statistically￨L￨RB￨O￨- sound￨L￨JJ￨O￨- mechanistic￨L￨JJ￨O￨A frameworks￨L￨NNS￨O￨- for￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- individual-to-individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Conventional￨U￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- SEIR￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- require￨L￨VBP￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- account￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- which￨L￨WDT￨O￨- specifies￨L￨VBZ￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- successful￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- in￨L￨IN￨O￨- class￨L￨NN￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- more￨L￨RBR￨O￨- challengingly￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- unsuccessful￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- who￨L￨WP￨O￨- has￨L￨VBZ￨O￨- remained￨L￨VBN￨O￨- susceptible￨L￨JJ￨O￨- in￨L￨IN￨O￨- class￨L￨NN￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 09￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Genomic￨U￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- characterisation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- among￨L￨IN￨O￨- blood￨L￨NN￨O￨- donors￨L￨NNS￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- Nuno￨U￨NNP￨O￨- R.￨U￨NNP￨O￨- Sabino2￨U￨NNP￨O￨- ,3￨L￨CD￨NUMBER￨- na2￨L￨NN￨O￨- &￨L￨CC￨O￨- NHLBI￨U￨NNP￨ORGANIZATION￨- Recipient￨U￨NNP￨O￨- Epidemiology￨U￨NNP￨O￨- and￨L￨CC￨O￨- Donor￨U￨NNP￨O￨- Evaluation￨U￨NN￨O￨- Study-III￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- REDS-III￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 15216￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Dengue￨U￨NNP￨O￨- virusPhylogeneticsViral￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- AbstractOutbreaks￨U￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- Dengue￨U￨NNP￨O￨- ,￨L￨,￨O￨- Zika￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Chikungunya￨U￨NNP￨LOCATION￨- viruses￨L￨NNS￨O￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- rapidly￨L￨RB￨O￨- in￨L￨IN￨O￨- immunologically￨L￨RB￨O￨- naïve￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- geographic￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- DENV￨U￨NN￨O￨- types￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- dramatically￨L￨RB￨O￨- increased￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨O￨- decades4￨L￨NN￨O￨- ,￨L￨,￨O￨- fueled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- main￨L￨JJ￨O￨- vector￨L￨NN￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨- mosquito￨L￨NN￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- ,￨L￨,￨O￨- international￨L￨JJ￨O￨- travel￨L￨NN￨O￨A and￨L￨CC￨O￨- trade￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- increasing￨L￨VBG￨O￨- urbanization￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- and￨L￨CC￨O￨- subtropics5￨L￨NN￨O￨- ,6￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- analysing￨L￨VBG￨O￨- 92￨L￨CD￨NUMBER￨- newly￨L￨RB￨O￨- generated￨L￨VBN￨O￨- viral￨L￨JJ￨O￨- genome￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- from￨L￨IN￨O￨- blood￨L￨NN￨O￨- donors￨L￨NNS￨O￨- and￨L￨CC￨O￨- recipients￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨- serotype￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Rio￨U￨NNP￨CITY￨- de￨L￨IN￨CITY￨- Janeiro￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Modelling￨U￨VBG￨O￨- analysis￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- viral￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- started￨L￨VBD￨O￨- in￨L￨IN￨O￨- early￨L￨JJ￨DATE￨- January￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- introductions￨L￨NNS￨O￨- ,￨L￨,￨O￨- most￨L￨RBS￨O￨- likely￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- northern￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- within-country￨L￨JJ￨O￨- air￨L￨NN￨O￨- travel￨L￨NN￨O￨A to￨L￨TO￨O￨- Rio￨U￨NNP￨CITY￨- de￨L￨IN￨CITY￨- Janeiro￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Brazil￨U￨NNP￨COUNTRY￨- has￨L￨VBZ￨O￨- reported￨L￨VBN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A cases￨L￨NNS￨O￨- worldwide￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- >￨L￨JJR￨O￨- 7.3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 20137￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- occurring￨L￨VBG￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- country8￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- BT￨U￨NNP￨O￨- tension￨L￨NN￨O￨- with￨L￨IN￨O￨- geographical￨L￨JJ￨O￨- and￨L￨CC￨O￨- socioeconomic￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- hypothesis￨L￨NN￨O￨- testing￨L￨NN￨O￨- ,￨L￨,￨O￨- criterion￨L￨NN￨O￨- χ2￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- entropy￨L￨NN￨O￨A of￨L￨IN￨O￨- random￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- and￨L￨CC￨O￨- total￨L￨JJ￨O￨- entropy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- indicators￨L￨NNS￨O￨- of￨L￨IN￨O￨- BT￨U￨NNP￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- growth￨L￨NN￨O￨- dynamic￨L￨NN￨O￨- were￨L￨VBD￨O￨- processed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- guidelines￨L￨NNS￨O￨A on￨L￨IN￨O￨- conducting￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- monitoring￨L￨NN￨O￨- of￨L￨IN￨O￨- exotic￨L￨JJ￨O￨- ,￨L￨,￨O￨- very￨L￨RB￨O￨- dangerous￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- unknown￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- OIE￨U￨NNP￨O￨- Animal￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- Code￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- significance￨L￨NN￨O￨- set￨L￨VBN￨O￨- at￨L￨IN￨O￨- 5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- April￨U￨NNP￨DATE￨- )￨L￨-RRB-￨O￨- 2016￨L￨CD￨DATE￨- ,￨L￨,￨O￨- BT￨U￨NNP￨ORGANIZATION￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- registered￨L￨VBN￨O￨- in￨L￨IN￨O￨- 12￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- African￨U￨JJ￨NATIONALITY￨- continent￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- 3987￨L￨CD￨NUMBER￨- outbreaks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 28￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- of￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- 156993￨L￨CD￨NUMBER￨- outbreaks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- 5684￨L￨CD￨NUMBER￨- outbreaks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- <￨L￨JJR￨O￨- 0.001￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- spread￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- .￨L￨.￨O￨- +Used￨U￨VBN￨O￨- coefficients￨L￨NNS￨O￨- similarly￨L￨RB￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- BT￨U￨NNP￨O￨- stationarity￨L￨NN￨O￨- on￨L￨IN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- lethality￨L￨NN￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- small￨L￨JJ￨O￨- cattle￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- why￨L￨WRB￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨A our￨L￨PRP$￨O￨- epizootical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- BT￨U￨NNP￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- make￨L￨VB￨O￨- a￨L￨DT￨O￨- schema￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- situation￨L￨NN￨O￨- and￨L￨CC￨O￨- expected￨L￨VBN￨O￨- forecasts￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- Bobbie￨U￨NNP￨PERSON￨- is￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- Alex￨U￨NNP￨PERSON￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- earlier￨L￨RBR￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- serial￨L￨JJ￨O￨- partnership￨L￨NN￨O￨A than￨L￨IN￨O￨- a￨L￨DT￨O￨- concurrent￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- focused￨L￨VBN￨O￨- relationship￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Conversely￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- Charlie￨U￨NNP￨PERSON￨- is￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- Alex￨U￨NNP￨PERSON￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- earlier￨L￨RBR￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- concurrent￨L￨JJ￨O￨- partnership￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- forced￨L￨VBN￨O￨- by￨L￨IN￨O￨- partnership￨L￨NN￨O￨- timing￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- serial￨L￨NN￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- illustrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- by￨L￨IN￨O￨- halving￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- and￨L￨CC￨O￨- doubling￨L￨VBG￨O￨- the￨L￨DT￨O￨- partnership￨L￨NN￨O￨A duration￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- concurrent￨L￨JJ￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- concurrent￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- at￨L￨IN￨O￨- exactly￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- times￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- could￨L￨MD￨O￨- occur￨L￨VB￨O￨- in￨L￨IN￨O￨- either￨L￨CC￨O￨- partnership￨L￨NN￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- comparisons￨L￨NNS￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- change￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- concurrency￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- conflated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- interactions￨L￨NNS￨O￨- per￨L￨IN￨O￨- individual￨L￨NN￨O￨- or￨L￨CC￨O￨- per￨L￨IN￨O￨- partnership￨L￨NN￨O￨A .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV-specific￨U￨JJ￨O￨- antibodies￨L￨NNS￨O￨A in￨L￨IN￨O￨- tropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- ambiguous￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- cross-reactive￨L￨JJ￨O￨- antibodies￨L￨NNS￨O￨- elicited￨L￨VBN￨O￨- by￨L￨IN￨O￨- previous￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- antigenically￨L￨RB￨O￨- related￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- widespread￨L￨JJ￨O￨- DENV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- limiting￨L￨VBG￨O￨- accurate￨L￨JJ￨O￨- diagnostic￨L￨JJ￨O￨- testing￨L￨NN￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- using￨L￨VBG￨O￨- highly￨L￨RB￨O￨- specific￨L￨JJ￨O￨- neutralization￨L￨NN￨O￨- tests￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Uncertainty￨U￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- ZIKV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- exposed￨L￨VBN￨O￨- has￨L￨VBZ￨O￨- key￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- trajectory￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- American￨U￨JJ￨NATIONALITY￨- ZIKV￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- studies￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- etiology￨L￨NN￨O￨- and￨L￨CC￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV-associated￨U￨JJ￨O￨- congenital￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- have￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- high￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- clinically￨L￨RB￨O￨- suspected￨L￨VBN￨O￨- ZIKV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨A of￨L￨IN￨O￨- laboratory-confirmed￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- explore￨L￨VB￨O￨- its￨L￨PRP$￨O￨- etiologic￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- congenital￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- project￨L￨VB￨O￨- the￨L￨DT￨O￨- trajectory￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- ZIKV￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- specimens￨L￨NNS￨O￨- sampled￨L￨VBN￨O￨- before￨L￨RB￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- ZIKV￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨A the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- in￨L￨IN￨O￨- Salvador￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- capital￨L￨NN￨O￨- of￨L￨IN￨O￨- Bahia￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- directly￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- pathogens￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- arthropod￨L￨NN￨O￨- transmitted￨L￨VBD￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨A species￨L￨NNS￨O￨A diversity￨L￨NN￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- interactions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- interest￨L￨NN￨O￨- as￨L￨IN￨O￨- co-occurring￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- of￨L￨IN￨O￨- low-competency￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dilution￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- influence￨L￨VB￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- competent￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- amplifying￨L￨VBG￨O￨- hosts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- or￨L￨CC￨O￨- decreasing￨L￨VBG￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- an￨L￨DT￨O￨- assemblage￨L￨NN￨O￨- containing￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- pathogen￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- area￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dilution￨L￨NN￨O￨- effect￨L￨NN￨O￨- is￨L￨VBZ￨O￨- said￨L￨VBN￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- when￨L￨WRB￨O￨- increasing￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨A species￨L￨NNS￨O￨A richness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- diversity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- metric￨L￨NN￨O￨- that￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- both￨L￨DT￨O￨- richness￨L￨NN￨O￨- and￨L￨CC￨O￨- relative￨L￨JJ￨O￨- abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- pathogen￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- maintains￨L￨VBZ￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- readily￨L￨RB￨O￨- transmits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- opposite￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ‘‘￨L￨``￨O￨- amplification￨L￨NN￨O￨- effect￨L￨NN￨O￨- ,￨L￨,￨O￨- ”￨L￨''￨O￨- occurs￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- increased￨L￨VBN￨O￨- host￨L￨NN￨TITLE￨A species￨L￨NNS￨O￨A richness/diversity￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- increased￨L￨VBN￨O￨- encounters￨L￨NNS￨O￨- between￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- concentration￨L￨NN￨O￨- influence￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- testing￨L￨VBG￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- null￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- IHNV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- fish￨L￨NN￨O￨- using￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- experimental￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- null￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- listed￨L￨VBN￨O￨- above￨L￨RB￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- manipulability￨L￨NN￨O￨- of￨L￨IN￨O￨- rainbow￨L￨NN￨O￨- trout￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- breed￨L￨VB￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen-free￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- captivity￨L￨NN￨O￨- ,￨L￨,￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- IHNV￨U￨NN￨O￨- viral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- fitness￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- interventions￨L￨NNS￨O￨- against￨L￨IN￨O￨- IHNV￨U￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- innate￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccine-induced￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A .￨L￨.￨O￨- +Heterogeneity￨U￨NN￨O￨- in￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- departure￨L￨NN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- null￨L￨JJ￨O￨A hypothesis￨L￨NN￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- present￨L￨JJ￨DATE￨- among￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- both￨L￨DT￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- challenge￨L￨NN￨O￨- dose￨L￨NN￨O￨- and￨L￨CC￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- constants￨L￨NNS￨O￨A in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- diagnosed￨L￨VBN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- undiagnosed￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- focus￨L￨NN￨O￨- will￨L￨MD￨O￨- then￨L￨RB￨O￨- be￨L￨VB￨O￨- given￨L￨VBN￨O￨- to￨L￨TO￨O￨- determination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- constants￨L￨NNS￨O￨A in￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- show￨L￨VB￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- constants￨L￨NNS￨O￨A depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Highly￨U￨RB￨O￨- specific￨L￨JJ￨O￨- ‘￨L￨``￨O￨- matching-allele￨L￨NN￨O￨- ’￨L￨''￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- parasites￨L￨NNS￨O￨A must￨L￨MD￨O￨- ‘￨L￨``￨O￨- match￨L￨VB￨O￨- ’￨L￨''￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- loci￨L￨NNS￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- ,￨L￨,￨O￨- commonly￨L￨RB￨O￨- generate￨L￨VBP￨O￨- coevolutionary￨L￨JJ￨O￨- ‘￨L￨``￨O￨- cycles￨L￨NNS￨O￨- ’￨L￨''￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- FSD￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- selection￨L￨NN￨O￨- favours￨L￨VBZ￨O￨- parasite￨L￨NN￨O￨- genotypes￨L￨NNS￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- infecting￨L￨VBG￨O￨- common￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- genotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- generating￨L￨VBG￨O￨- negative￨L￨JJ￨O￨- frequency-dependent￨L￨JJ￨O￨- selection￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- ‘￨L￨``￨O￨- gene-for-gene￨L￨NN￨O￨- ’￨L￨''￨O￨- interactions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- specificity￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- parasites￨L￨NNS￨O￨A vary￨L￨VBP￨O￨- from￨L￨IN￨O￨- specialists￨L￨NNS￨O￨- to￨L￨TO￨O￨- generalists￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- often￨L￨RB￨O￨- produce￨L￨VBP￨O￨- ARD￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- directional￨L￨JJ￨O￨- selection￨L￨NN￨O￨- favours￨L￨VBZ￨O￨- increasing￨L￨VBG￨O￨- resistance￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- ranges￨L￨NNS￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- there￨L￨EX￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- transition￨L￨NN￨O￨- to￨L￨TO￨O￨- FSD￨U￨NNP￨ORGANIZATION￨- if￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- costs￨L￨NNS￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- defence￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Theory￨U￨NNP￨O￨- predicts￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- coevolution￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- parasites￨L￨NNS￨O￨A may￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- coevolutionary￨L￨JJ￨O￨- stable￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- co-ESS￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- static￨L￨JJ￨O￨- within-population￨L￨NN￨O￨- dimorphism￨L￨NN￨O￨- or￨L￨CC￨O￨- polymorphism￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- escalation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- arms￨L￨NNS￨O￨- race￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- ARD￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- fluctuating￨L￨VBG￨O￨- selection￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- FSD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Theoretical￨U￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- primarily￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- specificity￨L￨NN￨O￨- between￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- parasites￨L￨NNS￨O￨A lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- fluctuating￨L￨VBG￨O￨- selection￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11,19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- using￨L￨VBG￨O￨- eco-evolutionary￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- for￨L￨IN￨O￨- varying￨L￨VBG￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- defence￨L￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨A infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- human￨L￨JJ￨O￨A mobility￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- :￨L￨:￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- impedance￨L￨NN￨O￨- modelKankoé￨L￨NN￨O￨- Sallah1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Roch￨U￨NNP￨PERSON￨- Giorgi1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Linus￨U￨NNP￨PERSON￨- Bengtsson4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Xin￨U￨NNP￨PERSON￨- Lu4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Erik￨U￨NNP￨PERSON￨- Wetter5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Paul￨U￨NNP￨PERSON￨- Adrien8￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Stanislas￨U￨NNP￨PERSON￨- Rebaudet9￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Renaud￨U￨NNP￨PERSON￨- Piarroux10￨U￨NNP￨O￨- and￨L￨CC￨O￨- Jean￨U￨NNP￨PERSON￨- Gaudart1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 16:42￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- a￨L￨DT￨O￨- great￨L￨JJ￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- in￨L￨IN￨O￨- contexts￨L￨NNS￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- scarcity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- his￨L￨PRP$￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨- tradeoff￨L￨NN￨O￨- between￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- virulence￨L￨NN￨O￨A were￨L￨VBD￨O￨- systematically￨L￨RB￨O￨- studied￨L￨VBN￨O￨- through￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- validated￨L￨VBD￨O￨- the￨L￨DT￨O￨- idea￨L￨NN￨O￨- that￨L￨IN￨O￨- non-vector-borne￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- relying￨L￨VBG￨O￨- on￨L￨IN￨O￨- direct￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- benign￨L￨JJ￨O￨- while￨L￨IN￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- mode￨L￨NN￨O￨- are￨L￨VBP￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- virulent￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Anderson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- May￨U￨NNP￨DATE￨- are￨L￨VBP￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- pioneers￨L￨NNS￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- mathematics￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- proposed￨L￨VBN￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- Ro￨U￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- pathogen￨L￨NN￨O￨- fitness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- written￨L￨VBN￨O￨- as￨L￨IN￨O￨- :￨L￨:￨O￨- #Mortality￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- virulence￨L￨NN￨O￨A for￨L￨IN￨O￨- its￨L￨PRP$￨O￨- simplicity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- would￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- virulence￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- will￨L￨MD￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- reduce￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- ’s￨L￨POS￨O￨- mobility￨L￨NN￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- theories￨L￨NNS￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- virulence￨L￨NN￨O￨A ,￨L￨,￨O￨- all￨L￨DT￨O￨- pathogens￨L￨NNS￨O￨- will￨L￨MD￨O￨- end￨L￨VB￨O￨- up￨L￨RP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- relationship￨L￨NN￨O￨- of￨L￨IN￨O￨- commensalism￨L￨NN￨O￨- or￨L￨CC￨O￨- mutualism￨L￨NN￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- being￨L￨VBG￨O￨- avirulent￨L￨JJ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Ewald￨U￨NNP￨PERSON￨- was￨L￨VBD￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- firsts￨L￨NNS￨O￨- to￨L￨TO￨O￨- argue￨L￨VB￨O￨- that￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- virulence￨L￨NN￨O￨A α￨L￨NN￨O￨- are￨L￨VBP￨O￨- linked￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- branching￨L￨VBG￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tree￨L￨NN￨O￨- roughly￨L￨RB￨O￨- approximates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- event￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- an￨L￨DT￨O￨- implicit￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- nonparametric￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A methods￨L￨NNS￨O￨- using￨L￨VBG￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- subtree￨L￨JJ￨O￨- clusters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- ‘￨L￨``￨O￨- hotspots￨L￨NNS￨O￨- ’￨L￨''￨O￨- of￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model-based￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- parametric￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- clustering￨L￨NN￨O￨A method￨L￨NN￨O￨- substantially￨L￨RB￨O￨- outperforms￨L￨VBZ￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- nonparametric￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- recovering￨L￨VBG￨O￨- clusters￨L￨NNS￨O￨- of￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- differences￨L￨NNS￨O￨- are￨L￨VBP￨O￨- recapitulated￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- HIV-1￨U￨NN￨MISC￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Subtree￨U￨NN￨O￨- methods￨L￨NNS￨O￨- define￨L￨VBP￨O￨- clusters￨L￨NNS￨O￨A relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- ancestors￨L￨NNS￨O￨- of￨L￨IN￨O￨- sequences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨- tree￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- quantities￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- branch￨L￨NN￨O￨- length￨L￨NN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- descendants￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ancestral￨L￨JJ￨O￨- node￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- fundamentally￨L￨RB￨O￨- new￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- genetic￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- tree￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- observed￨L￨VBN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- nonparametric￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A methods￨L￨NNS￨O￨- seem￨L￨VBP￨O￨- relatively￨L￨RB￨O￨- insensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Exploring￨U￨NNP￨O￨- Voluntary￨U￨NNP￨O￨- Vaccinating￨U￨NNP￨O￨- Behaviors￨U￨NNP￨O￨- using￨L￨VBG￨O￨- Evolutionary￨U￨JJ￨MISC￨- N-person￨U￨NN￨MISC￨- Threshold￨U￨NNP￨MISC￨- Games￨U￨NNPS￨MISC￨- Benyun￨U￨NNP￨MISC￨- Shi1￨U￨NN￨O￨- ,￨L￨,￨O￨- Weihao￨U￨NNP￨O￨- Wang2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Hongjun￨U￨NNP￨PERSON￨- Qiu1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Yu-Wang￨U￨NNP￨O￨- Chen3￨U￨NNP￨O￨- &￨L￨CC￨O￨- Shaoliang￨U￨NNP￨O￨- Peng1￨U￨NN￨O￨- ,4,5￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 16355￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- science￨L￨NN￨O￨- AbstractUnderstanding￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- voluntary￨L￨JJ￨O￨- vaccinating￨L￨VBG￨O￨A behaviors￨L￨NNS￨O￨- plays￨L￨VBZ￨O￨- essential￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- making￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- policies￨L￨NNS￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- vaccinepreventable￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- consideration￨L￨NN￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- N-person￨U￨NN￨MISC￨- threshold￨L￨NN￨O￨- game￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- dynamically￨L￨RB￨O￨- adjust￨L￨VB￨O￨- their￨L￨PRP$￨O￨- vaccinating￨L￨VBG￨O￨A strategies￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- payoffs￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- nonlinearly￨L￨RB￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reached￨L￨VBN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- well-mixed￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- relationships￨L￨NNS￨O￨- at￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨A cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- relative￨L￨JJ￨O￨A costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Towards￨U￨IN￨MISC￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A elimination￨L￨NN￨O￨- in￨L￨IN￨O￨- Savannakhet￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Lao￨U￨NNP￨NATIONALITY￨- PDR￨U￨NNP￨O￨- :￨L￨:￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- driven￨L￨VBN￨O￨- strategy￨L￨NN￨O￨- designSai￨L￨NNP￨O￨- Thein￨U￨NNP￨O￨- Than￨U￨IN￨O￨- Tun1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Lorenz￨U￨NNP￨PERSON￨- von￨L￨NNP￨O￨- Seidlein1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Tiengkham￨U￨NNP￨O￨- Pongvongsa3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Mayfong￨U￨NNP￨O￨- Mayxay2￨U￨NNP￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Sompob￨U￨NNP￨O￨- Saralamba1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Shwe￨U￨NNP￨O￨- Sin￨U￨NNP￨O￨- Kyaw1￨U￨NN￨O￨- ,￨L￨,￨O￨- Phetsavanh￨U￨NNP￨O￨- Chanthavilay5￨U￨NNP￨O￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Olivier￨U￨NNP￨PERSON￨- Celhay1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Tran￨U￨NNP￨PERSON￨- Dang￨U￨NNP￨PERSON￨- Nguyen7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Thu￨U￨NNP￨O￨- Nguyen-Anh￨U￨NNP￨O￨- Tran7￨U￨NN￨O￨- ,￨L￨,￨O￨- Daniel￨U￨NNP￨PERSON￨- M.￨U￨NNP￨PERSON￨- White1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 16:483￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- Plasmodium￨U￨NN￨O￨- falciparum￨L￨NN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- has￨L￨VBZ￨O￨- decreased￨L￨VBN￨O￨- substantially￨L￨RB￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DATE￨- 15￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- against￨L￨IN￨O￨- anti-malarial￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- and￨L￨CC￨O￨- insecticides￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- decline￨L￨NN￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- continue￨L￨VB￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- interventions￨L￨NNS￨O￨A comprised￨L￨VBD￨O￨- universal￨L￨JJ￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- early￨L￨JJ￨O￨- diagnosis￨L￨NN￨O￨- and￨L￨CC￨O￨- adequate￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- improved￨L￨VBD￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- long-lasting￨L￨JJ￨O￨- insecticidal￨L￨JJ￨O￨- nets￨L￨NNS￨O￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- monthly￨L￨JJ￨SET￨- rounds￨L￨NNS￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- drug￨L￨NN￨O￨- administration￨L￨NN￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- RTS￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- booster￨L￨NN￨O￨- dose￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- screening￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- imported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- modelling￨L￨NN￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sequential￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- five￨L￨CD￨NUMBER￨- available￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- integrated￨L￨VBN￨O￨- strategy￨L￨NN￨O￨- was￨L￨VBD￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- stop￨L￨VB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- 3-year￨L￨JJ￨DURATION￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- urgent￨L￨JJ￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- alternative￨L￨NN￨O￨- ,￨L￨,￨O￨- accelerated￨L￨VBD￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- like￨L￨IN￨O￨- Lao￨U￨NNP￨NATIONALITY￨- PDR￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- remaining￨L￨VBG￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- perform￨L￨VBP￨O￨- retrospective￨L￨JJ￨O￨- forecasting￨L￨NN￨O￨- over￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- seasons￨L￨NNS￨O￨- for￨L￨IN￨O￨- 95￨L￨CD￨NUMBER￨- cities￨L￨NNS￨O￨- using￨L￨VBG￨O￨- 4￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨A :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- no￨L￨DT￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨- ;￨L￨:￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- optimization￨L￨NN￨O￨- and￨L￨CC￨O￨- forecast￨L￨NN￨O￨- with￨L￨IN￨O￨- local￨L￨JJ￨O￨- climatological￨L￨JJ￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- historical￨L￨JJ￨O￨- average￨L￨JJ￨O￨- AH￨U￨NN￨O￨- conditions￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- optimization￨L￨NN￨O￨- and￨L￨CC￨O￨- forecast￨L￨NN￨O￨- with￨L￨IN￨O￨- local￨L￨JJ￨O￨- observed￨L￨VBN￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- AH￨U￨FW￨O￨- as￨L￨IN￨O￨- observed￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- optimization￨L￨NN￨O￨- with￨L￨IN￨O￨- observed￨L￨VBN￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨- and￨L￨CC￨O￨- forecast￨L￨VBN￨O￨- with￨L￨IN￨O￨- climatological￨L￨JJ￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecast￨L￨NN￨O￨- over￨L￨IN￨O￨- larger￨L￨JJR￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- US￨U￨NNP￨ORGANIZATION￨- CDC￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Human￨U￨NNP￨ORGANIZATION￨- Services￨U￨NNPS￨ORGANIZATION￨- multi-state￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- subtropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- heretofore￨L￨RB￨O￨- adopted￨L￨VBN￨O￨- a￨L￨DT￨O￨- SIRS￨U￨NN￨O￨- form￨L￨NN￨O￨- without￨L￨IN￨O￨- AH￨U￨NNP￨O￨- forcing￨L￨VBG￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- systems￨L￨NNS￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-recovered-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- first￨L￨JJ￨ORDINAL￨- optimized￨L￨VBN￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨A using￨L￨VBG￨O￨- observational￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- US￨U￨NNP￨COUNTRY￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- municipal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- first￨L￨RB￨ORDINAL￨- developed￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- AH-forced￨U￨JJ￨O￨- SIRS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- state￨L￨NN￨O￨- geographic￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Modeling￨U￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- temperate￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reproduced￨L￨VBN￨O￨- when￨L￨WRB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- observed￨L￨VBN￨O￨- AH￨U￨NN￨O￨- conditions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- ITNs￨U￨NNS￨O￨- and￨L￨CC￨O￨- IRS￨U￨NNP￨ORGANIZATION￨- :￨L￨:￨O￨- larviciding￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- attractive￨L￨JJ￨O￨- toxic￨L￨JJ￨O￨- sugar￨L￨NN￨O￨- baits￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ATSBs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- insecticide￨L￨NN￨O￨A spraying￨L￨VBG￨O￨- of￨L￨IN￨O￨- male￨L￨JJ￨O￨- mating￨L￨NN￨O￨- swarms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- mosquito-proofed￨L￨JJ￨O￨- housing￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- repellents￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- personal￨L￨JJ￨O￨- protection￨L￨NN￨O￨- measures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- topical￨L￨JJ￨O￨- repellents￨L￨NNS￨O￨- ,￨L￨,￨O￨- insecticide-treated￨L￨JJ￨O￨- clothing￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- systemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- topical￨L￨JJ￨O￨- insecticide-treated￨L￨JJ￨O￨- cattle￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- odor-baited￨L￨JJ￨O￨- traps￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨- spraying￨L￨VBG￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- package￨L￨NN￨O￨- of￨L￨IN￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A required￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- entomological￨L￨JJ￨O￨- inoculation￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- levels￨L￨NNS￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- local￨L￨JJ￨O￨- elimination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- African￨U￨JJ￨NATIONALITY￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- vectors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- Anopheles￨U￨NNP￨O￨- gambiae￨L￨NNS￨O￨- s.s￨L￨VBP￨O￨- .￨L￨.￨O￨- +Fortunately￨U￨RB￨O￨- ,￨L￨,￨O￨- field￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- promising￨L￨JJ￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- underutilized￨L￨VBN￨O￨- or￨L￨CC￨O￨- emerging￨L￨VBG￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- complement￨L￨VB￨O￨- ITNs￨U￨NNS￨O￨- and/or￨L￨CC￨O￨- IRS￨U￨NNP￨ORGANIZATION￨- by￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- resources￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- combining￨L￨VBG￨O￨- existing￨L￨VBG￨O￨- and￨L￨CC￨O￨- novel￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- in￨L￨IN￨O￨- synergistic￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- where￨L￨WRB￨O￨- ITNs￨U￨NNS￨O￨- and/or￨L￨CC￨O￨- IRS￨U￨NNP￨ORGANIZATION￨- are￨L￨VBP￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- but￨L￨CC￨O￨- where￨L￨WRB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A persists￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Where￨U￨WRB￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- made￨L￨VBD￨O￨- various￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨A processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- draw￨L￨VB￨O￨- inferences￨L￨NNS￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- Bayesian￨U￨JJ￨O￨- approach￨L￨NN￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- times￨L￨NNS￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- quantifies￨L￨VBZ￨O￨- them￨L￨PRP￨O￨- along￨L￨RP￨O￨- with￨L￨IN￨O￨- all￨L￨DT￨O￨- other￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- fit￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- published￨L￨VBN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- transmission￨L￨NN￨O￨- experiments￨L￨NNS￨O￨A for￨L￨IN￨O￨- foot-and-mouth￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FMDV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- African￨U￨JJ￨NATIONALITY￨- swine￨L￨NNS￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ASFV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- our￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- periods￨L￨NNS￨O￨A of￨L￨IN￨O￨- inoculated￨L￨VBN￨O￨- and￨L￨CC￨O￨- contact-challenged￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- has￨L￨VBZ￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 01￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Bayesian￨U￨NNP￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- transmission￨L￨NN￨O￨- experiments￨L￨NNS￨O￨A Ben￨U￨NNP￨O￨- Hu1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jose￨U￨NNP￨PERSON￨- L.￨U￨NNP￨PERSON￨- Gonzales￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Simon￨U￨NNP￨PERSON￨- Gubbins￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 16774￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- MicrobiologyViral￨U￨NNP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- AbstractEpidemiological￨U￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- livestock￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- inferred￨L￨VBN￨O￨- from￨L￨IN￨O￨- transmission￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- .￨L￨.￨O￨- +Focusing￨U￨VBG￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- package￨L￨NN￨O￨A that￨L￨WDT￨O￨- offers￨L￨VBZ￨O￨- detailed￨L￨JJ￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- inference￨L￨NN￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- applies￨L￨VBZ￨O￨- evidence￨L￨NN￨O￨- synthesis￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- to￨L￨TO￨O￨- combine￨L￨VB￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- stratified￨L￨VBN￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- risk￨L￨NN￨O￨- status￨L￨NN￨O￨- and￨L￨CC￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- age-stratified￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- package￨L￨NN￨O￨A is￨L￨VBZ￨O￨- particularly￨L￨RB￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- modelling￨L￨NN￨O￨- and￨L￨CC￨O￨- evaluating￨L￨VBG￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- directly￨L￨RB￨O￨- transmissible￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- use￨L￨VBP￨O￨- proxy￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- influenza-like-illness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- counts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- respiratory￨L￨JJ￨O￨- syncytial￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RSV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- exception￨L￨NN￨O￨- here￨L￨RB￨O￨- is￨L￨VBZ￨O￨- amei￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- R￨U￨NN￨O￨- package￨L￨NN￨O￨A for￨L￨IN￨O￨- optimising￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- management￨L￨NN￨O￨- framework￨L￨NN￨O￨- while￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- package￨L￨NN￨O￨- mainly￨L￨RB￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- high￨L￨JJ￨O￨- quality￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- implementation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Susceptible￨U￨NNP￨MISC￨- Exposed￨U￨VBN￨MISC￨- Infectious￨U￨JJ￨MISC￨- Removed￨U￨VBN￨MISC￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- previously￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- later￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- cost/benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- programme￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- Kingdom￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- adapted￨L￨VBD￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- it￨L￨PRP￨O￨- more￨L￨RBR￨O￨- generally￨L￨RB￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- previous￨L￨JJ￨O￨- research￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- lab￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- pH￨L￨NN￨COUNTRY￨- values￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- to10￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨A of￨L￨IN￨O￨- F.￨U￨NNP￨O￨- proliferatum￨L￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- pH￨L￨NN￨COUNTRY￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 10￨L￨CD￨NUMBER￨- had￨L￨VBD￨O￨- no￨L￨DT￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- but￨L￨CC￨O￨- affected￨L￨VBD￨O￨- fusaic￨L￨JJ￨O￨- acid￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- production￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- understanding￨L￨VBG￨O￨- secretomics￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- vital￨L￨JJ￨O￨- information￨L￨NN￨O￨- for￨L￨IN￨O￨- advances￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- extracellular￨L￨JJ￨O￨- proteins￨L￨NNS￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- pathogenicity￨L￨NN￨O￨- of￨L￨IN￨O￨- F￨U￨NN￨O￨- .￨L￨.￨O￨- +Numerous￨U￨JJ￨O￨- researches￨L￨VBZ￨O￨- were￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- pH￨L￨NN￨COUNTRY￨- signal￨L￨NN￨O￨- transduction￨L￨NN￨O￨- and￨L￨CC￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- pH￨L￨NN￨COUNTRY￨- regulation￨L￨NN￨O￨A and￨L￨CC￨O￨- fungal￨L￨JJ￨O￨- pathogenicity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- pathogenic￨L￨JJ￨O￨- microorganisms￨L￨NNS￨O￨- usually￨L￨RB￨O￨- secret￨L￨JJ￨O￨- proteins￨L￨NNS￨O￨A to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- their￨L￨PRP$￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- colonization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- disturbance￨L￨NN￨O￨- of￨L￨IN￨O￨- wooded￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- and￨L￨CC￨O￨- forests￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨A in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- white-footed￨L￨JJ￨O￨- mice￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- competent￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- ticks￨L￨NNS￨O￨- ;￨L￨:￨O￨- also￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- predation￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- ecologically￨L￨RB￨O￨- fragmented￨L￨JJ￨O￨- peri-urban￨L￨JJ￨O￨- built￨L￨VBN￨O￨- environment￨L￨NN￨O￨- areas￨L￨NNS￨O￨- will￨L￨MD￨O￨- increase￨L￨VB￨O￨- mouse￨L￨NN￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- note￨L￨VB￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- factors￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨A of￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- provider￨L￨NN￨O￨- 's￨L￨POS￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- non-specific￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- and￨L￨CC￨O￨- unrecognized￨L￨JJ￨O￨- tick￨L￨NN￨O￨- bites￨L￨VBZ￨O￨- may￨L￨MD￨O￨- delay￨L￨VB￨O￨- on-time￨L￨JJ￨O￨- diagnosis￨L￨NN￨O￨- of￨L￨IN￨O￨- LD￨U￨NN￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- chronic￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- PTLDS￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- factors￨L￨NNS￨O￨- may￨L￨MD￨O￨- influence￨L￨VB￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- LD￨U￨NN￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- USA￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- climate￨L￨NN￨O￨- ,￨L￨,￨O￨- prevention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- awareness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- and￨L￨CC￨O￨- recognition￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨A by￨L￨IN￨O￨- physicians￨L￨NNS￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- ticks￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- LD￨U￨NN￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- reservoir￨L￨NN￨O￨A hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- rodents￨L￨NNS￨O￨- and￨L￨CC￨O￨- tick￨L￨VB￨O￨- predators￨L￨NNS￨O￨- like￨L￨IN￨O￨- songbirds￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- in￨L￨IN￨O￨- Dutchess￨U￨NNP￨LOCATION￨- County￨U￨NNP￨LOCATION￨- located￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Hudson￨U￨NNP￨CITY￨- River￨U￨NNP￨TITLE￨- Valley￨U￨NNP￨CITY￨- of￨L￨IN￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- State￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- rise￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networking￨L￨NN￨O￨- sites￨L￨NNS￨O￨- like￨L￨IN￨O￨- Facebook￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- media￨L￨NNS￨O￨- like￨L￨IN￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- penetrated￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- lives￨L￨NNS￨O￨- from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- dimensions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- opinion￨L￨NN￨O￨A diffusion￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- more￨L￨RBR￨O￨- broadly￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- attracted￨L￨VBN￨O￨- the￨L￨DT￨O￨- attention￨L￨NN￨O￨- of￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- from￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- disciplines￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- memes￨L￨NNS￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- memes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- propagated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- know￨L￨VBP￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- know￨L￨VB￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- in￨L￨IN￨O￨- opinion￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- initially￨L￨RB￨O￨- there￨L￨EX￨O￨- exist￨L￨VBP￨O￨- several￨L￨JJ￨O￨- different￨L￨JJ￨O￨- opinions￨L￨NNS￨O￨A distributed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- opinions￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- people￨L￨NNS￨O￨- are￨L￨VBP￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- neighbours￨L￨NNS￨O￨- and￨L￨CC￨O￨- update￨L￨VB￨O￨- their￨L￨PRP$￨O￨- opinions￨L￨NNS￨O￨A ,￨L￨,￨O￨- often￨L￨RB￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- majority￨L￨NN￨O￨- rule￨L￨NN￨O￨- or￨L￨CC￨O￨- imitation￨L￨NN￨O￨- .￨L￨.￨O￨- +Opinion￨U￨NN￨O￨- or￨L￨CC￨O￨- product￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- economics￨L￨NNS￨O￨- literature￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- dynamic￨L￨JJ￨O￨- behaviours￨L￨NNS￨O￨- are￨L￨VBP￨O￨- commonly￨L￨RB￨O￨- termed￨L￨VBN￨O￨- social￨L￨JJ￨O￨- learning￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- latter￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- involve￨L￨VBP￨O￨- bounded￨L￨VBN￨O￨- confidence￨L￨NN￨O￨- between￨L￨IN￨O￨- people￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- opinions￨L￨NNS￨O￨A of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- are￨L￨VBP￨O￨- too￨L￨RB￨O￨- far￨L￨RB￨O￨- apart￨L￨RB￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- influence￨L￨VB￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- its￨L￨PRP$￨O￨- simplest￨L￨JJS￨O￨- form￨L￨NN￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- βN￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- that￨L￨WDT￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- p￨L￨NN￨O￨- of￨L￨IN￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- through￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- multiplied￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- –￨L￨:￨O￨- density￨L￨NN￨O￨A function￨L￨NN￨O￨- that￨L￨WDT￨O￨- equals￨L￨VBZ￨O￨- cN/A￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- area￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- linear￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- density-dependent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- c￨L￨NN￨O￨- when￨L￨WRB￨O￨- constant￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- frequency-dependent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- random￨L￨JJ￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- quickly￨L￨RB￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- expected￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- contact￨L￨NN￨O￨- –￨L￨:￨O￨- density￨L￨NN￨O￨A functions￨L￨NNS￨O￨- will￨L￨MD￨O￨- differently￨L￨RB￨O￨- affect￨L￨VB￨O￨- outbreak￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Sexually￨U￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- described￨L￨VBN￨O￨- using￨L￨VBG￨O￨- frequency-dependent￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- remain￨L￨VB￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- modelling￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- encountering￨L￨VBG￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- either￨L￨CC￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- frequency-dependent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- linearly￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- density-dependent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨RBS￨O￨- importantly￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- functions￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- in￨L￨IN￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- below￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- density￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- comprehensive￨L￨JJ￨O￨- phylodynamic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- available￨L￨JJ￨O￨- West￨U￨JJ￨MISC￨- African￨U￨JJ￨NATIONALITY￨- EBOV￨U￨NN￨O￨- genomes￨L￨NNS￨O￨A also￨L￨RB￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- population￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- explanatory￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- spatial￨L￨JJ￨O￨A analyses￨L￨NNS￨O￨- and￨L￨CC￨O￨- modelling￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- EBOV￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- have￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- population￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- influential￨L￨JJ￨O￨- factor￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- gravity￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- parametrized￨L￨VBN￨O￨- to￨L￨TO￨O￨- case-reporting￨L￨JJ￨O￨- data￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 30￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 32￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- how￨L￨WRB￨O￨- EBOV￨U￨NN￨O￨- molecular￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- virus￨L￨NN￨O￨- genomes￨L￨NNS￨O￨A ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- directly￨L￨RB￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Analogous￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- attracting￨L￨VBG￨O￨- force￨L￨NN￨O￨- between￨L￨IN￨O￨- physical￨L￨JJ￨O￨- masses￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- gravity￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- human￨L￨JJ￨O￨- movements￨L￨NNS￨O￨- as￨L￨IN￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- and￨L￨CC￨O￨- distance￨L￨NN￨O￨A between￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Measures￨U￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- macaques￨L￨NNS￨O￨- ’￨L￨POS￨O￨- network￨L￨NN￨O￨- centrality￨L￨NN￨O￨- —￨L￨:￨O￨- an￨L￨DT￨O￨- index￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- and￨L￨CC￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- social￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- potentially￨L￨RB￨O￨- their￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- —￨L￨:￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- show￨L￨VB￨O￨- clear￨L￨JJ￨O￨- and￨L￨CC￨O￨- consistent￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- time￨L￨NN￨O￨- spent￨L￨VBN￨O￨- in￨L￨IN￨O￨- close￨L￨JJ￨O￨- proximity￨L￨NN￨O￨A to￨L￨TO￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- tourists￨L￨NNS￨O￨- .￨L￨.￨O￨- +Disease￨U￨NN￨CAUSE_OF_DEATH￨- simulation￨L￨NN￨O￨- modelling￨L￨NN￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- while￨L￨IN￨O￨- higher-ranked￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- significantly￨L￨RB￨O￨- greater￨L￨JJR￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A within￨L￨IN￨O￨- the￨L￨DT￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- absolute￨L￨JJ￨O￨- terms￨L￨NNS￨O￨- there￨L￨RB￨O￨- was￨L￨VBD￨O￨- little￨L￨JJ￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- different￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- cause￨L￨VB￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 704￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 717￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asImplications￨L￨NNS￨O￨- of￨L￨IN￨O￨- Tourist￨U￨NNP￨O￨- –￨L￨:￨O￨- Macaque￨U￨NNP￨O￨- Interactions￨U￨NNS￨O￨- for￨L￨IN￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- TransmissionAuthorsAuthors￨U￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsCharlotte￨L￨NN￨O￨- CarneStuart￨U￨NN￨MISC￨- SempleAnn￨U￨NNP￨MISC￨- MacLarnonBonaventura￨U￨NNP￨MISC￨- MajoloLaëtitia￨U￨NNP￨MISC￨- MaréchalOpen￨U￨NNP￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- ContributionFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 65￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1.1￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨MISC￨- AbstractDuring￨U￨VBG￨O￨- wildlife￨L￨NN￨O￨- tourism￨L￨NN￨O￨- ,￨L￨,￨O￨- proximity￨L￨NN￨O￨A or￨L￨CC￨O￨- actual￨L￨JJ￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- people￨L￨NNS￨O￨- and￨L￨CC￨O￨- animals￨L￨NNS￨O￨- may￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- anthropozoonotic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- simulation￨L￨NN￨O￨- modelling￨L￨NN￨O￨A and￨L￨CC￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- animal￨L￨NN￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- behaviour￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- such￨L￨JJ￨O￨- risks￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- site￨L￨NN￨O￨- in￨L￨IN￨O￨- Morocco￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- tourists￨L￨NNS￨O￨- come￨L￨VBP￨O￨- to￨L￨TO￨O￨- see￨L￨VB￨O￨- wild￨L￨JJ￨O￨- Barbary￨U￨NNP￨O￨- macaques￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Macaca￨U￨NNP￨O￨- sylvanus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- observed￨L￨VBD￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- physical￨L￨JJ￨O￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- close￨L￨JJ￨O￨- proximity￨L￨NN￨O￨A between￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- macaques￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- during￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- periods￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- macaques￨L￨NNS￨O￨- were￨L￨VBD￨O￨- coughing￨L￨VBG￨O￨- and￨L￨CC￨O￨- sneezing￨L￨VBG￨O￨- heavily￨L￨RB￨O￨- ,￨L￨,￨O￨- highlighting￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- We￨U￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- proposed￨L￨VBD￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- for￨L￨IN￨O￨- those￨L￨DT￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- notified￨L￨VBN￨O￨- cases￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- tip￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- iceberg￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨- C￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- notified￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- varied￨L￨VBD￨O￨A between￨L￨IN￨O￨- 163,902￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 169,382￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- non-notified￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- varied￨L￨VBD￨O￨- between￨L￨IN￨O￨- 1,433,638￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 1,446,771￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- total￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- varied￨L￨VBD￨O￨- between￨L￨IN￨O￨- 1,597,540￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 1,616,153￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- incomplete￨L￨JJ￨O￨- notification￨L￨NN￨O￨- of￨L￨IN￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- non-notified￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- illustrated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A C￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- National￨U￨NNP￨O￨- or￨L￨CC￨O￨- local￨L￨JJ￨O￨- laws￨L￨NNS￨O￨- ,￨L￨,￨O￨- norms￨L￨NNS￨O￨- or￨L￨CC￨O￨- regulations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- sometimes￨L￨RB￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- countries￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- require￨L￨VBP￨O￨- medical￨L￨JJ￨O￨- providers￨L￨NNS￨O￨- to￨L￨TO￨O￨- report￨L￨VB￨O￨- notifiable￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨A authorities￨L￨NNS￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Estimating￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- under-reported￨L￨JJ￨O￨- age-dependent￨L￨JJ￨O￨- compulsorily￨L￨RB￨O￨- notification￨L￨NN￨O￨- databasesMarcos￨L￨NN￨O￨- Amaku1￨U￨NN￨O￨- ,￨L￨,￨O￨- Marcelo￨U￨NNP￨PERSON￨- Nascimento￨U￨NNP￨PERSON￨- Burattini1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Eleazar￨U￨NNP￨PERSON￨- Chaib1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Francisco￨U￨NNP￨PERSON￨- Antonio￨U￨NNP￨PERSON￨- Bezerra￨U￨NNP￨PERSON￨- Coutinho1￨U￨NN￨O￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- Greenhalgh3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Luis￨U￨NNP￨PERSON￨- Fernandez￨U￨NNP￨PERSON￨- Lopez1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Eduardo￨U￨NNP￨PERSON￨- Massad1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 14:23￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- practical￨L￨JJ￨O￨- yet￨L￨RB￨O￨- mathematically￨L￨RB￨O￨- rigorous￨L￨JJ￨O￨- and￨L￨CC￨O￨- computationally￨L￨RB￨O￨- efficient￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- that￨L￨WDT￨O￨- comprehensively￨L￨RB￨O￨- assimilate￨L￨VBP￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- uncertainty￨L￨NN￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- generate￨L￨VBP￨O￨A estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- ,￨L￨,￨O￨- behavior￨L￨NN￨O￨- changes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- test￨L￨NN￨O￨- hypotheses￨L￨NNS￨O￨- ,￨L￨,￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- evaluate￨L￨VB￨O￨- how￨L￨WRB￨O￨- behavior￨L￨NN￨O￨- changes￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- gain￨L￨NN￨O￨- insight￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- pathways￨L￨NNS￨O￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- optimize￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- generate￨L￨VBP￨O￨- short￨L￨JJ￨O￨- and￨L￨CC￨O￨- long-term￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- ,￨L￨,￨O￨- just￨L￨RB￨O￨- to￨L￨TO￨O￨- name￨L￨VB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Richards￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨A rate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- limitation￨L￨NN￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- deviation￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- S-shaped￨U￨JJ￨MISC￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- review￨L￨VBP￨O￨- and￨L￨CC￨O￨- illustrate￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- data￨L￨NNS￨O￨- assimilation￨L￨NN￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- connecting￨L￨VBG￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- data￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- case￨L￨NN￨O￨- counts￨L￨VBZ￨O￨- relating￨L￨VBG￨O￨- to￨L￨TO￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨A or￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g￨L￨NN￨O￨- ,￨L￨,￨O￨- daily￨L￨JJ￨SET￨- incident￨L￨NN￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- growth￨L￨NN￨O￨A phase￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- denoting￨L￨VBG￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- deceleration￨L￨NN￨O￨- of￨L￨IN￨O￨- growth￨L￨NN￨O￨- ”￨L￨''￨O￨- parameter￨L￨NN￨O￨- varied￨L￨VBD￨O￨- between￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- GRM￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- Richards￨U￨NNP￨PERSON￨- growth￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- free￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- logistic-type￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Multinational￨U￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- asymmetry￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨- influence￨L￨NN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- Amy￨U￨NNP￨PERSON￨- Wesolowski1￨U￨NNP￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Elisabeth￨U￨NNP￨PERSON￨- zu￨L￨NNP￨O￨- Erbach-Schoenberg2￨U￨NN￨O￨- ,3￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Andrew￨U￨NNP￨PERSON￨- J.￨U￨NNP￨PERSON￨- Metcalf￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,10￨L￨CD￨NUMBER￨- na2￨L￨NN￨O￨- Nature￨U￨NNP￨O￨- Communicationsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2069￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Developing￨U￨VBG￨O￨- worldEcological￨L￨JJ￨O￨- epidemiologyEcological￨L￨JJ￨O￨- modellingEnvironmental￨L￨JJ￨O￨- social￨L￨JJ￨O￨- sciences￨L￨NNS￨O￨- AbstractSeasonal￨U￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨A mobility￨L￨NN￨O￨A is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- ubiquitous￨L￨JJ￨O￨- and￨L￨CC￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- seasonality￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- limited￨L￨VBN￨O￨- by￨L￨IN￨O￨- data￨L￨NNS￨O￨- availability￨L￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- travel￨L￨NN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨A mobility￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- neglected￨L￨VBN￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- :￨L￨:￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- seasonal9￨L￨JJ￨O￨- ,10,11,12￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- this￨L￨DT￨O￨- broader￨L￨JJR￨O￨- pattern￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- also￨L￨RB￨O￨- fluctuates￨L￨VBZ￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- year￨L￨NN￨DATE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- increased￨L￨VBN￨O￨- travel￨L￨NN￨O￨A from￨L￨IN￨O￨- rural￨L￨JJ￨O￨- to￨L￨TO￨O￨- urban￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- after￨L￨IN￨O￨- national￨L￨JJ￨O￨- holidays￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- seasonal￨L￨JJ￨O￨- travel￨L￨NN￨O￨A and￨L￨CC￨O￨- directional￨L￨JJ￨O￨- asymmetries￨L￨NNS￨O￨- in￨L￨IN￨O￨- Kenya￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Namibia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Pakistan￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- spectrum￨L￨NN￨O￨- from￨L￨IN￨O￨- rural￨L￨JJ￨O￨- nomadic￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- to￨L￨TO￨O￨- highly￨L￨RB￨O￨- urbanized￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Estimating￨U￨VBG￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- which￨L￨WDT￨O￨- monitor￨L￨VBP￨O￨- respiratory￨L￨JJ￨O￨- healthcare￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- and￨L￨CC￨O￨- resource￨L￨NN￨O￨- use￨L￨VBP￨O￨- including￨L￨VBG￨O￨- general￨L￨JJ￨TITLE￨- practitioner￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- GP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- visits￨L￨NNS￨O￨- ,￨L￨,￨O￨- hospitalizations￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Wales￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- between￨L￨IN￨O￨- 7000￨L￨CD￨DATE￨- –￨L￨:￨O￨- 25,000￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- during￨L￨IN￨O￨- winter￨L￨NN￨DATE￨- periods￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- seen￨L￨VBN￨O￨- among￨L￨IN￨O￨- persons￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- 75￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- over￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- PHE￨U￨NNP￨ORGANIZATION￨- publish￨L￨VB￨O￨- weekly￨L￨JJ￨SET￨- surveillance￨L￨NN￨O￨- reports￨L￨NNS￨O￨- that￨L￨IN￨O￨- report￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza-like-illness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- GP￨U￨NN￨O￨- consultations￨L￨NNS￨O￨- ,￨L￨,￨O￨- respiratory￨L￨JJ￨O￨- hospitalizations￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- all-cause￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2014￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A ,￨L￨,￨O￨- geographical￨L￨JJ￨O￨- pilots￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- was￨L￨VBD￨O￨- offered￨L￨VBN￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- 4-to￨L￨JJ￨O￨- 11-year-old￨L￨JJ￨DURATION￨- children￨L￨NNS￨O￨- were￨L￨VBD￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- across￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- extension￨L￨NN￨O￨- is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- implemented￨L￨VBN￨O￨- by￨L￨IN￨O￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- England￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- PHE￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- stages￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- 2-and￨L￨JJ￨O￨- 3-Citation￨L￨NN￨O￨- –￨L￨:￨O￨- 2014￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- in￨L￨IN￨O￨- Zambia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- globally￨L￨RB￨O￨- have￨L￨VBP￨O￨- discussed￨L￨VBN￨O￨- ECF-related￨U￨JJ￨MISC￨- issues￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- quantification/modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- economic￨L￨JJ￨O￨A impacts￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- confirmed￨L￨VBD￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- ECF￨U￨NN￨ORGANIZATION￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- survey￨L￨NN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- conducted￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 699￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- key￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- affecting￨L￨VBG￨O￨- traditional￨L￨JJ￨O￨- cattle￨L￨NNS￨O￨A farmers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- by￨L￨IN￨O￨- several￨L￨JJ￨O￨- donor-funded￨L￨JJ￨O￨- projects￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- ASVEZA￨U￨NNP￨O￨- program￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Belgian￨U￨JJ￨NATIONALITY￨- government￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- farmers￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Government￨U￨NN￨O￨- of￨L￨IN￨O￨- Zambia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- ECF￨U￨NNP￨ORGANIZATION￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Eastern￨U￨NNP￨MISC￨- province￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- endemic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- provinces￨L￨NNS￨O￨- of￨L￨IN￨O￨- Zambia￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- uttermost￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- importance￨L￨NN￨O￨- in￨L￨IN￨O￨- Eastern￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Central￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Southern￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- where￨L￨WRB￨O￨- it￨L￨PRP￨O￨- causes￨L￨VBZ￨O￨- severe￨L￨JJ￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- losses￨L￨NNS￨O￨- among￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A farmers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +East￨U￨NNP￨LOCATION￨- Coast￨U￨NNP￨LOCATION￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ECF￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- protozoan￨L￨NN￨O￨- parasite￨L￨NN￨O￨- Theileria￨U￨FW￨O￨- parva￨L￨FW￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- transstadially￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- three-host￨L￨JJ￨O￨- tick￨L￨NN￨O￨- Rhipicephalus￨U￨JJ￨MISC￨- appendiculatus￨L￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- sense￨L￨NN￨O￨- expected￨L￨VBN￨O￨- :￨L￨:￨O￨- if￨L￨IN￨O￨- human￨L￨JJ￨O￨- weight￨L￨NN￨O￨A is￨L￨VBZ￨O￨- dynamic￨L￨JJ￨O￨- on￨L￨IN￨O￨- short￨L￨JJ￨O￨- timescales￨L￨NNS￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- quasi-equilibrium￨L￨NN￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- BMI￨U￨NNP￨O￨- distributions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- balance￨L￨NN￨O￨- between￨L￨IN￨O￨- drift￨L￨NN￨O￨- towards￨L￨IN￨O￨- the￨L￨DT￨O￨- center￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- diffusion￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- aggregate￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- multifactorial￨L￨JJ￨O￨- perturbations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- alternative￨L￨JJ￨O￨- explanations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- broadening￨L￨VBG￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- put￨L￨VBN￨O￨- forward￨L￨RB￨O￨- that￨L￨IN￨O￨- include￨L￨VBP￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- obesogenic￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- runaway￨L￨JJ￨O￨- train￨L￨NN￨CRIMINAL_CHARGE￨- ”￨L￨''￨O￨- theory￨L￨NN￨O￨- that￨L￨WDT￨O￨- BMI￨U￨NNP￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- right-skewed￨L￨JJ￨O￨- because￨L￨IN￨O￨- high-BMI￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- vicious￨L￨JJ￨O￨- self-reinforcing￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- weight￨L￨NN￨O￨A gain￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- data￨L￨NNS￨O￨- provides￨L￨VBZ￨O￨- strong￨L￨JJ￨O￨- indications￨L￨NNS￨O￨- that￨L￨WDT￨O￨- human￨L￨JJ￨O￨- BMI￨U￨NN￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- balance￨L￨NN￨O￨- between￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- drift￨L￨NN￨O￨A towards￨L￨IN￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- set￨L￨NN￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- diffusion￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- random￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- diet￨L￨NN￨O￨- and￨L￨CC￨O￨- physical￨L￨JJ￨O￨- activity￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- data￨L￨NN￨O￨A set￨L￨NN￨O￨A of￨L￨IN￨O￨- BMI￨U￨NN￨O￨- measurements￨L￨NNS￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 750,000￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- receiving￨L￨VBG￨O￨- Chicago-area￨U￨JJ￨CITY￨- medical￨L￨JJ￨O￨- services￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- mechanistic￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- BMI￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- informed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- trends￨L￨NNS￨O￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- data￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- low-BMI￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- on￨L￨IN￨O￨- average￨L￨JJ￨O￨- increase￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- weight￨L￨NN￨O￨A year-over-year￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- high-BMI￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- decrease￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- weight￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increase/decrease￨L￨NN￨O￨- being￨L￨VBG￨O￨- approximately￨L￨RB￨O￨- linear￨L￨JJ￨O￨- in￨L￨IN￨O￨- BMI￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Mathematical￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- study￨L￨NN￨O￨- design￨L￨NN￨O￨A or￨L￨CC￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- reviewSereina￨L￨NNP￨O￨- A.￨U￨NN￨O￨- 2017Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- offer￨L￨VBP￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- informing￨L￨VBG￨O￨- design￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- to￨L￨TO￨O￨- what￨L￨WP￨O￨- extent￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- planning￨L￨NN￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- inform￨L￨VB￨O￨- study￨L￨NN￨O￨- design￨L￨NN￨O￨A for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- transmitted￨L￨VBD￨O￨- between￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- animals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Eligible￨U￨JJ￨O￨- publications￨L￨NNS￨O￨- and￨L￨CC￨O￨- registered￨L￨VBN￨O￨- trials￨L￨NNS￨O￨- included￨L￨VBD￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- compartmental￨L￨JJ￨O￨- ,￨L￨,￨O￨- individual-based￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- Markov￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- were￨L￨VBD￨O￨- described￨L￨VBN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extracted￨L￨VBD￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- investigated￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- study￨L￨NN￨O￨- design￨L￨NN￨O￨A .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Dynamic￨U￨NNP￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Uzi￨U￨NNP￨O￨- Harush1￨U￨NNP￨O￨- &￨L￨CC￨O￨- Baruch￨U￨NNP￨O￨- Barzel1￨U￨NNP￨O￨- Nature￨U￨NNP￨O￨- Communicationsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2181￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksStatistical￨L￨JJ￨O￨- physics￨L￨NN￨O￨- AbstractAlthough￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- extensively￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- visualize￨L￨VB￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨- in￨L￨IN￨O￨- biological￨L￨JJ￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- technological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- translating￨L￨VBG￨O￨- topology￨L￨NN￨O￨- into￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- flow￨L￨NN￨O￨- continues￨L￨VBZ￨O￨- to￨L￨TO￨O￨- challenge￨L￨VB￨O￨- us￨L￨PRP￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- similar￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- fundamentally￨L￨RB￨O￨- different￨L￨JJ￨O￨- flow￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- uncover￨L￨VB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- actual￨L￨JJ￨O￨- flow￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- perturbative￨L￨JJ￨O￨- formalism￨L￨NN￨O￨- ,￨L￨,￨O￨- analytically￨L￨RB￨O￨- tracking￨L￨VBG￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- nodes/paths￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- flow￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- exposing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rules￨L￨NNS￨O￨- that￨L￨WDT￨O￨- link￨L￨VBP￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- flow￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- mapped￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- universal￨L￨JJ￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- topology￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- ultimately￨L￨RB￨O￨- allowing￨L￨VBG￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- main￨L￨JJ￨O￨- arteries￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨- .￨L￨.￨O￨- +Counter-intuitively￨U￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- formalism￨L￨NN￨O￨- predicts￨L￨VBZ￨O￨- a￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- frequently￨L￨RB￨O￨- encountered￨L￨VBN￨O￨- dynamics￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- flow￨L￨NN￨O￨A of￨L￨IN￨O￨- information￨L￨NN￨O￨- avoids￨L￨VBZ￨O￨- the￨L￨DT￨O￨- hubs￨L￨NNS￨O￨- ,￨L￨,￨O￨- favoring￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- peripheral￨L￨JJ￨O￨- pathways￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- striking￨L￨JJ￨O￨- disparity￨L￨NN￨O￨- between￨L￨IN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- determined￨L￨VBN￨O￨- solely￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes18￨L￨NN￨O￨- ,￨L￨,￨O￨- 23￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- genetic￨L￨JJ￨O￨- relatedness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- MRSA￨U￨NNP￨ORGANIZATION￨- isolates￨L￨NNS￨O￨A was￨L￨VBD￨O￨- determined￨L￨VBN￨O￨- using￨L￨VBG￨O￨- pulsed￨L￨JJ￨O￨- field￨L￨NN￨O￨- gel￨L￨NN￨O￨- electrophoresis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PFGE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- PFGE￨U￨NN￨O￨- banding￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- analysed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- The￨U￨DT￨O￨- MRSA￨U￨NNP￨ORGANIZATION￨- isolates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- spa-typed￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- using￨L￨VBG￨O￨- specific￨L￨JJ￨O￨- primers￨L￨NNS￨O￨- Table￨U￨NNP￨O￨- that￨L￨WDT￨O￨- targeted￨L￨VBD￨O￨- the￨L￨DT￨O￨- repetitive￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- region￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fc￨U￨NN￨MISC￨- binding￨L￨NN￨O￨- region￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- X￨U￨NN￨O￨- region￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- S.￨U￨NNP￨MISC￨- Nine￨U￨NNP￨NUMBER￨- representative￨L￨JJ￨TITLE￨- isolates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 71￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 100￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 131￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 133￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 134￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 143￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 165￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 183￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- randomly￨L￨RB￨O￨- selected￨L￨VBN￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- UPGMA￨U￨NNP￨ORGANIZATION￨- cluster￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spa-sequence￨L￨NN￨O￨- type￨L￨NN￨O￨- determination￨L￨NN￨O￨- using￨L￨VBG￨O￨- specific￨L￨JJ￨O￨- primers￨L￨NNS￨O￨- Table￨U￨NNP￨O￨- that￨L￨WDT￨O￨- targeted￨L￨VBD￨O￨- X￨U￨NN￨O￨- region￨L￨NN￨O￨- as￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- described￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Multilocus￨U￨JJ￨O￨- sequence￨L￨NN￨O￨- typing￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MLST￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- representative￨L￨JJ￨TITLE￨- MRSA￨U￨NNP￨O￨- isolates￨L￨NNS￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- nine￨L￨CD￨NUMBER￨- spa-typed￨L￨JJ￨O￨- MRSA￨U￨NNP￨ORGANIZATION￨- isolates￨L￨NNS￨O￨- targeting￨L￨VBG￨O￨- seven￨L￨CD￨NUMBER￨- housekeeping￨L￨JJ￨O￨- genes￨L￨NNS￨O￨- Table￨U￨NNP￨O￨- was￨L￨VBD￨O￨- PCR-amplified￨U￨JJ￨O￨- using￨L￨VBG￨O￨- specific￨L￨JJ￨O￨- primers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SCCmec-typing￨U￨NN￨O￨- and￨L￨CC￨O￨- CA-MRSA￨U￨NN￨O￨- and￨L￨CC￨O￨- HA-MRSA￨U￨NN￨O￨- designation￨L￨NN￨O￨- were￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- Using￨U￨VBG￨O￨- Specific￨U￨JJ￨O￨- Primer￨U￨NN￨O￨- pairs￨L￨NNS￨O￨- Table￨U￨NNP￨O￨- as￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- described￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- PCR￨U￨NN￨O￨- internal￨L￨JJ￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- targeting￨L￨VBG￨O￨A mecA￨L￨NNP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- assay￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- convergence￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- was￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- childhood￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- borne￨L￨VBD￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- valuable￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- support￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A development￨L￨NN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- provided￨L￨VBD￨O￨- a￨L￨DT￨O￨- platform￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- discussion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- research￨L￨NN￨O￨- challenges￨L￨NNS￨O￨- and￨L￨CC￨O￨- achievements￨L￨NNS￨O￨- on￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨A behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- considered￨L￨VBD￨O￨- a￨L￨DT￨O￨- multipatch￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨A the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- was￨L￨VBD￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨A behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assess￨L￨VBP￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- impact￨L￨VBP￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- AI￨U￨NN￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- CCS￨U￨NN￨ORGANIZATION￨- for￨L￨IN￨O￨- single￨L￨JJ￨O￨- and￨L￨CC￨O￨- co-infecting￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- CCS￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- market￨L￨NN￨O￨A turnover￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- R0￨U￨NN￨O￨- of￨L￨IN￨O￨- co-circulating￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- nature￨L￨NN￨O￨- and￨L￨CC￨O￨- rapid￨L￨JJ￨O￨- turnover￨L￨NN￨O￨A of￨L￨IN￨O￨- LBMs￨U￨NNS￨O￨- remain￨L￨VBP￨O￨- rare￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- generate￨L￨VBP￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- restricted￨L￨JJ￨O￨- to￨L￨TO￨O￨- single￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- age‐acquired￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- age‐related￨L￨JJ￨O￨- structuring￨L￨NN￨O￨- observed￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- colony￨L￨NN￨O￨- ,￨L￨,￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- GIV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- maintained￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- breeding￨L￨VBG￨O￨A population￨L￨NN￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- herd￨L￨NN￨O￨- effect￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Figure￨U￨NNP￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- this￨L￨DT￨O￨- and￨L￨CC￨O￨- shows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- significantly￨L￨RB￨O￨- lower￨L￨JJR￨O￨- per‐susceptible￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- FOI￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- occupied￨L￨VBN￨O￨- by￨L￨IN￨O￨- breeding￨L￨VBG￨O￨A guillemots￨L￨NNS￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- occupied￨L￨VBN￨O￨- by￨L￨IN￨O￨- prebreeding￨L￨VBG￨O￨- guillemots￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- this￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- actively￨L￨RB￨O￨- ejecting￨L￨VBG￨O￨- prebreeding￨L￨JJ￨O￨- guillemots￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- aged￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- attempt￨L￨VBP￨O￨- to￨L￨TO￨O￨- enter￨L￨VB￨O￨- breeding￨L￨VBG￨O￨A areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- breeding￨L￨VBG￨O￨- site￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Guillemots￨U￨NNS￨O￨- with￨L￨IN￨O￨- very￨L￨RB￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- neutralizing￨L￨VBG￨O￨- antibody￨L￨NN￨O￨- against￨L￨IN￨O￨- GIV￨U￨NN￨O￨- ,￨L￨,￨O￨- suggestive￨L￨JJ￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- spend￨L￨VB￨O￨- less￨L￨JJR￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- breeding￨L￨VBG￨O￨A colony￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- are￨L￨VBP￨O￨- less￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- breed￨L￨VB￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- many￨L￨JJ￨O￨- prebreeding￨L￨JJ￨O￨- guillemots￨L￨NNS￨O￨- are￨L￨VBP￨O￨- present￨L￨JJ￨DATE￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- colony￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- breeding￨L￨VBG￨O￨A guillemots￨L￨NNS￨O￨- are￨L￨VBP￨O￨- incubating￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- eggs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- wild￨L￨JJ￨O￨- Mojave￨U￨NNP￨O￨- desert￨L￨NN￨O￨- tortoise￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Gopherus￨U￨NN￨O￨- agassizii￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- emerging￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- burrow￨L￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- base￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- creosote￨L￨NN￨O￨- shrub￨L￨NN￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- evidence￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- 2‐year‐long￨L￨JJ￨O￨- ,￨L￨,￨O￨- seminatural￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- experiment￨L￨NN￨O￨A conducted￨L￨VBN￨O￨- on￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- ,￨L￨,￨O￨- previously￨L￨RB￨DATE￨- wild￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- antibody￨L￨NN￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- M.￨U￨NNP￨O￨- Because￨U￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progresses￨L￨VBZ￨O￨- slowly￨L￨RB￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- within￨L￨IN￨O￨- both￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- tortoises￨L￨NNS￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- evident￨L￨JJ￨O￨- in￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 276￨L￨CD￨NUMBER￨- tortoises￨L￨NNS￨O￨- without￨L￨IN￨O￨- signs￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- seronegative￨L￨JJ￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- seronegative￨L￨JJ￨O￨- and￨L￨CC￨O￨- experimentally￨L￨RB￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- M.￨U￨NN￨O￨- Although￨U￨IN￨O￨- sensitive￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- tests￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- in￨L￨IN￨O￨- tortoises￨L￨NNS￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- exist￨L￨VB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- experiment￨L￨NN￨O￨A ,￨L￨,￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- animals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- likely￨L￨JJ￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- mycoplasma￨L￨NN￨O￨- at￨L￨IN￨O￨- some￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- lives￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- animals￨L￨NNS￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- group￨L￨NN￨O￨- likely￨L￨JJ￨O￨- harbored￨L￨VBN￨O￨- low￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- M.￨U￨NN￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- quantify￨L￨VBP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- recrudescence￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Mycoplasma￨U￨NN￨O￨- agassizii￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- upper￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨A tract￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- URTD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- Mojave￨U￨NNP￨LOCATION￨- desert￨L￨NN￨O￨- tortoises￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Gopherus￨U￨NN￨O￨- agassizii￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- 20th￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- 40th￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- and￨L￨CC￨DATE￨- 60th￨L￨JJ￨DATE￨- days￨L￨NNS￨DATE￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨A case￨L￨NN￨O￨A was￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- box￨L￨NN￨O￨- plots￨L￨NNS￨O￨- of￨L￨IN￨O￨- MERS-CoV￨U￨NN￨O￨- incidences￨L￨NNS￨O￨- in￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- were￨L￨VBD￨O￨- computed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- variance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ANOVA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- control￨L￨NN￨O￨- intervention￨L￨NN￨O￨- was￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- MERS-CoV￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- immediately￨L￨RB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- confirmation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨A case￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- were￨L￨VBD￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 20th￨L￨JJ￨DATE￨- day￨L￨NN￨DATE￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- confirmation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- depicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- box￨L￨NN￨O￨- plots￨L￨NNS￨O￨- of￨L￨IN￨O￨- incidences￨L￨NNS￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- H￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- MERS-CoV￨U￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- intervention￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- 20th￨L￨JJ￨DATE￨- ,￨L￨,￨DATE￨- 40th￨L￨JJ￨DATE￨- ,￨L￨,￨DATE￨- and￨L￨CC￨DATE￨- 60th￨L￨JJ￨DATE￨- days￨L￨NNS￨DATE￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨A case￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- control￨L￨NN￨O￨- intervention￨L￨NN￨O￨- was￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- MERS-CoV￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- immediately￨L￨RB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- confirmation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨A case￨L￨NN￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- 10,000￨L￨CD￨NUMBER￨- stochastic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- computed￨L￨VBN￨O￨A by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨- with￨L￨IN￨O￨- initial￨L￨JJ￨O￨- values￨L￨NNS￨O￨- S￨U￨NN￨O￨- =￨L￨JJ￨O￨- 100,000￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- E￨U￨NN￨O￨- =￨L￨JJ￨O￨- 10￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- I￨U￨PRP￨O￨- =￨L￨JJ￨O￨- A￨U￨NN￨O￨- =￨L￨JJ￨O￨- H￨U￨NN￨O￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- β￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.085￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- l1￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- l2￨L￨NN￨O￨- =￨L￨JJ￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- κ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/6￨L￨CD￨NUMBER￨- .6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ρ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.585￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.6403￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/7￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- cascade￨L￨NN￨O￨A snapshot￨L￨NN￨O￨- consisting￨L￨VBG￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- infected/active￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- inference￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- cascade￨L￨NN￨O￨A that￨L￨WDT￨O￨- infects￨L￨VBZ￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- linear￨L￨JJ￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨O￨- node￨L￨NN￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- result￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- a￨L￨DT￨O￨- cascade￨L￨NN￨O￨- with￨L￨IN￨O￨- least￨L￨JJS￨O￨- difference￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- source￨L￨NN￨O￨A inference￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- tackled￨L￨VBN￨O￨- under￨L￨IN￨O￨- Independent￨U￨NNP￨ORGANIZATION￨- Cascade￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- IC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- and￨L￨CC￨O￨- topical￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨- interests￨L￨NNS￨O￨A ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- seasonal￨L￨JJ￨O￨- periodicity￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- summer￨L￨NN￨DATE￨- vacation￨L￨NN￨O￨- advertisements￨L￨NNS￨O￨- which￨L￨WDT￨O￨- spread￨L￨VBD￨O￨- more￨L￨RBR￨O￨- effectively￨L￨RB￨O￨- during￨L￨IN￨O￨- Spring￨U￨NN￨DATE￨- –￨L￨:￨O￨- Summer￨U￨NNP￨DATE￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- epidemic-based￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- analyzing￨L￨VBG￨O￨- such￨L￨JJ￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨- processes￨L￨NNS￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- three￨L￨CD￨NUMBER￨- indicative￨L￨JJ￨O￨- operational￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- and￨L￨CC￨O￨- results￨L￨VBZ￨O￨- that￨L￨IN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation-based￨L￨JJ￨O￨- formalism￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- framework￨L￨NN￨O￨- subject￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A modeling￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- between￨L￨IN￨O￨- information￨L￨NN￨O￨- propagation￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- associated￨L￨VBN￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- and￨L￨CC￨O￨- leveraging￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- that￨L￨WDT￨O￨- user￨L￨NN￨O￨- interests￨L￨NNS￨O￨- have￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Contrary￨U￨JJ￨O￨- to￨L￨TO￨O￨- previous￨L￨JJ￨O￨- works￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- user￨L￨NN￨O￨- interest￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- features￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- interest￨L￨NN￨O￨- periodicity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- useful￨L￨JJ￨O￨- information￨L￨NN￨O￨- within￨L￨IN￨O￨- such￨L￨JJ￨O￨- complex￨L￨JJ￨O￨- wireless-social￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- social-wireless￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- generalized￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- other￨L￨JJ￨O￨- types￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- straightforwardly￨L￨RB￨O￨- considered.Motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- proliferation￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- useful￨L￨JJ￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- generalized￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- useful￨L￨JJ￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected/informed￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- evolving￨L￨VBG￨O￨- user￨L￨NN￨O￨- interest￨L￨NN￨O￨- are￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- through￨L￨IN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- verified￨L￨VBN￨O￨- via￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A cause￨L￨VBP￨O￨- significant￨L￨JJ￨O￨- threats￨L￨NNS￨O￨- to￨L￨TO￨O￨- honey￨L￨NN￨O￨- bees￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- bacteria￨L￨NNS￨O￨- ,￨L￨,￨O￨- microsporidia￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- arthropods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- parasites￨L￨NNS￨O￨A include￨L￨VBP￨O￨- any￨L￨DT￨O￨- organism￨L￨NN￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Deformed￨U￨JJ￨O￨- Wing￨U￨NN￨O￨- Virus￨U￨NN￨O￨- that￨L￨WDT￨O￨- infects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- hemolymph￨L￨NN￨O￨- of￨L￨IN￨O￨- bees￨L￨NNS￨O￨- and￨L￨CC￨O￨- causes￨L￨VBZ￨O￨- deformed￨L￨VBN￨O￨- wings￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- Varroa￨U￨NNP￨O￨- destructor￨L￨NN￨O￨- mites￨L￨NNS￨O￨- that￨L￨WDT￨O￨- suck￨L￨VBP￨O￨- the￨L￨DT￨O￨- blood￨L￨NN￨O￨- of￨L￨IN￨O￨- bee￨L￨NN￨O￨- larvae￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- small￨L￨JJ￨O￨- hive￨L￨JJ￨O￨- beetles￨L￨NNS￨O￨- that￨L￨WDT￨O￨- parasitize￨L￨VBP￨O￨- the￨L￨DT￨O￨- honey￨L￨NN￨O￨- and￨L￨CC￨O￨- pollen￨L￨NN￨O￨- stores￨L￨NNS￨O￨- of￨L￨IN￨O￨- honey￨L￨NN￨O￨- bee￨L￨NN￨O￨- colonies￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ectoparasitic￨L￨JJ￨O￨- mite￨L￨JJ￨O￨- Varroa￨U￨NN￨O￨- destructor￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- it￨L￨PRP￨O￨- vectors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- cause￨L￨NN￨O￨A of￨L￨IN￨O￨- honey￨L￨NN￨O￨- bee￨L￨NN￨O￨- colony￨L￨NN￨O￨- losses￨L￨NNS￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- “￨L￨``￨O￨- parasite￨L￨NN￨O￨- ”￨L￨''￨O￨- to￨L￨TO￨O￨- broadly￨L￨RB￨O￨A refer￨L￨VB￨O￨- to￨L￨TO￨O￨- organisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- fitness￨L￨NN￨O￨- of￨L￨IN￨O￨- honey￨L￨NN￨O￨- bees￨L￨NNS￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- or￨L￨CC￨O￨- colony￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Why￨U￨WRB￨O￨- have￨L￨VBP￨O￨- honey￨L￨NN￨O￨- bee￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- management￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- had￨L￨VBD￨O￨- so￨L￨RB￨O￨- little￨L￨JJ￨O￨- success￨L￨NN￨O￨A ?￨L￨.￨O￨- +While￨U￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- understanding￨L￨NN￨O￨- is￨L￨VBZ￨O￨- undesirable￨L￨JJ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- scientific￨L￨JJ￨O￨- perspective￨L￨NN￨O￨A given￨L￨VBN￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- time-series￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- comprise￨L￨VBP￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- record￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- U.S.￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- troubling￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- perspective￨L￨NN￨O￨- in￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- leaves￨L￨VBZ￨O￨- in￨L￨IN￨O￨- limbo￨L￨NN￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- what￨L￨WP￨O￨- potential￨L￨JJ￨O￨- visitors￨L￨NNS￨O￨- should￨L￨MD￨O￨- do￨L￨VB￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- visits￨L￨NNS￨O￨- −￨L￨VBP￨O￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- people￨L￨NNS￨O￨- by￨L￨IN￨O￨- necessity￨L￨NN￨O￨- must￨L￨MD￨O￨- revisit￨L￨VB￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- Ground￨U￨NN￨LOCATION￨- Zero￨U￨NNP￨LOCATION￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- or￨L￨CC￨O￨- weekly￨L￨JJ￨SET￨- basis￨L￨NN￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- work￨L￨VBP￨O￨- or￨L￨CC￨O￨- live￨L￨VBP￨O￨- there￨L￨RB￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- have￨L￨VBP￨O￨- family￨L￨NN￨O￨- there￨L￨RB￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Zika￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- notable￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- geographical￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- Ground￨U￨NN￨LOCATION￨- Zero￨U￨NNP￨LOCATION￨- areas￨L￨NNS￨O￨- were￨L￨VBD￨O￨- specified￨L￨VBN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- Wynwood￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NNP￨O￨- 1a￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Miami￨U￨NNP￨CITY￨- Beach￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Little￨U￨NNP￨LOCATION￨- River￨U￨NNP￨TITLE￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- separated￨L￨VBN￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- drive￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- Miami￨U￨NNP￨CITY￨- area￨L￨NN￨O￨A .￨L￨.￨O￨- +However￨U￨RB￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- report￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- incorporated￨L￨VBN￨O￨- this￨L￨DT￨O￨- visit-revisit￨L￨NN￨O￨- feature￨L￨NN￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- then￨L￨RB￨O￨- been￨L￨VBN￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- these￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- U.S.￨U￨NNP￨COUNTRY￨- Ground￨U￨NN￨LOCATION￨- Zero￨U￨NNP￨LOCATION￨- outbreaks￨L￨NNS￨O￨A .￨L￨.￨O￨- +Potential￨U￨JJ￨O￨- visitors￨L￨NNS￨O￨- to￨L￨TO￨O￨- Ground￨U￨NNP￨LOCATION￨- Zero￨U￨NNP￨LOCATION￨- at￨L￨IN￨O￨- timestep￨L￨NN￨O￨- t￨L￨NN￨O￨- enter￨L￨VBP￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨A p￨L￨NN￨O￨- and￨L￨CC￨O￨- leave￨L￨VB￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- p￨L￨NN￨O￨- Their￨U￨PRP$￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- Ground￨U￨NN￨LOCATION￨- Zero￨U￨NNP￨LOCATION￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- q￨L￨NN￨O￨- of￨L￨IN￨O￨- getting￨L￨VBG￨O￨- bitten￨L￨NN￨O￨- and￨L￨CC￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- q￨L￨NN￨O￨- of￨L￨IN￨O￨- recovering￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- :￨L￨:￨O￨- Ground￨U￨NNP￨O￨- Zero￨U￨NNP￨NUMBER￨- (￨L￨-LRB-￨O￨- red￨L￨JJ￨O￨- shaded￨L￨JJ￨O￨- area￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- our￨L￨PRP$￨O￨- visit-revisit￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- extended￨L￨VBD￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- pair￨L￨NN￨O￨- formation￨L￨NN￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- at￨L￨IN￨O￨- most￨L￨JJS￨O￨- n￨L￨NN￨O￨- partners￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time.A￨L￨NN￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- In￨U￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨A stages￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- predominantly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨A approximation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- asymptomatically￨L￨RB￨O￨- exact￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity.KeywordsSI￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- Branching￨U￨VBG￨O￨- process￨L￨NN￨O￨- Basic￨U￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Dynamic￨U￨NNP￨O￨- network￨L￨NN￨O￨- Stochastic￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- Mathematics￨U￨NNP￨O￨- Subject￨U￨NNP￨O￨- Classification60J80￨U￨NNP￨O￨- 92D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSexually￨U￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- STIs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- ’s￨L￨POS￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- remaining￨L￨VBG￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- global￨L￨JJ￨O￨- threat￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infectious-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneously￨L￨RB￨O￨- mixing￨L￨VBG￨O￨- population￨L￨NN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨A approximation￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- partners￨L￨NNS￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unbounded￨L￨JJ￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- includes￨L￨VBZ￨O￨- as￨L￨IN￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- vaccinate￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- chosen￨L￨VBN￨O￨- uniformly￨L￨RB￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- binomial￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- vaccinating￨L￨VBG￨O￨- households￨L￨NNS￨O￨A at￨L￨IN￨O￨- random￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- concentrated￨L￨VBN￨O￨- at￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Households-based￨U￨JJ￨O￨- vaccination￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- those￨L￨DT￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- households￨L￨NNS￨O￨A of￨L￨IN￨O￨- size￨L￨NN￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- every￨L￨DT￨O￨- household￨L￨NN￨O￨- size￨L￨NN￨O￨- n￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- specify￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- outline￨L￨VB￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- lastly￨L￨RB￨O￨- introduce￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- action￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- on￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- receive￨L￨VBP￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- initiated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- chosen￨L￨VBN￨O￨- uniformly￨L￨RB￨O￨A at￨L￨IN￨O￨- random￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- all￨L￨DT￨O￨- assumed￨L￨VBD￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- time￨L￨NN￨O￨- that￨L￨IN￨O￨- such￨L￨JJ￨O￨- data-driven￨L￨JJ￨O￨- modelling￨L￨NN￨O￨A involving￨L￨VBG￨O￨- contagion￨L￨NN￨O￨- both￨L￨CC￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- cities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- through￨L￨IN￨O￨- geographic￨L￨JJ￨O￨- proximity￨L￨NN￨O￨- or￨L￨CC￨O￨- media￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- country￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- basis￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- performed￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- at￨L￨IN￨O￨- analysing￨L￨VBG￨O￨A these￨L￨DT￨O￨- data￨L￨NNS￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- sheds￨L￨VBZ￨O￨- new￨L￨JJ￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- riots￨L￨NNS￨O￨- as￨L￨IN￨O￨- instances￨L￨NNS￨O￨- of￨L￨IN￨O￨- collective￨L￨JJ￨O￨- human￨L￨JJ￨O￨- behaviour4￨L￨NN￨O￨- ,5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- regular￨L￨JJ￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A on￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- data-driven￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- BelgiumGiancarlo￨U￨NNP￨O￨- De￨U￨NNP￨O￨- Luca1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Kim￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Kerckhove2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Pietro￨U￨NNP￨O￨- Coletti2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Chiara￨U￨NNP￨PERSON￨- Poletto1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Nathalie￨U￨NNP￨PERSON￨- Bossuyt3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Niel￨U￨NNP￨PERSON￨- Hens2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Vittoria￨U￨NNP￨PERSON￨- Colizza1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profileBMC￨L￨NN￨MISC￨- Infectious￨U￨JJ￨MISC￨- DiseasesBMC￨U￨NN￨MISC￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18:29￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- School￨U￨NNP￨O￨- closure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- option￨L￨NN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- often￨L￨RB￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- larger￨L￨JJR￨O￨- vulnerability￨L￨NN￨O￨- to￨L￨TO￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- limited￨L￨JJ￨O￨- prior￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- mix￨L￨VBP￨O￨- at￨L￨IN￨O￨- school￨L￨NN￨O￨A with￨L￨IN￨O￨- high￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- thus￨L￨RB￨O￨- representing￨L￨VBG￨O￨- key￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- holiday-associated￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- affect￨L￨VBP￨O￨- seasonal￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- Changes￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- establish￨L￨VBP￨O￨- contacts￨L￨NNS￨O￨- during￨L￨IN￨O￨- holidays￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- ingredient￨L￨NN￨O￨- explaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- mitigating￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- regular￨L￨JJ￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A .￨L￨.￨O￨- +Christmas￨U￨NNP￨DATE￨- holidays￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- later￨L￨JJ￨O￨- school￨L￨NN￨O￨A breaks￨L￨NNS￨O￨- may￨L￨MD￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- stressing￨L￨VBG￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- calendar￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- process￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- one-class￨L￨JJ￨O￨- support￨L￨NN￨O￨- vector￨L￨NN￨O￨- machine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SVM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- determines￨L￨VBZ￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- flow￨L￨NN￨O￨A is￨L￨VBZ￨O￨- malicious￨L￨JJ￨O￨- or￨L￨CC￨O￨- normal￨L￨JJ￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- approach￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- two-stage￨L￨JJ￨O￨- process￨L￨NN￨O￨- for￨L￨IN￨O￨- detection￨L￨NN￨O￨A of￨L￨IN￨O￨- malicious￨L￨JJ￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- traffic￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- disparity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- node/edge￨L￨JJ￨O￨- turnover￨L￨NN￨O￨- ,￨L￨,￨O￨- highlighting￨L￨VBG￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- using￨L￨VBG￨O￨- lifetime-preserving￨L￨JJ￨O￨- reference￨L￨NN￨O￨A models￨L￨NNS￨O￨- when￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- edges￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- continuously￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- PT￨U￨NN￨O￨- implicitly￨L￨RB￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- edges￨L￨NNS￨O￨- and￨L￨CC￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- continuously￨L￨RB￨O￨A active￨L￨JJ￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- sampling￨L￨NN￨O￨- period￨L￨NN￨O￨- –￨L￨:￨O￨- an￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- hold￨L￨VB￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- PT￨U￨NN￨O￨- ,￨L￨,￨O￨- PTN￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- PTE￨U￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- spreading￨L￨VBG￨O￨A dynamics￨L￨NNS￨O￨A on￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- synthetic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- edge￨L￨NN￨O￨- lifespans￨L￨NNS￨O￨- and￨L￨CC￨O￨- tunable￨L￨JJ￨O￨- burstiness￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- four￨L￨CD￨NUMBER￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- enter￨L￨VBP￨O￨- and￨L￨CC￨O￨- leave￨L￨VBP￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- dynamically￨L￨RB￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Lifetime-preserving￨U￨JJ￨O￨- reference￨L￨NN￨O￨A models￨L￨NNS￨O￨- for￨L￨IN￨O￨- characterizing￨L￨VBG￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Mingwu￨U￨NNP￨O￨- Li1￨U￨NN￨O￨- ,￨L￨,￨O￨- Vikyath￨U￨NN￨PERSON￨- D￨U￨NN￨PERSON￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- randomly￨L￨RB￨O￨- permuted￨L￨JJ￨O￨- times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- reference￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- probe￨L￨VB￨O￨- how￨L￨WRB￨O￨- temporal￨L￨JJ￨O￨- features￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Wu￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- na1￨L￨CD￨NUMBER￨- Nature￨U￨NNP￨O￨- Communicationsvolume￨U￨NNP￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 218￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksEpidemiologyInfectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- AbstractOver￨U￨VBP￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- few￨L￨JJ￨DURATION￨- decades￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- global￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- built￨L￨VBN￨O￨- with￨L￨IN￨O￨- worldwide￨L￨JJ￨O￨- air-transportation￨L￨JJ￨O￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- how￨L￨WRB￨O￨- epidemics￨L￨NNS￨O￨- spread￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- SARS￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Ebola￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- metapopulation￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- built￨L￨VBN￨O￨- with￨L￨IN￨O￨- worldwide￨L￨JJ￨O￨- air-transportation￨L￨JJ￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- WAN￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- global￨L￨JJ￨O￨A spread￨L￨NN￨O￨A of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza1￨L￨NN￨O￨- ,2,3,4￨L￨NN￨O￨- ,￨L￨,￨O￨- SARS5￨U￨NN￨O￨- ,6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- MERS-CoV7￨U￨NN￨O￨- ,￨L￨,￨O￨- Ebola8￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Zika9￨U￨NN￨O￨- ,10￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A/H1N1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- West￨U￨NNP￨MISC￨- African￨U￨NNP￨NATIONALITY￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Liberia.ResultsMajor￨U￨NNP￨O￨- assumptions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- frameworkThroughout￨L￨NN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- only￨L￨RB￨O￨- global￨L￨JJ￨O￨A spread￨L￨NN￨O￨A of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- relatively￨L￨RB￨O￨- fast￨L￨JJ￨O￨- timescales￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- population￨L￨NN￨O￨- peak￨L￨NN￨O￨- within￨L￨IN￨O￨- 300￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- establishment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- MERS￨U￨NNS￨O￨- ,￨L￨,￨O￨- Ebola￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- demographics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- births￨L￨NNS￨O￨- ,￨L￨,￨O￨- aging￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- negligible￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- metapopulation￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- cities￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- travel￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- WAN￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- WAN￨U￨NNP￨O￨- metapopulation￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- Methods￨U￨NNS￨O￨- for￨L￨IN￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- Ebola￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- key￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- robustly￨L￨RB￨O￨- estimated￨L￨VBN￨O￨- in￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- from￨L￨IN￨O￨- public￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨A spread￨L￨NN￨O￨A at￨L￨IN￨O￨- very￨L￨RB￨O￨- low￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- cost￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- Markovian￨U￨JJ￨MISC￨- transmission￨L￨NN￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- re-parametrised￨L￨JJ￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- pairwise-like￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- many￨L￨JJ￨O￨- well-known￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- regular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- is￨L￨VBZ￨O￨- exponentially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- or￨L￨CC￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- length.KeywordsEpidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- Non-Markovian￨U￨JJ￨MISC￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- Mean-field￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- Mathematics￨U￨NNP￨O￨- Subject￨U￨NNP￨O￨- Classification92D30￨U￨NN￨O￨- 37N25￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- IntroductionThe￨U￨NNP￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- and￨L￨CC￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- mature￨L￨JJ￨O￨- and￨L￨CC￨O￨- fruitful￨L￨JJ￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- possible￨L￨JJ￨O￨- states￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- pairwise￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- considering￨L￨VBG￨O￨- separately￨L￨RB￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- and￨L￨CC￨O￨- all￨L￨DT￨O￨- possible￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- become￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighbours￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- MP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- formalism￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- living￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- patch￨L￨NN￨O￨- is￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dU￨L￨NNP￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- sigma￨L￨NN￨O￨A Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- dW￨L￨NN￨O￨- t￨L￨NN￨O￨- U￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- dt￨L￨NN￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- U￨U￨NNP￨O￨- U￨U￨NNP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- U￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- abundance￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- per-capita￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NNP￨PERSON￨- b￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- intraspecific￨L￨JJ￨O￨- competition￨L￨NN￨O￨- ,￨L￨,￨O￨- Pow￨U￨NNP￨O￨- sigma￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infinitesimal￨L￨JJ￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- per-capita￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- W￨U￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Brownian￨U￨JJ￨MISC￨- motion￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- long-term￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Rational￨U￨JJ￨MISC￨- Pow￨U￨NN￨MISC￨- sigma￨L￨NN￨O￨A 2￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- way￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- If￨U￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Rational￨U￨JJ￨O￨- Pow￨U￨NN￨O￨- sigma￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- U￨U￨NNP￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- u￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- U￨U￨NNP￨O￨- t￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- weakly￨L￨RB￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- unique￨L￨JJ￨O￨- invariant￨L￨JJ￨O￨- probability￨L￨NN￨O￨- measure￨L￨NN￨O￨- rho￨L￨NN￨O￨- on￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +which￨L￨WDT￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- sometimes￨L￨RB￨O￨- coupling￨L￨NN￨O￨- by￨L￨IN￨O￨- dispersal￨L￨NN￨O￨- can￨L￨MD￨O￨- make￨L￨VB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- persistent.KeywordsStochastic￨L￨JJ￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨A Density-dependence￨U￨NN￨MISC￨- Ergodicity￨U￨NNP￨MISC￨- Spatial￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- Lotka￨U￨NNP￨LOCATION￨- –￨L￨:￨O￨- Volterra￨U￨NNP￨CITY￨- model￨L￨NN￨TITLE￨- Lyapunov￨U￨NNP￨PERSON￨- exponent￨L￨NNP￨O￨- Habitat￨U￨NNP￨O￨- fragmentation￨L￨NN￨O￨- Stochastic￨U￨NNP￨O￨- environment￨L￨NN￨O￨- Dispersion￨U￨NNP￨O￨- A.￨U￨NNP￨O￨- Continuous-space￨U￨NNP￨O￨- discrete-time￨L￨JJ￨O￨- population￨L￨NN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- disperse￨L￨VBP￨O￨- and￨L￨CC￨O￨- experience￨L￨VBP￨O￨- uncorrelated￨L￨JJ￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- by￨L￨IN￨O￨- Hardin￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- density-dependent￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨A that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- dispersal￨L￨NN￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- complements￨L￨VBZ￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Evans￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨A sciences￨L￨NNS￨O￨- ,￨L￨,￨O￨- rumouring￨L￨VBG￨O￨- behaviour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- analysed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- collective￨L￨JJ￨O￨- sense-making￨L￨NN￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- understand￨L￨VB￨O￨- situations￨L￨NNS￨O￨- characterised￨L￨VBN￨O￨- by￨L￨IN￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- ,￨L￨,￨O￨- anxiety￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- official￨L￨JJ￨O￨- news￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rise￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨A media￨L￨NNS￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- even￨L￨RB￨O￨- better￨L￨JJR￨O￨- platform￨L￨NN￨O￨- for￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- rumours￨L￨NNS￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- Gaildraud￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- rumour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- informal￨L￨JJ￨O￨- noise￨L￨NN￨O￨- that￨L￨WDT￨O￨- exists￨L￨VBZ￨O￨- ,￨L￨,￨O￨- persists￨L￨VBZ￨O￨- ,￨L￨,￨O￨- becomes￨L￨VBZ￨O￨- evanescent￨L￨JJ￨O￨- and￨L￨CC￨O￨- disappears￨L￨VBZ￨O￨- as￨L￨RB￨O￨- fast￨L￨JJ￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- appeared￨L￨VBD￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- psychology￨L￨NN￨O￨- a￨L￨DT￨O￨- rumour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- declaration￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- plausible￨L￨JJ￨O￨- ,￨L￨,￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- news￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- widespread￨L￨JJ￨O￨A without￨L￨IN￨O￨- checking￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- rumours￨L￨NNS￨O￨- could￨L￨MD￨O￨- only￨L￨RB￨O￨- be￨L￨VB￨O￨- by￨L￨IN￨O￨- word￨L￨NN￨O￨- of￨L￨IN￨O￨- mouth￨L￨NN￨O￨A .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- tested￨L￨VBN￨O￨- strains￨L￨NNS￨O￨- are￨L￨VBP￨O￨- included￨L￨VBN￨O￨- those￨L￨DT￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- circulated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- incoming￨L￨JJ￨O￨- season￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- tests￨L￨NNS￨O￨- yield￨L￨VBP￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- adult￨L￨JJ￨O￨- and￨L￨CC￨O￨- elderly￨L￨JJ￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- a￨L￨DT￨O￨- joint￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- estimated￨L￨VBN￨O￨- age‐specific￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- and￨L￨CC￨O￨- reporting￨L￨VBG￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- derived￨L￨VBD￨O￨A an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- tested￨L￨VBN￨O￨- strain￨L￨NN￨O￨- coincides￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- circulating￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- season￨L￨NN￨O￨A ,￨L￨,￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- season￨L￨NN￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- that￨L￨IN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- summer￨L￨NN￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- negligible￨L￨JJ￨O￨- .￨L￨.￨O￨- +Historical￨U￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A activity￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- both￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- and￨L￨CC￨O￨- short-term￨L￨JJ￨O￨- predictability￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- use￨L￨VBP￨O￨- such￨L￨JJ￨O￨- autoregressive￨L￨JJ￨O￨- information￨L￨NN￨O￨- can￨L￨MD￨O￨- capture￨L￨VB￨O￨- and￨L￨CC￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- salient￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Santillana￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- ensemble￨L￨NN￨O￨- approach￨L￨NN￨O￨- combining￨L￨VBG￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- outperformed￨L￨VBD￨O￨- any￨L￨DT￨O￨- other￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- national￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A predictions￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- original￨L￨JJ￨O￨- network￨L￨NN￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- Xia￨U￨NNP￨O￨- et￨L￨FW￨O￨- al24￨L￨FW￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Delhi￨U￨NNP￨CITY￨- using￨L￨VBG￨O￨- network￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- did￨L￨VBD￨O￨A not￨L￨RB￨O￨- take￨L￨VB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- attributes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- slum￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- larger￨L￨JJR￨O￨- family￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- daily￨L￨JJ￨SET￨- activity￨L￨NN￨O￨- schedules￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- is￨L￨VBZ￨O￨- about￨L￨IN￨O￨- 1000￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- per￨L￨IN￨O￨- square￨L￨NN￨O￨- mile￨L￨NN￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- slums￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 100￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- higher￨L￨JJR￨O￨- .14￨L￨CD￨NUMBER￨- Larger￨U￨NN￨O￨- household￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- crowding￨L￨VBG￨O￨- make￨L￨VB￨O￨- it￨L￨PRP￨O￨- easier￨L￨JJR￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Baker￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨A al16￨L￨FW￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- among￨L￨IN￨O￨- children￨L￨NNS￨O￨- doubles￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- addition￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- adolescents￨L￨NNS￨O￨- or￨L￨CC￨O￨- adults￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- or￨L￨CC￨O￨- older￨L￨JJR￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- six-room￨L￨JJ￨O￨- house￨L￨NN￨O￨- .￨L￨.￨O￨- +Chen￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al4￨L￨FW￨O￨- used￨L￨VBN￨O￨- network￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- refined￨L￨VBN￨O￨A social￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- Delhi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- accounted￨L￨VBD￨O￨- for￨L￨IN￨O￨- slum￨L￨NN￨O￨- demographics￨L￨NNS￨O￨- and￨L￨CC￨O￨- slum￨L￨NN￨O￨- activities￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- study￨L￨VB￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- Delhi￨U￨NNP￨CITY￨- is￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- target￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- studying￨L￨VBG￨O￨- other￨L￨JJ￨O￨- slum￨L￨NN￨O￨- areas￨L￨NNS￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- outside￨L￨IN￨O￨- of￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨A types￨L￨NNS￨O￨- and￨L￨CC￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- examined￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- on￨L￨IN￨O￨- several￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- slum￨L￨NN￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- gender￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- Delhi￨U￨NNP￨CITY￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- original￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- network￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- refined￨L￨VBN￨O￨A (￨L￨-LRB-￨O￨- network￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +P.￨U￨NNP￨PERSON￨- Smith￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Roche￨U￨NNP￨O￨- :￨L￨:￨O￨- Grant￨U￨NNP￨O￨- Investigator￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- Consulting￨U￨NNP￨O￨- fee￨L￨NN￨O￨- C.￨U￨NNP￨PERSON￨- Chaiyakunapruk￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Roche￨U￨NNP￨O￨- :￨L￨:￨O￨- Grant￨U￨NNP￨O￨- Investigator￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- Consulting￨U￨NNP￨O￨- fee￨L￨NN￨O￨- and￨L￨CC￨O￨- Research￨U￨NN￨O￨- grant￨L￨NN￨O￨- K.￨U￨NNP￨PERSON￨- Kamauu￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Roche￨U￨NNP￨O￨- :￨L￨:￨O￨- Consultant￨U￨NN￨TITLE￨- and￨L￨CC￨O￨- Grant￨U￨NNP￨O￨- Investigator￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- Consulting￨U￨NNP￨O￨- fee￨L￨NN￨O￨- and￨L￨CC￨O￨- Research￨U￨NN￨O￨- support￨L￨NN￨O￨A R.￨U￨NNP￨PERSON￨- E.￨U￨NNP￨PERSON￨- Nelson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Roche￨U￨NNP￨O￨- :￨L￨:￨O￨- Consultant￨U￨NN￨TITLE￨- and￨L￨CC￨O￨- Grant￨U￨NNP￨O￨- Investigator￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- Consulting￨U￨NNP￨O￨- fee￨L￨NN￨O￨- ,￨L￨,￨O￨- Research￨U￨NNP￨O￨- grant￨L￨NN￨O￨- and￨L￨CC￨O￨- Research￨U￨NN￨O￨- support￨L￨NN￨O￨- M.￨U￨NN￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- were￨L￨VBD￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- rhinovirus￨L￨NN￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- not￨L￨RB￨O￨- previously￨L￨RB￨DATE￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- species￨L￨NNS￨O￨- other￨L￨JJ￨O￨- than￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- causative￨L￨JJ￨O￨- agent￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- chimpanzees￨L￨NNS￨O￨- by￨L￨IN￨O￨- directly￨L￨RB￨O￨- sampling￨L￨NN￨O￨- the￨L￨DT￨O￨- lesions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- dead￨L￨JJ￨O￨- animal￨L￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- noninvasive￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- from￨L￨IN￨O￨- feces￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- .￨L￨.￨O￨- +Anthroponotic￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- origin￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- respiratory￨L￨JJ￨O￨A viruses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- caused￨L￨VBN￨O￨- notable￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- chimpanzee￨L￨NN￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- –￨L￨:￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- molecular￨L￨JJ￨O￨- testing￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- postmortem￨L￨NN￨O￨- and￨L￨CC￨O￨- noninvasive￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- fecal￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- wild￨L￨JJ￨O￨- apes￨L￨NNS￨O￨- during￨L￨IN￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- implicated￨L￨VBN￨O￨- human￨L￨JJ￨O￨- paramyxoviruses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- family￨L￨NN￨O￨- Paramyxoviridae￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- anthroponotic￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- –￨L￨:￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Rhinovirus￨U￨NN￨O￨- C￨U￨NN￨O￨- causes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- human￨L￨JJ￨O￨- upper￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨A tract￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- most￨L￨JJS￨O￨- acute￨L￨JJ￨O￨- exacerbations￨L￨NNS￨O￨- of￨L￨IN￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- rhinovirus￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- mildly￨L￨RB￨O￨- symptomatic￨L￨JJ￨O￨- ,￨L￨,￨O￨- rhinovirus￨L￨NN￨O￨- C￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- influenza-like￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨A symptoms￨L￨NNS￨O￨- and￨L￨CC￨O￨- acute￨L￨JJ￨O￨- exacerbations￨L￨NNS￨O￨- of￨L￨IN￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- origin￨L￨NN￨O￨A of￨L￨IN￨O￨- rhinovirus￨L￨NN￨O￨- C￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- protective￨L￨JJ￨O￨- allele￨L￨NN￨O￨- among￨L￨IN￨O￨- modern￨L￨JJ￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- thought￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- occurred￨L￨VBN￨O￨- ≈￨L￨SYM￨O￨- 8,000￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- ago￨L￨RB￨DATE￨- .￨L￨.￨O￨- +Network￨U￨NNP￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- suggested￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- useful￨L￨JJ￨O￨- tool￨L￨NN￨O￨- in￨L￨IN￨O￨- prioritizing￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- by￨L￨IN￨O￨- targeting￨L￨VBG￨O￨A the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- or￨L￨CC￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Network￨U￨NNP￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- by￨L￨IN￨O￨- targeting￨L￨VBG￨O￨A those￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- or￨L￨CC￨O￨- locations￨L￨NNS￨O￨- most￨L￨RBS￨O￨- connected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Extensive￨U￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- has￨L￨VBZ￨O￨- demonstrated￨L￨VBN￨O￨A the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- prophylactic￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- Hawaiian￨U￨JJ￨MISC￨- monk￨L￨NN￨TITLE￨- seals￨L￨NNS￨O￨- against￨L￨IN￨O￨- morbillivirus￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- monovalent￨L￨JJ￨O￨- recombinant￨L￨JJ￨O￨- CDV￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- commercially￨L￨RB￨O￨- produced￨L￨VBN￨O￨- for￨L￨IN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- ferrets￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Purevax￨U￨NNP￨O￨- ,￨L￨,￨O￨- Merial￨U￨NNP￨ORGANIZATION￨- Inc.￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Duluth￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- GA￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- effective￨L￨JJ￨O￨- for￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- other￨L￨JJ￨O￨- carnivores￨L￨NNS￨O￨- including￨L￨VBG￨O￨- seals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- option￨L￨NN￨O￨A for￨L￨IN￨O￨- protecting￨L￨VBG￨O￨- Hawaiian￨U￨JJ￨MISC￨- monk￨L￨NN￨TITLE￨- seals￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- morbillivirus￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- this￨L￨DT￨O￨- basis￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- influences￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- manpower￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- alarm￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- development￨L￨NN￨O￨- effort￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- team￨L￨NN￨O￨- size￨L￨NN￨O￨- are￨L￨VBP￨O￨- examined￨L￨VBN￨O￨- through￨L￨IN￨O￨- computer￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨- team￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- involves￨L￨VBZ￨O￨- six￨L￨CD￨NUMBER￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- G￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- function￨L￨NN￨O￨- f￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- alarm￨L￨NN￨O￨- threshold￨L￨NN￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- development￨L￨NN￨O￨- effort￨L￨NN￨O￨A W￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- manpower￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨- team￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- dependent￨L￨JJ￨O￨- upon￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- function￨L￨NN￨O￨- f￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- manpower￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- alarm￨L￨NN￨O￨- threshold￨L￨NN￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- effort￨L￨NN￨O￨A W￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- G.￨U￨NNP￨O￨- +An￨U￨DT￨O￨- optimal￨L￨JJ￨O￨A solution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- stands￨L￨VBZ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- choice￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- team￨L￨NN￨O￨- size￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- company￨L￨NN￨O￨- ’s￨L￨POS￨O￨- respective￨L￨JJ￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- that￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- team￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- tradeoff￨L￨NN￨O￨- first￨L￨RB￨ORDINAL￨- goes￨L￨VBZ￨O￨- sharply￨L￨RB￨O￨- down￨L￨RB￨O￨- then￨L￨RB￨O￨- goes￨L￨VBZ￨O￨- slowly￨L￨RB￨O￨- up￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- respective￨L￨JJ￨O￨- optimal￨L￨JJ￨O￨A team￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- 47￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 27￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 21￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Resource￨U￨NNP￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨- network￨L￨NN￨O￨- Jian￨U￨NNP￨O￨- Jiang1￨U￨NNP￨O￨- ,2￨L￨NNP￨O￨- &￨L￨CC￨O￨- Tianshou￨U￨NNP￨O￨- Zhou2￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 1629￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComplex￨L￨NNP￨O￨- networks￨L￨NNS￨O￨- AbstractWhile￨U￨NNP￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- resource￨L￨NN￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- factor￨L￨NN￨O￨- in￨L￨IN￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- contagions￨L￨NNS￨O￨- ,￨L￨,￨O￨- outbreaks￨L￨NNS￨O￨- may￨L￨MD￨O￨- occur￨L￨VB￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- reach￨L￨VBP￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- previous￨L￨JJ￨O￨- studies1￨L￨NN￨O￨- ,2,3,4,5,6,7,8,9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- was￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- single￨L￨JJ￨O￨- or￨L￨CC￨O￨- monoplex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- apparently￨L￨RB￨O￨- a￨L￨DT￨O￨- simplification￨L￨NN￨O￨- since￨L￨IN￨O￨- in￨L￨IN￨O￨- reality￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨A spread￨L￨VBN￨O￨A often￨L￨RB￨O￨- through￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- channels￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- different￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- travelling￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- airports￨L￨NNS￨O￨- ,￨L￨,￨O￨- train￨L￨NN￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- bus￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- just￨L￨RB￨O￨- as￨L￨IN￨O￨- information￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- diffused￨L￨VBN￨O￨- through￨L￨IN￨O￨- different￨L￨JJ￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- mediums￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- Facebook￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A processes￨L￨NNS￨O￨- may￨L￨MD￨O￨- simultaneously￨L￨RB￨O￨- occur￨L￨VB￨O￨- through￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- spread￨L￨VB￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- homosexual￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- heterosexual￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +analyzed￨L￨VBN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨A coupled￨L￨JJ￨O￨- network￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- classic￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model14￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- a￨L￨DT￨O￨- mechanic￨L￨JJ￨TITLE￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- both￨L￨DT￨O￨- resource￨L￨NN￨O￨A factor￨L￨NN￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- assessment￨L￨NN￨O￨- and￨L￨CC￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- resilience￨L￨NN￨O￨A to￨L￨TO￨O￨- epidemics￨L￨NNS￨O￨- must￨L￨MD￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- functionalities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- profile￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- maintained￨L￨VBN￨O￨- or￨L￨CC￨O￨- recover￨L￨VB￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- adverse￨L￨JJ￨O￨- events.Even￨L￨NN￨O￨- though￨L￨IN￨O￨- the￨L￨DT￨O￨- assessment￨L￨NN￨O￨- and￨L￨CC￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- adverse￨L￨JJ￨O￨- events￨L￨NNS￨O￨- resilience￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- subject￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- research32￨L￨NN￨O￨- ,33,35,36￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- integration￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- computational￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- threats￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- largely￨L￨RB￨O￨- unexplored27￨L￨JJ￨O￨- ,37,38￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Resilience￨U￨NN￨O￨- management￨L￨NN￨O￨A during￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- Emanuele￨U￨NNP￨PERSON￨- Massaro￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,2,3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Alexander￨U￨NNP￨PERSON￨- Ganin￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Nicola￨U￨NNP￨MISC￨- Perra5￨U￨NNP￨O￨- ,6,7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Igor￨U￨NNP￨PERSON￨- Linkov1￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Alessandro￨U￨NNP￨PERSON￨- Vespignani6￨U￨NNP￨O￨- ,7,8￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 1859￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Computational￨U￨NNP￨O￨- sciencePhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractAssessing￨U￨VBG￨O￨- and￨L￨CC￨O￨- managing￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- considering￨L￨VBG￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- exceedingly￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- and￨L￨CC￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- extremely￨L￨RB￨O￨- expensive￨L￨JJ￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- resilience￨L￨NN￨O￨A to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- structured￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- defining￨L￨VBG￨O￨- the￨L￨DT￨O￨- system-wide￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- functionality￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- getting￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disruption￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- functionality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- deterioration￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- studying￨L￨VBG￨O￨- both￨L￨CC￨O￨- conceptual￨L￨JJ￨O￨- and￨L￨CC￨O￨- data-driven￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- integrated￨L￨JJ￨O￨- consideration￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- risks￨L￨NNS￨O￨- and￨L￨CC￨O￨- societal￨L￨JJ￨O￨- disruptions￨L￨NNS￨O￨- under￨L￨IN￨O￨- resilience￨L￨NN￨O￨A assessment￨L￨NN￨O￨- framework￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- insightful￨L￨JJ￨O￨- picture￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- might￨L￨MD￨O￨- impact￨L￨VB￨O￨- society￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- broaden￨L￨VB￨O￨- the￨L￨DT￨O￨- model-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- expanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- purview￨L￨NN￨O￨- by￨L￨IN￨O￨- including￨L￨VBG￨O￨- measures￨L￨NNS￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- resilience￨L￨NN￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- response￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- disturbances￨L￨NNS￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- aftermath￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- mitigation￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- recovery￨L￨NN￨O￨- and￨L￨CC￨O￨- retention￨L￨NN￨O￨- of￨L￨IN￨O￨- functionality28￨L￨NN￨O￨- ,29,30￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- he￨L￨PRP￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- cite￨L￨VB￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Darwin￨U￨NNP￨PERSON￨- itself￨L￨PRP￨O￨- ,￨L￨,￨O￨- Metchnikoff￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- student￨L￨NN￨TITLE￨- Charles￨U￨NNP￨PERSON￨- Nicolle￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- director￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Pasteur￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- Tunis￨U￨NNP￨CITY￨- for￨L￨IN￨O￨- 30￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- distinctive￨L￨JJ￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- '￨L￨``￨O￨- birth￨L￨NN￨O￨- ,￨L￨,￨O￨- life￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A '￨L￨POS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- notion￨L￨NN￨O￨- of￨L￨IN￨O￨- '￨L￨``￨O￨- mutation￨L￨NN￨O￨- '￨L￨''￨O￨- in￨L￨IN￨O￨- microorganisms￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- animal￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- can￨L￨MD￨O￨- act￨L￨VB￨O￨- as￨L￨IN￨O￨- '￨L￨``￨O￨- reservoirs￨L￨NNS￨O￨- '￨L￨''￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- idea￨L￨NN￨O￨- of￨L￨IN￨O￨- harnessing￨L￨VBG￨O￨- ecology￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- traced￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Pasteur￨U￨NNP￨O￨- and￨L￨CC￨O￨- Darwin￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨A biology￨L￨NN￨O￨- and￨L￨CC￨O￨- medical￨L￨JJ￨O￨- microbiology￨L￨NN￨O￨- have￨L￨VBP￨O￨- profoundly￨L￨RB￨O￨- changed￨L￨VBN￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- theoretically￨L￨RB￨O￨- and￨L￨CC￨O￨- empirically￨L￨RB￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- then￨L￨RB￨O￨- .￨L￨.￨O￨- +Historian￨U￨NN￨TITLE￨- of￨L￨IN￨O￨- science￨L￨NN￨O￨- Andrew￨U￨NNP￨PERSON￨- Mendelsohn￨U￨NNP￨PERSON￨- even￨L￨RB￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- laboratories￨L￨NNS￨O￨- of￨L￨IN￨O￨- Pasteur￨U￨NNP￨O￨- and￨L￨CC￨O￨- Koch￨U￨NNP￨PERSON￨- as￨L￨IN￨O￨- '￨L￨``￨O￨- the￨L￨DT￨O￨- earliest￨L￨JJS￨O￨- place￨L￨NN￨O￨- of￨L￨IN￨O￨- sustained￨L￨JJ￨O￨- experimental￨L￨JJ￨O￨- cellular-level￨L￨NNS￨O￨- in￨L￨FW￨O￨- vitro￨L￨FW￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- phenomena￨L￨NNS￨O￨- understood￨L￨VBN￨O￨- as￨L￨IN￨O￨- biological￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- and￨L￨CC￨O￨- evolutionary￨L￨JJ￨O￨A mechanisms￨L￨NNS￨O￨- '￨L￨POS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- Darwin￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- later￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- long￨L￨RB￨O￨- after￨L￨IN￨O￨- his￨L￨PRP$￨O￨- death￨L￨NN￨O￨- ,￨L￨,￨O￨- medical￨L￨JJ￨O￨A doctors￨L￨NNS￨O￨- in￨L￨IN￨O￨- Britain￨U￨NNP￨COUNTRY￨- brought￨L￨VBD￨O￨- his￨L￨PRP$￨O￨- ideas￨L￨NNS￨O￨- to￨L￨TO￨O￨- bear￨L￨VB￨O￨- on￨L￨IN￨O￨- issues￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- and￨L￨CC￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Evolutionary￨U￨JJ￨O￨- biology￨L￨NN￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- us￨L￨PRP￨O￨- understand￨L￨VB￨O￨- emerging￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- perhaps￨L￨RB￨O￨- already￨L￨RB￨O￨- foreseen￨L￨VBN￨O￨- by￨L￨IN￨O￨- Pasteur￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- test￨L￨VB￨O￨- our￨L￨PRP$￨O￨- hypothesis￨L￨NN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- remoteness￨L￨NN￨O￨- and￨L￨CC￨O￨- HSV-2￨U￨NN￨MISC￨- risk￨L￨NN￨O￨- in￨L￨IN￨O￨- Kaokoveld￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- ask￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- questions￨L￨NNS￨O￨- :￨L￨:￨O￨- At￨U￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- there￨L￨EX￨O￨- a￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- having￨L￨VBG￨O￨A a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- partners￨L￨NNS￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- ’s￨L￨POS￨O￨- residential￨L￨JJ￨O￨- region￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- partner￨L￨NN￨O￨- homophily￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- having￨L￨VBG￨O￨- HSV-2-specific￨U￨JJ￨O￨- antibodies￨L￨NNS￨O￨- ?￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- HSV-2￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- Kaokoveld￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- having￨L￨VBG￨O￨A a￨L￨DT￨O￨- high￨L￨JJ￨O￨- overall￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- women￨L￨NNS￨O￨- =￨L￨JJ￨O￨- 56￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- men￨L￨NNS￨O￨- =￨L￨JJ￨O￨- 29￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- HSV-2￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- heterogeneously￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- geographically￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- regions￨L￨NNS￨O￨- having￨L￨VBG￨O￨- significantly￨L￨RB￨O￨- higher￨L￨JJR￨O￨- prevalence￨L￨NN￨O￨- than￨L￨IN￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- here￨L￨RB￨O￨- whether￨L￨IN￨O￨- these￨L￨DT￨O￨- high￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- regions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- functionally￨L￨RB￨O￨- remote￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- as￨L￨IN￨O￨- having￨L￨VBG￨O￨A higher￨L￨JJR￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- partner￨L￨NN￨O￨- selection￨L￨NN￨O￨- than￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- so￨L￨RB￨O￨- ,￨L￨,￨O￨- do￨L￨VBP￨O￨- these￨L￨DT￨O￨- functionally￨L￨RB￨O￨- remote￨L￨JJ￨O￨- regions￨L￨NNS￨O￨A have￨L￨VBP￨O￨- sexual￨L￨JJ￨O￨- network￨L￨NN￨O￨- structures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- densely￨L￨RB￨O￨- connected￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- foster￨L￨VBP￨O￨- accelerated￨L￨VBN￨O￨- STI￨U￨NNP￨O￨- transmission￨L￨NN￨O￨- ?￨L￨.￨O￨- +Apart￨U￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- fluctuating￨L￨VBG￨O￨- environmental￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨A thresholds￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- in￨L￨IN￨O￨- field￨L￨NN￨O￨- populations￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- scarcity￨L￨NN￨O￨- ,￨L￨,￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- replicated￨L￨VBN￨O￨- experimentation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- ecology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- environmental￨L￨JJ￨O￨- and￨L￨CC￨O￨- density-mediated￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- simply￨L￨RB￨O￨- by￨L￨IN￨O￨- high￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- density￨L￨NN￨O￨- enhancing￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- contacts￨L￨NNS￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- or￨L￨CC￨O￨- an￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- spore￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- we￨L￨PRP￨O￨- further￨L￨RB￨O￨- examine￨L￨VB￨O￨- how￨L￨WRB￨O￨- parameter￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨- can￨L￨MD￨O￨- influence￨L￨VB￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨A probability￨L￨NN￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- robustness￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨- threshold￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- experimental￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Daphnia￨U￨NNP￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- environmentally￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- fungal￨L￨JJ￨O￨- parasite￨L￨NN￨O￨- .￨L￨.￨O￨- +Central￨U￨NNP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- to￨L￨TO￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- density￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨- threshold￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- below￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unable￨L￨JJ￨O￨- to￨L￨TO￨O￨- invade￨L￨VB￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- accessed￨L￨VBD￨O￨- the￨L￨DT￨O￨- PCR￨U￨NN￨O￨- positivity￨L￨NN￨O￨- for￨L￨IN￨O￨- VACV￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- cows￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- domestic￨L￨JJ￨O￨- and￨L￨CC￨O￨- wild￨L￨JJ￨O￨- mammals￨L￨NNS￨O￨- from￨L￨IN￨O￨- areas￨L￨NNS￨O￨- with￨L￨IN￨O￨- or￨L￨CC￨O￨- without￨L￨IN￨O￨- official￨L￨JJ￨O￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- VACV￨U￨NN￨O￨- zoonotic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- west￨L￨NN￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- São￨U￨NNP￨LOCATION￨- Paulo￨U￨NNP￨LOCATION￨- State￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- VACV￨U￨NN￨ORGANIZATION￨- has￨L￨VBZ￨O￨- once￨L￨RB￨DATE￨- isolated￨L￨VBN￨O￨- from￨L￨IN￨O￨- peritoneum￨L￨NN￨O￨- and￨L￨CC￨O￨- testicles￨L￨NNS￨O￨- samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- Mus￨U￨NN￨O￨- musculus￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- VACV￨U￨NN￨O￨- DNA￨U￨NN￨O￨- was￨L￨VBD￨O￨- once￨L￨RB￨DATE￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- opossums￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Didelphis￨U￨NN￨O￨- albiventris￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- dogs￨L￨NNS￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- VACV￨U￨NN￨ORGANIZATION￨- outbreaks￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- cows￨L￨NNS￨O￨- or￨L￨CC￨O￨- humans￨L￨NNS￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- species￨L￨NNS￨O￨- were￨L￨VBD￨O￨- established￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- Brazilian￨U￨JJ￨NATIONALITY￨- VACV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- positive￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- from￨L￨IN￨O￨- Anhembi￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- 0.7￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Bofete￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0.7￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- positivity￨L￨NN￨O￨- were￨L￨VBD￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- Torre￨U￨NNP￨PERSON￨- de￨L￨IN￨PERSON￨- Pedra￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- VACV￨U￨NN￨O￨- zoonotic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- were￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- reported￨L￨VBN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +VACV￨U￨NN￨O￨- DNA￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- also￨L￨RB￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- recipients￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨- samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- experimentally￨L￨RB￨O￨- infected￨L￨JJ￨O￨- cows￨L￨NNS￨O￨- and￨L￨CC￨O￨- mice￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- VACV￨U￨NN￨O￨- zoonotic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- VACV￨U￨NN￨O￨- DNA￨U￨NN￨O￨- was￨L￨VBD￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- milker￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- blood￨L￨NN￨O￨- of￨L￨IN￨O￨- her￨L￨PRP$￨O￨- two￨L￨CD￨NUMBER￨- daughters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- engaged￨L￨VBN￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- exposure￨L￨NN￨O￨- activity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 05￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Epidemic￨U￨NNP￨O￨- spreading￨L￨VBG￨O￨- in￨L￨IN￨O￨- modular￨L￨JJ￨O￨A time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Matthieu￨U￨NNP￨O￨- Nadini1￨U￨NN￨O￨- ,6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kaiyuan￨U￨NNP￨PERSON￨- Sun2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Enrico￨U￨NNP￨PERSON￨- Ubaldi￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Michele￨U￨NNP￨PERSON￨- Starnini4￨U￨NNP￨O￨- ,5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Alessandro￨U￨NNP￨PERSON￨- Rizzo￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Nicola￨U￨NNP￨O￨- Perra7￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2352￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksPhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractWe￨U￨NN￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- modular￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- that￨L￨IN￨O￨- modular￨L￨JJ￨O￨A structures￨L￨NNS￨O￨- induce￨L￨VBP￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- without￨L￨IN￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- unfolding￨L￨VBG￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- conducted￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨A scale￨L￨NN￨O￨A separation￨L￨NN￨O￨- which￨L￨WDT￨O￨- effectively￨L￨RB￨O￨- neglects￨L￨VBZ￨O￨- all￨L￨DT￨O￨- such￨L￨JJ￨O￨- features￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- creation￨L￨NN￨O￨- or￨L￨CC￨O￨- renewal￨L￨NN￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- correlated￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- driving￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time-scale￨L￨JJ￨O￨- considered27￨L￨NN￨O￨- ,28￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- 2-layer￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmissions￨L￨NNS￨O￨- across￨L￨IN￨O￨- female￨L￨JJ￨O￨- sex￨L￨NN￨O￨A workers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- FSWs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- persons￨L￨NNS￨O￨- who￨L￨WP￨O￨- inject￨L￨VBP￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- (￨L￨-LRB-￨O￨- PWID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- through￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- behaviors￨L￨NNS￨O￨- :￨L￨:￨O￨- unprotected￨L￨JJ￨O￨- sex￨L￨NN￨O￨- and￨L￨CC￨O￨- needle-sharing￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- remains￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- how￨L￨WRB￨O￨- significant￨L￨JJ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- bridge￨L￨NN￨O￨A individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- who￨L￨WP￨O￨- connect￨L￨VBP￨O￨- multiple￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- targeting￨L￨VBG￨O￨- different￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- modes￨L￨NNS￨O￨- across￨L￨IN￨O￨- key￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Behavioral￨U￨JJ￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- unveiled￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- female￨L￨JJ￨O￨- sex￨L￨NN￨O￨A workers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- FSWs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- persons￨L￨NNS￨O￨- who￨L￨WP￨O￨- inject￨L￨VBP￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- (￨L￨-LRB-￨O￨- PWID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- could￨L￨MD￨O￨- facilitate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- populations6￨L￨NN￨O￨- ,7,8,9￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- studies￨L￨NNS￨O￨- demonstrated￨L￨VBD￨O￨- that￨L￨IN￨O￨- bridge￨L￨NN￨O￨A individuals￨L￨NNS￨O￨- played￨L￨VBD￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmissions￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- patients￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- just￨L￨RB￨O￨- smaller￨L￨JJR￨O￨- than￨L￨IN￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- foot￨L￨NN￨O￨A and￨L￨CC￨O￨- mouth￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- pediatric￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mumps￨L￨NNS￨O￨- virus￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- causative￨L￨JJ￨O￨- agent￨L￨NN￨O￨- of￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- enveloped￨L￨JJ￨O￨- RNA￨U￨NN￨O￨- virus￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- mumps￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- preventable￨L￨JJ￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- doses￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mumps￨L￨NNS￨O￨- vaccine￨L￨NN￨O￨A in￨L￨IN￨O￨- many￨L￨JJ￨O￨- developed￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- nowadays￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- attenuated￨L￨VBN￨O￨- mumps￨L￨NNS￨O￨- virus￨L￨NN￨O￨A vaccine￨L￨NN￨O￨- was￨L￨VBD￨O￨- licensed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Namely￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- molecular-level￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- seeding￨L￨FW￨O￨- ,￨L￨,￨O￨- aggregation￨L￨NN￨O￨A ,￨L￨,￨O￨- short-range￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- biological￨L￨JJ￨O￨- tissue￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- inter-regional￨L￨JJ￨O￨- macroscopic￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- long-range￨L￨JJ￨O￨- MP￨U￨NN￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- brain￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- integrative￨L￨JJ￨O￨- methodological￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- historical￨L￨JJ￨O￨- overview￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- aimed￨L￨VBN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- MP￨U￨NN￨O￨- seeding￨L￨NN￨O￨- ,￨L￨,￨O￨- aggregation￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- propagation￨L￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- section￨L￨NN￨O￨- offers￨L￨VBZ￨O￨- an￨L￨DT￨O￨- overview￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- prion￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- seeding￨L￨NN￨O￨- ,￨L￨,￨O￨- aggregation￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- short-range￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ODEs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Eigen￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- prototype￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- autocatalysis￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- Prusiner￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 23￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- intended￨L￨VBD￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- conversion￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- prion￨L￨NN￨O￨- protein￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- PrPC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- agent￨L￨NN￨O￨- protein￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- usually￨L￨RB￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- PrPSc￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Fast￨U￨JJ￨O￨- and￨L￨CC￨O￨- accurate￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- source￨L￨NN￨O￨A in￨L￨IN￨O￨- large￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- Robert￨U￨NNP￨PERSON￨- Paluch1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Xiaoyan￨U￨NNP￨PERSON￨- Lu2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Krzysztof￨U￨NNP￨PERSON￨- Suchecki1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Bolesław￨U￨NNP￨PERSON￨- K.￨U￨NNP￨PERSON￨- Hołyst￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,4￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2508￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- scienceInformation￨L￨NN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- computation￨L￨NN￨O￨- AbstractSpread￨U￨NN￨O￨- over￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- ubiquitous￨L￨JJ￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- increasingly￨L￨RB￨O￨- wide￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- approach￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- observers￨L￨NNS￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- quality￨L￨NN￨O￨A information￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- spread￨L￨NN￨O￨- encounter￨L￨NN￨O￨- times￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- ignored￨L￨VBN￨O￨- and￨L￨CC￨O￨- potential￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- are￨L￨VBP￨O￨- selected￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- gradient￨L￨NN￨O￨- from￨L￨IN￨O￨- high￨L￨JJ￨O￨- quality￨L￨NN￨O￨- observers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Locating￨U￨VBG￨O￨- spread￨L￨NN￨O￨- sources￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- important￨L￨JJ￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Pinto￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Thiran￨U￨NNP￨O￨- and￨L￨CC￨O￨- Vetterli￨U￨NNP￨PERSON￨- introduced￨L￨VBD￨O￨- an￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PTVA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- act￨L￨VBP￨O￨- as￨L￨IN￨O￨- observers￨L￨NNS￨O￨- and￨L￨CC￨O￨- report￨L￨NN￨O￨- times￨L￨NNS￨O￨A at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- reached￨L￨VBD￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- had￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- research￨L￨NN￨O￨- questions￨L￨NNS￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- protozoal￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- children￨L￨NNS￨O￨- drinking￨L￨VBG￨O￨- from￨L￨IN￨O￨- contaminated￨L￨VBN￨O￨A tubewells￨L￨NNS￨O￨- ,￨L￨,￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- associated￨L￨VBN￨O￨- child￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- does￨L￨VBZ￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- child￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- attributable￨L￨JJ￨O￨- to￨L￨TO￨O￨- protozoa￨L￨NN￨O￨- in￨L￨IN￨O￨- drinking￨L￨NN￨O￨- water￨L￨NN￨O￨- compare￨L￨VB￨O￨- to￨L￨TO￨O￨- actual￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- all-pathogen/all-pathway￨L￨JJ￨O￨- child￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- stated￨L￨VBN￨O￨- alternatively￨L￨RB￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- much￨L￨JJ￨O￨- child￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- morbidity￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- consumption￨L￨NN￨O￨- of￨L￨IN￨O￨- protozoa-contaminated￨L￨JJ￨O￨- drinking￨L￨NN￨O￨- water￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- cryptosporidiosis￨L￨NN￨O￨- or￨L￨CC￨O￨- giardiasis￨L￨NN￨O￨- from￨L￨IN￨O￨- drinking￨L￨NN￨O￨- water￨L￨NN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- diarrhea￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- 3,835￨L￨CD￨NUMBER￨- children￨L￨NNS￨O￨- in￨L￨IN￨O￨- study￨L￨NN￨O￨- communities￨L￨NNS￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- contaminated￨L￨VBN￨O￨A tubewell￨L￨NN￨O￨- drinking￨L￨NN￨O￨- water￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- microbial￨L￨JJ￨O￨- risk￨L￨NN￨O￨- assessment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- QMRA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- inputs￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- QMRA￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- population￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- sanitation￨L￨NN￨O￨- intervention￨L￨NN￨O￨- trial￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- measured￨L￨VBN￨O￨- protozoal￨L￨JJ￨O￨- concentrations￨L￨NNS￨O￨- in￨L￨IN￨O￨- tubewells￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- caretaker-reported￨L￨JJ￨O￨- 7-day￨L￨JJ￨DURATION￨- recall￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- period￨L￨NN￨O￨- prevalence￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- site-specific￨L￨JJ￨O￨- population￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- address￨L￨VB￨O￨- these￨L￨DT￨O￨- research￨L￨NN￨O￨- questions￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- diarrhea￨L￨NN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- from￨L￨IN￨O￨- ingestion￨L￨NN￨O￨- of￨L￨IN￨O￨- Cryptosporidium￨U￨NN￨O￨- and/or￨L￨CC￨O￨- Giardia￨U￨NN￨O￨- in￨L￨IN￨O￨- contaminated￨L￨VBN￨O￨A tubewell￨L￨NN￨O￨- drinking￨L￨NN￨O￨- water￨L￨NN￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- QMRA￨U￨NN￨O￨- approach￨L￨NN￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Mosquito￨U￨NNP￨O￨- community￨L￨NN￨O￨- influences￨L￨VBZ￨O￨- West￨U￨NNP￨LOCATION￨- Nile￨U￨NNP￨LOCATION￨- virus￨L￨NN￨O￨- seroprevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- birds￨L￨NNS￨O￨A :￨L￨:￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- spillover￨L￨NN￨O￨- into￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- Josué￨U￨NNP￨O￨- Martínez-de￨U￨NNP￨O￨- la￨L￨NNP￨O￨- Puente￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,4￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Martina￨U￨NNP￨PERSON￨- Ferraguti1￨U￨NNP￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Santiago￨U￨NNP￨CITY￨- Ruiz2￨U￨NN￨O￨- ,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- Roiz1￨U￨NNP￨PERSON￨- ,5￨L￨CD￨NUMBER￨- nAff5￨L￨NN￨O￨- ,￨L￨,￨O￨- Francisco￨U￨NNP￨PERSON￨- Llorente3￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Elisa￨U￨NNP￨PERSON￨- Pérez-Ramírez3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Miguel￨U￨NNP￨PERSON￨- Ángel￨U￨NNP￨PERSON￨- Jiménez-Clavero3￨U￨NN￨O￨- ,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ramón￨U￨NNP￨PERSON￨- Soriguer1￨U￨NN￨O￨- ,4￨L￨NN￨O￨- &￨L￨CC￨O￨- Jordi￨U￨NNP￨O￨- Figuerola1￨U￨NN￨O￨- ,4￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2599￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- BiodiversityEcological￨U￨NNP￨O￨- epidemiology￨L￨NN￨O￨- AbstractMosquito￨U￨NNP￨O￨- community￨L￨NN￨O￨- composition￨L￨NN￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- central￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨- vector-borne￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- sampled￨L￨VBD￨O￨- 2544￨L￨CD￨DATE￨- birds￨L￨NNS￨O￨A and￨L￨CC￨O￨- 340829￨L￨CD￨NUMBER￨- mosquitoes￨L￨NNS￨O￨- in￨L￨IN￨O￨- 45￨L￨CD￨NUMBER￨- localities￨L￨NNS￨O￨- ,￨L￨,￨O￨- analysed￨L￨VBN￨O￨- in￨L￨IN￨O￨- 15￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- containing￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- urban￨L￨JJ￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- rural￨L￨JJ￨O￨- and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- natural￨L￨JJ￨O￨- area￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- evaluated￨L￨VBD￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- community￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- seroprevalence￨L￨NN￨O￨A of￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Nile￨U￨NNP￨LOCATION￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- WNV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- house￨L￨NN￨O￨- sparrows￨L￨NNS￨O￨- along￨L￨IN￨O￨- an￨L￨DT￨O￨- urbanisation￨L￨NN￨O￨- gradient￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- area￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +Human￨U￨JJ￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- was￨L￨VBD￨O￨- zero￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- localities￨L￨NNS￨O￨- where￨L￨WRB￨O￨- VNT-positive￨U￨JJ￨O￨- birds￨L￨NNS￨O￨A were￨L￨VBD￨O￨- captured￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- potentially￨L￨RB￨O￨- explains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- low￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- WNV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Locating￨U￨VBG￨O￨- multiple￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- sources￨L￨NNS￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- varying￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- sparse￨L￨JJ￨O￨A observations￨L￨NNS￨O￨- Zhao-Long￨U￨NNP￨O￨- Hu1￨U￨NN￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Zhesi￨U￨NNP￨PERSON￨- Shen￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Shinan￨U￨JJ￨O￨- Cao3￨U￨NN￨O￨- ,￨L￨,￨O￨- Boris￨U￨NNP￨O￨- Podobnik4￨U￨NNP￨O￨- ,5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Huijie￨U￨NNP￨O￨- Yang6￨U￨NNP￨O￨- ,￨L￨,￨O￨- Wen-Xu￨U￨NNP￨O￨- Wang2￨U￨NNP￨O￨- ,6￨L￨NNP￨O￨- &￨L￨CC￨O￨- Ying-Cheng￨U￨NNP￨O￨- Lai7￨U￨NN￨O￨- ,8￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2685￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksInformation￨L￨NN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- computation￨L￨NN￨O￨- AbstractData￨U￨NN￨O￨- based￨L￨VBN￨O￨- source￨L￨NN￨O￨- localization￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +Bridging￨U￨VBG￨O￨- structural￨L￨JJ￨O￨- observability￨L￨NN￨O￨- and￨L￨CC￨O￨- sparse￨L￨JJ￨O￨A signal￨L￨NN￨O￨- reconstruction￨L￨NN￨O￨- theories￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- locate￨L￨VB￨O￨- diffusion￨L￨NN￨O￨- sources￨L￨NNS￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- varying￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- solely￨L￨RB￨O￨- on￨L￨IN￨O￨- sparse￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- messenger￨L￨NN￨TITLE￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Choosing￨U￨VBG￨O￨- large￨L￨JJ￨O￨- degree￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- messengers￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- sparse￨L￨JJ￨O￨A observations￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- such￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- sufficient￨L￨JJ￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- sources￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- located￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- recent￨L￨JJ￨O￨- progress￨L￨NN￨O￨- ,￨L￨,￨O￨- locating￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- sources￨L￨NNS￨O￨A in￨L￨IN￨O￨- time￨L￨NN￨O￨- varying￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- outstanding￨L￨JJ￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +Counterintuitively￨U￨RB￨O￨- ,￨L￨,￨O￨- sources￨L￨NNS￨O￨A in￨L￨IN￨O￨- more￨L￨RBR￨O￨- rapidly￨L￨RB￨O￨- varying￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- identified￨L￨VBN￨O￨- more￨L￨RBR￨O￨- readily￨L￨RB￨O￨- with￨L￨IN￨O￨- fewer￨L￨JJR￨O￨- required￨L￨VBN￨O￨- messenger￨L￨NN￨TITLE￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- low-and￨L￨JJ￨O￨- middle-income￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- LMICs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- costs￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- considerable￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- ,￨L￨,￨O￨- estimated￨L￨VBN￨O￨- at￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- gross￨L￨JJ￨O￨- domestic￨L￨JJ￨O￨- product￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GDP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- only￨L￨RB￨O￨- 0.04￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 0.13￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- GDP￨U￨NNP￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- in￨L￨IN￨O￨- high￨L￨JJ￨O￨- income￨L￨NN￨O￨A countries￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2016￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- predictive￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- using￨L￨VBG￨O￨- weather￨L￨NN￨O￨- predictions￨L￨NNS￨O￨- and￨L￨CC￨O￨- dengue￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- projections￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- validate￨L￨VB￨O￨- the￨L￨DT￨O￨- explanatory￨L￨JJ￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- features￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- specific￨L￨JJ￨O￨- application￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- regression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- using￨L￨VBG￨O￨- features￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨A population￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ZIKV￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- has￨L￨VBZ￨O￨- spread￨L￨VBN￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- South￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨A mosquito￨L￨NN￨O￨- species￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- vector￨L￨NN￨O￨- for￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Predictions￨U￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NNP￨O￨- cases￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- utilizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨A mosquitoes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- average￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- region￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- .￨L￨.￨O￨- +Notably￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vast￨L￨JJ￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- modelling￨L￨NN￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- neglected￨L￨VBN￨O￨- the￨L￨DT￨O￨- microbial￨L￨JJ￨O￨- environment￨L￨NN￨O￨- :￨L￨:￨O￨- most￨L￨RBS￨O￨- mathematical￨L￨JJ￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A are￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- single￨L￨JJ￨O￨- or￨L￨CC￨O￨- sequential￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- broadly￨L￨RB￨O￨- simplified￨L￨VBN￨O￨- pathogen￨L￨NN￨O￨- ecology￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨A field￨L￨NN￨O￨- has￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- an￨L￨DT￨O￨- effort￨L￨NN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- realism￨L￨NN￨O￨- by￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- age-related￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- cross￨L￨NN￨O￨- immunity￨L￨NN￨O￨- after￨L￨IN￨O￨- previous￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 19,21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modelling￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- tool￨L￨NN￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- researchers￨L￨NNS￨O￨- to￨L￨TO￨O￨- probe￨L￨VB￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- intricacies￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- play￨L￨VB￨O￨- forward￨L￨RB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- to￨L￨TO￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- population-level￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- current￨L￨JJ￨DATE￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- or￨L￨CC￨O￨- severity￨L￨NN￨O￨- may￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- incomplete￨L￨JJ￨O￨- or￨L￨CC￨O￨- misguided￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- ignorance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨- change￨L￨NN￨O￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- aim￨L￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- coming￨L￨VBG￨O￨- season￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- describing￨L￨VBG￨O￨- numerous￨L￨JJ￨O￨- cascading￨L￨VBG￨O￨- phenomena￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- neural￨L￨JJ￨O￨- firing￨L￨NN￨O￨- or￨L￨CC￨O￨- social￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- threshold￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- weighted￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- largely￨L￨RB￨O￨- overlooked￨L￨VBN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Threshold￨U￨NNP￨O￨- driven￨L￨VBN￨O￨- contagion￨L￨NN￨O￨- on￨L￨IN￨O￨- weighted￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- Samuel￨U￨NNP￨PERSON￨- Unicomb1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Gerardo￨U￨NNP￨PERSON￨- Iñiguez￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,3￨L￨CD￨NUMBER￨- &￨L￨CC￨O￨- Márton￨U￨NNP￨O￨- Karsai1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 3094￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- scienceNonlinear￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- AbstractWeighted￨U￨VBN￨O￨- networks￨L￨NNS￨O￨- capture￨L￨VBP￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- where￨L￨WRB￨O￨- interaction￨L￨NN￨O￨- strength￨L￨NN￨O￨- is￨L￨VBZ￨O￨- meaningful￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- cascade￨L￨NN￨O￨- emergence￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- non-monotonously￨L￨RB￨O￨- on￨L￨IN￨O￨- weight￨L￨NN￨O￨A heterogeneities￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- accelerate￨L￨VBP￨O￨- or￨L￨CC￨O￨- decelerate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- non-trivial￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- spaces￨L￨NNS￨O￨- for￨L￨IN￨O￨- various￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- weight￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- fill￨L￨VBP￨O￨- this￨L￨DT￨O￨- gap￨L￨NN￨O￨- by￨L￨IN￨O￨- studying￨L￨VBG￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- over￨L￨IN￨O￨- synthetic￨L￨JJ￨O￨- and￨L￨CC￨O￨- real￨L￨JJ￨O￨- weighted￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- and￨L￨CC￨O￨- analytical￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- fast￨L￨JJ￨O￨- and￨L￨CC￨O￨- bursty￨L￨JJ￨O￨- human￨L￨JJ￨O￨- communication￨L￨NN￨O￨A networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- reported￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- animal￨L￨NN￨O￨- societies￨L￨NNS￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- very￨L￨RB￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- temporally￨L￨RB￨O￨- highly￨L￨RB￨O￨- resolved￨L￨VBN￨O￨- communication￨L￨NN￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- over￨L￨RP￨O￨- long￨L￨RB￨O￨- enough￨L￨RB￨O￨- timescales￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- burstiness￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 16￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Instead￨U￨RB￨O￨- of￨L￨IN￨O￨- tracking￨L￨VBG￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- piece￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- or￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- probe￨L￨VBP￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- comparison￨L￨NN￨O￨- against￨L￨IN￨O￨- a￨L￨DT￨O￨- randomized￨L￨VBN￨O￨- reference￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- how￨L￨WRB￨O￨- spreading￨L￨VBG￨O￨A dynamics￨L￨NNS￨O￨A reflect￨L￨VBP￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Human￨U￨JJ￨O￨- communication￨L￨NN￨O￨A networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- intermittent￨L￨JJ￨O￨- ,￨L￨,￨O￨- unpredictable￨L￨JJ￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- between￨L￨IN￨O￨- successive￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- heavy-tailed￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- burstiness￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Temporal￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- thus￨L￨RB￨O￨- acknowledge￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- linked￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- available￨L￨JJ￨O￨- while￨L￨IN￨O￨- these￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- and￨L￨CC￨O￨- crucially￨L￨RB￨O￨- account￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- ordering￨L￨VBG￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨A ,￨L￨,￨O￨- making￨L￨VBG￨O￨- them￨L￨PRP￨O￨- particularly￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Honeybee￨U￨NNP￨O￨- trophallaxis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- an￨L￨DT￨O￨- excellent￨L￨JJ￨O￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- exploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- of￨L￨IN￨O￨- burstiness￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- nonhuman￨L￨JJ￨O￨- animal￨L￨NN￨O￨- society￨L￨NN￨O￨- ,￨L￨,￨O￨- permitting￨L￨VBG￨O￨- a￨L￨DT￨O￨- cross-species￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- human￨L￨JJ￨O￨- communication￨L￨NN￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- bubonic￨L￨JJ￨O￨- plague￨L￨VBP￨O￨A by￨L￨IN￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- ectoparasite￨L￨NN￨O￨- vector￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- human￨L￨JJ￨O￨- fleas￨L￨NNS￨O￨- or￨L￨CC￨O￨- body￨L￨NN￨O￨- lice￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- five￨L￨CD￨NUMBER￨- compartments￨L￨NNS￨O￨- for￨L￨IN￨O￨- humans￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- with￨L￨IN￨O￨- mild￨L￨JJ￨O￨- bacteremia￨L￨NN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- bacteremia￨L￨NN￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- dead￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- applied￨L￨VBD￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- nine￨L￨CD￨NUMBER￨- outbreaks￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- Second￨U￨JJ￨ORDINAL￨- Pandemic￨U￨NN￨MISC￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- plague￨L￨VBP￨O￨A in￨L￨IN￨O￨- European￨U￨JJ￨NATIONALITY￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- validate￨L￨VB￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- pneumonic￨L￨JJ￨O￨- and￨L￨CC￨O￨- rat-associated￨L￨JJ￨O￨- plague￨L￨VB￨O￨A epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- additional￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- curves￨L￨NNS￨O￨- from￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- known￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- routes￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- Third￨U￨NNP￨ORDINAL￨- Pandemic￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- plague￨L￨VBP￨O￨A during￨L￨IN￨O￨- the￨L￨DT￨O￨- Second￨U￨JJ￨ORDINAL￨- Pandemic￨U￨NN￨MISC￨- are￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- mainly￨L￨RB￨O￨- on￨L￨IN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- commensal￨L￨JJ￨O￨- rats￨L￨NNS￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 21￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infectious￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- plague￨L￨VB￨O￨A transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- ectoparasite￨L￨NN￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- pneumonic￨L￨JJ￨O￨- and￨L￨CC￨O￨- rat￨L￨NN￨O￨- –￨L￨:￨O￨- flea￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- traits￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- resistance￨L￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- growth￨L￨NN￨O￨- respond￨L￨VBP￨O￨- similarly￨L￨RB￨O￨- to￨L￨TO￨O￨- temperature￨L￨NN￨O￨A changes￨L￨NNS￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- responses￨L￨NNS￨O￨- may￨L￨MD￨O￨- trade￨L￨VB￨O￨- off￨L￨RP￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- no￨L￨DT￨O￨- observed￨L￨VBN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- on￨L￨IN￨O￨- parasite￨L￨NN￨O￨- abundance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- change￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- temperature￨L￨NN￨O￨A can￨L￨MD￨O￨- have￨L￨VB￨O￨- differing￨L￨VBG￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- traits￨L￨NNS￨O￨- that￨L￨WDT￨O￨- together￨L￨RB￨O￨- determine￨L￨VBP￨O￨- outcomes￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- temperature￨L￨NN￨O￨A also￨L￨RB￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- traits￨L￨NNS￨O￨- that￨L￨WDT￨O￨- mediate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- survival￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- parasite￨L￨JJ￨O￨- development￨L￨NN￨O￨- rate￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- virulence￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- resistance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- tolerance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- parasites￨L￨NNS￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- traits￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- distinct￨L￨JJ￨O￨- temperature￨L￨NN￨O￨A responses￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- antagonistic￨L￨JJ￨O￨- and￨L￨CC￨O￨- synergistic￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- temperature￨L￨NN￨O￨- responses￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- traits￨L￨NNS￨O￨- that￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- net￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- changes￨L￨NNS￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Climate￨U￨NN￨O￨- change￨L￨NN￨O￨- –￨L￨:￨O￨- driven￨L￨VBN￨O￨- temperature￨L￨NN￨O￨A changes￨L￨NNS￨O￨- will￨L￨MD￨O￨- likely￨L￨RB￨O￨- impact￨L￨VB￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- parasite￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- both￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- traits￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- strongly￨L￨RB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- temperature￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- norovirus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- by￨L￨IN￨O￨- sampling￨L￨NN￨O￨- season￨L￨NN￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A ,￨L￨,￨O￨- R￨U￨NN￨O￨- e.￨L￨NNP￨O￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- when￨L￨WRB￨O￨- GII￨U￨NNP￨ORGANIZATION￨- .2￨L￨NN￨NUMBER￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 2015/16￨L￨CD￨NUMBER￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- GII￨U￨NN￨ORGANIZATION￨- .4￨L￨NN￨NUMBER￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- genotype￨L￨NN￨O￨- affecting￨L￨VBG￨O￨- infants￨L￨NNS￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- children￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 2016/17￨L￨CD￨NUMBER￨- seasons￨L￨NNS￨O￨- CI￨U￨NNP￨O￨- :￨L￨:￨O￨- confidence￨L￨NN￨O￨- interval￨L￨NN￨O￨- ;￨L￨:￨O￨- NA￨U￨NNP￨O￨- :￨L￨:￨O￨- not￨L￨RB￨O￨- applicable￨L￨JJ￨O￨- ;￨L￨:￨O￨- R￨U￨NN￨O￨- e￨L￨SYM￨O￨- :￨L￨:￨O￨- effective￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 2015/16￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- was￨L￨VBD￨O￨- higher￨L￨JJR￨O￨- at￨L￨IN￨O￨- 193￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- (￨L￨-LRB-￨O￨- 1,927￨L￨CD￨NUMBER￨- vs￨L￨CC￨O￨A 659￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 539￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- (￨L￨-LRB-￨O￨- 1,086￨L￨CD￨NUMBER￨- vs￨L￨CC￨O￨- 170￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 149￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- (￨L￨-LRB-￨O￨- 1,699￨L￨CD￨NUMBER￨- vs￨L￨CC￨O￨- 683￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- nursery￨L￨NN￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- kindergartens￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- elementary￨L￨JJ￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- attending￨L￨VBG￨O￨- schools￨L￨NNS￨O￨A or￨L￨CC￨O￨- nurseries￨L￨NNS￨O￨- were￨L￨VBD￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- norovirus￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Osaka￨U￨NNP￨LOCATION￨- prefecture￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1,5,15,19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- developed￨L￨VBD￨O￨- for￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- WNV￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- dengue￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- arboviral￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- exhibit￨L￨VB￨O￨- backward￨L￨RB￨O￨A bifurcation￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- violation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- threshold￨L￨NN￨O￨- condition￨L￨NN￨O￨- separating￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- endemicity￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- essential￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- microparasitic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- studied￨L￨VBN￨O￨- via￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- the￨L￨DT￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- or￨L￨CC￨O￨- compartments￨L￨NNS￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- defining￨L￨VBG￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- hosts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- latter￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- induced￨L￨VBD￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- death￨L￨NN￨O￨- rates￨L￨NNS￨O￨- among￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- particularly￨L￨RB￨O￨- important￨L￨JJ￨O￨- driving￨L￨VBG￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- backward￨L￨RB￨O￨A bifurcation￨L￨NN￨O￨- in￨L￨IN￨O￨- WNV￨U￨NNP￨O￨- ,￨L￨,￨O￨- dengue￨L￨NN￨O￨- ,￨L￨,￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- arboviral￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- host￨L￨NN￨TITLE￨- susceptible-exposed-infective-temporarily￨L￨JJ￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SEIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- vector￨L￨NN￨O￨- SEI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- tune￨L￨VB￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- that￨L￨WDT￨O￨- complexity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- parameters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- of￨L￨IN￨O￨- backward￨L￨RB￨O￨A bifurcation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- case￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- defines￨L￨VBZ￨O￨- a￨L￨DT￨O￨- bifurcation￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- critical￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- stable￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- emerges￨L￨VBZ￨O￨- and￨L￨CC￨O￨- establishes￨L￨VBZ￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DFE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- emerges￨L￨VBZ￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- generalize￨L￨VB￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- different￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- or￨L￨CC￨O￨- network￨L￨NN￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- in￨L￨IN￨O￨- those￨L￨DT￨O￨- papers￨L￨NNS￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- particular￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨A value￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- either￨L￨CC￨O￨- a￨L￨DT￨O￨- bipartite￨L￨JJ￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- random￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- arbitrary￨L￨JJ￨O￨- mixing￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- to￨L￨TO￨O￨- mixing￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- multi-type￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- process￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- converge￨L￨VB￨O￨- either￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- any￨L￨DT￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- in￨L￨IN￨O￨- either￨L￨CC￨O￨- group￨L￨NN￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- any￨L￨DT￨O￨- non-null￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- almost￨L￨RB￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- state￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨A the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- respective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- levels￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- stable￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- levels￨L￨NNS￨O￨- in￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- blue￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- sensitive￨L￨JJ￨O￨- group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- red￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨A level￨L￨NN￨O￨- m￨L￨NN￨O￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- would￨L￨MD￨O￨- imply￨L￨VB￨O￨- that￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- can￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- levels￨L￨NNS￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- community-associated￨L￨JJ￨O￨- methicillin-resistant￨L￨JJ￨O￨- Staphylococcus￨U￨FW￨MISC￨- aureus￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- MRSA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- targeting￨L￨VBG￨O￨- symptomatically￨L￨RB￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- asymptomatic￨L￨JJ￨O￨A carriers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- actually￨L￨RB￨O￨- incapable￨L￨JJ￨O￨- of￨L￨IN￨O￨- achieving￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- multiple￨L￨JJ￨O￨- control￨L￨NN￨O￨- types￨L￨NNS￨O￨- are￨L￨VBP￨O￨- implemented￨L￨VBN￨O￨- .￨L￨.￨O￨- +Neglecting￨U￨VBG￨O￨- asymptomatic￨L￨JJ￨O￨A carriers￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- significantly￨L￨RB￨O￨- overestimate￨L￨VB￨O￨- the￨L￨DT￨O￨- projected￨L￨VBN￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- overestimate￨L￨VB￨O￨- the￨L￨DT￨O￨- population-level￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- analysis￨L￨NN￨O￨- reveals￨L￨VBZ￨O￨- that￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- alter￨L￨VBP￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- asymptomatic￨L￨JJ￨O￨A carriers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- vulnerable￨L￨JJ￨O￨- to￨L￨TO￨O￨- being￨L￨VBG￨O￨- incorrectly￨L￨RB￨O￨- assessed￨L￨VBN￨O￨- by￨L￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- inappropriate￨L￨JJ￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A carriers￨L￨NNS￨O￨- to￨L￨TO￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- both￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- asymptomatic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- make￨L￨VB￨O￨- comparisons￨L￨NNS￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- collapsed￨L￨VBD￨O￨- each￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- form￨L￨NN￨O￨- where￨L￨WRB￨O￨- hosts￨L￨NNS￨O￨- belong￨L￨VBP￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- asymptomatic￨L￨JJ￨O￨A carriers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- symptomatically￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalent￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- on-demand￨L￨JJ￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨DATE￨- may￨L￨MD￨DATE￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- near-linear￨L￨JJ￨O￨- product￨L￨NN￨O￨- adoption￨L￨NN￨O￨A rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- product￨L￨NN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- S-shaped￨U￨JJ￨MISC￨- curves￨L￨NNS￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- social￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- track￨L￨VBP￨O￨- the￨L￨DT￨O￨- adoption￨L￨NN￨O￨A through￨L￨IN￨O￨- 70￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- unique￨L￨JJ￨O￨- voucher￨L￨NN￨O￨- codes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 48￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- codes￨L￨NNS￨O￨- in￨L￨IN￨O￨- Experiment￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- active￨L￨JJ￨O￨- information-seeking￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨- between￨L￨IN￨O￨- this￨L￨DT￨O￨- ODD￨U￨JJ￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- peer-to-peer￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- occur￨L￨VBP￨O￨- simultaneously￨L￨RB￨O￨- .￨L￨.￨O￨- +That￨U￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- once￨L￨RB￨DATE￨- product￨L￨NN￨O￨- adoption￨L￨NN￨O￨A is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- on-demand￨L￨JJ￨O￨- information￨L￨NN￨O￨- seeking￨L￨VBG￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- peer-to-peer￨L￨NNS￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- similarly￨L￨RB￨O￨- ranked￨L￨VBD￨O￨- list￨L￨NN￨O￨- through￨L￨IN￨O￨- search￨L￨NN￨O￨- engines￨L￨NNS￨O￨- and￨L￨CC￨O￨- Top￨U￨JJ￨O￨- 10￨L￨CD￨NUMBER￨- pages￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- disproportionately￨L￨RB￨O￨- rewards￨L￨VBZ￨O￨- products￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- list￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- may￨L￨MD￨O￨- see￨L￨VB￨O￨- winner-take-all￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- among￨L￨IN￨O￨- equivalent￨L￨JJ￨O￨- products￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- shaped￨L￨VBN￨O￨- by￨L￨IN￨O￨- search￨L￨NN￨O￨- engine￨L￨NN￨O￨- rankings￨L￨NNS￨O￨- as￨L￨IN￨O￨- interested￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- all￨L￨DT￨O￨- discover￨L￨VBP￨O￨- and￨L￨CC￨O￨- adopt￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- product￨L￨NN￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- equal￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- across￨L￨IN￨O￨- products￨L￨NNS￨O￨- when￨L￨WRB￨O￨- product￨L￨NN￨O￨- adoption￨L￨NN￨O￨A spreads￨L￨VBZ￨O￨- exclusively￨L￨RB￨O￨- along￨L￨IN￨O￨- social￨L￨JJ￨O￨- ties￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- product￨L￨NN￨O￨- adoption￨L￨NN￨O￨A processes￨L￨NNS￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- posting/searching￨L￨VBG￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- peer-to-peer￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- time-dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- drive￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- to￨L￨TO￨O￨- deploy￨L￨VB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulated￨L￨JJ￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- quantifying￨L￨VBG￨O￨- temporal￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- precision￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨A dying￨L￨VBG￨O￨- out￨L￨RP￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- CSA￨U￨NNP￨ORGANIZATION￨- integrates￨L￨VBZ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- outbreak￨L￨NN￨O￨A simulation￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- now￨L￨RB￨DATE￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- whether￨L￨IN￨O￨- instead￨L￨RB￨O￨- management￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- delayed￨L￨VBN￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- the￨L￨DT￨O￨- policy-maker￨L￨NN￨O￨- to￨L￨TO￨O￨- learn￨L￨VB￨O￨- more￨L￨JJR￨O￨- about￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- outbreak￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- farms￨L￨NNS￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- to￨L￨TO￨O￨- deploy￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- governing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- a￨L￨DT￨O￨- policy-maker￨L￨NN￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨A for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- statuses￨L￨NNS￨O￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- farm￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- all￨L￨RB￨O￨- known￨L￨VBN￨O￨- ,￨L￨,￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- simply￨L￨RB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- statuses￨L￨NNS￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- optimising￨L￨VBG￨O￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- straightforward￨L￨JJ￨O￨- .￨L￨.￨O￨- +Should￨U￨MD￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- management￨L￨NN￨O￨- always￨L￨RB￨O￨- be￨L￨VB￨O￨- introduced￨L￨VBN￨O￨- immediately￨L￨RB￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- can￨L￨MD￨O￨- it￨L￨PRP￨O￨- instead￨L￨RB￨O￨- be￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- to￨L￨TO￨O￨- introduce￨L￨VB￨O￨- control￨L￨NN￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨A ?￨L￨.￨O￨- +Frailty￨U￨NNP￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- survival￨L￨NN￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- dependence￨L￨NN￨O￨- and￨L￨CC￨O￨- unobserved￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- multivariate￨L￨JJ￨O￨- time‐to‐event￨L￨JJ￨O￨- data￨L￨NNS￨O￨- explicitly￨L￨RB￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- questions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- event￨L￨NN￨O￨A times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Clayton￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1978￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Hougaard￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Duchateau￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Janssen￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- in￨L￨IN￨O￨- shared￨L￨JJ￨O￨A and￨L￨CC￨O￨- correlated￨L￨VBD￨O￨- frailty￨L￨NN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- or￨L￨CC￨O￨- time￨L￨NN￨O￨- invariant￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- implying￨L￨VBG￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- ‘￨L￨``￨O￨- frailty￨L￨NN￨O￨- ’￨L￨''￨O￨- level￨L￨NN￨O￨- during￨L￨IN￨O￨- their￨L￨PRP$￨O￨- entire￨L￨JJ￨O￨- life￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- rather￨L￨RB￨O￨- restrictive￨L￨JJ￨O￨- .￨L￨.￨O￨- +Multivariate￨U￨JJ￨O￨- frailty￨L￨NN￨O￨- models￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- univariate￨L￨JJ￨O￨- frailty￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- mutual￨L￨JJ￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- event￨L￨NN￨O￨A times￨L￨NNS￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- conditional￨L￨JJ￨O￨- proportional￨L￨JJ￨O￨- hazards￨L￨NNS￨O￨- given￨L￨VBN￨O￨- latent￨L￨JJ￨O￨- frailty￨L￨NN￨O￨- terms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- correlated￨L￨VBN￨O￨- frailty￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- extends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- shared￨L￨JJ￨O￨A frailty￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- flexible￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- structure￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- frailty￨L￨NN￨O￨- terms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Yashin￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- introduced￨L￨VBN￨O￨- time￨L￨NN￨O￨- varying￨L￨VBG￨O￨- shared￨L￨VBN￨O￨A frailties￨L￨NNS￨O￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- immunizing￨L￨VBG￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Grown￨U￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- mature￨L￨JJ￨O￨- field￨L￨NN￨O￨- that￨L￨WDT￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- enhance￨L￨VB￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- phylodynamics￨L￨NNS￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- inference￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- analytical￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- recover￨L￨VB￨O￨- evolutionary￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- mutations￨L￨NNS￨O￨A that￨L￨WDT￨O￨- accumulate￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- genomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- rapidly￨L￨RB￨O￨- evolving￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- during￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- mutations￨L￨NNS￨O￨A may￨L￨MD￨O￨- confer￨L￨VB￨O￨- phenotypic￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- viruses￨L￨NNS￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- different￨L￨JJ￨O￨- cell￨L￨NN￨O￨- types￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- evade￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- immune￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- ,￨L￨,￨O￨- hosts￨L￨NNS￨O￨- or￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- mutations￨L￨NNS￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- molecular￨L￨JJ￨O￨- footprint￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- otherwise￨L￨RB￨O￨- not￨L￨RB￨O￨- directly￨L￨RB￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- simulation-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- date￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- occur￨L￨VB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- mid-point￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- censored￨L￨VBN￨O￨- interval￨L￨NN￨O￨A once￨L￨RB￨DATE￨- participants￨L￨NNS￨O￨- start￨L￨VBP￨O￨- to￨L￨TO￨O￨- miss￨L￨VB￨O￨- their￨L￨PRP$￨O￨- scheduled￨L￨VBN￨O￨- test￨L￨NN￨O￨- dates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Imputation￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- date￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- censored￨L￨VBN￨O￨- interval￨L￨NN￨O￨A ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- straightforward￨L￨JJ￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- and￨L￨CC￨O￨- produces￨L￨VBZ￨O￨- estimates￨L￨NNS￨O￨- very￨L￨RB￨O￨- close￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- some￨L￨DT￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- mid-point￨L￨NN￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- interval￨L￨NN￨O￨A censoring￨L￨VBG￨O￨- assumption￨L￨NN￨O￨- is￨L￨VBZ￨O￨- satisfied￨L￨VBN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- popular￨L￨JJ￨O￨- ad￨L￨NN￨O￨- hoc￨L￨FW￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- impute￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- date￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- mid-point￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- participant￨L￨NN￨O￨- ’s￨L￨POS￨O￨- censored￨L￨VBN￨O￨- interval￨L￨NN￨O￨A .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- aforementioned￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- considers￨L￨VBZ￨O￨- an￨L￨DT￨O￨- SEIQR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-infected-quarantined-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- imperfect￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- δ￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- p￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- isand￨L￨VBD￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- properties￨L￨NNS￨O￨- :￨L￨:￨O￨- When￨U￨WRB￨O￨- R1￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- holds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨A disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E0￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S0￨U￨NN￨O￨- ,￨L￨,￨O￨- 0,0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Λ￨U￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- δp￨L￨NN￨O￨- +￨L￨CC￨O￨- μ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 0,0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- δpΛ/μ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- δp￨L￨NN￨O￨- +￨L￨CC￨O￨- μ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- D￨U￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- R1￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- holds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨A globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- persist￨L￨VB￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- ℝ￨U￨SYM￨O￨- +5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨A positive￨L￨JJ￨O￨- local￨L￨JJ￨O￨- solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- t￨L￨NN￨O￨- ∈￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- −￨L￨CD￨NUMBER￨- ω￨L￨NN￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- explosion￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- ℝ￨U￨SYM￨O￨- +5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨A positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- ℝ￨U￨SYM￨O￨- +5￨L￨CD￨NUMBER￨- on￨L￨IN￨O￨- t￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- a.s￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- issues￨L￨NNS￨O￨- include￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨A takes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- complexity￨L￨NN￨O￨- increases￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- method￨L￨NN￨O￨- accuracy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- summary￨L￨NN￨O￨- statistic￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- accept/reject￨L￨JJ￨O￨- decision￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- constructed￨L￨VBN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infectious-Removed￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A data￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Conventional￨U￨JJ￨O￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- estimation￨L￨NN￨O￨- ,￨L￨,￨O￨- require￨L￨VBP￨O￨- explicit￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A data￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- approach￨L￨NN￨O￨- R0￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- slope￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A data￨L￨NNS￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- estimate￨L￨VB￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨A the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Generally￨U￨RB￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- about￨L￨IN￨O￨- patients￨L￨NNS￨O￨- are￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- by￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- practitioners￨L￨NNS￨O￨- via￨L￨IN￨O￨- passive￨L￨NN￨O￨- surveillance￨L￨NN￨O￨A systems￨L￨NNS￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- central￨L￨JJ￨O￨- database￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- trends￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- and￨L￨CC￨O￨- map￨L￨VB￨O￨- the￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- and￨L￨CC￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- via￨L￨IN￨O￨- sentinel￨L￨NN￨O￨- sites￨L￨NNS￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- inform￨L￨VB￨O￨- these￨L￨DT￨O￨- efforts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Meanwhile￨U￨RB￨O￨- ,￨L￨,￨O￨- academic￨L￨JJ￨O￨- researchers￨L￨NNS￨O￨- —￨L￨:￨O￨- often￨L￨RB￨O￨- in￨L￨IN￨O￨- high-income￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- —￨L￨:￨O￨- are￨L￨VBP￨O￨- developing￨L￨VBG￨O￨- increasingly￨L￨RB￨O￨- sophisticated￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- collect￨L￨VB￨O￨- and￨L￨CC￨O￨- analyse￨L￨VB￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- spatial￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- using￨L￨VBG￨O￨- new￨L￨JJ￨O￨- Big￨U￨NNP￨O￨- Data￨U￨NNP￨O￨- sources￨L￨NNS￨O￨- ,￨L￨,￨O￨- mobile-Health￨L￨NN￨O￨- or￨L￨CC￨O￨- m-Health￨L￨NN￨MISC￨- approaches￨L￨NNS￨O￨A or￨L￨CC￨O￨- mechanistic￨L￨JJ￨O￨- and￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- ongoing￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- to￨L￨TO￨O￨- implementation￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- promising￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- leverage￨L￨NN￨O￨- even￨L￨RB￨O￨- patchy￨L￨JJ￨O￨- and￨L￨CC￨O￨- low-quality￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- diverse￨L￨JJ￨O￨- new￨L￨JJ￨O￨- data￨L￨NNS￨O￨- streams￨L￨NNS￨O￨A that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- productively￨L￨RB￨O￨- harnessed￨L￨VBN￨O￨- to￨L￨TO￨O￨- strengthen￨L￨VB￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- when￨L￨WRB￨O￨- integrated￨L￨VBN￨O￨- with￨L￨IN￨O￨- existing￨L￨VBG￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +New￨U￨NNP￨O￨- innovations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- transform￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨A and￨L￨CC￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- Big￨U￨NNP￨ORGANIZATION￨- Data￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- mobile￨L￨JJ￨TITLE￨- health￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- and￨L￨CC￨O￨- cutting￨L￨VBG￨O￨- edge￨L￨NN￨O￨- quantitative￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- offer￨L￨VBP￨O￨- hope￨L￨NN￨O￨- for￨L￨IN￨O￨- disrupting￨L￨VBG￨O￨- traditional￨L￨JJ￨O￨- health￨L￨NN￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- improving￨L￨VBG￨O￨- health￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- latent￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- take￨L￨VB￨O￨- up￨L￨RP￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨A bed￨L￨NN￨O￨- resources￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- meanwhile￨L￨RB￨O￨- ,￨L￨,￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- hospital￨L￨NN￨O￨- resources￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- first￨L￨JJ￨ORDINAL￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Shan￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Zhu￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- formula￨L￨NN￨O￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- where￨L￨WRB￨O￨- μ1￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- resources￨L￨NNS￨O￨- and￨L￨CC￨O￨- few￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- μ0￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨- bed-population￨L￨NN￨O￨- ratio￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nonnegative￨L￨JJ￨O￨- constant￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- combined￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- psychological￨L￨JJ￨O￨- effect￨L￨NN￨O￨- and￨L￨CC￨O￨- available￨L￨JJ￨O￨- hospital￨L￨NN￨O￨A resources￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- βI￨L￨NN￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nonnegative￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- +￨L￨CC￨O￨- aI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- inhibition￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- psychological￨L￨JJ￨O￨A effect￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- introduce￨L￨VB￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- function￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- hospital￨L￨NN￨O￨A resources￨L￨NNS￨O￨- in￨L￨IN￨O￨- spreading￨L￨NN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- established￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- function￨L￨NN￨O￨- reflected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨A bed-population￨L￨NN￨O￨- ratio￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- formulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- EvoEpiFlu￨U￨NNP￨O￨- were￨L￨VBD￨O￨- implemented￨L￨VBN￨O￨- :￨L￨:￨O￨- as￨L￨IN￨O￨- its￨L￨PRP$￨O￨- name￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- continuous￨L￨JJ￨O￨- ’￨L￨''￨O￨- version￨L￨NN￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨A change￨L￨NN￨O￨- information￨L￨NN￨O￨- continuously￨L￨RB￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- via￨L￨IN￨O￨- an￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- index￨L￨NN￨O￨- constructed￨L￨VBN￨O￨- from￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- amino￨L￨NN￨O￨- acid￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- epitope￨L￨NN￨O￨- sites￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- antigen￨L￨NN￨O￨- protein￨L￨NN￨O￨- HA￨U￨NN￨O￨- between￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- and￨L￨CC￨DATE￨- past￨L￨JJ￨DATE￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- estimated￨L￨VBN￨O￨- during￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- optimization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- process-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- EvoEpiFlu￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- evolutionary￨L￨JJ￨O￨A information￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- modified￨L￨VBN￨O￨- SIRS￨U￨NN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- Susceptible￨U￨NNP￨O￨- ,￨L￨,￨O￨- Infected￨U￨JJ￨O￨- ,￨L￨,￨O￨- Recovered￨U￨VBN￨O￨- and￨L￨CC￨O￨- Susceptible￨U￨JJ￨O￨- immune￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- absolute￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- for￨L￨IN￨O￨- subtype￨L￨NN￨O￨- H3N2￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨ORGANIZATION￨- States4￨U￨NN￨O￨- .￨L￨.￨O￨- +EvoEpiFlu￨U￨NNP￨O￨- makes￨L￨VBZ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨- information￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- antigenic￨L￨JJ￨O￨- change￨L￨NN￨O￨- based￨L￨VBN￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- sequences￨L￨NNS￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- H3N2￨U￨NN￨O￨- incidence￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- summer￨L￨NN￨DATE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- upcoming￨L￨VBG￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨A .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- sequences￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- EvoEpiFlu￨U￨NNP￨PERSON￨- produces￨L￨VBZ￨O￨- skillful￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- one￨L￨CD￨NUMBER￨- season￨L￨NN￨O￨A ahead￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- summer￨L￨NN￨DATE￨- with￨L￨IN￨O￨- data￨L￨NNS￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- June￨U￨NNP￨DATE￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- total￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- H3N2￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- upcoming￨L￨VBG￨O￨- season￨L￨NN￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- subtype￨L￨NN￨O￨- H3N2￨U￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- dominant4￨L￨NN￨O￨- .￨L￨.￨O￨- +Bottom￨U￨NN￨O￨- panel￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- H3N2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- -2018￨L￨CD￨NUMBER￨- season￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- cluster￨L￨NN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- EvoEpiFlu￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- yellow￨L￨JJ￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- report￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- variation￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- that￨L￨WDT￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- varied￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- producer￨L￨NN￨TITLE￨- specialization￨L￨NN￨O￨- and￨L￨CC￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- producers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- percolation￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- increased￨L￨VBN￨O￨- specialization￨L￨NN￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- significantly￨L￨RB￨O￨- diminished￨L￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- resilience￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- PEDv￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- facilitating￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- hog￨L￨NN￨O￨- industry￨L￨NN￨O￨- were￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- transfer￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- between￨L￨IN￨O￨- premises￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- deliveries￨L￨NNS￨O￨- of￨L￨IN￨O￨- contaminated￨L￨VBN￨O￨A feed￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- contaminated￨L￨VBN￨O￨- livestock￨L￨NN￨O￨- and￨L￨CC￨O￨- feed￨L￨NN￨O￨- transportation￨L￨NN￨O￨- equipment￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- investigate￨L￨VB￨O￨- percolation￨L￨NN￨O￨A in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- experimental￨L￨JJ￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- numerically￨L￨RB￨O￨- assess￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- events￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- runs￨L￨VBZ￨O￨- scale￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- addition￨L￨NN￨O￨- of￨L￨IN￨O￨- producer￨L￨NN￨TITLE￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- address￨L￨VB￨O￨- this￨L￨DT￨O￨- question￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- /￨L￨:￨O￨- infective￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- computer￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- epidemiological￨L￨JJ￨O￨- events￨L￨NNS￨O￨- in￨L￨IN￨O￨- hog￨L￨NN￨O￨- production￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨A individual￨L￨NN￨O￨- may￨L￨MD￨O￨- spread￨L￨VB￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- recovered￨L￨JJ￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- reinfected￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- behaviour￨L￨NN￨O￨A and￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- and￨L￨CC￨O￨- recommendations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- futureDale￨L￨NN￨O￨- Weston1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Katharina￨U￨NNP￨PERSON￨- Hauck2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Richard￨U￨NNP￨PERSON￨- Amlôt1BMC￨U￨NNP￨O￨- Public￨U￨NNP￨O￨- HealthBMC￨U￨NNP￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18:336￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- are￨L￨VBP￨O￨- contextualised￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- psychological￨L￨JJ￨O￨- literature￨L￨NN￨O￨- concerning￨L￨VBG￨O￨- health￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- behaviour￨L￨NN￨O￨- change￨L￨NN￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- recommendations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- in￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Given￨U￨VBN￨MISC￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- person￨L￨NN￨O￨- to￨L￨TO￨O￨- person￨L￨NN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- critically￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- that￨L￨IN￨O￨- human￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- appropriately￨L￨RB￨O￨- represented￨L￨VBN￨O￨- within￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- scoping￨L￨VBG￨O￨- review￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- The￨U￨DT￨O￨- search￨L￨NN￨O￨- strategy￨L￨NN￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- terms￨L￨NNS￨O￨- relating￨L￨VBG￨O￨- to￨L￨TO￨O￨- behaviour￨L￨NN￨O￨A ,￨L￨,￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- fundamentally￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- greatly￨L￨RB￨O￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨- beliefs￨L￨NNS￨O￨- on￨L￨IN￨O￨- public￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- awareness￨L￨NN￨O￨- and￨L￨CC￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A for￨L￨IN￨O￨- driving￨L￨VBG￨O￨- the￨L￨DT￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- self-behavior.3￨L￨NN￨O￨- Risk￨U￨NN￨O￨- perception￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- awareness￨L￨NN￨O￨- or￨L￨CC￨O￨- belief￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- hazard￨L￨NN￨O￨- and/or￨L￨CC￨O￨- harm￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- shaping￨L￨VBG￨O￨- health-related￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- to￨L￨TO￨O￨- reducing￨L￨VBG￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- .4￨L￨CD￨NUMBER￨- Generally￨U￨RB￨O￨- ,￨L￨,￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- social￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- media￨L￨NNS￨O￨- release￨L￨NN￨O￨- by￨L￨IN￨O￨- health￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- ,￨L￨,￨O￨- observation￨L￨NN￨O￨- or￨L￨CC￨O￨- interaction￨L￨NN￨O￨- with￨L￨IN￨O￨- relation-specific￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- past￨L￨JJ￨DATE￨- experiences￨L￨NNS￨O￨- of￨L￨IN￨O￨- similar￨L￨JJ￨O￨- hazards￨L￨NNS￨O￨- ,￨L￨,￨O￨- habits￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- culture￨L￨NN￨O￨- .5￨L￨CD￨NUMBER￨- These￨U￨DT￨O￨- factors￨L￨NNS￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- health-seeking￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .1￨L￨NN￨NUMBER￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- about￨L￨IN￨O￨- intervention￨L￨NN￨O￨- and￨L￨CC￨O￨- management￨L￨NN￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- to￨L￨TO￨O￨- what￨L￨WP￨O￨- extent￨L￨NN￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- scenarios￨L￨NNS￨O￨- of￨L￨IN￨O￨- with/without￨L￨NN￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- preventive/protective￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- age-specific￨L￨JJ￨O￨- network-driven￨L￨JJ￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A influences￨L￨VBZ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .2￨L￨NN￨NUMBER￨- To￨U￨TO￨O￨- control￨L￨VB￨O￨- respiratory￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- ,￨L￨,￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- promotion￨L￨NN￨O￨- of￨L￨IN￨O￨- protective￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- suggested￨L￨VBN￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A and￨L￨CC￨O￨- behavior￨L￨NN￨O￨- across￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- .8,9￨L￨CD￨NUMBER￨- A￨U￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- people￨L￨NNS￨O￨- could￨L￨MD￨O￨- exchange￨L￨VB￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- risk-related￨L￨JJ￨O￨- events￨L￨NNS￨O￨- to￨L￨TO￨O￨- spur￨L￨VB￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- behavior￨L￨NN￨O￨- change￨L￨NN￨O￨- .10￨L￨CD￨NUMBER￨- Scherer￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Cho11￨U￨NN￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- individual￨L￨JJ￨O￨- perceptions￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- self-perception￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Funk￨U￨NNP￨O￨- et￨L￨FW￨O￨- al12￨L￨FW￨O￨- used￨L￨VBN￨O￨- SIR-based￨U￨JJ￨MISC￨- perceptual-influenza￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A on￨L￨IN￨O￨- behavioral￨L￨JJ￨O￨- change￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- reduction￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemiological￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- variances￨L￨NNS￨O￨- in￨L￨IN￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- by￨L￨IN￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- intuitive￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- local￨L￨JJ￨O￨- structures26￨L￨NN￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- attention￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨- in￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A process￨L￨NN￨O￨A ,￨L￨,￨O￨- largely￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- particularities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- models￨L￨NNS￨O￨- typically￨L￨RB￨O￨- deployed￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- these￨L￨DT￨O￨- processes.In￨L￨NN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- classified￨L￨VBN￨O￨- to￨L￨TO￨O￨- two￨L￨CD￨NUMBER￨- broad￨L￨JJ￨O￨- categories12￨L￨NN￨O￨- ,27￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- incorporated￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- viewed￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- independent￨L￨JJ￨RELIGION￨- event￨L￨NN￨O￨- across￨L￨IN￨O￨- different￨L￨JJ￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- its￨L￨PRP$￨O￨- neighbour￨L￨NN￨O￨- j￨L￨NN￨O￨- is￨L￨VBZ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- sociological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- viewed￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- interdependent￨L￨JJ￨O￨- event￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- its￨L￨PRP$￨O￨- neighbour￨L￨NN￨O￨- j￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- j￨L￨NN￨O￨- neighbours￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Yet￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- implication￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- premise￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- non-trivial￨L￨JJ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- exposures￨L￨NNS￨O￨- can￨L￨MD￨O￨- interfere￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨A process￨L￨NN￨O￨A and￨L￨CC￨O￨- affect￨L￨VB￨O￨- key￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- simple￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- discussed￨L￨VBN￨O￨- below.Consider￨L￨NN￨O￨- the￨L￨DT￨O￨- toy￨L￨NN￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- switch￨L￨VB￨O￨- states￨L￨NNS￨O￨- irreversibly￨L￨RB￨O￨- from￨L￨IN￨O￨- ‘￨L￨``￨O￨- non-affected￨L￨JJ￨O￨- ’￨L￨''￨O￨- to￨L￨TO￨O￨- ‘￨L￨``￨O￨- affected￨L￨VBN￨O￨- ’￨L￨''￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- probability￨L￨NN￨O￨- p.￨L￨NN￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Modelling￨U￨NNP￨O￨- indirect￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- during￨L￨IN￨O￨- failure￨L￨NN￨O￨- spreading￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- project￨L￨NN￨O￨- activity￨L￨NN￨O￨- network￨L￨NN￨O￨- Christos￨U￨NNP￨PERSON￨- Ellinas￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 4373￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksStatistical￨L￨JJ￨O￨- physics￨L￨NNS￨O￨- AbstractSpreading￨U￨VBG￨O￨- broadly￨L￨RB￨O￨- refers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- notion￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- entity￨L￨NN￨O￨- propagating￨L￨VBG￨O￨- throughout￨L￨IN￨O￨- a￨L￨DT￨O￨- networked￨L￨JJ￨O￨- system￨L￨NN￨O￨- via￨L￨IN￨O￨- its￨L￨PRP$￨O￨- interacting￨L￨VBG￨O￨- components￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- effect￨L￨NN￨O￨- in￨L￨IN￨O￨- key￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- final￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- event￨L￨NN￨O￨A size￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- propagation￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- spreading￨L￨VBG￨O￨- event￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Role￨U￨NN￨O￨- of￨L￨IN￨O￨- monkeys￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sylvatic￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨A virus￨L￨NN￨O￨- in￨L￨IN￨O￨- Senegal￨U￨NNP￨COUNTRY￨- Benjamin￨U￨NNP￨O￨- M.￨U￨NNP￨O￨- Hanley3￨U￨NNP￨O￨- Nature￨U￨NNP￨O￨- Communicationsvolume￨U￨NNP￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 1046￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Ecological￨U￨NNP￨O￨- epidemiologyEpidemiologyViral￨L￨NNP￨O￨- infectionVirology￨L￨NNP￨O￨- AbstractArboviruses￨U￨NNPS￨O￨- spillover￨L￨JJR￨O￨- into￨L￨IN￨O￨- humans￨L￨NNS￨O￨- either￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- one-step￨L￨JJ￨O￨- jump￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- into￨L￨IN￨O￨- humans￨L￨NNS￨O￨- or￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- two-step￨L￨JJ￨O￨- jump￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- amplification￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- and￨L￨CC￨O￨- thence￨L￨RB￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +Infant￨U￨NN￨O￨- monkeys￨L￨NNS￨O￨- were￨L￨VBD￨O￨- positive￨L￨JJ￨O￨- for￨L￨IN￨O￨- CHIKV￨U￨NNP￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A was￨L￨VBD￨O￨- not￨L￨RB￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- concurrent￨L￨JJ￨O￨- survey￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- was￨L￨VBD￨O￨- too￨L￨RB￨O￨- high￨L￨JJ￨O￨- for￨L￨IN￨O￨- monkeys￨L￨NNS￨O￨- alone￨L￨RB￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- continuous￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Over￨U￨IN￨O￨- 3￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- 737￨L￨CD￨NUMBER￨- monkeys￨L￨NNS￨O￨- were￨L￨VBD￨O￨- captured￨L￨VBN￨O￨- ,￨L￨,￨O￨- aged￨L￨VBN￨O￨- using￨L￨VBG￨O￨- anthropometry￨L￨NN￨O￨- and￨L￨CC￨O￨- dentition￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- tested￨L￨VBN￨O￨- for￨L￨IN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- CHIKV￨U￨NN￨O￨- by￨L￨IN￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- neutralizing￨L￨VBG￨O￨- antibodies￨L￨NNS￨O￨A .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- elucidate￨L￨VBP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- monkeys￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sylvatic￨L￨JJ￨O￨- ,￨L￨,￨O￨- enzootic￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨A virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- around￨L￨IN￨O￨- Kédougou￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Senegal￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- offspring￨L￨NN￨O￨- distribution￨L￨NN￨O￨- to￨L￨TO￨O￨- enable￨L￨VB￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨A from￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- phylogeny￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2011￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- jointly￨L￨RB￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- incidence￨L￨NN￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- phylogeny￨L￨NN￨O￨A reduced￨L￨VBD￨O￨- uncertainties￨L￨NNS￨O￨- in￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- that￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨A could￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- either￨L￨RB￨O￨- from￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- combining￨L￨VBG￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- should￨L￨MD￨O￨- provide￨L￨VB￨O￨- more￨L￨JJR￨O￨- accurate￨L￨JJ￨O￨- and￨L￨CC￨O￨- precise￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- precision￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- bias￨L￨NN￨O￨- of￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨A using￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +Besides￨U￨IN￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- pathogen￨L￨NN￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- playing￨L￨VBG￨O￨- an￨L￨DT￨O￨- increasingly￨L￨RB￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Volz￨U￨NNP￨PERSON￨- etal￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- scenarios￨L￨NNS￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- harbors￨L￨NNS￨O￨- substantial￨L￨JJ￨O￨- diversity￨L￨NN￨O￨A ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- which￨L￨WDT￨O￨- other￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- they￨L￨PRP￨O￨- infected￨L￨JJ￨O￨- —￨L￨:￨O￨- different￨L￨JJ￨O￨- lineages￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- transmitted￨L￨VBN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- points￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- donor￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- genome￨L￨NN￨O￨- sequenced￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- donor￨L￨NN￨O￨- may￨L￨MD￨O￨- only￨L￨RB￨O￨- represent￨L￨VB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- lineage￨L￨NN￨O￨- captured￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- a￨L￨DT￨O￨- diagnostic￨L￨JJ￨O￨- sample￨L￨NN￨O￨- was￨L￨VBD￨O￨- taken￨L￨VBN￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- lineages￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- within￨L￨IN￨O￨- that￨L￨DT￨O￨- individual￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- early￨L￨JJ￨O￨- works￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- area￨L￨NN￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- genomes￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- pair￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- identical￨L￨JJ￨O￨- or￨L￨CC￨O￨- near-identical￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- genomic￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨- investigations￨L￨NNS￨O￨- revealed￨L￨VBD￨O￨- the￨L￨DT￨O￨- complicating￨L￨JJ￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- introduced￨L￨VBN￨O￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- person-to-person￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A events￨L￨NNS￨O￨A from￨L￨IN￨O￨- genomic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- consider￨L￨VBP￨O￨- within-host￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- simulation￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ignored￨L￨VBN￨O￨- ,￨L￨,￨O￨- incorrect￨L￨JJ￨O￨- inferences￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- drawn￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A events￨L￨NNS￨O￨A that￨L￨WDT￨O￨- occurred￨L￨VBD￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- originally￨L￨RB￨O￨A used￨L￨VBD￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- tree￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- recently￨L￨RB￨DATE￨- showed￨L￨VBD￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- extend￨L￨VB￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- other￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- discrepant￨L￨JJ￨O￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- lg￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- spVL￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- heritability￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- questioned￨L￨VBN￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- methods￨L￨NNS￨O￨A and￨L￨CC￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- various￨L￨JJ￨O￨- adaptations￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- overcome￨L￨VB￨O￨- potential￨L￨JJ￨O￨- pitfalls￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- false￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- assumptions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- neutral￨L￨JJ￨IDEOLOGY￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- ultrametricity￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- imperfections￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- small￨L￨JJ￨O￨- data￨L￨NNS￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- cofactors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- measurement￨L￨NN￨O￨- error￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Phylogenetic￨U￨JJ￨O￨- comparative￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- measuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- so￨L￨RB￨O￨- called￨L￨VBN￨O￨- phylogenetic￨L￨JJ￨O￨- heritability￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- observed￨L￨VBN￨O￨- trait￨L￨NN￨O￨A values￨L￨NNS￨O￨- from￨L￨IN￨O￨- patients￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- (￨L￨-LRB-￨O￨- approximate￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- tree￨L￨NN￨O￨- inferred￨L￨VBD￨O￨- from￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- families￨L￨NNS￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- heritability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- trait￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- its￨L￨PRP$￨O￨- genetic￨L￨JJ￨O￨- basis￨L￨NN￨O￨- :￨L￨:￨O￨- Resemblance￨U￨NNP￨O￨- estimators￨L￨NNS￨O￨- measuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- trait-similarity￨L￨NN￨O￨- within￨L￨IN￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission-related￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Results￨U￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- these￨L￨DT￨O￨- estimators￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- report￨L￨VB￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- spVL￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- cohort￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- per￨L￨IN￨O￨- generation￨L￨NN￨O￨- given￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- entirely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- in￨L￨IN￨O￨- norovirus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- particular￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- of￨L￨IN￨O￨- noroviruses￨L￨NNS￨O￨- developed￨L￨VBN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- to￨L￨TO￨O￨- population￨L￨NN￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- a￨L￨DT￨O￨- remarkable￨L￨JJ￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- reproduction￨L￨NN￨O￨A numbers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Published￨U￨VBN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- norovirus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- demonstrate￨L￨VBP￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- relevant￨L￨JJ￨O￨- settings￨L￨NNS￨O￨A and￨L￨CC￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- local￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- settings￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- and￨L￨CC￨O￨- contrast￨L￨VB￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- for￨L￨IN￨O￨- norovirus￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- High￨U￨NNP￨MISC￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- elementary￨L￨JJ￨O￨- schools￨L￨NNS￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- observational￨L￨JJ￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- Matsumoto￨U￨NNP￨CITY￨- City￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- JapanMitsuo￨U￨NNP￨O￨- Uchida1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Minoru￨U￨NNP￨PERSON￨- Kaneko1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Yoshihiko￨U￨NNP￨PERSON￨- Hidaka2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hiroshi￨U￨NNP￨PERSON￨- Yamamoto3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Takayuki￨U￨NNP￨PERSON￨- Honda4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Shouhei￨U￨NNP￨O￨- Takeuchi5￨U￨NNP￨O￨- ,￨L￨,￨O￨- Masaya￨U￨NNP￨PERSON￨- Saito6￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Shigeyuki￨U￨NNP￨MISC￨- Kawa1BMC￨U￨NNP￨MISC￨- Infectious￨U￨JJ￨MISC￨- DiseasesBMC￨U￨NN￨MISC￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18:128￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- results￨L￨NNS￨O￨- were￨L￨VBD￨O￨- combined￨L￨VBN￨O￨- and￨L￨CC￨O￨- associations￨L￨NNS￨O￨- among￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨A measures￨L￨NNS￨O￨A including￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- mask￨L￨NN￨O￨- wearing￨L￨VBG￨O￨- ,￨L￨,￨O￨- hand￨L￨NN￨O￨- washing￨L￨VBG￨O￨- ,￨L￨,￨O￨- water￨L￨NN￨O￨- gargling￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- level￨L￨NN￨O￨- were￨L￨VBD￨O￨- evaluated￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- significant￨L￨JJ￨O￨- negative￨L￨JJ￨O￨- association￨L￨NN￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- between￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- between￨L￨IN￨O￨- other￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨A measures￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- .￨L￨.￨O￨- +2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- prevented￨L￨VBN￨O￨- by￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨A measures￨L￨NNS￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- wearing￨L￨VBG￨O￨- a￨L￨DT￨O￨- mask￨L￨NN￨O￨- ,￨L￨,￨O￨- gargling￨L￨VBG￨O￨- with￨L￨IN￨O￨- water￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hand￨L￨NN￨O￨- washing￨L￨VBG￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 2015￨L￨CD￨DATE￨- season￨L￨NN￨O￨- evaluated￨L￨VBD￨O￨A the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- diagnosed￨L￨VBN￨O￨- patients￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- school￨L￨NN￨O￨- and￨L￨CC￨O￨- calculated￨L￨VBN￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- schoolchildren￨L￨NNS￨O￨- .￨L￨.￨O￨- +Overall￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aimed￨L￨VBD￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- generation￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨A tools￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- adapted￨L￨VBN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- epidemiological￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- of￨L￨IN￨O￨- central￨L￨JJ￨O￨- importance￨L￨NN￨O￨- to￨L￨TO￨O￨- HIV-1￨U￨NN￨MISC￨- prevention￨L￨NN￨O￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- the￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- sequence￨L￨NN￨O￨- availability￨L￨NN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- resource-poor￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- fundamentally￨L￨RB￨O￨- from￨L￨IN￨O￨- well￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- concentrated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- wealthy￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- viral￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨A tools￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proven￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- these￨L￨DT￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- generated￨L￨VBD￨O￨- corresponding￨L￨JJ￨O￨- viral￨L￨JJ￨O￨A sequence￨L￨NN￨O￨- datasets￨L￨NNS￨O￨- comprising￨L￨VBG￨O￨- simulated￨L￨JJ￨O￨- pol￨L￨NN￨O￨- ,￨L￨,￨O￨- gag￨L￨NN￨O￨- and￨L￨CC￨O￨- env￨L￨NN￨O￨- genes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- as￨L￨RB￨O￨- full￨L￨JJ￨O￨- genome￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- brevity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- basic￨L￨JJ￨O￨- individual-level￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- those￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- sequenced￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Available￨U￨JJ￨O￨- viral￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨A techniques￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- of￨L￨IN￨O￨- concentrated￨L￨JJ￨O￨- HIV-1￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Phylogenetics￨U￨NNPS￨O￨- And￨U￨CC￨O￨- Networks￨U￨NNP￨O￨- for￨L￨IN￨O￨- Generalized￨U￨NNP￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- Epidemics￨U￨NNS￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- PANGEA-HIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- consortium￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- viral￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- across￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- their￨L￨PRP$￨O￨- viral￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨A relationship￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- marker￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- HIV-1￨U￨NN￨MISC￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Estimating￨U￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨- introduction￨L￨NN￨O￨- and￨L￨CC￨O￨- secondary￨L￨JJ￨O￨- autochthonous￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- Eduardo￨U￨NNP￨LOCATION￨- Massad1￨U￨NN￨O￨- ,2,3,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Marcos￨U￨NNP￨PERSON￨- Amaku￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Francisco￨U￨NNP￨PERSON￨- Antonio￨U￨NNP￨PERSON￨- Bezerra￨U￨NNP￨PERSON￨- Coutinho1￨U￨NN￨O￨- ,￨L￨,￨O￨- Claudio￨U￨NNP￨PERSON￨- José￨U￨NNP￨PERSON￨- Struchiner5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marcelo￨U￨NNP￨PERSON￨- Nascimento￨U￨NNP￨PERSON￨- Burattini1￨U￨NNP￨O￨- ,6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kamran￨U￨NNP￨PERSON￨- Khan7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jing￨U￨NNP￨PERSON￨- Liu-Helmersson8￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Joacim￨U￨NNP￨O￨- Rocklöv8￨U￨NNP￨O￨- ,￨L￨,￨O￨- Moritz￨U￨NNP￨PERSON￨- U.￨U￨NNP￨PERSON￨- G.￨U￨NNP￨PERSON￨- Kraemer9￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Annelies￨U￨NNP￨O￨- Wilder-Smith8￨U￨NN￨O￨- ,10,11￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 4629￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Experimental￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- diseaseInfectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- AbstractGiven￨U￨VBP￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- air￨L￨NN￨O￨- travel￨L￨NN￨O￨- ,￨L￨,￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- even￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- viremia￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- dengue￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- exported￨L￨VBN￨O￨- to￨L￨TO￨O￨- dengue￨L￨VB￨O￨- naïve￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- within￨L￨IN￨O￨- 24￨L￨CD￨DURATION￨- hours￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- applied￨L￨VBD￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue-viremic￨L￨JJ￨O￨- air￨L￨NN￨O￨- passengers￨L￨NNS￨O￨- from￨L￨IN￨O￨- 16￨L￨CD￨NUMBER￨- dengue-endemic￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- to￨L￨TO￨O￨- 27￨L￨CD￨NUMBER￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- exporting￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- travel￨L￨NN￨O￨- volume￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- viremic￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- models￨L￨NNS￨O￨- estimate￨L￨VBP￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- from￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 167￨L￨CD￨NUMBER￨- air￨L￨NN￨O￨- passengers￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- dengue-viremic￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- from￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A endemic￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 27￨L￨CD￨NUMBER￨- receiving￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- set￨L￨VBD￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨- introductions￨L￨NNS￨O￨- via￨L￨IN￨O￨- travelers￨L￨NNS￨O￨- into￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- autochthonous￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- .￨L￨.￨O￨- +Methodology￨U￨NNP￨O￨- Article￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Heterogeneous￨U￨JJ￨O￨- computing￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- fitting￨L￨JJ￨O￨- and￨L￨CC￨O￨- simulationThomas￨L￨NNP￨O￨- Kovac￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Tom￨U￨NNP￨PERSON￨- Haber￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Frank￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Reeth2￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Niel￨U￨NN￨PERSON￨- Hens1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- †￨L￨NN￨O￨- Contributed￨U￨VBD￨O￨- equallyBMC￨L￨NN￨O￨- BioinformaticsBMC￨U￨NN￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 19:101￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Over￨U￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- years￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- substantial￨L￨JJ￨O￨- effort￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- put￨L￨VBN￨O￨- into￨L￨IN￨O￨- enhancing￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- arsenal￨L￨NN￨O￨- in￨L￨IN￨O￨- fighting￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- technological￨L￨JJ￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- perspectives￨L￨NNS￨O￨- with￨L￨IN￨O￨- scientists￨L￨NNS￨O￨A from￨L￨IN￨O￨- different￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- teaming￨L￨VBG￨O￨- up￨L￨RP￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- potentially￨L￨RB￨O￨- urgent￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- particles￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- PSO￨U￨NNP￨ORGANIZATION￨- algorithm￨L￨NN￨O￨- are￨L￨VBP￨O￨- candidate￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- right￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- matter￨L￨NN￨O￨- of￨L￨IN￨O￨- optimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- which￨L￨WDT￨O￨- quantifies￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- well￨L￨RB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- focusses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- computational￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A and￨L￨CC￨O￨- applies￨L￨VBZ￨O￨- commonly￨L￨RB￨O￨- available￨L￨JJ￨O￨- graphics￨L￨NNS￨O￨- processing￨L￨VBG￨O￨- units￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- GPUs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- asynchronous￨L￨JJ￨O￨- particle￨L￨NN￨O￨- swarm￨L￨NN￨O￨- optimization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PSO￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- implementation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- where￨L￨WRB￨O￨- batches￨L￨NNS￨O￨- of￨L￨IN￨O￨- particles￨L￨NNS￨O￨A are￨L￨VBP￨O￨- sent￨L￨VBN￨O￨- asynchronously￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- CPU￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- GPU￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨O￨- evaluation￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- GPU￨U￨NNP￨ORGANIZATION￨- implementation￨L￨NN￨O￨A for￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- a￨L￨DT￨O￨- small-scale￨L￨JJ￨O￨- ODE￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- usceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- nfected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ecovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- discussed￨L￨VBN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- article￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- innovative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- extend￨L￨VB￨O￨- agent-based￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A by￨L￨IN￨O￨- capturing￨L￨VBG￨O￨- behavioral￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- decision-making￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- risky￨L￨JJ￨O￨- context￨L￨NN￨O￨- using￨L￨VBG￨O￨- machine￨L￨NN￨O￨- learning￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- .￨L￨.￨O￨- +Yet￨U￨RB￨O￨- ,￨L￨,￨O￨- current￨L￨JJ￨DATE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A rarely￨L￨RB￨O￨- consider￨L￨VBP￨O￨- simulating￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- protective￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- illustrate￨L￨VBP￨O￨- it￨L￨PRP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Kumasi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Ghana￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- spatial￨L￨JJ￨O￨A and￨L￨CC￨O￨- social￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- affect￨L￨VBP￨O￨- intelligent￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- corresponding￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidents￨L￨NNS￨O￨- .￨L￨.￨O￨- +Hand￨U￨VB￨O￨- ,￨L￨,￨O￨- foot￨L￨NN￨O￨- and￨L￨CC￨O￨- mouth￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- HFMD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- paediatric￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- usually￨L￨RB￨O￨- self-limiting￨L￨JJ￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- nervous￨L￨JJ￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CNS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- death￨L￨NN￨O￨- .1￨L￨NN￨NUMBER￨- 2￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- viruses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- cause￨L￨VBP￨O￨- HFMD￨U￨NN￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- widespread￨L￨JJ￨O￨- in￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- .3￨L￨NN￨NUMBER￨- Citation￨U￨NNP￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- 29￨L￨CD￨NUMBER￨- children￨L￨NNS￨O￨- died4￨L￨NN￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- harbinger￨L￨NN￨O￨- of￨L￨IN￨O￨- fatal￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- continued￨L￨VBN￨O￨- to￨L￨TO￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 170￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 98￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .6￨L￨CD￨NUMBER￨- These￨U￨DT￨O￨- fatal￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- influenced￨L￨VBN￨O￨- the￨L￨DT￨O￨- perceived￨L￨VBN￨O￨- severity￨L￨NN￨O￨A of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- and￨L￨CC￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- demand￨L￨NN￨O￨- for￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,7￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- phase￨L￨NN￨O￨- III￨U￨CD￨NUMBER￨- vaccine￨L￨NN￨O￨- trials￨L￨NNS￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ,8￨L￨CD￨NUMBER￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- through￨L￨IN￨O￨- Bayesian￨U￨JJ￨MISC￨- methods￨L￨NNS￨O￨- which￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- flexible￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- integrate￨L￨VB￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨A indices￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza11￨L￨NN￨O￨- 12￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- .13￨L￨CD￨NUMBER￨- To￨U￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- across￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- mortality￨L￨NN￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- against￨L￨IN￨O￨- it￨L￨PRP￨O￨- ,7￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- conducted￨L￨VBD￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- across￨L￨IN￨O￨- East￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Southeast￨U￨NNP￨O￨- Asia14￨U￨NNP￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- severity￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- usually￨L￨RB￨O￨- mild￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- where￨L￨WRB￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- vastly￨L￨RB￨O￨- exceed￨L￨VBP￨O￨- severe￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- efforts￨L￨NNS￨O￨- to￨L￨TO￨O￨- track￨L￨VB￨O￨- all￨L￨DT￨O￨- HFMD￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- indices￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- severity￨L￨NN￨O￨A are￨L￨VBP￨O￨- impractical￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- .9￨L￨CD￨NUMBER￨- With￨U￨IN￨O￨- the￨L￨DT￨O￨- exception￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- jurisdictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- much￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- subpopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- catchment￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- health￨L￨NN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- sentinel￨L￨NN￨O￨- clinics￨L￨NNS￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- passive￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- using￨L￨VBG￨O￨- symptomatic￨L￨JJ￨O￨- case￨L￨NN￨O￨- notifications￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- ref￨L￨NN￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Obtaining￨U￨VBG￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- comprehensive￨L￨JJ￨O￨- picture￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- synthesising￨L￨VBG￨O￨- available￨L￨JJ￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- studies￨L￨NNS￨O￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- severity￨L￨NN￨O￨A levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- serological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- estimate￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- notification￨L￨NN￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- clinically￨L￨RB￨O￨- identified￨L￨VBN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- hospital￨L￨NN￨O￨- records￨L￨NNS￨O￨- that￨L￨WDT￨O￨- showcase￨L￨NN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- more￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- CNS￨U￨NN￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- death￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- sCFR￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- computed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- poor￨L￨JJ￨O￨- reflection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- severity￨L￨NN￨O￨A and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- notification￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- antibody￨L￨NN￨O￨- titers￨L￨NNS￨O￨- against￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- HAI￨U￨NN￨O￨- assays￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- over￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- seasons￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- in￨L￨IN￨O￨- Singapore￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- supplementary￨L￨JJ￨O￨- real-time￨L￨JJ￨O￨- polymerase￨L￨NN￨O￨- chain￨L￨NN￨O￨- reaction￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- RT-PCR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- from￨L￨IN￨O￨- various￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- synthesized￨L￨VBD￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- RT-PCR￨U￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- repeated￨L￨VBN￨O￨- serological￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A evolution￨L￨NN￨O￨A of￨L￨IN￨O￨- HAI￨U￨NNP￨O￨- titers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- immediate￨L￨JJ￨O￨- aftermath￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- restriction￨L￨NN￨O￨- of￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- 4-fold￨L￨JJ￨O￨- rise￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- data￨L￨NN￨O￨- set￨L￨NN￨O￨- provided￨L￨VBN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A evolution￨L￨NN￨O￨A of￨L￨IN￨O￨- titers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- immediate￨L￨JJ￨O￨- aftermath￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- times￨L￨NNS￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- samples￨L￨NNS￨O￨- were￨L￨VBD￨O￨- taken￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- May￨U￨NNP￨DATE￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1B￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- temperature￨L￨NN￨O￨- forcing￨L￨VBG￨O￨- improves￨L￨VBZ￨O￨- forecast￨L￨NN￨O￨A accuracy￨L￨NN￨O￨- for￨L￨IN￨O￨- total￨L￨JJ￨O￨- human￨L￨JJ￨O￨- case￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨DATE￨- week￨L￨NN￨DATE￨- of￨L￨IN￨O￨- peak￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- abundance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- abundance￨L￨NN￨O￨- for￨L￨IN￨O￨- much￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- WNV￨U￨NN￨O￨- season￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- predicted￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- forecast￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- system￨L￨NN￨O￨- accurately￨L￨RB￨O￨- forecast￨L￨VBD￨O￨A mosquito￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨DATE￨- week￨L￨NN￨DATE￨- of￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- peak￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- accurately￨L￨RB￨O￨- predicted￨L￨VBD￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- WNV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- up￨L￨IN￨DURATION￨- to￨L￨TO￨DURATION￨- 9￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- reported￨L￨VBD￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨SET￨- week￨L￨NN￨SET￨- ,￨L￨,￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- WNV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 300￨L￨CD￨NUMBER￨- mosquitoes￨L￨NNS￨O￨- were￨L￨VBD￨O￨- sampled￨L￨VBN￨O￨- ,￨L￨,￨O￨- mosquito￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- assimilated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- EAKF￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- forecast￨L￨NN￨O￨A was￨L￨VBD￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- integrating￨L￨VBG￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ensemble￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- accurate￨L￨JJ￨O￨- and￨L￨CC￨O￨- reliable￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- WNV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- parsimonious￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- WNV￨U￨NN￨O￨- among￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨A and￨L￨CC￨O￨- birds￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- spillover￨L￨NN￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- such￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- proven￨L￨VBN￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- discriminating￨L￨VBG￨O￨- writing￨L￨VBG￨O￨- styles￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- robustness￨L￨NN￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- topological￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- usually￨L￨RB￨O￨- provide￨L￨VBP￨O￨- no￨L￨DT￨O￨- better￨L￨JJR￨O￨- results￨L￨NNS￨O￨- than￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- based￨L￨VBN￨O￨- e.g.￨L￨FW￨O￨- in￨L￨IN￨O￨- n-grams￨L￨JJ￨O￨- models￨L￨NNS￨O￨- when￨L￨WRB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- text￨L￨NN￨O￨A characterization￨L￨NN￨O￨- .￨L￨.￨O￨- +Traditional￨U￨JJ￨O￨- techniques￨L￨NNS￨O￨- use￨L￨VBP￨O￨- text￨L￨NN￨O￨A analytics￨L￨NNS￨O￨- and￨L￨CC￨O￨- natural￨L￨JJ￨O￨- language￨L￨NN￨O￨- processing￨L￨NN￨O￨- concepts￨L￨NNS￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- authors￨L￨NNS￨O￨- ’￨L￨POS￨O￨- writing￨L￨VBG￨O￨- styles￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paradigm￨L￨NN￨O￨- ,￨L￨,￨O￨- documents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- co-occurrence￨L￨NN￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- formed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- authors￨L￨NNS￨O￨A ’￨L￨POS￨O￨- fingerprints￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- classification￨L￨NN￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- study￨L￨NN￨O￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- integrative￨L￨JJ￨O￨- ,￨L￨,￨O￨- joint￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- numerous￨L￨JJ￨O￨- suggested￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- triggers￨L￨VBZ￨O￨- ,￨L￨,￨O￨- comparing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- importance￨L￨NN￨O￨- and￨L￨CC￨O￨- possible￨L￨JJ￨O￨- cooperation￨L￨NN￨O￨- in￨L￨IN￨O￨- triggering￨L￨VBG￨O￨- pan-US￨L￨JJ￨O￨- waves￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Computational￨U￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- factors￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A began￨L￨VBD￨O￨- with￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Resistant￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- traces￨L￨NNS￨O￨- its￨L￨PRP$￨O￨- origins￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨DATE￨- beginning￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- informative￨L￨JJ￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- predictors￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- initiation￨L￨NN￨O￨- of￨L￨IN￨O￨- pan-US￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A waves￨L￨NNS￨O￨- .￨L￨.￨O￨- +Initially￨U￨RB￨O￨- a￨L￨DT￨O￨- purely￨L￨RB￨O￨A theoretical￨L￨JJ￨O￨- tool￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- SIR-style￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- subsequently￨L￨RB￨O￨- enhanced￨L￨VBN￨O￨- with￨L￨IN￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- geographic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- application￨L￨NN￨O￨- to￨L￨TO￨O￨- specific￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distances￨L￨NNS￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- initiating￨L￨VBG￨O￨- each￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- wave￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- coevolution￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- and￨L￨CC￨O￨- awareness￨L￨NN￨O￨A ,￨L￨,￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- estimators￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- multiplex￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- disclose￨L￨VB￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- overlapping￨L￨VBG￨O￨- awareness￨L￨NN￨O￨A on￨L￨IN￨O￨- suicidal￨L￨JJ￨O￨- ideation￨L￨NN￨O￨- spreading￨L￨NN￨O￨- among￨L￨IN￨O￨- disordered￨L￨VBN￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- data-driven￨L￨JJ￨O￨- approach￨L￨NN￨O￨- by￨L￨IN￨O￨- integrating￨L￨VBG￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- modelling￨L￨NN￨O￨- approach￨L￨NN￨O￨- unveils￨L￨VBZ￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- distress￨L￨NN￨O￨- and￨L￨CC￨O￨- mental￨L￨JJ￨O￨- disorders￨L￨NNS￨O￨- propagation￨L￨NN￨O￨- and￨L￨CC￨O￨- suicidal￨L￨JJ￨O￨- ideation￨L￨NN￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- shedding￨L￨VBG￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- for￨L￨IN￨O￨- suicide￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Quantifying￨U￨VBG￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- distress￨L￨NN￨O￨- and￨L￨CC￨O￨- mental￨L￨JJ￨O￨- disorders￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- Marialisa￨U￨NNP￨O￨- Scatà1￨U￨NNP￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Alessandro￨U￨NNP￨PERSON￨- Di￨U￨NNP￨PERSON￨- Stefano1￨U￨NN￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Aurelio￨U￨NNP￨ORGANIZATION￨- La￨U￨NNP￨ORGANIZATION￨- Corte1￨U￨NNP￨ORGANIZATION￨- na1￨L￨NN￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Pietro￨U￨NNP￨ORGANIZATION￨- Liò2￨U￨NNP￨O￨- na1￨L￨NN￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 5005￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksPsychiatric￨L￨JJ￨O￨- disorders￨L￨NNS￨O￨- AbstractHeterogeneity￨U￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- beings￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- think￨L￨VB￨O￨- and￨L￨CC￨O￨- react￨L￨VB￨O￨- differently￨L￨RB￨O￨- to￨L￨TO￨O￨- social￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- .￨L￨.￨O￨- +Awareness￨U￨NN￨O￨- and￨L￨CC￨O￨- homophily￨L￨RB￨O￨- drive￨L￨VB￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- weigh￨L￨VB￨O￨- interactions￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- influencing￨L￨VBG￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- Kermack￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- incorporated￨L￨VBD￨O￨- the￨L￨DT￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- Ross￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- proposed￨L￨VBD￨O￨- new￨L￨JJ￨O￨- and￨L￨CC￨O￨- modern￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- later￨L￨RB￨O￨- became￨L￨VBD￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- basic￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A modeling￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- serve￨L￨VB￨O￨- this￨L￨DT￨O￨- purpose￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- exploited￨L￨VBN￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- progression￨L￨NN￨O￨- ,￨L￨,￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- trend￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- tailor￨L￨NN￨TITLE￨- related￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- modeling￨L￨NN￨O￨A framework￨L￨NN￨O￨- still￨L￨RB￨O￨- plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- mosquito-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Modelers￨U￨NNS￨O￨- are￨L￨VBP￨O￨- obligated￨L￨VBN￨O￨- to￨L￨TO￨O￨- comprehend￨L￨VB￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- frameworks￨L￨NNS￨O￨A but￨L￨CC￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- behind￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Infectious￨U￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A modeling￨L￨NN￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- interdisciplinary￨L￨JJ￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +What￨U￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- of￨L￨IN￨O￨- notable￨L￨JJ￨O￨- popularity￨L￨NN￨O￨- in￨L￨IN￨O￨- big￨L￨JJ￨O￨- data￨L￨NNS￨O￨- analytics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- online￨L￨JJ￨O￨A search￨L￨NN￨O￨- queries￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 11-12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- mainly￨L￨RB￨O￨- using￨L￨VBG￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Trends￨U￨NNPS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- popular￨L￨JJ￨O￨- open￨L￨JJ￨O￨- tool￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- integrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- research￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- ,￨L￨,￨O￨- mainly￨L￨RB￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- health-related￨L￨JJ￨O￨- topics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Google￨U￨NNP￨ORGANIZATION￨- Trends￨U￨NNPS￨ORGANIZATION￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- valid￨L￨JJ￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- subject￨L￨NN￨O￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- the￨L￨DT￨O￨- tool￨L￨NN￨O￨- ’s￨L￨POS￨O￨- contribution￨L￨NN￨O￨- to￨L￨TO￨O￨- forecasting￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 45-46￨L￨CD￨DATE￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- online￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- provided￨L￨VBN￨O￨- careful￨L￨JJ￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- examined￨L￨VBN￨O￨- terms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- online￨L￨NN￨O￨A queries￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- “￨L￨``￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- ”￨L￨''￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- were￨L￨VBD￨O￨- analyzed￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- nowcasting￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ie￨L￨FW￨O￨- ,￨L￨,￨O￨- forecasting￨L￨VBG￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- )￨L￨-RRB-￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- using￨L￨VBG￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Trends￨U￨NNPS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- if￨L￨IN￨O￨- nowcasting￨L￨JJ￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- using￨L￨VBG￨O￨- online￨L￨JJ￨O￨A search￨L￨NN￨O￨- traffic￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- further￨L￨JJ￨O￨- elaborate￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Pearson￨U￨NNP￨PERSON￨- correlations￨L￨NNS￨O￨- for￨L￨IN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Trends￨U￨NNPS￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨A “￨L￨``￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- ”￨L￨''￨O￨- between￨L￨IN￨O￨- each￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- were￨L￨VBD￨O￨- calculated￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- variation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- prospects￨L￨NNS￨O￨- for￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- control￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- the￨L￨DT￨O￨- abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- farms￨L￨NNS￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- initially￨L￨RB￨O￨- ,￨L￨,￨O￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- frequencies￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- longer￨L￨JJR￨O￨- the￨L￨DT￨O￨- breeding￨L￨VBG￨O￨- program￨L￨NN￨O￨- may￨L￨MD￨O￨- need￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- sustained￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- R0￨U￨NN￨O￨- to￨L￨TO￨O￨- below￨L￨IN￨O￨- unity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- correspondingly￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- the￨L￨DT￨O￨- population-level￨L￨JJ￨O￨- minimum￨L￨NN￨O￨- ARR￨U￨NN￨O￨- allele￨L￨NN￨O￨A frequency￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- objective￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- compliance￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- long￨L￨RB￨O￨- the￨L￨DT￨O￨- ram￨L￨NN￨O￨- selection￨L￨NN￨O￨- program￨L￨NN￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- maintained￨L￨VBN￨O￨- to￨L￨TO￨O￨- reach￨L￨VB￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- ARR￨U￨NN￨O￨- allele￨L￨NN￨O￨A frequency￨L￨NN￨O￨- and￨L￨CC￨O￨- achieve￨L￨VB￨O￨- scrapie￨L￨NN￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ARR￨U￨NN￨ORGANIZATION￨- allele￨L￨NN￨O￨A for￨L￨IN￨O￨- which￨L￨WDT￨O￨- this￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- is￨L￨VBZ￨O￨- attained￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- ARR￨U￨NN￨O￨- allele￨L￨NN￨O￨- frequency￨L￨NN￨O￨- for￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- concept￨L￨NN￨O￨- analogous￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- translate￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- within-flock￨L￨NN￨O￨- genotype￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨A into￨L￨IN￨O￨- a￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- within-flock￨L￨NN￨O￨- R0￨U￨NN￨O￨- values￨L￨NNS￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- serves￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- between-flock￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- for￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- quantification￨L￨NN￨O￨A of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- between-flock￨L￨NN￨O￨- heterogeneities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Centre￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Mathematical￨U￨JJ￨O￨- Modelling￨U￨NN￨O￨- of￨L￨IN￨O￨- Infectious￨U￨JJ￨O￨- Diseases￨U￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- CMMID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- London￨U￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Hygiene￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Tropical￨U￨NNP￨ORGANIZATION￨- Medicine￨U￨NNP￨ORGANIZATION￨- produced￨L￨VBD￨O￨- weekly￨L￨JJ￨SET￨- situation￨L￨NN￨O￨- reports￨L￨NNS￨O￨- presenting￨L￨VBG￨O￨- updates￨L￨NNS￨O￨- of￨L￨IN￨O￨- publicly￨L￨RB￨O￨- available￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- fits￨L￨NNS￨O￨- and￨L￨CC￨O￨- forecasts￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- experienced￨L￨VBN￨O￨- by￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- λ￨L￨NN￨O￨- =￨L￨JJ￨O￨- βI/N￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- I￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- β￨L￨VB￨O￨- the￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A rate￨L￨NN￨O￨A which￨L￨WDT￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- W￨U￨NNP￨O￨- denotes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Wiener￨U￨NNP￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- σ￨L￨IN￨O￨- the￨L￨DT￨O￨- volatility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- log-transform￨L￨NN￨O￨- ensures￨L￨VBZ￨O￨- positivity￨L￨NN￨O￨- of￨L￨IN￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨A change￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- different￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- modelled￨L￨VBD￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- used￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- trajectories￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Challenge￨U￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- forecasts￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- cases￨L￨NNS￨O￨- at￨L￨IN￨O￨- upcoming￨L￨JJ￨O￨- time￨L￨NN￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- forecasts￨L￨NNS￨O￨A in￨L￨IN￨O￨- these￨L￨DT￨O￨- situation￨L￨NN￨O￨- reports￨L￨NNS￨O￨- were￨L￨VBD￨O￨- produced￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- semi-mechanistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- estimated￨L￨VBD￨O￨- waning￨L￨VBG￨O￨- immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- severe￨L￨JJ￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A as￨L￨IN￨O￨- 1.41￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- after￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- calculated￨L￨VBD￨O￨- the￨L￨DT￨O￨- age-specific￨L￨JJ￨O￨- residual￨L￨JJ￨O￨- protection￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- persons￨L￨NNS￨O￨- 40￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 69￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- by￨L￨IN￨O￨- multiplying￨L￨VBG￨O￨- that￨L￨DT￨O￨- percentage￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- years￨L￨NNS￨DURATION￨- from￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- subtracting￨L￨VBG￨O￨- it￨L￨PRP￨O￨- from￨L￨IN￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- starting￨L￨VBG￨O￨- protection￨L￨NN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- researchers￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- optimistic￨L￨JJ￨O￨- about￨L￨IN￨O￨- residual￨L￨JJ￨O￨- vaccine-induced￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- assumed￨L￨VBD￨O￨- a￨L￨DT￨O￨- case-fatality￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CFR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- nonimmune￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- a￨L￨DT￨O￨- CFR￨U￨NN￨O￨- of￨L￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- –￨L￨:￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- reemerging￨L￨VBG￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Sydney￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- New￨U￨NNP￨LOCATION￨- South￨U￨NNP￨LOCATION￨- Wales￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- large￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- histories￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- estimates￨L￨VBZ￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ’s￨L￨POS￨O￨- immunologic￨L￨JJ￨O￨- status￨L￨NN￨O￨- .￨L￨.￨O￨- +Characteristics￨U￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- NY￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Sydney￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- New￨U￨NNP￨LOCATION￨- South￨U￨NNP￨LOCATION￨- Wales￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- population￨L￨NN￨O￨- 40￨L￨CD￨NUMBER￨A –￨L￨:￨O￨- 69￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- vaccinated￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- H1N1￨U￨NN￨O￨- 2009￨L￨CD￨DATE￨- pandemic￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- assessed￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- dimensionless￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- inversely￨L￨RB￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- affinity￨L￨NN￨O￨- epitopes￨L￨NNS￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- individual￨L￨JJ￨O￨- presents￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- viral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- qualitatively￨L￨RB￨O￨- reproduce￨L￨VB￨O￨- some￨L￨DT￨O￨- known￨L￨JJ￨O￨- trends￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +Incorporating￨U￨VBG￨O￨- such￨L￨JJ￨O￨- individual-level￨L￨JJ￨O￨- immunological￨L￨JJ￨O￨- information￨L￨NN￨O￨- into￨L￨IN￨O￨- population-level￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨A or￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- heterogeneities￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- recently￨L￨RB￨DATE￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- for￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- predict￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- using￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- 61￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- ethnicities￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- for￨L￨IN￨O￨- 81￨L￨CD￨NUMBER￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 85￨L￨CD￨NUMBER￨A Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- genome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- proteome￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- sequence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- prior￨L￨JJ￨O￨- belief￨L￨NN￨O￨- ascribed￨L￨VBN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- equal￨L￨JJ￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- measure￨L￨NN￨O￨- forms￨L￨VBZ￨O￨- the￨L￨DT￨O￨- sole￨L￨JJ￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- Bayesian￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- ranking￨L￨NN￨O￨- of￨L￨IN￨O￨- competing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- evidence￨L￨NN￨O￨A identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- unbiased￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- evidence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- which￨L￨WDT￨O￨- converges￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- evidence￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- samples￨L￨NNS￨O￨- N￨U￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- electronic￨L￨JJ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- appendix￨L￨NN￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- expression￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- deviance￨L￨NN￨O￨- information￨L￨NN￨O￨- criterion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DIC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A method￨L￨NN￨O￨- which￨L￨WDT￨O￨- tries￨L￨VBZ￨O￨- to￨L￨TO￨O￨- explicitly￨L￨RB￨O￨- balance￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- complexity￨L￨NN￨O￨- with￨L￨IN￨O￨- fit￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- calculates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- evidence￨L￨NN￨O￨A by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- generating￨L￨VBG￨O￨- samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- K￨U￨NNP￨O￨- separate￨L￨JJ￨O￨- MCMC￨U￨NN￨O￨- chains￨L￨NNS￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- temperatures￨L￨NNS￨O￨- ϕ1￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- ϕ2￨L￨NN￨O￨- >￨L￨JJR￨O￨- …￨L￨:￨O￨- >￨L￨JJR￨O￨- ϕ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- ‘￨L￨``￨O￨- observed￨L￨VBN￨O￨A data￨L￨NNS￨O￨A likelihood￨L￨NN￨O￨- ’￨L￨''￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- |￨L￨CD￨NUMBER￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- latent￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- x￨L￨CC￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- θ￨L￨VBP￨O￨- .￨L￨.￨O￨- +Sasaki￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- his￨L￨PRP$￨O￨- collaborators￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- intra-host￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- –￨L￨:￨O￨- antibodies￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- or￨L￨CC￨O￨- continuous￨L￨JJ￨O￨- one-dimensional￨L￨JJ￨O￨- strain￨L￨NN￨O￨- space￨L￨NN￨O￨A to￨L￨TO￨O￨- study￨L￨VB￨O￨- antigenic￨L￨JJ￨O￨- drift￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- virus￨L￨NN￨O￨- co-evolution￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- suggested￨L￨VBD￨O￨- an￨L￨DT￨O￨- elegant￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- RNA￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- evolution￨L￨NN￨O￨- where￨L￨WRB￨O￨- virus￨L￨NN￨O￨- types￨L￨NNS￨O￨- were￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- distributed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- one-dimensional￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- space￨L￨NN￨O￨A according￨L￨VBG￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- fitness￨L￨NN￨O￨- .￨L￨.￨O￨- +Probably￨U￨RB￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- direction￨L￨NN￨O￨- was￨L￨VBD￨O￨- done￨L￨VBN￨O￨- by￨L￨IN￨O￨- Pease￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- formulated￨L￨VBD￨O￨- a￨L￨DT￨O￨- simplistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- inter-host￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- evolution￨L￨NN￨O￨A to￨L￨TO￨O￨- study￨L￨VB￨O￨- evolutionary￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +Western￨U￨JJ￨O￨- Fence￨U￨NN￨O￨- Lizards￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- Sceloporus￨U￨NN￨MISC￨- occidentalis￨L￨NN￨MISC￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- with￨L￨IN￨O￨- Plasmodium￨U￨NN￨O￨- mexicanum￨L￨NN￨O￨- ,￨L￨,￨O￨- displayed￨L￨VBD￨O￨- a￨L￨DT￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- hemoglobin￨L￨NN￨O￨- concentration￨L￨NN￨O￨- and￨L￨CC￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- oxygen￨L￨NN￨O￨- consumption￨L￨NN￨O￨- following￨L￨VBG￨O￨- physical￨L￨JJ￨O￨A exertion￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- uninfected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- evidencing￨L￨VBG￨O￨- similar￨L￨JJ￨O￨- increased￨L￨VBN￨O￨- reliance￨L￨NN￨O￨- on￨L￨IN￨O￨- anaerobic￨L￨JJ￨O￨- metabolism￨L￨NN￨O￨- and￨L￨CC￨O￨- greater￨L￨JJR￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- energy￨L￨NN￨O￨- should￨L￨MD￨O￨- become￨L￨VB￨O￨- limiting￨L￨VBG￨O￨- primarily￨L￨RB￨O￨- in￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- protective￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- activity￨L￨NN￨O￨A and￨L￨CC￨O￨- pathogenesis￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- less￨L￨RBR￨O￨- so￨L￨RB￨O￨- of￨L￨IN￨O￨- tolerant￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- trade-offs￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- therefore￨L￨RB￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- be￨L￨VB￨O￨- apparent￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- wild￨L￨JJ￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- metabolic￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- impair￨L￨VB￨O￨- the￨L￨DT￨O￨- physical￨L￨JJ￨O￨- activity￨L￨NN￨O￨A of￨L￨IN￨O￨- Plasmodium-infected￨U￨JJ￨MISC￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- accordingly￨L￨RB￨O￨- ,￨L￨,￨O￨- classical￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- include￨L￨VBP￨O￨- muscle￨L￨NN￨O￨- aches￨L￨NNS￨O￨- ,￨L￨,￨O￨- contractures￨L￨NNS￨O￨- ,￨L￨,￨O￨- fatigue￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- weakness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- no￨L￨DT￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- Plasmodium￨U￨NN￨LOCATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- and￨L￨CC￨O￨- sprint￨L￨NN￨O￨- speed￨L￨NN￨O￨- in￨L￨IN￨O￨- western￨L￨JJ￨O￨A fence￨L￨NN￨O￨- lizards￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- locomotor￨L￨NN￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- Spiny￨U￨NNP￨O￨- lizards￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Sceloporus￨U￨NN￨O￨- jarrovii￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- natural￨L￨JJ￨O￨- Plasmodium￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- found￨L￨VBN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- reduced￨L￨VBN￨O￨- stamina￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- western￨L￨JJ￨O￨A fence￨L￨NN￨O￨- and￨L￨CC￨O￨- rainbow￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Agama￨U￨NN￨O￨- agama￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- lizards￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- assumptions￨L￨NNS￨O￨- Y1￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- Y6￨U￨NN￨O￨- lead￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- represents￨L￨VBZ￨O￨A the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- ξ￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- without￨L￨IN￨O￨- successful￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- prenatally￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- ϕ￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- waning￨L￨VBG￨O￨- vaccine￨L￨NN￨O￨- induced￨L￨VBD￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- characteristic￨L￨NN￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- epidemiological￨L￨JJ￨O￨- subclasses￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- latent￨L￨JJ￨O￨- L￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- acutely￨L￨RB￨O￨- infected￨L￨JJ￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- chronic￨L￨JJ￨O￨- carrier￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- C￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBN￨O￨- with￨L￨IN￨O￨- permanent￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- acute￨L￨JJ￨O￨- and￨L￨CC￨O￨- chronic￨L￨JJ￨O￨- carrier￨L￨NN￨O￨- infected￨L￨JJ￨O￨- subclasses￨L￨NNS￨O￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- acute￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- chronic￨L￨JJ￨O￨- carrier￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- epidemiological￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- and￨L￨CC￨O￨- retrieve￨L￨VB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- section￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- name￨L￨VB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- shall￨L￨MD￨O￨- return￨L￨VB￨O￨- :￨L￨:￨O￨- Historically￨U￨NNP￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- settlements￨L￨NNS￨O￨- followed￨L￨VBD￨O￨- the￨L￨DT￨O￨- river￨L￨NN￨TITLE￨- networks￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- water￨L￨NN￨O￨- resources￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- River￨U￨NN￨TITLE￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- home￨L￨NN￨O￨- to￨L￨TO￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- provide￨L￨VB￨O￨- hierarchical￨L￨JJ￨O￨- habitat￨L￨NN￨O￨- features￨L￨NNS￨O￨A for￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- freshwater￨L￨NN￨O￨- fish￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- stream￨L￨NN￨O￨- ecology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- pathways￨L￨NNS￨O￨- to￨L￨TO￨O￨- life-threatening￨L￨JJ￨O￨- waterborne￨L￨JJ￨O￨- human￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- zoonoses￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- passed￨L￨VBN￨O￨- between￨L￨IN￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- angle￨L￨NN￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- such￨L￨JJ￨O￨- features￨L￨NNS￨O￨A could￨L￨MD￨O￨- be￨L￨VB￨O￨- looked￨L￨VBN￨O￨- at￨L￨IN￨O￨- is￨L￨VBZ￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- linkages￨L￨NNS￨O￨- among￨L￨IN￨O￨- macroecological￨L￨JJ￨O￨- ‘￨L￨``￨O￨- laws￨L￨NNS￨O￨- ’￨L￨''￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- scaling￨L￨VBG￨O￨- theory￨L￨NN￨O￨- offers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- powerful￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- way￨L￨NN￨O￨- for￨L￨IN￨O￨- coherent￨L￨JJ￨O￨- ,￨L￨,￨O￨- unified￨L￨JJ￨O￨- descriptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- species￨L￨NNS￨O￨- ’￨L￨POS￨O￨- numbers￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- abundance￨L￨NN￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- remarkable￨L￨JJ￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- some￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- features￨L￨NNS￨O￨A ,￨L￨,￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- ’￨L￨POS￨O￨- persistence￨L￨NN￨O￨- times￨L￨NNS￨O￨- at￨L￨IN￨O￨- observation￨L￨NN￨O￨- sites￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- controlled￨L￨VBN￨O￨- more￨L￨RBR￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- landscape￨L￨NN￨O￨- where￨L￨WRB￨O￨- interactions￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- than￨L￨IN￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- features￨L￨NNS￨O￨- specific￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- ecosystem￨L￨NN￨O￨- .￨L￨.￨O￨- +River￨U￨NNP￨TITLE￨- networks￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- also￨L￨RB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- meta-ecosystems￨L￨NNS￨O￨- that￨L￨WDT￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- metabolism￨L￨NN￨O￨- of￨L￨IN￨O￨- terrestrial￨L￨JJ￨O￨- organic￨L￨JJ￨O￨- carbon￨L￨NN￨O￨- in￨L￨IN￨O￨- freshwater￨L￨NN￨O￨- ecosystems￨L￨NNS￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- carbon￨L￨NN￨O￨- cycle￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- nutrients￨L￨NNS￨O￨- removed￨L￨VBN￨O￨- from￨L￨IN￨O￨- streams￨L￨NNS￨O￨- and￨L￨CC￨O￨- reservoirs￨L￨NNS￨O￨- ,￨L￨,￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- stream￨L￨NN￨O￨- ecology￨L￨NN￨O￨A therein￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- ecohydrological￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- river￨L￨NN￨TITLE￨- network￨L￨NN￨O￨A structures￨L￨NNS￨O￨A and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- embedded￨L￨JJ￨O￨- hydrologic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- play￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- are￨L￨VBP￨O￨- strong￨L￨JJ￨O￨- ,￨L￨,￨O￨- chance￨L￨NN￨O￨- may￨L￨MD￨O￨- allow￨L￨VB￨O￨- some￨L￨DT￨O￨- virus￨L￨NN￨O￨- strains￨L￨NNS￨O￨- to￨L￨TO￨O￨- replicate￨L￨VB￨O￨- and￨L￨CC￨O￨- survive￨L￨VB￨O￨- while￨L￨IN￨O￨- others￨L￨NNS￨O￨- go￨L￨VBP￨O￨- extinct￨L￨JJ￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- drift￨L￨NN￨O￨A that￨L￨IN￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- "￨L￨``￨O￨- replicative￨L￨JJ￨O￨- drift￨L￨NN￨O￨- .￨L￨.￨O￨- "￨L￨''￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- generated￨L￨VBD￨O￨- quantitative￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- hypotheses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- HPAIVs￨U￨NNS￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨A hosts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- unlikely￨L￨JJ￨O￨- owing￨L￨NN￨O￨- to￨L￨TO￨O￨- unobserved￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- suppress￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- highly￨L￨RB￨O￨- pathogenic￨L￨JJ￨O￨- phenotypes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- testing￨L￨VBG￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- that￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- bird￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- HPAIV￨U￨NN￨O￨- poultry￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- self‐sustaining￨L￨VBG￨O￨- and￨L￨CC￨O￨- require￨L￨VB￨O￨- viral￨L￨JJ￨O￨- input￨L￨NN￨O￨- from￨L￨IN￨O￨- wild￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- by￨L￨IN￨O￨- testing￨L￨VBG￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- that￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- bird￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- reassortment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fully￨L￨RB￨O￨- Eurasian￨U￨JJ￨MISC￨- H5N8￨U￨NN￨O￨- with￨L￨IN￨O￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- LPAIVs￨U￨NNS￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- the￨L￨DT￨O￨- EA/NA￨U￨NN￨O￨- H5N2￨U￨NN￨O￨- provided￨L￨VBD￨O￨- a￨L￨DT￨O￨- fitness￨L￨NN￨O￨- advantage￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- reassortant￨L￨NN￨O￨- AIV￨U￨NN￨O￨- by￨L￨IN￨O￨- testing￨L￨VBG￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- that￨L￨WDT￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- EA/NA￨U￨NN￨O￨- H5N2￨U￨NN￨O￨- >￨L￨JJR￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- EA￨U￨NN￨ORGANIZATION￨- H5N8￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- wild￨L￨JJ￨O￨- bird￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- isolates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- tips￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨- tree￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- annotated￨L￨JJ￨O￨- with￨L￨IN￨O￨- strain￨L￨NN￨O￨- name￨L￨NN￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- IRD￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- sample￨L￨NN￨O￨- collection￨L￨NN￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- type￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- wild￨L￨JJ￨O￨A bird￨L￨NN￨O￨- or￨L￨CC￨O￨- poultry/domestic￨L￨JJ￨O￨- bird￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- state￨L￨NN￨O￨- or￨L￨CC￨O￨- province￨L￨NN￨O￨- of￨L￨IN￨O￨- collection￨L￨NN￨O￨- ,￨L￨,￨O￨- viral￨L￨JJ￨O￨- subtype￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- HA￨U￨NNP￨O￨- and￨L￨CC￨O￨- Neuraminidase￨U￨NNP￨MISC￨- [￨L￨-LRB-￨O￨- N￨U￨NNP￨O￨- ]￨L￨-RRB-￨O￨- combination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sequence￨L￨NN￨O￨- accession￨L￨NN￨O￨- identifier￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- modeled￨L￨VBD￨O￨- the￨L￨DT￨O￨- phylodynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- clade￨L￨NN￨O￨- 2.3.4.4￨L￨CD￨NUMBER￨- HA￨U￨NNP￨O￨- ,￨L￨,￨O￨- PB2￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- M￨U￨NN￨O￨- segments￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- multitype￨L￨JJ￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- time‐rooted￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨A tree￨L￨NN￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- inference￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- segment￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- viral￨L￨JJ￨O￨- migration￨L￨NN￨O￨- between￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- types￨L￨NNS￨O￨- using￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- nested￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- analysis￨L￨NN￨O￨- used￨L￨VBD￨O￨- all￨L￨DT￨O￨- isolated￨L￨VBN￨O￨- sequences￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- HA￨U￨NNP￨O￨- ,￨L￨,￨O￨- PB2￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- M￨U￨NN￨O￨- segments￨L￨NNS￨O￨- ,￨L￨,￨O￨- separately￨L￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- among￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- types￨L￨NNS￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- wild￨L￨JJ￨O￨A bird￨L￨NN￨O￨- or￨L￨CC￨O￨- poultry/domestic￨L￨JJ￨O￨- bird￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- once￨L￨RB￨DATE￨- sampled￨L￨VBN￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- virus￨L￨NN￨O￨- was￨L￨VBD￨O￨- removed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- because￨L￨IN￨O￨- wild￨L￨JJ￨O￨A bird￨L￨NN￨O￨- sampling￨L￨NN￨O￨- was￨L￨VBD￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- mortality￨L￨NN￨O￨- event￨L￨NN￨O￨- or￨L￨CC￨O￨- hunter￨L￨NN￨TITLE￨- harvest￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- operations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- biosecurity￨L￨NN￨O￨- and￨L￨CC￨O￨- depopulation￨L￨NN￨O￨- once￨L￨RB￨DATE￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- detected￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- isolate￨L￨NN￨O￨- was￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨A the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- meningitis￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- nine￨L￨CD￨NUMBER￨- African￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- by￨L￨IN￨O￨- adopting￨L￨VBG￨O￨- some￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- wavelet￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- studies￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- “￨L￨``￨O￨- international￨L￨JJ￨O￨- cooperation￨L￨NN￨O￨- in￨L￨IN￨O￨- Public￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- and￨L￨CC￨O￨- cross￨L￨VB￨O￨- disciplines￨L￨NNS￨O￨- studies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- recommended￨L￨VBN￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- this￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- ”￨L￨''￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- meningitis￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- cellular￨L￨JJ￨O￨- automata￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- was￨L￨VBD￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- five￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- asymptomatic￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- with￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨A ,￨L￨,￨O￨- carriers￨L￨NNS￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- died￨L￨VBD￨O￨- classes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- meningitis￨L￨NN￨CAUSE_OF_DEATH￨- becomes￨L￨VBZ￨O￨- worse￨L￨JJR￨O￨- when￨L￨WRB￨O￨- symptoms￨L￨NNS￨O￨A are￨L￨VBP￨O￨- not￨L￨RB￨O￨- detected￨L￨VBN￨O￨- early￨L￨RB￨O￨- enough￨L￨RB￨O￨- ;￨L￨:￨O￨- even￨L￨RB￨O￨- with￨L￨IN￨O￨- proper￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- could￨L￨MD￨O￨- die￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Those￨U￨DT￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- people￨L￨NNS￨O￨- tend￨L￨VBP￨O￨- to￨L￨TO￨O￨- mix￨L￨VB￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- assortative￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- intergenerational￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- vary￨L￨VB￨O￨- between￨L￨IN￨O￨- settings￨L￨NNS￨O￨A ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- household￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- others￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Variation￨U￨NN￨O￨- in￨L￨IN￨O￨- Wolbachia￨U￨JJ￨LOCATION￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- Aedes￨U￨NNS￨O￨- mosquitoes￨L￨NNS￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- invasiveness￨L￨NN￨O￨- and￨L￨CC￨O￨- vectorial￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- Jessica￨U￨NNP￨PERSON￨- G.￨U￨NNP￨PERSON￨- Studies￨U￨NNS￨PERSON￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- certain￨L￨JJ￨O￨- Wolbachia￨U￨JJ￨O￨- strains￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- wMel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- reduce￨L￨VB￨O￨- replication￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- laboratory￨L￨NN￨O￨- ,￨L￨,￨O￨- prompting￨L￨VBG￨O￨- the￨L￨DT￨O￨- release￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- carrying￨L￨VBG￨O￨- the￨L￨DT￨O￨- bacterium￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- vectorial￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- realistically￨L￨RB￨O￨- assessed￨L￨VBN￨O￨- in￨L￨IN￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- native￨L￨JJ￨O￨- non-carriers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- applied￨L￨VBD￨O￨- a￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- back-calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨A Chinese￨U￨JJ￨NATIONALITY￨- workers￨L￨NNS￨O￨- in￨L￨IN￨O￨- Angola￨U￨NNP￨COUNTRY￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- 11￨L￨CD￨NUMBER￨- unvaccinated￨L￨JJ￨O￨A Chinese￨U￨JJ￨NATIONALITY￨- workers￨L￨NNS￨O￨- acquired￨L￨VBD￨O￨- yellow￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- more￨L￨JJR￨O￨- Chinese￨U￨JJ￨NATIONALITY￨- workers￨L￨NNS￨O￨- in￨L￨IN￨O￨- Angola￨U￨NNP￨COUNTRY￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- vaccinated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Estimating￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨A Chinese￨U￨JJ￨NATIONALITY￨- workers￨L￨NNS￨O￨- against￨L￨IN￨O￨- yellow￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- AngolaA￨U￨NNP￨O￨- .￨L￨.￨O￨- +Eleven￨U￨CD￨NUMBER￨- unvaccinated￨L￨JJ￨O￨A Chinese￨U￨JJ￨NATIONALITY￨- nationals￨L￨NNS￨O￨- working￨L￨VBG￨O￨- in￨L￨IN￨O￨- Angola￨U￨NNP￨COUNTRY￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- imported￨L￨VBN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- presenting￨L￨VBG￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- importation￨L￨NN￨O￨- of￨L￨IN￨O￨- yellow￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- into￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- models￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- none￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 259,000￨L￨CD￨NUMBER￨- Chinese￨U￨NNP￨NATIONALITY￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- vaccinated￨L￨VBN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- yellow￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- mandated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- International￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- Regulations￨U￨NNPS￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- inequality￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- preventive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- in￨L￨IN￨O￨- rural￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- deforestation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- geographical￨L￨JJ￨O￨A diversity￨L￨NN￨O￨- allow￨L￨VBP￨O￨- the￨L￨DT￨O￨- circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- array￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- in￨L￨IN￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- 30￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 32￨L￨CD￨NUMBER￨- departments￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- program￨L￨NN￨O￨- gathers￨L￨VBZ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨A ,￨L￨,￨O￨- continually￨L￨RB￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ’s￨L￨POS￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- producing￨L￨VBG￨O￨- regional￨L￨JJ￨O￨- indicators￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Closer￨U￨JJR￨O￨- examination￨L￨NN￨O￨- of￨L￨IN￨O￨- TL￨U￨NN￨O￨- behavior￨L￨NN￨O￨- by￨L￨IN￨O￨- geographical￨L￨JJ￨O￨A region￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Amazon￨U￨NNP￨LOCATION￨- region￨L￨NN￨O￨- exhibits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- observed￨L￨VBN￨O￨- periods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Standardized￨U￨JJ￨O￨- Incidence￨U￨NN￨O￨- Ratios￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- calculated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Colombia￨U￨NNP￨COUNTRY￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨A considered￨L￨VBN￨O￨- using￨L￨VBG￨O￨- Empirical￨U￨NNP￨O￨- Bayes￨U￨NNP￨PERSON￨- smoothing￨L￨VBG￨O￨- method￨L￨NN￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- Clayton￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Kaldor￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- efficient￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- computational￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- pairwise￨L￨JJ￨O￨- calculations￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- the￨L￨DT￨O￨- distances￨L￨NNS￨O￨- between￨L￨IN￨O￨- every￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- farms￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- kernel￨L￨NN￨O￨A must￨L￨MD￨O￨- be￨L￨VB￨O￨- evaluated￨L￨VBN￨O￨- for￨L￨IN￨O￨- those￨L￨DT￨O￨- distances￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- estimation￨L￨NN￨O￨- process￨L￨NN￨O￨- formulates￨L￨VBZ￨O￨- an￨L￨DT￨O￨- equation￨L￨NN￨O￨- that￨L￨WDT￨O￨- approximates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expected￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- kernel￨L￨NN￨O￨- evaluations￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- average￨L￨JJ￨O￨- grid￨L￨NN￨O￨A cell￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- expressed￨L￨VBN￨O￨- as￨L￨IN￨O￨- farms￨L￨NNS￨O￨- per￨L￨IN￨O￨- cell￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- subsequently￨L￨RB￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- θ￨L￨NN￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- fewest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- kernel￨L￨NN￨O￨- calls￨L￨NNS￨O￨- are￨L￨VBP￨O￨- predicted￨L￨VBN￨O￨- .￨L￨.￨O￨- +Keeling￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Rohani￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- introduced￨L￨VBD￨O￨- another￨L￨DT￨O￨- technique￨L￨NN￨O￨- ,￨L￨,￨O￨- hereafter￨L￨RB￨O￨- denoted￨L￨VBN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- entry￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- pattern￨L￨NN￨O￨- landscape￨L￨NN￨O￨- of￨L￨IN￨O￨- farm￨L￨NN￨O￨- locations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- overlaid￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- grid￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- split￨L￨VBN￨O￨- up￨L￨RB￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- steps￨L￨NNS￨O￨- :￨L￨:￨O￨- Does￨U￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- possibly￨L￨RB￨O￨- enter￨L￨VB￨O￨- the￨L￨DT￨O￨- grid￨L￨NN￨O￨- cell￨L￨NN￨O￨- ?￨L￨.￨O￨- +From￨U￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- farm￨L￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- red￨L￨JJ￨O￨- star￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- cell￨L￨NN￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- evaluated￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- entire￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- grid￨L￨NN￨O￨A cells￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- occasionally￨L￨RB￨O￨- evaluated￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- green￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Secondly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- grid￨L￨NN￨O￨A size￨L￨NN￨O￨- estimation￨L￨NN￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- determining￨L￨VBG￨O￨- a￨L￨DT￨O￨- grid￨L￨NN￨O￨- size￨L￨NN￨O￨- configuration￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- subsample￨L￨NN￨O￨- and￨L￨CC￨O￨- conditional￨L￨JJ￨O￨- entry￨L￨NN￨O￨- algorithms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- ensures￨L￨VBZ￨O￨- fast￨L￨JJ￨O￨- computation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- its￨L￨PRP$￨O￨- performance￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- conclusions￨L￨NNS￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- implications￨L￨NNS￨O￨- drawn￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- many￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- depicting￨L￨VBG￨O￨- nosocomial￨L￨JJ￨O￨- MRSA￨U￨NNP￨O￨- transmission￨L￨NN￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- settings￨L￨NNS￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- mitigate￨L￨VB￨O￨- such￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- first￨L￨RB￨ORDINAL￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- delineate￨L￨VB￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sylvatic￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨A vectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- CHIKV￨U￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- shape￨L￨VBP￨O￨- these￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- association￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- presence￨L￨NN￨O￨- with￨L￨IN￨O￨- key￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- spillover￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- mosquito￨L￨NN￨O￨- and￨L￨CC￨O￨- CHIKV￨U￨NN￨O￨- abundance￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Ecological￨U￨NNP￨MISC￨- niche￨L￨NN￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- Aedes￨U￨NNP￨O￨- mosquito￨L￨NN￨O￨A vectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- southeastern￨L￨JJ￨O￨- SenegalRebecca￨U￨NN￨O￨- Richman1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Diawo￨U￨NNP￨O￨- Diallo3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Mawlouth￨U￨NNP￨O￨- Diallo3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Amadou￨U￨NNP￨PERSON￨- A.￨U￨NNP￨O￨- 2018Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Chikungunya￨U￨NNP￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- originated￨L￨VBD￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- sylvatic￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- non-human￨L￨JJ￨O￨- animal￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- mosquitoes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- forests￨L￨NNS￨O￨- of￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- therefore￨L￨RB￨O￨- modeled￨L￨VBD￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- CHIKV￨U￨NN￨O￨- mosquito￨L￨NN￨O￨A vectors￨L￨NNS￨O￨- over￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- sequential￨L￨JJ￨O￨- rainy￨L￨JJ￨O￨- seasons￨L￨NNS￨O￨- in￨L￨IN￨O￨- Kédougou￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Senegal￨U￨NNP￨COUNTRY￨- using￨L￨VBG￨O￨- Maxent￨U￨NNP￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Mosquito￨U￨NNP￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- in￨L￨IN￨O￨- fifty￨L￨CD￨NUMBER￨- sites￨L￨NNS￨O￨- distributed￨L￨VBN￨O￨- in￨L￨IN￨O￨- five￨L￨CD￨NUMBER￨- land￨L￨NN￨O￨A cover￨L￨NN￨O￨- classes￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- area￨L￨NN￨O￨- .￨L￨.￨O￨- +Genetic￨U￨JJ￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- pairs￨L￨NNS￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- sequence￨L￨NN￨O￨- databases￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- and￨L￨CC￨O￨- scalable￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- characterizing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- unreliable￨L￨JJ￨O￨- proxy￨L￨NN￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- inferences￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- clusters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- biased￨L￨VBN￨O￨- by￨L￨IN￨O￨- correlations￨L￨NNS￨O￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- sampling￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +HIV￨U￨NN￨CAUSE_OF_DEATH￨- genetic￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- routine￨L￨JJ￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- testing￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- few￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- widely￨L￨RB￨O￨- available￨L￨JJ￨O￨- observational￨L￨JJ￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- directly￨L￨RB￨O￨- informative￨L￨JJ￨O￨- about￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- See￨U￨VB￨O￨- the￨L￨DT￨O￨- The￨U￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PHIs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- com￨L￨NN￨O￨- bat￨L￨NN￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- pre-exposure￨L￨JJ￨O￨- prophylaxis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PrEP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- antiretroviral￨L￨JJ￨O￨- medications￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ARVs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- unknown￨L￨JJ￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- longer￨L￨JJR￨O￨- evolutionary￨L￨JJ￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- populations￨L￨NNS￨O￨- or￨L￨CC￨O￨- risk￨L￨NN￨O￨A groups￨L￨NNS￨O￨- with￨L￨IN￨O￨- higher￨L￨JJR￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- will￨L￨MD￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- paraphyletic￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- with￨L￨IN￨O￨- populations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- primarily￨L￨RB￨O￨- recipients￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨A is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- variable￨L￨JJ￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- between￨L￨IN￨O￨- risk￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- geographically￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Simulating￨U￨VBG￨O￨- SIR￨U￨NN￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- weighted￨L￨JJ￨O￨- shortest￨L￨JJS￨O￨A paths￨L￨NNS￨O￨- Dijana￨U￨NNP￨PERSON￨- Tolić1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Kaj-Kolja￨U￨NNP￨O￨- Kleineberg2￨U￨NNP￨O￨- &￨L￨CC￨O￨- Nino￨U￨NNP￨O￨- Antulov-Fantulin2￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 6562￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- science￨L￨NN￨O￨- AbstractWe￨U￨NN￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- SIR￨U￨NN￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- weighted￨L￨JJ￨O￨- shortest￨L￨JJS￨O￨- paths￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- different￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- neglecting￨L￨VBG￨O￨- dynamical￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- statistical￨L￨JJ￨O￨- independence￨L￨NN￨O￨- at￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- neighbourhood￨L￨NN￨O￨- ,￨L￨,￨O￨- pair￨L￨NN￨O￨- or￨L￨CC￨O￨- node￨L￨NN￨O￨- level￨L￨NN￨O￨- in￨L￨IN￨O￨- mean￨L￨JJ￨O￨- field￨L￨NN￨O￨- approximations11￨L￨NN￨O￨- ,12,13,14,15,16￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- neglecting￨L￨VBG￨O￨- loops￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- with￨L￨IN￨O￨- message￨L￨NN￨O￨- passing￨L￨NN￨O￨- or￨L￨CC￨O￨- belief￨L￨NN￨O￨- propagation￨L￨NN￨O￨A techniques17￨L￨NN￨O￨- ,18,19￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- neglecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- by￨L￨IN￨O￨- mapping￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- process20￨L￨NN￨O￨- ,21,22￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- run￨L￨NN￨O￨- using￨L￨VBG￨O￨- popular￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨- inference￨L￨NN￨O￨- tools￨L￨NNS￨O￨- like￨L￨IN￨O￨- MrBayes￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- BEAST￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- take￨L￨VB￨O￨- days￨L￨NNS￨DURATION￨- or￨L￨CC￨O￨- weeks￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- CPU￨U￨NNP￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- approximate￨L￨JJ￨O￨- a￨L￨DT￨O￨- posterior￨L￨JJ￨O￨A distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- update￨L￨VB￨O￨- a￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨A tree￨L￨NN￨O￨- with￨L￨IN￨O￨- new￨L￨JJ￨O￨- sequences￨L￨NNS￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- such￨L￨JJ￨O￨- tool￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- for￨L￨IN￨O￨- Bayesian￨U￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨- inference￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- each￨L￨DT￨O￨- generation￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- particles￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- a￨L￨DT￨O￨- posterior￨L￨JJ￨O￨A sample￨L￨NN￨O￨- of￨L￨IN￨O￨- trees￨L￨NNS￨O￨- on￨L￨IN￨O￨- sequences￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- updated￨L￨VBN￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- sample￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- posterior￨L￨NN￨O￨- on￨L￨IN￨O￨- sequences￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- Bayesian￨U￨JJ￨MISC￨- inference￨L￨NN￨O￨- treat￨L￨VB￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- set￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨- entity￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- entirety￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- that￨L￨WDT￨O￨- computation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨A probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- begins￨L￨VBZ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- particle￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- taxon￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- attached￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- tree￨L￨NN￨O￨- using￨L￨VBG￨O￨- proposal￨L￨NN￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- weight￨L￨NN￨O￨- is￨L￨VBZ￨O￨- computed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- particles￨L￨NNS￨O￨A are￨L￨VBP￨O￨- resampled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- weights￨L￨NNS￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- supplementary￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- targeting￨L￨VBG￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- adult￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- deemed￨L￨VBN￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨A immunity￨L￨NN￨O￨A and￨L￨CC￨O￨- avoid￨L￨VB￨O￨- another￨L￨DT￨O￨- major￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- that￨L￨DT￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- probabilistically￨L￨RB￨O￨- decline￨L￨VB￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- burden￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- sufficiently￨L￨RB￨O￨- elevating￨L￨VBG￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- level￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- recognized￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- essential￨L￨JJ￨O￨- step￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- rubella￨L￨NN￨O￨A and￨L￨CC￨O￨- CRS￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- medically￨L￨RB￨O￨- and￨L￨CC￨O￨- economically￨L￨RB￨O￨- justify￨L￨VB￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- pitfall￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- against￨L￨IN￨O￨- rubella￨L￨NN￨O￨A is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- sufficiently￨L￨RB￨O￨- immunized￨L￨VBN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- push￨L￨NN￨O￨- forward￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- at￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- cover￨L￨VB￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- status￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- enough￨L￨JJ￨O￨- doses￨L￨NNS￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- herd￨L￨NN￨O￨A immunity￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- practice￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- to￨L￨TO￨O￨- randomly￨L￨RB￨O￨- distribute￨L￨VB￨O￨- as￨L￨RB￨O￨- many￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- rubella￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- elevated￨L￨JJ￨O￨- to￨L￨TO￨O￨- women￨L￨NNS￨O￨- at￨L￨IN￨O￨- childbearing￨L￨JJ￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- insufficient￨L￨JJ￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- can￨L￨MD￨O￨- controversially￨L￨RB￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- fetus￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Applying￨U￨VBG￨O￨- MUOD￨U￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- roughly￨L￨RB￨O￨- 400￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- Google￨U￨NNP￨ORGANIZATION￨- +￨L￨CC￨O￨- users￨L￨NNS￨O￨A ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- allowed￨L￨VBN￨O￨- identifying￨L￨VBG￨O￨- and￨L￨CC￨O￨- discriminating￨L￨VBG￨O￨- automatically￨L￨RB￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- outlier￨L￨NN￨O￨- users￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- present￨L￨JJ￨DATE￨- features￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- definitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨- users￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- capacity￨L￨NN￨O￨- to￨L￨TO￨O￨- attract￨L￨VB￨O￨- engagement￨L￨NN￨O￨- ,￨L￨,￨O￨- capacity￨L￨NN￨O￨- to￨L￨TO￨O￨- attract￨L￨VB￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- followers￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- high￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- capacity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- report￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- unsupervised￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- Massive￨U￨JJ￨O￨- Unsupervised￨U￨JJ￨O￨- Outlier￨U￨NNP￨O￨- Detection￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- MUOD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- outliers￨L￨NNS￨O￨- detection￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- providing￨L￨VBG￨O￨- support￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨- users￨L￨NNS￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- allows￨L￨VBZ￨O￨- classifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- outlier￨L￨NN￨O￨- users￨L￨NNS￨O￨A in￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- different￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨- users￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 03￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Unsupervised￨U￨NNP￨O￨- Scalable￨U￨NNP￨O￨- Statistical￨U￨NNP￨O￨- Method￨U￨NNP￨O￨- for￨L￨IN￨O￨- Identifying￨U￨NNP￨O￨- Influential￨U￨NNP￨O￨- Users￨U￨NNP￨O￨- in￨L￨IN￨O￨- Online￨U￨NNP￨O￨- Social￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- A.￨U￨NNP￨O￨- Sguera5￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 6955￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComputational￨L￨NNP￨O￨- scienceComputer￨L￨NN￨O￨- scienceStatistics￨L￨NNS￨O￨- AbstractBillions￨U￨NNS￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨A interact￨L￨VBP￨O￨- intensively￨L￨RB￨O￨- every￨L￨DT￨SET￨- day￨L￨NN￨SET￨- via￨L￨IN￨O￨- Online￨U￨NNP￨O￨- Social￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- OSNs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Facebook￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Twitter￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- Google￨U￨NNP￨ORGANIZATION￨- +￨L￨CC￨O￨- .￨L￨.￨O￨- +Consider￨U￨VB￨O￨- a￨L￨DT￨O￨- physical￨L￨JJ￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- exactly￨L￨RB￨O￨- N￨U￨NN￨O￨- possible￨L￨JJ￨O￨- configurations￨L￨NNS￨O￨- and￨L￨CC￨O￨- let￨L￨VB￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- configuration￨L￨NN￨O￨A i￨L￨FW￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t.￨L￨NN￨O￨- To￨U￨TO￨O￨- formulate￨L￨VB￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- know￨L￨VB￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- transition￨L￨NN￨O￨- p￨L￨NN￨O￨- from￨L￨IN￨O￨- configuration￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- configuration￨L￨NN￨O￨- j.￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- monographs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- details￨L￨NNS￨O￨- .￨L￨.￨O￨- )￨L￨-RRB-￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- treat￨L￨VBP￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- p￨L￨NN￨O￨- may￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t.￨L￨NN￨O￨- Note￨U￨VBP￨O￨- that￨L￨IN￨O￨- even￨L￨RB￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- master￨L￨NN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- linear￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- interest￨L￨NN￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- intimately￨L￨RB￨O￨- connected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- Markov￨U￨NNP￨PERSON￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- finite￨L￨JJ￨O￨- configuration￨L￨NN￨O￨A spaces￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- uniquely￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- configurations￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- transition￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- probabilities￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- configuration￨L￨NN￨O￨A i￨L￨FW￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- given￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- configuration￨L￨NN￨O￨- j￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- τ￨L￨NN￨O￨- <￨L￨JJR￨O￨- t.￨L￨CD￨NUMBER￨- +These￨U￨DT￨O￨- different￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- applications￨L￨NNS￨O￨- are￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- lattice￨L￨NN￨O￨- structure￨L￨NN￨O￨- as￨L￨IN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- ties￨L￨NNS￨O￨A are￨L￨VBP￨O￨- regular￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- exhaustively￨L￨RB￨O￨- complete￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- maximally￨L￨RB￨O￨- complete￨L￨JJ￨O￨- structure￨L￨NN￨O￨- as￨L￨IN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- idealized￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- free￨L￨JJ￨IDEOLOGY￨- association￨L￨NN￨IDEOLOGY￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- connect￨L￨VB￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- other￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Erdõs-Rényi￨U￨NN￨O￨- generation￨L￨NN￨O￨- structure￨L￨NN￨O￨- with￨L￨IN￨O￨- every￨L￨DT￨O￨- possible￨L￨JJ￨O￨- tie￨L￨NN￨O￨- existing￨L￨VBG￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- 0.25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ties￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- graph￨L￨NN￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨DURATION￨- quarter￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- panel￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- empirically￨L￨RB￨O￨- observed￨L￨VBN￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- primates￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- Pan￨U￨NN￨O￨- troglodytes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Instead￨U￨RB￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- basic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- fitting￨L￨JJ￨O￨- network￨L￨NN￨O￨- arrangement￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- ideal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- maximally￨L￨RB￨O￨- complete￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- uniform￨L￨JJ￨O￨- ties￨L￨NNS￨O￨A to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- effectively￨L￨RB￨O￨- free￨L￨JJ￨IDEOLOGY￨- association￨L￨NN￨IDEOLOGY￨- among￨L￨IN￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- shown￨L￨VBN￨O￨- through￨L￨IN￨O￨- early￨L￨JJ￨O￨- critiques￨L￨NNS￨O￨- of￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- recently￨L￨RB￨DATE￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- resurgence￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- interactions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- random￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- instead￨L￨RB￨O￨- structured￨L￨VBN￨O￨- along￨L￨IN￨O￨- social￨L￨JJ￨O￨- ties￨L￨NNS￨O￨A between￨L￨IN￨O￨- specific￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- affiliative￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- mating￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- social￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Effective￨U￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- models￨L￨NNS￨O￨- take￨L￨VBP￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- and￨L￨CC￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- idealized￨L￨JJ￨O￨- population￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- Fisher￨U￨NNP￨PERSON￨- –￨L￨:￨O￨- Wright￨U￨NNP￨PERSON￨- populations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- groups￨L￨NNS￨O￨- are￨L￨VBP￨O￨- of￨L￨IN￨O￨- finite￨L￨JJ￨O￨- and￨L￨CC￨O￨- fixed￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨A ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- mate￨L￨VBP￨O￨- randomly￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- generations￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- overlap￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- specific￨L￨JJ￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨A and￨L￨CC￨O￨- outbreak￨L￨NN￨O￨- durations￨L￨NNS￨O￨- for￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- per￨L￨FW￨O￨- contact￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Clearly￨U￨RB￨O￨- ,￨L￨,￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- remains￨L￨VBZ￨O￨- within￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- starts￨L￨VBZ￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- interval.The￨L￨NN￨O￨- asymptotic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondarily￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Equality￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- gamma￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- beta￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- characterized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- if￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- le￨L￨DT￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- Equality￨U￨NN￨O￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- X￨U￨NN￨O￨- fulfilling￨L￨VBG￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- measurable￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- sigma￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- term￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- X￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- left￨L￨VBD￨O￨- Add￨U￨VB￨O￨- N￨U￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- right￨L￨NN￨O￨- X￨U￨NN￨O￨- beta￨L￨NN￨O￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- fulfil￨L￨VB￨O￨- some￨L￨DT￨O￨- technical￨L￨JJ￨O￨- condition￨L￨NN￨O￨A like￨L￨IN￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- Lipschitz￨U￨NNP￨PERSON￨- condition￨L￨NN￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- growth￨L￨NN￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- derived￨L￨VBN￨O￨- properties￨L￨NNS￨O￨- for￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- decision￨L￨NN￨O￨A problem￨L￨NN￨O￨- of￨L￨IN￨O￨- choosing￨L￨VBG￨O￨- the￨L￨DT￨O￨- cost-optimal￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- intensity.KeywordsContagion￨L￨NN￨O￨- Asymptotic￨U￨JJ￨O￨- properties￨L￨NNS￨O￨- Markov￨U￨NNP￨PERSON￨- processes￨L￨VBZ￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- This￨U￨DT￨O￨- research￨L￨NN￨O￨- was￨L￨VBD￨O￨- funded￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Austrian￨U￨JJ￨NATIONALITY￨- Science￨U￨NNP￨MISC￨- Fund￨U￨NNP￨MISC￨- FWF￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Project￨U￨NNP￨O￨- P￨U￨NN￨O￨- 24125-N13.1￨L￨NN￨O￨- IntroductionIn￨U￨NN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Basically￨U￨RB￨O￨- a￨L￨DT￨O￨- decision￨L￨NN￨O￨- maker￨L￨NN￨O￨- may￨L￨MD￨O￨- try￨L￨VB￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- paramters￨L￨NNS￨O￨- beta￨L￨NN￨O￨- and￨L￨CC￨O￨- gamma￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- fulfilled￨L￨VBN￨O￨- .1.2￨L￨CD￨NUMBER￨- Diffusion-type￨U￨JJ￨O￨- SIS￨U￨NN￨O￨- modelsWhile￨L￨NN￨O￨- many￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- in￨L￨IN￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- Diekmann￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Note￨U￨VB￨O￨- that￨L￨IN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- N￨U￨NNP￨O￨- Add￨U￨VB￨O￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- Y￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- it￨L￨PRP￨O￨- suffices￨L￨VBZ￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- replacing￨L￨VBG￨O￨- Y￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- Add￨U￨VB￨O￨- N￨U￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- whenever￨L￨WRB￨O￨- necessary￨L￨JJ￨O￨A .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- paradox￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- parameter￨L￨NN￨O￨- spaces￨L￨NNS￨O￨- Hengcong￨U￨JJ￨O￨- Liu1￨U￨NN￨O￨- ,￨L￨,￨O￨- Muhua￨U￨NNP￨PERSON￨- Zheng1￨U￨NNP￨O￨- &￨L￨CC￨O￨- Zonghua￨U￨NNP￨O￨- Liu1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 7517￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- science￨L￨NN￨O￨- AbstractIt￨U￨NN￨O￨- is￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- revealed￨L￨VBN￨O￨- from￨L￨IN￨O￨- amounts￨L￨NNS￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- of￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- loop￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- surprisingly￨L￨RB￨O￨- find￨L￨VBP￨O￨- a￨L￨DT￨O￨- paradox￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- loop￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- rate￨L￨NN￨O￨- increment￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transient￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- contradictory￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- spaces￨L￨NNS￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- long￨L￨RB￨O￨- enough￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- here￨L￨RB￨O￨- study￨L￨VB￨O￨- this￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- directly￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- find￨L￨VB￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- loop￨L￨NN￨O￨A ,￨L￨,￨O￨- implying￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- hysteresis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nature￨L￨NN￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transient￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- loop￨L￨NN￨O￨A will￨L￨MD￨O￨- increase￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- but￨L￨CC￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- .￨L￨.￨O￨- +That￨U￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- rate￨L￨NN￨O￨- increment￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- loop￨L￨NN￨O￨A will￨L￨MD￨O￨- decrease￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- but￨L￨CC￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- reachability￨L￨NN￨O￨- of￨L￨IN￨O￨- contagion￨L￨NN￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨A :￨L￨:￨O￨- how￨L￨WRB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- latency￨L￨NN￨O￨- can￨L￨MD￨O￨- exploit￨L￨VB￨O￨- the￨L￨DT￨O￨- rhythm￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- behaviorEwan￨L￨NN￨O￨- Colman1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Kristen￨U￨NNP￨PERSON￨- Spies1￨U￨NNP￨O￨- and￨L￨CC￨O￨- Shweta￨U￨NNP￨O￨- Bansal1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 18:219￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- symptoms￨L￨NNS￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- influence￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- withdraw￨L￨VB￨O￨- from￨L￨IN￨O￨- social￨L￨JJ￨O￨- activity￨L￨NN￨O￨- limiting￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- that￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- should￨L￨MD￨O￨- consider￨L￨VB￨O￨- contact￨L￨NN￨O￨- periodicity￨L￨NN￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- suggest￨L￨VBP￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- that￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- optimize￨L￨VB￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- synchronization￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- maximum￨L￨NN￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- results￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- synchronized￨L￨VBN￨O￨- with￨L￨IN￨O￨- human￨L￨JJ￨O￨- circadian￨L￨JJ￨O￨- rhythms￨L￨NNS￨O￨- of￨L￨IN￨O￨- 24￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- minimum￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- when￨L￨WRB￨O￨- latent￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- phase￨L￨NN￨O￨- with￨L￨IN￨O￨- circadian￨L￨JJ￨O￨- rhythms￨L￨NNS￨O￨- by￨L￨IN￨O￨- 12￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨A that￨L￨WDT￨O￨- incorporate￨L￨VBP￨O￨- behavioral￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- effectively￨L￨RB￨O￨- shorten￨L￨VB￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +Initial￨U￨JJ￨O￨- analyses￨L￨NNS￨O￨- and￨L￨CC￨O￨- forecasts￨L￨NNS￨O￨- were￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- January￨U￨NNP￨DATE￨- 23￨L￨CD￨DATE￨- to￨L￨TO￨O￨- March￨U￨NNP￨DATE￨- 29￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2015￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- week￨L￨NN￨DURATION￨A 13￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- year￨L￨NN￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- term￨L￨VBP￨O￨- the￨L￨DT￨DATE￨- Week￨U￨NN￨DATE￨- 13￨L￨CD￨NUMBER￨- report￨L￨NN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- forecasts￨L￨NNS￨O￨- was￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- through￨L￨IN￨O￨- April￨U￨NNP￨DATE￨- 26￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2015￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- week￨L￨NN￨DURATION￨- 17￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- termed￨L￨VBN￨O￨- the￨L￨DT￨DATE￨- Week￨U￨NN￨DATE￨- 17￨L￨CD￨NUMBER￨- report￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aims￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- analysis￨L￨NN￨O￨- were￨L￨VBD￨O￨- 2-fold￨L￨JJ￨O￨- :￨L￨:￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A susceptibility￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- expected￨L￨JJ￨O￨- future￨L￨JJ￨DATE￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Lola￨U￨NNP￨CITY￨- prefecture￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- color￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- subprefecture￨L￨NN￨O￨- coincides￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- up￨L￨IN￨DURATION￨- to￨L￨TO￨DURATION￨- week￨L￨NN￨DURATION￨A 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Comparing￨U￨VBG￨O￨- TOL￨U￨NN￨O￨- to￨L￨TO￨O￨- conventional￨L￨JJ￨O￨- treatment￨L￨NN￨O￨A ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- load￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ROL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- ,￨L￨,￨O￨- acute￨L￨JJ￨O￨- and￨L￨CC￨O￨- chronic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- ROL￨U￨NN￨O￨- always￨L￨RB￨O￨- outperforms￨L￨VBZ￨O￨- TOL￨U￨NN￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- that￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- resistance￨L￨NN￨O￨- can￨L￨MD￨O￨- emerge￨L￨VB￨O￨- against￨L￨IN￨O￨- ROL￨U￨NNP￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- chronic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-induced￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- increases￨L￨NNS￨O￨- for￨L￨IN￨O￨- low￨L￨JJ￨O￨- treatment￨L￨NN￨O￨A coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- carriers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- TOL￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- effective￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- even￨L￨RB￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- resistance￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- run￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- problematic￨L￨JJ￨O￨- epidemiologically￨L￨RB￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- the￨L￨DT￨O￨- zoonotic￨L￨JJ￨O￨- parasites￨L￨NNS￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- modes￨L￨NNS￨O￨- ,￨L￨,￨O￨- Trypanosoma￨U￨NNP￨PERSON￨- cruzi￨L￨NNP￨O￨- (￨L￨-LRB-￨O￨- Kinetoplastida￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- Trypanosomatidae￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- protozoan￨L￨NN￨O￨- parasite￨L￨NN￨O￨A which￨L￨WDT￨O￨- causes￨L￨VBZ￨O￨- Chagas￨U￨NNP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- ecology￨L￨NN￨O￨- that￨L￨WDT￨O￨- challenges￨L￨VBZ￨O￨- transmission￨L￨NN￨O￨- modelling￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- zoonotic￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- multi-host￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- or￨L￨CC￨O￨- parasites￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- various￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- may￨L￨MD￨O￨- differ￨L￨VB￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- contribution￨L￨NN￨O￨- to￨L￨TO￨O￨- parasite￨L￨NN￨O￨A transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- over￨L￨IN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- ecology￨L￨NN￨O￨- of￨L￨IN￨O￨- multi-host￨L￨JJ￨O￨- parasite￨L￨NN￨O￨A spread￨L￨VBN￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- potential￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- by￨L￨IN￨O￨- developing￨L￨VBG￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- ecomultiplex￨L￨NN￨O￨- ’￨L￨''￨O￨- framework￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- short￨L￨JJ￨O￨- for￨L￨IN￨O￨- ecological￨L￨JJ￨O￨- multiplex￨L￨JJ￨O￨- framework￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Secondly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ecomultiplex￨L￨JJ￨O￨- framework￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- metabolic￨L￨JJ￨O￨- theory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- species￨L￨NNS￨O￨- frequencies￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨- parasite￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- contribution￨L￨NN￨O￨- to￨L￨TO￨O￨- parasite￨L￨NN￨O￨A transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- ’￨L￨POS￨O￨- abundance￨L￨NN￨O￨- ,￨L￨,￨O￨- exposure￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- predict￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- antiviral￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- with￨L￨IN￨O￨- properly￨L￨RB￨O￨- timed￨L￨VBN￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- drug￨L￨NN￨O￨A usage￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- chemoprophylaxis￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- ways￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- keep￨L￨VB￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- low￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- a￨L￨DT￨O￨- drug￨L￨NN￨O￨A resistant￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strain￨L￨NN￨O￨- is￨L￨VBZ￨O￨- as￨L￨IN￨O￨- transmissible￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- non-resistant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- fitness￨L￨NN￨O￨- penalty￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- socially￨L￨RB￨O￨- suboptimal￨L￨JJ￨O￨- Nash￨U￨NNP￨PERSON￨- equilibrium￨L￨NN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- where￨L￨WRB￨O￨- both￨L￨DT￨O￨- players￨L￨NNS￨O￨- use￨L￨VBP￨O￨- antiviral￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- socially￨L￨RB￨O￨- optimal￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- actually￨L￨RB￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- players￨L￨NNS￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- previous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- isolation￨L￨NN￨O￨- from￨L￨IN￨O￨- other￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- conditions￨L￨NNS￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- decisions￨L￨NNS￨O￨- about￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- drug￨L￨NN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- can￨L￨MD￨O￨- affect￨L￨VB￨O￨- other￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- calls￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- tools￨L￨NNS￨O￨- like￨L￨IN￨O￨- game￨L￨NN￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- certain￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- make￨L￨VB￨O￨- sense￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- to￨L￨TO￨O￨- cooperate￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Prisoner￨U￨NNP￨O￨- 's￨L￨POS￨O￨- Dilemma￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- by￨L￨IN￨O￨- both￨L￨DT￨O￨- treating￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- level￨L￨NN￨O￨- and￨L￨CC￨O￨- thereby￨L￨RB￨O￨- avoiding￨L￨VBG￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- may￨L￨MD￨O￨- defect￨L￨NN￨O￨- by￨L￨IN￨O￨- adopting￨L￨VBG￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- treatment￨L￨NN￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- drug￨L￨NN￨O￨A resistant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- is￨L￨VBZ￨O￨- created￨L￨VBN￨O￨- and￨L￨CC￨O￨- spread￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- preventative￨L￨JJ￨O￨- measure￨L￨NN￨O￨- against￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- doses￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mumps￨L￨NNS￨O￨- vaccine￨L￨NN￨O￨A ,￨L￨,￨O￨- invented￨L￨VBN￨O￨- by￨L￨IN￨O￨- American￨U￨JJ￨NATIONALITY￨- microbiologist￨L￨NN￨TITLE￨- Maurice￨U￨NNP￨PERSON￨- Hilleman￨U￨NNP￨PERSON￨- at￨L￨IN￨O￨- Merck￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- fluctuate￨L￨VBP￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- seasonal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- incident￨L￨NN￨O￨A rate￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- whooping￨L￨JJ￨O￨- cough￨L￨NN￨O￨- ,￨L￨,￨O￨- polio￨L￨NNP￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- chickenpox￨L￨NN￨O￨- ,￨L￨,￨O￨- mumps￨L￨NNS￨O￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- Bjϕ￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- American￨U￨NNP￨ORGANIZATION￨- Academy￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Pediatrics￨U￨NNP￨ORGANIZATION￨- recommends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- routine￨L￨JJ￨O￨- administration￨L￨NN￨O￨- of￨L￨IN￨O￨- MMR￨U￨NN￨ORGANIZATION￨- vaccine￨L￨NN￨O￨- at￨L￨IN￨O￨- ages￨L￨NNS￨O￨A 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 40￨L￨CD￨PERCENT￨- percent￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- persons￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- mumps￨L￨NNS￨O￨- virus￨L￨NN￨O￨A do￨L￨VBP￨O￨- not￨L￨RB￨O￨- show￨L￨VB￨O￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- and￨L￨CC￨O￨- spread￨L￨VBN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- without￨L￨IN￨O￨- knowing￨L￨VBG￨O￨- it￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Mumps￨U￨NNP￨O￨- vaccination￨L￨NN￨O￨A is￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- universally￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- developed￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- nowadays￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- investigates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- absolute￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A and￨L￨CC￨O￨- inhomogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- improve￨L￨VB￨O￨- our￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- :￨L￨:￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- now-casting￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- predict￨L￨VBP￨O￨- future￨L￨JJ￨DATE￨- incidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- forecasting￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- contains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- materials￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- analysis￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- and￨L￨CC￨O￨- absolute￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- “￨L￨``￨O￨- transmission￨L￨NN￨O￨- ”￨L￨''￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- how￨L￨WRB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- alternatives￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- observation￨L￨NN￨O￨- ”￨L￨''￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- connects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- notifications￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- Bayesian￨U￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- more￨L￨RBR￨O￨- generally￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- selecting￨L￨VBG￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- predictive￨L￨JJ￨O￨A skill￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- by￨L￨IN￨O￨- “￨L￨``￨O￨- predictive￨L￨JJ￨O￨- skill￨L￨NN￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- future￨L￨JJ￨DATE￨- ”￨L￨''￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- forecast￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- conditional￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- already￨L￨RB￨O￨- observed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Building￨U￨NN￨O￨- on￨L￨IN￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- with￨L￨IN￨O￨- mechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨- filter￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- lab-confirmed￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- observed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Victorian￨U￨JJ￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Human￨U￨NNP￨ORGANIZATION￨- Services￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Australia￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- which￨L￨WDT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- now-casting￨L￨JJ￨O￨- and￨L￨CC￨O￨- forecasting￨L￨NN￨O￨A .￨L￨.￨O￨- +An￨U￨DT￨O￨- alternative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- restrain￨L￨VB￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- inhomogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨A of￨L￨IN￨O￨- real￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- divide￨L￨VBP￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- presented￨L￨VBD￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- broad￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- static￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨A network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ”￨L￨''￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- vector-borne￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mass-action￨L￨NN￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- network￨L￨NN￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- dynamic￨L￨JJ￨O￨- partnership￨L￨NN￨O￨- changes￨L￨NNS￨O￨- preferential￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- begin￨L￨VBP￨O￨- by￨L￨IN￨O￨- revisiting￨L￨VBG￨O￨- existing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- mass-action￨L￨NN￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨- network￨L￨NN￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- another￨L￨DT￨O￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- .￨L￨.￨O￨- +Unfortunately￨U￨RB￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- existing￨L￨VBG￨O￨A mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- through￨L￨IN￨O￨- networks￨L￨NNS￨O￨- require￨L￨VBP￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- expand￨L￨VBP￨O￨- on￨L￨IN￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- with￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- advances￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- incorporate￨L￨VBP￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- suite￨L￨NN￨O￨- of￨L￨IN￨O￨- empirically-derived￨L￨JJ￨O￨- ,￨L￨,￨O￨- unimodal￨L￨JJ￨O￨- thermal￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- known￨L￨VBN￨O￨- transmission-relevant￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- traits￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- temperature￨L￨NN￨O￨A mean￨L￨NN￨O￨- and￨L￨CC￨O￨- variation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- constant￨L￨JJ￨O￨- temperatures￨L￨NNS￨O￨- or￨L￨CC￨O￨- daily￨L￨JJ￨SET￨- temperature￨L￨NN￨O￨- variation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- regimes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiologically-relevant￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- peak￨L￨NN￨O￨- incidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- vectorial￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- directly￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- field-relevant￨L￨JJ￨O￨- temperature￨L￨NN￨O￨A regimes￨L￨NNS￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- across￨L￨IN￨O￨- temperature￨L￨NN￨O￨- means￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 38￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- ranges￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- predicted￨L￨VBN￨O￨- suitable￨L￨JJ￨O￨- range￨L￨NN￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- included￨L￨VBD￨O￨- seasonal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- temperature￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examined￨L￨VBD￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- varied￨L￨VBD￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- temperature￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- began￨L￨VBD￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- temperature￨L￨NN￨O￨- regimes￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- set￨L￨VBD￨O￨- T￨U￨NN￨O￨- =￨L￨JJ￨O￨- 40.0￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- =￨L￨JJ￨O￨- 25.0￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- T￨U￨NN￨O￨- =￨L￨JJ￨O￨- 10.0￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- temperature￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- default￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Appendix￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- varied￨L￨VBD￨O￨- the￨L￨DT￨O￨- temperature￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- from￨L￨IN￨O￨- 10.0￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- to￨L￨TO￨O￨- 40.0￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- in￨L￨IN￨O￨- increments￨L￨NNS￨O￨- of￨L￨IN￨O￨- 0.1￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- How￨U￨WRB￨O￨- do￨L￨VBP￨O￨- temperature￨L￨NN￨O￨A mean￨L￨NN￨O￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- range￨L￨NN￨O￨- interact￨L￨VBP￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ?￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- bats￨L￨NNS￨O￨- were￨L￨VBD￨O￨- indeed￨L￨RB￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- and￨L￨CC￨O￨- unique￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- of￨L￨IN￨O￨- filoviruses￨L￨NNS￨O￨- as￨L￨IN￨O￨- EBOV￨U￨NN￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- outbreaks￨L￨NNS￨O￨- might￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- primarily￨L￨RB￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- direct￨L￨JJ￨O￨A human-bat￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- by￨L￨IN￨O￨- other￨L￨JJ￨O￨- means￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- infected￨L￨JJ￨O￨- primate￨L￨JJ￨O￨- carcasses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- bushmeat￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- bat￨L￨NN￨O￨- feces￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- Predictive￨U￨NNP￨O￨- Spatial￨U￨NNP￨O￨- Distribution￨U￨NN￨O￨- Framework￨U￨NN￨O￨- for￨L￨IN￨O￨- Filovirus-Infected￨U￨NNP￨O￨- Bats￨U￨NNP￨O￨- Graziano￨U￨NNP￨O￨- Fiorillo1￨U￨NN￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Paolo￨U￨NNP￨PERSON￨- Bocchini￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- na1￨L￨NN￨O￨- &￨L￨CC￨O￨- Javier￨U￨NNP￨O￨- Buceta2￨U￨NNP￨O￨- ,3￨L￨CD￨NUMBER￨- na1￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 7970￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsEcological￨L￨JJ￨O￨- epidemiologyViral￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- AbstractTools￨U￨NNS￨O￨- with￨L￨IN￨O￨- predictive￨L￨JJ￨O￨A capabilities￨L￨NNS￨O￨- in￨L￨IN￨O￨- regards￨L￨VBZ￨O￨- of￨L￨IN￨O￨- filovirus￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- mainly￨L￨RB￨O￨- anthropocentric￨L￨JJ￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- disregarded￨L￨VBN￨O￨- the￨L￨DT￨O￨- ecological￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- contribute￨L￨VBP￨O￨- to￨L￨TO￨O￨- shift￨L￨VB￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- paradigm￨L￨NN￨O￨- by￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- putative￨L￨JJ￨O￨- main￨L￨JJ￨O￨- zoonotic￨L￨JJ￨O￨- niche￨L￨NN￨O￨- of￨L￨IN￨O￨- filoviruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- bats￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- link￨L￨NN￨O￨- to￨L￨TO￨O￨- environmental￨L￨JJ￨O￨A drivers￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- implement￨L￨VBP￨O￨- a￨L￨DT￨O￨- regression￨L￨NN￨O￨- analysis￨L￨NN￨O￨- using￨L￨VBG￨O￨- factual￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- correlate￨L￨VB￨O￨- environmental￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- bats￨L￨NNS￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- outbreaks￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨A exposure￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- to￨L￨TO￨O￨- bats￨L￨NNS￨O￨- in￨L￨IN￨O￨- Africa9￨U￨NN￨O￨- .￨L￨.￨O￨- +Case￨U￨NN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- classroom￨L￨NN￨O￨- teaching￨L￨NN￨O￨- to￨L￨TO￨O￨- introduce￨L￨VB￨O￨- students￨L￨NNS￨O￨- to￨L￨TO￨O￨- key￨L￨JJ￨O￨A epidemiological￨L￨JJ￨O￨A concepts￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- serial￨L￨NN￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Participation￨U￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- real-time￨L￨JJ￨O￨- simulated￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- analysing￨L￨VBG￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- data￨L￨NNS￨O￨- reinforces￨L￨VBZ￨O￨- and￨L￨CC￨O￨- affords￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- important￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨A while￨L￨IN￨O￨- gaining￨L￨VBG￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- these￨L￨DT￨O￨- ,￨L￨,￨O￨- initial￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- include￨L￨VBP￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- onward￨L￨RB￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- understanding￨L￨VBG￨O￨- key￨L￨JJ￨O￨A epidemiological￨L￨JJ￨O￨A features￨L￨NNS￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- possible￨L￨JJ￨O￨- control￨L￨NN￨O￨- policies￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- approach￨L￨NN￨O￨- involved￨L￨VBD￨O￨- real-time￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- among￨L￨IN￨O￨- participants￨L￨NNS￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- ranged￨L￨VBD￨O￨- from￨L￨IN￨O￨- university￨L￨NN￨O￨- undergraduate￨L￨JJ￨O￨- students￨L￨NNS￨O￨- to￨L￨TO￨O￨- academic￨L￨JJ￨O￨- professors￨L￨NNS￨O￨- ,￨L￨,￨O￨- attending￨L￨VBG￨O￨- an￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- training￨L￨NN￨O￨- course￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- few￨L￨JJ￨O￨- training￨L￨NN￨O￨- modules￨L￨NNS￨O￨- that￨L￨WDT￨O￨- explicitly￨L￨RB￨O￨- use￨L￨VBP￨O￨- real-time￨L￨JJ￨O￨- simulated￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- participants￨L￨NNS￨O￨A themselves￨L￨PRP￨O￨- comprise￨L￨VBP￨O￨- the￨L￨DT￨O￨- dataset￨L￨NN￨O￨- they￨L￨PRP￨O￨- subsequently￨L￨RB￨O￨- analyse￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- recent￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨A and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- underscores￨L￨VBZ￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- better￨L￨JJR￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- forecasting.Methods￨L￨NNS￨O￨- :￨L￨:￨O￨- To￨U￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- suitability￨L￨NN￨O￨- of￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- forecasting￨L￨NN￨O￨- emerging￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Defense￨U￨NNP￨ORGANIZATION￨- Advanced￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- Projects￨U￨NNP￨ORGANIZATION￨- Agency￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- DARPA￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2015￨L￨CD￨DATE￨- DARPA￨U￨NNP￨O￨- Chikungunya￨U￨NNP￨O￨- Challenge￨U￨NNP￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- need￨L￨NN￨O￨A to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- quality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics.KeywordsChikungunyaForecastingMorphological￨L￨JJ￨O￨- modelsMechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- BackgroundMathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- a￨L￨DT￨DURATION￨- century￨L￨NN￨DURATION￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Forecasting￨U￨NN￨O￨- approaches￨L￨NNS￨O￨- vary￨L￨VBP￨O￨- substantially￨L￨RB￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- method￨L￨NN￨O￨- and￨L￨CC￨O￨- complexity￨L￨NN￨O￨A ;￨L￨:￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- use￨L￨NN￨O￨- human￨L￨JJ￨O￨- judgment￨L￨NN￨O￨- or￨L￨CC￨O￨- prediction￨L￨NN￨O￨- markets￨L￨NNS￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- use￨L￨NN￨O￨- purely￨L￨RB￨O￨- statistical￨L￨JJ￨O￨- or￨L￨CC￨O￨- machine￨L￨NN￨O￨- learning￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- others￨L￨NNS￨O￨- rely￨L￨VBP￨O￨- upon￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- varying￨L￨VBG￨O￨- complexity￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- recently￨L￨RB￨DATE￨- have￨L￨VB￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- systems￨L￨NNS￨O￨- begun￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- designed￨L￨VBN￨O￨- specifically￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- task￨L￨NN￨O￨- of￨L￨IN￨O￨- providing￨L￨VBG￨O￨- regularly￨L￨RB￨O￨- updated￨L￨VBN￨O￨- quantitative￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- analogous￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- weather￨L￨NN￨O￨- prediction￨L￨NN￨O￨- .￨L￨.￨O￨- +Challenge￨U￨NN￨O￨- participants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 38￨L￨CD￨NUMBER￨- during￨L￨IN￨O￨- final￨L￨JJ￨O￨- evaluation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- provided￨L￨VBD￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨A epidemics￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- six-month￨L￨JJ￨DURATION￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- September￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2014￨L￨CD￨DATE￨- to￨L￨TO￨O￨- February￨U￨NNP￨DATE￨- 16￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2015￨L￨CD￨DATE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- evaluated￨L￨VBN￨O￨- by￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- reported￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Pan￨U￨NNP￨ORGANIZATION￨- American￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- PAHO￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- resistance￨L￨NN￨O￨- breakdown￨L￨NN￨O￨- or￨L￨CC￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- erosion￨L￨NN￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- cultivars￨L￨NNS￨O￨- becoming￨L￨VBG￨O￨- ineffective￨L￨JJ￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- their￨L￨PRP$￨O￨- durability￨L￨NN￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- chemicals￨L￨NNS￨O￨- ,￨L￨,￨O￨- agronomic￨L￨JJ￨O￨- practices￨L￨NNS￨O￨A ,￨L￨,￨O￨- varying￨L￨VBG￨O￨- crop￨L￨NN￨O￨- diversity￨L￨NN￨O￨- either￨L￨CC￨O￨- temporally￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- crop￨L￨NN￨O￨- rotations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- spatially￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- pyramiding￨L￨VBG￨O￨- ,￨L￨,￨O￨- mixtures￨L￨NNS￨O￨- ,￨L￨,￨O￨- mosaics￨L￨NNS￨O￨- of￨L￨IN￨O￨- fields￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- or￨L￨CC￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- cultural￨L￨JJ￨O￨- practices￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- for￨L￨IN￨O￨- landscape‐scale￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- spite￨L￨NN￨O￨- of￨L￨IN￨O￨- considerable￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- from￨L￨IN￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- landscape￨L￨NN￨O￨A organization￨L￨NN￨O￨- can￨L￨MD￨O￨- affect￨L￨VB￨O￨- pathogen￨L￨NN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- impede￨L￨VB￨O￨- adaptation￨L￨NN￨O￨- to￨L￨TO￨O￨- host￨L￨NN￨TITLE￨- resistance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨A crop￨L￨NN￨O￨- cultivars￨L￨NNS￨O￨- against￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- typically￨L￨RB￨O￨- reduces￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- associated￨L￨VBN￨O￨- yield￨L￨NN￨O￨- losses￨L￨NNS￨O￨- in￨L￨IN￨O￨- agricultural￨L￨JJ￨O￨- production￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- either￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- or￨L￨CC￨O￨- quantitative￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- pathogen￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- towards￨L￨IN￨O￨- increased￨L￨VBN￨O￨- infectivity￨L￨NN￨O￨- or￨L￨CC￨O￨- aggressiveness￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- resistant￨L￨JJ￨O￨A host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- penalized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- fitness￨L￨NN￨O￨- cost￨L￨NN￨O￨- on￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- such￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- ,￨L￨,￨O￨- new￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- may￨L￨MD￨O￨- quickly￨L￨RB￨O￨- emerge￨L￨VB￨O￨- in￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- total￨L￨JJ￨O￨- breakdown￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- resistance￨L￨NN￨O￨A gene￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- susceptible-latent-breakingout-quarantine-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SLBQRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- preserves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- at￨L￨IN￨O￨- all￨L￨DT￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- domain￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- continuous￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- structure￨L￨NN￨O￨- preserving￨L￨NN￨O￨- numerical￨L￨JJ￨O￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- motivation￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- the￨L￨DT￨O￨- reliable￨L￨JJ￨O￨- positivity￨L￨NN￨O￨- preserving￨L￨VBG￨O￨- numerical￨L￨JJ￨O￨- schemes￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨A network￨L￨NN￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- of￨L￨IN￨O￨- reliability￨L￨NN￨O￨- ,￨L￨,￨O￨- efficiency￨L￨NN￨O￨- and￨L￨CC￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- preserving￨L￨VBG￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- NSFD￨U￨NN￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- SLBQRS￨U￨NNP￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- numerical￨L￨JJ￨O￨- scheme￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- justify￨L￨VB￨O￨- negative￨L￨JJ￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- because￨L￨IN￨O￨- negative￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- meaningless￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effort￨L￨NN￨O￨A available￨L￨JJ￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- quantity￨L￨NN￨O￨- of￨L￨IN￨O￨- operational￨L￨JJ￨O￨- equipment￨L￨NN￨O￨- or￨L￨CC￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- personnel￨L￨NNS￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- H￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- surface￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- bivariate￨L￨JJ￨O￨- Gaussian￨U￨JJ￨MISC￨- density￨L￨NN￨O￨- function￨L￨NN￨O￨- with￨L￨IN￨O￨- mean￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epicenter￨L￨NN￨O￨- x0￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- represent￨L￨VB￨O￨- a￨L￨DT￨O￨- central￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- point￨L￨NN￨O￨- or￨L￨CC￨O￨- medical￨L￨JJ￨O￨- facility￨L￨NN￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- originates￨L￨VBZ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- variance-covariance￨L￨NN￨O￨- matrix￨L￨NN￨O￨- I.￨U￨NN￨O￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- analogous￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- person￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- immunized￨L￨VBN￨O￨- at￨L￨IN￨O￨- location￨L￨NN￨O￨- x￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- where￨L￨WRB￨O￨- local￨L￨JJ￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- smoothing￨L￨VBG￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- kernel￨L￨NN￨O￨- K￨U￨NN￨O￨- with￨L￨IN￨O￨- parameter￨L￨NN￨O￨- α￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- effort￨L￨NN￨O￨- ,￨L￨,￨O￨- H￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- below￨L￨IN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- parameterized￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- values￨L￨NNS￨O￨- :￨L￨:￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- τ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- δ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ρ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- intensity￨L￨NN￨O￨- ε￨L￨NN￨O￨- =￨L￨JJ￨O￨- 20￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨A scale￨L￨NN￨O￨- α￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Supplementary￨U￨NNP￨O￨- Information￨U￨NNP￨O￨- for￨L￨IN￨O￨- sensitivity￨L￨NN￨O￨- of￨L￨IN￨O￨- results￨L￨NNS￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- illustrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- distribution￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- promptness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- response￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- employed￨L￨VBN￨O￨A a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- combined￨L￨VBN￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- vaccines￨L￨NNS￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- .￨L￨.￨O￨- +Dias￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- an￨L￨DT￨O￨- adaptation￨L￨NN￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- seen￨L￨VBN￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- attempts￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- in￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- herds￨L￨NNS￨O￨- using￨L￨VBG￨O￨- IBM￨U￨NNP￨ORGANIZATION￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- describe￨L￨VBP￨O￨- expressive￨L￨JJ￨O￨- developments￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨A of￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- less￨L￨JJR￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- IBM￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- such￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- other￨L￨JJ￨O￨- works￨L￨NNS￨O￨- that￨L￨WDT￨O￨- use￨L￨VBP￨O￨- IBM￨U￨NNP￨ORGANIZATION￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- brucellosis￨L￨NN￨O￨- as￨L￨IN￨O￨- seen￨L￨VBN￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- outside-host￨L￨JJ￨O￨- bacterial￨L￨JJ￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨A and￨L￨CC￨O￨- phage-resistant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- phage￨L￨NN￨O￨- resistance￨L￨NN￨O￨- determines￨L￨VBZ￨O￨- phage￨L￨NN￨O￨- therapy￨L￨NN￨O￨- outcome￨L￨NN￨O￨- from￨L￨IN￨O￨- stable￨L￨JJ￨O￨- coexistence￨L￨NN￨O￨- to￨L￨TO￨O￨- local￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- extinction￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- PPR￨U￨NNP￨ORGANIZATION￨- virus￨L￨NN￨O￨- are￨L￨VBP￨O￨- sick￨L￨JJ￨O￨- small￨L￨JJ￨O￨- ruminant￨L￨NN￨O￨- animals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- release￨L￨VBP￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- with￨L￨IN￨O￨- nasal￨L￨JJ￨O￨- and￨L￨CC￨O￨- teary￨L￨JJ￨O￨- outflows￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- with￨L￨IN￨O￨- feces￨L￨NNS￨O￨- ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 1st￨L￨JJ￨DATE￨- day￨L￨NN￨DATE￨- of￨L￨IN￨O￨- febrile￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- manifestation￨L￨NN￨O￨- of￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- signs￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 2-3￨L￨CD￨NUMBER￨- days￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- their￨L￨PRP$￨O￨- appearance￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- PPR￨U￨NNP￨ORGANIZATION￨- occurrence￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- were￨L￨VBD￨O￨- obliged￨L￨VBN￨O￨- to￨L￨TO￨O￨- determinate￨L￨VB￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- of￨L￨IN￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- different￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- consequences￨L￨NNS￨O￨- depending￨L￨VBG￨O￨A on￨L￨IN￨O￨- various￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- that￨L￨WDT￨O￨- PPR￨U￨NNP￨ORGANIZATION￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- appearance￨L￨NN￨O￨A may￨L￨MD￨O￨- vary￨L￨VB￨O￨- from￨L￨IN￨O￨- area￨L￨NN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- predisposition￨L￨NN￨O￨- or￨L￨CC￨O￨- existing￨L￨VBG￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- Geo-information￨U￨JJ￨MISC￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- QuickMAP￨U￨NN￨O￨- has￨L￨VBZ￨O￨- processed￨L￨VBN￨O￨- clustering￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- outbreaks￨L￨NNS￨O￨- incidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- cases/or￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- focus￨L￨NN￨O￨A of￨L￨IN￨O￨- PPR￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- mapping￨L￨NN￨O￨- .￨L￨.￨O￨- +Peste￨U￨NNP￨O￨- des￨L￨NNP￨O￨- petits￨L￨VBZ￨O￨- ruminants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PPR￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- contagious￨L￨JJ￨O￨- ,￨L￨,￨O￨- emergent￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transboundary￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- affects￨L￨VBZ￨O￨- goats￨L￨NNS￨O￨- and￨L￨CC￨O￨- sheep￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Specific￨U￨JJ￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- resulting￨L￨VBG￨O￨- case￨L￨NN￨O￨- counts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- factors￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨A strain￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- specific￨L￨JJ￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- either￨L￨RB￨O￨- reduce￨L￨VB￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aid￨L￨NN￨O￨- included￨L￨VBD￨O￨- health￨L￨NN￨O￨A care￨L￨NN￨O￨A resources￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- affected￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- altered￨L￨VBD￨O￨- individual￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- quickly￨L￨RB￨O￨- contained￨L￨VBD￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- limited￨L￨VBD￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- immensely￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- evident￨L￨JJ￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- early￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- Sudan￨U￨NNP￨COUNTRY￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- reflection￨L￨NN￨O￨- of￨L￨IN￨O￨- preparedness￨L￨NN￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨A care￨L￨NN￨O￨A providers￨L￨NNS￨O￨- and￨L￨CC￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- public￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Report￨U￨NNP￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- WHO￨U￨WP￨O￨- /￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Unlike￨U￨IN￨O￨- previous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- simply￨L￨RB￨O￨- reduce￨L￨VB￨O￨A various￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- education￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- different￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- group￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- protocols￨L￨NNS￨O￨A are￨L￨VBP￨O￨- not￨L￨RB￨O￨- followed￨L￨VBN￨O￨- ,￨L￨,￨O￨- hospital￨L￨NN￨O￨- settings￨L￨NNS￨O￨- can￨L￨MD￨O￨- produce￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- during￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- outbreaks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- ZVL￨U￨NN￨O￨- is￨L￨VBZ￨O￨- curable￨L￨JJ￨O￨- using￨L￨VBG￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- miltefosine￨L￨NN￨O￨- ,￨L￨,￨O￨- paromomycin￨L￨NN￨O￨- and￨L￨CC￨O￨- liposomal￨L￨JJ￨O￨- amphotericin￨L￨NN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- basic￨L￨JJ￨O￨- anti-ZVL￨L￨JJ￨O￨- preventive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- personal￨L￨JJ￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- sandfly￨L￨JJ￨O￨- bites￨L￨VBZ￨O￨- and￨L￨CC￨O￨- sandfly-reduction￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- spraying￨L￨VBG￨O￨- anti-sandfly￨L￨JJ￨O￨- insecticides￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- animal￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨A habitats￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- remain￨L￨VBP￨O￨- perhaps￨L￨RB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- combating￨L￨VBG￨O￨- ZVL￨U￨NNP￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- ZVL￨U￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- and/or￨L￨CC￨O￨- reservoir￨L￨NN￨O￨A populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Carvalho￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- references￨L￨NNS￨O￨- therein￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +proposed￨L￨VBN￨O￨- mechanistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- ZVL￨U￨NN￨O￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- animal￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨A populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- theoretical￨L￨JJ￨O￨- extensions￨L￨NNS￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨A rates￨L￨NNS￨O￨A beyond￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- in￨L￨IN￨O￨- ODEs￨U￨NNS￨O￨- have￨L￨VBP￨O￨- only￨L￨RB￨O￨- started￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- developed￨L￨VBN￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- constant￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- rates￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- exponentially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- are￨L￨VBP￨O￨- epidemiologically￨L￨RB￨O￨- unrealistic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Next￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- spent￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- class￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨A rates￨L￨NNS￨O￨A in￨L￨IN￨O￨- ODE￨U￨NNP￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- dog￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- vector￨L￨NN￨O￨- transmitting￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- ;￨L￨:￨O￨- Those￨U￨DT￨O￨- three￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- humans￨L￨NNS￨O￨A ,￨L￨,￨O￨- dogs￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- constants￨L￨NNS￨O￨- ;￨L￨:￨O￨- Both￨U￨CC￨O￨- human￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- indexed￨L￨VBN￨O￨- as￨L￨IN￨O￨- h￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- dog￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- indexed￨L￨VBN￨O￨- as￨L￨IN￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- categories￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- and￨L￨CC￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- but￨L￨CC￨O￨- without￨L￨IN￨O￨- noticeable￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- l￨L￨NN￨O￨- and￨L￨CC￨O￨- l￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- latent￨L￨JJ￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- clinically￨L￨RB￨O￨- ill￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- immunes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- z￨L￨SYM￨O￨- and￨L￨CC￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- must￨L￨MD￨O￨- add￨L￨VB￨O￨- an￨L￨DT￨O￨- entrance￨L￨NN￨O￨- term￨L￨NN￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- natality￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- choose￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-induced￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- humans￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- clinically￨L￨RB￨O￨- ill￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- maintain￨L￨VB￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- latent￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- humans￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Zoonotic￨U￨JJ￨O￨- Visceral￨U￨JJ￨O￨- Leishmaniasis￨U￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- major￨L￨JJ￨O￨- human￨L￨JJ￨O￨A and￨L￨CC￨O￨- veterinary￨L￨JJ￨O￨- medical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- that￨L￨WDT￨O￨- involves￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- trypanosomatids￨L￨NNS￨O￨- protozoan￨L￨NN￨O￨- from￨L￨IN￨O￨- Leishmania￨U￨NN￨LOCATION￨- complex￨L￨NN￨O￨- ,￨L￨,￨O￨- arthropod￨L￨NN￨O￨- vectors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- the￨L￨DT￨O￨- female￨L￨JJ￨O￨- sandfly￨L￨JJ￨O￨- Lutzomyia￨U￨NN￨O￨- longipalpis￨L￨NN￨O￨- and￨L￨CC￨O￨- Lutzomyia￨U￨NN￨PERSON￨- cruzi￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- vector￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- small￨L￨JJ￨O￨- companion￨L￨NN￨TITLE￨- animal￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dog￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- reservoir￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- new￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- updated￨L￨VBD￨O￨A most￨L￨JJS￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- calculated￨L￨VBN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- value￨L￨NN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- sensitivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- infinitesimal￨L￨JJ￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- varies￨L￨VBZ￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- infected￨L￨JJ￨O￨- flies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- bite￨L￨VB￨O￨- on￨L￨IN￨O￨- any￨L￨DT￨O￨- category￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨A population￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- cell￨L￨NN￨O￨- in￨L￨IN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- Since￨U￨IN￨O￨- our￨L￨PRP$￨O￨- goal￨L￨NN￨O￨- concerns￨L￨VBZ￨O￨- the￨L￨DT￨O￨- minimization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨A people￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vicinity￨L￨NN￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimization￨L￨NN￨O￨- criterion￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- cell￨L￨NN￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- it￨L￨PRP￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- objective￨L￨NN￨O￨- functionwhere￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- severity￨L￨NN￨O￨- weights￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- controls￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- travel-blocking￨L￨JJ￨O￨- vicinity￨L￨NN￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- restrict￨L￨VB￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A people￨L￨NNS￨O￨A coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- and￨L￨CC￨O￨- aiming￨L￨VBG￨O￨- to￨L￨TO￨O￨- reach￨L￨VB￨O￨- the￨L￨DT￨O￨- cell￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- travel-blocking￨L￨JJ￨O￨- vicinity￨L￨NN￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- approach￨L￨NN￨O￨- will￨L￨MD￨O￨- show￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- blocker￨L￨NN￨TITLE￨- control￨L￨NN￨O￨- on￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- people￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- cell￨L￨NN￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨A people￨L￨NNS￨O￨A coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- cell￨L￨NN￨O￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- cells￨L￨NNS￨O￨- from￨L￨IN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- multi-cells￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- vicinity￨L￨NN￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A strategy￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- represent￨L￨VB￨O￨- good￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- studies￨L￨NNS￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- results￨L￨NNS￨O￨- were￨L￨VBD￨O￨- calculated￨L￨VBN￨O￨- across￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- health￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- :￨L￨:￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- hospitalization￨L￨NN￨O￨- ,￨L￨,￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- ICU￨U￨NN￨O￨- admission￨L￨NN￨O￨- ,￨L￨,￨O￨- peak￨L￨JJ￨O￨- demand￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- acute-care￨L￨JJ￨O￨- hospital￨L￨NN￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- peak￨L￨NN￨O￨- ICU￨U￨NN￨O￨- demand￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- capacity￨L￨NN￨O￨- and￨L￨CC￨O￨- total￨L￨JJ￨O￨- deaths￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- recognizing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- distribution￨L￨NN￨O￨- could￨L￨MD￨O￨- prioritize￨L￨VB￨O￨- high-risk￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- interest￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- geographical￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- accommodate￨L￨VB￨O￨- surges￨L￨VBZ￨O￨- in￨L￨IN￨O￨- patient￨L￨NN￨O￨- demand￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- would￨L￨MD￨O￨- therefore￨L￨RB￨O￨- benefit￨L￨VB￨O￨- from￨L￨IN￨O￨- early￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- hospital-resource￨L￨JJ￨O￨- adequacy￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- InFluNet￨U￨NNP￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- developed￨L￨VBD￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨- —￨L￨:￨O￨- we￨L￨PRP￨O￨- project￨L￨VBP￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- second-wave￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- burden￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- location￨L￨NN￨O￨- under￨L￨IN￨O￨- various￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- method￨L￨NN￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- :￨L￨:￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- susceptibility￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infectivity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- mean￨L￨VB￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- either￨L￨DT￨O￨- symptomatically￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- IC/N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- asymptomatically￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- IA/N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- cost-effective￨L￨JJ￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- containing￨L￨VBG￨O￨- pandemic￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- mitigating￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- associated￨L￨VBN￨O￨- burdens￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- effects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- especially￨L￨RB￨O￨- influential￨L￨JJ￨O￨- for￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- relatively￨L￨RB￨O￨- long￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- populations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- few￨L￨JJ￨O￨- but￨L￨CC￨O￨- long￨L￨JJ￨O￨- lasting￨L￨JJ￨O￨- partnerships￨L￨NNS￨O￨A .￨L￨.￨O￨- +If￨U￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- form￨L￨NN￨O￨- long￨L￨RB￨O￨- lasting￨L￨JJ￨O￨- partnerships￨L￨NNS￨O￨A and￨L￨CC￨O￨- have￨L￨VBP￨O￨- repeated￨L￨VBN￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- individual￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- spreads￨L￨VBZ￨O￨- via￨L￨IN￨O￨- those￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- partnerships￨L￨NNS￨O￨A are￨L￨VBP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- order￨L￨NN￨O￨- of￨L￨IN￨O￨- magnitude￨L￨NN￨O￨- ,￨L￨,￨O￨- partnership￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- interacts￨L￨VBZ￨O￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- itself￨L￨PRP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- such￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- pair￨L￨NN￨O￨A formation￨L￨NN￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- first￨L￨RB￨ORDINAL￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- by￨L￨IN￨O￨- Dietz￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Hadeler￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- partnerships￨L￨NNS￨O￨A are￨L￨VBP￨O￨- monogamous￨L￨JJ￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- susceptibles￨L￨NNS￨O￨- are￨L￨VBP￨O￨- protected￨L￨VBN￨O￨- from￨L￨IN￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- as￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- partnership￨L￨NN￨O￨- lasts￨L￨VBZ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A among￨L￨IN￨O￨- foxes￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- inspired￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- rabies￨L￨NNP￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- on￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨- and￨L￨CC￨O￨- designing￨L￨VBG￨O￨- useful￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- pioneer￨L￨NN￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- Anderson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jackson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- May￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Smith￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1981￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- subclasses￨L￨NNS￨O￨- of￨L￨IN￨O￨- fox￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- epidemiological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A in￨L￨IN￨O￨- fox￨L￨NN￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +Clayton￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Duke-Sylvester￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Gross￨U￨NNP￨O￨- ,￨L￨,￨O￨- Lenhart￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Real￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Ding￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Gross￨U￨NNP￨O￨- ,￨L￨,￨O￨- Langston￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Lenhart￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Real￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- SEIRS￨U￨NNP￨ORGANIZATION￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A in￨L￨IN￨O￨- raccoons￨L￨NNS￨O￨- .￨L￨.￨O￨- +Rabies￨U￨NN￨O￨- virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- present￨L￨JJ￨DATE￨- among￨L￨IN￨O￨- various￨L￨JJ￨O￨- mammal￨L￨NN￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- red￨L￨JJ￨O￨- fox￨L￨NN￨O￨- and￨L￨CC￨O￨- raccoon￨L￨NN￨O￨- dog￨L￨NN￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- raccoon￨L￨NN￨O￨- ,￨L￨,￨O￨- red￨L￨JJ￨O￨- fox￨L￨NN￨O￨- ,￨L￨,￨O￨- skunk￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- insectivorous￨L￨JJ￨O￨- bats￨L￨NNS￨O￨- in￨L￨IN￨O￨- North￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- domestic￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨A ,￨L￨,￨O￨- insectivorous￨L￨JJ￨O￨- and￨L￨CC￨O￨- vampire￨L￨NN￨O￨- bats￨L￨NNS￨O￨- in￨L￨IN￨O￨- South￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨- ,￨L￨,￨O￨- bat￨L￨NN￨O￨- ,￨L￨,￨O￨- Chinese￨U￨JJ￨NATIONALITY￨- ferret￨L￨VBP￨O￨- badger￨L￨NN￨O￨- ,￨L￨,￨O￨- raccoon￨L￨NN￨O￨- dog￨L￨NN￨O￨- ,￨L￨,￨O￨- rat￨L￨NN￨O￨- ,￨L￨,￨O￨- fox￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- wolf￨L￨NN￨O￨- in￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Dimitrov￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hallam￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Rupprecht￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Turmelle￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- McCracken￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- presented￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- rabies￨L￨NNP￨O￨A virus￨L￨NN￨O￨- in￨L￨IN￨O￨- bats￨L￨NNS￨O￨- and￨L￨CC￨O￨- George￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Especially￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- work￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rates￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- spreading￨L￨VBG￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +And￨U￨CC￨O￨- this￨L￨DT￨O￨- invites￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- follow￨L￨VB￨O￨- the￨L￨DT￨O￨- precious￨L￨JJ￨O￨- works￨L￨NNS￨O￨- and￨L￨CC￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- combining￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- influence￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- with￨L￨IN￨O￨- both￨L￨DT￨O￨- individual￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- and￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- increased￨L￨VBD￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- availed￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- individual￨L￨JJ￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- increasing￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- findings￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- closely￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Environmental￨U￨JJ￨O￨- variability￨L￨NN￨O￨- is￨L￨VBZ￨O￨- especially￨L￨RB￨O￨- important￨L￨JJ￨O￨- in￨L￨IN￨O￨- modeling￨L￨NN￨O￨- zoonotic￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- waterborne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Ebola￨U￨NNP￨O￨- ,￨L￨,￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Stochastic￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨A in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- births￨L￨NNS￨O￨- ,￨L￨,￨O￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- impacts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outcome￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- sections￨L￨NNS￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- stochastic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- formulated￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infectious-Recovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Ross￨U￨NNP￨PERSON￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A host-vector￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- additional￨L￨JJ￨O￨- examples￨L￨NNS￨O￨A and￨L￨CC￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- consult￨L￨VB￨O￨- the￨L￨DT￨O￨- textbooks￨L￨NNS￨O￨- and￨L￨CC￨O￨- papers￨L￨NNS￨O￨- listed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- references￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- well-known￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- illustration￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- host-vector￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- can￨L￨MD￨O￨- play￨L￨VB￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- helping￨L￨VBG￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- possible￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A by￨L￨IN￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- determining￨L￨VBG￨O￨- threshold￨L￨NN￨O￨- quantities￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- survival￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- elaborate￨L￨VB￨O￨- on￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨- for￨L￨IN￨O￨- ODE￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- bearing￨L￨VBG￨O￨- in￨L￨IN￨O￨- mind￨L￨NN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- meaning￨L￨NN￨O￨- of￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- how￨L￨WRB￨O￨- this￨L￨DT￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- guide￨L￨VB￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemiological￨L￨JJ￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨A individual￨L￨JJ￨O￨A introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- acquired￨L￨VBN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- healthy￨L￨JJ￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- acquire￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Sections￨U￨NNS￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- apply￨L￨VB￨O￨- these￨L￨DT￨O￨- ideas￨L￨NNS￨O￨A to￨L￨TO￨O￨- models￨L￨NNS￨O￨- specific￨L￨JJ￨O￨- for￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Nile￨U￨NNP￨LOCATION￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- birds￨L￨NNS￨O￨- ,￨L￨,￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- anthrax￨L￨NN￨O￨- in￨L￨IN￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- numerical￨L￨JJ￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- references￨L￨NNS￨O￨A given￨L￨VBN￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- proofs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- detailed￨L￨VBN￨O￨- here￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Model-based￨U￨JJ￨MISC￨- assessments￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- done￨L￨VBN￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- :￨L￨:￨O￨- this￨L￨DT￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- for￨L￨IN￨O￨- MERS-CoV￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Middle￨U￨NNP￨LOCATION￨- East￨U￨NNP￨LOCATION￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- [￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- chikungunya￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2017￨L￨CD￨DATE￨- ZIKV￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- Guadeloupe￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Martinique￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Saint-Martin￨U￨NNP￨PERSON￨- was￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- by￨L￨IN￨O￨- local￨L￨JJ￨O￨- sentinel￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- practitioners￨L￨NNS￨O￨- and￨L￨CC￨O￨- reported￨L￨VBD￨O￨- weekly￨L￨JJ￨SET￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- health￨L￨NN￨O￨A authorities￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- hierarchical￨L￨JJ￨O￨A statistical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- and￨L￨CC￨O￨- extract￨L￨VB￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- historical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- distributions￨L￨NNS￨O￨- for￨L￨IN￨O￨- required￨L￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Griffiths￨U￨NNP￨PERSON￨- phases￨L￨NNS￨O￨- in￨L￨IN￨O￨- infinite-dimensional￨L￨JJ￨O￨- ,￨L￨,￨O￨- non-hierarchical￨L￨JJ￨O￨- modular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- Wesley￨U￨NNP￨PERSON￨- Cota￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Géza￨U￨NNP￨O￨- Ódor￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Silvio￨U￨NNP￨PERSON￨- C.￨U￨NNP￨PERSON￨- Ferreira￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 9144￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksPhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractGriffiths￨U￨NNP￨O￨- phases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- GPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneities￨L￨NNS￨O￨- on￨L￨IN￨O￨- modular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- ,￨L￨,￨O￨- rid￨L￨JJ￨O￨- of￨L￨IN￨O￨- fine￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- tuning￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- activity￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- evolving￨L￨VBG￨O￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- highly￨L￨RB￨O￨- modular￨L￨JJ￨O￨A structure￨L￨NN￨O￨- and￨L￨CC￨O￨- organized￨L￨VBN￨O￨- non-hierarchically￨L￨RB￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- extended￨L￨JJ￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- regions￨L￨NNS￨O￨- with￨L￨IN￨O￨- continuously￨L￨RB￨O￨- changing￨L￨VBG￨O￨- dynamical￨L￨JJ￨O￨- exponents￨L￨NNS￨O￨- for￨L￨IN￨O￨- single￨L￨JJ￨O￨- network￨L￨NN￨O￨- realizations￨L￨NNS￨O￨- ,￨L￨,￨O￨- preserved￨L￨VBN￨O￨- after￨L￨IN￨O￨- finite￨L￨JJ￨O￨A size￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- GP￨U￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- conjectured￨L￨VBD￨O￨- requirement￨L￨NN￨O￨- for￨L￨IN￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- modular￨L￨JJ￨O￨A structures￨L￨NNS￨O￨- was￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- modules￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- hierarchically￨L￨RB￨O￨- organized￨L￨VBN￨O￨- and￨L￨CC￨O￨- possess￨L￨VBP￨O￨- finite￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- .￨L￨.￨O￨- +Subsequent￨U￨JJ￨O￨- development￨L￨NN￨O￨- has￨L￨VBZ￨O￨- largely￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- Bayesian￨U￨JJ￨MISC￨- approaches￨L￨NNS￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- prior￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- piecewise￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- techniques￨L￨NNS￨O￨- are￨L￨VBP￨O￨- derivatives￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- skyline￨L￨NN￨O￨- coalescent￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- piecewise￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- nonparametric￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- its￨L￨PRP$￨O￨- logarithm￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- Brownian￨U￨JJ￨MISC￨- motion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Genealogies￨U￨NNS￨O￨- often￨L￨RB￨O￨- provide￨L￨VBP￨O￨- very￨L￨RB￨O￨- little￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A near￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- sample￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- exponentially￨L￨RB￨O￨- increasing￨L￨VBG￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Below￨U￨IN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- prior￨L￨JJ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- autoregressive￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- study￨L￨NN￨O￨- illustrated￨L￨VBD￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨- theory￨L￨NN￨O￨- in￨L￨IN￨O￨- establishing￨L￨VBG￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- educational￨L￨JJ￨O￨- campaign￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- cutting￨L￨VBG￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- indirect￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- via￨L￨IN￨O￨- free-living￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- symptoms￨L￨NNS￨O￨- and￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- present￨L￨VBP￨DATE￨- symptoms￨L￨NNS￨O￨- but￨L￨CC￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- hospital￨L￨NN￨O￨- and￨L￨CC￨O￨- hospitalized￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- present￨L￨VBP￨DATE￨- symptoms￨L￨NNS￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- admitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- hospital￨L￨NN￨O￨- could￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- HFMD￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Thailand￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- roles￨L￨NNS￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- contaminated￨L￨VBN￨O￨- environments￨L￨NNS￨O￨- were￨L￨VBD￨O￨- investigated￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨A results￨L￨NNS￨O￨A show￨L￨VBP￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- factors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- delay￨L￨VB￨O￨- and￨L￨CC￨O￨- prevent￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Thailand￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- HFMD￨U￨NN￨O￨- models￨L￨NNS￨O￨- only￨L￨RB￨O￨- analysed￨L￨VBD￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- hand-washing￨L￨NN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨A contact￨L￨NN￨O￨A rate￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +applied￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- without￨L￨IN￨O￨- hospitalized￨L￨VBN￨O￨A but￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- hospitalized￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- with￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +HFMD￨U￨NN￨O￨- spreads￨L￨NNS￨O￨- mainly￨L￨RB￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- under￨L￨IN￨O￨- five￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- these￨L￨DT￨O￨- viruses￨L￨NNS￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Three￨U￨CD￨NUMBER￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- simulated￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- are￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- :￨L￨:￨O￨- daily￨L￨JJ￨SET￨- snapshots￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- black￨L￨JJ￨O￨- line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- weekly￨L￨JJ￨SET￨- aggregated￨L￨JJ￨O￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- reporting￨L￨NN￨O￨A error￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- perfect￨L￨JJ￨O￨- reporting￨L￨NN￨O￨- ,￨L￨,￨O￨- blue￨L￨JJ￨O￨- line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- weekly￨L￨JJ￨SET￨- aggregated￨L￨JJ￨O￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- with￨L￨IN￨O￨- reporting￨L￨VBG￨O￨- error￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- imperfect￨L￨JJ￨O￨- reporting￨L￨NN￨O￨- ,￨L￨,￨O￨- red￨L￨JJ￨O￨- line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- top￨L￨JJ￨O￨- panel￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- calculated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- :￨L￨:￨O￨- daily￨L￨JJ￨SET￨- snapshots￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- black￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- weekly￨L￨JJ￨SET￨A case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- blue￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- monthly￨L￨JJ￨SET￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- red￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Estimates￨U￨NNS￨O￨- for￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- reporting￨L￨VBG￨O￨A efficacy￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- USA￨U￨NNP￨COUNTRY￨- are￨L￨VBP￨O￨- around￨L￨IN￨O￨- 45￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- NumericCitation￨U￨NN￨O￨- In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- raw￨L￨JJ￨O￨- weekly￨L￨JJ￨SET￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- bottom￨L￨JJ￨O￨- row￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- aggregated￨L￨VBN￨O￨- into￨L￨IN￨O￨- bi-weekly￨L￨JJ￨SET￨- and￨L￨CC￨O￨- four-weekly￨L￨JJ￨DURATION￨- reports￨L￨NNS￨O￨- .￨L￨.￨O￨- +Transmission￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- birth￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- with￨L￨IN￨O￨- average￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 106￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- importation￨L￨NN￨O￨- rate￨L￨NN￨O￨- ζ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- case￨L￨NN￨O￨- per￨L￨IN￨O￨- week￨L￨NN￨DURATION￨A ,￨L￨,￨O￨- mean￨L￨VB￨O￨- life￨L￨NN￨O￨- expectancy￨L￨NN￨O￨- of￨L￨IN￨O￨- 70￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- mean￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- 1￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- case￨L￨NN￨O￨- aggregation￨L￨NN￨O￨- and￨L￨CC￨O￨- reporting￨L￨VBG￨O￨A error￨L￨NN￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- mismatch￨L￨NN￨O￨- between￨L￨IN￨O￨- snapshots￨L￨NNS￨O￨- and￨L￨CC￨O￨- imperfect￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- interacting￨L￨VBG￨O￨- factors￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- —￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- chickenpox￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A may￨L￨MD￨O￨- impact￨L￨VB￨O￨- shingles￨L￨NNS￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- epidemiology￨L￨NN￨O￨- —￨L￨:￨O￨- complements￨L￨VBZ￨O￨- conventional￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- offers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- controlled￨L￨JJ￨O￨- study￨L￨NN￨O￨- using￨L￨VBG￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- exogenous￨L￨JJ￨O￨- VZV-CMI￨U￨NN￨O￨- boosting￨L￨VBG￨O￨A has￨L￨VBZ￨O￨- sparked￨L￨VBN￨O￨- a￨L￨DT￨O￨- debate￨L￨NN￨O￨- about￨L￨IN￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- chickenpox￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- will￨L￨MD￨O￨- limit￨L￨VB￨O￨- the￨L￨DT￨O￨- boosting￨L￨VBG￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- shingles￨L￨NNS￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to-date￨L￨NN￨O￨- is￨L￨VBZ￨O￨- largely￨L￨RB￨O￨- inconclusive￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- studies￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- shingles￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- increasing￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- recent￨L￨JJ￨DURATION￨- decades￨L￨NNS￨DURATION￨- prior￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- chickenpox￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- previous￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- studies￨L￨NNS￨O￨A of￨L￨IN￨O￨- shingles￨L￨NNS￨O￨- and￨L￨CC￨O￨- chickenpox￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- conducted￨L￨VBN￨O￨- using￨L￨VBG￨O￨- aggregate￨L￨JJ￨O￨- population-level￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- drift￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- immunity￨L￨NN￨O￨- generates￨L￨VBZ￨O￨- virus￨L￨NN￨O￨- strains￨L￨NNS￨O￨A that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- covered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- requires￨L￨VBZ￨O￨- frequent￨L￨JJ￨O￨- reformulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- drifted￨L￨VBN￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- relative￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- strains￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- cross-immunity￨L￨NN￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extend￨L￨VBP￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- antigenically￨L￨RB￨O￨- distinct￨L￨JJ￨O￨- co-circulating￨L￨JJ￨O￨- strains￨L￨NNS￨O￨A and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- which￨L￨WDT￨O￨- targets￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- trivalent￨L￨JJ￨O￨- inactivated￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- primarily￨L￨RB￨O￨- induces￨L￨VBZ￨O￨- humoral￨L￨JJ￨O￨- strain-specific￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- directed￨L￨VBN￨O￨- against￨L￨IN￨O￨- HA￨U￨NNP￨O￨- and￨L￨CC￨O￨- NA￨U￨NNP￨O￨- included￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- and￨L￨CC￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- generate￨L￨VB￨O￨- broad￨L￨JJ￨O￨- cross-immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- mismatched￨L￨JJ￨O￨- strains￨L￨NNS￨O￨A .￨L￨.￨O￨- +Cases￨U￨NNS￨O￨- analyzed￨L￨VBD￨O￨- just￨L￨RB￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- 42￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- were￨L￨VBD￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- strains￨L￨NNS￨O￨A antigenically￨L￨RB￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- strain￨L￨NN￨O￨- included￨L￨VBD￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- season￨L￨NN￨O￨- ’s￨L￨POS￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Opinions￨U￨NNS￨O￨- ,￨L￨,￨O￨- behaviours￨L￨NNS￨O￨- ,￨L￨,￨O￨- knowledge￨L￨NN￨O￨- or￨L￨CC￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- concepts￨L￨NNS￨O￨A that￨L￨WDT￨O￨- spread￨L￨VBP￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- chance￨L￨NN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- they￨L￨PRP￨O￨- encounter￨L￨VBP￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- concepts￨L￨NNS￨O￨A has￨L￨VBZ￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- real-world￨L￨JJ￨O￨- environments￨L￨NNS￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- multiple￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨A active￨L￨JJ￨O￨- simultaneously￨L￨RB￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- concept￨L￨NN￨O￨- interaction￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- concept￨L￨NN￨O￨- ’s￨L￨POS￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- .￨L￨.￨O￨- +Existing￨U￨VBG￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨- spread￨L￨NN￨O￨- typically￨L￨RB￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- concept￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- that￨L￨DT￨O￨- concepts￨L￨NNS￨O￨A block￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨- ,￨L￨,￨O￨- preventing￨L￨VBG￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- from￨L￨IN￨O￨- activating￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- that￨L￨IN￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- most￨L￨JJS￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- influence￨L￨NN￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- select￨L￨VB￨O￨- seed￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- concept￨L￨NN￨O￨A we￨L￨PRP￨O￨- wish￨L￨VBP￨O￨- to￨L￨TO￨O￨- maximise￨L￨VB￨O￨- .￨L￨.￨O￨- +Climate￨U￨NN￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- precipitation￨L￨NN￨O￨- significantly￨L￨RB￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- life￨L￨NN￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A mosquitoes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- thus￨L￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- factors￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- two-patch￨L￨JJ￨O￨- dengue￨L￨NN￨O￨A transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- seasonality￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- patch-specific￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- Aedes￨U￨NNS￨O￨- mosquitoes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- on￨L￨IN￨O￨- Jeju￨U￨NNP￨LOCATION￨- Island￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- humid￨L￨JJ￨O￨- subtropical￨L￨JJ￨O￨- climate￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- warmer￨L￨JJR￨O￨- than￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- in￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- inflow￨L￨NN￨O￨- of￨L￨IN￨O￨- travelers￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- island￨L￨NN￨O￨A has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- increased￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- autochthonous￨L￨JJ￨O￨- dengue￨L￨NN￨O￨- transmission￨L￨NN￨O￨- on￨L￨IN￨O￨- Jeju￨U￨NNP￨LOCATION￨- Island￨U￨NNP￨LOCATION￨- is￨L￨VBZ￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- susceptible-exposed-infectious-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- dengue￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Chen￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Hsieh￨U￨NNP￨PERSON￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- variation￨L￨NN￨O￨- on￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single-strain￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Assuming￨U￨VBG￨O￨- that￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- routine￨L￨JJ￨O￨- RCV￨U￨NN￨O￨- coverage￨L￨NN￨O￨A rates￨L￨NNS￨O￨- will￨L￨MD￨O￨- reflect￨L￨VB￨O￨- current￨L￨JJ￨DATE￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- RCV￨U￨NNP￨O￨- coverage￨L￨NN￨O￨- rates￨L￨NNS￨O￨- will￨L￨MD￨O￨- likely￨L￨RB￨O￨- range￨L￨VB￨O￨- between￨L￨IN￨O￨- 53￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- 96￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- across￨L￨IN￨O￨- Indian￨U￨JJ￨NATIONALITY￨- states￨L￨NNS￨O￨- ’￨L￨POS￨O￨- rural￨L￨JJ￨O￨- and￨L￨CC￨O￨- urban￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- areas￨L￨NNS￨O￨- with￨L￨IN￨O￨- coverage￨L￨NN￨O￨- below￨L￨IN￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- long-and￨L￨JJ￨O￨- short-term￨L￨JJ￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- examining￨L￨VBG￨O￨- childhood￨L￨NN￨O￨- immunisation￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- suggested￨L￨VBN￨O￨- that￨L￨IN￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- RCV￨U￨NN￨O￨- coverage￨L￨NN￨O￨A is￨L￨VBZ￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- long-term￨L￨JJ￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- incidence￨L￨NN￨O￨- post-RCV￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- contexts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- short-term￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- annual￨L￨JJ￨SET￨- )￨L￨-RRB-￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- post-RCV￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨JJ￨O￨- year￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Greece￨U￨NNP￨COUNTRY￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- Costa￨U￨NNP￨COUNTRY￨- Rica￨U￨NNP￨COUNTRY￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- 1998￨L￨CD￨DATE￨- –￨L￨:￨O￨- 99￨L￨CD￨NUMBER￨- rubella￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- both￨L￨DT￨O￨- these￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- followed￨L￨VBD￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- low￨L￨JJ￨O￨- coverage￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- RCV￨U￨NN￨O￨- introduction￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulated￨L￨JJ￨O￨- rubella￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- across￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- vaccination￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- CRS￨U￨NNP￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- mosquito￨L￨NN￨O￨- bites￨L￨VBZ￨O￨A was￨L￨VBD￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- proximity￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- aquatic￨L￨JJ￨O￨- habitats￨L￨NNS￨O￨- of￨L￨IN￨O￨- immature￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- house￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- insecticide￨L￨NN￨O￨- use￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- movements￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- forth￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- individual￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- biting￨L￨VBG￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- mosquito￨L￨NN￨O￨- bites￨L￨VBZ￨O￨A some￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- others￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- human￨L￨JJ￨O￨- sex￨L￨NN￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- pregnancy￨L￨NN￨O￨- ,￨L￨,￨O￨- defensive￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- blood￨L￨NN￨O￨- type￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- odors￨L￨NNS￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- others￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- compartmental-type￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- generally￨L￨RB￨O￨- assumed￨L￨VBD￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- bites￨L￨VBZ￨O￨A of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- can￨L￨MD￨O￨- bite￨L￨VB￨O￨- any￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- equal￨L￨JJ￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- addressed￨L￨VBN￨O￨- using￨L￨VBG￨O￨- meta-population￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨A and/or￨L￨CC￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- sets￨L￨NNS￨O￨A match￨L￨VBP￨O￨- the￨L￨DT￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- ,￨L￨,￨O￨- node￨L￨NN￨O￨- attributes￨L￨NNS￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- GWESP￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- geometrically￨L￨RB￨O￨- weighted￨L￨JJ￨O￨- edgewise￨L￨NN￨O￨- shared￨L￨VBD￨O￨- partner￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- statistic￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- triangles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Faux￨U￨NNP￨ORGANIZATION￨- Magnolia￨U￨NNP￨ORGANIZATION￨- network￨L￨NN￨O￨- matches￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Add￨U￨VB￨O￨- Health￨U￨NNP￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨A ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- triangles￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- ERGM￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- candidate￨L￨NN￨TITLE￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- gives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- observing￨L￨VBG￨O￨A an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- α￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- x￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Networks￨U￨NNP￨O￨- drawn￨L￨VBN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- have￨L￨VBP￨O￨- values￨L￨NNS￨O￨A of￨L￨IN￨O￨- these￨L￨DT￨O￨- statistics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- closely￨L￨RB￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- otherwise￨L￨RB￨O￨- random￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- sets￨L￨NNS￨O￨A are￨L￨VBP￨O￨- generated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- GWESP￨U￨NN￨MISC￨- statistic￨L￨NN￨O￨- ,￨L￨,￨O￨- 0.25￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 0.5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- Bayesian￨U￨JJ￨O￨- fitting￨L￨JJ￨O￨- models￨L￨NNS￨O￨- explore￨L￨VBP￨O￨- an￨L￨DT￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- matches￨L￨VBZ￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- various￨L￨JJ￨O￨- simplifications￨L￨NNS￨O￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- simpler￨L￨JJR￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨A process￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- relatively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- MCMC￨U￨NN￨ORGANIZATION￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- incorporate￨L￨VBP￨O￨- stochasticity￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- observation￨L￨NN￨O￨A ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- variable￨L￨JJ￨O￨- generation-interval￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- not￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- known￨L￨VBN￨O￨- when￨L￨WRB￨O￨- fitting￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- relatively￨L￨RB￨O￨- straightforward￨L￨JJ￨O￨- to￨L￨TO￨O￨- relax￨L￨VB￨O￨- this￨L￨DT￨O￨- assumption￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- finer￨L￨JJR￨TITLE￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- reporting￨L￨VBG￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- in￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- but￨L￨CC￨O￨- fitting￨L￨JJ￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- we￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- explore￨L￨VB￨O￨- these￨L￨DT￨O￨- questions￨L￨NNS￨O￨- here￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- generated￨L￨VBD￨O￨- test￨L￨NN￨O￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- discrete-time￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- observation￨L￨NN￨O￨A process￨L￨NN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- reporting￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- fit￨L￨VBP￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- simulations￨L￨NNS￨O￨- using￨L￨VBG￨O￨- Bayesian￨U￨JJ￨MISC￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- true￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- latent￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- unobserved￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- variable￨L￨NN￨O￨A .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Under￨U￨IN￨O￨- a￨L￨DT￨O￨- favorable￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- cost-saving￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- negative￨L￨JJ￨O￨- incremental￨L￨JJ￨O￨- cost-effective￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- ;￨L￨:￨O￨- ICER￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- costs￨L￨VBZ￨O￨- up￨L￨RP￨O￨- to￨L￨TO￨O￨- US$￨U￨$￨MONEY￨- 6￨L￨CD￨MONEY￨- per￨L￨IN￨O￨- individual￨L￨NN￨O￨- without￨L￨IN￨O￨- herd￨L￨NN￨O￨A immunity￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- US$￨U￨$￨MONEY￨- 4￨L￨CD￨MONEY￨- per￨L￨IN￨O￨- individual￨L￨NN￨O￨- with￨L￨IN￨O￨- 8￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Using￨U￨VBG￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Colombian￨U￨JJ￨NATIONALITY￨- population￨L￨NN￨O￨- setting￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- conducted￨L￨VBD￨O￨- cost-effectiveness￨L￨NN￨O￨- analysis￨L￨NN￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- pre-existing￨L￨JJ￨O￨- herd￨L￨NN￨O￨A immunity￨L￨NN￨O￨A .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Cost-effectiveness￨U￨NN￨MISC￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- Zika￨U￨NNP￨PERSON￨- vaccine￨L￨NN￨O￨- candidate￨L￨NN￨TITLE￨A :￨L￨:￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- for￨L￨IN￨O￨- ColombiaAffan￨U￨NNP￨O￨- Shoukat1￨U￨NN￨O￨- ,￨L￨,￨O￨- Thomas￨U￨NNP￨PERSON￨- Vilches2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Seyed￨U￨NNP￨O￨- M￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- elevated￨L￨JJ￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- arises￨L￨VBZ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- with￨L￨IN￨O￨- either￨L￨CC￨O￨- reproduction￨L￨NN￨O￨- later￨L￨RB￨O￨- in￨L￨IN￨O￨- life￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- a0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- z￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- juveniles￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- reproduce￨L￨VB￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- maturation￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- g0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- z￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a0￨L￨NN￨O￨- and￨L￨CC￨O￨- g0￨L￨NN￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- reproduction￨L￨NN￨O￨- and￨L￨CC￨O￨- maturation￨L￨NN￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- when￨L￨WRB￨O￨- juvenile￨L￨JJ￨O￨- and￨L￨CC￨O￨- adult￨L￨JJ￨O￨A susceptibility￨L￨NN￨O￨- are￨L￨VBP￨O￨- equal￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- high￨L￨JJ￨O￨- when￨L￨WRB￨O￨- hosts￨L￨NNS￨O￨- have￨L￨VBP￨O￨- short￨L￨JJ￨O￨- or￨L￨CC￨O￨- long￨L￨JJ￨O￨- lifespans￨L￨NNS￨O￨- and￨L￨CC￨O￨- low￨L￨JJ￨O￨- or￨L￨CC￨O￨- high￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- reaching￨L￨VBG￨O￨- maturity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- in￨L￨IN￨O￨- between￨L￨IN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- and￨L￨CC￨O￨- mode￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- what￨L￨WP￨O￨- drives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- hosts￨L￨NNS￨O￨- trade-off￨L￨NN￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- with￨L￨IN￨O￨- maturation￨L￨NN￨O￨- or￨L￨CC￨O￨- reproduction￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- adult￨L￨JJ￨O￨A stage￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- growth￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- important￨L￨JJ￨O￨- during￨L￨IN￨O￨- juvenile￨L￨JJ￨O￨- than￨L￨IN￨O￨- during￨L￨IN￨O￨- adult￨L￨JJ￨O￨A stages￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- only￨L￨RB￨O￨- occurs￨L￨VBZ￨O￨- between￨L￨IN￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- maturation/adult￨L￨NN￨O￨- reproduction￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- elevated￨L￨JJ￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- well-mixed￨L￨JJ￨O￨- ,￨L￨,￨O￨- asexual￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- where￨L￨WRB￨O￨- adult￨L￨JJ￨O￨A susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- held￨L￨VBN￨O￨- constant￨L￨JJ￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- far￨L￨RB￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨A could￨L￨MD￨O￨- help￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- make￨L￨VBP￨O￨- judgements￨L￨NNS￨O￨- about￨L￨IN￨O￨- policy￨L￨NN￨O￨- ,￨L￨,￨O￨- infer￨L￨VBP￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- side￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- lies￨L￨VBZ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- track￨L￨VBP￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- towards￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- providing￨L￨VBG￨O￨- early￨L￨JJ￨O￨- warnings￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- away￨L￨RB￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- of￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- external￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- Wiggins￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- written￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨A field￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- overdot￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- derivative￨L￨JJ￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- phase￨L￨NN￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- θ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- explain￨L￨VB￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- challenges￨L￨NNS￨O￨- in￨L￨IN￨O￨- further￨L￨JJ￨O￨- developing￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- make￨L￨VB￨O￨- reference￨L￨NN￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- elements￨L￨NNS￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- 's￨L￨POS￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- arises￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- case￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvalues￨L￨NNS￨O￨A of￨L￨IN￨O￨- F￨U￨NN￨O￨- are￨L￨VBP￨O￨- continuous￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- θ￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- none￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvalues￨L￨NNS￨O￨- have￨L￨VBP￨O￨- zero￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- potentially￨L￨RB￨O￨- robust￨L￨JJ￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- slowing￨L￨VBG￨O￨- down￨L￨RB￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- 's￨L￨POS￨O￨- dynamics￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- approached￨L￨VBN￨O￨- .￨L￨.￨O￨- +Where￨U￨WRB￨O￨- livestock￨L￨NN￨O￨A share￨L￨NN￨O￨- grazing￨L￨NN￨O￨- land￨L￨NN￨O￨- with￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- border￨L￨NN￨O￨- of￨L￨IN￨O￨- conservation￨L￨NN￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- parasite￨L￨JJ￨O￨- species￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- both￨L￨CC￨O￨- wild￨L￨JJ￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨- in￨L￨IN￨O￨- livestock￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- parasites￨L￨NNS￨O￨- in￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- through￨L￨IN￨O￨- spillover￨L￨NN￨O￨- between￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- arid￨L￨JJ￨O￨- and￨L￨CC￨O￨- semi‐arid￨L￨JJ￨O￨- ecosystems￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- this￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- rainfall￨L￨NNS￨O￨- limits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- survival￨L￨NN￨O￨- and￨L￨CC￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- free‐living￨L￨VBG￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- worms￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- also￨L￨RB￨O￨- driving￨L￨VBG￨O￨- seasonal￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- potential￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨A diversity￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- migration￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- concentration￨L￨NN￨O￨- of￨L￨IN￨O￨- grazers￨L￨NNS￨O￨- around￨L￨IN￨O￨- seasonally￨L￨RB￨O￨- scarce￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- parasite￨L￨NN￨O￨- infects￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- six￨L￨CD￨NUMBER￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- ungulate￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- area￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- of￨L￨IN￨O￨- livestock￨L￨NN￨O￨A locally￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Gastrointestinal￨U￨JJ￨O￨- nematodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- worms￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- production￨L￨NN￨O￨- and￨L￨CC￨O￨- fitness￨L￨NN￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- ungulate￨L￨JJ￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- domestic￨L￨JJ￨O￨A populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Predictive￨U￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- offer￨L￨VBP￨O￨A a￨L￨DT￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- effective￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- use￨L￨NN￨O￨- is￨L￨VBZ￨O￨- growing￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Meanwhile￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- was￨L￨VBD￨O￨- initially￨L￨RB￨O￨- mainly￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- already￨L￨RB￨O￨- detected￨L￨VBN￨O￨- as￨L￨IN￨O￨- infected￨L￨VBN￨O￨- in￨L￨IN￨O￨- Corsica￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- areas￨L￨NNS￨O￨- surrounding￨L￨VBG￨O￨- positive￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- sampled￨L￨VBN￨O￨- host￨L￨NN￨TITLE￨- genera￨L￨NN￨O￨- and￨L￨CC￨O￨- sampled￨L￨VBN￨O￨- municipalities￨L￨NNS￨O￨- were￨L￨VBD￨O￨- later￨L￨RB￨O￨- significantly￨L￨RB￨O￨- increased￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- lower￨L￨JJR￨O￨- panel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨JJR￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- X.￨U￨NNP￨MISC￨- fastidiosa￨L￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- highly￨L￨RB￨O￨- diverse￨L￨JJ￨O￨- plant￨L￨NN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- Corsica￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- large￨L￨JJ￨O￨- wild￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- hidden￨L￨JJ￨O￨A compartment/infection￨L￨NN￨O￨- reservoir￨L￨NN￨O￨- hypothesis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- plausible￨L￨JJ￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- and￨L￨CC￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- tested￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- multi‐host￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- settled￨L￨VBN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- environments￨L￨NNS￨O￨- mixing￨L￨VBG￨O￨- cultivated￨L￨VBN￨O￨- ,￨L￨,￨O￨- urban￨L￨JJ￨O￨- and￨L￨CC￨O￨- wild￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- unravelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- underlies￨L￨VBZ￨O￨- observations￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- complicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- hidden￨L￨JJ￨O￨A compartment￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- hosts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- observable￨L￨JJ￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- play￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- reservoir￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- observations￨L￨NNS￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- observable￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- .￨L￨.￨O￨- +fastidiosa￨L￨NN￨O￨- to￨L￨TO￨O￨- invade￨L￨VB￨O￨- new￨L￨JJ￨O￨- environments￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- facilitated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- numerous￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- varying￨L￨VBG￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- range￨L￨NN￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- preference￨L￨NN￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- multi‐host￨L￨JJ￨O￨- nature￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- difficulty￨L￨NN￨O￨- in￨L￨IN￨O￨- observing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- or￨L￨CC￨O￨- symptoms￨L￨NNS￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- other￨L￨JJ￨O￨- disorders￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- water￨L￨NN￨O￨- stress￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- framework￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete‐time￨L￨JJ￨O￨- Susceptible￨U￨NNP￨O￨- –￨L￨:￨O￨- Infected￨U￨JJ￨O￨- –￨L￨:￨O￨- Removed￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- hidden￨L￨JJ￨O￨A compartment￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- surveillance/control￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- and￨L￨CC￨O￨- results￨L￨VBZ￨O￨- A￨U￨DT￨O￨- stochastic￨L￨JJ￨O￨- lattice-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- couples￨L￨VBZ￨O￨- a￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- dispersal￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- susceptible-exposed-infected-recovered￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- environments￨L￨NNS￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- factors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- determinants￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- climate￨L￨NN￨O￨- suitability￨L￨NN￨O￨- ,￨L￨,￨O￨- life￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- population￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Simple￨U￨JJ￨O￨- ,￨L￨,￨O￨- lumped-population￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A prevalence￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- insufficient￨L￨JJ￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- environmental￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- applicability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- capturing￨L￨VBG￨O￨- the￨L￨DT￨O￨- climate-driven￨L￨JJ￨O￨- hydrologic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- variability￨L￨NN￨O￨- on￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- A￨U￨DT￨O￨- stochastic￨L￨JJ￨O￨- lattice-based￨L￨JJ￨O￨- integrated￨L￨VBN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- put￨L￨VBN￨O￨- forward￨L￨RB￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Identifying￨U￨VBG￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- gained￨L￨VBN￨O￨- great￨L￨JJ￨O￨- attention￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- research￨L￨NN￨O￨- community￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A is￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- its￨L￨PRP$￨O￨- position￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- proposed￨L￨VBN￨O￨- K-shell￨U￨NN￨MISC￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- ClusterRank￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- ranking￨L￨NN￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- contagion￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- rich￨L￨JJ￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- ,￨L￨,￨O￨- discontinuous￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hybrid￨L￨NN￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- ,￨L￨,￨O￨- criticality￨L￨NN￨O￨- ,￨L￨,￨O￨- tricriticality￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- double￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- a￨L￨DT￨O￨- double￨L￨JJ￨O￨A phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- showing￨L￨VBG￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- transition￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- following￨L￨VBG￨O￨- discontinuous￨L￨JJ￨O￨- transition￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- adopted￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- double￨L￨JJ￨O￨- transition￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- phase￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- following￨L￨VBG￨O￨- simple￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A become￨L￨VBP￨O￨- adopted￨L￨VBN￨O￨- but￨L￨CC￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- complex￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- remain￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- diagram￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- complex￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A .￨L￨.￨O￨- +With￨U￨IN￨O￨- this￨L￨DT￨O￨- probability￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- simple￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A get￨L￨VB￨O￨- adopted￨L￨VBN￨O￨- and￨L￨CC￨O￨- trigger￨L￨VB￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- manuscript￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- information￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- interactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- meta-paths￨L￨NNS￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Information￨U￨NNP￨O￨- Spread￨U￨NNP￨O￨- and￨L￨CC￨O￨- Topic￨U￨NNP￨O￨- Diffusion￨U￨NNP￨O￨- in￨L￨IN￨O￨- Heterogeneous￨U￨JJ￨O￨- Information￨U￨NN￨O￨- Networks￨U￨NNP￨O￨- Soheila￨U￨NNP￨O￨- Molaei1￨U￨NN￨O￨- ,￨L￨,￨O￨- Sama￨U￨FW￨PERSON￨- Babaei1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Mostafa￨U￨NNP￨PERSON￨- Salehi￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,2￨L￨NN￨O￨- &￨L￨CC￨O￨- Mahdi￨U￨NNP￨TITLE￨- Jalili3￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 9549￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Computer￨U￨NNP￨O￨- scienceInformation￨L￨NN￨O￨- technologyScientific￨L￨JJ￨O￨- data￨L￨NNS￨O￨- AbstractDiffusion￨U￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- largely￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- mainly￨L￨RB￨O￨- addressed￨L￨VBN￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A in￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- consist￨L￨VBP￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A types￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- natural￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccine-derived￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- distinguished￨L￨VBN￨O￨- ,￨L￨,￨O￨- interpreting￨L￨VBG￨O￨- serological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- historical￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- achieved￨L￨VBN￨O￨- both￨L￨CC￨O￨- through￨L￨IN￨O￨- routine￨L￨JJ￨O￨- services￨L￨NNS￨O￨- and￨L￨CC￨O￨- SIAs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- illustrate￨L￨VBP￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- coverage￨L￨NN￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- of￨L￨IN￨O￨- poor￨L￨JJ￨O￨- quality￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- misrepresent￨L￨VB￨O￨- population￨L￨NN￨O￨A immunity￨L￨NN￨O￨A because￨L￨IN￨O￨- most￨L￨JJS￨O￨- countries￨L￨NNS￨O￨- lack￨L￨VBP￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- under￨L￨IN￨O￨- field￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- an￨L￨DT￨O￨- average￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- overestimate￨L￨VB￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- weak￨L￨JJ￨O￨- cold￨L￨JJ￨O￨- chain￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- analytic￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- population￨L￨NN￨O￨A immunity￨L￨NN￨O￨A profiles￨L￨NNS￨O￨- from￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- necessarily￨L￨RB￨O￨- rely￨L￨VBP￨O￨- on￨L￨IN￨O￨- indirect￨L￨JJ￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- direct￨L￨JJ￨O￨- measurement￨L￨NN￨O￨- .￨L￨.￨O￨- +Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- design￨L￨NN￨O￨- ,￨L￨,￨O￨- serological￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- can￨L￨MD￨O￨- reveal￨L￨VB￨O￨- “￨L￨``￨O￨- immunity￨L￨NN￨O￨A gaps￨L￨NNS￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- ie￨L￨FW￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- or￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- below￨L￨IN￨O￨- some￨L￨DT￨O￨- operational￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- identifying￨L￨VBG￨O￨- areas￨L￨NNS￨O￨- for￨L￨IN￨O￨- additional￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Elimination￨U￨NN￨O￨- efforts￨L￨NNS￨O￨- include￨L￨VBP￨O￨- attaining￨L￨NN￨O￨- and￨L￨CC￨O￨- sustaining￨L￨VBG￨O￨- high￨L￨JJ￨O￨- coverage￨L￨NN￨O￨A with￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- dose￨L￨NN￨O￨- of￨L￨IN￨O￨- MCV￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- scaling￨L￨VBG￨O￨- up￨L￨IN￨O￨- of￨L￨IN￨O￨- routine￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- dose￨L￨NN￨O￨- of￨L￨IN￨O￨- MCV￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- RCVs￨U￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- supplemental￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- [￨L￨-LRB-￨O￨- SIAs￨U￨NNS￨O￨- ]￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- campaigns￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- MCV￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- RCV￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- Measles￨U￨NNP￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- these￨L￨DT￨O￨- travellers￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- after￨L￨IN￨O￨- its￨L￨PRP$￨O￨- introduction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Δ￨U￨NN￨O￨- =￨L￨JJ￨O￨- 52￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- bywhere￨L￨JJ￨O￨- σ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potentially￨L￨RB￨O￨- infective￨L￨JJ￨O￨- contact￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- arrived￨L￨VBD￨O￨- at￨L￨IN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- t0￨L￨NN￨O￨- and￨L￨CC￨O￨- remains￨L￨VBZ￨O￨- infective￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- 1weeks￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨A rate￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disease-induced￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- θ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- t0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Heaviside￨U￨NNP￨O￨- step￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- countries￨L￨NNS￨O￨- where￨L￨WRB￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- controlled￨L￨VBN￨O￨- in￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- decades￨L￨NNS￨DURATION￨- are￨L￨VBP￨O￨- reporting￨L￨VBG￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- exotic￨L￨JJ￨O￨- and￨L￨CC￨O￨- frequently￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- spread￨L￨VBN￨O￨- by￨L￨IN￨O￨- infected￨L￨JJ￨O￨- travellers/immigrants￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- recent￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A spreading￨L￨VBG￨O￨- by￨L￨IN￨O￨- travellers￨L￨NNS￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- Zika￨U￨NN￨O￨- virus￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Latin￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- imported￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- French￨U￨JJ￨NATIONALITY￨- Polynesia￨U￨NN￨O￨- by￨L￨IN￨O￨- infected￨L￨JJ￨O￨- travellers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Situations￨U￨NNS￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨A small￨L￨JJ￨O￨A number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- travel￨L￨VBP￨O￨- to￨L￨TO￨O￨- previously￨L￨RB￨DATE￨- disease-free￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- critical￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- b￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- p￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- β1￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- EV71￨U￨NN￨O￨- ;￨L￨:￨O￨- β2￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- CVA16￨U￨NN￨O￨- ;￨L￨:￨O￨- μ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- α￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- per-capita￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨- from￨L￨IN￨O￨- latent￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- q￨L￨JJ￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- EV71￨U￨NN￨O￨- from￨L￨IN￨O￨- latent￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- accordingly￨L￨RB￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- q￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- CVA16￨U￨NN￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- human￨L￨JJ￨O￨- enteroviruses￨L￨NNS￨O￨- serotypes￨L￨NNS￨O￨- from￨L￨IN￨O￨- latent￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- d1￨L￨NN￨O￨- ,￨L￨,￨O￨- d2￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- induced￨L￨VBD￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- I1￨U￨NN￨O￨- ,￨L￨,￨O￨- I2￨U￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- γ1￨L￨NN￨O￨- ,￨L￨,￨O￨- γ2￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- I1￨U￨NN￨O￨- ,￨L￨,￨O￨- I2￨U￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- ω￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- η1￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- η2￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- controls￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A coefficient￨L￨NN￨O￨A β￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- byIt￨L￨NN￨O￨- is￨L￨VBZ￨O￨- clear￨L￨JJ￨O￨- thatwhich￨L￨NN￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- have￨L￨VBP￨O￨- contributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- decrease￨L￨VB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibria￨L￨NNS￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A of￨L￨IN￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- the￨L￨DT￨O￨- Lyapunov￨U￨NN￨MISC￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨A bounded￨L￨VBN￨O￨- feasible￨L￨JJ￨O￨- region￨L￨NN￨O￨- :￨L￨:￨O￨- Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- may￨L￨MD￨O￨- reduce￨L￨VB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equivalent￨L￨JJ￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- Λ￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- b￨L￨NN￨O￨- +￨L￨CC￨O￨- pbη1￨L￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- +￨L￨CC￨O￨- η1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- positively￨L￨RB￨O￨- invariant￨L￨JJ￨O￨- setIn￨L￨NN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- discuss￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +Directly￨U￨RB￨O￨- calculating￨L￨VBG￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A P0￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S0￨U￨NN￨O￨- ,￨L￨,￨O￨- E0￨U￨NN￨O￨- ,￨L￨,￨O￨- I0￨U￨NN￨O￨- ,￨L￨,￨O￨- T0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- S0￨U￨NN￨O￨- =￨L￨JJ￨O￨- Λ￨U￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- E0￨U￨NN￨O￨- =￨L￨JJ￨O￨- I0￨U￨NN￨O￨- =￨L￨JJ￨O￨- T0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A of￨L￨IN￨O￨- collective￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- local￨L￨JJ￨O￨- perturbations￨L￨NNS￨O￨- trigger￨L￨VBP￨O￨- global￨L￨JJ￨O￨- activity￨L￨NN￨O￨- cascades￨L￨NNS￨O￨- that￨L￨WDT￨O￨- propagate￨L￨VB￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- linear￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Mišić￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,￨L￨,￨O￨- 2015￨L￨CD￨DATE￨- ;￨L￨:￨O￨- O￨U￨NN￨O￨- ’￨L￨''￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- diffusion￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- statistical￨L￨JJ￨O￨- associations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- functional￨L￨JJ￨O￨A connectivity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- distributed￨L￨VBN￨O￨- areas￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Goñi￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,￨L￨,￨O￨- 2013￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- functional￨L￨JJ￨O￨- brain￨L￨NN￨O￨- networks￨L￨NNS￨O￨- into￨L￨IN￨O￨- coherent￨L￨JJ￨O￨- modules￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- R￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- biological￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨- develops￨L￨VBZ￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- cascade￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- two￨L￨CD￨NUMBER￨- signals￨L￨NNS￨O￨A synergistically￨L￨RB￨O￨- spread￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- two￨L￨CD￨NUMBER￨- signals￨L￨NNS￨O￨- ,￨L￨,￨O￨- endowed￨L￨JJ￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- content￨L￨NN￨O￨- ,￨L￨,￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- ultimately￨L￨RB￨O￨- integrate￨L￨VB￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- report￨L￨NN￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- integration￨L￨NN￨O￨- of￨L￨IN￨O￨- neural￨L￨JJ￨O￨- signals￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- mesoscale￨L￨NN￨O￨- Drosophila￨U￨FW￨O￨- connectome￨L￨FW￨O￨- ,￨L￨,￨O￨- previously￨L￨RB￨DATE￨- reconstructed￨L￨VBN￨O￨- from￨L￨IN￨O￨- 12,995￨L￨CD￨NUMBER￨- images￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- neurons￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +IBMs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- well-suited￨L￨JJ￨O￨- for￨L￨IN￨O￨- creating￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨- and￨L￨CC￨O￨- studying￨L￨VBG￨O￨- intervention￨L￨NN￨O￨- impact￨L￨NN￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- allow￨L￨VBP￨O￨- for￨L￨IN￨O￨- attributes￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- added￨L￨VBN￨O￨- to￨L￨TO￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- environments￨L￨NNS￨O￨- without￨L￨IN￨O￨- exponentially￨L￨RB￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- items￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- compartments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- tracked￨L￨VBN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- making￨L￨VBG￨O￨- the￨L￨DT￨O￨- code￨L￨NN￨O￨- and￨L￨CC￨O￨- documentation￨L￨NN￨O￨- openly￨L￨RB￨O￨- available￨L￨JJ￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- team￨L￨NN￨O￨- hopes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- enable￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- researchers￨L￨NNS￨O￨- ,￨L￨,￨O￨- policy-makers￨L￨NNS￨O￨- ,￨L￨,￨O￨- implementers￨L￨NNS￨O￨- and￨L￨CC￨O￨- funders￨L￨NNS￨O￨- to￨L￨TO￨O￨- access￨L￨NN￨O￨- modeling￨L￨NN￨O￨- software￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- staffing￨L￨NN￨O￨- more￨L￨RBR￨O￨- commonly￨L￨RB￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- academic￨L￨JJ￨O￨- and￨L￨CC￨O￨- similar￨L￨JJ￨O￨- organizations￨L￨NNS￨O￨- .￨L￨.￨O￨- +IBMs￨U￨NNS￨O￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- or￨L￨CC￨O￨- micro-simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- use￨L￨VBP￨O￨- computer￨L￨NN￨O￨- simulation￨L￨NN￨O￨- to￨L￨TO￨O￨- track￨L￨VB￨O￨- interacting￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- environment￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- summarize￨L￨VBP￨O￨- the￨L￨DT￨O￨- decade-long￨L￨JJ￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- freely￨L￨RB￨O￨- available￨L￨JJ￨O￨A individual-based￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- EMOD￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- expanded￨L￨VBN￨O￨- beyond￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- other￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- share￨L￨VBP￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- gives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- flexibility￨L￨NN￨O￨- to￨L￨TO￨O￨- add￨L￨VB￨O￨- demographic￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- flexibility￨L￨NN￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- transmission￨L￨NN￨O￨- might￨L￨MD￨O￨- occur￨L￨VB￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- still￨L￨RB￨O￨- preserving￨L￨VBG￨O￨- SEIRS￨U￨NNP￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- internal￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +falciparum￨L￨NN￨O￨A prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- strains￨L￨NNS￨O￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- artemisinin-resistance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- k13￨L￨NN￨O￨- mutation￨L￨NN￨O￨- plus￨L￨CC￨O￨- a￨L￨DT￨O￨- slow￨L￨JJ￨O￨- clearing￨L￨NN￨O￨- phenotype￨L￨NN￨O￨- ,￨L￨,￨O￨- henceforth￨L￨NN￨O￨- ‘￨L￨``￨O￨- mutants￨L￨NNS￨O￨- ’￨L￨POS￨O￨- )￨L￨-RRB-￨O￨- until￨L￨IN￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨ORGANIZATION￨- criteria￨L￨NNS￨O￨- of￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨- partial￨L￨JJ￨O￨- artemisinin￨L￨NN￨O￨- resistance￨L￨NN￨O￨- is￨L￨VBZ￨O￨- met￨L￨VBN￨O￨- .￨L￨.￨O￨- +falciparum￨L￨NN￨O￨A prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- exposure-acquired￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- time-to-emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- artemisinin￨L￨NN￨O￨- resistance￨L￨NN￨O￨- .￨L￨.￨O￨- +I.￨U￨NN￨O￨- Fowkes1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 17:279￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Artemisinin-resistant￨U￨JJ￨O￨- Plasmodium￨U￨NN￨O￨- falciparum￨L￨NN￨O￨A has￨L￨VBZ￨O￨- emerged￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Greater￨U￨NNP￨LOCATION￨- Mekong￨U￨NNP￨LOCATION￨- Subregion￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- has￨L￨VBZ￨O￨- yet￨L￨RB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- immense￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- to￨L￨TO￨O￨- systematically￨L￨RB￨O￨- investigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- disparities￨L￨NNS￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- overall￨L￨JJ￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- via￨L￨IN￨O￨- metrics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- inoculation￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- vectorial￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- forth￨L￨RB￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemiology￨L￨NN￨O￨A of￨L￨IN￨O￨- CL￨U￨NN￨O￨- is￨L￨VBZ￨O￨- complex￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- intraand￨L￨JJ￨O￨- inter-specific￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- ,￨L￨,￨O￨- reservoir￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- sandfly￨L￨RB￨O￨- vectors￨L￨NNS￨O￨- ,￨L￨,￨O￨- clinical￨L￨JJ￨O￨- manifestations￨L￨NNS￨O￨- and￨L￨CC￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- therapy￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- multiple￨L￨JJ￨O￨- circulating￨L￨VBG￨O￨- Leishmania￨U￨NNP￨O￨- species￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- geographical￨L￨JJ￨O￨- area￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- 20￨L￨CD￨NUMBER￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- was￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Madrid￨U￨NNP￨CITY￨- autonomous￨L￨JJ￨O￨A community￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- around￨L￨RB￨O￨- 0.5￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- 100,000￨L￨CD￨NUMBER￨- inhabitants￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Leishmaniasis￨U￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨A in￨L￨IN￨O￨- Colombia￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- Colombia￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- America￨U￨NNP￨COUNTRY￨- region￨L￨NN￨O￨- with￨L￨IN￨O￨- highest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- supplement￨L￨VB￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨A with￨L￨IN￨O￨- more￨L￨JJR￨O￨- up-to-date￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- nowcast￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- provide￨L￨VBP￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- incidence￨L￨NN￨O￨- during￨L￨IN￨O￨- more￨L￨RBR￨O￨- recent￨L￨JJ￨DURATION￨- weeks￨L￨NNS￨DURATION￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- available￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- forecast￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- using￨L￨VBG￨O￨- online￨L￨JJ￨O￨- search￨L￨NN￨O￨- trends￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- twitter￨L￨NN￨O￨- feeds￨L￨VBZ￨O￨- [￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- access￨L￨NN￨O￨- logs￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza-related￨L￨JJ￨O￨- webpages￨L￨NNS￨O￨- at￨L￨IN￨O￨- Wikipedia￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- online￨L￨JJ￨O￨- news￨L￨NN￨O￨- and￨L￨CC￨O￨- informal￨L￨JJ￨O￨- reports￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- electronic￨L￨JJ￨O￨- health￨L￨NN￨O￨- records￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- methods￨L￨NNS￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- model-inference￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- super-ensemble￨L￨NN￨O￨- of￨L￨IN￨O￨- eight￨L￨CD￨NUMBER￨- statistical￨L￨JJ￨O￨- and￨L￨CC￨O￨- mechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- —￨L￨:￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2017￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- point￨L￨NN￨O￨- and￨L￨CC￨O￨- probabilistic￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨A in￨L￨IN￨O￨- real￨L￨JJ￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- FluSight￨U￨NN￨O￨- competition￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compare￨L￨VBP￨O￨- and￨L￨CC￨O￨- report￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- seven￨L￨CD￨NUMBER￨- targets￨L￨NNS￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- evaluated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- measures￨L￨NNS￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- logarithmic￨L￨JJ￨O￨- scoring￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- absolute￨L￨JJ￨O￨- error￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- forecasts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2014￨L￨CD￨DATE￨- season￨L￨NN￨O￨- ,￨L￨,￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- 's￨L￨POS￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- Division￨U￨NNP￨MISC￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- coordinating￨L￨VBG￨O￨- with￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- groups￨L￨NNS￨O￨- to￨L￨TO￨O￨- assemble￨L￨VB￨O￨- real-time￨L￨JJ￨O￨- weekly￨L￨JJ￨SET￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecasts￨L￨NNS￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨ORGANIZATION￨- National￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Human￨U￨NNP￨ORGANIZATION￨- Services￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- HHS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- regional￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- measure￨L￨VBP￨O￨- the￨L￨DT￨O￨- improvement￨L￨NN￨O￨- in￨L￨IN￨O￨- forecast￨L￨NN￨O￨- accuracy￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- nowcasts￨L￨NNS￨O￨- as￨L￨IN￨O￨- supplements￨L￨NNS￨O￨- to￨L￨TO￨O￨- near￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- ILI￨U￨NN￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulated￨L￨JJ￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- decision-making￨L￨NN￨O￨- by￨L￨IN￨O￨- fitting￨L￨NN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- confirmed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- herd-level￨L￨NN￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- at￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨- intervals￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- historical￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- foot-and-mouth￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- FMD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- economically￨L￨RB￨O￨- important￨L￨JJ￨O￨- livestock￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- forward￨L￨RB￨O￨A simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- culling￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- management￨L￨NN￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- total￨L￨JJ￨O￨- culls￨L￨NNS￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- disease-freedom￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- outlined￨L￨VBN￨O￨- frameworks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- combine￨L￨VBP￨O￨- Bayesian￨U￨JJ￨MISC￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- generating￨L￨VBG￨O￨- real-time￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- severity￨L￨NN￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- aiming￨L￨VBG￨O￨- to￨L￨TO￨O￨- assimilate￨L￨VB￨O￨- available￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- into￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- estimates￨L￨NNS￨O￨A as￨L￨IN￨O￨- rapidly￨L￨RB￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Forward￨U￨RB￨O￨- simulations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- therefore￨L￨RB￨O￨- conditional￨L￨JJ￨O￨- upon￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨A state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- inferred￨L￨VBN￨O￨- ,￨L￨,￨O￨- undetected￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- having￨L￨VBG￨O￨- enacted￨L￨VBN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- controls￨L￨NNS￨O￨- until￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- question￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- become￨L￨VBP￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- improve￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- manner￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unfolding￨L￨VBG￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- estimates￨L￨NNS￨O￨A of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- where￨L￨WRB￨O￨- likely￨L￨JJ￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- located￨L￨JJ￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- but￨L￨CC￨O￨- undetected￨L￨JJ￨O￨- farms￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- repeated￨L￨VBD￨O￨- these￨L￨DT￨O￨- forward￨L￨RB￨O￨A simulations￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- point￨L￨NN￨O￨- using￨L￨VBG￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- fitted￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- we￨L￨PRP￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- done￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- we￨L￨PRP￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- done￨L￨VBN￨O￨- in￨L￨IN￨O￨- retrospect￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- variations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨A abundance￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- running￨L￨VBG￨O￨- computer￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- CA￨U￨NNP￨STATE_OR_PROVINCE￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- cell￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- CA￨U￨NNP￨STATE_OR_PROVINCE￨- lattice￨L￨NN￨O￨A is￨L￨VBZ￨O￨- occupied￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- individual￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- cell￨L￨NN￨O￨- there￨L￨EX￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- S-individual￨U￨JJ￨MISC￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- P￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- v￨L￨LS￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- eight￨L￨CD￨NUMBER￨- surrounding￨L￨VBG￨O￨- neighbors￨L￨NNS￨O￨A and￨L￨CC￨O￨- η￨L￨NN￨O￨- is￨L￨VBZ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- I-neighbors￨U￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- CA￨U￨NNP￨STATE_OR_PROVINCE￨- lattice￨L￨NN￨O￨A is￨L￨VBZ￨O￨- V￨U￨NN￨O￨- =￨L￨JJ￨O￨- ∑￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- ultimate￨L￨JJ￨O￨- elimination￨L￨NN￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- merely￨L￨RB￨O￨- marginal￨L￨JJ￨O￨- declines￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- philanthropic￨L￨JJ￨O￨- funders￨L￨NNS￨O￨- ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- others￨L￨NNS￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- better￨L￨RBR￨O￨- armed￨L￨VBN￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- justify￨L￨VB￨O￨- and￨L￨CC￨O￨- target￨L￨VB￨O￨- efforts￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- longest￨L￨JJS￨O￨- last￨L￨JJ￨O￨- mile￨L￨NN￨O￨- ,￨L￨,￨O￨- ”￨L￨''￨O￨- especially￨L￨RB￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- tipping￨L￨JJ￨O￨- point￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- crossed￨L￨VBN￨O￨- and￨L￨CC￨O￨- all￨L￨PDT￨O￨- that￨L￨DT￨O￨- remains￨L￨VBZ￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- sustain￨L￨VB￨O￨- the￨L￨DT￨O￨- gains￨L￨NNS￨O￨- already￨L￨RB￨O￨- achieved￨L￨VBN￨O￨- and￨L￨CC￨O￨- allow￨L￨VB￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- run￨L￨VB￨O￨- its￨L￨PRP$￨O￨- course￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- has￨L￨VBZ￨O￨- already￨L￨RB￨O￨- been￨L￨VBN￨O￨- crossed￨L￨VBN￨O￨- ,￨L￨,￨O￨- elimination￨L￨NN￨O￨A only￨L￨RB￨O￨- requires￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- policy￨L￨NN￨O￨- be￨L￨VB￨O￨- maintained￨L￨VBN￨O￨- while￨L￨IN￨O￨- transient￨L￨JJ￨O￨- chains￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- allowed￨L￨VBN￨O￨- to￨L￨TO￨O￨- peter￨L￨VB￨O￨- out￨L￨RP￨O￨- ;￨L￨:￨O￨- alternatively￨L￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- near￨L￨IN￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- crossed￨L￨VBN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- increases￨L￨VBZ￨O￨- in￨L￨IN￨O￨- effort￨L￨NN￨O￨- or￨L￨CC￨O￨- pulse￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- supplementary￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- push￨L￨VB￨O￨- the￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- process￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- tipping￨L￨JJ￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- not￨L￨RB￨O￨- all￨L￨DT￨O￨- switching￨L￨NN￨O￨- among￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- states￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- preceded￨L￨VBN￨O￨- by￨L￨IN￨O￨- leading￨L￨VBG￨O￨- indicators￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transcritical￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨- that￨L￨WDT￨O￨- occurs￨L￨VBZ￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- elimination￨L￨NN￨O￨A does￨L￨VBZ￨O￨- ,￨L￨,￨O￨- implying￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- will￨L￨MD￨O￨- contain￨L￨VB￨O￨- statistical￨L￨JJ￨O￨- signatures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- elimination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- indicators￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- critical￨L￨JJ￨O￨- slowing￨L￨VBG￨O￨- down￨L￨RP￨O￨- may￨L￨MD￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- means￨L￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- how￨L￨WRB￨O￨- successful￨L￨JJ￨O￨- elimination￨L￨NN￨O￨A efforts￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- by￨L￨IN￨O￨- indicating￨L￨VBG￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- tipping￨L￨JJ￨O￨- point￨L￨NN￨O￨- has￨L￨VBZ￨O￨- already￨L￨RB￨O￨- been￨L￨VBN￨O￨- crossed￨L￨VBN￨O￨- or￨L￨CC￨O￨- is￨L￨VBZ￨O￨- close￨L￨RB￨O￨- at￨L￨IN￨O￨- hand￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- endemism￨L￨NN￨O￨- and￨L￨CC￨O￨- disease-free￨L￨JJ￨O￨- status￨L￨NN￨O￨- are￨L￨VBP￨O￨- alternative￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- threshold￨L￨NN￨O￨- acting￨L￨VBG￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- tipping￨L￨JJ￨O￨- point￨L￨NN￨O￨A between￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- question￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨A leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- successful￨L￨JJ￨O￨- promotion￨L￨NN￨O￨- campaign.Up￨L￨NN￨O￨- to￨L￨TO￨O￨- now￨L￨RB￨DATE￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- were￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- for￨L￨IN￨O￨- ranking￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- identifying￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- spreading￨L￨NN￨O￨- ability￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 09￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Identification￨U￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- HybridRank￨U￨NNP￨O￨- algorithm￨L￨NN￨O￨- Sara￨U￨NNP￨O￨- Ahajjam1￨U￨NNP￨O￨- &￨L￨CC￨O￨- Hassan￨U￨NNP￨O￨- Badir1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 11932￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Computer￨U￨NNP￨O￨- scienceEngineering￨L￨VBG￨O￨- AbstractIdentifying￨U￨VBG￨O￨- the￨L￨DT￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- who￨L￨WP￨O￨- is￨L￨VBZ￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- maximization￨L￨NN￨O￨- through￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- paper￨L￨NN￨O￨- of￨L￨IN￨O￨- Lü￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 6￨L￨CD￨NUMBER￨- reviewed￨L￨VBN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- art￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- proposed￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- approaches￨L￨NNS￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- vital￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- HybridRank￨U￨NNP￨O￨- algorithm￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- hybrid￨L￨NN￨O￨- centrality￨L￨NN￨O￨- measure￨L￨NN￨O￨- for￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨A using￨L￨VBG￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Kitsak￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 7￨L￨CD￨NUMBER￨- put￨L￨VBD￨O￨- forward￨L￨RB￨O￨- a￨L￨DT￨O￨- fast￨L￨JJ￨O￨- node￨L￨NN￨O￨- ranking￨L￨NN￨O￨A method￨L￨NN￨O￨- called￨L￨VBN￨O￨- k-shell￨L￨JJ￨O￨- decomposition￨L￨NN￨O￨- for￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- computational￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- global￨L￨JJ￨O￨- mass￨L￨NN￨O￨- gatherings￨L￨NNS￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- modelling￨L￨NN￨O￨- study￨L￨NN￨O￨- provided￨L￨VBD￨O￨- important￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- support￨L￨NN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- decision￨L￨NN￨O￨- making￨L￨VBG￨O￨- during￨L￨IN￨O￨- school￨L￨NN￨O￨A outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- school-based￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- programme￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- among￨L￨IN￨O￨- school￨L￨NN￨O￨A children￨L￨NNS￨O￨- in￨L￨IN￨O￨- Shenzhen￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- school-based￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- intervention￨L￨NN￨O￨- .￨L￨.￨O￨- +Panel￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- simulation￨L￨NN￨O￨- results￨L￨VBZ￨O￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- threshold￨L￨NN￨O￨- set￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 10￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- week￨L￨NN￨DURATION￨- per￨L￨IN￨O￨- school￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- presentation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- patient￨L￨NN￨O￨A infectious￨L￨JJ￨O￨- with￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- ED￨U￨NNP￨O￨- in￨L￨IN￨O￨- Dallas￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Texas￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 180￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- hospital￨L￨NN￨O￨- personnel￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- were￨L￨VBD￨O￨- in￨L￨IN￨O￨- close￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- this￨L￨DT￨O￨- patient￨L￨NN￨O￨- or￨L￨CC￨O￨- with￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- nurses￨L￨NNS￨O￨- who￨L￨WP￨O￨- became￨L￨VBD￨O￨- infected￨L￨JJ￨O￨- after￨L￨IN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- patient￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- implemented￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observed￨L￨VBD￨O￨- 293,181￨L￨CD￨NUMBER￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- 4,732￨L￨CD￨NUMBER￨- patient￨L￨NN￨O￨A and￨L￨CC￨O￨- 85￨L￨CD￨NUMBER￨- staff￨L￨NN￨O￨- participants￨L￨NNS￨O￨- during￨L￨IN￨O￨- 81￨L￨CD￨NUMBER￨- shifts￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- (￨L￨-LRB-￨O￨- July￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2009￨L￨CD￨DATE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- June￨U￨NNP￨DATE￨- 30￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- objectives￨L￨NNS￨O￨- were￨L￨VBD￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risks￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- contacts￨L￨NNS￨O￨A and￨L￨CC￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- individual￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- differential￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- the￨L￨DT￨O￨- social-contact￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ED￨U￨NNP￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- 12-hour￨L￨JJ￨DURATION￨- shift￨L￨NN￨O￨A .￨L￨.￨O￨- +Susceptible￨U￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- time-and￨L￨JJ￨O￨- age-dependent￨L￨JJ￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- i￨L￨FW￨O￨- denote￨L￨FW￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- age￨L￨NN￨O￨A ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 89￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- age￨L￨NN￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- j￨L￨NN￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- C￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- matrix￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- i￨L￨FW￨O￨- with￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- j￨L￨NN￨O￨- ;￨L￨:￨O￨- finally￨L￨RB￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- hypothesis￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- age-independent￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- proportionality￨L￨NN￨O￨- factor￨L￨NN￨O￨- driving￨L￨VBG￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- contacts￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- where￨L￨WRB￨O￨- This￨U￨DT￨O￨- simple￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- accounts￨L￨NNS￨O￨- for￨L￨IN￨O￨- linear￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- below￨L￨IN￨O￨- 3￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨A and￨L￨CC￨O￨- aims￨L￨VBZ￨O￨- at￨L￨IN￨O￨- illustrating￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- attendance￨L￨NN￨O￨- at￨L￨IN￨O￨- day-care￨L￨NN￨O￨- centers￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- hypothesized￨L￨VBN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- young￨L￨JJ￨O￨- ages￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- ascribable￨L￨JJ￨O￨- to￨L￨TO￨O￨- increased￨L￨VBN￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- age￨L￨NN￨O￨A groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- possibly￨L￨RB￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- inclusion￨L￨NN￨O￨- in￨L￨IN￨O￨- nurseries￨L￨NNS￨O￨- or￨L￨CC￨O￨- day-care￨L￨JJ￨O￨- centers￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- model￨L￨NN￨TITLE￨- M1￨U￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨A i￨L￨FW￨O￨- with￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- j￨L￨NN￨O￨- is￨L￨VBZ￨O￨- computed￨L￨VBN￨O￨- as￨L￨IN￨O￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Where￨U￨WRB￨O￨- measles￨L￨VBZ￨O￨A is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- extinct￨L￨JJ￨O￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- susceptibility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- high￨L￨JJ￨O￨- ,￨L￨,￨O￨- generally￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- accumulation￨L￨NN￨O￨- of￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- births￨L￨NNS￨O￨- ,￨L￨,￨O￨- outbreak￨L￨NN￨O￨- risk￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- shaped￨L￨VBN￨O￨- by￨L￨IN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- human￨L￨JJ￨O￨- travel￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- characterise￨L￨VB￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- anticipate￨L￨VB￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A spatial￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- existing￨L￨VBG￨O￨- data-streams￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- attempt￨L￨VBP￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2013￨L￨CD￨DATE￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- our￨L￨PRP$￨O￨- prediction￨L￨NN￨O￨- by￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- estimated￨L￨VBN￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- risk￨L￨NN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- observed￨L￨VBN￨O￨- via￨L￨IN￨O￨- available￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Settings￨U￨NNS￨O￨- with￨L￨IN￨O￨- sufficiently￨L￨RB￨O￨- detailed￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- pre-vaccination￨L￨JJ￨O￨- allow￨L￨VBP￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- another￨L￨DT￨O￨- important￨L￨JJ￨O￨- variable￨L￨NN￨O￨- for￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- connectivity￨L￨NN￨O￨- underpinning￨L￨VBG￨O￨- re-introduction￨L￨NN￨O￨- events￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Pakistan￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- country￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- >￨L￨JJR￨O￨- 185￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- mobile￨L￨JJ￨TITLE￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- birth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- 31￨L￨CD￨NUMBER￨- births￨L￨NNS￨O￨- per￨L￨IN￨O￨- 1000￨L￨CD￨DATE￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- substantial￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Supplementary￨U￨NNP￨O￨- Information￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- health￨L￨NN￨O￨- system￨L￨NN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- quality￨L￨NN￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- the￨L￨DT￨O￨- landscape￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- remains￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨A can￨L￨MD￨O￨- provide￨L￨VB￨O￨- broad￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- arbovirus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- cross-sectional￨L￨JJ￨O￨- serosurveys￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- contemporary￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- characterising￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- cohort-based￨L￨JJ￨O￨- seroepidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- in￨L￨IN￨O￨- island￨L￨NN￨O￨- settings￨L￨NNS￨O￨- where￨L￨WRB￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infrequent￨L￨JJ￨O￨- and￨L￨CC￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- tested￨L￨VBD￨O￨- the￨L￨DT￨O￨- paired￨L￨JJ￨O￨- samples￨L￨NNS￨O￨A for￨L￨IN￨O￨- anti-DENV￨L￨JJ￨O￨- IgG￨U￨NN￨O￨- antibodies￨L￨NNS￨O￨- using￨L￨VBG￨O￨- ELISA￨U￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- recombinant￨L￨JJ￨O￨- antigen-based￨L￨JJ￨O￨- microsphere￨L￨NN￨O￨- immunoassay￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MIA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- combined￨L￨VBN￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- possible￨L￨JJ￨O￨- explanations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨A caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- DENV-3￨U￨NN￨MISC￨- occurred￨L￨VBD￨O￨- in￨L￨IN￨O￨- Fiji￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 25,000￨L￨CD￨NUMBER￨- suspected￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- reported￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NNP￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- followed￨L￨VBD￨O￨- up￨L￨RP￨O￨- participants￨L￨NNS￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- survey￨L￨NN￨O￨- in￨L￨IN￨O￨- Central￨U￨NNP￨ORGANIZATION￨- Division￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- paired￨L￨JJ￨O￨- pre-and￨L￨JJ￨O￨- post-outbreak￨L￨JJ￨O￨- serological￨L￨JJ￨O￨- samples￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Materials￨U￨NNPS￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Compared￨U￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- 314,437￨L￨CD￨NUMBER￨- fewer￨L￨JJR￨O￨- cases￨L￨NNS￨O￨- occurred￨L￨VBD￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- simulated￨L￨JJ￨O￨- vector￨L￨NN￨O￨A control￨L￨NN￨O￨A only￨L￨RB￨O￨- in￨L￨IN￨O￨- 301￨L￨CD￨NUMBER￨- municipalities￨L￨NNS￨O￨- that￨L￨WDT￨O￨- had￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- reported￨L￨VBN￨O￨- DENV￨U￨NN￨O￨- ,￨L￨,￨O￨- illustrating￨L￨VBG￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- previous￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- ,￨L￨,￨O￨- data-driven￨L￨JJ￨O￨- ,￨L￨,￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- CHIKV￨U￨NN￨O￨- mitigation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- previous￨L￨JJ￨O￨- DENV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +van￨L￨NN￨O￨- Panhuis￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,7￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 12201￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Computational￨U￨NNP￨O￨- modelsInfectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- AbstractNew￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- emerge￨L￨VB￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- illustrated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨- virus￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- Latin￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- explored￨L￨VBD￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- about￨L￨IN￨O￨- previous￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DENV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- CHIKV￨U￨NNP￨O￨- mitigation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- vector￨L￨NN￨O￨A control￨L￨NN￨O￨A in￨L￨IN￨O￨- all￨L￨DT￨O￨- 521￨L￨CD￨NUMBER￨- municipalities￨L￨NNS￨O￨- with￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- populations￨L￨NNS￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- 402,940￨L￨CD￨NUMBER￨- fewer￨L￨JJR￨O￨- clinical￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- CHIKV￨U￨NN￨ORGANIZATION￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- baseline￨L￨NN￨O￨- scenario￨L￨NN￨O￨- without￨L￨IN￨O￨- intervention￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- temporal-network￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- measured￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- component￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- lifetime￨L￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- temporal-network￨L￨JJ￨O￨- percolation￨L￨NN￨O￨- has￨L￨VBZ￨O￨- strong￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- to￨L￨TO￨O￨- directed￨L￨VBN￨O￨- percolation.Weighted￨L￨JJ￨O￨- event￨L￨NN￨O￨- graphs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- static￨L￨JJ￨O￨- ,￨L￨,￨O￨- weighted￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- directed￨L￨VBD￨O￨- acyclic￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- DAGs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- encapsulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- δt-constrained￨L￨JJ￨O￨- time-respecting￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- δt￨L￨NN￨O￨- simultaneously￨L￨RB￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Mapping￨U￨NN￨O￨- temporal-network￨L￨NN￨O￨- percolation￨L￨NN￨O￨A to￨L￨TO￨O￨- weighted￨L￨JJ￨O￨- ,￨L￨,￨O￨- static￨L￨JJ￨O￨- event￨L￨NN￨O￨- graphs￨L￨NNS￨O￨- Mikko￨U￨NNP￨PERSON￨- Kivelä1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jordan￨U￨NNP￨CITY￨- Cambe2￨U￨NNP￨O￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jari￨U￨NNP￨PERSON￨- Saramäki1￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Márton￨U￨NNP￨O￨- Karsai2￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 12357￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- sciencePhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractThe￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- diffusion-like￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- correlations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- very￨L￨RB￨O￨- low￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- δt￨L￨NN￨O￨- ,￨L￨,￨O￨- network-wide￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unlikely￨L￨JJ￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- percolate￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- value￨L￨NN￨O￨- δt￨L￨NN￨O￨- may￨L￨MD￨O￨- provide￨L￨VB￨O￨- the￨L￨DT￨O￨- pathways￨L￨NNS￨O￨- for￨L￨IN￨O￨- infecting￨L￨VBG￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network.Therefore￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- limit￨L￨NN￨O￨- δt￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- percolation￨L￨NN￨O￨A problem￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- connectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- paths￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- follow￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- within￨L￨IN￨O￨- δt￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- event￨L￨NN￨O￨- graph￨L￨NN￨O￨- as￨L￨IN￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- computational￨L￨JJ￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal-network￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- this￨L￨DT￨O￨- representation￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- percolation￨L￨NN￨O￨- in￨L￨IN￨O￨- artificial￨L￨JJ￨O￨- and￨L￨CC￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- percolation￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- event￨L￨NN￨O￨- graphs￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- and￨L￨CC￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- rationale￨L￨NN￨O￨- for￨L￨IN￨O￨- ABM￨U￨NNP￨O￨- use￨L￨VBP￨O￨- over￨L￨IN￨O￨- other￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨A centres￨L￨NNS￨O￨- around￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- points￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- represent￨L￨VB￨O￨- increased￨L￨VBN￨O￨- stochasticity￨L￨NN￨O￨- in￨L￨IN￨O￨- low-transmission￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- high-resolution￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- heterogeneities￨L￨NNS￨O￨- in￨L￨IN￨O￨- drug￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- efficacies￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- individual￨L￨JJ￨O￨- patient￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Agent-based￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A :￨L￨:￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- reviewNeal￨L￨NNP￨O￨- R.￨U￨NNP￨O￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- modellers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- increasingly￨L￨RB￨O￨- adopting￨L￨VBG￨O￨- agent-based￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- model￨L￨VBP￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- vectors￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- their￨L￨PRP$￨O￨- interactions￨L￨NNS￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- 90￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- ,￨L￨,￨O￨- characterizing￨L￨VBG￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ABMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- relevant￨L￨JJ￨O￨- to￨L￨TO￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- approaches￨L￨NNS￨O￨- provides￨L￨VBZ￨O￨- avenues￨L￨NNS￨O￨- for￨L￨IN￨O￨- further￨L￨JJ￨O￨- exploration￨L￨NN￨O￨- of￨L￨IN￨O￨- agent-based￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- for￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- eradication￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- PPRV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- small￨L￨JJ￨O￨A ruminant￨L￨NN￨O￨- populations￨L￨NNS￨O￨- acting￨L￨VBG￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- targeted￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- within￨L￨IN￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- immunized￨L￨VBN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- viral￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- global￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- heavily￨L￨RB￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- immunization￨L￨NN￨O￨- of￨L￨IN￨O￨- small￨L￨JJ￨O￨- ruminant￨L￨NN￨O￨- populations￨L￨NNS￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- organization￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨A ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- efficacious￨L￨JJ￨O￨- attenuated￨L￨VBN￨O￨- live￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- producing￨L￨VBG￨O￨- lifelong￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- all￨L￨DT￨O￨- PPRV￨U￨NN￨ORGANIZATION￨- serotypes￨L￨NNS￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- administration￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- campaigns￨L￨NNS￨O￨A are￨L￨VBP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- costly￨L￨JJ￨O￨- and￨L￨CC￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- ’s￨L￨POS￨O￨- thermolability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- accessibility￨L￨NN￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- small￨L￨JJ￨O￨- ruminant￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- precise￨L￨JJ￨O￨- census￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- national￨L￨JJ￨O￨- animal￨L￨NN￨O￨- identification￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- fitting￨L￨JJ￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- PPRV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- survey￨L￨NN￨O￨- results￨L￨VBZ￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- PPRV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- Ethiopian￨U￨JJ￨NATIONALITY￨- small￨L￨JJ￨O￨A ruminant￨L￨NN￨O￨- village￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- elimination￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- simulated￨L￨JJ￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- PPRV￨U￨NN￨O￨- between￨L￨IN￨O￨- small￨L￨JJ￨O￨A ruminants￨L￨NNS￨O￨- —￨L￨:￨O￨- sheep￨L￨NN￨O￨- and￨L￨CC￨O￨- goats￨L￨NNS￨O￨- —￨L￨:￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- Ethiopian￨U￨JJ￨NATIONALITY￨- villages￨L￨NNS￨O￨- .￨L￨.￨O￨- +Beyond￨U￨IN￨O￨- evolutionary￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- invasion￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- invading￨L￨VBG￨O￨- and￨L￨CC￨O￨- invaded￨L￨VBD￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- face￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- complexity￨L￨NN￨O￨A ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- offer￨L￨VBP￨O￨- valuable￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- synthesize￨L￨VB￨O￨- information￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- observed￨L￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- test￨L￨VB￨O￨- different￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- key￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Wallinga￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Teunis￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- requires￨L￨VBZ￨O￨- only￨L￨RB￨O￨- case￨L￨NN￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- serial￨L￨NN￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨A of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- R￨U￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- factor￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- huge￨L￨JJ￨O￨- complexity￨L￨NN￨O￨A is￨L￨VBZ￨O￨- non-stationarity￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- evolve￨L￨VBP￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Model-based￨U￨JJ￨MISC￨- analyses￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨A and￨L￨CC￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- knowledge￨L￨NN￨O￨- gaps￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- that￨L￨DT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨JJ￨O￨- or￨L￨CC￨O￨- impossible￨L￨JJ￨O￨- to￨L￨TO￨O￨- test￨L￨NN￨O￨- using￨L￨VBG￨O￨- animal￨L￨NN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- long-term￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- through￨L￨IN￨O￨- and￨L￨CC￨O￨- across￨L￨IN￨O￨- many￨L￨JJ￨O￨- seasons￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- serological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- can￨L￨MD￨O￨- vary￨L￨VB￨O￨- substantially￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- criteria￨L￨NNS￨O￨- used￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- produce￨L￨VBP￨O￨- estimates￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- vastly￨L￨RB￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- antibodies￨L￨NNS￨O￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- completely￨L￨RB￨O￨A understood￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Assumptions￨U￨NNS￨O￨- around￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- can￨L￨MD￨O￨- propagate￨L￨VB￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- modelling￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- we￨L￨PRP￨O￨- understand￨L￨VBP￨O￨- and￨L￨CC￨O￨- characterise￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- estimating￨L￨VBG￨O￨A the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- calculating￨L￨VBG￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- policy￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- careful￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- high-quality￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- estimating￨L￨VBG￨O￨A both￨L￨CC￨O￨- population￨L￨NN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- present￨L￨JJ￨DATE￨- and￨L￨CC￨O￨- future￨L￨JJ￨DATE￨- modeling￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- few￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- completely￨L￨RB￨O￨A susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- estimates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- genes￨L￨NNS￨O￨A showed￨L￨VBD￨O￨- increased￨L￨VBN￨O￨- expression￨L￨NN￨O￨- between￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 4￨L￨CD￨NUMBER￨- dpi￨L￨NNS￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- genotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- stronger￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- two￨L￨CD￨NUMBER￨- pectate￨L￨NN￨O￨- lyases￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- hydrolase￨L￨NN￨O￨- were￨L￨VBD￨O￨- expressed￨L￨VBN￨O￨- higher￨L￨JJR￨O￨- at￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- dpi￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- acetyltransferase￨L￨NN￨O￨- activity￨L￨NN￨O￨- was￨L￨VBD￨O￨- highly￨L￨RB￨O￨- enriched￨L￨VBN￨O￨- at￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- dpi￨L￨NNS￨O￨- .￨L￨.￨O￨- +Genes￨U￨NNS￨O￨- with￨L￨IN￨O￨- unique￨L￨JJ￨O￨- ,￨L￨,￨O￨- high￨L￨JJ￨O￨- up-regulation￨L￨NN￨O￨- by￨L￨IN￨O￨- Fg￨U￨NN￨O￨- in￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- 1￨L￨CD￨NUMBER￨- were￨L￨VBD￨O￨- mostly￨L￨RB￨O￨- transiently￨L￨RB￨O￨- expressed￨L￨VBN￨O￨- at￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- dpi￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- many￨L￨JJ￨O￨- defense-associated￨L￨JJ￨O￨- genes￨L￨NNS￨O￨A were￨L￨VBD￨O￨- up-regulated￨L￨VBN￨O￨- at￨L￨IN￨O￨- both￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 4￨L￨CD￨NUMBER￨- dpi￨L￨NNS￨O￨- in￨L￨IN￨O￨- Nyubai￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- unique￨L￨JJ￨O￨- genes￨L￨NNS￨O￨- up-regulated￨L￨VBN￨O￨- in￨L￨IN￨O￨- HC374￨U￨NN￨O￨- were￨L￨VBD￨O￨- detected￨L￨VBN￨O￨- at￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- dpi￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyzed￨L￨VBD￨O￨- transcriptomics￨L￨NNS￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- wheat￨L￨NN￨O￨- genotypes￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Nyubai￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Wuhan￨U￨NNP￨ORGANIZATION￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- HC374￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Shaw￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 4￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- post￨L￨JJ￨O￨- inoculation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dpi￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- Fg￨U￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- RNA-seq￨U￨JJ￨MISC￨- technology￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- susceptible￨L￨JJ￨O￨- genotype￨L￨NN￨O￨- Shaw￨U￨NNP￨PERSON￨- exhibited￨L￨VBD￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨A DEGs￨U￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- 2270￨L￨CD￨NUMBER￨- DEGs￨U￨NNS￨O￨- associating￨L￨VBG￨O￨- with￨L￨IN￨O￨- FHB￨U￨NN￨O￨- susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- A￨U￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 37,772￨L￨CD￨NUMBER￨- differentially￨L￨RB￨O￨- expressed￨L￨VBN￨O￨- genes￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- DEGs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- ,￨L￨,￨O￨- 28,961￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- wheat￨L￨NN￨O￨- and￨L￨CC￨O￨- 8811￨L￨CD￨DATE￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- to￨L￨TO￨O￨- guide￨L￨VB￨O￨- strategic￨L￨JJ￨O￨- thinking￨L￨VBG￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- zones￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- targeted￨L￨VBN￨O￨- for￨L￨IN￨O￨- elimination￨L￨NN￨O￨A ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- maintained￨L￨VBN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- areas￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- elimination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- technically￨L￨RB￨O￨- possible￨L￨JJ￨O￨- in￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- areas￨L￨NNS￨O￨- being￨L￨VBG￨O￨- considered￨L￨VBN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- but￨L￨CC￨O￨- resources￨L￨NNS￨O￨- to￨L￨TO￨O￨- intensify￨L￨VB￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- elimination￨L￨NN￨O￨- are￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- targeting￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- area￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Targeting￨U￨NN￨O￨- isolated￨L￨VBD￨O￨- islands￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- elimination￨L￨NN￨O￨A may￨L￨MD￨O￨- also￨L￨RB￨O￨- have￨L￨VB￨O￨- value￨L￨NN￨O￨- as￨L￨IN￨O￨- tests￨L￨NNS￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- technologies￨L￨NNS￨O￨- or￨L￨CC￨O￨- systems￨L￨NNS￨O￨- ;￨L￨:￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- whether￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- low￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- areas￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- strategy￨L￨NN￨O￨- than￨L￨IN￨O￨- focusing￨L￨VBG￨O￨- those￨L￨DT￨O￨- resources￨L￨NNS￨O￨- on￨L￨IN￨O￨- eliminating￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- higher￨L￨JJR￨O￨- transmission￨L￨NN￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- when￨L￨WRB￨O￨- these￨L￨DT￨O￨- lower￨L￨JJR￨O￨- transmission￨L￨NN￨O￨- areas￨L￨NNS￨O￨- face￨L￨VBP￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- importation￨L￨NN￨O￨- from￨L￨IN￨O￨- neighbouring￨L￨VBG￨O￨- higher￨L￨JJR￨O￨- transmission￨L￨NN￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- sites￨L￨NNS￨O￨- are￨L￨VBP￨O￨- additionally￨L￨RB￨O￨- characterised￨L￨VBN￨O￨- by￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- at￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- annual￨L￨JJ￨SET￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- vulnerability￨L￨NN￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- required￨L￨VBN￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- intensified￨L￨VBN￨O￨- control￨L￨NN￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- T.￨U￨FW￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- and￨L￨CC￨O￨- T￨U￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- intensified￨L￨VBN￨O￨- measures￨L￨NNS￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- elimination￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- and/or￨L￨CC￨O￨- financial￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- these￨L￨DT￨O￨- additional￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- measures￨L￨NNS￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- areas￨L￨NNS￨O￨- simultaneously￨L￨RB￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- overall￨L￨JJ￨O￨- elimination￨L￨NN￨O￨A can￨L￨MD￨O￨- only￨L￨RB￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- intensified￨L￨VBN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- area￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- case￨L￨NN￨O￨- until￨L￨IN￨O￨- local￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- interrupted￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- wish￨L￨VBP￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- hypothetical￨L￨JJ￨O￨- issue￨L￨NN￨O￨- :￨L￨:￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- product￨L￨NN￨O￨- for￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- particular￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- serotype￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- aforementioned￨L￨JJ￨O￨- antibody-dependent￨L￨JJ￨O￨- enhancement￨L￨NN￨O￨- does￨L￨VBZ￨O￨- occur￨L￨VB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- there￨L￨EX￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- particular￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- while￨L￨IN￨O￨- simultaneously￨L￨RB￨O￨- contributing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- serotypes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- antibody￨L￨NN￨O￨- enhancement.Our￨L￨NN￨O￨- conceptual￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- formulation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- guided￨L￨VBN￨O￨- by￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- recent￨L￨JJ￨O￨- immunological￨L￨JJ￨O￨- cross-reactivity￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- confirmed￨L￨VBN￨O￨- that￨L￨IN￨O￨- convalescent￨L￨JJ￨O￨- plasma￨L￨NN￨O￨- following￨L￨VBG￨O￨- dengue￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- enhance￨L￨VB￨O￨- Zika￨U￨NN￨PERSON￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- global￨L￨JJ￨O￨- efforts￨L￨NNS￨O￨- of￨L￨IN￨O￨- developing￨L￨VBG￨O￨- dengue￨L￨JJ￨O￨- and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- vaccines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- intensified￨L￨VBN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- whether￨L￨IN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- may￨L￨MD￨O￨- affect￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- another￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- antibody-dependent￨L￨JJ￨O￨- enhancement￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Through￨U￨IN￨O￨- a￨L￨DT￨O￨- conceptual￨L￨JJ￨O￨- co-infection￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- parametrized￨L￨VBN￨O￨- by￨L￨IN￨O￨- reported￨L￨VBN￨O￨- dengue￨L￨NN￨O￨A and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- immunological￨L￨JJ￨O￨- cross-reactivity￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- evaluate￨L￨VBP￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- on￨L￨IN￨O￨- Zika￨U￨NN￨PERSON￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- season￨L￨NN￨O￨- when￨L￨WRB￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- particular￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨- serotype￨L￨NN￨O￨- is￨L￨VBZ￨O￨- involved￨L￨VBN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- appropriately￨L￨RB￨O￨- designed￨L￨VBN￨O￨- and￨L￨CC￨O￨- optimized￨L￨VBN￨O￨- dengue￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- help￨L￨VB￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- spread￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- ,￨L￨,￨O￨- counter-intuitively￨L￨RB￨O￨- ,￨L￨,￨O￨- reduce￨L￨VB￨O￨- Zika￨U￨NN￨PERSON￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- identify￨L￨VBP￨O￨- optimal￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- coverages￨L￨NNS￨O￨- for￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- dengue￨L￨NN￨O￨- and￨L￨CC￨O￨- simultaneously￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- Zika￨U￨NNP￨PERSON￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- coverages￨L￨NNS￨O￨- exceeding￨L￨VBG￨O￨- which￨L￨WDT￨O￨- dengue￨L￨VBP￨O￨- vaccination￨L￨NN￨O￨- will￨L￨MD￨O￨- increase￨L￨VB￨O￨- Zika￨U￨NNP￨PERSON￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 03￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Mechanistic￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- popularity￨L￨NN￨O￨- prediction￨L￨NN￨O￨- Sijuan￨U￨NNP￨O￨- Ma1￨U￨NN￨O￨- ,￨L￨,￨O￨- Ling￨U￨NNP￨PERSON￨- Feng￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- &￨L￨CC￨O￨- Choy-Heng￨U￨NNP￨O￨- Lai1￨U￨NN￨O￨- ,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 13126￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- scienceInformation￨L￨NN￨O￨- technologyInformation￨L￨NN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- computation￨L￨NN￨O￨- AbstractOnline￨U￨NNP￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A are￨L￨VBP￨O￨- becoming￨L￨VBG￨O￨- major￨L￨JJ￨O￨- platforms￨L￨NNS￨O￨- for￨L￨IN￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- exchange￨L￨VB￨O￨- opinions￨L￨NNS￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A have￨L￨VBP￨O￨- higher￨L￨JJR￨O￨- order￨L￨NN￨O￨- correlations￨L￨NNS￨O￨- among￨L￨IN￨O￨- node￨L￨NN￨O￨- degrees￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- for￨L￨IN￨O￨- directed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- like￨L￨IN￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- spreading￨L￨VBG￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- previous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- users￨L￨NNS￨O￨- ’￨L￨POS￨O￨- limited￨L￨JJ￨O￨- attention￨L￨NN￨O￨- and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- interests￨L￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- retweet￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨A Twitter￨U￨NNP￨ORGANIZATION￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- both￨L￨CC￨O￨- non-trivial￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- structures￨L￨NNS￨O￨- and￨L￨CC￨O￨- non-standard￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- for￨L￨IN￨O￨- viral￨L￨JJ￨O￨- tweets￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- overload￨L￨NN￨O￨- for￨L￨IN￨O￨- retweeting￨L￨VBG￨O￨- behaviors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- in￨L￨IN￨O￨- line￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨O￨- and￨L￨CC￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- sublinear￨L￨JJ￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- consider￨L￨VBP￨O￨- discrete￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- states￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- “￨L￨``￨O￨- susceptible￨L￨JJ￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- infected￨L￨JJ￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- recovered￨L￨VBN￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reduce￨L￨VB￨O￨- bias/increase￨L￨NN￨O￨- precision￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- state-specific￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- multi-state￨L￨JJ￨O￨- CMR￨U￨NN￨O￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- several￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- gradually￨L￨RB￨O￨- increased￨L￨VBD￨O￨- uncertainty￨L￨NN￨O￨A by￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- assigning￨L￨VBG￨O￨- each￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- equal￨L￨JJ￨O￨- amount￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NN￨O￨- set￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- “￨L￨``￨O￨- homogeneity￨L￨NN￨O￨- ”￨L￨''￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- Figure￨U￨NNP￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- homogeneity￨L￨NN￨O￨- scenario￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- gradually￨L￨RB￨O￨- increased￨L￨VBD￨O￨- uncertainty￨L￨NN￨O￨A by￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- assigning￨L￨VBG￨O￨- each￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- equal￨L￨JJ￨O￨- amount￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NN￨O￨- set￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- evaluated￨L￨VBD￨O￨- how￨L￨WRB￨O￨- increasing￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- U￨U￨NNP￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- affected￨L￨VBN￨O￨- bias￨L￨NN￨O￨- and￨L￨CC￨O￨- precision￨L￨NN￨O￨- of￨L￨IN￨O￨- eco-epidemiological￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- purpose￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- partial￨L￨JJ￨O￨- observation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- some￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- detected￨L￨VBN￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- field￨L￨NN￨O￨- session￨L￨NN￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- are￨L￨VBP￨O￨- assigned￨L￨VBN￨O￨- an￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- “￨L￨``￨O￨- U￨U￨NNP￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- occasion￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- ubiquity￨L￨NN￨O￨- and￨L￨CC￨O￨- negative￨L￨JJ￨O￨- fitness￨L￨NN￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- organisms￨L￨NNS￨O￨- gaining￨L￨VBG￨O￨- fitness￨L￨NN￨O￨- benefits￨L￨NNS￨O￨- from￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- exploitation￨L￨NN￨O￨- ,￨L￨,￨O￨- microbial￨L￨JJ￨O￨A symbionts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- protection￨L￨NN￨O￨- greatly￨L￨RB￨O￨- benefit￨L￨VBP￨O￨- hosts￨L￨NNS￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- line￨L￨NN￨O￨- of￨L￨IN￨O￨- defense￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- mutualisms￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- coadapted￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- species￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- protection￨L￨NN￨O￨- for￨L￨IN￨O￨- host￨L￨NN￨TITLE￨A ,￨L￨,￨O￨- within‐host￨L￨JJ￨O￨- colonization￨L￨NN￨O￨- for￨L￨IN￨O￨- bacterium￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- greatest￨L￨JJS￨O￨- in￨L￨IN￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- coevolved￨L￨VBN￨O￨- host‐defensive￨L￨JJ￨O￨- bacterium￨L￨NN￨O￨- populations￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- widespread￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- defensive￨L￨JJ￨O￨- mutualisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- arise￨L￨VBP￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- coadapted￨L￨VBN￨O￨- and￨L￨CC￨O￨- shaped￨L￨VBN￨O￨- by￨L￨IN￨O￨- reciprocal￨L￨JJ￨O￨- selection￨L￨NN￨O￨- between￨L￨IN￨O￨- host￨L￨NN￨TITLE￨A and￨L￨CC￨O￨- microbe￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- microbial￨L￨JJ￨O￨A symbionts￨L￨NNS￨O￨- can￨L￨MD￨O￨- determine￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- parasites￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- through￨L￨IN￨O￨- defensive￨L￨JJ￨O￨- mutualism￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- originating￨L￨VBG￨O￨A from￨L￨IN￨O￨- a￨L￨DT￨O￨- source￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- nearest￨L￨JJS￨O￨- neighbour￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- GENs￨U￨NNS￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- utility￨L￨NN￨O￨- in￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Dynamics￨U￨NNP￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- likewise￨L￨RB￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- an￨L￨DT￨O￨- origin￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- destination￨L￨NN￨O￨- node￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- sources￨L￨NNS￨O￨- and￨L￨CC￨O￨- sinks￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- node￨L￨NN￨O￨- given￨L￨VBN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- originating￨L￨VBG￨O￨A at￨L￨IN￨O￨- another￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- centrality￨L￨NN￨O￨A of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- measured￨L￨VBN￨O￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- ways￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- PageRank￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- betweenness￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- centralities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- GENs￨U￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- centrality￨L￨NN￨O￨A using￨L￨VBG￨O￨- the￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- importance￨L￨NN￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- global￨L￨JJ￨O￨- centralities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- common￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- is￨L￨VBZ￨O￨- valuable￨L￨JJ￨O￨- for￨L￨IN￨O￨- correlating￨L￨VBG￨O￨- dose￨L￨NN￨O￨A and￨L￨CC￨O￨- response￨L￨NN￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- has￨L￨VBZ￨O￨- occurred￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- a￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- biological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- dose￨L￨NN￨O￨- ,￨L￨,￨O￨- dictate￨L￨VBP￨O￨- individual￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- correlative￨L￨JJ￨O￨- descriptions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- predictive￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Current￨U￨JJ￨DATE￨- dose￨L￨NN￨O￨A –￨L￨:￨O￨- response￨L￨NN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- typically￨L￨RB￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- single￨L￨JJ￨O￨- hit￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- ingested￨L￨VBN￨O￨- pathogen￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- cause￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- independent￨L￨JJ￨RELIGION￨- action￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- any￨L￨DT￨O￨- particular￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- is￨L￨VBZ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- ingested￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Logically￨U￨RB￨O￨- building￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- understanding￨L￨NN￨O￨- that￨L￨WDT￨O￨- listeriosis￨L￨VBZ￨O￨- is￨L￨VBZ￨O￨- dose-dependent￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- quantification￨L￨NN￨O￨- of￨L￨IN￨O￨- dose￨L￨NN￨O￨A –￨L￨:￨O￨- response￨L￨NN￨O￨- relationships￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- via￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- supported￨L￨VBN￨O￨- by￨L￨IN￨O￨- animal￨L￨NN￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g￨L￨FW￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨A ,￨L￨,￨O￨- drawing￨L￨VBG￨O￨- from￨L￨IN￨O￨- ‘￨L￨``￨O￨- humanized￨L￨JJ￨O￨- ’￨L￨''￨O￨- transgenic￨L￨JJ￨O￨- murine￨L￨JJ￨O￨- models￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- guinea￨L￨NN￨COUNTRY￨- pigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- rabbits￨L￨NNS￨O￨- ,￨L￨,￨O￨- scientific￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- explored￨L￨VBN￨O￨- the￨L￨DT￨O￨- intracellular￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- its￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- cross￨L￨VB￨O￨- the￨L￨DT￨O￨- intestinal￨L￨JJ￨O￨- wall￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +compared￨L￨VBN￨O￨- six￨L￨CD￨NUMBER￨- dose￨L￨NN￨O￨A –￨L￨:￨O￨- response￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- illustrating￨L￨VBG￨O￨- vast￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- respective￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- when￨L￨WRB￨O￨- extrapolating￨L￨VBG￨O￨- from￨L￨IN￨O￨- high￨L￨JJ￨O￨- to￨L￨TO￨O￨- low￨L￨JJ￨O￨- doses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- screening￨L￨NN￨O￨A and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- HCV￨U￨NN￨O￨- birth￨L￨NN￨O￨- cohort￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 1975￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- population￨L￨NN￨O￨- health￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- next￨L￨JJ￨DURATION￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- payer￨L￨NN￨O￨- ’s￨L￨POS￨O￨- perspective￨L￨NN￨O￨- under￨L￨IN￨O￨- spending￨L￨NN￨O￨- budget￨L￨NN￨O￨- constraints￨L￨NNS￨O￨- .￨L￨.￨O￨- +HCV￨U￨NN￨O￨- screening￨L￨NN￨O￨A can￨L￨MD￨O￨- help￨L￨VB￨O￨- identify￨L￨VB￨O￨- HCV-infected￨U￨JJ￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- potential￨L￨JJ￨O￨- liver￨L￨NN￨O￨- damage￨L￨NN￨O￨- and￨L￨CC￨O￨- consequently￨L￨RB￨O￨- allow￨L￨VBP￨O￨- efficient￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- improving￨L￨VBG￨O￨- population￨L￨NN￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- lowering￨L￨VBG￨O￨- HCV-related￨U￨JJ￨MISC￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- project￨L￨VB￨O￨- the￨L￨DT￨O￨- societal￨L￨JJ￨O￨- benefit￨L￨NN￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- discounted￨L￨JJ￨O￨- quality-adjusted￨L￨JJ￨O￨- life-years￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- QALYs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- US￨U￨NNP￨COUNTRY￨- age￨L￨NN￨O￨- cohorts￨L￨NNS￨O￨- with￨L￨IN￨O￨- given￨L￨VBN￨O￨- budget￨L￨NN￨O￨- limits￨L￨NNS￨O￨- and￨L￨CC￨O￨- optimized￨L￨VBN￨O￨- screening￨L￨NN￨O￨A and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- implementation￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨ORGANIZATION￨- Preventive￨U￨NNP￨ORGANIZATION￨- Services￨U￨NNPS￨ORGANIZATION￨- Task￨U￨NNP￨ORGANIZATION￨- Force￨U￨NNP￨ORGANIZATION￨- both￨L￨CC￨O￨- shifted￨L￨VBD￨O￨- their￨L￨PRP$￨O￨- stances￨L￨NNS￨O￨- on￨L￨IN￨O￨- HCV￨U￨NN￨O￨- screening￨L￨NN￨O￨A ,￨L￨,￨O￨- recommending￨L￨VBG￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- providers￨L￨NNS￨O￨- to￨L￨TO￨O￨- offer￨L￨VB￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- new￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- people￨L￨NNS￨O￨- born￨L￨VBN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- age￨L￨NN￨O￨- cohorts￨L￨NNS￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 75￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- HCV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- 73￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- HCV-associated￨U￨JJ￨O￨- mortality￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- decision￨L￨NN￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- chronic￨L￨JJ￨O￨- HCV￨U￨NN￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- that￨L￨WDT￨O￨- mimics￨L￨VBZ￨O￨- HCV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- progression￨L￨NN￨O￨- ,￨L￨,￨O￨- screening￨L￨NN￨O￨A ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- lessons￨L￨NNS￨O￨- that￨L￨WDT￨O￨- underpins￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- modeling￨L￨NN￨O￨- rinderpest￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- distinguishing￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- vs.￨L￨CC￨O￨- This￨U￨DT￨O￨- observation￨L￨NN￨O￨- may￨L￨MD￨O￨- seem￨L￨VB￨O￨- self-evident￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- consideration￨L￨NN￨O￨- of￨L￨IN￨O￨- past￨L￨NN￨DATE￨A analyses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- demonstrates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- inappropriately￨L￨RB￨O￨- aggregated￨L￨VBD￨O￨- geography￨L￨NN￨O￨- can￨L￨MD￨O￨- mask￨L￨NN￨O￨- vital￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- mitigation￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- of￨L￨IN￨O￨- older￨L￨JJR￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- relatively￨L￨RB￨O￨- uncontrolled￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- includes￨L￨VBZ￨O￨- rinderpest￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨A ,￨L￨,￨O￨- geographic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- perform￨L￨VB￨O￨- historically￨L￨RB￨O￨- successful￨L￨JJ￨O￨- mitigations￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- culling￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- reduction￨L￨NN￨O￨- .￨L￨.￨O￨- +Past￨U￨JJ￨DATE￨- and￨L￨CC￨O￨- potential￨L￨JJ￨O￨- rinderpest￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- single￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- entities￨L￨NNS￨O￨- amenable￨L￨JJ￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- reasonably￨L￨RB￨O￨- well-defined￨L￨JJ￨O￨- presentation￨L￨NN￨O￨- and￨L￨CC￨O￨- progression￨L￨NN￨O￨A of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- biological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- support￨L￨VBP￨O￨- modeling￨L￨NN￨O￨- rinderpest￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- entity￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- Shim￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- approved￨L￨VBN￨O￨- dengue￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Philippines￨U￨NNPS￨COUNTRY￨- and￨L￨CC￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- with￨L￨IN￨O￨- appropriated￨L￨VBN￨O￨- pricing￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Philippines￨U￨NNPS￨COUNTRY￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- potential￨L￨NN￨O￨- to￨L￨TO￨O￨- confer￨L￨VB￨O￨- the￨L￨DT￨O￨- excellent￨L￨JJ￨O￨- value￨L￨NN￨O￨- were￨L￨VBD￨O￨- possible￨L￨JJ￨O￨- .￨L￨.￨O￨- +Esteva￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Vargus￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovery￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- populations￨L￨NNS￨O￨- while￨L￨IN￨O￨- Chanprasopchai￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Pongsumpun￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Tang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A hemorrhagic￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- included￨L￨VBD￨O￨- an￨L￨DT￨O￨- age￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- tetravalent￨L￨JJ￨O￨- dengue￨L￨NN￨O￨A vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Dengvaxia￨U￨NN￨O￨- ™￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- countries￨L￨NNS￨O￨- at￨L￨IN￨O￨- danger￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A viruses￨L￨NNS￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- are￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- discuss￨L￨VBP￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- directed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- proposing￨L￨VBG￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- ranking￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- named￨L￨VBN￨O￨- ClusterRank￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- is￨L￨VBZ￨O￨- effective￨L￨JJ￨O￨- but￨L￨CC￨O￨- mainly￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- local￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- lacking￨L￨VBG￨O￨- global￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- hybrid￨L￨JJ￨O￨- degree￨L￨NN￨O￨- centrality￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- HC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- weighted￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- theory￨L￨NN￨O￨- improves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- extent￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- ignores￨L￨VBZ￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- use￨L￨NN￨O￨- generalizing￨L￨VBG￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- shortest￨L￨JJS￨O￨- paths￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- node￨L￨NN￨O￨- centrality￨L￨NN￨O￨A in￨L￨IN￨O￨- weighted￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- has￨L￨VBZ￨O￨- certain￨L￨JJ￨O￨- accuracy￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- mainly￨L￨RB￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- local￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- comprehensiveness￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- semi-local￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measure￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- tradeoff￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- low-relevant￨L￨JJ￨O￨- degree￨L￨NN￨O￨- centrality￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- time-consuming￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- betweenness￨L￨NN￨O￨- or￨L￨CC￨O￨- closeness￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- new￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- centrality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EffC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- rank￨L￨VB￨O￨- the￨L￨DT￨O￨- spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- predicts￨L￨VBZ￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- VT￨U￨NN￨STATE_OR_PROVINCE￨- serotypes￨L￨NNS￨O￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- within￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- PCV￨U￨NN￨O￨- introduction￨L￨NN￨O￨- in￨L￨IN￨O￨- RV￨U￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- near-complete￨L￨JJ￨O￨- replacement￨L￨NN￨O￨- by￨L￨IN￨O￨- NVT￨U￨NN￨O￨- serotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- little￨L￨JJ￨O￨- or￨L￨CC￨O￨- no￨L￨DT￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- carriage￨L￨NN￨O￨A prevalence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- A￨U￨NNP￨O￨- &￨L￨CC￨O￨- B￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- >￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- adults￨L￨NNS￨O￨- .￨L￨.￨O￨- +Pre-PCV￨U￨JJ￨O￨- carriage￨L￨NN￨O￨A estimates￨L￨VBZ￨O￨- across￨L￨IN￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- for￨L￨IN￨O￨- VT￨U￨NN￨STATE_OR_PROVINCE￨- (￨L￨-LRB-￨O￨- left￨L￨JJ￨O￨- panel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- NVT￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- right￨L￨JJ￨O￨- panel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- survey￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- plain￨L￨JJ￨O￨- vertical￨L￨JJ￨O￨- lines￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- meta-regression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- dotted￨L￨VBN￨O￨- vertical￨L￨JJ￨O￨- lines￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- estimates￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- manuscript￨L￨NN￨O￨- we￨L￨PRP￨O￨- explored￨L￨VBD￨O￨- the￨L￨DT￨O￨- differential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- carriage￨L￨NN￨O￨A and￨L￨CC￨O￨- invasive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- catch-up￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- targeting￨L￨VBG￨O￨- various￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- explored￨L￨VBD￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- introduction￨L￨NN￨O￨- delay￨L￨NN￨O￨- .￨L￨.￨O￨- +Legend￨U￨NNP￨O￨- :￨L￨:￨O￨- Predicted￨U￨VBD￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- VT￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- NVT￨U￨NNP￨O￨- and￨L￨CC￨O￨- overall￨L￨JJ￨O￨- carriage￨L￨NN￨O￨A in￨L￨IN￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- olds￨L￨NNS￨O￨- without￨L￨IN￨O￨- a￨L￨DT￨O￨- catch-up￨L￨NN￨O￨- campaign￨L￨NN￨O￨- .￨L￨.￨O￨- +B￨U￨NN￨O￨- :￨L￨:￨O￨- Predicted￨U￨VBN￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- VT￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- NVT￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- overall￨L￨JJ￨O￨- carriage￨L￨NN￨O￨A in￨L￨IN￨O￨- ≥￨L￨CD￨NUMBER￨- 5￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- olds￨L￨NNS￨O￨- in￨L￨IN￨O￨- RV￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- spatial￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- kernel￨L￨NN￨O￨- quantifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- hazard￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- per￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- unit￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨DURATION￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- posed￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- premises￨L￨NNS￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- premises￨L￨NNS￨O￨- located￨L￨VBN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- distance￨L￨NN￨O￨- away￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Minnesota￨U￨NNP￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- Iowa￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- severe￨L￨JJ￨O￨- :￨L￨:￨O￨- 180￨L￨CD￨NUMBER￨- commercial￨L￨JJ￨O￨- premises￨L￨NNS￨O￨A were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- with￨L￨IN￨O￨- devastating￨L￨VBG￨O￨- consequences￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- H5N2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- analyzed￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- kernel￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- turkey￨L￨NN￨COUNTRY￨- premises￨L￨NNS￨O￨A had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Eurasian￨U￨JJ￨MISC￨- HPAI￨U￨NN￨MISC￨- H5N8￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- IAV￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- frequently￨L￨RB￨O￨- recorded￨L￨VBN￨O￨- in￨L￨IN￨O￨- swine￨L￨NNS￨O￨- herds￨L￨NNS￨O￨- with￨L￨IN￨O￨- risks￨L￨NNS￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- gaps￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- IAV￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- limited￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- conducted￨L￨VBN￨O￨- on￨L￨IN￨O￨- IAV￨U￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- pig￨L￨NN￨O￨- farm￨L￨NN￨O￨A level￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Their￨U￨PRP$￨O￨- findings￨L￨NNS￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- as￨L￨RB￨O￨- long￨L￨JJ￨O￨- as￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- inflow￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- farm￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- persists￨L￨VBZ￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- small￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- IAV￨U￨NN￨O￨- in￨L￨IN￨O￨- swine￨L￨NNS￨O￨- that￨L￨WDT￨O￨- showed￨L￨VBD￨O￨- a￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- finishing￨L￨VBG￨O￨- herd￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- seroprevalence￨L￨NN￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- between￨L￨IN￨O￨- farrow-to-finish￨L￨JJ￨O￨- farm￨L￨NN￨O￨A herd￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- seroprevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- factors￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A including￨L￨VBG￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- levels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- work￨L￨NN￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- maternally￨L￨RB￨O￨- derived￨L￨VBN￨O￨- immunity￨L￨NN￨O￨- on￨L￨IN￨O￨- IAV￨U￨NN￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- farrow-to-finish￨L￨JJ￨O￨- farm￨L￨NN￨O￨A .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Quantifying￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- groups￨L￨NNS￨O￨A and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- inequalities￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modelJames￨L￨NNS￨O￨- D.￨U￨NNP￨O￨- Methods￨U￨NNS￨O￨- To￨U￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- on￨L￨IN￨O￨- inequalities￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- integrates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- calibrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- epidemiologic￨L￨JJ￨O￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- suggests￨L￨VBZ￨O￨- realistic￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- contributing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- —￨L￨:￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- —￨L￨:￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- social￨L￨JJ￨O￨- groups￨L￨NNS￨O￨A can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- twice￨L￨RB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- high-risk￨L￨JJ￨O￨- population￨L￨NN￨O￨- group￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- low-risk￨L￨JJ￨O￨- population￨L￨NN￨O￨- group￨L￨NN￨O￨- .￨L￨.￨O￨- +Importantly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- contrary￨L￨JJ￨O￨- to￨L￨TO￨O￨- social￨L￨JJ￨O￨- policy￨L￨NN￨O￨- intentions￨L￨NNS￨O￨- ,￨L￨,￨O￨- promoting￨L￨VBG￨O￨- an￨L￨DT￨O￨- equal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- uptake￨L￨NN￨O￨A across￨L￨IN￨O￨- population￨L￨NN￨O￨- groups￨L￨NNS￨O￨- may￨L￨MD￨O￨- magnify￨L￨VB￨O￨- inequalities￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- amplified￨L￨VBD￨O￨- this￨L￨DT￨O￨- inequality￨L￨NN￨O￨- further￨L￨RB￨O￨- :￨L￨:￨O￨- equal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- uptake￨L￨NN￨O￨A across￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- groups￨L￨NNS￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- seven￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- high-risk￨L￨JJ￨O￨- group￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- among￨L￨IN￨O￨- laboratories￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- only￨L￨RB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- birth￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- date￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- sample￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- optimal￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- distinguishing￨L￨VBG￨O￨- between￨L￨IN￨O￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- negatives￨L￨NNS￨O￨- tests￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- unknown￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- in￨L￨IN￨O￨- CDV￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- wolves￨L￨NNS￨O￨- and￨L￨CC￨O￨- grizzly￨L￨JJ￨O￨- bears￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- GYE￨U￨NNP￨O￨- using￨L￨VBG￨O￨- serological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DATE￨- 30￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨A .￨L￨.￨O￨- +During￨U￨IN￨O￨- these￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- coyotes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Canis￨U￨NN￨MISC￨- latrans￨L￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- cougars￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Puma￨U￨NNP￨ORGANIZATION￨- concolor￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- CDV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- comparable￨L￨JJ￨O￨- information￨L￨NN￨O￨- is￨L￨VBZ￨O￨- lacking￨L￨VBG￨O￨A for￨L￨IN￨O￨- bear￨L￨NN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- GYE￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- CDV￨U￨NN￨O￨- exposure￨L￨NN￨O￨- in￨L￨IN￨O￨- bears￨L￨NNS￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- correlated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨A of￨L￨IN￨O￨- distemper￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- wolves￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- often￨L￨RB￨O￨- consist￨L￨VBP￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- systems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- parameter￨L￨NN￨O￨- settings/perturbations￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- multiple￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- and￨L￨CC￨O￨- boundary￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- recent￨L￨JJ￨O￨- work￨L￨NN￨O￨- points￨L￨VBZ￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- ensemble￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- inadequate￨L￨JJ￨O￨- to￨L￨TO￨O￨- correctly￨L￨RB￨O￨- separate￨L￨VB￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- structural￨L￨JJ￨O￨- uncertainty￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- study￨L￨NN￨O￨- using￨L￨VBG￨O￨- large￨L￨JJ￨O￨- climate￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ensembles￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- perturbation￨L￨NN￨O￨- approach￨L￨NN￨O￨- involved￨L￨VBD￨O￨- defining￨L￨VBG￨O￨- a￨L￨DT￨O￨- prior￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A from￨L￨IN￨O￨- expert￨L￨JJ￨O￨- opinion￨L￨NN￨O￨- or￨L￨CC￨O￨- field￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- applying￨L￨VBG￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- performance￨L￨NN￨O￨- criterion￨L￨NN￨O￨- to￨L￨TO￨O￨- reject￨L￨VB￨O￨- some￨L￨DT￨O￨- parameter￨L￨NN￨O￨- combinations￨L￨NNS￨O￨- a￨L￨DT￨O￨- posteriori￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- climate￨L￨NN￨O￨- information￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- drive￨L￨VB￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- observed￨L￨VBN￨O￨- clinical￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- highland￨L￨NN￨O￨- tea￨L￨NN￨O￨- plantation￨L￨NN￨O￨- location￨L￨NN￨O￨- in￨L￨IN￨O￨- East￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- weather￨L￨NN￨O￨- prediction￨L￨NN￨O￨- and￨L￨CC￨O￨- climate￨L￨NN￨O￨- projection￨L￨NN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- cascade￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- errors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- and￨L￨CC￨O￨- boundary￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- system￨L￨NN￨O￨- itself￨L￨PRP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- uncertainty￨L￨NN￨O￨A with￨L￨IN￨O￨- regard￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- setting￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- evaluated￨L￨VBN￨O￨- by￨L￨IN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- susceptibility￨L￨NN￨O￨- index￨L￨NN￨O￨A S￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- giant￨L￨JJ￨O￨- component￨L￨NN￨O￨- σ￨L￨NN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- well-known￨L￨JJ￨O￨- existing￨L￨VBG￨O￨- metrics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Jaccard￨U￨NNP￨PERSON￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- Bridgeness￨U￨NNP￨MISC￨- index￨L￨NN￨O￨- ,￨L￨,￨O￨- Betweenness￨U￨NN￨O￨- centrality￨L￨NN￨O￨- and￨L￨CC￨O￨- Reachability￨U￨NN￨MISC￨- index￨L￨NN￨O￨- in￨L￨IN￨O￨- nine￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Identifying￨U￨NNP￨O￨- critical￨L￨JJ￨O￨- edges￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- En-Yu￨U￨JJ￨O￨- Yu1￨U￨NN￨O￨- ,￨L￨,￨O￨- Duan-Bing￨U￨JJ￨O￨- Chen1￨U￨NN￨O￨- ,2￨L￨NN￨O￨- &￨L￨CC￨O￨- Jun-Yan￨U￨NN￨MISC￨- Zhao3￨U￨NN￨MISC￨- Scientific￨U￨NNP￨MISC￨- Reportsvolume￨U￨NNP￨MISC￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 14469￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksInformation￨L￨NN￨O￨- technology￨L￨NN￨O￨- AbstractThe￨U￨NNP￨O￨- critical￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- extraordinary￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- which￨L￨WDT￨O￨- play￨L￨VBP￨O￨- more￨L￨JJR￨O￨- significant￨L￨JJ￨O￨- role￨L￨NN￨O￨- than￨L￨IN￨O￨- other￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- critical￨L￨JJ￨O￨- edges￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- attracted￨L￨VBN￨O￨- much￨L￨JJ￨O￨- attention￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- theoretical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +Experimental￨U￨JJ￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- method￨L￨NN￨O￨- outperforms￨L￨VBZ￨O￨- these￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- critical￨L￨JJ￨O￨- edges￨L￨NNS￨O￨A both￨L￨CC￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- connectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- dynamic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- disseminate￨L￨VB￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- ranking￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- BCCMOD￨U￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- cliques￨L￨NNS￨O￨- and￨L￨CC￨O￨- paths￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨A in￨L￨IN￨O￨- this￨L￨DT￨O￨- report￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- average￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- expect￨L￨VBP￨O￨- that￨L￨IN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- less￨L￨JJR￨O￨- vaccinated￨L￨VBN￨O￨A populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- more￨L￨RBR￨O￨- vaccinated￨L￨VBN￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- strains￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- better￨L￨RBR￨O￨- targeted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recent￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- from￨L￨IN￨O￨- test-negative￨L￨JJ￨O￨- design￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TND￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2010￨L￨CD￨DATE￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2017￨L￨CD￨DATE￨- show￨L￨NN￨O￨- lower￨L￨JJR￨O￨A VE￨U￨NN￨O￨- against￨L￨IN￨O￨- H3N2￨U￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- H1N1￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- A1￨U￨NN￨O￨- and￨L￨CC￨O￨- Figure￨U￨NN￨O￨- A2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Vaccines￨U￨NNS￨O￨- might￨L￨MD￨O￨- also￨L￨RB￨O￨- distinguish￨L￨VB￨O￨- between￨L￨IN￨O￨- strains￨L￨NNS￨O￨A defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- other￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- lineages￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- A4￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- clades￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A/H3N2￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- A5￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- ,￨L￨,￨O￨- seasonal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A coverage￨L￨NN￨O￨- averaged￨L￨VBD￨O￨- 43.4￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- ranged￨L￨VBD￨O￨- from￨L￨IN￨O￨- 32.6￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- to￨L￨TO￨O￨- 46.1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2009￨L￨CD￨DATE￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2015￨L￨CD￨DATE￨- seasons￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- within-host￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- different￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- virus￨L￨NN￨O￨- compete￨L￨VB￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- cells￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- variant￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- virions￨L￨NNS￨O￨- each￨L￨DT￨O￨- variant￨L￨JJ￨O￨- produces￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- virions￨L￨NNS￨O￨- successfully￨L￨RB￨O￨- infect￨L￨VB￨O￨- further￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- cells￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- possibility￨L￨NN￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- variant￨L￨JJ￨O￨- coexistence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- if￨L￨IN￨O￨- cells￨L￨NNS￨O￨A infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- produce￨L￨VBP￨O￨- more￨L￨JJR￨O￨- virions￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- virions￨L￨NNS￨O￨- ,￨L￨,￨O￨- than￨L￨IN￨O￨- singly￨L￨RB￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Ló￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Díaz-Muñ￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- variants￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- infect￨L￨VB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- cells￨L￨NNS￨O￨A inside￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Issues￨U￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- banking￨L￨VBG￨O￨- efficiency￨L￨NN￨O￨A have￨L￨VBP￨O￨- long￨L￨RB￨O￨- been￨L￨VBN￨O￨- emphasized￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- wherein￨L￨WRB￨O￨- financial￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- analysis￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- data￨L￨NNS￨O￨- envelopment￨L￨NN￨O￨- analysis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DEA￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- semi-nonparametric￨L￨JJ￨O￨- envelopment￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- StoNED￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- frontier￨L￨NN￨O￨- analysis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SFA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- production￨L￨NN￨O￨- or￨L￨CC￨O￨- cost￨L￨NN￨O￨- frontier￨L￨NN￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- productivity￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- production￨L￨NN￨O￨- systems￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- multiple￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- structure￨L￨NN￨O￨- ;￨L￨:￨O￨- these￨L￨DT￨O￨- include￨L￨VBP￨O￨- new￨L￨JJ￨O￨- energy￨L￨NN￨O￨- enterprises￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- iron￨L￨NN￨O￨- and￨L￨CC￨O￨- steel￨L￨NN￨O￨- industry￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- service￨L￨NN￨O￨- industry￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- commercial￨L￨JJ￨O￨- banks￨L￨NNS￨O￨- and￨L￨CC￨O￨- supply￨L￨NN￨O￨- chains￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- assessed￨L￨VBN￨O￨- banking￨L￨NN￨O￨- performance￨L￨NN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- undesirable￨L￨JJ￨O￨- outputs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- non-performing￨L￨JJ￨O￨- loans￨L￨NNS￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Huang￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- super￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Khodabakhshi￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- Webb￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- retail￨L￨JJ￨O￨- Banks￨U￨NNS￨O￨- ;￨L￨:￨O￨- Puri￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +Infection￨U￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- serotype￨L￨NN￨O￨A is￨L￨VBZ￨O￨- immunizing￨L￨VBG￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- get￨L￨VB￨O￨- HFMD￨U￨JJ￨O￨- multiple￨L￨JJ￨O￨- times￨L￨NNS￨O￨- if￨L￨IN￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +EV-A71￨U￨NN￨O￨- has￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- ongoing￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- development￨L￨NN￨O￨- ;￨L￨:￨O￨- monovalent￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- against￨L￨IN￨O￨- this￨L￨DT￨O￨- serotype￨L￨NN￨O￨A do￨L￨VBP￨O￨- not￨L￨RB￨O￨- protect￨L￨VB￨O￨- against￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- CV-A16￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨RB￨ORDINAL￨- reported￨L￨VBN￨O￨A cases￨L￨NNS￨O￨A of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- CV-A16￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- EV-A71￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨A >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- management￨L￨NN￨O￨- is￨L￨VBZ￨O￨- optimized￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- value￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨- per￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- treatments￨L￨NNS￨O￨- decrease￨L￨VBP￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- when￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨A >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- management￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- optimized￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- value￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- improvement￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- expenditures￨L￨NNS￨O￨- or￨L￨CC￨O￨- losses￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- sea￨L￨NN￨O￨- lice￨L￨NN￨O￨- in￨L￨IN￨O￨- salmon￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- value￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- expenditures￨L￨NNS￨O￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- losses￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 0.065￨L￨CD￨MONEY￨- €￨L￨$￨MONEY￨- /￨L￨:￨O￨- unit￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨A /￨L￨:￨O￨- kg￨L￨NN￨O￨- production￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- at￨L￨IN￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨A .￨L￨.￨O￨- +Genetic￨U￨JJ￨O￨- improvement￨L￨NN￨O￨- of￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨A lowers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- loss-expenditure￨L￨JJ￨O￨- frontier￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨A illness￨L￨NN￨CAUSE_OF_DEATH￨- given￨L￨VBN￨O￨- HEV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- thought￨L￨VBN￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- with￨L￨IN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- about￨L￨RB￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- adults￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- genotypes￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- death￨L￨NN￨O￨- given￨L￨VBN￨O￨- symptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- approximately￨L￨RB￨O￨- 2￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- non-pregnant￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- pregnant￨L￨JJ￨O￨- women￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- vaccine￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- >￨L￨JJR￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- efficacy￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- dose￨L￨NN￨O￨- schedule￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 6￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- clinical￨L￨JJ￨O￨- trial￨L￨NN￨O￨- involving￨L￨VBG￨O￨- 109,959￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- HEV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- setting￨L￨NN￨O￨- ,￨L￨,￨O￨- primarily￨L￨RB￨O￨- with￨L￨IN￨O￨- genotype￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- both￨L￨DT￨O￨- pre-emptive￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- prior￨L￨JJ￨O￨- to￨L￨TO￨O￨- HEV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- reactive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- once￨L￨RB￨DATE￨- HEV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- already￨L￨RB￨O￨- underway￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- selecting￨L￨VBG￨O￨A different￨L￨JJ￨O￨- target￨L￨NN￨O￨- groups￨L￨NNS￨O￨- to￨L￨TO￨O￨- receive￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- do￨L￨VB￨O￨- this￨L￨DT￨O￨- we￨L￨PRP￨O￨- fitted￨L￨VBD￨O￨- dynamic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- large￨L￨JJ￨O￨- HEV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- IDP￨U￨NNP￨O￨- camps￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- general￨L￨JJ￨TITLE￨- and￨L￨CC￨O￨- simple￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨A of￨L￨IN￨O￨- virus￨L￨NN￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- annual￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- train￨L￨VB￨O￨- them￨L￨PRP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- analytic￨L￨JJ￨O￨A predictions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- ,￨L￨,￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- common￨L￨JJ￨O￨- ancestor￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- cross-immunity￨L￨NN￨O￨- distance￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- either￨L￨RB￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- normalization￨L￨NN￨O￨- condition￨L￨NN￨O￨- The￨U￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- mutations￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- rare￨L￨JJ￨O￨- ,￨L￨,￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- below￨L￨IN￨O￨- in￨L￨IN￨O￨- subsection￨L￨NN￨O￨- Mutation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- analytic￨L￨JJ￨O￨A approach￨L￨NN￨O￨- combining￨L￨VBG￨O￨- a￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- framework￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- theory￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- multivariable￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- regression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- comparing￨L￨VBG￨O￨- VL￨U￨NNP￨O￨- to￨L￨TO￨O￨- recent￨L￨JJ￨O￨- asymptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- rK39￨L￨NN￨O￨- ELISA￨U￨NN￨O￨- positivity￨L￨NN￨O￨A and￨L￨CC￨O￨- LST￨U￨NN￨O￨- negativity￨L￨NN￨O￨- at￨L￨IN￨O￨- baseline￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- living￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- household￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- case￨L￨NN￨O￨- was￨L￨VBD￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- significantly￨L￨RB￨O￨- increased￨L￨VBN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- OR￨U￨NN￨STATE_OR_PROVINCE￨- =￨L￨JJ￨O￨- 2.85￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- 1.45￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5.61￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.003￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- was￨L￨VBD￨O￨- substantially￨L￨RB￨O￨- higher￨L￨JJR￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- living￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- household￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- case￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- OR￨U￨NN￨STATE_OR_PROVINCE￨- =￨L￨JJ￨O￨- 6.37￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- 3.30￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12.28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- <￨L￨JJR￨O￨- 0.0001￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- decreased￨L￨VBD￨O￨- relatively￨L￨RB￨O￨- quickly￨L￨RB￨O￨- with￨L￨IN￨O￨- distance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- OR￨U￨NN￨STATE_OR_PROVINCE￨- =￨L￨JJ￨O￨- 1.85￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- 0.95￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3.60￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.07￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- household￨L￨NN￨O￨- without￨L￨IN￨O￨- VL￨U￨NNP￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 50m￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- rK39￨L￨NN￨O￨- ELISA￨U￨NN￨O￨- positivity￨L￨NN￨O￨A and￨L￨CC￨O￨- LST￨U￨NN￨O￨- positivity￨L￨NN￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- strongly￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- proximity￨L￨NN￨O￨- to￨L￨TO￨O￨- previous￨L￨JJ￨O￨- VL￨U￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Associations￨U￨NNS￨O￨- between￨L￨IN￨O￨- VL￨U￨NNP￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- asymptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- rK39￨L￨NN￨O￨- ELISA￨U￨NN￨O￨- positivity￨L￨NN￨O￨A or￨L￨CC￨O￨- LST￨U￨NN￨O￨- positivity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- distance￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- VL￨U￨NNP￨O￨- case￨L￨NN￨O￨- were￨L￨VBD￨O￨- assessed￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- odds￨L￨NNS￨O￨- ratios￨L￨NNS￨O￨- of￨L￨IN￨O￨- having￨L￨VBG￨O￨- VL￨U￨NNP￨O￨- or￨L￨CC￨O￨- being￨L￨VBG￨O￨- rK39￨L￨NN￨O￨- ELISA/LST-positive￨U￨JJ￨O￨- if￨L￨IN￨O￨- living￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- household￨L￨NN￨O￨- as￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- household￨L￨NN￨O￨- but￨L￨CC￨O￨- <￨L￨JJR￨O￨- 50m￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- closest￨L￨JJS￨O￨- previous￨L￨JJ￨O￨- VL￨U￨NNP￨O￨- case￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- living￨L￨VBG￨O￨- >￨L￨JJR￨O￨- 50m￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨O￨- xenodiagnosis￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- asymptomatic￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- high￨L￨JJ￨O￨- anti-leishmanial￨L￨JJ￨O￨- antibody￨L￨NN￨O￨- titres￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- agglutination￨L￨NN￨O￨- test￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DAT￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- rK39￨L￨NN￨O￨- enzyme-linked￨L￨JJ￨O￨- immunosorbent￨L￨JJ￨O￨- assay￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ELISA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- symptoms￨L￨NNS￨O￨- or￨L￨CC￨O￨- prior￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- failed￨L￨VBD￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- sandflies￨L￨NNS￨O￨- fed￨L￨VBN￨O￨- upon￨L￨IN￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- VL￨U￨NN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- post￨L￨NN￨O￨- kala-azar￨L￨JJ￨O￨- dermal￨L￨JJ￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- PKDL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- cases￨L￨NNS￨O￨- infected￨L￨JJ￨O￨- sandflies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- mechanisms￨L￨NNS￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- temperature￨L￨NN￨O￨A is￨L￨VBZ￨O￨- hypothesized￨L￨VBN￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- STEC￨U￨NN￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- spent￨L￨VBD￨O￨- engaged￨L￨VBN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- grazing￨L￨NN￨O￨- vs.￨L￨CC￨O￨- We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- STEC￨U￨NN￨ORGANIZATION￨- among￨L￨IN￨O￨- grazing￨L￨NN￨O￨- cattle￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- mechanisms￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- seasonality￨L￨NN￨O￨- in￨L￨IN￨O￨- STEC￨U￨NNP￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- grazing￨L￨NN￨O￨- cattle￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- ABM￨U￨NNP￨MISC￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- STEC￨U￨NN￨ORGANIZATION￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- varying￨L￨VBG￨O￨- mechanisms￨L￨NNS￨O￨- linking￨L￨VBG￨O￨- temperature￨L￨NN￨O￨A and￨L￨CC￨O￨- STEC￨U￨NN￨ORGANIZATION￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Proposed￨U￨VBN￨O￨- mechanisms￨L￨NNS￨O￨- include￨L￨VBP￨O￨- enhanced￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- mediated￨L￨VBN￨O￨- by￨L￨IN￨O￨- water￨L￨NN￨O￨- and￨L￨CC￨O￨- flies￨L￨VBZ￨O￨- at￨L￨IN￨O￨- higher￨L￨JJR￨O￨- temperature￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- increased￨L￨VBD￨O￨- susceptibility￨L￨NN￨O￨- linked￨L￨VBN￨O￨- to￨L￨TO￨O￨- hormonal￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- length￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- how￨L￨WRB￨O￨- temperature￨L￨NN￨O￨A fluctuation￨L￨NN￨O￨- caused￨L￨VBD￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- STEC￨U￨NN￨ORGANIZATION￨- incidence￨L￨NN￨O￨- among￨L￨IN￨O￨- grazing￨L￨NN￨O￨- cattle￨L￨NNS￨O￨- by￨L￨IN￨O￨- influencing￨L￨VBG￨O￨- diurnal￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- global￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨A of￨L￨IN￨O￨- trachoma￨L￨NN￨O￨- continues￨L￨VBZ￨O￨- to￨L￨TO￨O￨- decline￨L￨VB￨O￨- it￨L￨PRP￨O￨- becomes￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- challenging￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- and￨L￨CC￨O￨- confirm￨L￨VB￨O￨- TF￨U￨NN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- training￨L￨NN￨O￨- graders￨L￨NNS￨O￨- becomes￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- expensive￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- sero-surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- trachoma￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- currently￨L￨RB￨DATE￨- being￨L￨VBG￨O￨- evaluated￨L￨VBN￨O￨- as￨L￨IN￨O￨- more￨L￨JJR￨O￨- long-term￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- low-level￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- re-emergence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- PCR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- simulated￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨A data￨L￨NNS￨O￨A within￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- community￨L￨NN￨O￨- of￨L￨IN￨O￨- 3,000￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1/3rd￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- were￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- aged￨L￨JJ￨O￨- 1-9￨L￨CD￨NUMBER￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- TF￨U￨NN￨O￨- and￨L￨CC￨O￨- PCR￨U￨NN￨O￨- positive￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- validated￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- that￨L￨WDT￨O￨- was￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- parsimonious￨L￨JJ￨O￨- and￨L￨CC￨O￨- appropriate￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- when￨L￨WRB￨O￨- fitting￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- cross-section￨L￨NN￨O￨- of￨L￨IN￨O￨- age-specific￨L￨JJ￨O￨- PCR￨U￨NN￨O￨- and￨L￨CC￨O￨- TF￨U￨NN￨O￨- prevalence￨L￨NN￨O￨A data￨L￨NNS￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- evaluate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- TF￨U￨NN￨O￨- and￨L￨CC￨O￨- PCR￨U￨NN￨O￨- positive￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- changes￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- intervention￨L￨NN￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- during￨L￨IN￨O￨- re-emergence￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- if￨L￨IN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- how￨L￨WRB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- impacts￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- prevalence￨L￨NN￨O￨A data￨L￨NNS￨O￨A at￨L￨IN￨O￨- different￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- PCR￨U￨NN￨O￨- and￨L￨CC￨O￨- TF￨U￨NN￨O￨- positive￨L￨JJ￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Mathematical￨U￨JJ￨MISC￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- vancomycin-resistant￨L￨JJ￨O￨- enterococci￨L￨NN￨O￨- transmission￨L￨NN￨O￨- during￨L￨IN￨O￨- passive￨L￨NN￨O￨- surveillance￨L￨NN￨O￨A and￨L￨CC￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- with￨L￨IN￨O￨- contact￨L￨NN￨O￨- isolation￨L￨NN￨O￨- highlights￨L￨VBZ￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- and￨L￨CC￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- acquisitionAgnes￨L￨NNS￨O￨- Loo￨U￨NNP￨O￨- Yee￨U￨NNP￨O￨- Cheah1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Allen￨U￨NNP￨PERSON￨- C.￨U￨NNP￨O￨- 2018Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Clinical￨U￨JJ￨MISC￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- with￨L￨IN￨O￨- contact￨L￨NN￨O￨- isolation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- reduced￨L￨VBN￨O￨- vancomycin-resistant￨L￨JJ￨O￨- enterococci￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- VRE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- prevalence￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- passive￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- using￨L￨VBG￨O￨- pre-and￨L￨JJ￨O￨- post-intervention￨L￨JJ￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- imperfect￨L￨JJ￨O￨- observation￨L￨NN￨O￨- and￨L￨CC￨O￨- serial￨L￨NN￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- VRE￨U￨NN￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- can￨L￨MD￨O￨- better￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨A and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- contact￨L￨NN￨O￨- isolation￨L￨NN￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- performed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- pre-and￨L￨JJ￨O￨- post-implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- with￨L￨IN￨O￨- contact￨L￨NN￨O￨- isolation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- haematology-oncology￨L￨JJ￨O￨- ward￨L￨NN￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- its￨L￨PRP$￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- real‐time￨L￨JJ￨O￨- publication￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- data￨L￨NNS￨O￨- stream￨L￨NN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- accurate￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- outbreak￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 13￨L￨CD￨NUMBER￨- Nsoesie￨U￨NN￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- used￨L￨VBN￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- peak￨L￨NN￨O￨- timing￨L￨NN￨O￨- in￨L￨IN￨O￨- Seattle￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Washington￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- 5‐6￨L￨CD￨NUMBER￨- weeks￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- .14￨L￨CD￨NUMBER￨- Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- Shaman￨U￨NN￨O￨- and￨L￨CC￨O￨- Karspeck￨U￨NN￨PERSON￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- real‐time￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecast￨L￨NN￨O￨- for￨L￨IN￨O￨- New￨U￨NNP￨CITY￨- York￨U￨NNP￨CITY￨- City￨U￨NNP￨CITY￨- using￨L￨VBG￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- generated￨L￨VBD￨O￨- skillful￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- peak￨L￨NN￨O￨- timing￨L￨NN￨O￨- 7￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- peak￨L￨NN￨O￨- .15￨L￨CD￨NUMBER￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- had￨L￨VBD￨O￨- well‐documented￨L￨VBN￨O￨- limitations￨L￨NNS￨O￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- A/H1N1￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic9￨L￨NN￨O￨- ,￨L￨,￨O￨- 16￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- inflated￨L￨VBD￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- A/H3N2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ‐￨L￨SYM￨O￨- 13￨L￨CD￨NUMBER￨- season￨L￨NN￨O￨- .9￨L￨CD￨NUMBER￨- Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- new￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- using￨L￨VBG￨O￨- online￨L￨JJ￨O￨- search￨L￨NN￨O￨- queries￨L￨NNS￨O￨- ,12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 17￨L￨CD￨NUMBER￨- tweets￨L￨NNS￨O￨- ,18￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 19￨L￨CD￨NUMBER￨- Wikipedia￨U￨NNP￨ORGANIZATION￨- access￨L￨NN￨O￨- logs￨L￨NNS￨O￨- ,20￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 21￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- public￨L￨JJ￨O￨- generated￨L￨VBN￨O￨- content￨L￨NN￨O￨- ;￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 23￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- was￨L￨VBD￨O￨- only￨L￨RB￨O￨- available￨L￨JJ￨O￨- at￨L￨IN￨O￨- national￨L￨JJ￨O￨- and￨L￨CC￨O￨- regional￨L￨JJ￨O￨- geographic￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- forecast￨L￨NN￨O￨- of￨L￨IN￨O￨- more￨L￨JJR￨O￨- local￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- these￨L￨DT￨O￨- issues￨L￨NNS￨O￨- by￨L￨IN￨O￨- testing￨L￨VBG￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecast￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- using￨L￨VBG￨O￨- 6￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- county￨L￨NN￨O￨- departments￨L￨NNS￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- in￨L￨IN￨O￨- Arizona￨U￨NNP￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- Indiana￨U￨NNP￨STATE_OR_PROVINCE￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- forecast￨L￨NN￨O￨A accuracy￨L￨NN￨O￨- and￨L￨CC￨O￨- utility￨L￨NN￨O￨- when￨L￨WRB￨O￨- incorporating￨L￨VBG￨O￨- different￨L￨JJ￨O￨- local￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- types￨L￨NNS￨O￨- .￨L￨.￨O￨- +Little￨U￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- despite￨L￨IN￨O￨- a￨L￨DT￨O￨- renewed￨L￨VBN￨O￨- research￨L￨NN￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- tropical￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- increased￨L￨VBN￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- .16￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 17￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 18￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 19￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 20￨L￨CD￨NUMBER￨- To￨U￨TO￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- tropical￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- concentrated￨L￨VBN￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- annual￨L￨JJ￨SET￨- seasonality21￨L￨NN￨O￨- ,￨L￨,￨O￨- 22￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 23￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 24￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 26￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 27￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 29￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- viruses￨L￨NNS￨O￨- show￨L￨VBP￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- year‐round￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- .30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 31￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 32￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 33￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 34￨L￨CD￨NUMBER￨- A￨U￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- question￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- received￨L￨VBN￨O￨- less￨L￨JJR￨O￨- attention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- syndromic￨L￨JJ￨O￨- influenza‐like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- surveillance￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- peaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- troughs￨L￨NNS￨O￨- as￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- by￨L￨IN￨O￨- several￨L￨JJ￨O￨- research￨L￨NN￨O￨- groups￨L￨NNS￨O￨- for￨L￨IN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- 's￨L￨POS￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- prediction￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Flu￨U￨NNP￨CAUSE_OF_DEATH￨- Trends￨U￨VBZ￨O￨- .7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10￨L￨CD￨NUMBER￨- Critiques￨U￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- included￨L￨VBD￨O￨- its￨L￨PRP$￨O￨- reliance￨L￨NN￨O￨- on￨L￨IN￨O￨- Internet￨U￨NN￨MISC￨- search￨L￨NN￨O￨- behavior￨L￨NN￨O￨- remaining￨L￨VBG￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- overfitting￨L￨JJ￨O￨- effect￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- given￨L￨VBN￨O￨- too￨L￨RB￨O￨- much￨L￨JJ￨O￨- weight￨L￨NN￨O￨- to￨L￨TO￨O￨- associations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- training￨L￨NN￨O￨- data￨L￨NNS￨O￨- sets￨L￨VBZ￨O￨- only￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- specific￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- incorrect￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- .9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- challenge￨L￨NN￨O￨- in￨L￨IN￨O￨- big‐data￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨A is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- narrow￨L￨VB￨O￨- the￨L￨DT￨O￨- gap￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- point￨L￨NN￨O￨- describing￨L￨VBG￨O￨- it￨L￨PRP￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- large￨L￨JJ￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- points￨L￨NNS￨O￨- are￨L￨VBP￨O￨- grounded￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- antibody￨L￨NN￨O￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reasons￨L￨NNS￨O￨- for￨L￨IN￨O￨- disagreement￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- literature￨L￨NN￨O￨- as￨L￨IN￨O￨- some￨L￨DT￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- claim￨L￨VBP￨O￨- support￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- transmission￨L￨NN￨O￨- season21￨L￨NN￨O￨- ,￨L￨,￨O￨- 26￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 29￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 39￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 40￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 42￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 47￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 48￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 49￨L￨CD￨NUMBER￨- while￨L￨IN￨O￨- others￨L￨NNS￨O￨- show￨L￨VBP￨O￨- mixed￨L￨JJ￨O￨- or￨L￨CC￨O￨- no￨L￨DT￨O￨- evidence￨L￨NN￨O￨- .22￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 27￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 46￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 50￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 51￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 52￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 53￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 54￨L￨CD￨NUMBER￨- Among￨U￨IN￨O￨- these￨L￨DT￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- weakly￨L￨RB￨O￨- supported￨L￨VBN￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- being￨L￨VBG￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- policy￨L￨NN￨O￨- to￨L￨TO￨O￨- advocate￨L￨VB￨O￨- for￨L￨IN￨O￨- particular￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- timings￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- incorrectly￨L￨RB￨O￨- identified￨L￨VBN￨O￨- seasonal￨L￨JJ￨O￨- signals￨L￨NNS￨O￨- .29￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 49￨L￨CD￨NUMBER￨- For￨U￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- studies￨L￨NNS￨O￨- with￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- data27￨L￨NN￨O￨- ,￨L￨,￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 55￨L￨CD￨NUMBER￨- have￨L￨VBP￨O￨- generally￨L￨RB￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- annual￨L￨JJ￨SET￨- seasonal￨L￨JJ￨O￨- signals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- supported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- shows￨L￨VBZ￨O￨- an￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- progressing￨L￨VBG￨O￨- from￨L￨IN￨O￨- tropical￨L￨JJ￨O￨A to￨L￨TO￨O￨- temperate￨L￨VB￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .30￨L￨CD￨NUMBER￨- A￨U￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- example￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- study￨L￨NN￨O￨- published￨L￨VBN￨O￨- using￨L￨VBG￨O￨- sentinel￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- large￨L￨JJ￨O￨- wintertime￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- peaks￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- north￨L￨NN￨O￨- to￨L￨TO￨O￨- smaller￨L￨JJR￨O￨- less￨L￨RBR￨O￨- predictable￨L￨JJ￨O￨- peaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- subtropics￨L￨NNS￨O￨- .63￨L￨CD￨NUMBER￨- Beyond￨U￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- examples￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- hard￨L￨JJ￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- paucity￨L￨NN￨O￨- of￨L￨IN￨O￨- long‐term￨L￨JJ￨O￨- consistent￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- tropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- temperate￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- agencies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- rely￨L￨VB￨O￨- on￨L￨IN￨O￨- ILI￨U￨NN￨O￨- reporting￨L￨VBG￨O￨- to￨L￨TO￨O￨- signal￨L￨VB￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 35￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 36￨L￨CD￨NUMBER￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- known￨L￨VBN￨O￨- whether￨L￨IN￨O￨- ILI￨U￨NNP￨O￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- correlate￨L￨VBP￨O￨- in￨L￨IN￨O￨- tropical￨L￨JJ￨O￨A countries￨L￨NNS￨O￨- .37￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 38￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- looking￨L￨VBG￨O￨- at￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and/or￨L￨CC￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- drawbacks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- recommended￨L￨VBD￨O￨- that￨L￨IN￨O￨- populations￨L￨NNS￨O￨- at￨L￨IN￨O￨- higher￨L￨JJR￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- hospitalizations￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨- .1￨L￨CD￨NUMBER￨- Healthy￨U￨JJ￨O￨- school‐going￨L￨JJ￨O￨- children￨L￨NNS￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- excluded￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- defined￨L￨VBN￨O￨- vulnerable￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- contracting￨L￨VBG￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- increased￨L￨VBN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- frequent￨L￨JJ￨O￨- close￨L￨JJ￨O￨- contact￨L￨NN￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- .2￨L￨NN￨NUMBER￨- School‐based￨U￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨A programs￨L￨NNS￨O￨- have￨L￨VBP￨O￨- therefore￨L￨RB￨O￨- been￨L￨VBN￨O￨- recommended￨L￨VBN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- settings￨L￨NNS￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- existing￨L￨VBG￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- programs￨L￨NNS￨O￨- but￨L￨CC￨O￨- remain￨L￨VBP￨O￨- rare￨L￨JJ￨O￨- globally￨L￨RB￨O￨- .3￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- free￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- policy￨L￨NN￨O￨- was￨L￨VBD￨O￨- launched￨L￨VBN￨O￨- in￨L￨IN￨O￨- primary￨L￨JJ￨O￨- ,￨L￨,￨O￨- secondary￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- schoolchildren￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- 6‐18￨L￨CD￨NUMBER￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨O￨- .5￨L￨CD￨NUMBER￨- Temporary￨U￨JJ￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- POVs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- established￨L￨VBN￨O￨- at￨L￨IN￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- students￨L￨NNS￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- parent￨L￨NN￨O￨- 's￨L￨POS￨O￨- written￨L￨VBN￨O￨- consent￨L￨NN￨O￨- are￨L￨VBP￨O￨- organized￨L￨VBN￨O￨- to￨L￨TO￨O￨- receive￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- there￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- judging￨L￨VBG￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- intensities￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- with￨L￨IN￨O￨- vs￨L￨CC￨O￨A without￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- averted￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- medically￨L￨RB￨O￨- attended￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- outpatient￨L￨NN￨O￨- and￨L￨CC￨O￨- emergency￨L￨NN￨O￨- attended￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- ‐￨L￨SYM￨O￨- 2016￨L￨CD￨DATE￨- seasons￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- vs￨L￨CC￨O￨A without￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- equals￨L￨VBZ￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- averted￨L￨VBN￨O￨- by￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Beijing￨U￨NNP￨CITY￨- among￨L￨IN￨O￨- children￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- 5‐14￨L￨CD￨NUMBER￨- years￨L￨NNS￨DURATION￨- using￨L￨VBG￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Next￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- were￨L￨VBD￨O￨- again￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- without￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Evaluating￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- Usutu￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- circulation￨L￨NN￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- :￨L￨:￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨A niche￨L￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- modelsYanchao￨L￨NN￨O￨- Cheng1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Nils￨U￨NNP￨PERSON￨- Benjamin￨U￨NNP￨PERSON￨- Tjaden1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Anja￨U￨NNP￨PERSON￨- Jaeschke1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Renke￨U￨NNP￨PERSON￨- Lühken2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Ute￨U￨NNP￨O￨- Ziegler3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Stephanie￨U￨NNP￨PERSON￨- Margarete￨U￨NNP￨PERSON￨- Thomas1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Carl￨U￨NNP￨PERSON￨- Beierkuhnlein1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 17:35￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Usutu￨U￨NNP￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- USUV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- mosquito-borne￨L￨JJ￨O￨- flavivirus￨L￨NN￨O￨- ,￨L￨,￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- of￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Europe￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- range￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- implemented￨L￨VBD￨O￨- a￨L￨DT￨O￨- parallel￨L￨JJ￨O￨- approach￨L￨NN￨O￨- incorporating￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- commonly￨L￨RB￨O￨- applied￨L￨VBN￨O￨- modelling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Maxent￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- correlation-based￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨A niche￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- susceptible-exposed-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- environmental￨L￨JJ￨O￨A niche￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- depicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- situation￨L￨NN￨O￨- better￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- with￨L￨IN￨O￨- USUV￨U￨NN￨ORGANIZATION￨- still￨L￨RB￨O￨- being￨L￨VBG￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- invasive￨L￨JJ￨O￨- stage￨L￨NN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- chance￨L￨NN￨O￨- for￨L￨IN￨O￨- under-estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- environmental￨L￨JJ￨O￨A niche￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- run￨L￨VBN￨O￨- with￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- bio-climatic￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- source￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- climatic￨L￨JJ￨O￨- suitability￨L￨NN￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- models￨L￨NNS￨O￨- show￨L￨VBP￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨A for￨L￨IN￨O￨- USUV￨U￨NN￨O￨- in￨L￨IN￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- France￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Pannonian￨U￨NNP￨LOCATION￨- Basin￨U￨NNP￨LOCATION￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- northern￨L￨JJ￨O￨- Italy￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- assimilation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- also￨L￨RB￨O￨- as￨L￨IN￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- point￨L￨NN￨O￨- processors￨L￨NNS￨O￨- ,￨L￨,￨O￨- Kalman￨U￨NNP￨PERSON￨- filters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- linear￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- regression￨L￨NN￨O￨A method￨L￨NN￨O￨- meant￨L￨VBN￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- inverse￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- estimating￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- often￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- solving￨L￨VBG￨O￨- a￨L￨DT￨O￨- forward￨L￨RB￨O￨- problem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- issuing￨L￨VBG￨O￨- a￨L￨DT￨O￨- forecast￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- was￨L￨VBD￨O￨- initially￨L￨RB￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- contexts￨L￨NNS￨O￨- of￨L￨IN￨O￨- space￨L￨NN￨O￨- travel￨L￨NN￨O￨- by￨L￨IN￨O￨- Kalman￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Brownian￨U￨NNP￨MISC￨- motion￨L￨NN￨O￨- by￨L￨IN￨O￨- Thiele￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Cases￨U￨NNS￨O￨- were￨L￨VBD￨O￨- mostly￨L￨RB￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- urban￨L￨JJ￨O￨- prefectures￨L￨NNS￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Tokyo￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- adjacent￨L￨JJ￨O￨A areas￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Osaka￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- areas￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- Osaka￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- metapopulation￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- spatiotemporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- over￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- patches￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- line￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- total￨L￨NN￨O￨A of￨L￨IN￨O￨- 47￨L￨CD￨NUMBER￨- prefectures￨L￨NNS￨O￨- in￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Top￨U￨JJ￨O￨- :￨L￨:￨O￨- Weekly￨U￨NNP￨SET￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- notified￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Kanto￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Tokyo￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- adjacent￨L￨JJ￨O￨A prefectures￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Kansai￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Osaka￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- adjacent￨L￨JJ￨O￨- prefectures￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨NN￨O￨A of￨L￨IN￨O￨- 16,730￨L￨CD￨NUMBER￨- notified￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- 4,116￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 24.6￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- 3,600￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 21.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- from￨L￨IN￨O￨- Tokyo￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Osaka￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- largest￨L￨JJS￨O￨- prefectures￨L￨NNS￨O￨- in￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2013￨L￨CD￨DATE￨- rubella￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- mostly￨L￨RB￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- urban￨L￨JJ￨O￨- areas￨L￨NNS￨O￨A .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- who￨L￨WP￨O￨- interacts￨L￨VBZ￨O￨- with￨L￨IN￨O￨- whom￨L￨WP￨O￨- ,￨L￨,￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- comprehensively￨L￨RB￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- systems20.Non-Poissonian￨L￨JJ￨O￨- bursty￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- constituents￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- strongly￨L￨RB￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- taking￨L￨VBG￨O￨- place￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- system21￨L￨NN￨O￨- ,22,23,24,25,26,27,28,29,30,31,32￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Correlated￨U￨JJ￨O￨- bursts￨L￨NNS￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A slow￨L￨VB￨O￨- down￨L￨RP￨O￨- spreading￨L￨VBG￨O￨- Takayuki￨U￨NNP￨PERSON￨- Hiraoka￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Hang-Hyun￨U￨NNP￨PERSON￨- Jo￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 15321￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- science￨L￨NN￨O￨- AbstractSpreading￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- place￨L￨NN￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- temporal￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- show￨L￨VBP￨O￨- non-Poissonian￨L￨JJ￨MISC￨- bursty￨L￨JJ￨O￨- nature￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- those￨L￨DT￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- two-step￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- probabilistic￨L￨JJ￨O￨- SI￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- inhomogeneous￨L￨JJ￨O￨A and￨L￨CC￨O￨- correlated￨L￨VBD￨O￨- IETs￨U￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- correlated￨L￨VBD￨O￨- bursts￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- non-Poissonian￨L￨JJ￨MISC￨- temporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- fully￨L￨RB￨O￨- understood￨L￨VBN￨O￨- both￨L￨CC￨O￨- by￨L￨IN￨O￨- inhomogeneous￨L￨JJ￨O￨A interevent￨L￨JJ￨O￨- times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IETs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- IETs18￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨A is￨L￨VBZ￨O￨- constant￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ∀￨L￨NN￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- classes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨A the￨L￨DT￨O￨- global￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- Zika￨U￨NNP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- approximated￨L￨VBD￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- via￨L￨IN￨O￨- both￨L￨CC￨O￨- mosquitoes￨L￨NNS￨O￨- and￨L￨CC￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- β￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- used￨L￨VBN￨O￨- here￨L￨RB￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- helps￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- observing￨L￨VBG￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- consequently￨L￨RB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨A of￨L￨IN￨O￨- Rio￨U￨NNP￨CITY￨- de￨L￨IN￨CITY￨- Janeiro￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- individual-level￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- measured￨L￨VBN￨O￨- in￨L￨IN￨O￨- appropriate￨L￨JJ￨O￨- animal￨L￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- carefully￨L￨RB￨O￨- designed￨L￨VBN￨O￨- trials￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- population-level￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- predicted￨L￨VBN￨O￨- using￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- intervention￨L￨NN￨O￨A feasibility￨L￨NN￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- relates￨L￨VBZ￨O￨- to￨L￨TO￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- logistics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- recently￨L￨RB￨DATE￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- computational￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- computing￨L￨VBG￨O￨- Dynamic￨U￨NNP￨O￨- Optimal￨U￨JJ￨O￨- Control￨U￨NN￨O￨- Policies￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- DOCPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- year-to-year￨L￨JJ￨O￨- relative￨L￨JJ￨O￨- investment￨L￨NN￨O￨- in￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- prevention￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- minimize￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- incident￨L￨NN￨O￨- cases￨L￨NNS￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- represented￨L￨VBD￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- MSM￨U￨NNP￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- encompassing￨L￨VBG￨O￨- 9￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- dividing￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- virally￨L￨RB￨O￨- suppressed￨L￨VBD￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- treatment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- T￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- protected￨L￨VBD￨O￨- susceptible￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- susceptibility￨L￨NN￨O￨- intervention￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- DOCPs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- robust￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- deployment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨A rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- and￨L￨CC￨O￨- behavioral￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- system￨L￨NN￨O￨- alone￨L￨RB￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- most￨L￨RBS￨O￨- data-driven￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- attempt￨L￨VBP￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- characteristic￨L￨JJ￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- in￨L￨IN￨O￨- isolation￨L￨NN￨O￨- —￨L￨:￨O￨- typically￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- short-time￨L￨JJ￨O￨- memory￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- or￨L￨CC￨O￨- with￨L￨IN￨O￨- long-time￨L￨JJ￨O￨- abrupt￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- external￨L￨JJ￨O￨- or￨L￨CC￨O￨- systemic￨L￨JJ￨O￨- events￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Change￨U￨NNP￨O￨- points￨L￨NNS￨O￨- ,￨L￨,￨O￨- memory￨L￨NN￨O￨A and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Tiago￨U￨NNP￨O￨- P.￨U￨NNP￨O￨- Peixoto1￨U￨NNP￨O￨- ,2￨L￨NNP￨O￨- &￨L￨CC￨O￨- Laetitia￨U￨NNP￨O￨- Gauvin2￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 15511￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComplex￨L￨NNP￨O￨- networksComputational￨L￨NNP￨O￨- science￨L￨NN￨O￨- AbstractDynamic￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- temporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- that￨L￨WDT￨O￨- vary￨L￨VBP￨O￨- across￨L￨IN￨O￨- different￨L￨JJ￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- affect￨L￨VB￨O￨- processes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- take￨L￨VBP￨O￨- place￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- do￨L￨VBP￨O￨- so￨L￨RB￨O￨- by￨L￨IN￨O￨- developing￨L￨VBG￨O￨- an￨L￨DT￨O￨- arbitrary-order￨L￨NN￨O￨- mixed￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- change￨L￨NN￨O￨- points￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- nonparametric￨L￨JJ￨O￨- Bayesian￨U￨JJ￨MISC￨- formulation￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- order￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- position￨L￨NN￨O￨- of￨L￨IN￨O￨- change￨L￨NN￨O￨- points￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- from￨L￨IN￨O￨- data￨L￨NNS￨O￨- without￨L￨IN￨O￨- overfitting￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- unified￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- both￨L￨CC￨O￨- aspects￨L￨NNS￨O￨- simultaneously￨L￨RB￨O￨- ,￨L￨,￨O￨- detecting￨L￨VBG￨O￨- short￨L￨JJ￨O￨- and￨L￨CC￨O￨- long-time￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- sPop￨L￨NN￨O￨- packages￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- flexible￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨A and￨L￨CC￨O￨- development￨L￨NN￨O￨- categories￨L￨NNS￨O￨- ,￨L￨,￨O￨- include￨L￨VBP￨O￨- both￨L￨CC￨O￨- deterministic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- offer￨L￨NN￨O￨- high-speed￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- parameter￨L￨NN￨O￨- inference￨L￨NN￨O￨- .￨L￨.￨O￨- +Incorporating￨U￨VBG￨O￨- age￨L￨NN￨O￨A dependency￨L￨NN￨O￨- in￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- challenging￨L￨VBG￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- keep￨L￨VB￨O￨- track￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- ILI￨U￨NN￨O￨- +￨L￨CC￨O￨- proxy￨L￨NN￨O￨A provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- that￨L￨WDT￨O￨- correlates￨L￨VBZ￨O￨- linearly￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- hospitalizations￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pdm09￨L￨NN￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- ;￨L￨:￨O￨- some￨L￨DT￨O￨- have￨L￨VBP￨O￨- argued￨L￨VBN￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- metric￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨RBR￨O￨- linear￨L￨JJ￨O￨- correlate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- than￨L￨IN￨O￨- ILI￨U￨NN￨O￨- rates￨L￨NNS￨O￨- alone￨L￨RB￨O￨- or￨L￨CC￨O￨- laboratory￨L￨NN￨O￨- detection￨L￨NN￨O￨- rates￨L￨NNS￨O￨- alone￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- multiplied￨L￨VBD￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- ILI￨U￨NN￨O￨- rates￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨O￨- virus￨L￨NN￨O￨- detection￨L￨NN￨O￨- rates￨L￨NNS￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- proxy￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- ILI￨U￨NNP￨O￨- +￨L￨CC￨O￨- proxy￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- each￨L￨DT￨SET￨- week￨L￨NN￨SET￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- ,￨L￨,￨O￨- panel￨L￨NN￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- reviewed￨L￨VBD￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closures￨L￨NNS￨O￨A on￨L￨IN￨O￨- community￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- health￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- school￨L￨NN￨O￨- closures￨L￨NNS￨O￨A ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨O￨- ,￨L￨,￨O￨- Yamagata￨U￨NNP￨LOCATION￨- lineage￨L￨NN￨O￨- ,￨L￨,￨O￨- occurred￨L￨VBD￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- 2016-2017￨L￨CD￨DURATION￨- epizootiological￨L￨JJ￨O￨- inspection￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- RF￨U￨NN￨O￨- revealed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨A remained￨L￨VBD￨O￨- critical￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨- incurred￨L￨VBN￨O￨- LSD￨U￨NN￨O￨- stated￨L￨VBN￨O￨- as￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- problems￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- RF￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +SBV￨U￨NN￨ORGANIZATION￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- territory￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- RF￨U￨NN￨O￨- appeared￨L￨VBD￨O￨A only￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- season￨L￨NN￨O￨- after￨L￨IN￨O￨- its￨L￨PRP$￨O￨- first￨L￨JJ￨ORDINAL￨- appearance￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- asymptomatic￨L￨JJ￨O￨- in￨L￨IN￨O￨- adult￨L￨JJ￨O￨- ruminants￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- milk￨L￨NN￨O￨- drop￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- diarrhea￨L￨NN￨O￨- ,￨L￨,￨O￨- congenital￨L￨JJ￨O￨- malformations￨L￨NNS￨O￨- in￨L￨IN￨O￨- newborn￨L￨JJ￨O￨- and￨L￨CC￨O￨- abortions￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SBV￨U￨NN￨ORGANIZATION￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- RF￨U￨NN￨O￨- were￨L￨VBD￨O￨- 36.78￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- and￨L￨CC￨O￨- seriousness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Office￨U￨NNP￨ORGANIZATION￨- International￨U￨NNP￨ORGANIZATION￨- des￨L￨NNP￨ORGANIZATION￨- Epizootics￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- OIE￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Rosselkhoznadzor￨U￨NNP￨MISC￨- include￨L￨VBP￨O￨- ASF￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- BT￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- other￨L￨JJ￨O￨- nosocomial￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Schmallenberg￨U￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SBV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Lumpy￨U￨JJ￨O￨- skin￨L￨NN￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- LSD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- 10￨L￨CD￨DURATION￨A years￨L￨NNS￨DURATION￨A (￨L￨-LRB-￨O￨- until￨L￨IN￨O￨- February￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- RF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 1.209￨L￨CD￨NUMBER￨- LSD￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- reported￨L￨VBN￨O￨- globally￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- total￨L￨JJ￨O￨A population￨L￨NN￨O￨- of￨L￨IN￨O￨- 20.548￨L￨CD￨NUMBER￨- animals￨L￨NNS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- visibility￨L￨NN￨O￨- into￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- vaccine￨L￨NN￨O￨- inventory￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- tracking￨L￨VBG￨O￨- inventory￨L￨NN￨O￨- levels￨L￨NNS￨O￨- geographically￨L￨RB￨O￨A and￨L￨CC￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- allocation￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- can￨L￨MD￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- visibility￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- supply￨L￨NN￨O￨- chain￨L￨NN￨O￨- caused￨L￨VBD￨O￨- some￨L￨DT￨O￨- areas￨L￨NNS￨O￨- to￨L￨TO￨O￨- end￨L￨VB￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- with￨L￨IN￨O￨- excess￨L￨JJ￨O￨- inventory￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- leftover￨L￨JJR￨O￨- vaccine￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- other￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- especially￨L￨RB￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- uptake￨L￨NN￨O￨A rates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- experienced￨L￨JJ￨O￨- unmet￨L￨JJ￨O￨- demand￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- states￨L￨NNS￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- visibility￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- uptake￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- inventory￨L￨NN￨O￨- levels￨L￨NNS￨O￨- geographically￨L￨RB￨O￨A .￨L￨.￨O￨- +As￨U￨IN￨O￨- new￨L￨JJ￨O￨- batches￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨A became￨L￨VBD￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- were￨L￨VBD￨O￨- allocated￨L￨VBN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- ’s￨L￨POS￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- population-based￨L￨JJ￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- pro-rata￨L￨JJ￨O￨- ”￨L￨''￨O￨- allocation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Compelling￨U￨JJ￨O￨- genetic￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- domestic￨L￨JJ￨O￨A cats￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- haemoplasmas￨L￨NNS￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- felids￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- among￨L￨IN￨O￨- some￨L￨DT￨O￨- wild￨L￨JJ￨O￨- felids￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- suggest￨L￨VB￨O￨- persistent￨L￨JJ￨O￨- onward￨L￨RB￨O￨- transmission￨L￨NN￨O￨- following￨L￨VBG￨O￨- spillover￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- widely￨L￨RB￨O￨- acknowledged￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- known￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- multiple￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- infecting￨L￨VBG￨O￨- domestic￨L￨JJ￨O￨A dogs￨L￨NNS￨O￨- and￨L￨CC￨O￨- cats￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- other￨L￨JJ￨O￨- mammalian￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- evaluates￨L￨VBZ￨O￨- spillover￨L￨NN￨O￨- of￨L￨IN￨O￨- CMhm￨U￨NN￨O￨- in￨L￨IN￨O￨- domestic￨L￨JJ￨O￨A and￨L￨CC￨O￨- wild￨L￨JJ￨O￨- felids￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- and￨L￨CC￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- onward￨L￨RB￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analyze￨L￨VBP￨O￨- field￨L￨NN￨O￨- surveys￨L￨NNS￨O￨- of￨L￨IN￨O￨- sympatric￨L￨JJ￨O￨- domestic￨L￨JJ￨O￨A cats￨L￨NNS￨O￨- ,￨L￨,￨O￨- bobcats￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- pumas￨L￨NNS￨O￨- from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- in￨L￨IN￨O￨- conjunction￨L￨NN￨O￨- with￨L￨IN￨O￨- global￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- CMhm￨U￨NN￨O￨- in￨L￨IN￨O￨- felids￨L￨NNS￨O￨- .￨L￨.￨O￨- +CMhm￨U￨NN￨O￨- DNA￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- isolated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- saliva￨L￨NN￨O￨- of￨L￨IN￨O￨- domestic￨L￨JJ￨O￨A cats￨L￨NNS￨O￨- and￨L￨CC￨O￨- vampire￨L￨NN￨O￨- bats￨L￨NNS￨O￨- ,￨L￨,￨O￨- implicating￨L￨VBG￨O￨- social￨L￨JJ￨O￨- grooming￨L￨NN￨O￨- and￨L￨CC￨O￨- aggression￨L￨NN￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- direct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- –￨L￨:￨O￨- including￨L￨VBG￨O￨- diversified￨L￨JJ￨O￨- testing￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- as￨L￨IN￨O￨- prevention￨L￨NN￨O￨A ,￨L￨,￨O￨- PrEP￨U￨NN￨O￨- and￨L￨CC￨O￨- harm￨L￨NN￨O￨- reduction￨L￨NN￨O￨- –￨L￨:￨O￨- have￨L￨VBP￨O￨- multiplied￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- application￨L￨NN￨O￨- across￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- is￨L￨VBZ￨O￨- uneven￨L￨JJ￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- far￨L￨RB￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- impact￨L￨NN￨O￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- PrEP￨U￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- toolkit￨L￨NN￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- accurately￨L￨RB￨O￨- captured￨L￨VBN￨O￨- in￨L￨IN￨O￨- New￨U￨NNP￨LOCATION￨- South￨U￨NNP￨LOCATION￨- Wales￨U￨NNP￨LOCATION￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- observed￨L￨VBD￨O￨- a￨L￨DT￨O￨- 35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- state‐wide￨L￨JJ￨O￨- new￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- diagnoses￨L￨NNS￨O￨- in￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- following￨L￨VBG￨O￨- rapid￨L￨JJ￨O￨- scale‐up￨L￨NN￨O￨- of￨L￨IN￨O￨- PrEP￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- EPIC￨U￨NN￨O￨- trial￨L￨NN￨O￨A ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- seroconversions￨L￨NNS￨O￨- amongst￨L￨IN￨O￨- 3927￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- follow‐up￨L￨JJ￨O￨- amongst￨L￨IN￨O￨- trial￨L￨NN￨O￨- participants￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +MRC￨U￨NNP￨ORGANIZATION￨- Clinical￨U￨JJ￨ORGANIZATION￨- Trials￨U￨NNS￨ORGANIZATION￨- Unit￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- College￨U￨NNP￨ORGANIZATION￨- London￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- London￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- Within￨U￨IN￨O￨- and￨L￨CC￨O￨- beyond￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- PrEP￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- undoubtedly￨L￨RB￨O￨- contributing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- decline￨L￨NN￨O￨A in￨L￨IN￨O￨- new￨L￨JJ￨O￨- diagnoses￨L￨NNS￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- gay￨L￨JJ￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- benefit￨L￨NN￨O￨- is￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- precisely￨L￨RB￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impressive￨L￨JJ￨O￨- decline￨L￨NN￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- city￨L￨NN￨O￨- clinics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- universal￨L￨JJ￨O￨- .￨L￨.￨O￨- +European￨U￨JJ￨NATIONALITY￨- Centre￨U￨NNP￨O￨- for￨L￨IN￨O￨- Disease￨U￨NNP￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- ECDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Stockholm￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Sweden￨U￨NNP￨COUNTRY￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- increasing￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- European￨U￨JJ￨NATIONALITY￨- region￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- whole￨L￨JJ￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- large￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- Western￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Central￨U￨NNP￨O￨- and￨L￨CC￨O￨- Eastern￨U￨NNP￨LOCATION￨- Europe￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conducted￨L￨VBD￨O￨- active￨L￨JJ￨O￨- ,￨L￨,￨O￨- national￨L￨JJ￨O￨- ,￨L￨,￨O￨- laboratory-based￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- invasive￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- IPD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- serotyping￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- testing￨L￨NN￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- A￨U￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- decision￨L￨NN￨O￨- support￨L￨NN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- informatics￨L￨NNS￨O￨- supporting￨L￨VBG￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- areas￨L￨NNS￨O￨- for￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaksRachel￨L￨NN￨O￨- Beard1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Elizabeth￨U￨NNP￨PERSON￨- Wentz3￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Matthew￨U￨NNP￨PERSON￨- Scotch1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 17:38￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Zoonotic￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- substantial￨L￨JJ￨O￨- portion￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- burden￨L￨NN￨O￨- on￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- programs￨L￨NNS￨O￨- to￨L￨TO￨O￨- maintain￨L￨VB￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- preventative￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- decision￨L￨NN￨O￨- support￨L￨NN￨O￨- systems￨L￨NNS￨O￨- developed￨L￨VBD￨O￨- to￨L￨TO￨O￨- assist￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Spatial￨U￨JJ￨O￨- decision￨L￨NN￨O￨A support￨L￨NN￨O￨- tools￨L￨NNS￨O￨- can￨L￨MD￨O￨- equip￨L￨VB￨O￨- heath￨L￨NN￨O￨- care￨L￨NN￨O￨- officials￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- analytics￨L￨NNS￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- modeling￨L￨NN￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- visual￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- effectively￨L￨RB￨O￨- make￨L￨VB￨O￨- decisions￨L￨NNS￨O￨- and￨L￨CC￨O￨- policy￨L￨NN￨O￨- recommendations￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- facilitate￨L￨VB￨O￨- data￨L￨NNS￨O￨- collection￨L￨NN￨O￨- ,￨L￨,￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- decision-making￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- decision￨L￨NN￨O￨A support￨L￨NN￨O￨- systems￨L￨NNS￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DATE￨- 10￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- has￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- The￨U￨DT￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- ,￨L￨,￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- modeling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- SDSS￨U￨NNS￨ORGANIZATION￨- that￨L￨WDT￨O￨- target￨L￨VBP￨O￨- zoonotic￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- were￨L￨VBD￨O￨- described￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- urban￨L￨JJ￨O￨A tourists￨L￨NNS￨O￨- '￨L￨POS￨O￨- satisfaction￨L￨NN￨O￨- may￨L￨MD￨O￨- produce￨L￨VB￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- effect￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- channels￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- pure￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- technology￨L￨NN￨O￨- spillover￨L￨NN￨O￨- effect￨L￨NN￨O￨- —￨L￨:￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- tourists￨L￨NNS￨O￨- ’￨L￨POS￨O￨- experiences￨L￨NNS￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨- tourism￨L￨NN￨O￨- attractions￨L￨NNS￨O￨- ,￨L￨,￨O￨- urban￨L￨JJ￨O￨- tourism￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- will￨L￨MD￨O￨- travel￨L￨VB￨O￨- to￨L￨TO￨O￨- cities￨L￨NNS￨O￨- with￨L￨IN￨O￨- similar￨L￨JJ￨O￨- attractions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- produced￨L￨VBN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- and￨L￨CC￨O￨- emulate￨L￨VB￨O￨- them￨L￨PRP￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- traffic￨L￨NN￨O￨- overflow￨L￨NN￨O￨- effect￨L￨NN￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- convenience￨L￨NN￨O￨- of￨L￨IN￨O￨- transportation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- tourists￨L￨NNS￨O￨- ’￨L￨POS￨O￨- travel￨L￨NN￨O￨- frequency￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- also￨L￨RB￨O￨- probes￨L￨NNS￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- intra-regional￨L￨JJ￨O￨- spillover￨L￨JJ￨O￨- effect￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨A tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- urban￨L￨JJ￨O￨- GDP￨U￨NN￨O￨- income￨L￨NN￨O￨- and￨L￨CC￨O￨- urban￨L￨JJ￨O￨- living￨L￨NN￨O￨- standards￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- might￨L￨MD￨O￨- sheds￨L￨VB￨O￨- new￨L￨JJ￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- facilitate￨L￨VB￨O￨- greater￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Tourism￨U￨NNP￨O￨- industry￨L￨NN￨O￨- market￨L￨NN￨O￨- rules￨L￨NNS￨O￨- .￨L￨.￨O￨- +Before￨U￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨A tourists￨L￨NNS￨O￨- ’￨L￨POS￨O￨- satisfaction￨L￨NN￨O￨- on￨L￨IN￨O￨- urban￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- GDP￨U￨NN￨O￨- income￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- must￨L￨MD￨O￨- first￨L￨RB￨ORDINAL￨- figure￨L￨VB￨O￨- out￨L￨RP￨O￨- how￨L￨WRB￨O￨- urban￨L￨JJ￨O￨- tourists￨L￨NNS￨O￨- '￨L￨POS￨O￨- satisfaction￨L￨NN￨O￨- directly￨L￨RB￨O￨- affects￨L￨VBZ￨O￨- intra-regional￨L￨JJ￨O￨- GDP￨U￨NN￨O￨- income￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- effect￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- effect￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- extent￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- ’s￨L￨POS￨O￨- potential￨L￨JJ￨O￨- innovation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨A tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- urban￨L￨JJ￨O￨- macro-economy￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- perspective￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- say￨L￨VB￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- panel￨L￨NN￨O￨- Durbin￨U￨NNP￨PERSON￨- econometric￨L￨JJ￨O￨- regression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- taking￨L￨VBG￨O￨- urban￨L￨JJ￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- independent￨L￨JJ￨RELIGION￨- variable￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- factors￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- with￨L￨IN￨O￨- tourist￨L￨NN￨O￨- attractions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨A of￨L￨IN￨O￨- tourists￨L￨NNS￨O￨- ’￨L￨POS￨O￨- host-guest￨L￨JJ￨O￨- contact￨L￨NN￨O￨- preference￨L￨NN￨O￨- on￨L￨IN￨O￨- perceived￨L￨VBN￨O￨- destination￨L￨NN￨O￨- image￨L￨NN￨O￨- and￨L￨CC￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- of￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ’s￨L￨POS￨O￨- historical￨L￨JJ￨O￨- and￨L￨CC￨O￨- cultural￨L￨JJ￨O￨- Cities￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- City￨U￨NNP￨O￨- features￨L￨VBZ￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- satisfaction￨L￨NN￨O￨- of￨L￨IN￨O￨- Urban￨U￨NNP￨O￨- Visitors￨U￨NNPS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Research￨U￨NN￨O￨- on￨L￨IN￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- in￨L￨IN￨O￨- Smart￨U￨JJ￨O￨- tourism￨L￨NN￨O￨- scenic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Satisfaction￨U￨NN￨ORGANIZATION￨- Evaluation￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Tourist￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Influence￨U￨NN￨ORGANIZATION￨- Factors￨U￨NNS￨ORGANIZATION￨- Analysis￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- Rural￨U￨JJ￨O￨- Tourism￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Mimicking￨U￨VBG￨O￨- methods￨L￨NNS￨O￨- from￨L￨IN￨O￨- non-STIs￨L￨JJ￨MISC￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- utilised￨L￨VBN￨O￨- deterministic￨L￨JJ￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ODE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- simplify￨L￨VB￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- while￨L￨IN￨O￨- other￨L￨JJ￨O￨- have￨L￨VBP￨O￨- adopted￨L￨VBN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- ,￨L￨,￨O￨- subdividing￨L￨VBG￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- sexual￨L￨JJ￨O￨A activity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- or￨L￨CC￨O￨- previous￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- experience￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨A behaviour￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- strongly￨L￨RB￨O￨- upon￨L￨IN￨O￨- several￨L￨JJ￨O￨- compounding￨L￨VBG￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- sex￨L￨NN￨O￨- ,￨L￨,￨O￨- sexual￨L￨JJ￨O￨- preference￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- cultural￨L￨JJ￨O￨- norms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- partners￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- trends￨L￨NNS￨O￨- across￨L￨IN￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- extreme￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨A partners￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- partnership￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- scale-free￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- furthermore￨L￨RB￨O￨- ,￨L￨,￨O￨- trends￨L￨NNS￨O￨- shift￨L￨NN￨O￨- across￨L￨IN￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Natsal-3￨U￨NN￨MISC￨- survey￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- captured￨L￨VBN￨O￨- by￨L￨IN￨O￨- parsimonious￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- annual￨L￨JJ￨SET￨- rates￨L￨NNS￨O￨- —￨L￨:￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- mixture￨L￨NN￨O￨- of￨L￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- distributions￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Natsal-3￨U￨NN￨O￨- survey￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- -12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- distributions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- partnerships￨L￨NNS￨O￨- that￨L￨WDT￨O￨- involve￨L￨VBP￨O￨- unprotected￨L￨JJ￨O￨- sex￨L￨NN￨O￨A and￨L￨CC￨O￨- can￨L￨MD￨O￨- therefore￨L￨RB￨O￨- allow￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- STIs￨U￨NNS￨O￨- .￨L￨.￨O￨- +Experimentally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- exploring￨L￨VBG￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- centrality￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- k-core￨L￨NN￨O￨- measure￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- with￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- accuracy￨L￨NN￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- information￨L￨NN￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- graph￨L￨NN￨O￨A and￨L￨CC￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compute￨L￨VBP￨O￨- the￨L￨DT￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨A exploration￨L￨NN￨O￨- sampling￨L￨NN￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- accurately￨L￨RB￨O￨- identifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- any￨L￨DT￨O￨- prior￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- apart￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- collected￨L￨VBN￨O￨- samples/subgraphs￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conduct￨L￨VBP￨O￨- extensive￨L￨JJ￨O￨- experiments￨L￨NNS￨O￨- in￨L￨IN￨O￨- eight￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨A world￨L￨NN￨O￨A networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- serve￨L￨VBP￨O￨- as￨L￨IN￨O￨- ground￨L￨NN￨O￨- truth￨L￨NN￨O￨- identifiers￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- spreading￨L￨VBG￨O￨- efficiency￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- Rank￨U￨NNP￨O￨- Degree￨U￨NNP￨O￨- graph￨L￨NN￨O￨A sampling￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Pre-emptive￨U￨JJ￨MISC￨- spectral￨L￨JJ￨O￨- graph￨L￨NN￨O￨- protection￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- on￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨A social￨L￨JJ￨O￨- networksArie￨L￨NNP￨O￨- Wahyu￨U￨NNP￨O￨- Wijayanto1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- and￨L￨CC￨O￨- Tsuyoshi￨U￨NNP￨PERSON￨- Murata1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 3:5￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractConstructing￨U￨NNP￨O￨- effective￨L￨JJ￨O￨- and￨L￨CC￨O￨- scalable￨L￨JJ￨O￨- protection￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- over￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenging￨L￨JJ￨O￨- issue￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- address￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- suppressing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨A social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- allocating￨L￨VBG￨O￨- protection￨L￨NN￨O￨- resources￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- different￨L￨JJ￨O￨- layers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨A graph￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- k￨L￨NN￨O￨- budget￨L￨NN￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- survived￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- maximized￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- MultiplexShield￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- employs￨L￨VBZ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- graph￨L￨NN￨O￨- spectral￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- degree￨L￨NN￨O￨- centrality￨L￨NN￨O￨- and￨L￨CC￨O￨- layer-wise￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- pre-emptively￨L￨RB￨O￨- select￨L￨JJ￨O￨- k￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- for￨L￨IN￨O￨- protection￨L￨NN￨O￨A .￨L￨.￨O￨- +Multiplex￨U￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- multiplelayers￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- appear￨L￨VBP￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- layers￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- resulting￨L￨VBG￨O￨- age-structured￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- ;￨L￨:￨O￨- readers￨L￨NNS￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- additional￨L￨JJ￨O￨- detail￨L￨NN￨O￨- are￨L￨VBP￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- S1￨U￨NN￨O￨- Appendix￨U￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- ∘￨L￨SYM￨O￨- indicates￨L￨VBZ￨O￨A the￨L￨DT￨O￨- Hadamard￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- element-wise￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- product￨L￨NN￨O￨- ;￨L￨:￨O￨- ×￨L￨SYM￨O￨- indicates￨L￨VBZ￨O￨- matrix￨L￨NN￨O￨- multiplication￨L￨NN￨O￨- ;￨L￨:￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- matrix￨L￨NN￨O￨- :￨L￨:￨O￨- f￨L￨LS￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- occur￨L￨VBP￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- children￨L￨NNS￨O￨- ;￨L￨:￨O￨- similarly￨L￨RB￨O￨- f￨L￨FW￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- occur￨L￨VBP￨O￨- with￨L￨IN￨O￨- adults￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- f￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- f￨L￨FW￨O￨- ;￨L￨:￨O￨- f￨L￨LS￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- adult￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- occur￨L￨VBP￨O￨- with￨L￨IN￨O￨- children￨L￨NNS￨O￨- ;￨L￨:￨O￨- f￨L￨LS￨O￨- =￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- f￨L￨SYM￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- adult￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- occur￨L￨VBP￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- adults￨L￨NNS￨O￨- ;￨L￨:￨O￨- ω￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- aging￨L￨NN￨O￨- rate￨L￨NN￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- carries￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- meaning￨L￨NN￨O￨- with￨L￨IN￨O￨- c1￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- investigates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- particle￨L￨NN￨O￨- filtering￨L￨VBG￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- —￨L￨:￨O￨- adhering￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- —￨L￨:￨O￨- Exposure￨U￨NN￨O￨- —￨L￨:￨O￨- Infectious￨U￨JJ￨O￨- —￨L￨:￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- structure￨L￨NN￨O￨- —￨L￨:￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A to￨L￨TO￨O￨- recurrently￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- anticipate￨L￨VB￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- outbreak￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- in￨L￨IN￨O￨- pre-vaccination￨L￨JJ￨O￨- era￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- seeks￨L￨VBZ￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- more￨L￨JJR￨O￨- accurate￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- a￨L￨DT￨O￨- computational￨L￨JJ￨O￨- statistics￨L￨NNS￨O￨- technique￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- insights￨L￨NNS￨O￨- from￨L￨IN￨O￨- ongoing￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- although￨L￨IN￨O￨- noisy￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- although￨L￨IN￨O￨- fraught￨L￨JJ￨O￨- by￨L￨IN￨O￨- systematic￨L￨JJ￨O￨- errors￨L￨NNS￨O￨- ,￨L￨,￨O￨- omissions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- divergence￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- mitigating￨L￨VBG￨O￨- important￨L￨JJ￨O￨- weaknesses￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- .￨L￨.￨O￨- +Similar￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- aggregate￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- age￨L￨NN￨O￨A group￨L￨NN￨O￨A across￨L￨IN￨O￨- the￨L￨DT￨O￨- timeframe￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- pyramid￨L￨NN￨O￨- of￨L￨IN￨O￨- Saskatchewan￨U￨NNP￨STATE_OR_PROVINCE￨- NumericCitation￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- employed￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- equals￨L￨VBZ￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- project￨L￨NN￨O￨- employs￨L￨VBZ￨O￨- a￨L￨DT￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- state-equation￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- particle￨L￨NN￨O￨- filtering￨L￨VBG￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Caswell1￨U￨NN￨O￨- are￨L￨VBP￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- absorbing￨L￨VBG￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨A in￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- ecological￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Caswell￨U￨NNP￨PERSON￨- .2￨L￨NN￨NUMBER￨- The￨U￨DT￨O￨- reader￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- alerted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- perturbation￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- long‐standing￨L￨VBG￨O￨- problem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- survey￨L￨NN￨O￨- by￨L￨IN￨O￨- Avrachenkov￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- suggested￨L￨VBN￨O￨- by￨L￨IN￨O￨- Caswell1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- aligned￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- perturbed￨L￨VBN￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- other￨L￨JJ￨O￨- works￨L￨NNS￨O￨- .4￨L￨RB￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- essentially￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- bounding￨L￨VBG￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- stationary￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- functional￨L￨JJ￨O￨- space￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- one‐step￨L￨JJ￨O￨- transition￨L￨NN￨O￨- probability￨L￨NN￨O￨- matrix￨L￨NN￨O￨- P￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete‐time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- is￨L￨VBZ￨O￨- replaced￨L￨VBN￨O￨- by￨L￨IN￨O￨- another￨L￨DT￨O￨- one‐step￨L￨JJ￨O￨- transition￨L￨NN￨O￨- probability￨L￨NN￨O￨- matrix￨L￨NN￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- papers￨L￨NNS￨O￨- by￨L￨IN￨O￨- Li￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 6￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Seneta￨U￨NN￨O￨- .8￨L￨NN￨NUMBER￨- For￨U￨IN￨O￨- CTMCs￨U￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- steady‐state￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- measured￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infinitesimal￨L￨JJ￨O￨- generator￨L￨NN￨O￨- Q￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- perturbed￨L￨VBN￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- ϵ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- sufficiently￨L￨RB￨O￨- small￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- matrix￨L￨NN￨O￨- Q￨U￨NNP￨O￨- ∗￨L￨CD￨NUMBER￨- satisfies￨L￨NNS￨O￨- certain￨L￨JJ￨O￨- weak￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- section￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Altman￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 9￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- papers￨L￨NNS￨O￨- by￨L￨IN￨O￨- Altman￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,9￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Heidergott￨U￨NNP￨LOCATION￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 10￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- representative￨L￨JJ￨TITLE￨- contributions￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- denumerable￨L￨JJ￨O￨- and￨L￨CC￨O￨- finite￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨- with￨L￨IN￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- queueing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- setting￨L￨NN￨O￨- of￨L￨IN￨O￨- perturbed￨L￨VBN￨O￨- QBD￨U￨NN￨O￨- processes￨L￨NNS￨O￨- analyzed￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- by￨L￨IN￨O￨- Li￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Liu28￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- excellent￨L￨JJ￨O￨- work￨L￨NN￨O￨- where￨L￨WRB￨O￨- censoring￨L￨VBG￨O￨- techniques￨L￨NNS￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- integral￨L￨JJ￨O￨- functionals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- discuss￨L￨VB￨O￨- infinitesimal￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- perturbed￨L￨VBN￨O￨- structured￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨A and￨L￨CC￨O￨- Markovian￨U￨JJ￨O￨- arrival￨L￨NN￨O￨- streams￨L￨NNS￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- related￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Dendievel￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,29￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- perturbed￨L￨VBN￨O￨- stationary￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- QBD￨U￨NN￨O￨- process￨L￨NN￨O￨- are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- restricting￨L￨VBG￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- two￨L￨CD￨NUMBER￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- states￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- transmission￨L￨NN￨O￨- pathways￨L￨NNS￨O￨- of￨L￨IN￨O￨- diarrhea￨L￨NN￨O￨- using￨L￨VBG￨O￨- symptoms￨L￨NNS￨O￨- occurrence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- individual￨L￨JJ￨O￨- households￨L￨NNS￨O￨A consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- family￨L￨NN￨O￨- members￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- children￨L￨NNS￨O￨- and￨L￨CC￨O￨- adults￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- subject￨L￨NN￨O￨- to￨L￨TO￨O￨- waterborne￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- contamination￨L￨NN￨O￨- and￨L￨CC￨O￨- possibly￨L￨RB￨O￨- also￨L￨RB￨O￨- other￨L￨JJ￨O￨- risks￨L￨NNS￨O￨- effecting￨L￨VBG￨O￨- baseline￨L￨NN￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- see￨L￨VBP￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- additionally￨L￨RB￨O￨- compounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- programs￨L￨NNS￨O￨- operate￨L￨VBP￨O￨- with￨L￨IN￨O￨- limited￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- diarrhea￨L￨NN￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- demographics￨L￨NNS￨O￨- ,￨L￨,￨O￨- reported￨L￨VBD￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- diarrhea￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- possibly￨L￨RB￨O￨- some￨L￨DT￨O￨- outcome￨L￨NN￨O￨- measures￨L￨NNS￨O￨- on￨L￨IN￨O￨- households￨L￨NNS￨O￨A or￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- testing￨L￨VBG￨O￨- positive￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- observational￨L￨JJ￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- to￨L￨TO￨O￨- first￨L￨RB￨ORDINAL￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- household-level￨L￨JJ￨O￨- occurrence￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- parametric￨L￨JJ￨O￨- resampling￨L￨NN￨O￨- technique￨L￨NN￨O￨- akin￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- synthetic￨L￨JJ￨O￨- likelihood￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- approximate￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- occurrence￨L￨NN￨O￨- across￨L￨IN￨O￨- households￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- count￨L￨NN￨TITLE￨- data￨L￨NNS￨O￨- X1￨U￨NN￨O￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- X￨U￨NN￨O￨- represents￨L￨VBZ￨O￨- household￨L￨NN￨O￨- level￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- cases￨L￨NNS￨O￨- among￨L￨IN￨O￨- adults￨L￨NNS￨O￨A and￨L￨CC￨O￨- juveniles￨L￨NNS￨O￨- under￨L￨IN￨O￨- and￨L￨CC￨O￨- contaminated￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- clean￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- environments￨L￨NNS￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- generative￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- observed￨L￨VBN￨O￨- likelihood￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- numerically￨L￨RB￨O￨- solved￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- three￨L￨CD￨NUMBER￨- steady-state￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- :￨L￨:￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- PrEP￨U￨NN￨O￨- coverage￨L￨NN￨O￨A per￨L￨IN￨O￨- risk￨L￨NN￨O￨- group￨L￨NN￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- ART￨U￨NN￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- for￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- PrEP￨U￨NN￨O￨- uptake￨L￨NN￨O￨A and￨L￨CC￨O￨- determined￨L￨VBD￨O￨- which￨L￨WDT￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- PrEP￨U￨NN￨O￨- uptake￨L￨NN￨O￨- ,￨L￨,￨O￨- effectiveness￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- elimination￨L￨NN￨O￨- .￨L￨.￨O￨- +Daily￨U￨NNP￨SET￨- or￨L￨CC￨O￨- intermittent￨L￨JJ￨O￨- PrEP￨U￨NN￨O￨- uptake￨L￨NN￨O￨A was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- trials￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- cohort￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- clinical￨L￨JJ￨O￨- practice￨L￨NN￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- assumed￨L￨VBD￨O￨- universal￨L￨JJ￨O￨- ART￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- daily￨L￨JJ￨SET￨A PrEP￨U￨NN￨O￨- use￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- 's￨L￨POS￨O￨- risk￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- analytical￨L￨JJ￨O￨A modeling￨L￨NN￨O￨- achieve￨L￨VB￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- WSN￨U￨NNP￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- compartmentalization￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- health￨L￨NN￨O￨- status￨L￨NN￨O￨- ,￨L￨,￨O￨- agent￨L￨NN￨O￨- modeling￨L￨NN￨O￨- would￨L￨MD￨O￨- enable￨L￨VB￨O￨- the￨L￨DT￨O￨- building￨L￨NN￨O￨- of￨L￨IN￨O￨- agent￨L￨NN￨O￨- simulators￨L￨NNS￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- spatial￨L￨JJ￨O￨- capabilities￨L￨NNS￨O￨- using￨L￨VBG￨O￨- simple￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- formalized￨L￨VBN￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- achieving￨L￨VBG￨O￨- the￨L￨DT￨O￨- productive￨L￨JJ￨O￨- and￨L￨CC￨O￨- supplementary￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- agent-based￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- to￨L￨TO￨O￨- analytical￨L￨JJ￨O￨A modeling￨L￨NN￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- equation-based￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- analytical￨L￨JJ￨O￨A )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- we￨L￨PRP￨O￨- adopt￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- gleaned￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- extant￨L￨JJ￨O￨- literature￨L￨NN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- referred￨L￨VBD￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- Epidemic￨U￨JJ￨O￨- Modeling￨U￨NN￨O￨- and￨L￨CC￨O￨- Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- Cyber￨U￨NNP￨O￨- Dynamical￨U￨NNP￨O￨- Systems￨U￨NNPS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- because￨L￨IN￨O￨- agent￨L￨NN￨O￨A modeling￨L￨NN￨O￨- employs￨L￨VBZ￨O￨- simple￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- that￨L￨WDT￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- complex￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- phenomenon￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- agent￨L￨NN￨O￨A modeling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- based￨L￨VBN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IBMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- complementarily￨L￨RB￨O￨- add￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- equation-based￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- .￨L￨.￨O￨- +ABC￨U￨NNP￨ORGANIZATION￨- then￨L￨RB￨O￨- offers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- alternative￨L￨NN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- for￨L￨IN￨O￨- fitting￨L￨JJ￨O￨A complex￨L￨NN￨O￨- individual-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- include￨L￨VB￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- sparse￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- parameter￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- fitted￨L￨JJ￨O￨- models￨L￨NNS￨O￨- must￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- if￨L￨IN￨O￨- robust￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- data￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- challenging￨L￨VBG￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- noisy￨L￨JJ￨O￨A and￨L￨CC￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- modelled￨L￨VBN￨O￨- by￨L￨IN￨O￨- simple￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- such￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- approximate￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- computation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- valid￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- fitting￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- fitting￨L￨JJ￨O￨A using￨L￨VBG￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- global￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- highlight￨L￨VB￨O￨- common￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- and￨L￨CC￨O￨- good￨L￨JJ￨O￨- practice￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- identify￨L￨VB￨O￨- any￨L￨DT￨O￨- gaps￨L￨NNS￨O￨- for￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- research￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- type￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- input￨L￨NN￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- parametrise￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- validation￨L￨NN￨O￨A data￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- accuracy￨L￨NN￨O￨- and￨L￨CC￨O￨- judge￨L￨NN￨TITLE￨- quality￨L￨NN￨O￨- .￨L￨.￨O￨- +Directed￨U￨NNP￨O￨- by￨L￨IN￨O￨- this￨L￨DT￨O￨- view￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨A what￨L￨WP￨O￨- modelling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- potential￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- what￨L￨WP￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- parametrise￨L￨VB￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Validation￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- multi-component￨L￨JJ￨O￨- process￨L￨NN￨O￨- involving￨L￨VBG￨O￨- :￨L￨:￨O￨- conceptual￨L￨JJ￨O￨- validation￨L￨NN￨O￨A ,￨L￨,￨O￨- logical￨L￨JJ￨O￨- validation￨L￨NN￨O￨- ,￨L￨,￨O￨- experimental￨L￨JJ￨O￨- validation￨L￨NN￨O￨- ,￨L￨,￨O￨- operational￨L￨JJ￨O￨- validation￨L￨NN￨O￨- and￨L￨CC￨O￨- validation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- validation￨L￨NN￨O￨A of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- models￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Meslé￨U￨NNP￨LOCATION￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- explored￨L￨VBN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- previous‐generation￨L￨JJ￨O￨- antimicrobials￨L￨NNS￨O￨- become￨L￨VBP￨O￨- clinically￨L￨RB￨O￨- ineffective￨L￨JJ￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- or￨L￨CC￨O￨- habitats￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- local￨L￨JJ￨O￨- competitive￨L￨JJ￨O￨A displacement￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial‐sensitive￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- by￨L￨IN￨O￨- antimicrobial‐resistant￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- common￨L￨JJ￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- competitive￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- among￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- strains￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- intricately￨L￨RB￨O￨- linked￨L￨VBN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- interactions￨L￨NNS￨O￨- with￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- decoupling￨L￨VBG￨O￨- local￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- from￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- selection￨L￨NN￨O￨- regimes￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- hope￨L￨VBP￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- managing￨L￨VBG￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- over￨L￨IN￨O￨- space￨L￨NN￨O￨- that￨L￨WDT￨O￨- apply￨L￨VBP￨O￨- across￨L￨IN￨O￨- systems￨L￨NNS￨O￨- when￨L￨WRB￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- governing￨L￨VBG￨O￨- local￨L￨JJ￨O￨- competitive￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- between￨L￨IN￨O￨- antimicrobial‐resistant￨L￨JJ￨O￨- and￨L￨CC￨O￨- antimicrobial‐susceptible￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- often￨L￨RB￨O￨- differ￨L￨VBP￨O￨- considerably￨L￨RB￨O￨- from￨L￨IN￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- herbivorous￨L￨JJ￨O￨- pests￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- question￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- domains￨L￨NNS￨O￨- concerns￨L￨VBZ￨O￨- a￨L￨DT￨O￨- balancing￨L￨NN￨O￨- act￨L￨NN￨O￨- :￨L￨:￨O￨- How￨U￨WRB￨O￨- can￨L￨MD￨O￨- the￨L￨DT￨O￨- migratory￨L￨JJ￨O￨- and￨L￨CC￨O￨- competitive￨L￨JJ￨O￨A potential￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial‐sensitive￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- be￨L￨VB￨O￨- leveraged￨L￨VBN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- strong￨L￨JJ￨O￨- selective￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- anthropogenic￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- antimicrobial￨L￨JJ￨O￨- use￨L￨NN￨O￨- or￨L￨CC￨O￨- agricultural￨L￨JJ￨O￨- toxins￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ?￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- antimicrobial‐sensitive￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- occupying￨L￨VBG￨O￨- sites￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- antimicrobial￨L￨JJ￨O￨- are￨L￨VBP￨O￨- displaced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- antimicrobial‐resistant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨A strain￨L￨NN￨O￨- 's￨L￨POS￨O￨- colonization￨L￨NN￨O￨- rate￨L￨NN￨O￨- c￨L￨NN￨O￨- of￨L￨IN￨O￨- empty￨L￨JJ￨O￨- patches￨L￨NNS￨O￨- .￨L￨.￨O￨- +Study￨U￨NNP￨O￨- protocol￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Study￨U￨NNP￨MISC￨- protocol￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- iMPaCT￨L￨NN￨O￨- project￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- longitudinal￨L￨JJ￨O￨- cohort￨L￨NN￨O￨- study￨L￨NN￨O￨- assessing￨L￨VBG￨O￨- psychological￨L￨JJ￨O￨- determinants￨L￨NNS￨O￨- ,￨L￨,￨O￨- sexual￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- chlamydia￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- re￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- heterosexual￨L￨JJ￨O￨- STI￨U￨NN￨O￨- clinic￨L￨NN￨O￨- visitorsDaphne￨L￨NNP￨O￨- A.￨U￨NNP￨O￨- 2018Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Chlamydia￨U￨NN￨O￨- trachomatis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- chlamydia￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- reported￨L￨VBN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- STI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- severe￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- longitudinal￨L￨JJ￨O￨- cohort￨L￨NN￨O￨- study￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- conducted￨L￨VBN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- between￨L￨IN￨O￨- psychological￨L￨JJ￨O￨- and￨L￨CC￨O￨- behavioural￨L￨JJ￨O￨- determinants￨L￨NNS￨O￨- and￨L￨CC￨O￨- chlamydia￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- re￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- heterosexual￨L￨JJ￨O￨- STI￨U￨NN￨O￨- clinic￨L￨NN￨O￨- visitors￨L￨NNS￨O￨- aged￨L￨VBN￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- makes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- psychological￨L￨JJ￨O￨- determinants￨L￨NNS￨O￨- and￨L￨CC￨O￨- behaviour￨L￨NN￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- on￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨A transmission￨L￨NN￨O￨- especially￨L￨RB￨O￨- important￨L￨JJ￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- unaware￨L￨JJ￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- preventive￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- or￨L￨CC￨O￨- health-care￨L￨NN￨O￨- seeking￨L￨VBG￨O￨- behaviour￨L￨NN￨O￨- mostly￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- psychological￨L￨JJ￨O￨A determinants￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Mathematical￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- life￨L￨NN￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- taenia-cysticercosis￨L￨NN￨O￨- :￨L￨:￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- chemotherapy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Part￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Marco￨U￨NNP￨O￨- V.￨U￨NNP￨O￨- 2018Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Taenia￨U￨NNP￨O￨- solium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- aetiological￨L￨JJ￨O￨- agent￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- taeniasis￨L￨NN￨O￨- ,￨L￨,￨O￨- pig￨L￨NN￨O￨A cysticercosis￨L￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- neurocysticercosis￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- serious￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- problems￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- adult￨L￨JJ￨O￨- worms￨L￨NNS￨O￨- tends￨L￨VBZ￨O￨A to￨L￨TO￨O￨- rapidly￨L￨RB￨O￨- stabilize￨L￨VB￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- parasite￨L￨NN￨O￨- per￨L￨IN￨O￨- individual￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- taeniasis￨L￨NN￨O￨- ,￨L￨,￨O￨- pig￨L￨NN￨O￨A and￨L￨CC￨O￨- human￨L￨JJ￨O￨- cysticercosis￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- taeniasis-cysticercosis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- assortativity￨L￨NN￨O￨- between￨L￨IN￨O￨- networks￨L￨NNS￨O￨- was￨L￨VBD￨O￨- defined￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- results￨L￨NNS￨O￨- were￨L￨VBD￨O￨- demonstrated￨L￨VBN￨O￨- :￨L￨:￨O￨- assortative￨L￨JJ￨O￨A connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- networks￨L￨NNS￨O￨- lowered￨L￨VBD￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- hop￨L￨NN￨O￨- length￨L￨NN￨O￨- and￨L￨CC￨O￨- enhanced￨L￨VBN￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- disassortative￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- networks￨L￨NNS￨O￨- distributed￨L￨VBN￨O￨- the￨L￨DT￨O￨- communication￨L￨NN￨O￨- loads￨L￨NNS￨O￨- of￨L￨IN￨O￨- internetwork￨L￨NN￨O￨- links￨L￨NNS￨O￨- and￨L￨CC￨O￨- enhanced￨L￨VBD￨O￨- robustness￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- single￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- assortativity￨L￨NN￨O￨- provided￨L￨VBN￨O￨- low￨L￨JJ￨O￨- hop￨L￨NN￨O￨- length￨L￨NN￨O￨- ,￨L￨,￨O￨- high￨L￨JJ￨O￨- information￨L￨NN￨O￨A diffusion￨L￨NN￨O￨A efficiency￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- communication￨L￨NN￨O￨- load￨L￨NN￨O￨- on￨L￨IN￨O￨- edges￨L￨NNS￨O￨- .￨L￨.￨O￨- +Nodes￨U￨NNS￨O￨- of￨L￨IN￨O￨- similar￨L￨JJ￨O￨- degree￨L￨NN￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- exhibit￨L￨VBP￨O￨- high￨L￨JJ￨O￨- assortativity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- termed￨L￨VBN￨O￨- as￨L￨IN￨O￨- assortative￨L￨JJ￨O￨A mixing￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- carefully￨L￨RB￨O￨- adjust￨L￨VB￨O￨- assortativity￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- involved￨L￨JJ￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- possessed￨L￨VBD￨O￨- the￨L￨DT￨O￨- desired￨L￨VBN￨O￨- degree￨L￨NN￨O￨A of￨L￨IN￨O￨- assortativity￨L￨NN￨O￨- .￨L￨.￨O￨- +Compartmental￨U￨JJ￨O￨- models￨L￨NNS￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- or￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- phylodynamic￨L￨JJ￨O￨A inference￨L￨NN￨O￨- ,￨L￨,￨O￨- non-parametric￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- skyline￨L￨NN￨O￨- coalescent￨L￨NN￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- sampling-birth-death￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- flexible￨L￨JJ￨O￨- framework￨L￨NN￨O￨- enables￨L￨VBZ￨O￨- phylodynamic￨L￨JJ￨O￨A inference￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- published￨L￨VBN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- variants￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- non-genetic￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Phylogeographic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- migration￨L￨NN￨O￨A rates￨L￨NNS￨O￨- between￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- demes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- phylogeographic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- time-varying￨L￨JJ￨O￨- or￨L￨CC￨O￨- state-dependent￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- or￨L￨CC￨O￨- migration￨L￨NN￨O￨- rates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +Parameters￨U￨NNS￨O￨- estimated￨L￨VBN￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- mechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨A and￨L￨CC￨O￨- forecasting￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- quantification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- removal￨L￨NN￨O￨- strategy￨L￨NN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- outperforms￨L￨VBZ￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- those￨L￨DT￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- preserves￨L￨VBZ￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- proposal￨L￨NN￨O￨- concentrates￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- link￨L￨NN￨O￨A and￨L￨CC￨O￨- thus￨L￨RB￨O￨- enabling￨L￨VBG￨O￨- containment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- removal￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- emphasized￨L￨VBN￨O￨- that￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- make￨L￨VBP￨O￨- use￨L￨NN￨O￨- only￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- decide￨L￨VB￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- edges￨L￨NNS￨O￨A have￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- removed￨L￨VBN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- or￨L￨CC￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- are￨L￨VBP￨O￨- ignored￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- determination￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- link￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- importance￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- cope￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨A only￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- participation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- How￨U￨WRB￨O￨- Physical￨U￨JJ￨O￨- Proximity￨U￨NNP￨O￨- Shapes￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- Social￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- Arkadiusz￨U￨NNP￨O￨- Stopczynski1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Alex￨U￨NNP￨PERSON￨- ‘￨L￨``￨PERSON￨- Sandy￨U￨NNP￨PERSON￨- ’￨L￨''￨O￨- Pentland2￨U￨NNP￨O￨- &￨L￨CC￨O￨- Sune￨U￨NNP￨PERSON￨- Lehmann￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 17722￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComputational￨L￨NNP￨O￨- science￨L￨NN￨O￨- AbstractSocial￨U￨NNP￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- humans￨L￨NNS￨O￨- create￨L￨VBP￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- –￨L￨:￨O￨- despite￨L￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- online￨L￨NN￨O￨- communication￨L￨NN￨O￨- –￨L￨:￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- mediated￨L￨VBN￨O￨- through￨L￨IN￨O￨- physical￨L￨JJ￨O￨- proximity￨L￨NN￨O￨A remain￨L￨VBP￨O￨- a￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- way￨L￨NN￨O￨- for￨L￨IN￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- connect￨L￨VB￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- networks￨L￨NNS￨O￨- arise￨L￨VBP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- behavioral￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- quantitatively￨L￨RB￨O￨- measure￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proximity￨L￨NN￨O￨A network￨L￨NN￨O￨- –￨L￨:￨O￨- short-range￨L￨JJ￨O￨- versus￨L￨CC￨O￨- long-range￨L￨JJ￨O￨- –￨L￨:￨O￨- impacts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Bulletin￨U￨NNP￨O￨- of￨L￨IN￨O￨- Mathematical￨U￨NNP￨O￨- Biology￨U￨NNP￨O￨- pp￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asThe￨L￨NNP￨O￨- Final￨U￨NNP￨O￨- Size￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Serious￨U￨JJ￨O￨- EpidemicAuthorsAuthors￨U￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsFred￨L￨JJ￨O￨- BrauerOpen￨U￨NN￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 38￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨MISC￨- AbstractIn￨U￨NNP￨MISC￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- serious￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- behavioral￨L￨JJ￨O￨- response￨L￨NN￨O￨- that￨L￨WDT￨O￨- decreases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- considerably￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- taking￨L￨VBG￨O￨- this￨L￨DT￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- may￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- much￨L￨RB￨O￨- smaller￨L￨JJR￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- than￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- take￨L￨VB￨O￨- this￨L￨DT￨O￨- into￨L￨IN￨O￨- account.KeywordsEpidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- Final￨U￨JJ￨O￨- size￨L￨NN￨O￨- relations￨L￨NNS￨O￨- Behavioral￨U￨JJ￨O￨- response￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionIt￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- standard￨L￨JJ￨O￨- practice￨L￨NN￨O￨- in￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- to￨L￨TO￨O￨- formulate￨L￨VB￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- observed￨L￨VBN￨O￨- early￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨A and￨L￨CC￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- management￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- suggestions￨L￨NNS￨O￨- include￨L￨VBP￨O￨- metapopulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- including￨L￨VBG￨O￨- cross-coupling￨L￨JJ￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨- in￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reactive￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- early￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Further￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- quarantine￨L￨NN￨O￨- could￨L￨MD￨O￨- do￨L￨VB￨O￨- nothing￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- travel￨L￨NN￨O￨- of￨L￨IN￨O￨- rats￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- did￨L￨VBD￨O￨- little￨L￨JJ￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- .2￨L￨NN￨NUMBER￨- A￨U￨DT￨O￨- Variable-Contact-Rate￨U￨NNP￨O￨- Epidemic￨U￨NNP￨O￨- ModelAnother￨U￨NNP￨O￨- direction￨L￨NN￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- well￨L￨RB￨O￨- worth￨L￨JJ￨O￨- further￨L￨JJ￨O￨- exploration￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- decreasing￨L￨VBG￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨A .￨L￨.￨O￨- +There￨U￨EX￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- mechanism￨L￨NN￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨A rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- from￨L￨IN￨O￨- incidence￨L￨NN￨O￨- data.A￨L￨NN￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- slower￨L￨JJR￨O￨- than￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- possible￨L￨JJ￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- pointed￨L￨VBN￨O￨- out￨L￨RP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- 2015￨L￨CD￨DATE￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- general￨L￨JJ￨TITLE￨- growth￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- where￨L￨WRB￨O￨- C￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- up￨L￨RP￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- p￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- deceleration￨L￨NN￨O￨- of￨L￨IN￨O￨- growth￨L￨NN￨O￨- ”￨L￨''￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- exponential￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- if￨L￨IN￨O￨- Equality￨U￨NN￨O￨- p￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- but￨L￨CC￨O￨- solutions￨L￨NNS￨O￨- with￨L￨IN￨O￨- polynomial￨L￨JJ￨O￨- growth￨L￨NN￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨PERSON￨- StrictLessThan￨U￨NNP￨PERSON￨- 0￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨- points￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- reasons￨L￨NNS￨O￨- for￨L￨IN￨O￨- persistent￨L￨JJ￨O￨- cultural￨L￨JJ￨O￨A diversity￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- less￨L￨JJR￨O￨- clarity￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- cultural￨L￨JJ￨O￨- influence￨L￨NN￨O￨- with￨L￨IN￨O￨- fundamental￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- micro-level￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 996￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 1023￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asBetween￨L￨NN￨O￨- Monoculture￨U￨NN￨O￨- and￨L￨CC￨O￨- Cultural￨U￨JJ￨O￨- Polarization￨U￨NN￨O￨- :￨L￨:￨O￨- Agent-based￨U￨JJ￨MISC￨- Models￨U￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Interplay￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Social￨U￨NNP￨ORGANIZATION￨- Influence￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- Cultural￨U￨JJ￨O￨- DiversityAuthorsAuthors￨U￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsAndreas￨L￨NNS￨O￨- FlacheOpen￨U￨NNP￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 464￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨MISC￨- AbstractSocial￨U￨NNP￨MISC￨- influence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- social￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- .￨L￨.￨O￨- +I￨U￨PRP￨O￨- give￨L￨VBP￨O￨- a￨L￨DT￨O￨- brief￨L￨JJ￨O￨- overview￨L￨NN￨O￨- illustrating￨L￨VBG￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- agent-based￨L￨JJ￨O￨- modelers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- decades￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- conditions￨L￨NNS￨O￨- and￨L￨CC￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- cultural￨L￨JJ￨O￨A diversity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- agent-based￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- unraveling￨L￨VBG￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- interplay￨L￨NN￨O￨A between￨L￨IN￨O￨- simple￨L￨JJ￨O￨- first￨L￨JJ￨ORDINAL￨- principles￨L￨NNS￨O￨- of￨L￨IN￨O￨- interpersonal￨L￨JJ￨O￨- social￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- and￨L￨CC￨O￨- emergent￨L￨JJ￨O￨- societal￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Very￨U￨RB￨O￨- often￨L￨RB￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- social￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- ,￨L￨,￨O￨- influence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- assimilative￨L￨JJ￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- more￨L￨RBR￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- others￨L￨NNS￨O￨- they￨L￨PRP￨O￨- interact￨L￨VBP￨O￨- with￨L￨IN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- below-threshold￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- initiated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- approximation￨L￨NN￨O￨A via￨L￨IN￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- works￨L￨VBZ￨O￨- well￨L￨RB￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- above-threshold￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- initiated￨L￨VBN￨O￨- at￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- methods￨L￨NNS￨O￨- from￨L￨IN￨O￨- Hamiltonian￨U￨JJ￨IDEOLOGY￨- statistical￨L￨JJ￨O￨- mechanics￨L￨NNS￨O￨- yield￨L￨VBP￨O￨- correct￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- as￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- widely-used￨L￨JJ￨O￨- Ornstein-Uhlenbeck￨U￨NNP￨MISC￨- diffusion￨L￨NN￨O￨- approximation￨L￨NN￨O￨- gives￨L￨VBZ￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- poor￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- may￨L￨MD￨O￨- retain￨L￨VB￨O￨- some￨L￨DT￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨- comparisons￨L￨NNS￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- detailed￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- approximation￨L￨NN￨O￨- can￨L￨MD￨O￨- give￨L￨VB￨O￨- good￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- provide￨L￨VB￨O￨- correct￨L￨JJ￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- asymptotic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- relied￨L￨VBN￨O￨- upon￨L￨IN￨O￨- without￨L￨IN￨O￨- some￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- external￨L￨JJ￨O￨- validation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- eg￨L￨FW￨O￨- simulation￨L￨NN￨O￨- studies￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +KeywordsStochastic￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- Large￨U￨JJ￨O￨- deviations￨L￨NNS￨O￨- Endemic￨U￨JJ￨O￨- fade-out￨L￨NN￨O￨- Persistence￨U￨NN￨O￨- time￨L￨NN￨O￨- Mathematics￨U￨NNP￨O￨- Subject￨U￨NNP￨O￨- Classification￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- 92D30￨L￨NN￨O￨- 60J28￨L￨CD￨NUMBER￨- Download￨U￨VB￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- article￨L￨NN￨O￨- textNotesAcknowledgmentsElliott￨L￨NN￨O￨- Tjia￨U￨NN￨O￨- was￨L￨VBD￨O￨- supported￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- studentship￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Engineering￨U￨NNP￨O￨- and￨L￨CC￨O￨- Physical￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- Council￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +J￨U￨NNP￨O￨- Appl￨U￨NNP￨O￨- Probab￨U￨NNP￨O￨- 53:203￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 215MathSciNetCrossRefGoogle￨L￨JJ￨O￨- ScholarBritton￨U￨NN￨O￨- T￨U￨NN￨O￨- ,￨L￨,￨O￨- Neal￨U￨NNP￨PERSON￨- P￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS-household-epidemic￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +J￨U￨NNP￨O￨- Math￨U￨NNP￨O￨- Biol￨U￨NNP￨O￨- 41:559￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 580MathSciNetCrossRefGoogle￨L￨NN￨O￨- ScholarAndersson￨U￨NN￨O￨- H￨U￨NN￨O￨- ,￨L￨,￨O￨- Djehiche￨U￨NN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1998￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- threshold￨L￨NN￨O￨- limit￨L￨NN￨O￨- theorem￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨A logistic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +J￨U￨NNP￨O￨- Appl￨U￨NNP￨O￨- Probab￨U￨NNP￨O￨- 35:662￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 670MathSciNetCrossRefGoogle￨L￨JJ￨O￨- ScholarAsaf￨U￨NN￨O￨- M￨U￨NN￨O￨- ,￨L￨,￨O￨- Meerson￨U￨NN￨PERSON￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- Extinction￨U￨NN￨O￨- of￨L￨IN￨O￨- metastable￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- important￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨A and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- illustrated￨L￨VBN￨O￨- by￨L￨IN￨O￨- some￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- examples.KeywordsPermanence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinctionLyapunov￨L￨NN￨O￨- functionalStochastic￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- theoremStrong￨L￨NN￨O￨- number￨L￨NN￨O￨- theorem￨L￨NN￨O￨- of￨L￨IN￨O￨- martingale￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionAs￨U￨NNPS￨O￨- we￨L￨PRP￨O￨- all￨L￨DT￨O￨- know￨L￨VBP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- Lotka￨U￨NNP￨LOCATION￨- –￨L￨:￨O￨- Volterra￨U￨NNP￨CITY￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- well￨L￨RB￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- competition￨L￨NN￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- ecology￨L￨NN￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- on￨L￨IN￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- separately￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- condition￨L￨NN￨O￨- to￨L￨TO￨O￨- maintain￨L￨VB￨O￨- permanence￨L￨NN￨O￨A and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- proper￨L￨JJ￨O￨- Lyapunov￨U￨NNP￨O￨- functional￨L￨JJ￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- strong￨L￨JJ￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- for￨L￨IN￨O￨- martingales￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- several￨L￨JJ￨O￨- important￨L￨JJ￨O￨- inequalities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Permanence￨U￨NN￨MISC￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- high-dimensional￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- resource￨L￨NN￨O￨- competition￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- noiseLi￨L￨NN￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- Xiaoqiang￨U￨NNP￨PERSON￨- Wang2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Qimin￨U￨NNP￨O￨- Zhang1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:441￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- resource￨L￨NN￨O￨- competition￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- noises￨L￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- Tillman￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- scholars￨L￨NNS￨O￨- also￨L￨RB￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- predicted￨L￨VBD￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- competition￨L￨NN￨O￨A results￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- resource￨L￨NN￨O￨- requirement￨L￨NN￨O￨- among￨L￨IN￨O￨- competing￨L￨VBG￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Mathematical￨U￨JJ￨MISC￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- education￨L￨NN￨O￨A on￨L￨IN￨O￨- tungiasis￨L￨NN￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- neglected￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- many￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- communitiesRachel￨L￨NNP￨O￨- A.￨U￨NN￨O￨- Orwa4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:426￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- and￨L￨CC￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- jigger￨L￨NN￨TITLE￨- infestation￨L￨NN￨O￨- incorporating￨L￨VBG￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- education￨L￨NN￨O￨- using￨L￨VBG￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- established￨L￨VBD￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- stabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨A equilibria￨L￨NNS￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- breaks￨L￨VBZ￨O￨- out￨L￨RP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨- or￨L￨CC￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- eventually￨L￨RB￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- c-Jun￨L￨NN￨O￨- N-terminal￨U￨JJ￨O￨- kinases￨L￨NNS￨O￨- differentially￨L￨RB￨O￨- regulate￨L￨VBP￨O￨- TNFand￨U￨NN￨MISC￨- TLRs-mediated￨U￨JJ￨MISC￨- necroptosis￨L￨NN￨O￨- through￨L￨IN￨O￨- their￨L￨PRP$￨O￨- kinase-dependent￨L￨JJ￨O￨- and￨L￨CC￨O￨- -￨L￨:￨O￨- independent￨L￨JJ￨RELIGION￨- activities￨L￨NNS￨O￨- Mengtao￨U￨NNP￨O￨- Cao1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Fei￨U￨NNP￨O￨- Chen1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Ni￨U￨NN￨MISC￨- Xie1￨U￨NN￨O￨- ,￨L￨,￨O￨- Meng-Yao￨U￨NNP￨O￨- Cao3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Pengfei￨U￨NNP￨PERSON￨- Chen1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Qi￨U￨NNP￨O￨- Lou1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yanli￨U￨NNP￨PERSON￨- Zhao1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Chen￨U￨NNP￨PERSON￨- He4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Shuyuan￨U￨NNP￨PERSON￨- Zhang5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Xinyang￨U￨NNP￨CITY￨- Song6￨U￨NNP￨O￨- ,￨L￨,￨O￨- Yu￨U￨NNP￨PERSON￨- Sun￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Weimin￨U￨NNP￨PERSON￨- Zhu7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Lisha￨U￨NNP￨PERSON￨- Mou1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Shaodong￨U￨NNP￨PERSON￨- Luan5￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Hanchao￨U￨NNP￨O￨- Gao1￨U￨NN￨O￨- ,5￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- Cell￨U￨NN￨O￨- Death￨U￨NNP￨O￨- &￨L￨CC￨O￨- Diseasevolume￨U￨NNP￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 1140￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- Cell￨U￨NN￨O￨- death￨L￨NN￨O￨- and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- responseNecroptosis￨L￨NN￨O￨- AbstractTumor￨U￨NN￨O￨- necrosis￨L￨NN￨O￨- factor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TNF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Toll-like￨U￨JJ￨MISC￨- receptor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TLR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 3/TLR4￨L￨NN￨O￨- activation￨L￨NN￨O￨- trigger￨L￨NN￨O￨- necroptotic￨L￨JJ￨O￨- cell￨L￨NN￨O￨A death￨L￨NN￨O￨- through￨L￨IN￨O￨- downstream￨L￨JJ￨O￨- signaling￨L￨NN￨O￨- complex￨L￨NN￨O￨- containing￨L￨VBG￨O￨- receptor-interacting￨L￨JJ￨O￨- protein￨L￨NN￨O￨- kinase￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- RIPK1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- RIPK3￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- pseudokinase￨L￨NN￨O￨- mixed￨L￨JJ￨O￨- lineage￨L￨NN￨O￨- kinase-domain-like￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- MLKL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Meanwhile￨U￨RB￨O￨- ,￨L￨,￨O￨- blocking￨L￨VBG￨O￨- the￨L￨DT￨O￨- kinase￨L￨NN￨O￨- activity￨L￨NN￨O￨- of￨L￨IN￨O￨- JNK￨U￨NN￨O￨- dramatically￨L￨RB￨O￨- reduced￨L￨VBD￨O￨- TNF￨U￨NN￨O￨- and￨L￨CC￨O￨- TLRs-induced￨U￨JJ￨O￨- necroptotic￨L￨JJ￨O￨- cell￨L￨NN￨O￨A death￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 267￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asEpidemiological￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- waning￨L￨VBG￨O￨- immunization￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨A populationAuthorsAuthors￨L￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsEwa￨L￨NNP￨MISC￨- GrelaMichael￨U￨NNP￨MISC￨- StichAmit￨U￨NNP￨MISC￨- K￨U￨NNP￨MISC￨- ChattopadhyayOpen￨U￨NNP￨MISC￨- AccessRegular￨U￨NNP￨MISC￨- ArticleFirst￨U￨NNP￨MISC￨- Online￨U￨NNP￨MISC￨- :￨L￨:￨O￨- 01￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 50￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- Abstract￨U￨JJ￨O￨- This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- SIRV￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- study￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- containing￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- 4-tiered￨L￨JJ￨O￨- population￨L￨NN￨O￨- compartment￨L￨NN￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBD￨O￨- agents￨L￨NNS￨O￨- .￨L￨.￨O￨- +J.￨U￨NNP￨O￨- B￨U￨NNP￨O￨- 88￨L￨CD￨NUMBER￨A ,￨L￨,￨O￨- 326￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ADSCrossRefGoogle￨U￨NN￨O￨- Scholar8￨U￨NN￨O￨- .￨L￨.￨O￨- +Nunes￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- N.R.￨U￨NNP￨PERSON￨- Bernardino￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- J.M.￨U￨NNP￨PERSON￨- Pacheco￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- M.C.￨U￨NNP￨PERSON￨- Gomes￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- J.￨U￨NNP￨O￨- 233￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 553￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2005￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- CrossRefGoogle￨U￨NNP￨O￨- Scholar6￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 1215￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1230￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asEfficient￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- hbox￨L￨NN￨O￨- Pow￨U￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- M￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- schemes￨L￨NNS￨O￨- for￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- kinetic￨L￨JJ￨O￨- modelsAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsAndrew￨L￨NN￨O￨- GolightlyTheodore￨U￨NN￨O￨- KypraiosOpen￨U￨NN￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 748￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractFitting￨U￨VBG￨O￨- stochastic￨L￨JJ￨O￨- kinetic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- Markov￨U￨NNP￨PERSON￨- jump￨L￨NN￨O￨A processes￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- paradigm￨L￨NN￨O￨- is￨L￨VBZ￨O￨- complicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- intractability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed-data￨L￨JJ￨O￨- likelihood￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- method￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- recently￨L￨RB￨DATE￨- proposed￨L￨VBN￨O￨- constructs￨L￨NNS￨O￨- for￨L￨IN￨O￨- sampling￨L￨NN￨O￨- conditioned￨L￨VBN￨O￨- jump￨L￨NN￨O￨A processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- inference￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- typically￨L￨RB￨O￨- require￨L￨VBP￨O￨- fewer￨L￨JJR￨O￨- state￨L￨NN￨O￨- particles￨L￨NNS￨O￨- than￨L￨IN￨O￨- when￨L￨WRB￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- bootstrap￨L￨NN￨O￨- filter￨L￨NN￨O￨- .￨L￨.￨O￨- +Computing￨U￨NNP￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- weights￨L￨NNS￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- hbox￨L￨NN￨O￨- Pow￨U￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- M￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- requires￨L￨VBZ￨O￨- running￨L￨VBG￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨A filter￨L￨NN￨O￨- over￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- states￨L￨NNS￨O￨- to￨L￨TO￨O￨- unbiasedly￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- the￨L￨DT￨O￨- intractable￨L￨JJ￨O￨- observed-data￨L￨JJ￨O￨- likelihood￨L￨NN￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- time￨L￨NN￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- rejuvenation￨L￨NN￨O￨- step￨L￨NN￨O￨- is￨L￨VBZ￨O￨- key￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- proposed￨L￨VBN￨O￨- Mul￨U￨NN￨O￨- hbox￨L￨NN￨O￨- Pow￨U￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- M￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- pseudo-marginal￨L￨JJ￨O￨- analogue￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- idealised￨L￨JJ￨O￨- scheme￨L￨NN￨O￨A known￨L￨VBN￨O￨- as￨L￨IN￨O￨- iterated￨L￨JJ￨O￨- batch￨L￨NN￨O￨- importance￨L￨NN￨O￨- sampling￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- an￨L￨DT￨O￨- auxiliary￨L￨JJ￨O￨- particle￨L￨NN￨O￨A filter￨L￨NN￨O￨- inside￨L￨IN￨O￨- the￨L￨DT￨O￨- Mul￨U￨NN￨O￨- hbox￨L￨NN￨O￨- Pow￨U￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- M￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- scheme￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- persistence￨L￨NN￨O￨- time￨L￨NN￨O￨- tau￨L￨NN￨O￨A for￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- endemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- satisfies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- sim￨L￨NN￨O￨- to￨L￨TO￨O￨- denote￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- sides￨L￨NNS￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- C￨U￨NN￨O￨- are￨L￨VBP￨O￨- constants￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- values￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- upon￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- upon￨L￨IN￨O￨- N.￨U￨NNP￨O￨- For￨U￨IN￨O￨- multidimensional￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- most￨L￨RBS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- only￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cruder￨L￨JJR￨O￨- form￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Limit￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- N￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- log￨L￨NN￨O￨- tau￨L￨NN￨O￨- N￨U￨NN￨O￨- -￨L￨:￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- leading-order￨L￨NN￨O￨- constant￨L￨NN￨O￨- A￨U￨NN￨O￨- via￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2016￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- extended￨L￨VBD￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- Andersson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Djehiche￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 1998￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- quite￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- on￨L￨IN￨O￨- insensitivity￨L￨NN￨O￨- in￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- Zachary￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- leading-order￨L￨NN￨O￨- constant￨L￨NN￨O￨A A￨U￨NN￨O￨- takes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- value￨L￨NN￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- distribution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- provided￨L￨VBN￨O￨- only￨L￨RB￨O￨- that￨L￨IN￨O￨- its￨L￨PRP$￨O￨- mean￨L￨NN￨O￨- is￨L￨VBZ￨O￨- held￨L￨VBN￨O￨- constant￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- prefactor￨L￨NN￨O￨- constant￨L￨JJ￨O￨- C￨U￨NN￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- appropriately￨L￨RB￨O￨- modified.A￨L￨NN￨O￨- different￨L￨JJ￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- Andersson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Djehiche￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 1998￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- established￨L￨VBN￨O￨- in￨L￨IN￨O￨- Clancy￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- alternatively￨L￨RB￨O￨- be￨L￨VB￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- describing￨L￨VBG￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- directed￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- annealed￨L￨JJ￨O￨- network￨L￨NN￨O￨- approximation.KeywordsStochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- Large￨U￨JJ￨O￨- deviations￨L￨NNS￨O￨- Endemic￨U￨JJ￨O￨- fade-out￨L￨NN￨O￨- Stochastic￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- Superspreaders￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionFor￨U￨NNP￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- long-term￨L￨JJ￨O￨- quasi-stable￨L￨JJ￨O￨- endemicity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- variable￨L￨NN￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- interest￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨A time￨L￨NN￨O￨- until￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- or￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- formula￨L￨NN￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- leading-order￨L￨NN￨O￨- constant￨L￨NN￨O￨- A￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Limit￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- N￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- log￨L￨NN￨O￨- tau￨L￨NN￨O￨A N￨U￨NN￨O￨- -￨L￨:￨O￨- A￨U￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Rumor￨U￨NN￨MISC￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- complex￨L￨NN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- hesitating￨L￨VBG￨O￨- mechanismXiongding￨L￨NN￨O￨- Liu1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2View￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Tao￨U￨NNP￨O￨- Li1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Mi￨U￨NNP￨O￨- Tian3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:391￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨NN￨O￨A ,￨L￨,￨O￨- controlling￨L￨VBG￨O￨- and￨L￨CC￨O￨- killing￨L￨VBG￨O￨- rumor￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- importance￨L￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- dramatic￨L￨JJ￨O￨- importance￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- managing￨L￨NN￨O￨- and￨L￨CC￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor.Rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨NN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- attracted￨L￨VBN￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- attention￨L￨NN￨O￨- from￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- rumor￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- comprehensively￨L￨RB￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨NN￨O￨A in￨L￨IN￨O￨- detail￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- corresponding￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- formulate￨L￨VB￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +presented￨L￨VBN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨VBG￨O￨A model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- demographics￨L￨NNS￨O￨- on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Ibeas4￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2018:390￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- multicontroller￨L￨JJ￨O￨- structure￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIADR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-symptomatic￨L￨JJ￨O￨- infectious-asymptomatic￨L￨JJ￨O￨- infectious-dead￨L￨NN￨O￨- lying￨L￨VBG￨O￨- bodies￨L￨NNS￨O￨- recovered￨L￨VBN￨O￨- by￨L￨IN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- immune￨L￨JJ￨O￨- ,￨L￨,￨O￨- subpopulations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- controls￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- feedback￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subpopulation￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- antiviral￨L￨JJ￨O￨A treatment￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- subpopulation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨- removal￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- lying￨L￨VBG￨O￨- bodies￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- supervisory￨L￨JJ￨O￨- loss￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- cost￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- function￨L￨NN￨O￨- incorporates￨L￨VBZ￨O￨- several￨L￨JJ￨O￨- additive￨L￨JJ￨O￨- weighted￨L￨JJ￨O￨- terms￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- loss￨L￨NN￨O￨- function￨L￨NN￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- antiviral￨L￨JJ￨O￨A treatment￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- bodies￨L￨NNS￨O￨- removal￨L￨NN￨O￨- efforts.KeywordsEpidemicsVaccinationTreatmentImpulsive￨L￨JJ￨O￨- controlsRemovalSupervisionSwitching￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionRelevant￨U￨JJ￨O￨- attention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- paid￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DATE￨- two￨L￨CD￨DATE￨- decades￨L￨NNS￨DATE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- integro-differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- difference￨L￨NN￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- boundedness￨L￨NN￨O￨- ,￨L￨,￨O￨- oscillatory￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- positivity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stability￨L￨NN￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- injection￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- feedback￨L￨NN￨O￨- regular￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- impulsive￨L￨JJ￨O￨A control￨L￨NN￨O￨- laws￨L￨NNS￨O￨- are￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- in￨L￨IN￨O￨- proposed￨L￨VBN￨O￨- true-mass￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- uncertainties￨L￨NNS￨O￨- and￨L￨CC￨O￨- eventual￨L￨JJ￨O￨- delays￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- supervised￨L￨JJ￨O￨- multicontroller￨L￨NN￨O￨- scheme￨L￨NN￨O￨A consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- parallel￨L￨JJ￨O￨- disposal￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- alternative￨L￨JJ￨O￨- controller￨L￨NN￨TITLE￨- parameterizations￨L￨NNS￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- switching￨L￨NN￨O￨- scheme￨L￨NN￨O￨- that￨L￨WDT￨O￨- chooses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- active￨L￨JJ￨O￨- controller￨L￨NN￨TITLE￨- through￨L￨IN￨O￨- consecutive￨L￨JJ￨O￨- time￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- supervisory￨L￨JJ￨O￨- decision￨L￨NN￨O￨- scheme￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- A￨U￨NN￨O￨- switched￨L￨VBD￨O￨- multicontroller￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIADR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- monitored￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- and￨L￨CC￨O￨- supervised￨L￨JJ￨O￨- transients￨L￨NNS￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨A costsM￨L￨NN￨O￨- .￨L￨.￨O￨- +Transmission￨U￨NNP￨O￨- tree￨L￨NN￨O￨- reconstruction￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- specify￨L￨VB￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- locations￨L￨NNS￨O￨A to￨L￨TO￨O￨- overall￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- characterise￨L￨VBP￨O￨- heterogeneous￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- within￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- identify￨L￨VB￨O￨- transmission￨L￨NN￨O￨- routes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- concept￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- implement￨L￨VBP￨O￨- the￨L￨DT￨O￨- within-host￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- introduced￨L￨VBN￨O￨- with￨L￨IN￨O￨- TransPhylo￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- distinct￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨A genetic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- outbreaker￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- demonstrate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- even￨L￨RB￨O￨- complex￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- results￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- successfully￨L￨RB￨O￨- included￨L￨VBN￨O￨- with￨L￨IN￨O￨- minimal￨L￨JJ￨O￨- effort￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- R￨U￨NN￨O￨- package￨L￨NN￨O￨- re-implements￨L￨NNS￨O￨- and￨L￨CC￨O￨- extends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- introduced￨L￨VBN￨O￨- with￨L￨IN￨O￨- outbreaker￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- most￨L￨RBS￨O￨- importantly￨L￨RB￨O￨- also￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- modular￨L￨JJ￨O￨- platform￨L￨NN￨O￨- allowing￨L￨VBG￨O￨- users￨L￨NNS￨O￨- to￨L￨TO￨O￨- specify￨L￨VB￨O￨- custom￨L￨NN￨O￨- models￨L￨NNS￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- optimised￨L￨JJ￨O￨- inferential￨L￨JJ￨O￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +2018Published￨L￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Reconstructing￨U￨VBG￨O￨- individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A events￨L￨NNS￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- valuable￨L￨JJ￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- help￨L￨NN￨O￨- inform￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- policy￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- establish￨L￨VBP￨O￨- faculty￨L￨NN￨O￨- hiring￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- mechanism￨L￨NN￨O￨- that￨L￨WDT￨O￨- drives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- persistent￨L￨JJ￨O￨- epistemic￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- elite￨L￨NN￨O￨- institutions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- lower￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- structural￨L￨JJ￨O￨- inequality￨L￨NN￨O￨- in￨L￨IN￨O￨- shaping￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- ideas￨L￨NNS￨O￨A in￨L￨IN￨O￨- science.KeywordsSocial￨L￨JJ￨O￨- inequalitySociology￨L￨NN￨O￨- of￨L￨IN￨O￨- scienceComputational￨L￨JJ￨O￨- social￨L￨JJ￨O￨- scienceFaculty￨L￨NN￨O￨- hiring￨L￨VBG￨O￨- networksInformation￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionA￨U￨NN￨O￨- core￨L￨NN￨O￨- principle￨L￨NN￨O￨- of￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- progress￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- free￨L￨JJ￨O￨- exchange￨L￨NN￨O￨- of￨L￨IN￨O￨- ideas￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- enables￨L￨VBZ￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- ideas￨L￨NNS￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- scientific￨L￨JJ￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +Having￨U￨VBG￨O￨- established￨L￨VBN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- then￨L￨RB￨O￨- analyze￨L￨VBP￨O￨- its￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- using￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- generic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- ideas￨L￨NNS￨O￨A and￨L￨CC￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- where￨L￨WRB￨O￨- an￨L￨DT￨O￨- idea￨L￨NN￨O￨- originates￨L￨VBZ￨O￨- on￨L￨IN￨O￨- its￨L￨PRP$￨O￨- longterm￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Analyzing￨U￨VBG￨O￨- five￨L￨CD￨NUMBER￨- popular￨L￨JJ￨O￨- research￨L￨NN￨O￨- topics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- empirically￨L￨RB￨O￨- that￨L￨IN￨O￨- faculty￨L￨NN￨O￨- hiring￨L￨NN￨O￨- can￨L￨MD￨O￨- and￨L￨CC￨O￨- does￨L￨VBZ￨O￨- facilitate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- ideas￨L￨NNS￨O￨A in￨L￨IN￨O￨- science￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- faculty￨L￨NN￨O￨- hiring￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- embody￨L￨VBP￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- researcher￨L￨NN￨TITLE￨- transitions￨L￨NNS￨O￨- from￨L￨IN￨O￨- doctoral￨L￨JJ￨O￨- to￨L￨TO￨O￨- faculty￨L￨NN￨O￨- institutions￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- shaping￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- ideas￨L￨NNS￨O￨A in￨L￨IN￨O￨- computer￨L￨NN￨O￨- science￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- where￨L￨WRB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- an￨L￨DT￨O￨- idea￨L￨NN￨O￨- originates￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Past￨U￨JJ￨DATE￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- scholarly￨L￨JJ￨O￨- productivity￨L￨NN￨O￨- show￨L￨NN￨O￨- dramatic￨L￨JJ￨O￨- epistemic￨L￨JJ￨O￨- inequality￨L￨NN￨O￨- :￨L￨:￨O￨- scientists￨L￨NNS￨O￨- at￨L￨IN￨O￨- elite￨L￨NN￨O￨- institutions￨L￨NNS￨O￨- produce￨L￨VBP￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- articles￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- play￨L￨VBP￨O￨- an￨L￨DT￨O￨- outsized￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- setting￨L￨VBG￨O￨- the￨L￨DT￨O￨- pace￨L￨NN￨O￨- and￨L￨CC￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- scientific￨L￨JJ￨O￨A achievement￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- receive￨L￨VB￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- professional￨L￨JJ￨O￨- awards￨L￨NNS￨O￨- and￨L￨CC￨O￨- recognition￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- the￨L￨DT￨O￨- endangered￨L￨VBN￨O￨- species.Assume￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Allee￨U￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- African￨U￨JJ￨NATIONALITY￨- wild￨L￨JJ￨O￨- dog￨L￨NN￨O￨- species￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- x￨L￨CC￨O￨- Tuple￨U￨NNP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- x￨L￨NN￨O￨- Mul￨U￨NN￨O￨- biggl￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- biggr￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- biggl￨L￨NN￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- biggr￨L￨NN￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- K￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- x￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Allee￨U￨NNP￨O￨- effect￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- mating￨L￨VBG￨O￨- restrictions￨L￨NNS￨O￨- .￨L￨.￨O￨- +So￨U￨IN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- African￨U￨JJ￨NATIONALITY￨- wild￨L￨JJ￨O￨- dog￨L￨NN￨O￨- impulsive￨L￨JJ￨O￨A feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Allee￨U￨NN￨O￨- effect￨L￨NN￨O￨- and￨L￨CC￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- y￨L￨NNP￨O￨- Tuple￨U￨NNP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- A￨U￨NN￨MISC￨- Lycaon￨U￨NN￨MISC￨- pictus￨L￨NN￨O￨- impulsive￨L￨JJ￨O￨A state￨L￨NN￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Allee￨U￨NN￨O￨- effect￨L￨NN￨O￨- and￨L￨CC￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- delayYaning￨L￨VBG￨O￨- Li1￨U￨NN￨O￨- ,￨L￨,￨O￨- Huidong￨U￨NNP￨O￨- Cheng1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- and￨L￨CC￨O￨- Yanhui￨U￨NN￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2018:367￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractAllee￨U￨NNP￨O￨- effect￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- sparse￨L￨JJ￨O￨- effect￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- active￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 26￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- 6th-order￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- various￨L￨JJ￨O￨- Equality￨U￨NNP￨O￨- h￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- 0.90000000000000002￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- h￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- h￨L￨NN￨O￨- Mul￨U￨NN￨O￨- mbox￨L￨NN￨O￨- Mul￨U￨NN￨O￨- o￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- m￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- l￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NN￨O￨- h￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- 1.1000000000000001￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- in￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Figure￨U￨NNP￨O￨- 11￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- optimum￨L￨NN￨O￨- and￨L￨CC￨O￨- minimum￨L￨NN￨O￨A values￨L￨NNS￨O￨- of￨L￨IN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Figure￨U￨NN￨O￨- 12￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- optimum￨L￨NN￨O￨- and￨L￨CC￨O￨- minimum￨L￨NN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- F￨U￨NN￨O￨- t￨L￨NN￨O￨- Figure￨U￨NN￨O￨- 13￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- optimum￨L￨NN￨O￨- and￨L￨CC￨O￨- minimum￨L￨NN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- t￨L￨NN￨O￨- By￨U￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- figures￨L￨NNS￨O￨- note￨L￨VBP￨O￨- the￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- HAM￨U￨NN￨O￨- .￨L￨.￨O￨- +,￨L￨,￨O￨- and￨L￨CC￨O￨- fixing￨L￨VBG￨O￨- Equality￨U￨NN￨O￨- s￨L￨NNS￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ith-order￨L￨NN￨O￨- deformation￨L￨NN￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- and￨L￨CC￨O￨- Then￨U￨RB￨O￨- the￨L￨DT￨O￨- ith-order￨L￨NN￨O￨- deformation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- i￨L￨FW￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- or￨L￨CC￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- becomes￨L￨VBZ￨O￨- 6￨L￨CD￨NUMBER￨- Numerical￨U￨JJ￨O￨- resultsConsider￨L￨NN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- values￨L￨NNS￨O￨A for￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- Mathematica￨U￨NNP￨O￨- software￨L￨NN￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- sixth-order￨L￨NN￨O￨- expansions￨L￨NNS￨O￨- for￨L￨IN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- F￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- G￨U￨NN￨O￨- t￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 7￨L￨CD￨NUMBER￨- DiscussionWe￨U￨NN￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- containing￨L￨VBG￨O￨- h￨L￨NN￨O￨- by￨L￨IN￨O￨- showing￨L￨VBG￨O￨- an￨L￨DT￨O￨- easy￨L￨JJ￨O￨- technique￨L￨NN￨O￨- for￨L￨IN￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- adjustment￨L￨NN￨O￨- of￨L￨IN￨O￨- curves￨L￨NNS￨O￨- ensuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- convergence￨L￨NN￨O￨- of￨L￨IN￨O￨- solution￨L￨NN￨O￨- series￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- recommended￨L￨VBN￨O￨- by￨L￨IN￨O￨- Liao￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Schematic￨U￨JJ￨O￨- figure￨L￨NN￨O￨A of￨L￨IN￨O￨- EIAV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Parameter￨U￨NN￨O￨- meanings￨L￨NNS￨O￨- of￨L￨IN￨O￨- EIAV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- Parameters￨U￨NNS￨O￨- and￨L￨CC￨O￨- variables￨L￨NNS￨O￨- meaningDependent￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- E￨U￨NN￨O￨- susceptible￨L￨JJ￨O￨- F￨U￨NN￨O￨- infected￨L￨JJ￨O￨- G￨U￨NN￨O￨- VirusParameters￨U￨NNS￨O￨- and￨L￨CC￨O￨- constantsΛrecruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- β￨L￨VBP￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- μ￨L￨NN￨O￨- decay￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- production￨L￨NN￨O￨- ψ￨L￨NN￨O￨- clearance￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- α￨L￨NN￨O￨- virus￨L￨NN￨O￨- cleared￨L￨VBN￨O￨- by￨L￨IN￨O￨- neutralizing￨L￨VBG￨O￨- antibodies￨L￨NNS￨O￨- ω￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ρ￨L￨VBP￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cell￨L￨NN￨O￨- killing￨L￨NN￨O￨- by￨L￨IN￨O￨- CTLS￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- Mathematical￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- EIAV￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- 4.1￨L￨CD￨NUMBER￨- Boundedness￨U￨NN￨O￨- and￨L￨CC￨O￨- positivity￨L￨NN￨O￨- Theorem￨U￨NNP￨O￨- 4.1￨L￨CD￨NUMBER￨- Let￨U￨VB￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- residual￨L￨JJ￨O￨A functions￨L￨NNS￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 24￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 26￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Following￨U￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- square￨L￨JJ￨O￨- residual￨L￨JJ￨O￨- error￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- sixth-order￨L￨NN￨O￨- approximation￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 28￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 29￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- h￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- h￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- h￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- Mul￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- E￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- F￨U￨NN￨O￨- h￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- G￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- minimal￨L￨JJ￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- .￨L￨.￨O￨- +Tipsri￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Chinviriyasit￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- bifurcating￨L￨VBG￨O￨- periodic￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- and￨L￨CC￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence.In￨L￨NN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- net￨L￨JJ￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- acquired￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- encounters￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- noted￨L￨VBN￨O￨- that￨L￨IN￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- monitors￨L￨VBZ￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- variables￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- nonnegative.The￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- GreaterThan￨U￨NNP￨O￨- Equality￨U￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- theta￨L￨IN￨O￨A phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- theta￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Banach￨U￨NNP￨O￨- space￨L￨NN￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- mapping￨L￨VBG￨O￨- the￨L￨DT￨O￨- interval￨L￨NN￨O￨- into￨L￨IN￨O￨- It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- functional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- that￨L￨WDT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- solution￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- satisfying￨L￨VBG￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2016a￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- derive￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- error￨L￨NN￨O￨- bounds￨L￨NNS￨O￨A by￨L￨IN￨O￨- making￨L￨VBG￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- periodicity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- value￨L￨NN￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- recourse￨L￨NN￨O￨- function￨L￨NN￨O￨- Q￨U￨NNP￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- convex￨L￨NN￨O￨- approximation￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Q￨U￨NNP￨O￨- hat￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- intuition￨L￨NN￨O￨- behind￨L￨IN￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- imposing￨L￨VBG￨O￨- restrictions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- higher-order￨L￨JJ￨O￨- derivatives￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- pdf￨L￨NN￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- exclude￨L￨VB￨O￨- the￨L￨DT￨O￨- piecewise￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- pdf￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- jump￨L￨NN￨O￨- discontinuities.To￨L￨NN￨O￨- obtain￨L￨VB￨O￨- these￨L￨DT￨O￨- error￨L￨NN￨O￨- bounds￨L￨VBZ￨O￨A we￨L￨PRP￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- bounds￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- expectation￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- by￨L￨IN￨O￨- Romeijnders￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +van￨L￨NN￨PERSON￨- der￨L￨FW￨PERSON￨- Vlerk￨U￨FW￨PERSON￨- passed￨L￨VBN￨O￨- away￨L￨RB￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- writing￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .1￨L￨CD￨NUMBER￨- IntroductionConsider￨U￨NNP￨O￨- the￨L￨DT￨O￨- two-stage￨L￨JJ￨O￨- recourse￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- random￨L￨JJ￨O￨- right-hand￨L￨JJ￨O￨- side￨L￨NN￨O￨- eta￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- recourse￨L￨NN￨O￨- function￨L￨NN￨O￨- Q￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- tender￨L￨NN￨O￨- variables￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- z￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- R￨U￨NNP￨O￨- mathbb￨L￨NN￨O￨A m￨L￨NN￨O￨- as￨L￨IN￨O￨- Q￨U￨NNP￨O￨- z￨L￨SYM￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- function￨L￨NN￨O￨- v￨L￨LS￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- Mul￨U￨NN￨O￨- s￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- R￨U￨NNP￨O￨- mathbb￨L￨NN￨O￨- m￨L￨NN￨O￨- as￨L￨IN￨O￨- v￨L￨LS￨O￨- s￨L￨PRP￨O￨- This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- two-stage￨L￨JJ￨O￨- decision￨L￨NN￨O￨- problem￨L￨NN￨O￨- under￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- bounds￨L￨VBZ￨O￨A on￨L￨IN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨JJ￨O￨- -1￨L￨CD￨NUMBER￨- Q￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Vert￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- hat￨L￨NN￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- total￨L￨JJ￨O￨- variation￨L￨NN￨O￨- bounds￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- expectation￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- Math￨U￨NNP￨O￨- Program￨U￨NNP￨O￨- 157:3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 46￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2016b￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- error￨L￨NN￨O￨- bounds￨L￨NNS￨O￨A for￨L￨IN￨O￨- convex￨L￨NN￨O￨- approximations￨L￨NNS￨O￨- of￨L￨IN￨O￨- simple￨L￨JJ￨O￨- integer￨L￨NN￨O￨- recourse￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +AMR￨U￨NNP￨ORGANIZATION￨- determinants￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- survive￨L￨VB￨O￨A in￨L￨IN￨O￨- environments￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- sludge￨L￨NN￨O￨- and￨L￨CC￨O￨- wastewater￨L￨NN￨O￨- treatment￨L￨NN￨O￨- systems￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- and￨L￨CC￨O￨- accelerating￨L￨VBG￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- AMR.Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- important￨L￨JJ￨O￨- decision￨L￨NN￨O￨- support￨L￨NN￨O￨- tools￨L￨NNS￨O￨- in￨L￨IN￨O￨- medicine￨L￨NN￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- published￨L￨VBD￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- on￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨A models￨L￨NNS￨O￨A on￨L￨IN￨O￨- AMR￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- still￨L￨RB￨O￨- a￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- major￨L￨JJ￨O￨- improvements￨L￨NNS￨O￨- of￨L￨IN￨O￨- AMR￨U￨NNP￨ORGANIZATION￨- models￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- regarding￨L￨VBG￨O￨- implementing￨L￨VBG￨O￨- important￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- including￨L￨VBG￨O￨- resistance￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- and￨L￨CC￨O￨- inter-species￨L￨NNS￨O￨- cooperation￨L￨NN￨O￨- .￨L￨.￨O￨- +Objective￨U￨NN￨O￨- The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- published￨L￨VBN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- AMR￨U￨NNP￨ORGANIZATION￨- development￨L￨NN￨O￨A and￨L￨CC￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- restricts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- useful￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- Many￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨A models￨L￨NNS￨O￨A of￨L￨IN￨O￨- AMR￨U￨NNP￨ORGANIZATION￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- spread￨L￨VBN￨O￨- exist￨L￨VBP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- quarantine￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- alpha￨L￨NN￨O￨- mu￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- alpha￨L￨NN￨O￨- mu￨L￨NN￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- sigma￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- sigma￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- quarantined￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Parameters￨U￨NNPS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- meanings￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ParameterDescription￨U￨NN￨O￨- A￨U￨NN￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- β￨L￨NN￨O￨- The￨U￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- μ￨L￨NN￨O￨- The￨U￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- populations￨L￨NNS￨O￨- c￨L￨NN￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- recovers￨L￨VBZ￨O￨- and￨L￨CC￨O￨- comes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- ε￨L￨NN￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- some￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- people￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infective￨L￨JJ￨O￨- α￨L￨NN￨O￨- The￨U￨DT￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- quarantined￨L￨VBN￨O￨A population￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- sigma￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- quarantined￨L￨VBN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- population￨L￨NN￨O￨- sigma￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- quarantined￨L￨VBN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- population￨L￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- quarantined￨L￨VBN￨O￨- populationWith￨L￨NN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- they￨L￨PRP￨O￨- NumericCitation￨U￨NN￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- also￨L￨RB￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- domain￨L￨NN￨O￨- of￨L￨IN￨O￨- attraction￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- that￨L￨DT￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- Hopf￨U￨NN￨PERSON￨- bifurcation￨L￨NN￨O￨A are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- stated￨L￨VBN￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- evolve￨L￨VBP￨O￨- by￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- there￨L￨EX￨O￨- appear￨L￨VBP￨O￨- some￨L￨DT￨O￨- symptoms￨L￨NNS￨O￨- needing￨L￨VBG￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- dwSSA￨L￨NN￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- systems￨L￨NNS￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infectious￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBD￨O￨- –￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- yeast￨L￨NN￨O￨- polarization￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- —￨L￨:￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- its￨L￨PRP$￨O￨- computational￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- dwSSA.KeywordsStochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- Rare￨U￨JJ￨O￨- event￨L￨NN￨O￨A probability￨L￨NN￨O￨- estimation￨L￨NN￨O￨- SSA￨U￨NNP￨ORGANIZATION￨- dwSSA￨L￨NNP￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨- Importance￨U￨NN￨O￨- sampling￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionWhen￨U￨NNP￨PERSON￨- Gillespie￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1976￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 1977￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- introduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SSA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- use￨L￨NN￨O￨- was￨L￨VBD￨O￨- deemed￨L￨VBN￨O￨- purely￨L￨RB￨O￨- academic￨L￨JJ￨O￨- as￨L￨IN￨O￨- computers￨L￨NNS￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- powerful￨L￨JJ￨O￨- enough￨L￨JJ￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- SSA￨U￨NNP￨ORGANIZATION￨- simulations￨L￨NNS￨O￨- except￨L￨IN￨O￨- for￨L￨IN￨O￨- toy￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +in￨L￨IN￨O￨- J￨U￨NNP￨O￨- Chem￨U￨NNP￨MISC￨- Phys￨U￨NNP￨MISC￨- 134:044110￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2011￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- dwSSA￨L￨NNP￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- significantly￨L￨RB￨O￨- improves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- convergence￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rare￨L￨JJ￨O￨A event￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- multilevel￨L￨JJ￨O￨- cross-entropy￨L￨JJ￨O￨- method￨L￨NN￨O￨- in￨L￨IN￨O￨- dwSSA￨L￨NN￨O￨- is￨L￨VBZ￨O￨- either￨L￨CC￨O￨- unable￨L￨JJ￨O￨- to￨L￨TO￨O￨- converge￨L￨VB￨O￨- or￨L￨CC￨O￨- converges￨L￨VBZ￨O￨- very￨L￨RB￨O￨- slowly￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- dwSSA￨L￨NN￨O￨- +￨L￨CC￨O￨- +￨L￨CC￨O￨- that￨L￨WDT￨O￨- contains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- and￨L￨CC￨O￨- improved￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- computing￨L￨VBG￨O￨- optimal￨L￨JJ￨O￨- importance￨L￨NN￨O￨- sampling￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unable￨L￨JJ￨O￨- to￨L￨TO￨O￨- reach￨L￨VB￨O￨- the￨L￨DT￨O￨- rare￨L￨JJ￨O￨A event￨L￨NN￨O￨- with￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- speed￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- wSSA￨L￨NN￨O￨- bias￨L￨NN￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- IS￨U￨VBZ￨O￨- parameters￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- recorded￨L￨VBN￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- reaction￨L￨NN￨O￨- selection￨L￨NN￨O￨- step￨L￨NN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- an￨L￨DT￨O￨- unbiased￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rare￨L￨JJ￨O￨A event￨L￨NN￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- centrality￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- weak￨L￨JJ￨O￨- ties￨L￨NNS￨O￨- in￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- large￨L￨JJ￨O￨- empirical￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- metric￨L￨JJ￨O￨- outperforms￨L￨VBZ￨O￨- other￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- links￨L￨NNS￨O￨- that￨L￨WDT￨O￨- drive￨L￨VBP￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network.KeywordsSocial￨L￨JJ￨O￨- networksLink￨L￨NN￨O￨- centrality￨L￨NN￨O￨- measuresDiffusion￨L￨NN￨O￨- processesWeak￨L￨NN￨O￨- tie￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionThe￨U￨NNP￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- commonly￨L￨RB￨O￨- measured￨L￨VBN￨O￨- through￨L￨IN￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨O￨- Access￨U￨NN￨O￨- Link￨U￨NN￨O￨- transmission￨L￨NN￨O￨- centrality￨L￨NN￨O￨A in￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networksQian￨L￨NN￨O￨- Zhang1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Márton￨U￨NNP￨O￨- Karsai1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Alessandro￨U￨NNP￨PERSON￨- Vespignani1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:33￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractUnderstanding￨U￨VBG￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmitting￨L￨VBG￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- ways￨L￨NNS￨O￨- to￨L￨TO￨O￨- hinder￨L￨VB￨O￨- or￨L￨CC￨O￨- postpone￨L￨VB￨O￨- ongoing￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- contrary￨L￨NN￨O￨- ,￨L￨,￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- global￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- betweenness￨L￨NN￨O￨- and￨L￨CC￨O￨- closeness￨L￨NN￨O￨- centrality￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Katz￨U￨NNP￨PERSON￨- centrality￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- k-shell￨L￨JJ￨O￨- index￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- subgraph￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- induced￨L￨VBD￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- may￨L￨MD￨O￨- better￨L￨RB￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- or￨L￨CC￨O￨- link￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- measure￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- centrality￨L￨NN￨O￨A ,￨L￨,￨O￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- by￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- whom￨L￨WP￨O￨- they￨L￨PRP￨O￨- transfer￨L￨VBP￨O￨- information￨L￨NN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- measures￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- provide￨L￨VB￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- links￨L￨NNS￨O￨A play￨L￨VBP￨O￨- global￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Basic￨U￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- hybrid￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- modelShujing￨L￨NN￨O￨- Gao1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yunbo￨U￨NNP￨O￨- Tu1￨U￨NN￨O￨- and￨L￨CC￨O￨- Jialin￨U￨NN￨PERSON￨- Wang1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2018:310￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- hybrid￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-periodic￨L￨JJ￨O￨- pulses￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- period￨L￨NN￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +52:224￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 234￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- established￨L￨JJ￨O￨- model.KeywordsHybrid￨L￨NN￨O￨- systemBasic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- numberNext￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- operator￨L￨NN￨TITLE￨A 1￨L￨CD￨NUMBER￨- IntroductionThe￨U￨NNP￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- secondary￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- will￨L￨MD￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- if￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- initial￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- naïve￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- operator￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Xiao￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- gave￨L￨VBD￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- impulsive￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- pulses￨L￨NNS￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- uninfected￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- List￨U￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- functions￨L￨NNS￨O￨- Parameters￨U￨NNS￨O￨- and￨L￨CC￨O￨- functions￨L￨NNS￨O￨- Meaning￨U￨VBG￨O￨- Values￨U￨NNS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Susceptible￨U￨JJ￨O￨- computers￨L￨NNS￨O￨A at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NN￨O￨- S￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- 20￨L￨CD￨NUMBER￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Infected￨U￨JJ￨O￨- computers￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 15￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Recovered￨U￨VBN￨O￨- computers￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- 10￨L￨CD￨NUMBER￨- f￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Rate￨U￨NNP￨O￨- of￨L￨IN￨O￨- external￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- false￨L￨JJ￨O￨- lambda￨L￨NN￨O￨- Rate￨U￨NN￨O￨- of￨L￨IN￨O￨- infecting￨L￨VBG￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- computer￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 0.001￨L￨CD￨NUMBER￨- varepsilon￨L￨NN￨O￨- Rate￨U￨NN￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- for￨L￨IN￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- varepsilon￨L￨NN￨O￨- 0.10000000000000001￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- Rate￨U￨NN￨O￨- of￨L￨IN￨O￨- removing￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- Equality￨U￨NN￨O￨- d￨L￨NN￨O￨- 0.10000000000000001￨L￨CD￨NUMBER￨- Main￨U￨NNP￨O￨- ideaLet￨L￨NNP￨O￨- L￨U￨NNP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- operators￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨ORGANIZATION￨- g￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨O￨- text￨L￨NN￨O￨- Pow￨U￨NN￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- text￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- constant￨L￨JJ￨O￨- values￨L￨NNS￨O￨- c￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- c￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VB￨O￨- Equality￨U￨NN￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- c￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Now￨U￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- homotopy￨L￨JJ￨O￨- maps￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- q￨L￨NN￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- u￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- m￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- i￨L￨FW￨ORGANIZATION￨- Mul￨U￨FW￨ORGANIZATION￨- c￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- C￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- n￨L￨NN￨O￨- o￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- embedding￨L￨NN￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- hbar￨L￨NN￨O￨- Mul￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ne￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- convergence￨L￨NN￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- auxiliary￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- ,￨L￨,￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- operators￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- N￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- operators￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- According￨U￨VBG￨O￨- to￨L￨TO￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- zero-order￨L￨NN￨O￨- deformation￨L￨NN￨O￨- ,￨L￨,￨O￨- equations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Now￨U￨RB￨DATE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- write￨L￨VB￨O￨- the￨L￨DT￨O￨- Taylor￨U￨NNP￨PERSON￨- series￨L￨NN￨O￨- for￨L￨IN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- q￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- For￨U￨IN￨O￨- more￨L￨JJR￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- vectors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- Mul￨U￨NN￨O￨- displaystyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- Mul￨U￨NN￨O￨- displaystyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- tilde￨L￨VBP￨O￨- Mul￨U￨NN￨O￨- displaystyle￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- tilde￨L￨NN￨O￨- Differentiating￨U￨VBG￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +and￨L￨CC￨O￨- putting￨L￨VBG￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- q￨L￨VBD￨O￨- 0￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- mth-order￨L￨NN￨O￨- deformation￨L￨NN￨O￨- equations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- L￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨PERSON￨- left￨L￨VBD￨O￨- Mul￨U￨NNP￨PERSON￨- right￨L￨RB￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- chi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- -￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- g￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- hbar￨L￨NN￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NNP￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Mul￨U￨NN￨PERSON￨- begin￨L￨VBP￨O￨- Mul￨U￨NN￨ORGANIZATION￨- g￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨O￨- e￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- By￨U￨IN￨O￨- putting￨L￨VBG￨O￨- false￨L￨JJ￨O￨- and￨L￨CC￨O￨- applying￨L￨VBG￨O￨- the￨L￨DT￨O￨- inverse￨L￨JJ￨O￨- operators￨L￨NNS￨O￨A Pow￨U￨VBP￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- -1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Pow￨U￨NN￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- g￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨O￨- e￨L￨SYM￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- chi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- -￨L￨:￨O￨- 1￨L￨CD￨DATE￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- hbar￨L￨NN￨O￨- Integral￨U￨JJ￨O￨- Pow￨U￨NN￨O￨- limits￨L￨NNS￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mth-order￨L￨NN￨O￨- approximate￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- as￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- displaystyle￨L￨NN￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Sum￨U￨NN￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- j￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Numerical￨U￨JJ￨O￨- illustrationIn￨L￨NN￨O￨- this￨L￨DT￨O￨- section￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- HAM￨U￨NN￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- hbar￨L￨SYM￨O￨- -￨L￨:￨O￨- curves￨L￨NNS￨O￨- are￨L￨VBP￨O￨- plotted￨L￨VBN￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- convergence￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- residual￨L￨JJ￨O￨- errors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- theses￨L￨DT￨O￨- regions.KeywordsSusceptible￨L￨NN￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBD￨O￨- model￨L￨NN￨TITLE￨- Modified￨U￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- Computer￨U￨NN￨O￨- virus￨L￨NN￨O￨- Homotopy￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- method￨L￨NN￨O￨- hbar￨L￨SYM￨O￨- -￨L￨:￨O￨- Curve￨U￨NN￨O￨- IntroductionIn￨U￨NN￨O￨- recent￨L￨JJ￨DURATION￨- decades￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- computer￨L￨NN￨O￨- systems￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- great￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- of￨L￨IN￨O￨- life￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 211￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 222￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asSolving￨L￨VBG￨O￨- a￨L￨DT￨O￨- modified￨L￨VBN￨O￨- nonlinear￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨A viruses￨L￨NNS￨O￨- by￨L￨IN￨O￨- homotopy￨L￨NN￨O￨- analysis￨L￨NN￨O￨- methodAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsSamad￨L￨NNP￨O￨- NoeiaghdamMuhammad￨U￨NNP￨MISC￨- SulemanHüseyin￨U￨NNP￨MISC￨- BudakOpen￨U￨NNP￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- PaperFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 215￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨MISC￨- AbstractThe￨U￨NNP￨MISC￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBD￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- homotopy￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HAM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- numerical￨L￨JJ￨O￨- example￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨A process￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- improvements￨L￨NNS￨O￨- after￨L￨IN￨O￨- taking￨L￨VBG￨O￨- corresponding￨L￨JJ￨O￨- measures.KeywordsSIR￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- Oversaturated￨U￨JJ￨O￨- conditions￨L￨NNS￨O￨- Congestion￨U￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- Congestion￨U￨NN￨O￨- propagation￨L￨NN￨O￨- rate￨L￨NN￨O￨- Gray￨U￨NNP￨O￨- system￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- Communicated￨U￨VBN￨O￨- by￨L￨IN￨O￨- Xuesong￨U￨NNP￨PERSON￨- Zhou￨U￨NNP￨PERSON￨- .1￨L￨CD￨NUMBER￨- IntroductionCongestion￨U￨NNP￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨- transit￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- becoming￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- concerns￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transportation￨L￨NN￨O￨- system￨L￨NN￨O￨- agencies￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- oversaturated￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- gray￨L￨JJ￨O￨- system￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨A rate￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- joint￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- influential￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- passenger￨L￨NN￨O￨- flow￨L￨NN￨O￨- ,￨L￨,￨O￨- train￨L￨NN￨CRIMINAL_CHARGE￨- headway￨L￨NN￨O￨- ,￨L￨,￨O￨- passenger￨L￨NN￨O￨- transfer￨L￨NN￨O￨- convenience￨L￨NN￨O￨- ,￨L￨,￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- congestion￨L￨NN￨O￨- occurring￨L￨VBG￨O￨- ,￨L￨,￨O￨- initial￨L￨JJ￨O￨- congested￨L￨JJ￨O￨- station￨L￨NN￨O￨- and￨L￨CC￨O￨- station￨L￨NN￨O￨- capacity￨L￨NN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- ,￨L￨,￨O￨- Zang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- boundary￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- congestion￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- traffic￨L￨NN￨O￨- flow￨L￨NN￨O￨A theory￨L￨NN￨O￨- .￨L￨.￨O￨- +Stephen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- described￨L￨VBD￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- oversaturated￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- in￨L￨IN￨O￨- rail￨L￨NN￨O￨- transit￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- combustion￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- he￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨A is￨L￨VBZ￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- ripple￨L￨NN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- calculating￨L￨VBG￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- constructed￨L￨VBN￨O￨- .￨L￨.￨O￨- +And￨U￨CC￨O￨- references￨L￨NNS￨O￨A [￨L￨-LRB-￨O￨- 56￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 58￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- thought￨L￨VBD￨O￨- the￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- transformation.In￨L￨NN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- stochastic￨L￨JJ￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- disturbance￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- build￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Brownian￨U￨JJ￨MISC￨- motion￨L￨NN￨O￨- with￨L￨IN￨O￨- intensity￨L￨NN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- sigma￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- process￨L￨NN￨O￨- diagram￨L￨NN￨O￨- for￨L￨IN￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- By￨U￨IN￨O￨- using￨L￨VBG￨O￨- LaSalle￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- invariance￨L￨NN￨O￨- principle￨L￨NN￨O￨- and￨L￨CC￨O￨- Lyapunov￨U￨NNP￨PERSON￨- direct￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Equality￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- Lambda￨U￨NNP￨ORGANIZATION￨- beta￨L￨NN￨O￨- Pow￨U￨NN￨O￨- mu￨L￨NN￨O￨A Add￨U￨VB￨O￨- alpha￨L￨NN￨O￨- Add￨U￨VB￨O￨- r￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- r￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- -1￨L￨CD￨NUMBER￨- was￨L￨VBD￨O￨- established￨L￨VBN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable.As￨L￨NNPS￨O￨- we￨L￨PRP￨O￨- all￨L￨DT￨O￨- know￨L￨VBP￨O￨- ,￨L￨,￨O￨- real￨L￨JJ￨O￨- life￨L￨NN￨O￨- is￨L￨VBZ￨O￨- filled￨L￨VBN￨O￨- with￨L￨IN￨O￨- randomness￨L￨NN￨O￨- and￨L￨CC￨O￨- unpredictability￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- both￨L￨DT￨O￨- transfer￨L￨NN￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- transfer￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- proposed￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Λ￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transfer￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mortality￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- return￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Extinction￨U￨NN￨MISC￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- transfer￨L￨NN￨O￨A from￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- to￨L￨TO￨O￨- susceptibleYi￨L￨NN￨O￨- Song1￨U￨NN￨O￨- ,￨L￨,￨O￨- Anqi￨U￨JJ￨O￨- Miao1￨U￨NN￨O￨- ,￨L￨,￨O￨- Tongqian￨U￨JJ￨O￨- Zhang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Xinzeng￨U￨NN￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Jianxin￨U￨NNP￨PERSON￨- Liu3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:293￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- transfer￨L￨NN￨O￨- from￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- discussed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Stochastic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- better￨L￨RB￨O￨- conform￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- situation￨L￨NN￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- many￨L￨JJ￨O￨- scholars￨L￨NNS￨O￨- have￨L￨VBP￨O￨- done￨L￨VBN￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- randomness￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- references￨L￨NNS￨O￨A [￨L￨-LRB-￨O￨- 28￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 38￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- effect￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- references￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 39￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 42￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- set￨L￨VBD￨O￨- up￨L￨RP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- algorithms￨L￨NNS￨O￨- a￨L￨DT￨O￨- selection￨L￨NN￨O￨A threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- that￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- structural￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- graph￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- improves￨L￨VBZ￨O￨- significantly￨L￨RB￨O￨- the￨L￨DT￨O￨- selection￨L￨NN￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- seed￨L￨NN￨O￨- set￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- multi-hops￨L￨JJ￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- select￨L￨VB￨O￨- most￨L￨RBS￨O￨- influential￨L￨JJ￨O￨- users￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- distinct￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- measure￨L￨VBP￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- selected￨L￨VBN￨O￨- seed￨L￨NN￨O￨A set￨L￨NN￨O￨- performed￨L￨VBN￨O￨- by￨L￨IN￨O￨- our￨L￨PRP$￨O￨- algorithms￨L￨NNS￨O￨- and￨L￨CC￨O￨- existing￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- diffusion￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- screening￨L￨NN￨O￨- assay￨L￨NN￨O￨- for￨L￨IN￨O￨- Selective￨U￨JJ￨O￨- Dimerizing￨U￨VBG￨O￨- Glucocorticoid￨U￨NN￨O￨- Receptor￨U￨NN￨O￨- Agonists￨U￨NNS￨O￨- and￨L￨CC￨O￨- Modulators￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- SEDIGRAM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- effective￨L￨JJ￨O￨- against￨L￨IN￨O￨- acute￨L￨JJ￨O￨- inflammation￨L￨NN￨O￨- Jolien￨U￨NN￨O￨- Souffriau1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Melanie￨U￨NNP￨PERSON￨- Eggermont1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Sara￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Ryckeghem1￨U￨NN￨PERSON￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kelly￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Looveren1￨U￨NN￨PERSON￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Lise￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Wyngene1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Evelien￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Hamme3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marnik￨U￨NNP￨O￨- Vuylsteke4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Rudi￨U￨NNP￨PERSON￨- Beyaert￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Karolien￨U￨NNP￨O￨- De￨U￨NNP￨O￨- Bosscher5￨U￨NNP￨O￨- ,6￨L￨NNP￨O￨- &￨L￨CC￨O￨- Claude￨U￨NNP￨O￨- Libert1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 12894￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Acute￨U￨JJ￨O￨- inflammationSepsis￨L￨NN￨O￨- AbstractIt￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨- that￨L￨IN￨O￨- glucocorticoid￨L￨NN￨O￨- receptor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- agonists￨L￨NNS￨O￨- that￨L￨WDT￨O￨- promote￨L￨VBP￨O￨- GR￨U￨NN￨O￨- homodimerization￨L￨NN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- standard￨L￨JJ￨O￨- glucocorticoids￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Dexamethasone￨U￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- anti-inflammatory￨L￨JJ￨O￨- molecules￨L￨NNS￨O￨- against￨L￨IN￨O￨- acute￨L￨JJ￨O￨- and￨L￨CC￨O￨- life-threatening￨L￨JJ￨O￨- inflammatory￨L￨JJ￨O￨A conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- principle￨L￨NN￨O￨- experiment￨L￨NN￨O￨A ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- candidate￨L￨NN￨TITLE￨- compounds￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- identified￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- potentially￨L￨RB￨O￨- interesting￨L￨JJ￨O￨- compounds￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Cortivazol￨U￨NN￨O￨- and￨L￨CC￨O￨- AZD2906￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- strong￨L￨JJ￨O￨- protection￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- mouse￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- aggressive￨L￨JJ￨O￨- TNF-induced￨U￨JJ￨O￨- lethal￨L￨JJ￨O￨- inflammation￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- screening￨L￨JJ￨O￨- pipeline￨L￨NN￨O￨- for￨L￨IN￨O￨- SEDIGRAM￨U￨NNP￨O￨- may￨L￨MD￨O￨- assist￨L￨VB￨O￨- the￨L￨DT￨O￨- search￨L￨NN￨O￨- for￨L￨IN￨O￨- compounds￨L￨NNS￨O￨- that￨L￨WDT￨O￨- promote￨L￨VBP￨O￨- GR￨U￨NN￨O￨- dimerization￨L￨NN￨O￨- and￨L￨CC￨O￨- limit￨L￨NN￨O￨- overwhelming￨L￨JJ￨O￨- acute￨L￨JJ￨O￨- inflammatory￨L￨JJ￨O￨A responses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- issues￨L￨NNS￨O￨- are￨L￨VBP￨O￨- being￨L￨VBG￨O￨- addressed￨L￨VBN￨O￨- by￨L￨IN￨O￨- searching￨L￨VBG￨O￨- for￨L￨IN￨O￨- new￨L￨JJ￨O￨- molecules￨L￨NNS￨O￨- with￨L￨IN￨O￨- enhanced￨L￨VBN￨O￨- GC￨U￨NN￨O￨- therapeutic￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- and￨L￨CC￨O￨- fewer￨L￨JJR￨O￨A or￨L￨CC￨O￨- less￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- side￨L￨NN￨O￨- effects.GCs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- lipophilic￨L￨JJ￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- they￨L￨PRP￨O￨- penetrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- cell￨L￨NN￨O￨- membrane￨L￨NN￨O￨- and￨L￨CC￨O￨- bind￨L￨VBP￨O￨- the￨L￨DT￨O￨- GC￨U￨NN￨O￨- receptor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- analysis￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- universal￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- TL￨U￨NN￨O￨- and￨L￨CC￨O￨- δ15N￨L￨NN￨O￨- that￨L￨WDT￨O￨- permits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- robust￨L￨JJ￨O￨- prognostic￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- configuration￨L￨NN￨O￨- of￨L￨IN￨O￨- food￨L￨NN￨O￨A webs￨L￨NNS￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- all￨L￨DT￨O￨- system￨L￨NN￨O￨- components￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reliably￨L￨RB￨O￨- analysed￨L￨VBN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- saturated￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- rate￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨JJ￨O￨- eta￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨NNP￨ORGANIZATION￨- V￨U￨NNP￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- eta￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- lose￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- join￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- become￨L￨VBP￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- crashing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- half￨L￨NN￨O￨- saturation￨L￨NN￨O￨- constant￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- saturation￨L￨NN￨O￨- constant￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Having￨U￨VBG￨O￨- this￨L￨DT￨O￨- idea￨L￨NN￨O￨- in￨L￨IN￨O￨- mind￨L￨NN￨O￨- and￨L￨CC￨O￨- considering￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- may￨L￨MD￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- worth￨L￨JJ￨O￨- investigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- Hopf￨U￨NNP￨O￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨JJ￨O￨- eta￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- V￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- eta￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers.The￨L￨NN￨O￨- organization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Stability￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcationBy￨L￨NNP￨O￨- direct￨L￨JJ￨O￨- computation￨L￨NN￨O￨- we￨L￨PRP￨O￨- get￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨A delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equation￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- 3￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- with￨L￨IN￨O￨- For￨U￨IN￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +Combining￨U￨VBG￨O￨- the￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- predation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- eco-epidemiological￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- prey￨L￨NN￨O￨- refuge￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- prey￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- variables￨L￨NNS￨O￨- Mul￨U￨NNP￨O￨- Phi￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- bigl￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- rewriting￨L￨VBG￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 3￨L￨CD￨NUMBER￨- EquilibriaAll￨U￨NN￨ORGANIZATION￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Y￨U￨NN￨O￨- c￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- alpha￨L￨NN￨O￨A Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 3.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- trivial￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Theorem￨U￨NNP￨O￨- 4.1￨L￨CD￨NUMBER￨- Supposing￨U￨VBG￨O￨- that￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- B￨U￨NN￨O￨- underline￨L￨VBP￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- B￨U￨NN￨O￨- overline￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictLessThan￨U￨NN￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- underline￨L￨VBP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- gamma￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- dfrac￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- K￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨PERSON￨- K￨U￨NN￨PERSON￨- Pow￨U￨NN￨PERSON￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- K￨U￨NNP￨O￨- K￨U￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- dfrac￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- K￨U￨NNP￨O￨- alpha￨L￨NN￨O￨A -1￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- K￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨PERSON￨- StrictLessThan￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- K￨U￨NNP￨PERSON￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- K￨U￨NNP￨O￨- alpha￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- c￨L￨NN￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- e￨L￨SYM￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- alpha￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- .￨L￨.￨O￨- +Theorem￨U￨NNP￨O￨- 4.2￨L￨CD￨NUMBER￨- Assuming￨U￨VBG￨O￨- that￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- B￨U￨NN￨O￨- underline￨L￨VBP￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- B￨U￨NN￨O￨- overline￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NN￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- overline￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- K￨U￨NNP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨A -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- K￨U￨NNP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- alpha￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- alpha￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 4.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- negative￨L￨JJ￨O￨- real￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- A￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- iff￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 4.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Inequality￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 4.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- term￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 4.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- inequality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- inequality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- always￨L￨RB￨O￨- holds￨L￨VBZ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- biggl￨L￨NN￨O￨- Mul￨U￨NN￨O￨- biggr￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- c￨L￨NN￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- e￨L￨SYM￨O￨- -1￨L￨CD￨NUMBER￨- If￨U￨IN￨O￨- StrictLessThan￨U￨JJ￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- has￨L￨VBZ￨O￨- its￨L￨PRP$￨O￨- ecological￨L￨JJ￨O￨- meanings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- spatio-temporal￨L￨JJ￨O￨- realizations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- instructive￨L￨JJ￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- and￨L￨CC￨O￨- exploring￨L￨VBG￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- influences￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- its￨L￨PRP$￨O￨- speed￨L￨NN￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- evolution.KeywordsAgent-based￨L￨JJ￨O￨- modelDiffusion￨L￨NN￨O￨- processSpreading￨L￨NN￨O￨- processStochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- algorithmHuman￨L￨NN￨O￨- mobility￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionModeling￨U￨NN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- topic￨L￨NN￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- relevance￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- and￨L￨CC￨O￨- understanding￨L￨VBG￨O￨- many￨L￨JJ￨O￨- real-world￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- migration￨L￨NN￨O￨- and￨L￨CC￨O￨- traffic￨L￨NN￨O￨- flows￨L￨VBZ￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- processes￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- innovations￨L￨NNS￨O￨A [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Human￨U￨JJ￨MISC￨- mobility￨L￨NN￨O￨A and￨L￨CC￨O￨- innovation￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- ancient￨L￨JJ￨O￨- times￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- approachNataša￨L￨NN￨O￨- Djurdjevac￨U￨NN￨O￨- Conrad1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Luzie￨U￨NN￨O￨- Helfmann1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Johannes￨U￨NNP￨PERSON￨- Zonker1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Stefanie￨U￨NNP￨PERSON￨- Winkelmann1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Christof￨U￨NNP￨PERSON￨- Schütte1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 7:24￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractHuman￨U￨NNP￨O￨- mobility￨L￨NN￨O￨- always￨L￨RB￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- great￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- cultural￨L￨JJ￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- technological￨L￨JJ￨O￨- ideas￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- innovations￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- ancient￨L￨JJ￨O￨- world￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- human￨L￨JJ￨O￨- movements￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- innovations￨L￨NNS￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- changing￨L￨VBG￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- agents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- changing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- positions￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨A processes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- happened￨L￨VBD￨O￨- in￨L￨IN￨O￨- ancient￨L￨JJ￨O￨- times￨L￨NNS￨O￨- faces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- additional￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- that￨L￨WDT￨O￨- available￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- limited￨L￨JJ￨O￨- and￨L￨CC￨O￨- sparse￨L￨JJ￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- structuring￨L￨VBG￨O￨- information￨L￨NN￨O￨- overload￨L￨NN￨O￨- issues￨L￨NNS￨O￨- which￨L￨WDT￨O￨- extends￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- overload￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- decision-making￨L￨JJ￨O￨- process.KeywordsInformation￨L￨NN￨O￨- processing￨L￨NN￨O￨- Information￨U￨NN￨O￨- management￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- Information￨U￨NN￨O￨- overload￨L￨NN￨O￨- Literature￨U￨NN￨O￨- review￨L￨NN￨O￨- Bibliometric￨U￨JJ￨MISC￨- literature￨L￨NN￨O￨A analysis￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionInformation￨U￨NN￨O￨- overload￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- decisive￨L￨JJ￨O￨- factor￨L￨NN￨O￨- driving￨L￨VBG￨O￨- negative￨L￨JJ￨O￨- “￨L￨``￨O￨- work￨L￨NN￨O￨- environments￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- that￨L￨IN￨O￨- ]￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- killing￨L￨VBG￨O￨- productivity￨L￨NN￨O￨- ,￨L￨,￨O￨- dampening￨L￨VBG￨O￨- creativity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- making￨L￨VBG￨O￨- us￨L￨PRP￨O￨- unhappy￨L￨JJ￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Business￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- pp￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 44￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asInformation￨L￨NN￨O￨- overload￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- age￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- from￨L￨IN￨O￨- business￨L￨NN￨O￨- administration￨L￨NN￨O￨A ,￨L￨,￨O￨- business￨L￨NN￨O￨- psychology￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- related￨L￨JJ￨O￨- disciplines￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- bibliometric￨L￨JJ￨O￨- approach￨L￨NN￨O￨- and￨L￨CC￨O￨- framework￨L￨NN￨O￨- developmentAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsPeter￨L￨NNP￨O￨- Gordon￨U￨NNP￨O￨- RoetzelOpen￨U￨NNP￨O￨- AccessOriginal￨U￨NNP￨O￨- ResearchFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1.8￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- AbstractIn￨U￨VBP￨O￨- the￨L￨DT￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- overload￨L￨NN￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- media￨L￨NNS￨O￨- ,￨L￨,￨O￨- virtual￨L￨JJ￨O￨- collaboration￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rises￨L￨VBZ￨O￨- rapidly￨L￨RB￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- business￨L￨NN￨O￨- administration￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- subjects￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- reveals￨L￨VBZ￨O￨- research￨L￨NN￨O￨- directions￨L￨NNS￨O￨- and￨L￨CC￨O￨- bridges￨L￨NNS￨O￨- of￨L￨IN￨O￨- literature￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- fields￨L￨NNS￨O￨- of￨L￨IN￨O￨- business￨L￨NN￨O￨- administration￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- accounting￨L￨NN￨O￨- ,￨L￨,￨O￨- finance￨L￨NN￨O￨- ,￨L￨,￨O￨- health￨L￨NN￨O￨- management￨L￨NN￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- innovation￨L￨NN￨O￨- management￨L￨NN￨O￨- ,￨L￨,￨O￨- international￨L￨JJ￨O￨- management￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- marketing￨L￨NN￨O￨- ,￨L￨,￨O￨- manufacturing￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- organizational￨L￨JJ￨O￨- science￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- review￨L￨NN￨O￨- article￨L￨NN￨O￨- analyzes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- overload￨L￨NN￨O￨- literature￨L￨NN￨O￨- in￨L￨IN￨O￨- business￨L￨NN￨O￨- administration￨L￨NN￨O￨A and￨L￨CC￨O￨- related￨L￨JJ￨O￨- interdisciplinary￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- and￨L￨CC￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- and￨L￨CC￨O￨- overarching￨L￨JJ￨O￨- overview￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- bibliometric￨L￨JJ￨O￨- literature￨L￨NN￨O￨- analysis￨L￨NN￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- snowball￨L￨NN￨O￨- sampling￨L￨NN￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- review￨L￨NN￨O￨- article￨L￨NN￨O￨- identifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- research￨L￨NN￨O￨- streams￨L￨NNS￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- pulse￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨A overload-related￨L￨JJ￨O￨- research￨L￨NN￨O￨- and￨L￨CC￨O￨- suggest￨L￨VBP￨O￨- new￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- addressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- and￨L￨CC￨O￨- identifies￨L￨VBZ￨O￨- concrete￨L￨JJ￨O￨- open￨L￨JJ￨O￨- gaps￨L￨NNS￨O￨- for￨L￨IN￨O￨- further￨L￨JJ￨O￨- research￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- illustrate￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- empirically￨L￨RB￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Gaussian￨U￨JJ￨MISC￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- application￨L￨NN￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modelling.KeywordsABC￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- Sequential￨U￨NNP￨ORGANIZATION￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- Slice￨U￨VB￨ORGANIZATION￨- sampling￨L￨NN￨O￨- Infectious￨U￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- Electronic￨U￨JJ￨O￨- supplementary￨L￨JJ￨O￨- materialThe￨L￨NN￨O￨- online￨L￨NN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- doi￨L￨FW￨O￨- :￨L￨:￨O￨- 10.1007￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- s11222-017-9764-4￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- contains￨L￨VBZ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- authorized￨L￨VBN￨O￨- users￨L￨NNS￨O￨- .1￨L￨CD￨NUMBER￨- IntroductionApproximate￨U￨NNP￨O￨- Bayesian￨U￨NNP￨O￨- computation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- approximate￨L￨JJ￨O￨- inference￨L￨NN￨O￨A ,￨L￨,￨O￨- used￨L￨VBN￨O￨- when￨L￨WRB￨O￨- likelihoods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- impossible￨L￨JJ￨O￨- or￨L￨CC￨O￨- impractical￨L￨JJ￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- numerically￨L￨RB￨O￨- but￨L￨CC￨O￨- simulating￨L￨VBG￨O￨- datasets￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- is￨L￨VBZ￨O￨- straightforward￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- parameter￨L￨NN￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rare￨L￨JJ￨O￨A event￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- roughly￨L￨RB￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- observations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- rare￨L￨JJ￨O￨A event￨L￨NN￨O￨- probability￨L￨NN￨O￨- estimator￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- estimate￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- pseudo-marginal￨L￨JJ￨O￨- Metropolis￨U￨NNP￨O￨- –￨L￨:￨O￨- Hastings￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- parameter￨L￨NN￨O￨- inference￨L￨NN￨O￨- .￨L￨.￨O￨- +EverittTheodore￨U￨NNP￨MISC￨- KypraiosOpen￨U￨NNP￨MISC￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 3.8￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨MISC￨- AbstractApproximate￨U￨NNP￨MISC￨- Bayesian￨U￨NNP￨MISC￨- computation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- methods￨L￨NNS￨O￨- permit￨L￨VBP￨O￨- approximate￨L￨JJ￨O￨- inference￨L￨NN￨O￨A for￨L￨IN￨O￨- intractable￨L￨JJ￨O￨- likelihoods￨L￨NNS￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 891￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 904￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asA￨L￨NN￨O￨- network￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- online￨L￨JJ￨O￨- community￨L￨NN￨O￨- commissioning￨L￨VBG￨O￨- dataAuthorsAuthors￨L￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsClement￨L￨NNP￨O￨- LeeAndrew￨U￨NNP￨O￨- GarbettDarren￨U￨NNP￨O￨- J.￨U￨NNP￨O￨- WilkinsonOpen￨U￨NNP￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 02￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 5.9￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- AbstractA￨U￨NN￨O￨- statistical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- preferential￨L￨JJ￨O￨- attachment￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- sequentially￨L￨RB￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- simple￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- ,￨L￨,￨O￨- usually￨L￨RB￨O￨- describes￨L￨VBZ￨O￨- real-life￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- better￨L￨RBR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- assuming￨L￨VBG￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Bernoulli￨U￨NNP￨MISC￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- any￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- connected￨L￨VBN￨O￨- ,￨L￨,￨O￨- does￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- online￨L￨JJ￨O￨- commissioning￨L￨VBG￨O￨- data.KeywordsStochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- MCMC￨U￨NNP￨O￨- Random￨U￨NNP￨O￨- graphs￨L￨NNS￨O￨- Preferential￨U￨JJ￨O￨- attachment￨L￨NN￨O￨- Community￨U￨NN￨O￨- commissioning￨L￨VBG￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSocial￨U￨NNP￨ORGANIZATION￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- popular￨L￨JJ￨O￨- research￨L￨NN￨O￨- topic￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DURATION￨- couple￨L￨NN￨DURATION￨- of￨L￨IN￨DURATION￨- decades￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- thanks￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- unprecedentedly￨L￨RB￨O￨- large￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- internet￨L￨NN￨O￨- data￨L￨NNS￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- computers￨L￨NNS￨O￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- details￨L￨NNS￨O￨- ties￨L￨NNS￨O￨- between￨L￨IN￨O￨- people￨L￨NNS￨O￨- or￨L￨CC￨O￨- objects￨L￨NNS￨O￨- all￨L￨DT￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- flexibly￨L￨RB￨O￨- modelled￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- completely￨L￨RB￨O￨- independent￨L￨JJ￨RELIGION￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- sum￨L￨VB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- even￨L￨RB￨O￨- integer.One￨L￨JJ￨O￨- prominent￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨A life￨L￨NN￨O￨A is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- scale-free￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- approximately￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Albert￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- stress￨L￨VBP￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- retain￨L￨VB￨O￨- the￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- noise￨L￨NN￨O￨- derived￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- emphasise￨L￨VB￨O￨- this￨L￨DT￨O￨- point￨L￨NN￨O￨- by￨L￨IN￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- selection￨L￨NN￨O￨A compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- made￨L￨VBN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- model.KeywordsStochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- Population￨U￨NNP￨O￨- genetics￨L￨NNS￨O￨- Time-scale￨U￨JJ￨MISC￨- separation￨L￨NN￨O￨- Effective￨U￨JJ￨O￨- models￨L￨NNS￨O￨- Noise-induced￨U￨JJ￨MISC￨- selection￨L￨NN￨O￨- Population￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionIn￨U￨NN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- articles￨L￨NNS￨O￨- on￨L￨IN￨O￨- biological￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- published￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Journal￨U￨NNP￨O￨- of￨L￨IN￨O￨- Statistical￨U￨NNP￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- natural￨L￨JJ￨O￨- to￨L￨TO￨O￨- ask￨L￨VB￨O￨- what￨L￨WP￨O￨- expertise￨L￨NN￨O￨- and￨L￨CC￨O￨- insights￨L￨NNS￨O￨- statistical￨L￨JJ￨O￨- physicists￨L￨NNS￨O￨- can￨L￨MD￨O￨- bring￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- what￨L￨WP￨O￨- way￨L￨NN￨O￨- might￨L￨MD￨O￨- their￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- subject￨L￨JJ￨O￨- differ￨L￨VBP￨O￨- from￨L￨IN￨O￨- biologists￨L￨NNS￨O￨- .￨L￨.￨O￨- +That￨U￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- start￨L￨VB￨O￨- with￨L￨IN￨O￨- genes￨L￨NNS￨O￨- as￨L￨IN￨O￨- basic￨L￨JJ￨O￨- constituents￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- type￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- allele￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- location￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- carrying￨L￨VBG￨O￨- the￨L￨DT￨O￨- gene￨L￨NN￨O￨- is￨L￨VBZ￨O￨- located￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- island￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sex￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- carrying￨L￨VBG￨O￨- the￨L￨DT￨O￨- gene￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.Secondly￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨A description￨L￨NN￨O￨- contains￨L￨VBZ￨O￨- too￨L￨RB￨O￨- much￨L￨JJ￨O￨- detail￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- irrelevant￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- macroscale￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mesoscale￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- some￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- element￨L￨NN￨O￨- is￨L￨VBZ￨O￨- retained￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- derive￨L￨VB￨O￨- a￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- or￨L￨CC￨O￨- effective￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- contains￨L￨VBZ￨O￨- parameters￨L￨NNS￨O￨- which￨L￨WDT￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- description￨L￨NN￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- encapsulate￨L￨VB￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- description.Thirdly￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- generic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- include￨L￨VBP￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- haploid￨L￨NN￨O￨- Moran￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨A number￨L￨NN￨O￨- of￨L￨IN￨O￨- islands￨L￨NNS￨O￨- with￨L￨IN￨O￨- selection￨L￨NN￨O￨- and￨L￨CC￨O￨- mutation￨L￨NN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- Lotka￨U￨NNP￨LOCATION￨- –￨L￨:￨O￨- Volterra￨U￨NNP￨CITY￨- competition￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- islands￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- Lotka￨U￨NNP￨LOCATION￨- –￨L￨:￨O￨- Volterra￨U￨NNP￨CITY￨- competition￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Hardy￨U￨NNP￨O￨- –￨L￨:￨O￨- Weinberg￨U￨NNP￨PERSON￨- approximation￨L￨NN￨O￨- from￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- principles￨L￨NNS￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- best￨L￨JJS￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- treatment￨L￨NN￨O￨- immediately￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- to￨L￨TO￨O￨- wait￨L￨VB￨O￨- and￨L￨CC￨O￨- see￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progresses￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- partly￨L￨RB￨O￨- because￨L￨IN￨O￨- learning￨L￨NN￨O￨- may￨L￨MD￨O￨- occur￨L￨VB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies.The￨L￨NNP￨O￨- real￨L￨JJ￨O￨- options￨L￨NNS￨O￨A approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- actions￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- convenient￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- couple￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨- with￨L￨IN￨O￨- economic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- presented￨L￨VBN￨O￨- here￨L￨RB￨O￨- have￨L￨VBP￨O￨- important￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- options￨L￨NNS￨O￨A approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- given￨L￨VBN￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression.KeywordsReal￨L￨NN￨O￨- options￨L￨NNS￨O￨- Logistic￨U￨NNP￨O￨- SDE￨U￨NNP￨O￨- Disease￨U￨NNP￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- Stochastic￨U￨NNP￨O￨- epidemics￨L￨NNS￨O￨- Optimal￨U￨JJ￨O￨- timing￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionInvasive￨U￨NNP￨O￨- pests￨L￨NNS￨O￨- and￨L￨CC￨O￨- pathogens￨L￨NNS￨O￨- are￨L￨VBP￨O￨- increasing￨L￨VBG￨O￨- worldwide￨L￨RB￨O￨- ,￨L￨,￨O￨- posing￨L￨VBG￨O￨- a￨L￨DT￨O￨- threat￨L￨NN￨O￨- to￨L￨TO￨O￨- agriculture￨L￨NN￨O￨- and￨L￨CC￨O￨- forestry￨L￨NN￨O￨- production￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A.￨U￨NN￨O￨- GilliganOpen￨U￨NNP￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1k￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨MISC￨- AbstractThe￨U￨NNP￨MISC￨- real￨L￨JJ￨O￨- options￨L￨NNS￨O￨A approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- within￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- economics￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- to￨L￨TO￨O￨- minimise￨L￨VB￨O￨- the￨L￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- invasive￨L￨JJ￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- pests￨L￨NNS￨O￨- and￨L￨CC￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- used￨L￨VBN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- appropriately￨L￨RB￨O￨- capture￨L￨VB￨O￨- uncertainty￨L￨NN￨O￨A in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- excessive￨L￨JJ￨O￨- delay￨L￨NN￨O￨- before￨L￨IN￨O￨- treatment￨L￨NN￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- option￨L￨NN￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- realised￨L￨VBN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- error￨L￨NN￨O￨- analysis￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- residuals￨L￨NNS￨O￨- witnesses￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- convergence￨L￨NN￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- EPA￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- globally￨L￨RB￨O￨- convergent￨L￨JJ￨O￨- non-standard￨L￨JJ￨O￨- finite￨L￨JJ￨O￨- difference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NSFD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- larger￨L￨JJR￨O￨- time￨L￨NN￨O￨- steps.KeywordsNonlinear￨L￨JJ￨O￨- modelEvolutionary￨L￨JJ￨O￨- computingPadé￨L￨NN￨O￨- approximationOptimization￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionA￨U￨NN￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- malicious￨L￨JJ￨O￨- code￨L￨NN￨O￨- which￨L￨WDT￨O￨- executes￨L￨VBZ￨O￨- harmful￨L￨JJ￨O￨- and￨L￨CC￨O￨- unauthorized￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- like￨L￨IN￨O￨- erasing￨L￨VBG￨O￨- necessary￨L￨JJ￨O￨- files￨L￨NNS￨O￨- ,￨L￨,￨O￨- accessing￨L￨VBG￨O￨- confidential￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- personal￨L￨JJ￨O￨- information￨L￨NN￨O￨- like￨L￨IN￨O￨- passwords￨L￨NNS￨O￨- ,￨L￨,￨O￨- account￨L￨VBP￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- lists￨L￨NNS￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- involve￨L￨VBP￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- susceptible-infected-recovered-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- susceptible-exposed-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- SEIQS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- quarantined￨L￨VBN￨O￨- class￨L￨NN￨O￨- included￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- SEIRS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- SEIQRS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- SEIRS-V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- vaccinated￨L￨VBN￨O￨- subpopulation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on.Mathematical￨L￨JJ￨O￨- tool-based￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨A analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- essential￨L￨JJ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- investigations￨L￨NNS￨O￨- for￨L￨IN￨O￨- acquiring￨L￨VBG￨O￨- better￨L￨JJR￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- impact￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- deriving￨L￨VBG￨O￨- mechanisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Numerical￨U￨JJ￨MISC￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A in￨L￨IN￨O￨- computer￨L￨NN￨O￨- networks￨L￨NNS￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- innovative￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- Padé￨U￨NN￨O￨- approximation￨L￨NN￨O￨- schemeJavaid￨L￨NN￨O￨- Ali1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Muhammad￨U￨NNP￨PERSON￨- Saeed1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Muhammad￨U￨NNP￨PERSON￨- Rafiq2￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Shaukat￨U￨NNP￨O￨- Iqbal3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:214￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- work￨L￨NN￨O￨- proposes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- mesh￨L￨NN￨O￨- free￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- Padé￨U￨NN￨O￨- approximation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EPA￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨- closed￨L￨JJ￨O￨- form￨L￨NN￨O￨- numerical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- computer￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- computational￨L￨JJ￨O￨- architecture￨L￨NN￨O￨- of￨L￨IN￨O￨- EPA￨U￨NNP￨ORGANIZATION￨- scheme￨L￨NN￨O￨- assimilates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Padé￨U￨NN￨O￨- approximation￨L￨NN￨O￨A to￨L￨TO￨O￨- transform￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- nonlinear￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- equivalent￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +Differential￨U￨JJ￨O￨- evolution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- closed￨L￨JJ￨O￨A form￨L￨NN￨O￨A numerical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- developed￨L￨VBN￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- CDRs-based￨U￨JJ￨MISC￨- indicators￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- spatial￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- and￨L￨CC￨O￨- interactions￨L￨NNS￨O￨- hold￨L￨VBP￨O￨- promise￨L￨NN￨O￨- for￨L￨IN￨O￨- gaining￨L￨VBG￨O￨- insight￨L￨NN￨O￨- of￨L￨IN￨O￨- contagion￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- for￨L￨IN￨O￨- developing￨L￨VBG￨O￨- mitigation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- decision-making￨L￨JJ￨O￨- during￨L￨IN￨O￨- country-level￨L￨JJ￨O￨- epidemics.KeywordsSpatial￨L￨JJ￨O￨- networksMobile￨L￨NN￨O￨- phone￨L￨NN￨O￨A dataHuman￨L￨NNP￨O￨- mobilityEpidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionEpidemic￨U￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- healthcare￨L￨NN￨O￨- challenge￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- represent￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- suffering￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- A￨U￨DT￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial-based￨L￨JJ￨O￨- targeted￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- mitigation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- using￨L￨VBG￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨A dataStefania￨L￨NNP￨O￨- Rubrichi1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Zbigniew￨U￨NNP￨PERSON￨- Smoreda1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Mirco￨U￨NNP￨PERSON￨- Musolesi2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:17￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractEpidemic￨U￨NNP￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- healthcare￨L￨NN￨O￨- challenge￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- represent￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- of￨L￨IN￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- employing￨L￨VBG￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- meta-population￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨A Call￨U￨VB￨O￨- Detail￨U￨NNP￨O￨- Records￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- CDRs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- mobility￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- may￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approaches￨L￨NNS￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- provide￨L￨VB￨O￨- further￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨A data￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- effectively￨L￨RB￨O￨- exploited￨L￨VBN￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- spatial￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- relationship￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ’￨L￨POS￨O￨- contagion￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- different￨L￨JJ￨O￨- existing￨L￨VBG￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨A dimension￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- and￨L￨CC￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- relevance￨L￨NN￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- risk￨L￨NN￨O￨- sub-population￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- candidates￨L￨NNS￨O￨- for￨L￨IN￨O￨- isolation￨L￨NN￨O￨- countermeasures￨L￨NNS￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- PreliminariesTo￨U￨NN￨O￨- make￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- be￨L￨VB￨O￨- biologically￨L￨RB￨O￨- significant￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- list￨L￨VBP￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Assumption￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- theta￨L￨IN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- theta￨L￨IN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- xi￨L￨VB￨O￨A a￨L￨DT￨O￨- are￨L￨VBP￨O￨- non-negative￨L￨JJ￨O￨- and￨L￨CC￨O￨- belong￨L￨VBP￨O￨- to￨L￨TO￨O￨- with￨L￨IN￨O￨- respective￨L￨JJ￨O￨- essential￨L￨JJ￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- beta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- beta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- beta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- beta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- theta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- theta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨ORGANIZATION￨- bar￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- xi￨L￨NN￨O￨- in￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- xi￨L￨VB￨O￨- a￨L￨DT￨O￨- are￨L￨VBP￨O￨- Lipschitz￨U￨NNP￨PERSON￨- continuous￨L￨JJ￨O￨- on￨L￨IN￨O￨- R￨U￨NN￨O￨- with￨L￨IN￨O￨- coefficients￨L￨NNS￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- xi￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- GreaterThan￨U￨NNP￨O￨- Abs￨U￨NNS￨O￨- Add￨U￨VBP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- theta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨MISC￨- Abs￨U￨NNS￨MISC￨- Add￨U￨VBP￨MISC￨- theta￨L￨IN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- xi￨L￨NN￨O￨- a￨L￨DT￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨O￨- theta￨L￨IN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- StrictGreaterThan￨U￨NNP￨O￨- a￨L￨DT￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- Lyapunov￨U￨NNP￨O￨- functionals￨L￨NNS￨O￨- and￨L￨CC￨O￨- LaSalle￨U￨NNP￨O￨- ’s￨L￨POS￨O￨- invariance￨L￨NN￨O￨- principle￨L￨NN￨O￨- and￨L￨CC￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable.KeywordsAge-structured￨L￨JJ￨O￨- modelSaturating￨L￨NN￨O￨- incidenceAsymptotic￨L￨JJ￨O￨- smoothnessLyapunov￨L￨NN￨O￨- functionalGlobal￨L￨NN￨O￨- stability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionHepatitis￨U￨NN￨O￨- B￨U￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- contagious￨L￨JJ￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- hard￨L￨JJ￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- its￨L￨PRP$￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +□￨L￨SYM￨O￨- Proposition￨U￨NN￨O￨- 2.2￨L￨CD￨NUMBER￨- If￨U￨IN￨O￨- Mul￨U￨NN￨O￨- X￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- X￨U￨NN￨O￨- mathcal￨L￨JJ￨O￨A and￨L￨CC￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- constant￨L￨JJ￨O￨- GreaterThan￨U￨NNP￨O￨- M￨U￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Lambda￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- statements￨L￨NNS￨O￨- hold￨L￨VBP￨O￨- for￨L￨IN￨O￨- GreaterThan￨U￨NNP￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- LessThan￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- LessThan￨U￨NNP￨PERSON￨- i￨L￨FW￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- gamma￨L￨NN￨O￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- both￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- follow￨L￨VBP￨O￨- the￨L￨DT￨O￨- Susceptible-Infective-Recovered￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- survive￨L￨VB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- evolve￨L￨VB￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- timescale￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- closely￨L￨RB￨O￨- matched￨L￨VBN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A on￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- depends.KeywordsSIR￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- Epidemics￨U￨NNS￨O￨- Superinfection￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- Branching￨U￨VBG￨O￨- processes￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSuperinfections￨U￨NNS￨ORGANIZATION￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- global￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- morbidity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- epidemiological￨L￨JJ￨O￨- language￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- coupled￨L￨VBN￨O￨- Susceptible-Infective-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- ;￨L￨:￨O￨- empty￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- sites￨L￨NNS￨O￨- are￨L￨VBP￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- host￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- secondary￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- parasite￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 171￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 1122￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1135￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asA￨L￨NN￨O￨- Re-entrant￨U￨JJ￨O￨- Phase￨U￨NN￨O￨- Transition￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Survival￨U￨NN￨O￨- of￨L￨IN￨O￨- Secondary￨U￨JJ￨O￨- Infections￨U￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- NetworksAuthorsAuthors￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- affiliationsSam￨L￨NNP￨MISC￨- MoorePeter￨U￨NNP￨MISC￨- MörtersTim￨U￨NNP￨MISC￨- RogersOpen￨U￨NNP￨MISC￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 275￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨O￨- AbstractWe￨U￨NNP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- currently￨L￨RB￨DATE￨- carrying￨L￨VBG￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- primary￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- sparse￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- mapped￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- time-sensitive￨L￨JJ￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- primary￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Multiscale￨U￨NNP￨O￨- unfolding￨L￨VBG￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- geometric￨L￨JJ￨O￨A renormalization￨L￨NN￨O￨- Guillermo￨U￨NNP￨PERSON￨- García-Pérez1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Marián￨U￨NNP￨PERSON￨- Boguñá￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- &￨L￨CC￨O￨- M.￨U￨NNP￨O￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- small-world￨L￨JJ￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- complicates￨L￨VBZ￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- renormalization￨L￨NN￨O￨- group￨L￨NN￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- coexisting￨L￨VBG￨O￨- scales￨L￨NNS￨O￨- .￨L￨.￨O￨- +ADSArticle￨U￨NN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Scholar4.Song￨U￨NNP￨O￨- ,￨L￨,￨O￨- C.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Havlin￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- S.￨U￨NNP￨O￨- Nature￨U￨NNP￨O￨- 433￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 392￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 395￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2005￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +99￨L￨CD￨NUMBER￨A ,￨L￨,￨O￨- 038701￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- this￨L￨DT￨O￨- in￨L￨IN￨O￨- no￨L￨DT￨O￨- way￨L￨NN￨O￨- excludes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- prospect￨L￨NN￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- MSMs￨U￨NNS￨MISC￨- provide￨L￨VBP￨O￨- good￨L￨JJ￨O￨- justifications￨L￨NNS￨O￨- for￨L￨IN￨O￨- policy￨L￨NN￨O￨A decisions￨L￨NNS￨O￨- ,￨L￨,￨O￨- my￨L￨PRP$￨O￨- arguments￨L￨NNS￨O￨- caution￨L￨VBP￨O￨- against￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- preference￨L￨NN￨O￨- for￨L￨IN￨O￨- MSMs￨U￨NNS￨O￨- over￨L￨IN￨O￨- ASMs￨U￨NNS￨O￨- for￨L￨IN￨O￨- policy￨L￨NN￨O￨- decision￨L￨NN￨O￨- purposes￨L￨NNS￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- problems￨L￨NNS￨O￨- in￨L￨IN￨O￨- particular.KeywordsEvidence-based￨L￨JJ￨O￨- policy￨L￨NN￨O￨- Epidemiology￨U￨NNP￨O￨- Modeling￨U￨NNP￨O￨- Macro￨U￨NNP￨O￨- versus￨L￨CC￨O￨- micro￨L￨JJ￨O￨- Microsimulations￨U￨NNPS￨MISC￨- Agent-based￨U￨JJ￨MISC￨- modeling￨L￨NN￨O￨- Robustness￨U￨NNP￨O￨- Isolation￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionEpidemic￨U￨JJ￨O￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Synthese￨U￨JJ￨O￨- pp￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asChoosing￨L￨VBG￨O￨- the￨L￨DT￨O￨- right￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- policy￨L￨NN￨O￨- decision-making￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A epidemiologyAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsTill￨L￨NN￨O￨- Grüne-YanoffOpen￨U￨NN￨O￨- AccessS.I.￨U￨NNP￨O￨- :￨L￨:￨O￨- Philosophy￨U￨NN￨O￨- of￨L￨IN￨O￨- EpidemiologyFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 204￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨O￨- AbstractPolicymakers￨U￨NNPS￨O￨- increasingly￨L￨RB￨O￨- draw￨L￨VB￨O￨- on￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- simulation￨L￨NN￨O￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- justify￨L￨VB￨O￨- their￨L￨PRP$￨O￨- decisions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- dimensions￨L￨NNS￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨A target￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- accurate￨L￨JJ￨O￨- measurement￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- included￨L￨VBD￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mechanisms￨L￨NNS￨O￨- modeled￨L￨VBD￨O￨- simultaneously￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ways￨L￨NNS￨O￨- of￨L￨IN￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- structural￨L￨JJ￨O￨- uncertainty￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- analyzing￨L￨VBG￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DATE￨- 20￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- discusses￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- justify￨L￨VB￨O￨- strategy￨L￨NN￨O￨- choice￨L￨NN￨O￨- with￨L￨IN￨O￨- reference￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- respective￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Discussing￨U￨VBG￨O￨- the￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- distinguishes￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- :￨L￨:￨O￨- Massive￨U￨JJ￨O￨- Simulation￨U￨NN￨O￨- Models￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- MSMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Abstract￨U￨NNP￨O￨- Simulation￨U￨NNP￨O￨- Models￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- ASMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Macro￨U￨NNP￨MISC￨- Equation￨U￨NNP￨MISC￨- Models￨U￨NNS￨MISC￨- (￨L￨-LRB-￨O￨- MEMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- perform￨L￨VBP￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- messages￨L￨NNS￨O￨- originating￨L￨VBG￨O￨- from￨L￨IN￨O￨- different￨L￨JJ￨O￨- organizations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨- aid￨L￨NN￨O￨A community￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- reach.KeywordsWeb￨L￨NN￨O￨- crawlingGlobal￨L￨NN￨O￨- health￨L￨NN￨O￨- architectureComplex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionInternational￨U￨JJ￨O￨- aid￨L￨NN￨O￨- —￨L￨:￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- Global￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- Architecture￨U￨NNP￨O￨- ”￨L￨''￨O￨- NumericCitation￨U￨NNP￨O￨- when￨L￨WRB￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- health￨L￨NN￨O￨- topics￨L￨NNS￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- —￨L￨:￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- system￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- web￨L￨NN￨O￨- crawling￨L￨VBG￨O￨- to￨L￨TO￨O￨- collect￨L￨VB￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- activities￨L￨NNS￨O￨- of￨L￨IN￨O￨- international￨L￨JJ￨O￨- aid￨L￨NN￨O￨A organizations￨L￨NNS￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- health-related￨L￨JJ￨O￨- topics￨L￨NNS￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- depict￨L￨VB￨O￨- this￨L￨DT￨O￨- complex￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- relationships￨L￨NNS￨O￨- among￨L￨IN￨O￨- organizations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Mapping￨U￨NN￨MISC￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨- health￨L￨NN￨O￨- aid￨L￨NN￨O￨A community￨L￨NN￨O￨- using￨L￨VBG￨O￨- web￨L￨NN￨O￨- dataMichele￨L￨NN￨O￨- Coscia1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Katsumasa￨U￨NNP￨O￨- Hamaguchi3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Maria￨U￨NNP￨PERSON￨- Elena￨U￨NNP￨PERSON￨- Pinglo3￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Antonio￨U￨NNP￨O￨- Giuffrida3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:12￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractInternational￨U￨NNP￨O￨- aid￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- it￨L￨PRP￨O￨- involves￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- issues￨L￨NNS￨O￨- ,￨L￨,￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- donors￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- systematically￨L￨RB￨O￨- collecting￨L￨VBG￨O￨- co-occurrences￨L￨NNS￨O￨- of￨L￨IN￨O￨- issues￨L￨NNS￨O￨- ,￨L￨,￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- organization￨L￨NN￨O￨- names￨L￨NNS￨O￨- from￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- hundred￨L￨CD￨NUMBER￨- websites￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- multilayer￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- issues￨L￨NNS￨O￨- are￨L￨VBP￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- organizations￨L￨NNS￨O￨A .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- decide￨L￨VBP￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- speech￨L￨NN￨O￨- each￨L￨DT￨O￨- aid￨L￨NN￨O￨A organization￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- public￨L￨JJ￨O￨- communications￨L￨NNS￨O￨- ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- their￨L￨PRP$￨O￨- websites￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- further￨L￨RB￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- fractional￨L￨JJ￨O￨- order￨L￨NN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- D￨U￨NN￨O￨- alpha￨L￨NN￨O￨A S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Lambda￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- Equality￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- D￨U￨NN￨O￨- alpha￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- r￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- D￨U￨NN￨O￨- alpha￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- r￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- mu￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Pow￨U￨NN￨O￨- D￨U￨NN￨O￨- alpha￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Caputo￨U￨NNP￨PERSON￨- fractional￨L￨JJ￨O￨- derivative￨L￨NN￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- LessThan￨U￨NN￨O￨- StrictLessThan￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- function￨L￨NN￨O￨- f￨L￨FW￨O￨- t￨L￨NN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- first￨L￨JJ￨ORDINAL￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equivalent￨L￨JJ￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- D￨U￨NN￨O￨- alpha￨L￨NN￨O￨A S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Lambda￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Also￨U￨RB￨O￨- ,￨L￨,￨O￨- another￨L￨DT￨O￨- advantage￨L￨NN￨O￨- for￨L￨IN￨O￨- using￨L￨VBG￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- derivative￨L￨NN￨O￨- is￨L￨VBZ￨O￨- enlarging￨L￨VBG￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- systems.In￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- works￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- fractional￨L￨JJ￨O￨- order￨L￨NN￨O￨- derivative￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- are￨L￨VBP￨O￨- mainly￨L￨RB￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- SIR-type￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- linear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨NN￨O￨A and￨L￨CC￨O￨- c￨L￨NN￨O￨- satisfy￨L￨VBP￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- xi￨L￨NN￨O￨- F￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- prime￨L￨JJ￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- textstyle￨L￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- xi￨L￨NNP￨O￨- Mul￨U￨NNP￨O￨- J￨U￨NNP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- ast￨L￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- xi￨L￨NN￨O￨- F￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- prime￨L￨JJ￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨NN￨O￨- Mul￨U￨NN￨O￨- J￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- ast￨L￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- Similar￨U￨JJ￨O￨- to￨L￨TO￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- shall￨L￨MD￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- phi￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- satisfying￨L￨VBG￨O￨- Equality￨U￨NNP￨O￨- Limit￨U￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- xi￨L￨NN￨O￨- xi￨L￨NN￨O￨- Mul￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- k￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- homogeneous￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Equality￨U￨NN￨O￨- k￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- -1￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- c￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- provided￨L￨VBN￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- When￨U￨WRB￨O￨- the￨L￨DT￨O￨- scalar￨L￨JJ￨O￨- equation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- concerned￨L￨VBN￨O￨- ,￨L￨,￨O￨- Jin￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Zhao￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- with￨L￨IN￨O￨- dispersal￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Dunbar￨U￨NNP￨PERSON￨- [￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- much￨L￨JJ￨O￨- attention￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨- to￨L￨TO￨O￨- traveling￨L￨VBG￨O￨- wave￨L￨NN￨O￨A solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- reaction￨L￨NN￨O￨- –￨L￨:￨O￨- diffusion￨L￨NN￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- predator￨L￨NN￨O￨- –￨L￨:￨O￨- prey￨L￨NN￨O￨- nonlinearities￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- energy￨L￨NN￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- Equality￨U￨NNP￨O￨- bigl￨L￨NN￨O￨- u￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- u￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- bigl￨L￨NN￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨NN￨O￨A Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨RB￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- traveling￨L￨VBG￨O￨- wave￨L￨NN￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- functions￨L￨NNS￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- represent￨L￨VBP￨O￨- saturated￨L￨JJ￨O￨A growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- microorganism￨L￨NN￨O￨- population￨L￨NN￨O￨- under￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- nutrients.It￨L￨NN￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- reality￨L￨NN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- inevitably￨L￨RB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- random￨L￨JJ￨O￨- disturbances￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 48￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 54￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨A stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- try￨L￨VB￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- criteria￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- mean￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- microorganism￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- memristive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- recast￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- tractable￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- defining￨L￨VBG￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- state-dependent￨L￨JJ￨O￨- switched￨L￨VBN￨O￨- signals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- calculation￨L￨NN￨O￨- cost￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- effectively￨L￨RB￨O￨- when￨L￨WRB￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- weights￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- robust￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- method.On￨L￨NN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complex-valued￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- undergone￨L￨VBN￨O￨- a￨L￨DT￨O￨- research￨L￨NN￨O￨- upsurge￨L￨NN￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- extensive￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- radar￨L￨NN￨O￨- imaging￨L￨NN￨O￨- ,￨L￨,￨O￨- electromagnetic￨L￨JJ￨O￨- waves￨L￨NNS￨O￨- ,￨L￨,￨O￨- remote￨L￨JJ￨O￨- sensing￨L￨VBG￨O￨- ,￨L￨,￨O￨- quantum￨L￨NN￨O￨- devices￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- situation￨L￨NN￨O￨- prompts￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- current￨L￨JJ￨DATE￨- research.Considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- inevitability￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- practical￨L￨JJ￨O￨- projects￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 50￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 57￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- discussions￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- estimation￨L￨NN￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- complex-valued￨L￨JJ￨O￨- memristive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- delays￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- State￨U￨NN￨O￨- estimation￨L￨NN￨O￨- for￨L￨IN￨O￨- complex-valued￨L￨JJ￨O￨- memristive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- delaysRunan￨L￨NN￨O￨- Guo1￨U￨NN￨O￨- ,￨L￨,￨O￨- Ziye￨U￨NN￨O￨- Zhang1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Ming￨U￨VBG￨O￨- Gao2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:118￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- estimation￨L￨NN￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- complex-valued￨L￨JJ￨O￨- memristive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- delays￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- embodied￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- respects￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- state￨L￨NN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- complex-valued￨L￨JJ￨O￨- memristive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- delays￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- no￨L￨DT￨O￨- information￨L￨NN￨O￨- published￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- estimation￨L￨NN￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- memristor-based￨L￨JJ￨O￨- complex-valued￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- logistic￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- y￨L￨NNP￨O￨- Tuple￨U￨NNP￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- y￨L￨RB￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- C￨U￨NN￨O￨- is￨L￨VBZ￨O￨- environment￨L￨NN￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨A abundance￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NN￨O￨- C￨U￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NN￨O￨- alpha￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- conversion￨L￨NN￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- prey￨L￨NN￨O￨- into￨L￨IN￨O￨- predator￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- situation￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- taken￨L￨VBN￨O￨- over￨L￨RP￨O￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- denominator￨L￨NN￨O￨- ;￨L￨:￨O￨- this￨L￨DT￨O￨- modification￨L￨NN￨O￨- prevents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- predator￨L￨NN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- prey￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- equation￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- y￨L￨NNP￨O￨- Tuple￨U￨NNP￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- y￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨NNP￨ORGANIZATION￨- y￨L￨NNP￨ORGANIZATION￨- Tuple￨U￨NNP￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +All￨U￨PDT￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- A￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- half￨L￨NN￨O￨- saturation￨L￨NN￨O￨A constant￨L￨JJ￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- transfer￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- is￨L￨VBZ￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- lose￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- join￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- crashing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- all￨L￨DT￨O￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- half￨L￨NN￨O￨- saturation￨L￨NN￨O￨- constant￨L￨JJ￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- I￨U￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- rate￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- induced￨L￨VBD￨O￨- crashing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- Dénes￨U￨NNPS￨PERSON￨- and￨L￨CC￨O￨- Röst￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- Tuple￨U￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- f￨L￨LS￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- f￨L￨LS￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- -1￨L￨CD￨NUMBER￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- Equality￨U￨VBP￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- constant￨L￨JJ￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- compartments￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- denoted￨L￨VBN￨O￨A by￨L￨IN￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- e-epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- Tuple￨U￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- V￨U￨NN￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- alpha￨L￨NN￨O￨A Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- E￨U￨NN￨ORGANIZATION￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- a￨L￨DT￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- :￨L￨:￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- E￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- I￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- GreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- V￨U￨NNP￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- V￨U￨NNP￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- Lyapunov￨U￨NN￨PERSON￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨JJ￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- treatment￨L￨NN￨O￨A functions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- several￨L￨JJ￨O￨- authors￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- some￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 27￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 31￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 35￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 38￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- incidences￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- particles￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- forms￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- f￨L￨FW￨O￨- V￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- f￨L￨FW￨O￨- and￨L￨CC￨O￨- g￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- forces￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- virus￨L￨NN￨O￨- particles￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- and￨L￨CC￨O￨- satisfy￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- properties￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- false￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- It￨U￨PRP￨O￨- then￨L￨RB￨O￨- follows￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- value￨L￨NN￨O￨- theorem￨L￨NN￨O￨- that￨L￨WDT￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Epidemiologically￨U￨RB￨O￨- ,￨L￨,￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- spread￨L￨VB￨O￨- if￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- incidences￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- f￨L￨FW￨O￨- V￨U￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- become￨L￨VBP￨O￨- faster￨L￨RBR￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- particles￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- increase￨L￨VBP￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- per￨L￨FW￨O￨- capita￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- by￨L￨IN￨O￨- virus￨L￨NN￨O￨- particles￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- will￨L￨MD￨O￨- slow￨L￨VB￨O￨- down￨L￨RP￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- certain￨L￨JJ￨O￨- inhibition￨L￨NN￨O￨- effect￨L￨NN￨O￨- since￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- V￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- f￨L￨LS￨O￨- V￨U￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- T￨U￨NN￨O￨- partial￨L￨JJ￨O￨A Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dT￨L￨NNP￨O￨- lambda￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- I￨U￨PRP￨O￨- partial￨L￨JJ￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- V￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- V￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- V￨U￨NN￨O￨- x￨L￨CC￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- D￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Delta￨U￨NN￨O￨- V￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- uninfected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- free￨L￨JJ￨O￨- virus￨L￨NN￨O￨- at￨L￨IN￨O￨- position￨L￨NN￨O￨- x￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- D￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Δ￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Laplacian￨U￨JJ￨MISC￨- operator.Notice￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- studies￨L￨NNS￨O￨- mentioned￨L￨VBD￨O￨- only￨L￨RB￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- virus-to-cell￨L￨JJ￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- bloodstream￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- cells￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- state￨L￨NN￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- cells￨L￨NNS￨O￨- W￨U￨NNP￨O￨- t￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- reads￨L￨VBZ￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- T￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- W￨U￨NNP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- uninfected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- productively￨L￨RB￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- free￨L￨JJ￨O￨- virus￨L￨NN￨O￨- particles￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- uninfected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- virus-to-cell￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- inspired￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- aforementioned￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- T￨U￨NN￨O￨- partial￨L￨JJ￨O￨A Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dT￨L￨NNP￨O￨- lambda￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- W￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- gamma￨L￨NN￨O￨- W￨U￨NN￨O￨- x￨L￨CC￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- f￨L￨FW￨O￨- V￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- I￨U￨PRP￨O￨- partial￨L￨JJ￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- W￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- I￨U￨PRP￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- cell-to-cell￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- means￨L￨NNS￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- problem￨L￨NN￨O￨A of￨L￨IN￨O￨- ISFC￨U￨NN￨O￨- is￨L￨VBZ￨O￨- transformed￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- unspecified￨L￨JJ￨O￨- time￨L￨NN￨O￨- with￨L￨IN￨O￨- inequality￨L￨NN￨O￨- constraints￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- constraint￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- arrival￨L￨NN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Problem￨U￨NNP￨O￨- statement￨L￨NN￨O￨- and￨L￨CC￨O￨- translationConsider￨L￨NN￨O￨- the￨L￨DT￨O￨- ISFC￨U￨NN￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨PERSON￨- t￨L￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathbb￨L￨NN￨O￨A ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- hat￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- boldsymbol￨L￨NN￨O￨- y￨L￨NN￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨PERSON￨- boldsymbol￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- f￨L￨FW￨ORGANIZATION￨- Mul￨U￨FW￨ORGANIZATION￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- vectors.Denote￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- satisfying￨L￨VBG￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- Mul￨U￨NN￨O￨- hat￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bigl￨L￨NN￨O￨- Mul￨U￨NN￨O￨- boldsymbol￨L￨NN￨O￨- y￨L￨NN￨O￨- For￨U￨IN￨O￨- convenience￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- abbreviated￨L￨JJ￨O￨- to￨L￨TO￨O￨- Mul￨U￨NN￨O￨- hat￨L￨NN￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- boldsymbol￨L￨NN￨O￨- y￨L￨NN￨O￨- or￨L￨CC￨O￨- Mul￨U￨NN￨O￨- hat￨L￨NN￨O￨- Mul￨U￨NN￨O￨- boldsymbol￨L￨NN￨O￨- y￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- problem￨L￨NN￨O￨A of￨L￨IN￨O￨- state￨L￨NN￨O￨- impulse￨L￨NN￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- transformed￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- unspecified￨L￨JJ￨O￨- time￨L￨NN￨O￨- with￨L￨IN￨O￨- inequality￨L￨NN￨O￨- constraint￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- constraint￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- arrival￨L￨NN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- much￨L￨JJ￨O￨- literature￨L￨NN￨O￨- considered￨L￨VBN￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- regime￨L￨NN￨O￨- switching￨L￨NN￨O￨A ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- System￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- false￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- by￨L￨IN￨O￨- Liu￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- author￨L￨NN￨TITLE￨- ignored￨L￨VBD￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- degenerate￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- matrix￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- ensure￨L￨VB￨O￨- uniform￨L￨JJ￨O￨- ellipticity.Throughout￨L￨NN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- or￨L￨CC￨O￨- matrix￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- to￨L￨TO￨O￨- denote￨L￨VB￨O￨- its￨L￨PRP$￨O￨- transpose￨L￨NN￨O￨- ;￨L￨:￨O￨- set￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- vector￨L￨NN￨O￨- ;￨L￨:￨O￨- set￨L￨VBN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨JJ￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- linear￨L￨JJ￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Remark￨U￨NN￨O￨- 1.1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Lemma￨U￨NN￨PERSON￨- 2.1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Incorporating￨U￨VBG￨O￨- color￨L￨NN￨O￨- noise￨L￨NN￨O￨A into￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- get￨L￨VBP￨O￨- a￨L￨DT￨O￨- regime-switching￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Lambda￨U￨NNP￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- mu￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- varepsilon￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- gamma￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- alpha￨L￨NN￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- sigma￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constants.In￨L￨NN￨O￨- the￨L￨DT￨O￨- earlier￨L￨JJR￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- regime￨L￨NN￨O￨- switching￨L￨NN￨O￨- was￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- population￨L￨NN￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- color￨L￨NN￨O￨- noise￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- author￨L￨NN￨TITLE￨- considered￨L￨VBN￨O￨- deterministic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Markovian￨U￨JJ￨O￨- switching￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- Pow￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- s￨L￨VBZ￨O￨- mathcal￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- becomes￨L￨VBZ￨O￨- extinct￨L￨JJ￨O￨- exponentially￨L￨RB￨O￨- ;￨L￨:￨O￨- whereas￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- s￨L￨VBZ￨O￨- mathcal￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- beta￨L￨NN￨O￨- i￨L￨FW￨O￨- alpha￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- can￨L￨MD￨O￨- converge￨L￨VB￨O￨- in￨L￨IN￨O￨- Pow￨U￨NNP￨O￨- L￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- invariant￨L￨JJ￨O￨- density.KeywordsStationary￨L￨JJ￨O￨- distributionMarkov￨L￨NN￨O￨- semigroupsAsymptotic￨L￨JJ￨O￨- stabilityMSC47D0760J6060H1092D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionInfectious￨U￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- noise￨L￨NN￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- typical￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- long-time￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- can￨L￨MD￨O￨- converge￨L￨VB￨O￨- in￨L￨IN￨O￨- Pow￨U￨NNP￨O￨- L￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- invariant￨L￨JJ￨O￨- density.In￨L￨NN￨O￨- reality￨L￨NN￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- for￨L￨IN￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨A there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- another￨L￨DT￨O￨- important￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- noise￨L￨NN￨O￨- :￨L￨:￨O￨- color￨L￨NN￨O￨- noise￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- switch￨L￨VB￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- environmental￨L￨JJ￨O￨- regime￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- stationary￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- r￨L￨NN￨O￨- t￨L￨NN￨O￨- which￨L￨WDT￨O￨- satisfies￨L￨VBZ￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- Gamma￨U￨NNP￨ORGANIZATION￨- pi￨L￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- Sum￨U￨NNP￨O￨- pi￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- Tuple￨U￨NNP￨ORGANIZATION￨- i￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- pi￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- forall￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- mathbb￨L￨NN￨O￨A .￨L￨.￨O￨- +RIPK3-deficient￨U￨JJ￨O￨- mice￨L￨NNS￨O￨A have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- protected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- direct￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- necroptosis￨L￨NN￨O￨- in￨L￨FW￨O￨- vivo￨L￨FW￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- limited￨L￨VBN￨O￨- .￨L￨.￨O￨- +Green4￨U￨NN￨O￨- ,￨L￨,￨O￨- Christian￨U￨NNP￨RELIGION￨- Hugo1￨U￨NNP￨O￨- &￨L￨CC￨O￨- Andreas￨U￨NNP￨PERSON￨- Linkermann￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- Cell￨U￨NN￨O￨- Death￨U￨NNP￨O￨- &￨L￨CC￨O￨- Diseasevolume￨U￨NNP￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 359￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- A￨U￨DT￨O￨- Correction￨U￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨A was￨L￨VBD￨O￨- published￨L￨VBN￨O￨- on￨L￨IN￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- This￨U￨DT￨O￨- article￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- updated￨L￨VBN￨O￨- AbstractReceptor-interacting￨U￨JJ￨O￨- protein￨L￨NN￨O￨- kinases￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 3￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- RIPK1/3￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- best￨L￨RB￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- mediating￨L￨VBG￨O￨- a￨L￨DT￨O￨- regulated￨L￨JJ￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- necrosis￨L￨NN￨O￨- ,￨L￨,￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- necroptosis￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- both￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- MLKL-ko￨U￨JJ￨O￨- mice￨L￨NNS￨O￨A were￨L￨VBD￨O￨- significantly￨L￨RB￨O￨- protected￨L￨VBN￨O￨- from￨L￨IN￨O￨- injury￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- that￨L￨WDT￨O￨- was￨L￨VBD￨O￨- slightly￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- statistically￨L￨RB￨O￨- significantly￨L￨RB￨O￨- exceeding￨L￨VBG￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- RIPK3-deficient￨U￨JJ￨O￨- mice￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- sought￨L￨VBD￨O￨- to￨L￨TO￨O￨- further￨L￨RB￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- activation￨L￨NN￨O￨A of￨L￨IN￨O￨- necroptosis￨L￨NN￨O￨- in￨L￨IN￨O￨- kidney￨L￨NN￨O￨- ischemia-reperfusion￨L￨NN￨O￨- injury￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IRI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- TNFα-induced￨U￨JJ￨MISC￨- severe￨L￨JJ￨O￨- inflammatory￨L￨JJ￨O￨- response￨L￨NN￨O￨- syndrome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- RIPK3-dependent￨U￨JJ￨O￨- injury￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- further￨L￨RBR￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- mode￨L￨NN￨O￨- of￨L￨IN￨O￨- regulation￨L￨NN￨O￨- of￨L￨IN￨O￨- cell￨L￨NN￨O￨A death￨L￨NN￨O￨- by￨L￨IN￨O￨- MLKL￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- screened￨L￨VBD￨O￨- a￨L￨DT￨O￨- panel￨L￨NN￨O￨- of￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- plasma￨L￨NN￨O￨- membrane￨L￨NN￨O￨- channel￨L￨NN￨O￨- blockers￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- phenytoin￨L￨NN￨O￨- to￨L￨TO￨O￨- inhibit￨L￨VB￨O￨- necroptosis￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- b￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨A Add￨U￨VB￨O￨- E￨U￨NN￨O￨- I￨U￨PRP￨O￨- h￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- without￨L￨IN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- population￨L￨NN￨O￨- becoming￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- again￨L￨RB￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- Qi￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Cui￨U￨NNP￨PERSON￨- established￨L￨VBD￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- SEIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- forming￨L￨VBG￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨A Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- h￨L￨NN￨O￨- S￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- also￨L￨RB￨O￨- satisfied￨L￨VBD￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- characteristics.In￨L￨NN￨O￨- real￨L￨JJ￨O￨- life￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- transmitted￨L￨VBN￨O￨- through￨L￨IN￨O￨- both￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- HBV￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stability￨U￨NN￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resistance￨L￨NN￨O￨- SEIRS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rateJianwen￨L￨NN￨O￨- Jia1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- and￨L￨CC￨O￨- Jing￨U￨NN￨O￨- Xiao1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2018:75￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- SEIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- general￨L￨JJ￨TITLE￨- form￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resistance￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Add￨U￨VB￨O￨- E￨U￨NN￨O￨- I￨U￨PRP￨O￨- h￨L￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- h￨L￨NN￨O￨- satisfies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- for￨L￨IN￨O￨- GreaterThan￨U￨NNP￨O￨- x￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨PERSON￨- h￨L￨NN￨O￨- x￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- equality￨L￨NN￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- Equality￨U￨NN￨O￨- x￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- ′￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- differentiation￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- Re￨U￨NNP￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Re￨U￨NNP￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- geometric￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- some￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- projective￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A of￨L￨IN￨O￨- fractional-order￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- was￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- investigated￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- Laplace￨U￨NNP￨CITY￨- transform￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- special￨L￨JJ￨O￨- Lyapunov￨U￨NNP￨PERSON￨- functions￨L￨NNS￨O￨- were￨L￨VBD￨O￨- derived￨L￨VBN￨O￨- for￨L￨IN￨O￨- synchronization￨L￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Projective￨U￨JJ￨MISC￨- synchronization￨L￨NN￨O￨A of￨L￨IN￨O￨- fractional-order￨L￨NN￨O￨- delayed￨L￨VBN￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- comparison￨L￨NN￨O￨- principleWeiwei￨L￨NN￨O￨- Zhang1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Jinde￨U￨NNP￨PERSON￨- Cao2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ranchao￨U￨NNP￨O￨- Wu4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Ahmed￨U￨NNP￨PERSON￨- Alsaedi5￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Fuad￨U￨NNP￨PERSON￨- E.￨U￨NNP￨O￨- Alsaadi6￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:73￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- considers￨L￨VBZ￨O￨- projective￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨- of￨L￨IN￨O￨- fractional-order￨L￨NN￨O￨- delayed￨L￨VBN￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- results￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- projective￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A of￨L￨IN￨O￨- fractional-order￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- were￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- [￨L￨-LRB-￨O￨- 30￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 32￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- LMI-based￨U￨JJ￨MISC￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- Mittag￨U￨NNP￨O￨- –￨L￨:￨O￨- Leffler￨U￨NNP￨PERSON￨- projective￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A for￨L￨IN￨O￨- fractional-order￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- was￨L￨VBD￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- unavoidable￨L￨JJ￨O￨- in￨L￨IN￨O￨- biological￨L￨JJ￨O￨- ,￨L￨,￨O￨- engineering￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- works￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- constructed￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- followed￨L￨VBD￨O￨- the￨L￨DT￨O￨- Logistic￨U￨JJ￨O￨- growth￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- γ￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- ε￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-induced￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- beta￨L￨NN￨O￨A I￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NN￨O￨- beta￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- textstyle￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Pow￨U￨NNP￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- All￨U￨PDT￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- nonnegative￨L￨JJ￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- The￨U￨DT￨MISC￨- persistence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Logistic￨U￨JJ￨O￨- growthJiamin￨L￨NN￨O￨- Liu1￨U￨NN￨O￨- ,￨L￨,￨O￨- Lijuan￨U￨NNP￨PERSON￨- Chen1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Fengying￨U￨NNP￨O￨- Wei1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:68￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Logistic￨U￨JJ￨O￨- growth￨L￨NN￨O￨A are￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- always￨L￨RB￨O￨- exists￨L￨VBZ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- LessThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- a￨L￨DT￨O￨- beta￨L￨NN￨O￨A Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- shall￨L￨MD￨O￨A consider￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- deterministic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- endemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NNP￨O￨- b￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- a￨L￨DT￨O￨- -1￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- N.Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- periodic￨L￨JJ￨O￨A coefficients￨L￨NNS￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- main￨L￨JJ￨O￨- concerns￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- are￨L￨VBP￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- What￨U￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- and￨L￨CC￨O￨- positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ?￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Random￨U￨NNP￨MISC￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- sizeDianli￨L￨NNS￨O￨- Zhao1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Sanling￨U￨VBG￨O￨- Yuan1￨U￨NN￨O￨- and￨L￨CC￨O￨- Haidong￨U￨NNP￨O￨- Liu2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:64￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- coefficients￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- this￨L￨DT￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- perturbations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- like￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- For￨U￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Lin￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Jiang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- solution￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- they￨L￨PRP￨O￨- showed￨L￨VBD￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- survival￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- understand￨L￨VBP￨O￨- the￨L￨DT￨O￨- instant￨L￨JJ￨O￨- situation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- contacting￨L￨VBG￨O￨- with￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- Zhang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Sun￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- feedback￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- :￨L￨:￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- Theta￨U￨NNP￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- link￨L￨NN￨O￨- pointing￨L￨VBG￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Theta￨U￨NNP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- langle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- rangle￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Sum￨U￨NN￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- P￨U￨NN￨O￨- k￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- P￨U￨NN￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- has￨L￨VBZ￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- with￨L￨IN￨O￨- Equality￨U￨NN￨O￨- Mul￨U￨NN￨O￨- langle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- rangle￨L￨NN￨O￨- Sum￨U￨NN￨O￨- Mul￨U￨NN￨O￨- P￨U￨NN￨O￨- k￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- StrictGreaterThan￨U￨NN￨O￨- alpha￨L￨NN￨O￨A 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- fear￨L￨NN￨O￨- factor￨L￨NN￨O￨- .￨L￨.￨O￨- ”￨L￨''￨O￨- +This￨U￨DT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- written￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- They￨U￨PRP￨O￨- obtained￨L￨VBD￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- lambda￨L￨NN￨ORGANIZATION￨A Mul￨U￨NN￨ORGANIZATION￨- langle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- k￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- rangle￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- langle￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- rangle￨L￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- gamma￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- langle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- k￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- rangle￨L￨NN￨O￨- Sum￨U￨NN￨O￨- Mul￨U￨NN￨O￨- P￨U￨NN￨O￨- Pow￨U￨NN￨O￨- k￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Tuple￨U￨NN￨ORGANIZATION￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- Mul￨U￨NN￨PERSON￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- I￨U￨PRP￨PERSON￨- Mul￨U￨VBP￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Theta￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equation￨L￨NN￨O￨- f￨L￨FW￨O￨- Theta￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 1.6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Application￨U￨NN￨MISC￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- inequalities￨L￨NNS￨O￨- to￨L￨TO￨O￨- global￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNS￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨A treatment￨L￨NN￨O￨- functionShengqiang￨L￨NN￨O￨- Zhang1￨U￨NN￨O￨- ,￨L￨,￨O￨- Xinzhu￨U￨FW￨O￨- Meng1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- and￨L￨CC￨O￨- Xinzeng￨U￨NN￨O￨- Wang1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2018:50￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNS￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- standard￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- saturated￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- nu￨L￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- lambda￨L￨NN￨O￨A I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- dN￨L￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dS￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- d￨L￨NN￨O￨- r￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- d￨L￨NN￨O￨- nu￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- λ￨L￨VBP￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- ν￨L￨NN￨O￨- and￨L￨CC￨O￨- r￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- Mul￨U￨JJ￨O￨- lambda￨L￨NN￨O￨A Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- SIRS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- Mul￨U￨NNP￨O￨- lambda￨L￨NN￨O￨A Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- p￨L￨NN￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- q￨L￨VBP￨O￨- alpha￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- mean￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNS￨O￨- epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- techniques￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- inequalities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- A￨U￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨- through￨L￨IN￨O￨- social￨L￨JJ￨O￨- networking￨L￨NN￨O￨- sitesAli￨L￨NN￨O￨- Alessa1￨U￨NN￨O￨- and￨L￨CC￨O￨- Miad￨U￨NN￨O￨- Faezipour1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 15:2￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractEarly￨U￨NNP￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- reduce￨L￨VB￨O￨- their￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- in￨L￨IN￨O￨- daily￨L￨JJ￨SET￨- lives￨L￨NNS￨O￨- .￨L￨.￨O￨- +Search￨U￨VB￨O￨- engines￨L￨NNS￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- networking￨L￨NN￨O￨- sites￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- track￨L￨VB￨O￨A trends￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- seven￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- ten￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- faster￨L￨RBR￨O￨- than￨L￨IN￨O￨- government￨L￨NN￨O￨- agencies￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Center￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +CDC￨U￨NNP￨ORGANIZATION￨- uses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Illness-Like￨U￨NNP￨ORGANIZATION￨- Influenza￨U￨NNP￨ORGANIZATION￨- Surveillance￨U￨NNP￨ORGANIZATION￨- Network￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- ILINet￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- program￨L￨NN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- Influenza-Like￨U￨NNP￨O￨- Illness￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- sent￨L￨VBN￨O￨- by￨L￨IN￨O￨- thousands￨L￨NNS￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- providers￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- that￨L￨DT￨O￨- reason￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- real￨L￨JJ￨O￨- time￨L￨NN￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- track￨L￨VB￨O￨A ILI￨U￨NNP￨O￨- using￨L￨VBG￨O￨- social￨L￨JJ￨O￨- networking￨L￨NN￨O￨- sites￨L￨NNS￨O￨- .￨L￨.￨O￨- +Social￨U￨NNP￨O￨- media￨L￨NNS￨O￨- data￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Twitter￨U￨NNP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- getting￨L￨VBG￨O￨A early￨L￨JJ￨O￨- warnings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- Pow￨U￨NN￨ORGANIZATION￨- D￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- alpha￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- g￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- h￨L￨NN￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- e￨L￨SYM￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Lambda￨U￨NNP￨ORGANIZATION￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- mu￨L￨NN￨O￨A Equality￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- D￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- alpha￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 3.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- reduces￨L￨VBZ￨O￨- to￨L￨TO￨O￨- false￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 3.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Second￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- let￨L￨VBD￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- makes￨L￨VBZ￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- h￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- leqslant￨L￨NN￨O￨- t￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- FDE￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelLet￨L￨NN￨O￨- us￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- IDE￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- g￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Add￨U￨VB￨O￨- Lambda￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- mu￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- constructed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Iwami￨U￨NNP￨LOCATION￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Section￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- discusses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- fixed￨L￨VBN￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- discretized-time￨L￨JJ￨O￨- SI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- state-dependent￨L￨JJ￨O￨- impulse￨L￨NN￨O￨- fishing￨L￨NN￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- predators￨L￨NNS￨O￨- are￨L￨VBP￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- supplementing￨L￨VBG￨O￨- preys￨L￨NNS￨O￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- Equality￨U￨NNP￨O￨- f￨L￨LS￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- y￨L￨NN￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- a￨L￨DT￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NN￨O￨- f￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- y￨L￨NN￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- impulsive￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨PERSON￨- textstyle￨L￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨A fish￨L￨NN￨O￨- and￨L￨CC￨O￨- predator￨L￨NN￨O￨- fish￨L￨NN￨O￨- densities￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Periodic￨U￨JJ￨MISC￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- prey-predator￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- harvestingJianmei￨L￨NN￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- Huidong￨U￨NNP￨O￨- Cheng1Email￨U￨NNP￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Hongxia￨U￨NNP￨O￨- Liu1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Yanhui￨U￨NNP￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2018:41￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- prey-predator￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- state-dependent￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨- harvesting￨L￨NN￨O￨- and￨L￨CC￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- harvesting￨L￨NN￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- replenishment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- prey￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- harvesting￨L￨VBG￨O￨- rate￨L￨NN￨O￨- are￨L￨VBP￨O￨- linearly￨L￨RB￨O￨- related￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- selected￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨A fish￨L￨NN￨O￨- density￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- to￨L￨TO￨O￨- h￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- x￨L￨CC￨O￨- h￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ecological￨L￨JJ￨O￨- balance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fishery￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- disorder￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- must￨L￨MD￨O￨- replenish￨L￨VB￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨- fish￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- replenishment￨L￨NN￨O￨- rate￨L￨NN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- tau￨L￨VBD￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- harvest￨L￨NN￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨- fish￨L￨NN￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- Mul￨U￨NN￨O￨- q￨L￨NN￨O￨- in￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- harvest￨L￨VBP￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨- fish￨L￨NN￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- in￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- while￨L￨IN￨O￨- harvesting￨L￨VBG￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨- fish￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Preliminaries￨U￨NNPS￨O￨- Definition￨U￨NNP￨O￨- 2.1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Consider￨U￨VB￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- differential￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- state-dependent￨L￨JJ￨O￨- impulse￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- triangle￨L￨NN￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- beta￨L￨NN￨O￨- x￨L￨CC￨O￨- y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- dynamic￨L￨JJ￨O￨- system￨L￨NN￨O￨- constituted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨A mappings￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- a￨L￨DT￨O￨- semi-continuous￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- denoted￨L￨VBN￨O￨- as￨L￨IN￨O￨- Omega￨U￨NNP￨O￨- .￨L￨.￨O￨- +Inspired￨U￨VBN￨O￨- by￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- 39￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 43￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- unilateral￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- Gompertz￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- indicate￨L￨VBP￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- densities￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- patches￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- K￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- within￨L￨IN￨O￨- patch￨L￨NN￨O￨A two￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- migration￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- from￨L￨IN￨O￨- patch￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- patch￨L￨NN￨O￨- two￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- K￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Preliminaries￨U￨NNPS￨O￨- Definition￨U￨NNP￨O￨- 2.1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Consider￨U￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- state-dependent￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- dynamic￨L￨JJ￨O￨- system￨L￨NN￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- solution￨L￨NN￨O￨A mapping￨L￨NN￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- a￨L￨DT￨O￨- semicontinuous￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- Omega￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- function￨L￨NN￨O￨- φ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- mapping￨L￨NN￨O￨- that￨L￨WDT￨O￨- meets￨L￨VBZ￨O￨- Equality￨U￨NN￨O￨- varphi￨L￨NN￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- }￨L￨-RRB-￨O￨- M￨U￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- order-one￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨A of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- geometry￨L￨NN￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- monotonicity￨L￨NN￨O￨- of￨L￨IN￨O￨- successor￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- order-one￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- geometry￨L￨NN￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- successor￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- tools￨L￨NNS￨O￨A implement￨L￨VBP￨O￨- numerical￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- compute￨L￨VBP￨O￨- probabilities￨L￨NNS￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- precision￨L￨NN￨O￨- ,￨L￨,￨O￨- suffering￨L￨VBG￨O￨- though￨L￨IN￨O￨- from￨L￨IN￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- explosion￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- simulation￨L￨NN￨O￨- engines￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- statistical￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- when￨L￨WRB￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- too￨L￨RB￨O￨- large.All￨L￨JJ￨O￨- classic￨L￨JJ￨O￨- quantitative￨L￨JJ￨O￨- verification￨L￨NN￨O￨- tools￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- fully￨L￨RB￨O￨- specified￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- application￨L￨NN￨O￨- domains￨L￨NNS￨O￨- like￨L￨IN￨O￨- system￨L￨NN￨O￨- biology￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- many￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- data￨L￨NNS￨O￨- or￨L￨CC￨O￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- belong￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- range￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- Tools￨U￨NNS￨O￨- and￨L￨CC￨O￨- Algorithms￨U￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Construction￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Analysis￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- pp￨L￨NN￨O￨- 396-413￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asBayesian￨L￨JJ￨O￨- Statistical￨U￨JJ￨O￨- Parameter￨U￨NN￨O￨- Synthesis￨U￨NN￨O￨- for￨L￨IN￨O￨- Linear￨U￨NNP￨O￨- Temporal￨U￨JJ￨O￨- Properties￨U￨NNPS￨O￨- of￨L￨IN￨O￨- Stochastic￨U￨NNP￨O￨- ModelsAuthorsAuthors￨U￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsLuca￨L￨NNP￨O￨- BortolussiSimone￨U￨NNP￨MISC￨- SilvettiOpen￨U￨NNP￨MISC￨- AccessConference￨U￨NNP￨MISC￨- paperFirst￨L￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- 3￨L￨CD￨NUMBER￨- Readers￨U￨NNS￨O￨- 1.2￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- Part￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Lecture￨U￨NNP￨O￨- Notes￨U￨NNP￨O￨- in￨L￨IN￨O￨- Computer￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- book￨L￨NN￨O￨- series￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LNCS￨U￨NN￨O￨- ,￨L￨,￨O￨- volume￨L￨NN￨O￨- 10806￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- AbstractParameterized￨U￨NNP￨O￨- verification￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- properties￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- research￨L￨NN￨O￨- area￨L￨NN￨O￨- ,￨L￨,￨O￨- being￨L￨VBG￨O￨- extremely￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- model-based￨L￨JJ￨O￨- design￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- parameter￨L￨NN￨O￨- synthesis￨L￨NN￨O￨- for￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- looking￨L￨VBG￨O￨- for￨L￨IN￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- satisfies￨L￨VBZ￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- time￨L￨NN￨O￨- specification￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- greater￨L￨JJR￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- less￨L￨JJR￨O￨- )￨L￨-RRB-￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- linear￨L￨JJ￨O￨- time￨L￨NN￨O￨- specifications￨L￨NNS￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- constraints￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨A models￨L￨NNS￨O￨A than￨L￨IN￨O￨- Markov￨U￨NNP￨PERSON￨- Chains.KeywordsParameter￨U￨NNP￨O￨- synthesis￨L￨NN￨O￨- Parametric￨U￨NNP￨ORGANIZATION￨- verification￨L￨NN￨O￨- Smoothed￨U￨VBN￨O￨- model￨L￨NN￨TITLE￨- checking￨L￨VBG￨O￨- Gaussian￨U￨NNP￨O￨- Processes￨U￨NNP￨O￨- Download￨U￨VB￨O￨- conference￨L￨NN￨O￨- paper￨L￨NN￨O￨- PDF1￨U￨NN￨O￨- IntroductionOverview￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- relying￨L￨VBG￨O￨- on￨L￨IN￨O￨- simulation￨L￨NN￨O￨- and￨L￨CC￨O￨- leveraging￨L￨VBG￨O￨- a￨L￨DT￨O￨- machine￨L￨NN￨O￨- learning￨L￨NN￨O￨- method￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Gaussian￨U￨NNP￨O￨- Processes￨U￨NNP￨O￨- for￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- parametric￨L￨JJ￨O￨A verification￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- Smoothed￨U￨VBN￨O￨- Model￨U￨NNP￨TITLE￨- Checking￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Holling￨U￨JJ￨PERSON￨- type￨L￨NN￨O￨- II￨U￨CD￨NUMBER￨- functional￨L￨JJ￨O￨- response￨L￨NN￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨- and￨L￨CC￨O￨- obtained￨L￨VBN￨O￨- sufficient￨L￨JJ￨O￨A conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- principle￨L￨NN￨O￨- of￨L￨IN￨O￨- competitive￨L￨JJ￨O￨- exclusion￨L￨NN￨O￨- ;￨L￨:￨O￨- they￨L￨PRP￨O￨- also￨L￨RB￨O￨- provided￨L￨VBD￨O￨- numerical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- to￨L￨TO￨O￨- verify￨L￨VB￨O￨- their￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- Milstein￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- higher￨L￨JJR￨O￨- order￨L￨NN￨O￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +Zhao￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Yuan￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- formulated￨L￨VBD￨O￨- a￨L￨DT￨O￨- single-species￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- periodic￨L￨JJ￨O￨A coefficients￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- fluctuation￨L￨NN￨O￨- ;￨L￨:￨O￨- they￨L￨PRP￨O￨- obtained￨L￨VBD￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- condition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- .￨L￨.￨O￨- +Standard￨U￨NNP￨O￨- Brownian￨U￨NNP￨O￨- motion￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- system.Scholars￨L￨NNS￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- by￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- obtained￨L￨VBN￨O￨A many￨L￨JJ￨O￨- important￨L￨JJ￨O￨- results￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- periodic￨L￨JJ￨O￨A wash-out￨L￨JJ￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- established￨L￨JJ￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- nontrivial￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Li￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- competition￨L￨NN￨O￨- turbidostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- inconstant￨L￨JJ￨O￨- dilution￨L￨NN￨O￨- rate￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨ORGANIZATION￨- d￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- k￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- dynamic￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- deterministic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- expressed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- mu￨L￨NN￨O￨A p￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- A￨U￨DT￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- alpha￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- mu￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- V￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- A￨U￨DT￨O￨- q￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- input￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- members￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- q￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LessThan￨U￨NN￨ORGANIZATION￨- LessThan￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- for￨L￨IN￨O￨- newborns￨L￨NNS￨O￨- ;￨L￨:￨O￨- β￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- proportional￨L￨JJ￨O￨- coefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- losing￨L￨VBG￨O￨- immunity￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-caused￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- regime￨L￨NN￨O￨- switching￨L￨NN￨O￨A SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- Lévy￨U￨NNP￨O￨- noise.Keywordsstochastic￨L￨NNP￨O￨- SIS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- modelvaccinationLévy￨L￨NN￨O￨- noiseMarkov￨L￨NN￨O￨- switchingglobal￨L￨NN￨O￨- positive￨L￨JJ￨O￨- solutionasymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionIt￨U￨NN￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- SARS￨U￨NNP￨O￨- ,￨L￨,￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- always￨L￨RB￨O￨- bring￨L￨VB￨O￨- great￨L￨JJ￨O￨- harm￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- threat￨L￨NN￨O￨- individual￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- society￨L￨NN￨O￨- and￨L￨CC￨O￨- frequent￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- among￨L￨IN￨O￨- people￨L￨NNS￨O￨- can￨L￨MD￨O￨- accelerate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Zhao￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Jiang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- stochastically￨L￨RB￨O￨- perturbed￨L￨VBN￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- B￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Equality￨U￨NN￨O￨- i￨L￨FW￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- Brownian￨U￨JJ￨MISC￨- motions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sigma￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- intensities￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- application￨L￨NN￨O￨- to￨L￨TO￨O￨- perturbed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- discussed.KeywordsSemi-Markov￨L￨JJ￨O￨- process￨L￨NN￨O￨- Perturbation￨U￨NN￨O￨- Asymptotic￨U￨JJ￨O￨- expansion￨L￨NN￨O￨- Regenerative￨U￨JJ￨O￨- process￨L￨NN￨O￨- Renewal￨U￨NN￨O￨- equation￨L￨NN￨O￨- Solidarity￨U￨NNP￨ORGANIZATION￨- property￨L￨NN￨O￨- First￨U￨NNP￨ORDINAL￨- hitting￨L￨VBG￨O￨- time￨L￨NN￨O￨- Mathematics￨U￨NNS￨O￨- Subject￨U￨NNP￨O￨- Classifications￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- 60K15￨L￨NNP￨O￨- 41A60￨L￨CD￨NUMBER￨- 60K05￨L￨NNP￨O￨- Download￨U￨VB￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- article￨L￨NN￨O￨- textReferencesAllen￨L￨NN￨O￨- LJS￨U￨NN￨O￨- ,￨L￨,￨O￨- Burgin￨U￨NNP￨PERSON￨- AM￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Comparison￨U￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Linear￨U￨JJ￨O￨- Algebra￨U￨NNP￨O￨- Appl￨U￨NN￨O￨- 386:243￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 259MathSciNetCrossRefzbMATHGoogle￨L￨JJ￨O￨- ScholarBlanchet￨U￨NN￨O￨- J￨U￨NN￨O￨- ,￨L￨,￨O￨- Zwart￨U￨NN￨PERSON￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- Asymptotic￨U￨JJ￨O￨- expansions￨L￨NNS￨O￨- of￨L￨IN￨O￨- defective￨L￨JJ￨O￨- renewal￨L￨NN￨O￨- equations￨L￨NNS￨O￨- with￨L￨IN￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- perturbed￨L￨VBN￨O￨- risk￨L￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- processor￨L￨NN￨TITLE￨- sharing￨L￨NN￨O￨- queues￨L￨NNS￨O￨- .￨L￨.￨O￨- +Math￨U￨NNP￨O￨- Biosci￨U￨NNP￨O￨- 163:1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 33MathSciNetCrossRefzbMATHGoogle￨L￨NN￨O￨- ScholarAltman￨U￨NN￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- Avrachenkov￨U￨NNP￨PERSON￨- KE￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Núñez-Queija￨U￨NNP￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2004￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Perturbation￨U￨NN￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- denumerable￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨- with￨L￨IN￨O￨- application￨L￨NN￨O￨A to￨L￨TO￨O￨- queueing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Pow￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- D￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- serves￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- predicts￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- coexistence￨L￨NN￨O￨A will￨L￨MD￨O￨- exist￨L￨VB￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- operator￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- related￨L￨JJ￨O￨- eigenvalue￨L￨NN￨O￨- problems￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- first-order￨L￨JJ￨O￨- differential￨L￨JJ￨O￨A equations￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- ,￨L￨,￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ith￨L￨NN￨O￨- species￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- widehat￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ith￨L￨NN￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- K￨U￨NN￨O￨- widehat￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- widehat￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- harvesting￨L￨VBG￨O￨- effort￨L￨NN￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- species￨L￨NNS￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨LS￨NUMBER￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- illustrated￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- to￨L￨TO￨O￨- verify￨L￨VB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- results￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study.Keywordsfractional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equationsstability￨L￨NN￨O￨- analysismutualism￨L￨NN￨O￨- modelCaputo￨L￨NN￨O￨- fractional￨L￨JJ￨O￨A derivativeLyapunov￨L￨NN￨O￨- function￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionA￨U￨NN￨O￨- population￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- delay￨L￨NN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- fractional￨L￨JJ￨O￨A differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 31￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 35￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- linearization￨L￨NN￨O￨- and￨L￨CC￨O￨- Lyapunov￨U￨NN￨PERSON￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- popular￨L￨JJ￨O￨- technique￨L￨NN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- without￨L￨IN￨O￨- visibly￨L￨RB￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- equations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 36￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 38￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨PERSON￨- StrictLessThan￨U￨NNP￨PERSON￨- 1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- and￨L￨CC￨O￨- LessThan￨U￨NNP￨O￨- LessThan￨U￨NNP￨O￨- LessThan￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- q￨L￨VB￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- q￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Let￨U￨VB￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- q￨L￨NN￨O￨- and￨L￨CC￨O￨- GreaterThan￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- Pow￨U￨NN￨O￨- p￨L￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- N￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- q￨L￨VB￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- 2.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- are￨L￨VBP￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- mild￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- u￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2.5￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2.5￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2.5￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- (￨L￨-LRB-￨O￨- 2.6￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2.6￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2.6￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- zeta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- alpha￨L￨NN￨O￨A }￨L￨-RRB-￨O￨- theta￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- density￨L￨NN￨O￨- function￨L￨NN￨O￨- defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Γ￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- contour￨L￨NN￨O￨- starting￨L￨VBG￨O￨- and￨L￨CC￨O￨- ending￨L￨VBG￨O￨- at￨L￨IN￨O￨- −￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- the￨L￨DT￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- semigroups￨L￨NNS￨O￨- G￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- for￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- operators￨L￨NNS￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- T￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- alpha￨L￨NN￨O￨A }￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- alpha￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- t￨L￨NN￨O￨- for￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- ones.Consider￨L￨NN￨O￨- the￨L￨DT￨O￨- fractional￨L￨JJ￨O￨- system￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- d￨L￨NN￨O￨- alpha￨L￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- dt￨L￨NN￨O￨- alpha￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- A￨U￨DT￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- f￨L￨FW￨O￨- x￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2.7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- in￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mul￨U￨NN￨PERSON￨- A￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NN￨O￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- f￨L￨FW￨O￨- Mul￨U￨FW￨O￨- Pow￨U￨NN￨O￨- C￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- D￨U￨NN￨ORGANIZATION￨- f￨L￨FW￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- solution￨L￨NN￨O￨- in￨L￨IN￨O￨- Besov￨U￨NNP￨LOCATION￨- spaces￨L￨NNS￨O￨A for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- regularity￨L￨NN￨O￨- initial￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- matter￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- solution￨L￨NN￨O￨- ,￨L￨,￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- discrete￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- global￨L￨JJ￨O￨A asymptotic￨L￨JJ￨O￨A stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibria￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- Lyapunov￨U￨NNP￨PERSON￨- functionals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- schemes￨L￨NNS￨O￨- ,￨L￨,￨O￨- Mickens￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- efficient￨L￨JJ￨O￨- in￨L￨IN￨O￨- preserving￨L￨VBG￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A asymptotic￨L￨JJ￨O￨A stability￨L￨NN￨O￨- for￨L￨IN￨O￨- equilibria￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- [￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- PreliminariesRearranging￨U￨VBG￨O￨- the￨L￨DT￨O￨- equations￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- gives￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- It￨U￨PRP￨O￨- follows￨L￨VBZ￨O￨- from￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- initial￨L￨JJ￨O￨A condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- remain￨L￨VBP￨O￨- nonnegative￨L￨JJ￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stationary￨U￨JJ￨MISC￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- information￨L￨NN￨O￨- interventionKangbo￨L￨NN￨O￨- Bao1￨U￨NN￨O￨- and￨L￨CC￨O￨- Qimin￨U￨NNP￨O￨- Zhang1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:352￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- intervention￨L￨NN￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- noise￨L￨NN￨O￨A is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- noise￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathscr￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- stationary￨L￨JJ￨O￨A distribution￨L￨NN￨O￨A is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- prevalent￨L￨JJ￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- production￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathscr￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- which￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨A or￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- SIR￨U￨NN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- information￨L￨NN￨O￨A intervention￨L￨NN￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- information￨L￨NN￨O￨- could￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- noise￨L￨NN￨O￨A is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathscr￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- die￨L￨VB￨O￨- out￨L￨RP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A problems￨L￨NNS￨O￨- are￨L￨VBP￨O￨- procured￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- Pontryagin￨U￨NNP￨LOCATION￨- ’s￨L￨POS￨O￨- maximum￨L￨NN￨O￨- principle￨L￨NN￨O￨- and￨L￨CC￨O￨- determined￨L￨VBD￨O￨- numerically￨L￨RB￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- progressive-regressive￨L￨JJ￨O￨- discrete￨L￨JJ￨O￨- schema￨L￨NN￨O￨- that￨L￨WDT￨O￨- converges￨L￨VBZ￨O￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- convenient￨L￨JJ￨O￨- test￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Forward-Backward￨U￨NNP￨MISC￨- Sweep￨U￨NNP￨MISC￨- Method￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- FBSM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control.Keywordsdiscrete￨L￨NN￨O￨- marital￨L￨JJ￨O￨- status￨L￨NN￨O￨- modelmonogamous￨L￨JJ￨O￨- marriagePontryagin￨L￨NN￨O￨- ’s￨L￨POS￨O￨- maximum￨L￨NN￨O￨- principleoptimal￨L￨NN￨O￨- control￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionThere￨U￨NNP￨O￨- are￨L￨VBP￨O￨- different￨L￨JJ￨O￨- categories￨L￨NNS￨O￨- of￨L￨IN￨O￨- marriage￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Discrete￨U￨NNP￨MISC￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- marital￨L￨JJ￨O￨- status￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- monogamous￨L￨JJ￨O￨- marriage￨L￨NN￨O￨- caseMustapha￨L￨NN￨O￨- Lhous1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Mostafa￨U￨NNP￨PERSON￨- Rachik2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Hassan￨U￨NNP￨PERSON￨- Laarabi2￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Ahmed￨U￨NNP￨PERSON￨- Abdelhak3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:339￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- marital￨L￨JJ￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- family￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- awareness￨L￨NN￨O￨- campaign￨L￨NN￨O￨- to￨L￨TO￨O￨- educate￨L￨VB￨O￨- virgin￨L￨JJ￨O￨- men￨L￨NNS￨O￨- and￨L￨CC￨O￨- women￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- marriage￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- society￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- control￨L￨NN￨O￨- characterizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- legal￨L￨JJ￨O￨- procedures￨L￨NNS￨O￨- ,￨L￨,￨O￨- administrative￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- heavy￨L￨JJ￨O￨- financial￨L￨JJ￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- divorces￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- treat￨L￨VB￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- monogamous￨L￨JJ￨O￨- marriage.Mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- functioning￨L￨NN￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- evolution￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- Pow￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- s￨L￨VBZ￨O￨- mathcal￨L￨JJ￨O￨A 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- becomes￨L￨VBZ￨O￨- extinct￨L￨JJ￨O￨- exponentially￨L￨RB￨O￨- ;￨L￨:￨O￨- whereas￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- s￨L￨VBZ￨O￨- mathcal￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- beta￨L￨NN￨O￨- i￨L￨FW￨O￨- alpha￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- can￨L￨MD￨O￨- converge￨L￨VB￨O￨- in￨L￨IN￨O￨- Pow￨U￨NNP￨O￨- L￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- invariant￨L￨JJ￨O￨- density.Keywordsstationary￨L￨JJ￨O￨- distributionMarkov￨L￨NN￨O￨- semigroupsasymptotic￨L￨JJ￨O￨- stabilityMSC47D0760J6060H1092D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionA￨U￨NN￨O￨- deterministic￨L￨JJ￨O￨- Susceptible-Infective￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- standard￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Lambda￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Here￨U￨RB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- Λ￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- influx￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-related￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate.Because￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- noises￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- appearing￨L￨VBG￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- emphatically￨L￨RB￨O￨- not￨L￨RB￨O￨- constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +Incorporating￨U￨VBG￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- noises￨L￨NNS￨O￨- into￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- get￨L￨VBP￨O￨- a￨L￨DT￨O￨- regime-switching￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- Lambda￨U￨NNP￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sigma￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constants.Recently￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- long-time￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- regime￨L￨NN￨O￨- switching￨L￨NN￨O￨A was￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- ellipticity￨L￨NN￨O￨- condition￨L￨NN￨O￨- was￨L￨VBD￨O￨- needed￨L￨VBN￨O￨- when￨L￨WRB￨O￨- proving￨L￨VBG￨O￨- the￨L￨DT￨O￨- ergodicity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- Lyapunov￨U￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- attractiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system.Keywordsepidemic￨L￨JJ￨O￨- spreadingscale-free￨L￨JJ￨O￨- networkbasic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- numberglobal￨L￨JJ￨O￨- attractivenesstime￨L￨NN￨O￨- delay￨L￨NN￨O￨A 1￨L￨CD￨NUMBER￨- IntroductionFollowing￨U￨NNP￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- seminal￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- small-world￨L￨JJ￨O￨- network￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- by￨L￨IN￨O￨- Watts￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Strogatz￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- p￨L￨NN￨O￨- k￨L￨NN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- node￨L￨NN￨O￨- with￨L￨IN￨O￨- k￨L￨NN￨O￨- links￨L￨NNS￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- distributed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- Equality￨U￨NN￨O￨- p￨L￨NN￨O￨- k￨L￨NN￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- Pow￨U￨NN￨O￨- k￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- StrictLessThan￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- le￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- suggested￨L￨VBN￨O￨- by￨L￨IN￨O￨- Barabási￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Albert￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- researchers￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Chen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- present￨L￨VB￨DATE￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- functional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨A represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨- vector￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- network.Assuming￨L￨VBG￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- N￨U￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- suppose￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- time-invariant￨L￨JJ￨O￨- and￨L￨CC￨O￨- p￨L￨NN￨O￨- k￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Kang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Fu￨U￨NNP￨PERSON￨- also￨L￨RB￨O￨- established￨L￨VBD￨O￨- a￨L￨DT￨O￨- functional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on.Considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- individual￨L￨NN￨O￨- may￨L￨MD￨O￨- become￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- Chen￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Sun￨U￨NNP￨PERSON￨- discussed￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- without￨L￨IN￨O￨- delay￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- give￨L￨VBP￨O￨- an￨L￨DT￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- prove￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- when￨L￨WRB￨O￨- StrictLessThan￨U￨NNP￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- uniformly￨L￨RB￨O￨- persistent￨L￨JJ￨O￨- when￨L￨WRB￨O￨- StrictGreaterThan￨U￨NNP￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- competition￨L￨NN￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A effectXuejin￨L￨NN￨O￨- Lv1￨U￨NN￨O￨- ,￨L￨,￨O￨- Lu￨U￨NNP￨PERSON￨- Wang2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Xinzhu￨U￨NNP￨O￨- Meng1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2017:296￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- competition￨L￨NN￨O￨- chemostat￨L￨NN￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- impulsive￨L￨JJ￨O￨- toxicant￨L￨NN￨O￨- input￨L￨NN￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- qualitative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A stochastic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- mean￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- microorganisms￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- high-dimensional￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- between￨L￨IN￨O￨- persistence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- between￨L￨IN￨O￨- persistence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A toxicant￨L￨NN￨O￨- input￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- microorganisms￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- polluted￨L￨JJ￨O￨- environment￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Mathematical￨U￨JJ￨MISC￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- macroalgaeArtorn￨L￨NN￨O￨- Nokkaew1￨U￨NN￨O￨- ,￨L￨,￨O￨- Charin￨U￨NNP￨O￨- Modchang2￨U￨NNP￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Somkid￨U￨NNP￨O￨- Amornsamankul3￨U￨NNP￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yongwimon￨U￨NNP￨O￨- Lenbury3￨U￨NNP￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Busayamas￨U￨NNP￨O￨- Pimpunchat5￨U￨NNP￨O￨- and￨L￨CC￨O￨- Wannapong￨U￨NNP￨O￨- Triampo2￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2017:288￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractUnderstanding￨U￨VBG￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- algae￨L￨NN￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- significant￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨A for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- intervention￨L￨NN￨O￨- and/or￨L￨CC￨O￨- prevention￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- reason￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- computationally￨L￨RB￨O￨- model￨L￨VBP￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- algae￨L￨NN￨O￨- reservoir￨L￨NN￨O￨- or￨L￨CC￨O￨- container￨L￨NN￨O￨- systems￨L￨NNS￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- patches￨L￨NNS￨O￨A or￨L￨CC￨O￨- clusters￨L￨NNS￨O￨- of￨L￨IN￨O￨- algae￨L￨NN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SEIR￨U￨NN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- dividing￨L￨VBG￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- never￨L￨RB￨O￨- contacted￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- S￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- hesitate￨L￨VB￨O￨- state￨L￨NN￨O￨- not￨L￨RB￨O￨- spreading￨L￨VBG￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- E￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- accepted￨L￨VBN￨O￨- and￨L￨CC￨O￨- spread￨L￨VBN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- I￨U￨PRP￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- ,￨L￨,￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- know￨L￨VBP￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- but￨L￨CC￨O￨- have￨L￨VBP￨O￨- ceased￨L￨VBN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- it￨L￨PRP￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- R.￨U￨NNP￨O￨- Based￨U￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- hypotheses￨L￨NNS￨O￨- and￨L￨CC￨O￨- notation￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- reaction￨L￨NN￨O￨- rate￨L￨NN￨O￨- equations￨L￨NNS￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- StrictGreaterThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- k￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- acceptability￨L￨NN￨O￨- of￨L￨IN￨O￨- k￨L￨NN￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- Theta￨U￨NNP￨O￨- t￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- satisfying￨L￨VBG￨O￨- Equality￨U￨NNP￨O￨- Theta￨U￨NNP￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- langle￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- rangle￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- Pow￨U￨NNP￨O￨- i￨L￨FW￨O￨- -1￨L￨CD￨NUMBER￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- will￨L￨MD￨O￨- contact￨L￨VB￨O￨- this￨L￨DT￨O￨- individual￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- ;￨L￨:￨O￨- P￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- i.￨L￨NN￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- immigration￨L￨NN￨O￨- and￨L￨CC￨O￨- emigration￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- hesitating￨L￨VBG￨O￨- mechanism￨L￨NN￨O￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- comprehensively￨L￨RB￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- globally￨L￨RB￨O￨- asymptotical￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A in￨L￨IN￨O￨- detail.The￨L￨NNP￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- demographics￨L￨NNS￨O￨- on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networksChen￨L￨NN￨O￨- Wan1￨U￨NN￨O￨- ,￨L￨,￨O￨- Tao￨U￨NNP￨O￨- Li1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Zhicheng￨U￨NNP￨O￨- Sun1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:253￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-infected-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- demographics￨L￨NNS￨O￨- on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- references￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- hesitating￨L￨VBG￨O￨- mechanism￨L￨NN￨O￨- ,￨L￨,￨O￨- neither￨L￨CC￨O￨- could￨L￨MD￨O￨- serve￨L￨VB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- strict￨L￨JJ￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Geometrical￨U￨JJ￨MISC￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- predator-prey￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- multi￨L￨NNS￨O￨- state-dependent￨L￨JJ￨O￨- impulseJianmei￨L￨NN￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- Huidong￨U￨NNP￨O￨- Cheng1Email￨U￨NNP￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Xinzhu￨U￨FW￨O￨- Meng1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- BG￨U￨NNP￨ORGANIZATION￨- Sampath￨U￨NNP￨ORGANIZATION￨- Aruna￨U￨NNP￨ORGANIZATION￨- Pradeep3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:252￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- predator-prey￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Holling￨U￨NNP￨PERSON￨- type-I￨L￨NN￨O￨- functional￨L￨JJ￨O￨- response￨L￨NN￨O￨- and￨L￨CC￨O￨- multi￨L￨JJ￨O￨- state￨L￨NN￨O￨- impulsive￨L￨JJ￨O￨A feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- established￨L￨VBN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- pesticide￨L￨NN￨O￨- spraying￨L￨VBG￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- release￨L￨NN￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- enemies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- linearly￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- given￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- impulse￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- pest￨L￨NN￨O￨- management￨L￨NN￨O￨- control￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- impulse￨L￨NN￨O￨- was￨L￨VBD￨O￨- presented￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- were￨L￨VBD￨O￨- studied￨L￨VBN￨O￨- by￨L￨IN￨O￨- Zhang￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- established￨L￨VBN￨O￨- a￨L￨DT￨O￨- pest￨L￨NN￨O￨- control￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Holling￨U￨NNP￨PERSON￨- type-I￨L￨NN￨O￨- functional￨L￨JJ￨O￨A response￨L￨NN￨O￨- and￨L￨CC￨O￨- studied￨L￨VBD￨O￨- its￨L￨PRP$￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- attractiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- order-1￨L￨NN￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- worthy￨L￨JJ￨O￨- to￨L￨TO￨O￨- note￨L￨VB￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- scholars￨L￨NNS￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- state￨L￨NN￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- on￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- reaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +considered￨L￨VBN￨O￨- a￨L￨DT￨O￨- pest￨L￨NN￨O￨- management￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- state￨L￨NN￨O￨- impulsive￨L￨JJ￨O￨A control￨L￨NN￨O￨- and￨L￨CC￨O￨- Holling￨U￨NN￨PERSON￨- type-II￨L￨JJ￨O￨- functional￨L￨JJ￨O￨- response￨L￨NN￨O￨- and￨L￨CC￨O￨- focused￨L￨VBD￨O￨- their￨L￨PRP$￨O￨- attention￨L￨NN￨O￨- on￨L￨IN￨O￨- geometric￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- further￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- readers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- directed￨L￨VBN￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨A the￨L￨DT￨O￨- references￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 35￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 37￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Parameters￨U￨NNPS￨O￨- Description￨U￨NN￨O￨- A￨U￨DT￨O￨- The￨U￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- by￨L￨IN￨O￨- birth￨L￨NN￨O￨- or￨L￨CC￨O￨- immigration￨L￨NN￨O￨- μ￨L￨NN￨O￨- Per￨U￨IN￨O￨- capita￨L￨NN￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- θ￨L￨NN￨O￨- The￨U￨DT￨O￨- duration￨L￨NN￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- compartment￨L￨NN￨O￨A a￨L￨DT￨O￨- Age￨U￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- lapsed￨L￨VBN￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- became￨L￨VBD￨O￨- infectious￨L￨JJ￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- removed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- a￨L￨DT￨O￨- γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- with￨L￨IN￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- a￨L￨DT￨O￨- recovers￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ν￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- θ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- compartment￨L￨NN￨O￨- for￨L￨IN￨O￨- duration￨L￨NN￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- progress￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- δ￨L￨NN￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- treated￨L￨VBN￨O￨- individual￨L￨JJ￨O￨- leaves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- treated￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- p￨L￨NN￨O￨- The￨U￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨- infected￨L￨VBN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- directly1￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- The￨U￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨- infected￨L￨VBN￨O￨- to￨L￨TO￨O￨- enter￨L￨VB￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- class￨L￨NN￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- treated￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- sequel￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- further￨L￨RB￨O￨- make￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- suitable￨L￨JJ￨O￨- Lyapunov￨U￨NNP￨PERSON￨- functionals￨L￨NNS￨O￨- and￨L￨CC￨O￨- LaSalle￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- invariance￨L￨NN￨O￨- principle￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- proven￨L￨VBN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable.Keywordstuberculosisage￨L￨JJ￨O￨- structurestabilityLyapunov￨L￨NN￨O￨- functionalLaSalle￨L￨NN￨O￨- ’s￨L￨POS￨O￨- invariance￨L￨NN￨O￨- principleMSC37N2592B0537B25￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionTuberculosis￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- Mycobacterium￨U￨NN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- acquired￨L￨VBN￨O￨- through￨L￨IN￨O￨- airborne￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- active￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Active￨U￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- developing￨L￨VBG￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- 2-5￨L￨CD￨NUMBER￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- most￨L￨JJS￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- remain￨L￨VBP￨O￨- latent￨L￨JJ￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- until￨L￨IN￨O￨- immune￨L￨JJ￨O￨- compromise￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- aging￨L￨VBG￨O￨- or￨L￨CC￨O￨- co-infection￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- illnesses￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 26￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- boundary￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- X￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1.6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- X￨U￨NN￨O￨- mathscr￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathbb￨L￨NN￨O￨A ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- integrable￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- from￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- into￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- simultaneously￨L￨RB￨O￨- releasing￨L￨VBG￨O￨- Wolbachia-harboring￨U￨JJ￨MISC￨- female￨L￨NN￨O￨- and￨L￨CC￨O￨- male￨L￨JJ￨O￨A mosquitoes￨L￨NNS￨O￨- will￨L￨MD￨O￨- achieve￨L￨VB￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- replacement￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- releasing￨L￨VBG￨O￨- only￨L￨RB￨O￨- Wolbachia-harboring￨U￨JJ￨MISC￨- male￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- will￨L￨MD￨O￨- suppress￨L￨VB￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- eradicate￨L￨VB￨O￨- wild￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- eventually￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- only￨L￨RB￨O￨- releasing￨L￨VBG￨O￨- male￨L￨JJ￨O￨A Wolbachia￨U￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- control￨L￨NN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NN￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- formulate￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- control￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- releasing￨L￨VBG￨O￨- transgenosis￨L￨NN￨O￨- mosquitoes￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- introducing￨L￨VBG￨O￨- bacterium￨L￨NN￨O￨- Wolbachia￨U￨NNP￨O￨- into￨L￨IN￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A and￨L￨CC￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- suspected￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 2.5020￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Modeling￨U￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- Liping￨U￨NNP￨O￨- Wang1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Hongyong￨U￨NNP￨PERSON￨- Zhao1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Sergio￨U￨NNP￨PERSON￨- Muniz￨U￨NNP￨PERSON￨- Oliva2￨U￨NNP￨O￨- &￨L￨CC￨O￨- Huaiping￨U￨NNP￨O￨- Zhu3￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 7721￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsEpidemiology￨L￨NNP￨O￨- AbstractZika￨U￨NNP￨O￨- virus￨L￨NN￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- reemerging￨L￨VBG￨O￨- mosquito-borne￨L￨JJ￨O￨- flavivirus￨L￨NN￨O￨- ,￨L￨,￨O￨- started￨L￨VBD￨O￨- spread￨L￨NN￨O￨- across￨L￨IN￨O￨- Central￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Southern￨U￨NNP￨ORGANIZATION￨- America￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- recently￨L￨RB￨DATE￨- to￨L￨TO￨O￨- North￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- the￨L￨DT￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- mathematically￨L￨RB￨O￨- expressed￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- p.￨L￨NN￨O￨- 47￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨A Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- bilinear￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- system￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- p.￨L￨NN￨O￨- 62￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨A I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- dS￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- d￨L￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Dynamical￨U￨JJ￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- double￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- hypothesisAnqi￨L￨NN￨O￨- Miao1￨U￨NN￨O￨- ,￨L￨,￨O￨- Xinyang￨U￨NNP￨CITY￨- Wang1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Tongqian￨U￨NNP￨O￨- Zhang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Wei￨U￨NNP￨PERSON￨- Wang3￨U￨NNP￨O￨- and￨L￨CC￨O￨- BG￨U￨NNP￨ORGANIZATION￨- Sampath￨U￨NNP￨ORGANIZATION￨- Aruna￨U￨NNP￨ORGANIZATION￨- Pradeep4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:226￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- double￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- analysed￨L￨VBN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- firstly￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- neglecting￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨A disturbance￨L￨NN￨O￨- and￨L￨CC￨O￨- obtained￨L￨VBD￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibria￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨- semi-dynamic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- hot￨L￨JJ￨O￨- topic￨L￨NN￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- and￨L￨CC￨O￨- science￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- tactics￨L￨NNS￨O￨- should￨L￨MD￨O￨- only￨L￨RB￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- once￨L￨RB￨DATE￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- reach￨L￨VBP￨O￨- a￨L￨DT￨O￨- prescribed￨L￨VBN￨O￨- given￨L￨VBN￨O￨- threshold.Following￨L￨VBG￨O￨- this￨L￨DT￨O￨- idea￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- PVS￨U￨NNS￨O￨- and￨L￨CC￨O￨- pulse￨L￨NN￨O￨- treatment￨L￨NN￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PTS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- authors￨L￨NNS￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Nonlinear￨U￨JJ￨MISC￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨A strategy￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- resource￨L￨NN￨O￨- limitationZhi￨L￨NNP￨O￨- Long￨U￨NNP￨O￨- He1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Ji￨U￨NN￨O￨- Gang￨U￨NN￨O￨- Li1￨U￨NN￨O￨- ,￨L￨,￨O￨- Lin￨U￨NNP￨PERSON￨- Fei￨U￨NNP￨PERSON￨- Nie2￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Zhen￨U￨NNP￨O￨- Zhao3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:209￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- impulse￨L￨NN￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- to￨L￨TO￨O￨- keep￨L￨VB￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- first￨L￨RB￨ORDINAL￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- PVS￨U￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- periodical￨L￨JJ￨O￨- repetitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A vaccinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- cohorts￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- confirmed￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- and￨L￨CC￨O￨- effective￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases.In￨L￨NN￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- application￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- eradication￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- sometimes￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- both￨L￨CC￨O￨- practically￨L￨RB￨O￨- and￨L￨CC￨O￨- economically￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- resource￨L￨NN￨O￨- limitation￨L￨NN￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨- function￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨A scheme￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- practical￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- ,￨L￨,￨O￨- impulse￨L￨NN￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- often￨L￨RB￨O￨- occurs￨L￨VBZ￨O￨- at￨L￨IN￨O￨- state-dependent￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- reasonable￨L￨JJ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- a￨L￨DT￨O￨- strategy￨L￨NN￨O￨- of￨L￨IN￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨A to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- issues￨L￨NNS￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- –￨L￨:￨O￨- wavelet￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- economic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- statistical￨L￨JJ￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- modelling￨L￨NN￨O￨- –￨L￨:￨O￨- we￨L￨PRP￨O￨- aimed￨L￨VBD￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- climatic￨L￨JJ￨O￨A and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- Highly￨U￨RB￨O￨- Pathogenic￨U￨JJ￨O￨- Avian￨U￨JJ￨O￨- Influenza￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- domestic￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- Vietnam￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Economic￨U￨NNP￨O￨- factors￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- zoonotic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- demand￨L￨NN￨O￨- for￨L￨IN￨O￨- poultry￨L￨NN￨O￨- meat￨L￨NN￨O￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Vietnam￨U￨NNP￨COUNTRY￨- Alexis￨U￨NNP￨PERSON￨- Delabouglise￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Marc￨U￨NNP￨PERSON￨- Choisy3￨U￨NNP￨O￨- ,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Thang￨U￨NNP￨O￨- D.￨U￨NNP￨O￨- Pfeiffer1￨U￨NNP￨O￨- ,7￨L￨NNP￨O￨- &￨L￨CC￨O￨- Guillaume￨U￨NNP￨O￨- Fournié1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 5905￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- virusStatistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- AbstractWhile￨U￨NNP￨O￨- climate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- presented￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- factor￨L￨NN￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- anthropogenic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- commonly￨L￨RB￨O￨- evaluated￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- temporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- incidence￨L￨NN￨O￨- are￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- across￨L￨IN￨O￨- these￨L￨DT￨O￨- 3￨L￨CD￨NUMBER￨- regions￨L￨NNS￨O￨- :￨L￨:￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- H5N1￨U￨NN￨O￨- incidence￨L￨NN￨O￨- coincide￨L￨VBP￨O￨- with￨L￨IN￨O￨- Lunar￨U￨JJ￨MISC￨- New￨U￨JJ￨DATE￨- Year￨U￨NN￨DATE￨- festival￨L￨NN￨O￨- ,￨L￨,￨O￨- occurring￨L￨VBG￨O￨- in￨L￨IN￨O￨- January-February￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 3￨L￨CD￨NUMBER￨- climatic￨L￨JJ￨O￨A regions￨L￨NNS￨O￨- for￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 8￨L￨CD￨NUMBER￨- study￨L￨NN￨O￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- while￨L￨IN￨O￨- climatic￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- North￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Centre￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- South￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- setting￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- want￨L￨VBP￨O￨- to￨L￨TO￨O￨- localize￨L￨VB￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- based￨L￨VBN￨O￨- exclusively￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- observers￨L￨NNS￨O￨- –￨L￨:￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- reveal￨L￨VB￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- –￨L￨:￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- where￨L￨WRB￨O￨- such￨L￨JJ￨O￨- observers￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- placed.We￨L￨JJ￨O￨- show￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- observer￨L￨NN￨O￨- placement￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- node-to-node￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- delays￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- intricate￨L￨JJ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- CSTCS￨U￨NNP￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- Lyapunov￨U￨NN￨O￨- function￨L￨NN￨O￨- and￨L￨CC￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- symbol￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- derivative￨L￨NN￨O￨- are￨L￨VBP￨O￨- complex￨L￨JJ￨O￨- and￨L￨CC￨O￨- technical￨L￨JJ￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- circumstances￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- coupling￨L￨NN￨O￨A structure.Motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- discussions￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- coupling￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- CSs￨U￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- CSTCS￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- general￨L￨JJ￨TITLE￨- CSs￨U￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- f￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- bigl￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- t￨L￨NN￨O￨- Sum￨U￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- bigl￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- l￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- f￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- continuous￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨A strength￨L￨NN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- Xu￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ren￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIR￨U￨NN￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- limited￨L￨JJ￨O￨- anti-virus￨L￨JJ￨O￨- ability￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- varrho￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- E￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- where￨L￨WRB￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- latent￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- where￨L￨WRB￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- breaking￨L￨VBG￨O￨- out￨L￨RP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- equipped￨L￨VBN￨O￨- with￨L￨IN￨O￨- anti-virus￨L￨JJ￨O￨- software￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- above￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- delays￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- E￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- E￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varepsilon￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- E￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- p￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- computers￨L￨NNS￨O￨A and￨L￨CC￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- that￨L￨WDT￨O￨- anti-virus￨L￨JJ￨O￨- software￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Xu￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Ren￨U￨NN￨PERSON￨- NumericCitation￨U￨NN￨PERSON￨- studied￨L￨VBN￨O￨- stabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- virus-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- virus￨L￨NN￨O￨- equilibrium.However￨L￨NNP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- pointed￨L￨VBN￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- neglects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- computers￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- that￨L￨WDT￨O￨- anti-virus￨L￨JJ￨O￨- software￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Dynamical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- by￨L￨IN￨O￨- scholars￨L￨NNS￨O￨- at￨L￨IN￨O￨- home￨L￨NN￨O￨- and￨L￨CC￨O￨- abroad￨L￨RB￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- predator-prey￨L￨JJ￨O￨- models￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨A models￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 31￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- still￨L￨RB￨O￨- lack￨L￨VBP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- needs￨L￨VBZ￨O￨- more￨L￨JJR￨O￨- attention￨L￨NN￨O￨- by￨L￨IN￨O￨- medical￨L￨JJ￨O￨- staff￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemiologists￨L￨NNS￨O￨A ,￨L￨,￨O￨- mathematicians￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- stakeholders.Mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- in￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- some￨L￨DT￨O￨- useful￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Modeling￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- quarantine￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- diseaseThomas￨L￨NNP￨MISC￨- Wetere￨U￨NNP￨MISC￨- Tulu1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Boping￨U￨VBG￨O￨- Tian1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Zunyou￨U￨NN￨O￨- Wu2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2017:178￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractEbola￨U￨NNP￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- severe￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- case￨L￨NN￨O￨A fatality￨L￨NN￨O￨A rate￨L￨NN￨O￨A which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- treat￨L￨NN￨O￨- now￨L￨RB￨DATE￨- .￨L￨.￨O￨- +Last￨U￨JJ￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- least￨L￨JJS￨O￨- ,￨L￨,￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- epidemic.Keywordsmathematical￨L￨JJ￨O￨- modelingCaputo￨L￨NN￨O￨- derivativestabilityepidemic￨L￨JJ￨O￨- modelnumerical￨L￨JJ￨O￨- simulationMSC37N2592D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionEbola￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- severe￨L￨JJ￨O￨- and￨L￨CC￨O￨- often￨L￨RB￨O￨- deadly￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- killing￨L￨NN￨O￨- between￨L￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- named￨L￨VBN￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- river￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Democratic￨U￨JJ￨IDEOLOGY￨- Republic￨U￨NN￨LOCATION￨- of￨L￨IN￨LOCATION￨- Congo￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- formerly￨L￨RB￨O￨- Zaire￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- case￨L￨NN￨O￨A fatality￨L￨NN￨O￨A rate￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- both￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- quarantine￨L￨NN￨O￨A to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- and￨L￨CC￨O￨- comprehensively￨L￨RB￨O￨- analyzed￨L￨VBN￨O￨- using￨L￨VBG￨O￨- fractional￨L￨JJ￨O￨- derivative￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Caputo￨U￨NNP￨O￨- derivative￨L￨NN￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- also￨L￨RB￨O￨- seen￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- for￨L￨IN￨O￨- getting￨L￨VBG￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- time￨L￨NN￨O￨- if￨L￨IN￨O￨- they￨L￨PRP￨O￨- survived￨L￨VBD￨O￨- his/her￨L￨JJR￨O￨- first￨L￨JJ￨ORDINAL￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Individual￨U￨JJ￨MISC￨- position￨L￨NN￨O￨- diversity￨L￨NN￨O￨- in￨L￨IN￨O￨- dependence￨L￨NN￨O￨A socioeconomic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- increases￨L￨VBZ￨O￨- economic￨L￨JJ￨O￨- outputWen-Jie￨L￨NN￨O￨- Xie1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yan-Hong￨U￨NNP￨PERSON￨- Yang1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ming-Xia￨U￨NNP￨O￨- Li2￨U￨NNP￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Zhi-Qiang￨U￨NNP￨PERSON￨- Jiang1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Wei-Xing￨U￨JJ￨O￨- Zhou1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 6:10￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- big￨L￨JJ￨O￨- data￨L￨NNS￨O￨- recorded￨L￨VBN￨O￨- from￨L￨IN￨O￨- massively￨L￨RB￨O￨- multiplayer￨L￨JJ￨O￨- online￨L￨NN￨O￨- role-playing￨L￨NN￨O￨- games￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MMORPGs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- a￨L￨DT￨O￨- deeper￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- network￨L￨NN￨O￨- positions￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- economic￨L￨JJ￨O￨- outputs￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- classical￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vital￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- Tuple￨U￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- mu￨L￨NN￨O￨A Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- N￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- N￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- above￨L￨IN￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- inflow￨L￨NN￨O￨- of￨L￨IN￨O￨- newborns￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- μN￨L￨NN￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- classes￨L￨NNS￨O￨- at￨L￨IN￨O￨- rates￨L￨NNS￨O￨- μN￨L￨NN￨O￨- ,￨L￨,￨O￨- μI￨L￨NN￨O￨- and￨L￨CC￨O￨- μR￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- denoting￨L￨VBG￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- Tuple￨U￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨A Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- presented￨L￨VBD￨O￨- four￨L￨CD￨NUMBER￨- discrete￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- forward￨L￨JJ￨O￨- Euler￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- backward￨L￨RB￨O￨- Euler￨U￨NNP￨PERSON￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- discussed￨L￨VBD￨O￨A the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- discretizations￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Robinson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Holmes￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- discussed￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Schrödingerean￨U￨JJ￨MISC￨- predator-prey￨L￨NN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- undergoes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- flip￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨A and￨L￨CC￨O￨- Hopf￨U￨NN￨PERSON￨- bifurcation￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- center￨L￨NN￨O￨- manifold￨L￨NN￨O￨- theorem￨L￨NN￨O￨- and￨L￨CC￨O￨- bifurcation￨L￨NN￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +Guckenheimer￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Holmes￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- examined￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- non-monotonic￨L￨JJ￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- also￨L￨RB￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- derived￨L￨VBD￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- calculation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- equilibriums￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- grouped￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- three￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictGreaterThan￨U￨NNP￨PERSON￨- c￨L￨NN￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NNP￨O￨- a￨L￨DT￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- b￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- c￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- trivial￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- semi-trivial￨L￨JJ￨O￨- equilibria￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +Levins￨U￨NNP￨PERSON￨- posed￨L￨VBD￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- general￨L￨JJ￨TITLE￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- site￨L￨NN￨O￨- occupancy￨L￨NN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dp￨L￨NNP￨O￨- Pow￨U￨NNP￨O￨- dt￨L￨NNP￨O￨A -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- p￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- colonization￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- m￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- morality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- local￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asHellRank￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- Hellinger-based￨U￨JJ￨MISC￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨- for￨L￨IN￨O￨- bipartite￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networksAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsSeyed￨L￨NNP￨O￨- Mohammad￨U￨NNP￨PERSON￨- TaheriHamidreza￨U￨NNP￨PERSON￨- MahyarMohammad￨U￨NNP￨PERSON￨- FirouziElahe￨U￨NNP￨O￨- Ghalebi￨U￨NNP￨MISC￨- K.Radu￨U￨NNP￨MISC￨- GrosuAli￨U￨NNP￨MISC￨- MovagharOpen￨U￨NNP￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- ArticleFirst￨U￨NNP￨MISC￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1.5￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractMeasuring￨U￨VBG￨O￨- centrality￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- bipartite￨L￨JJ￨O￨- mode￨L￨NN￨O￨- ,￨L￨,￨O￨- poses￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- requirement￨L￨NN￨O￨- of￨L￨IN￨O￨- full￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- properly￨L￨RB￨O￨- detecting￨L￨VBG￨O￨- top-k￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- representative￨L￨JJ￨TITLE￨- users￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- partial￨L￨JJ￨O￨- ranking￨L￨JJ￨O￨- similarity￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- HellRank￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- conventional￨L￨JJ￨O￨- metrics￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Kendall￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Spearman￨U￨NNP￨PERSON￨- rank￨L￨NN￨O￨- correlation￨L￨NN￨O￨- coefficient.KeywordsBipartite￨L￨NN￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- Top-k￨U￨JJ￨MISC￨- central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- Hellinger￨U￨NNP￨O￨- distance￨L￨NN￨O￨- Recommender￨U￨NN￨MISC￨- systems￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSocial￨U￨NNP￨O￨- networking￨L￨VBG￨O￨- sites￨L￨NNS￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- important￨L￨JJ￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- modern￨L￨JJ￨O￨- society￨L￨NN￨O￨- with￨L￨IN￨O￨- hundreds￨L￨NNS￨O￨- of￨L￨IN￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨- nowadays￨L￨RB￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- overcome￨L￨VB￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- mentioned￨L￨VBN￨O￨- challenges￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- HellRank￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- accurate￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- bipartite￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- experimentally￨L￨RB￨O￨- evaluate￨L￨VBP￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HellRank￨U￨NNP￨O￨- measure￨L￨NN￨O￨- in￨L￨IN￨O￨- correlation￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- on￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +HellRank￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Hellinger￨U￨NNP￨O￨- distance￨L￨NN￨O￨A between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- side￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- bipartite￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- features￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Epi-features￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- included￨L￨VBD￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- output￨L￨NN￨O￨- of￨L￨IN￨O￨- forecasting￨L￨NN￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- provide￨L￨VBP￨O￨- suitable￨L￨JJ￨O￨- error￨L￨NN￨O￨A measures￨L￨VBZ￨O￨- that￨L￨DT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- methods￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- Epi-features￨U￨NNS￨MISC￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- framework￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- combining￨L￨VBG￨O￨- different￨L￨JJ￨O￨- features￨L￨NNS￨O￨- ,￨L￨,￨O￨- error￨L￨NN￨O￨A measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ranking￨L￨JJ￨O￨- schema￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- forecasts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Further￨U￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- experimental￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- no￨L￨DT￨O￨- single￨L￨JJ￨O￨- method￨L￨NN￨O￨- dominates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- in￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- all￨L￨DT￨O￨- Epi-features￨U￨NNS￨MISC￨- when￨L￨WRB￨O￨- evaluated￨L￨VBN￨O￨- across￨L￨IN￨O￨- error￨L￨NN￨O￨A measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- different￨L￨JJ￨O￨- error￨L￨NN￨O￨A measures￨L￨VBZ￨O￨- lead￨L￨NN￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- rankings￨L￨NNS￨O￨- even￨L￨RB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- Epi-feature￨U￨NN￨MISC￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- geometric￨L￨JJ￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- resolve￨L￨VB￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- asymptotical￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- with￨L￨IN￨O￨- bilinear￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rates.Motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- HIV/AIDS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stability￨U￨NN￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A and￨L￨CC￨O￨- treatmentJianwen￨L￨NN￨O￨- Jia1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Gailing￨U￨NN￨O￨- Qin1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2017:136￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractAn￨U￨NNP￨O￨- HIV/AIDS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HIV/AIDS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model.In￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨A plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- carrying￨L￨VBG￨O￨- out￨L￨RP￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- geometric￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Anderson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- R.M.￨U￨NNP￨PERSON￨- May￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- Infectious￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨A :￨L￨:￨O￨- Dynamics￨U￨NNP￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Scholar2.H.W￨U￨NNP￨O￨- .￨L￨.￨O￨- +KeywordsComputational￨U￨NNP￨O￨- Methods￨U￨NNS￨O￨- Download￨U￨VBP￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨A the￨L￨DT￨O￨- full￨L￨JJ￨O￨- article￨L￨NN￨O￨- textReferences1.R.M￨L￨NN￨O￨- .￨L￨.￨O￨- +Hethcote￨U￨NNP￨O￨- ,￨L￨,￨O￨- SIAM￨U￨NNP￨COUNTRY￨- Rev.￨U￨NNP￨TITLE￨- 42￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 599￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- MathSciNetCrossRefADSGoogle￨U￨NNP￨O￨- Scholar3.T￨U￨NNP￨O￨- .￨L￨.￨O￨- +1.2￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- new￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vicinity￨L￨NN￨O￨- travel-blocking￨L￨NN￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- We￨U￨PRP￨O￨- suggest￨L￨VBP￨O￨- here￨L￨RB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- multi-regions￨L￨JJ￨O￨- discrete-time￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial-temporal￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- which￨L￨WDT￨O￨- emerges￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- domain￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- Ω￨U￨NN￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- grid￨L￨NN￨O￨- of￨L￨IN￨O￨- colored￨L￨VBN￨O￨- cells￨L￨NNS￨O￨A which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- uniform￨L￨JJ￨O￨- in￨L￨IN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- suggest￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- approach￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- travel-blocking￨L￨JJ￨O￨- vicinity￨L￨NN￨O￨- strategy￨L￨NN￨O￨- which￨L￨WDT￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- a￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- cells￨L￨NNS￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- patch￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- restricting￨L￨VBG￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighboring￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- .￨L￨.￨O￨- +Explicitly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- an￨L￨DT￨O￨- objective￨L￨JJ￨O￨- function￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- cells￨L￨NNS￨O￨A or￨L￨CC￨O￨- patch￨L￨NN￨O￨- with￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- m￨L￨NN￨O￨- M￨U￨NN￨O￨- ,￨L￨,￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- system￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- C￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- *￨L￨SYM￨O￨- q￨L￨SYM￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- controls￨L￨NNS￨O￨- functions￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- as￨L￨IN￨O￨- effectiveness￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- travel-blocking￨L￨JJ￨O￨- operations￨L￨NNS￨O￨- followed￨L￨VBD￨O￨- between￨L￨IN￨O￨- P￨U￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- harvest￨L￨NN￨O￨- by￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A flocculant￨L￨NN￨O￨- inputTongqian￨L￨NN￨O￨- Zhang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Wanbiao￨U￨NNP￨O￨- Ma1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Xinzhu￨U￨NN￨O￨- Meng2￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2017:115￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractA￨U￨NNP￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- continuous￨L￨JJ￨O￨- microbial￨L￨JJ￨O￨- culture￨L￨NN￨O￨- and￨L￨CC￨O￨- harvest￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- chemostat￨L￨NN￨O￨- ,￨L￨,￨O￨- incorporating￨L￨VBG￨O￨- a￨L￨DT￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- and￨L￨CC￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- and￨L￨CC￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- DDEs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- microbial￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- culture￨L￨NN￨O￨A and￨L￨CC￨O￨- harvest￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- F￨U￨NN￨O￨- t￨L￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- concentration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- substrate￨L￨NN￨O￨- ,￨L￨,￨O￨- microbia￨L￨NN￨O￨- and￨L￨CC￨O￨- flocculating￨L￨VBG￨O￨- agent￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- culture￨L￨NN￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- and￨L￨CC￨O￨- impulsive￨L￨JJ￨O￨A harvest￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- x￨L￨CC￨O￨- F￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- T￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨- effect￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- F￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- gamma￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- input￨L￨NN￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- flocculant￨L￨NN￨O￨- at￨L￨IN￨O￨- every￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨- period￨L￨NN￨O￨- T.￨U￨FW￨O￨- +Analysis￨U￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- microbial￨L￨JJ￨O￨- culture￨L￨NN￨O￨- and￨L￨CC￨O￨- harvest￨L￨NN￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- by￨L￨IN￨O￨- adjusting￨L￨VBG￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- ,￨L￨,￨O￨- impulsive￨L￨JJ￨O￨A period￨L￨NN￨O￨- or￨L￨CC￨O￨- input￨L￨NN￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- flocculant￨L￨NN￨O￨- .￨L￨.￨O￨- +Theoretical￨U￨JJ￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- microbe-extinction￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- permanent￨L￨JJ￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨- .￨L￨.￨O￨- +Biologically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- result￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- significance￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- incubation￨L￨NN￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- small￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- phase￨L￨NN￨O￨- will￨L￨MD￨O￨- enhance￨L￨VB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- state￨L￨NN￨O￨- if￨L￨IN￨O￨- both￨L￨DT￨O￨- components￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- are￨L￨VBP￨O￨- non-trivial￨L￨JJ￨O￨- ;￨L￨:￨O￨- otherwise￨L￨RB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- will￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- disturbed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- illustrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- stability￨L￨NN￨O￨A theorem.KeywordsSEIRS￨L￨NN￨O￨- modelstochastic￨L￨JJ￨O￨- transmissionalmost￨L￨NN￨O￨- sure￨L￨JJ￨O￨- exponential￨L￨JJ￨O￨- stability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionIn￨U￨NN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- articles￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- published￨L￨VBN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- sufficiently￨L￨RB￨O￨- small￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨A parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- exponential￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- whenever￨L￨WRB￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- invariant￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- below￨L￨IN￨O￨- unity￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- being￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- Novel￨U￨JJ￨O￨- Method￨U￨NN￨O￨- of￨L￨IN￨O￨- Evaluating￨U￨VBG￨O￨- Knee￨U￨NN￨O￨- Joint￨U￨NNP￨O￨- Stability￨U￨NN￨O￨- of￨L￨IN￨O￨- Patients￨U￨NNS￨O￨- with￨L￨IN￨O￨- Knee￨U￨NN￨O￨- Osteoarthritis￨U￨NN￨O￨- :￨L￨:￨O￨- Multiscale￨U￨NNP￨ORGANIZATION￨- Entropy￨U￨NNP￨ORGANIZATION￨- Analysis￨U￨NN￨ORGANIZATION￨- with￨L￨IN￨O￨- A￨U￨DT￨O￨- Knee-Aiming￨U￨JJ￨O￨- Task￨U￨NNP￨O￨- Diange￨U￨NNP￨O￨- Zhou1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Shijie￨U￨NNP￨PERSON￨- Zhang2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hui￨U￨NNP￨O￨- Zhang2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Long￨U￨NNP￨O￨- Jiang1￨U￨NN￨O￨- ,￨L￨,￨O￨- Jue￨U￨NN￨O￨- Zhang2￨U￨NN￨O￨- ,3￨L￨NN￨O￨- &￨L￨CC￨O￨- Jing￨U￨NNP￨O￨- Fang2￨U￨NNP￨O￨- ,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 354￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- OsteoarthritisQuality￨U￨NNP￨O￨- of￨L￨IN￨O￨- lifeStatistics￨L￨NNPS￨O￨- AbstractDeteriorating￨U￨NNP￨O￨- knee￨L￨NN￨O￨- stability￨L￨NN￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factor￨L￨NN￨O￨- that￨L￨WDT￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- aggregative￨L￨NN￨O￨- of￨L￨IN￨O￨- osteoarthritis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- OA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- attempt￨L￨VBP￨O￨- to￨L￨TO￨O￨- depict￨L￨VB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- knee￨L￨NN￨O￨- joint￨L￨NN￨O￨A from￨L￨IN￨O￨- a￨L￨DT￨O￨- holistic￨L￨JJ￨O￨- viewpoint￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- index￨L￨NN￨O￨- of￨L￨IN￨O￨- knee￨L￨NN￨O￨- joint￨L￨JJ￨O￨- stability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IKJS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- thus￨L￨RB￨O￨- extracted￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compared￨L￨VBD￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- of￨L￨IN￨O￨- IKJS￨U￨NN￨O￨- in￨L￨IN￨O￨- 57￨L￨CD￨NUMBER￨- healthy￨L￨JJ￨O￨- volunteers￨L￨NNS￨O￨- and￨L￨CC￨O￨- 55￨L￨CD￨NUMBER￨- patients￨L￨NNS￨O￨A with￨L￨IN￨O￨- OA￨U￨NN￨O￨- before￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- total￨L￨JJ￨O￨- knee￨L￨NN￨O￨- replacement￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TKR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- conclusion￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- IKJS￨U￨NNS￨ORGANIZATION￨- that￨L￨WDT￨O￨- employs￨L￨VBZ￨O￨- the￨L￨DT￨O￨- knee-aiming￨L￨JJ￨O￨- task￨L￨NN￨O￨- is￨L￨VBZ￨O￨- feasible￨L￨JJ￨O￨- for￨L￨IN￨O￨- quantitatively￨L￨RB￨O￨- determining￨L￨VBG￨O￨- knee￨L￨NN￨O￨- stability￨L￨NN￨O￨A .￨L￨.￨O￨- +Also￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- IKJS￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- operated￨L￨VBN￨O￨- leg￨L￨NN￨O￨- in￨L￨IN￨O￨- patients￨L￨NNS￨O￨A with￨L￨IN￨O￨- knee￨L￨NN￨O￨- OA￨U￨NN￨O￨- increased￨L￨VBD￨O￨- remarkably￨L￨RB￨O￨- after￨L￨IN￨O￨- TKR￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- <￨L￨JJR￨O￨- 0.0001￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- numeric￨L￨JJ￨O￨- replications￨L￨NNS￨O￨- for￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- are￨L￨VBP￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- attained￨L￨VBN￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- good￨L￨JJ￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- theoretical￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- displaying￨L￨VBG￨O￨- a￨L￨DT￨O￨- vital￨L￨JJ￨O￨- perception￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A coupled￨L￨VBN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- babesiosis￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- tick￨L￨VB￨O￨- populations.Keywordsbovine￨L￨NN￨O￨- babesiosisstabilitypredictor-corrector￨L￨NN￨O￨- techniquereproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionBovine￨U￨NNP￨O￨- babesiosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BB￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- communicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- bite￨L￨NN￨O￨- of￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- bovine￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- humid￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Fractional-order￨U￨NN￨MISC￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- babesiosis￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- tick￨L￨VB￨O￨- populationsZain￨L￨NNP￨O￨- Ul￨U￨NNP￨O￨- Abadin￨U￨NNP￨O￨- Zafar1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Kashif￨U￨NNP￨PERSON￨- Rehan3￨U￨NN￨O￨- and￨L￨CC￨O￨- M￨U￨NN￨O￨- Mushtaq1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2017:86￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- article￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- earlier￨L￨JJR￨O￨- suggested￨L￨VBN￨O￨- in￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- philosophy￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- reliable￨L￨JJ￨O￨- agenda￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- comportment￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- worldwide￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- StrictLessThan￨U￨NNP￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- verified￨L￨VBN￨O￨- by￨L￨IN￨O￨- comparison￨L￨NN￨O￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- parameter￨L￨NN￨O￨- StrictLessThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- LaSalle-Lyapunov￨U￨NNP￨O￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A free￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DFE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- introduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- babesiosis￨L￨NN￨O￨- and￨L￨CC￨O￨- tick￨L￨VB￨O￨- populations￨L￨NNS￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- frequently￨L￨RB￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- modeling￨L￨NN￨O￨- memory-dependent￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- physical￨L￨JJ￨O￨- and￨L￨CC￨O￨- life￨L￨NN￨O￨- sciences￨L￨NNS￨O￨- that￨L￨WDT￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨A derivatives￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- better￨L￨JJR￨O￨- agreement￨L￨NN￨O￨- between￨L￨IN￨O￨- solutions￨L￨NNS￨O￨- and￨L￨CC￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- integer￨L￨NN￨O￨- order￨L￨NN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- constant.The￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- constant￨L￨JJ￨O￨- are￨L￨VBP￨O￨- classical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- given￨L￨VBN￨O￨- for￨L￨IN￨O￨- short-term￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +What￨U￨WP￨O￨- is￨L￨VBZ￨O￨- more￨L￨JJR￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- choice￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- function￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- gives￨L￨VBZ￨O￨- a￨L￨DT￨O￨- classical￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- population.We￨L￨NN￨O￨- also￨L￨RB￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- memory￨L￨NN￨O￨A dependence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- obesity￨L￨NN￨O￨- contagion￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- A￨U￨DT￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- obesity￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- non-constant￨L￨JJ￨O￨- populationElif￨L￨NN￨O￨- Demirci1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2017:79￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- fractional￨L￨JJ￨O￨- order￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- obesity￨L￨NN￨O￨- contagion￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- also￨L￨RB￨O￨- considered￨L￨VBD￨O￨- obesity￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- gave￨L￨VBD￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- obesity￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 129￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 141￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asA￨L￨NN￨O￨- slow-fast￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- decomposition￨L￨NN￨O￨- links￨L￨NNS￨O￨- neutral￨L￨JJ￨IDEOLOGY￨A and￨L￨CC￨O￨- non-neutral￨L￨JJ￨O￨- coexistence￨L￨NN￨O￨- in￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- multi-strain￨L￨JJ￨O￨- pathogensAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsErida￨L￨NN￨MISC￨- GjiniSten￨U￨NN￨MISC￨- MadecOpen￨U￨NN￨MISC￨- AccessORIGINAL￨U￨NN￨MISC￨- PAPERFirst￨U￨NN￨MISC￨- Online￨U￨NN￨MISC￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 858￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- AbstractUnderstanding￨U￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- multi-type￨L￨JJ￨O￨- microbial￨L￨JJ￨O￨- ecosystems￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenge￨L￨NN￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- advancing￨L￨VBG￨O￨- molecular￨L￨JJ￨O￨- technologies￨L￨NNS￨O￨- for￨L￨IN￨O￨- diversity￨L￨NN￨O￨- resolution￨L￨NN￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- slow-fast￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- approach￨L￨VBP￨O￨- interpolates￨L￨VBZ￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- neutral￨L￨JJ￨IDEOLOGY￨A and￨L￨CC￨O￨- non-neutral￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- multi-strain￨L￨JJ￨O￨- coexistence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- quantifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- asymmetries￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- maintenance￨L￨NN￨O￨- and￨L￨CC￨O￨- stabilisation￨L￨NN￨O￨- of￨L￨IN￨O￨- diversity.KeywordsNeutrality￨L￨NN￨O￨- Diversity￨U￨NN￨O￨- Slow￨U￨JJ￨O￨- manifold￨L￨NN￨O￨- Epidemiological￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- Coinfection￨U￨NNP￨O￨- Competition￨U￨NNP￨O￨- Cooperation￨U￨NNP￨O￨- The￨U￨NNP￨O￨- original￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- was￨L￨VBD￨O￨- revised￨L￨VBN￨O￨- :￨L￨:￨O￨- Mistakes￨U￨NNS￨O￨- were￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- publishing￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- Goldstone￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- idea￨L￨NN￨O￨- of￨L￨IN￨O￨- slow￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- spontaneously￨L￨RB￨O￨- broken￨L￨VBN￨O￨- symmetries￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- direct￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- in￨L￨IN￨O￨- co-colonization￨L￨NN￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- competition￨L￨NN￨O￨- to￨L￨TO￨O￨- facilitation￨L￨NN￨O￨- between￨L￨IN￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- the￨L￨DT￨O￨- reader￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- user￨L￨NN￨O￨- friendly￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- techniques￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- that￨L￨WDT￨O￨- exists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- ecological￨L￨JJ￨O￨- science￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- pitfalls￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- avoided￨L￨VBN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- introduction￨L￨NN￨O￨- to￨L￨TO￨O￨- inference￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- from￨L￨IN￨O￨- spatiotemporal￨L￨JJ￨O￨A datasets.KeywordsEpidemiology￨L￨NNP￨O￨- Modelling￨U￨NNP￨O￨- Bayesian￨U￨NNP￨O￨- Inference￨U￨NNP￨O￨- Simulation￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- Spatio-temporal￨U￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSpatiotemporal￨U￨NNP￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- those￨L￨DT￨O￨- that￨L￨WDT￨O￨- contain￨L￨VBP￨O￨- both￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- location￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- review￨L￨VB￨O￨- some￨L￨DT￨O￨- useful￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- pertinent￨L￨JJ￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- spatiotemporal￨L￨JJ￨O￨A dataset￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- generated￨L￨VBN￨O￨- datasets￨L￨NNS￨O￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- techniques￨L￨NNS￨O￨- .2￨L￨NN￨NUMBER￨- Network￨U￨NNP￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- spatiotemporal￨L￨JJ￨O￨- dataPurely￨L￨NNP￨O￨- spatial￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- confounded￨L￨VBN￨O￨- in￨L￨IN￨O￨- modelling￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- occasional￨L￨JJ￨O￨- long-distance￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Martínez-Ló￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- “￨L￨``￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ”￨L￨''￨O￨- .￨L￨.￨O￨- +Traditionally￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- common￨L￨JJ￨O￨A to￨L￨TO￨O￨- ignore￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- instead￨L￨RB￨O￨- process￨L￨NN￨O￨- known￨L￨JJ￨O￨- or￨L￨CC￨O￨- modelled￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- analysis￨L￨NN￨O￨- :￨L￨:￨O￨- common￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- included￨L￨VBN￨O￨- aggregation￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- over￨L￨IN￨O￨- some￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- time￨L￨NN￨O￨- frame￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- snapshot￨L￨NN￨O￨- ”￨L￨''￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- taking￨L￨VBG￨O￨- an￨L￨DT￨O￨- average￨L￨JJ￨O￨- network￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- longer￨L￨JJR￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- a￨L￨DT￨O￨- phenomenological￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- write￨L￨VB￨O￨- simple￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- solve￨L￨VB￨O￨- them￨L￨PRP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- farms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- spatially￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- temporally￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- potentially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- animals￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- veterinary￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨DATE￨- may￨L￨MD￨DATE￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- records￨L￨NNS￨O￨- of￨L￨IN￨O￨- tests￨L￨NNS￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- location￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- a￨L￨DT￨O￨- farm￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- or￨L￨CC￨O￨- simply￨L￨RB￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- recording￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- mandated￨L￨VBN￨O￨- by￨L￨IN￨O￨- governments￨L￨NNS￨O￨- and￨L￨CC￨O￨- provides￨L￨VBZ￨O￨- researchers￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- wealth￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- algorithm￨L￨NN￨O￨- is￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- by￨L￨IN￨O￨- exploiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model.Consider￨L￨NN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- system￨L￨NN￨O￨- representing￨L￨VBG￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- x￨L￨CC￨O￨- Add￨U￨VB￨O￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- f￨L￨FW￨O￨- bigl￨L￨FW￨O￨- x￨L￨CC￨O￨- k￨L￨NN￨O￨- Mul￨U￨NN￨O￨- mathbf￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- p￨L￨NN￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨A x￨L￨CC￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- vector￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- mathbf￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- p￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- l￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- R￨U￨NN￨O￨- l￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- Mul￨U￨NN￨O￨- f￨L￨FW￨O￨- Pow￨U￨FW￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- mathbb￨L￨VBG￨O￨- -1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuously￨L￨RB￨O￨- differentiable￨L￨JJ￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- execute￨L￨VB￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- task￨L￨NN￨O￨- ,￨L￨,￨O￨- first￨L￨RB￨ORDINAL￨- one￨L￨CD￨NUMBER￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- the￨L￨DT￨O￨- identifiability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- unknown￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- impossible￨L￨JJ￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- problem.Identification￨L￨NN￨O￨- of￨L￨IN￨O￨- systems￨L￨NNS￨O￨- deals￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨A of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- previous￨L￨JJ￨O￨- information￨L￨NN￨O￨- available￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- a￨L￨DT￨O￨- parameterized￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- uniquely￨L￨RB￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- since￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- experimental￨L￨JJ￨O￨- design￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- using￨L￨VBG￨O￨- experimental￨L￨JJ￨O￨- data.The￨L￨NN￨O￨- identifiability￨L￨NN￨O￨- problem￨L￨NN￨O￨A is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- determination￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- parameter￨L￨NN￨O￨- sets￨L￨NNS￨O￨- which￨L￨WDT￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- input-output￨L￨JJ￨O￨- response￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- problem￨L￨NN￨O￨- this￨L￨DT￨O￨- linear￨L￨JJ￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- Equality￨U￨NN￨O￨- x￨L￨CC￨O￨- Add￨U￨VB￨O￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- A￨U￨NN￨O￨- Mul￨U￨NN￨O￨- mathbf￨L￨NN￨O￨- p￨L￨NN￨O￨- x￨L￨CC￨O￨- k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NN￨O￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨A A￨U￨NN￨O￨- Mul￨U￨NN￨O￨- mathbf￨L￨NN￨O￨- p￨L￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Add￨U￨VB￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- mu￨L￨NN￨O￨- Equality￨U￨NN￨O￨- Derivative￨U￨JJ￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Add￨U￨VB￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- alpha￨L￨NN￨O￨- mu￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- sigma￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- sigma￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨JJ￨O￨- eta￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- mu￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- percentages￨L￨NNS￨O￨- of￨L￨IN￨O￨- uninfected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- no￨L￨DT￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- latent￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- breaking￨L￨VBG￨O￨- out￨L￨RP￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- quarantined￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- computers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- external￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Internet￨U￨NN￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- internal￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- disconnected￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Internet￨U￨NN￨MISC￨- ;￨L￨:￨O￨- σ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- crashing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- computers￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- δ￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Stability￨U￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcationAccording￨L￨NNP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- obtain￨L￨VB￨O￨- that￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Add￨U￨VB￨O￨- alpha￨L￨NN￨O￨- mu￨L￨NN￨O￨A Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨MISC￨- mu￨L￨NN￨MISC￨- Add￨U￨VB￨MISC￨- alpha￨L￨NN￨O￨- gamma￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- The￨U￨DT￨O￨- linearized￨L￨VBN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- L￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- L￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 32￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 33￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 43￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 44￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 54￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- B￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 55￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- b￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 53￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- The￨U￨DT￨O￨- characteristic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Add￨U￨VB￨O￨- p￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- p￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 5￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- tau￨L￨VBD￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- q￨L￨VB￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- q￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- When￨U￨WRB￨O￨- Equality￨U￨NNP￨O￨- tau￨L￨VBD￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Suppose￨U￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- inequalities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- satisfied￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- condition￨L￨NN￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Then￨U￨RB￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable.For￨L￨JJ￨O￨- StrictGreaterThan￨U￨NNP￨O￨- tau￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- Equality￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- omega￨L￨FW￨O￨- StrictGreaterThan￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- this￨L￨DT￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- delayed￨L￨VBN￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨A S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Add￨U￨VB￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- mu￨L￨NN￨O￨- Equality￨U￨NN￨O￨- Derivative￨U￨JJ￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Add￨U￨VB￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- alpha￨L￨NN￨O￨- mu￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- sigma￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- sigma￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨JJ￨O￨- eta￨L￨NN￨O￨- B￨U￨NN￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- tau￨L￨FW￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- mu￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Qualitative￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- breaking-out￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- InternetZizhen￨U￨NNP￨O￨- Zhang1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Yougang￨U￨NN￨O￨- Wang1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2017:31￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- generalize￨L￨VB￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- SLBQRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clean￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- breaking￨L￨VBG￨O￨- out￨L￨RP￨O￨- computers￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- quarantined￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- .￨L￨.￨O￨- +DAVA￨U￨NNP￨PERSON￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- treats￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- sub-graphs￨L￨NNS￨O￨- as￨L￨IN￨O￨- super￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- all￨L￨DT￨O￨- its￨L￨PRP$￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- neighbors￨L￨NNS￨O￨- as￨L￨IN￨O￨- rooted￨L￨JJ￨O￨- bidirectional￨L￨JJ￨O￨- sub-trees￨L￨NNS￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- representational￨L￨JJ￨O￨- optimal￨L￨JJ￨O￨- solution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- adjacent￨L￨JJ￨O￨A neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- root￨L￨NN￨O￨- super￨L￨JJ￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- node￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- solution￨L￨NN￨O￨A that￨L￨WDT￨O￨- seeks￨L￨VBZ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- local￨L￨JJ￨O￨- recalculations.KeywordsDynamic￨L￨JJ￨O￨- networksImmunizationDominance￨L￨NN￨O￨- tree￨L￨NN￨O￨- BackgroundEvent￨U￨NN￨O￨- propagation￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complex￨L￨NN￨O￨- and￨L￨CC￨O￨- frequently￨L￨RB￨O￨- studied￨L￨VBN￨O￨- human￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- trivial￨L￨JJ￨O￨- situation￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- available￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- non-infected￨L￨JJ￨O￨- adjacent￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- effective￨L￨JJ￨O￨- solution￨L￨NN￨O￨A for￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- sparse￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- Data-Aware￨U￨NNP￨O￨- Vaccine￨U￨NNP￨O￨- Allocation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- DAVA￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2095￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asAgent-based￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A diffusionAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsEllen-Wien￨L￨JJ￨O￨- AugustijnTom￨U￨NN￨MISC￨- DoldersumJuliana￨U￨NNP￨MISC￨- UseyaDenie￨U￨NNP￨MISC￨- AugustijnOpen￨U￨NNP￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- PaperFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 05￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1.5￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- introduces￨L￨VBZ￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- micro-scale￨L￨JJ￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 8,500￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- cumulative￨L￨JJ￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 1.2￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- unusually￨L￨RB￨O￨- high￨L￨JJ￨O￨- figure￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- likely￨L￨JJ￨O￨- attributable￨L￨JJ￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- other￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- unpreparedness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Haitian￨U￨JJ￨NATIONALITY￨- health￨L￨NN￨O￨- infrastructure￨L￨NN￨O￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- such￨L￨PDT￨O￨- an￨L￨DT￨O￨- emergency￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- earthquake￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- low￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- extinction￨L￨NN￨O￨- highlights￨L￨VBZ￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- targeted￨L￨VBN￨O￨- and￨L￨CC￨O￨- effective￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- to￨L￨TO￨O￨- possibly￨L￨RB￨O￨- stop￨L￨VB￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Haiti.KeywordsHaiti￨U￨NNP￨O￨- Cholera￨U￨NNP￨CAUSE_OF_DEATH￨- Extinction￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- Stochastic￨U￨NNP￨O￨- simulator￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionThe￨U￨NNP￨O￨- largest￨L￨JJS￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- ever￨L￨RB￨O￨- recorded￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- pandemic￨L￨JJ￨O￨- wave￨L￨NN￨O￨- is￨L￨VBZ￨O￨- striking￨L￨JJ￨O￨- Haiti￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2055￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asOn￨L￨NN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Haiti￨U￨NNP￨COUNTRY￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A epidemicAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsEnrico￨L￨NNP￨O￨- BertuzzoFlavio￨U￨NNP￨MISC￨- FingerLorenzo￨U￨NNP￨MISC￨- MariMarino￨U￨NNP￨MISC￨- GattoAndrea￨U￨NNP￨MISC￨- RinaldoOpen￨U￨NNP￨MISC￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2.3￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 10￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractMore￨U￨NN￨O￨- than￨L￨IN￨O￨- three￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- its￨L￨PRP$￨O￨- appearance￨L￨NN￨O￨- in￨L￨IN￨O￨- Haiti￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- already￨L￨RB￨O￨- caused￨L￨VBN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 8,500￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- and￨L￨CC￨O￨- 695,000￨L￨CD￨NUMBER￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- feared￨L￨VBN￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- endemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Cholera￨U￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- spatially-explicit￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- hosted￨L￨VBN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- local￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- through￨L￨IN￨O￨- hydrologic￨L￨JJ￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨A mobility￨L￨NN￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- SParSE￨U￨JJ￨O￨- outputs￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- hypersurface￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- filtered￨L￨VBN￨O￨- using￨L￨VBG￨O￨- user-defined￨L￨JJ￨O￨- cost￨L￨NN￨O￨- functions￨L￨NNS￨O￨- or￨L￨CC￨O￨- constraints￨L￨NNS￨O￨- to￨L￨TO￨O￨- further￨L￨JJ￨O￨- refine￨L￨VB￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨A characterization.SParSE￨L￨NN￨O￨- is￨L￨VBZ￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- components￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- multi-level￨L￨JJ￨O￨- cross-entropy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- exponential￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- interpolation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- inverse￨L￨JJ￨O￨- biasing￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- below￨L￨IN￨O￨- for￨L￨IN￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- intrinsic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- even￨L￨RB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- reactions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- multi-level￨L￨JJ￨O￨- CE￨U￨NN￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- exhibit￨L￨VB￨O￨- slow￨L￨JJ￨O￨- convergence￨L￨NN￨O￨A properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- when￨L￨WRB￨O￨- initial￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- are￨L￨VBP￨O￨- far￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- hypersurface￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- Stochastic￨U￨NNP￨O￨- Parameter￨U￨NNP￨O￨- Search￨U￨VB￨O￨- for￨L￨IN￨O￨- Events￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- SParSE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- efficiently￨L￨RB￨O￨- sample￨L￨NN￨O￨- biochemical￨L￨JJ￨O￨- reaction￨L￨NN￨O￨- rate￨L￨NN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- a￨L￨DT￨O￨- user-specified￨L￨JJ￨O￨- target￨L￨NN￨O￨- event￨L￨NN￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- error￨L￨NN￨O￨- tolerance￨L￨NN￨O￨- .￨L￨.￨O￨- +SParSE￨U￨VB￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- components￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- multi-level￨L￨JJ￨O￨- cross-entropy￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- identifies￨L￨VBZ￨O￨- biasing￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- push￨L￨VB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- toward￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨A of￨L￨IN￨O￨- interest￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- related￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- biasing￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- optional￨L￨JJ￨O￨- interpolation￨L￨NN￨O￨- of￨L￨IN￨O￨- identified￨L￨VBN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +SParSE￨U￨VB￨O￨- +￨L￨CC￨O￨- +￨L￨CC￨O￨- makes￨L￨VBZ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- leaping￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- accelerate￨L￨VBP￨O￨- the￨L￨DT￨O￨- convergence￨L￨NN￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- event￨L￨NN￨O￨A ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- low￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨A to￨L￨TO￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- robust￨L￨JJ￨O￨- ,￨L￨,￨O￨- easy￨L￨JJ￨O￨- ,￨L￨,￨O￨- reliable￨L￨JJ￨O￨- and￨L￨CC￨O￨- quick￨L￨JJ￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- time.KeywordsCryptosporidiosisHomotopyGastrointestinalDecompositionNoninteger￨L￨NN￨O￨- BackgroundHuman￨U￨NN￨O￨- cryptosporidiosis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- cryptosporidium￨L￨NN￨O￨- protozoan￨L￨NN￨O￨- and￨L￨CC￨O￨- constitutes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- gastrointestinal￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- usually￨L￨RB￨O￨- connected￨L￨VBN￨O￨- with￨L￨IN￨O￨- recreational￨L￨JJ￨O￨- water￨L￨NN￨O￨- use￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- Australia￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- other￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Approximate￨U￨JJ￨MISC￨- solution￨L￨NN￨O￨A of￨L￨IN￨O￨- cryptosporidiosis￨L￨NN￨O￨- modelEbenezer￨L￨NN￨O￨- Bonyah1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Abdon￨U￨NNP￨PERSON￨- Atangana2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Kazeem￨U￨NNP￨PERSON￨- Okosun3￨U￨NN￨O￨- and￨L￨CC￨O￨- Muhammad￨U￨NNP￨PERSON￨- Altaf￨U￨NNP￨PERSON￨- Khan4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 3:2￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractCryptosporidium￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- waterborne￨L￨NN￨O￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- faecal￨L￨JJ￨O￨- –￨L￨:￨O￨- oral￨L￨JJ￨O￨- path￨L￨NN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- recreational￨L￨JJ￨O￨- water￨L￨NN￨O￨- facilities￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- numerical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- approximate￨L￨JJ￨O￨A solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- function￨L￨NN￨O￨- form￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- noninteger-order￨L￨JJ￨O￨- derivative￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- probable￨L￨JJ￨O￨- approximate￨L￨JJ￨O￨A solution￨L￨NN￨O￨- of￨L￨IN￨O￨- integer￨L￨NN￨O￨- and￨L￨CC￨O￨- noninteger￨L￨NN￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- cryptosporidiosis￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approximate￨L￨JJ￨O￨A or￨L￨CC￨O￨- estimate￨L￨NN￨O￨- solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- through￨L￨IN￨O￨- recent￨L￨JJ￨O￨- developed￨L￨JJ￨O￨- analytic￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- homotopy￨L￨JJ￨O￨- decomposition￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HDM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- studying￨L￨VBG￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- constrained￨L￨VBN￨O￨A control￨L￨NN￨O￨- ,￨L￨,￨O￨- special￨L￨JJ￨O￨- care￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- given￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- interplay￨L￨NN￨O￨- with￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- effects.KeywordsDisease￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- modelling￨L￨VBG￨O￨- Control￨U￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- Bifurcations￨U￨NNS￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionThere￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- increasing￨L￨VBG￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- integration￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- with￨L￨IN￨O￨- economic￨L￨JJ￨O￨- considerations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- by￨L￨IN￨O￨- constrained￨L￨VBN￨O￨A control￨L￨NN￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- limited￨L￨JJ￨O￨- resources.In￨L￨NN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- select￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- constrained￨L￨VBN￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- its￨L￨PRP$￨O￨- deterministic￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- its￨L￨PRP$￨O￨- simplicity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- mathematically￨L￨RB￨O￨- rich￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- stable￨L￨JJ￨O￨- fixed￨L￨JJ￨O￨- points￨L￨NNS￨O￨- and￨L￨CC￨O￨- stable￨L￨JJ￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨A arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- global￨L￨JJ￨O￨- bifurcations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- despite￨L￨IN￨O￨- its￨L￨PRP$￨O￨- simplicity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- mathematically￨L￨RB￨O￨- rich￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- including￨L￨VBG￨O￨- stable￨L￨JJ￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨A and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- global￨L￨JJ￨O￨- bifurcations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- in￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- mathop￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- constant￨L￨JJ￨O￨- StrictGreaterThan￨U￨NNP￨O￨- xi￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- mathop￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Proof￨U￨NNP￨O￨- By￨U￨IN￨O￨- choosing￨L￨VBG￨O￨- Equality￨U￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- k￨L￨NN￨O￨- Rational￨U￨JJ￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- upsilon￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Equality￨U￨NNP￨O￨- theta￨L￨NN￨O￨A 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- Lemma￨U￨NNP￨LOCATION￨- 2.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- sufficiently￨L￨RB￨O￨- large￨L￨JJ￨O￨- k￨L￨NN￨O￨- and￨L￨CC￨O￨- LessThan￨U￨NN￨MISC￨- StrictLessThan￨U￨NNP￨MISC￨- Add￨U￨VB￨MISC￨- k￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- By￨U￨IN￨O￨- applying￨L￨VBG￨O￨- Lemma￨U￨NNP￨PERSON￨- 2.2￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- Then￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- follows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- Noting￨U￨VBG￨O￨- that￨L￨IN￨O￨- LessThan￨U￨NNP￨MISC￨- StrictLessThan￨U￨NNP￨MISC￨- Add￨U￨VB￨MISC￨- k￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- yields￨L￨NNS￨O￨- that￨L￨WDT￨O￨- Mul￨U￨VBP￨O￨- mathop￨L￨NN￨O￨- sup￨L￨NN￨O￨- This￨U￨DT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- mathop￨L￨VB￨O￨- To￨U￨TO￨O￨- prove￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- choose￨L￨VBP￨O￨- Equality￨U￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- xi￨L￨NN￨O￨- Add￨U￨VB￨O￨- k￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- k￨L￨NN￨O￨- Rational￨U￨JJ￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- upsilon￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Equality￨U￨NNP￨O￨- theta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- Lemma￨U￨NNP￨O￨- 2.2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- persistent￨L￨JJ￨O￨- in￨L￨IN￨O￨- mean￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- mathop￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NN￨O￨- D￨U￨NN￨O￨- Add￨U￨VB￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- sigma￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- mu￨L￨NN￨O￨A phi￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- eta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- phi￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- eta￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- mu￨L￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- phi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- phi￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- eta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- mu￨L￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- phi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- phi￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- eta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- mu￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- mu￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- sigma￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- verified￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- is￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- exponentially￨L￨RB￨O￨- stable￨L￨JJ￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨A -1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- improves￨L￨VBZ￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- permits￨L￨VBZ￨O￨- solutions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- positive￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- theorem￨L￨NN￨O￨- on￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- stability￨L￨NN￨O￨- in￨L￨IN￨O￨- mean￨L￨JJ￨O￨- square￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Subsequently￨U￨NNP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Witbooi￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- integral￨L￨JJ￨O￨A equation￨L￨NN￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- avoid￨L￨VB￨O￨- considering￨L￨VBG￨O￨- various￨L￨JJ￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ad￨L￨NN￨O￨- hoc.The￨L￨NN￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- approach￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- cover￨L￨VB￨O￨- various￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- for￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- on￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- interval￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- or￨L￨CC￨O￨- fractional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- unified￨L￨JJ￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- avoids￨L￨VBZ￨O￨- treating￨L￨VBG￨O￨- these￨L￨DT￨O￨- problems￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- case-by-case￨L￨JJ￨O￨- basis￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Positive￨U￨JJ￨MISC￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- integral￨L￨JJ￨O￨A equations￨L￨NNS￨O￨- with￨L￨IN￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equationsChunfang￨L￨NN￨O￨- Shen1￨U￨NN￨O￨- ,￨L￨,￨O￨- Hui￨U￨NNP￨O￨- Zhou1￨U￨NNP￨O￨- and￨L￨CC￨O￨- Liu￨U￨NNP￨PERSON￨- Yang1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2016:260￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- Guo-Krasnoselskii￨U￨NNP￨LOCATION￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- nonexistence￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- integral￨L￨JJ￨O￨- equation￨L￨NN￨O￨- with￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- generalization￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- for￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- on￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- interval￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- or￨L￨CC￨O￨- fractional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- giving￨L￨VBG￨O￨- some￨L￨DT￨O￨- examples￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- show￨L￨VB￨O￨- how￨L￨WRB￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- on￨L￨IN￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- or￨L￨CC￨O￨- fractional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations.Keywordspositive￨L￨JJ￨O￨- solutionboundary￨L￨JJ￨O￨- value￨L￨NN￨O￨- problemintegral￨L￨JJ￨O￨- equationfixed￨L￨JJ￨O￨- pointconeMSC45C0534B18￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionWe￨U￨NN￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- eigenvalues￨L￨NNS￨O￨- yielding￨L￨VBG￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- integral￨L￨JJ￨O￨A equations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- lambda￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- H1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- f￨L￨LS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Song￨U￨NN￨O￨- and￨L￨CC￨O￨- Chen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- predator-prey￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- structure￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- u￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- immature￨L￨JJ￨O￨- and￨L￨CC￨O￨- mature￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- t￨L￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- predator.Positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- n-dimensional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- system￨L￨NN￨O￨- or￨L￨CC￨O￨- fractional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- boundary￨L￨NN￨O￨A conditions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- received￨L￨VBN￨O￨- wide￨L￨JJ￨O￨- attention￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- distinguished￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- in￨L￨IN￨O￨- engineering￨L￨NN￨O￨- ,￨L￨,￨O￨- science￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- biology￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- nonexistence￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- integral￨L￨JJ￨O￨A equation￨L￨NN￨O￨- system￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- H1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- H2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- so￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- may￨L￨MD￨O￨- include￨L￨VB￨O￨- some￨L￨DT￨O￨- known￨L￨JJ￨O￨- results￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- unconsidered￨L￨JJ￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- formulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- integral￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- like￨L￨IN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- Quebec￨U￨NNP￨STATE_OR_PROVINCE￨- City￨U￨NNP￨LOCATION￨- presents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- location￨L￨NN￨O￨- for￨L￨IN￨O￨- expansion￨L￨NN￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- as￨L￨RB￨O￨- ,￨L￨,￨O￨- Las￨U￨NNP￨CITY￨- Vegas￨U￨NNP￨CITY￨- is￨L￨VBZ￨O￨- suboptimal.KeywordsLocational￨L￨JJ￨O￨- QualityGreat￨U￨NNP￨ORGANIZATION￨- Toronto￨U￨NNP￨ORGANIZATION￨- AreaNational￨U￨NNP￨ORGANIZATION￨- Hockey￨U￨NN￨ORGANIZATION￨- LeagueSeason￨U￨NN￨O￨- TicketBasic￨U￨NNP￨O￨- Reproductive￨U￨NNP￨O￨- Ratio￨U￨NNP￨O￨- IntroductionExpansion￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- National￨U￨NNP￨ORGANIZATION￨- Hockey￨U￨NN￨ORGANIZATION￨- League￨U￨NN￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- NHL￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- conversation￨L￨NN￨O￨- topic￨L￨NN￨O￨- of￨L￨IN￨O￨- team￨L￨NN￨O￨- owners￨L￨NNS￨O￨- ,￨L￨,￨O￨- players￨L￨NNS￨O￨- and￨L￨CC￨O￨- fans￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Success￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- NHL￨U￨NN￨ORGANIZATION￨- team￨L￨NN￨O￨- will￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- locational￨L￨JJ￨O￨- quality￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- city￨L￨NN￨O￨A or￨L￨CC￨O￨- geographic￨L￨JJ￨O￨- region￨L￨NN￨O￨- that￨L￨WDT￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- a￨L￨DT￨O￨- team￨L￨NN￨O￨- through￨L￨IN￨O￨- thick￨L￨JJ￨O￨- and￨L￨CC￨O￨- thin￨L￨JJ￨O￨- .￨L￨.￨O￨- +Success￨U￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- expansion￨L￨NN￨O￨A team￨L￨NN￨O￨- will￨L￨MD￨O￨- rely￨L￨VB￨O￨- on￨L￨IN￨O￨- approved￨L￨VBN￨O￨- geographic￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- importantly￨L￨RB￨O￨- fan￨L￨NN￨O￨- support￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- relocation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Atlanta￨U￨NNP￨ORGANIZATION￨- Thrashers￨U￨NNPS￨ORGANIZATION￨- to￨L￨TO￨O￨- Winnipeg￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- team￨L￨NN￨O￨- was￨L￨VBD￨O￨- renamed￨L￨VBN￨O￨- the￨L￨DT￨O￨- Winnipeg￨U￨NNP￨ORGANIZATION￨- Jets￨U￨NNS￨ORGANIZATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- the￨L￨DT￨O￨- Phoenix￨U￨NNP￨ORGANIZATION￨- Coyotes￨U￨NNPS￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- speculation￨L￨NN￨O￨- that￨L￨IN￨O￨- Quebec￨U￨NNP￨STATE_OR_PROVINCE￨- City￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- Quebec￨U￨NNP￨ORGANIZATION￨- Nordiques￨U￨NNPS￨ORGANIZATION￨- were￨L￨VBD￨O￨- moved￨L￨VBN￨O￨- to￨L￨TO￨O￨- form￨L￨VB￨O￨- the￨L￨DT￨O￨- Colorado￨U￨NNP￨ORGANIZATION￨- Avalanche￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- could￨L￨MD￨O￨- provide￨L￨VB￨O￨- an￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- location￨L￨NN￨O￨- for￨L￨IN￨O￨- relocation￨L￨NN￨O￨- or￨L￨CC￨O￨- expansion￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- this￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨A structure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- assessed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ways￨L￨NNS￨O￨- :￨L￨:￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- predictions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- routine￨L￨JJ￨O￨- drug￨L￨NN￨O￨- therapy￨L￨NN￨O￨- ,￨L￨,￨O￨- general￨L￨JJ￨TITLE￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- VC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- mass￨L￨NN￨O￨- drug￨L￨NN￨O￨- administration￨L￨NN￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- these￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- between￨L￨IN￨O￨- models￨L￨NNS￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- among￨L￨IN￨O￨- other￨L￨JJ￨O￨- things￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- and￨L￨CC￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- drug￨L￨NN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- introduction￨L￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- Murray￨U￨NNP￨O￨- JD￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2003￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Mathematical￨U￨JJ￨O￨- Biology￨U￨NN￨O￨- II￨U￨CD￨NUMBER￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 18￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- but￨L￨CC￨O￨- different￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- structures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- simple￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- to￨L￨TO￨O￨- complex￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- compared￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- and￨L￨CC￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- policy￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- sensitivity￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨A structure￨L￨NN￨O￨A .￨L￨.￨O￨- +Yet￨U￨CC￨O￨- there￨L￨EX￨O￨- may￨L￨MD￨O￨- still￨L￨RB￨O￨- be￨L￨VB￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- predictions￨L￨NNS￨O￨- between￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- equivalent￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- but￨L￨CC￨O￨- different￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨A structure￨L￨NN￨O￨A .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- single￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨A structure￨L￨NN￨O￨A that￨L￨WDT￨O￨- fits￨L￨VBZ￨O￨- all￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- different￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Ruan￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨A Mul￨U￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- Pow￨U￨NNP￨MISC￨- Add￨U￨VB￨MISC￨- Pow￨U￨NN￨MISC￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- saturated￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- obtained￨L￨VBN￨O￨- rich￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NN￨O￨- model.Wang￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- considered￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- form￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- d￨L￨NN￨O￨- Mul￨U￨NN￨PERSON￨- S￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- I￨U￨PRP￨O￨- a￨L￨DT￨O￨- Pow￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- d￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- removed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- lose￨L￨VBP￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- return￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- Pow￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- policies￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- valid￨L￨JJ￨O￨- contact￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- a￨L￨DT￨O￨- Pow￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- .￨L￨.￨O￨- +He￨U￨PRP￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- Equality￨U￨NN￨O￨- N￨U￨NN￨O￨- Add￨U￨VB￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- a￨L￨DT￨O￨- nonmonotonic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- StrictGreaterThan￨U￨NN￨O￨- f￨L￨FW￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- I￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- StrictGreaterThan￨U￨NNP￨O￨- xi￨L￨NN￨O￨A 0￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- Pow￨U￨VBP￨O￨- f￨L￨SYM￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- xi￨L￨VBP￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- Pow￨U￨VBP￨O￨- f￨L￨SYM￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- I￨U￨PRP￨O￨- xi￨L￨VBP￨O￨- .￨L￨.￨O￨- +Capasso￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Serio￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- delta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- StrictGreaterThan￨U￨NN￨O￨- delta￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- present￨L￨JJ￨DATE￨- ,￨L￨,￨O￨- lots￨L￨NNS￨O￨- of￨L￨IN￨O￨- scholars￨L￨NNS￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- traveling￨L￨VBG￨O￨- wave￨L￨NN￨O￨- solutions￨L￨NNS￨O￨- play￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- long-time￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- reaction-diffusion￨L￨NN￨O￨- models￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 24￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +van￨L￨NN￨O￨- den￨L￨NN￨O￨- Driessche￨U￨NNP￨O￨- and￨L￨CC￨O￨- Watmough￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- also￨L￨RB￨O￨- studied￨L￨VBD￨O￨- an￨L￨DT￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- k￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- StrictGreaterThan￨U￨NNP￨O￨- b￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨PERSON￨- m￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- k￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- see￨L￨VB￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NN￨PERSON￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Lambda￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- mu￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- when￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- Mul￨U￨NN￨PERSON￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- S￨U￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- some￨L￨DT￨O￨- limitations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- exponential￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- Pow￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stochastic￨U￨NNP￨MISC￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- modelBo￨L￨NN￨O￨- Yang1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2016:226￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- latent￨L￨JJ￨O￨- patients￨L￨NNS￨O￨A and￨L￨CC￨O￨- active￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- Mul￨U￨JJ￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A which￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- Pow￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- s￨L￨NNS￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- exchange￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A network￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- analyzes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- properties￨L￨NNS￨O￨- and￨L￨CC￨O￨- correlation￨L￨NN￨O￨- among￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- energy￨L￨NN￨O￨- field￨L￨NN￨O￨- and￨L￨CC￨O￨- graph￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Node￨U￨NN￨MISC￨- importance￨L￨NN￨O￨- evaluation￨L￨NN￨O￨- method￨L￨NN￨O￨- in￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A network￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- energy￨L￨NN￨O￨- field￨L￨NN￨O￨- modelQindong￨L￨NN￨O￨- Sun1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yimin￨U￨NNP￨O￨- Qiao1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Jiamin￨U￨NNP￨O￨- Wang3￨U￨NNP￨O￨- and￨L￨CC￨O￨- Si￨U￨NNP￨O￨- Shen1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2016:199￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- puts￨L￨VBZ￨O￨- forward￨L￨RB￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- importance￨L￨NN￨O￨- evaluation￨L￨NN￨O￨- method￨L￨NN￨O￨- in￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A network￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- energy￨L￨NN￨O￨- field￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- stability￨L￨NN￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A network￨L￨NN￨O￨- performance￨L￨NN￨O￨- .￨L￨.￨O￨- +Appropriate￨U￨JJ￨O￨- node￨L￨NN￨O￨- importance￨L￨NN￨O￨- evaluation￨L￨NN￨O￨A method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- precondition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- node￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- stability￨L￨NN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- internal￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- denote￨L￨VB￨O￨- the￨L￨DT￨O￨- saturation￨L￨NN￨O￨A effect￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- use￨L￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- replace￨L￨VB￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Impact￨U￨NN￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A detoxication￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- virusXianxiu￨L￨NN￨O￨- Zhang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Chuandong￨U￨NNP￨LOCATION￨- Li1￨U￨NN￨O￨- and￨L￨CC￨O￨- Tingwen￨U￨NN￨MISC￨- Huang3￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2016:218￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- detoxication￨L￨NN￨O￨- and￨L￨CC￨O￨- saturation￨L￨NN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- impulsive￨L￨JJ￨O￨A detoxication￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- saturation￨L￨NN￨O￨- effects￨L￨NNS￨O￨- prohibit￨L￨VBP￨O￨- virus￨L￨NN￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- established￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theoretical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- virus-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BRR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨A ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- uniformly￨L￨RB￨O￨- permanent￨L￨JJ￨O￨- when￨L￨WRB￨O￨- BRR￨U￨NN￨ORGANIZATION￨- exceeds￨L￨VBZ￨O￨- unity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- supercritical￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- BRR￨U￨NN￨O￨- equals￨L￨VBZ￨O￨- unity￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- A￨U￨NN￨O￨- coupled￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- government￨L￨NN￨O￨- communication￨L￨NN￨O￨- and￨L￨CC￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- emergenciesJiuping￨L￨VBG￨O￨- Xu1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Mengxiang￨U￨NN￨O￨- Zhang1￨U￨NN￨O￨- and￨L￨CC￨O￨- Jingneng￨U￨NN￨MISC￨- Ni1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2016:208￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- dissemination￨L￨NN￨O￨- of￨L￨IN￨O￨- official￨L￨JJ￨O￨A messages￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- rumors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- both￨L￨DT￨O￨- key￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- in￨L￨IN￨O￨- emergency￨L￨NN￨O￨- situations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Official￨U￨NNP￨O￨- dissemination￨L￨NN￨O￨- of￨L￨IN￨O￨- emergency￨L￨NN￨O￨- event￨L￨NN￨O￨- information￨L￨NN￨O￨- through￨L￨IN￨O￨- official￨L￨NN￨O￨A and￨L￨CC￨O￨- sanctioned￨L￨VBN￨O￨- channels￨L￨NNS￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- public￨L￨NN￨O￨- ’s￨L￨POS￨O￨- behavior￨L￨NN￨O￨- since￨L￨IN￨O￨- false￨L￨JJ￨O￨- rumors￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- quashed￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- information￨L￨NN￨O￨- confirmed￨L￨VBD￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rapid￨L￨JJ￨O￨- dissemination￨L￨NN￨O￨- of￨L￨IN￨O￨- government￨L￨NN￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- and￨L￨CC￨O￨- essential￨L￨JJ￨O￨- measure￨L￨NN￨O￨- to￨L￨TO￨O￨- combat￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- false￨L￨JJ￨O￨- rumors￨L￨NNS￨O￨A and￨L￨CC￨O￨- to￨L￨TO￨O￨- guide￨L￨VB￨O￨- public￨L￨JJ￨O￨- opinion￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- coupled￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- established￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- official￨L￨JJ￨O￨A government￨L￨NN￨O￨- communiques￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- rumors￨L￨NNS￨O￨- during￨L￨IN￨O￨- emergencies￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- discussed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- official￨L￨JJ￨O￨A message￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- has￨L￨VBZ￨O￨- positive￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- thwarting￨L￨VBG￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Influence￨U￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- mobility￨L￨NN￨O￨- on￨L￨IN￨O￨- virus￨L￨NN￨O￨- spreading￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨A in￨L￨IN￨O￨- multi-hop￨L￨JJ￨O￨- networkPeng￨L￨NN￨O￨- Li1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Siyu￨U￨NN￨O￨- Liu1￨U￨NN￨O￨- ,￨L￨,￨O￨- Jiyu￨U￨NNP￨PERSON￨- Jin1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Zhisen￨U￨NN￨MISC￨- Wang1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2016:172￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractMulti-hop￨U￨NNP￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- received￨L￨VBN￨O￨- growing￨L￨VBG￨O￨- attention￨L￨NN￨O￨- recently￨L￨RB￨DATE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- widely￨L￨RB￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- network￨L￨NN￨O￨- communication￨L￨NN￨O￨- technology￨L￨NN￨O￨- .￨L￨.￨O￨- +Virus￨U￨NN￨O￨- spreading￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨A are￨L￨VBP￨O￨- examined￨L￨VBN￨O￨- through￨L￨IN￨O￨- contact￨L￨NN￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- communication￨L￨NN￨O￨- radius￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- distribution￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- node￨L￨NN￨O￨- mobility￨L￨NN￨O￨- has￨L￨VBZ￨O￨- significant￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- virus￨L￨NN￨O￨- spreading￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stability￨U￨NN￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fractional-order￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- equilibriumsDavood￨L￨NN￨O￨- Rostamy1￨U￨NN￨O￨- and￨L￨CC￨O￨- Ehsan￨U￨NN￨MISC￨- Mottaghi1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2016:170￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- fractional-order￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Caputo￨U￨NNP￨O￨- derivative￨L￨NN￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨VBZ￨O￨- increases￨L￨NNS￨O￨- by￨L￨IN￨O￨- choosing￨L￨VBG￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- α￨L￨NN￨O￨- .￨L￨.￨O￨- +Mathematically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- containing￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- lead￨L￨NN￨O￨- to￨L￨TO￨O￨- multiple￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A points￨L￨NNS￨O￨A and￨L￨CC￨O￨- show￨L￨VBP￨O￨- bifurcation￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- applying￨L￨VBG￨O￨- fractional￨L￨JJ￨O￨A calculus￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- reason￨L￨NN￨O￨- that￨L￨WDT￨O￨- intra-domains￨L￨VBZ￨O￨- interventions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- people￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- domain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- neighborhood￨L￨NN￨O￨- ,￨L￨,￨O￨- town￨L￨NN￨O￨- or￨L￨CC￨O￨- city￨L￨NN￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- travel-blocking￨L￨NN￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- approach￨L￨NN￨O￨- presenting￨L￨VBG￨O￨- inter-domains￨L￨NNS￨O￨- interventions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- health-policy￨L￨NN￨O￨- makers￨L￨NNS￨O￨- could￨L￨MD￨O￨- follow￨L￨VB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- restricting￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- suspicious￨L￨JJ￨O￨- people￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- participate￨L￨VB￨O￨- in￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- HIV/AIDS￨U￨NN￨O￨- via￨L￨IN￨O￨- travel￨L￨NN￨O￨- ,￨L￨,￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- domains￨L￨NNS￨O￨A at￨L￨IN￨O￨- high-risk￨L￨JJ￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- enter￨L￨VB￨O￨- domains￨L￨NNS￨O￨- with￨L￨IN￨O￨- lower￨L￨JJR￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +Sometimes￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most-deadly￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- fact￨L￨NN￨O￨- believed￨L￨VBD￨O￨- that￨L￨IN￨O￨- awareness￨L￨NN￨O￨A may￨L￨MD￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- social￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- for￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- this￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- could￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- consciousness￨L￨NN￨O￨- amongst￨L￨IN￨O￨- children￨L￨NNS￨O￨- and￨L￨CC￨O￨- adults￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Song￨U￨NN￨O￨- and￨L￨CC￨O￨- Pang￨U￨NN￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIQR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infective-quarantined-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- input￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dS￨L￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- sigma￨L￨NN￨O￨A Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- sigma￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- p￨L￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- d￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dR￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- ,￨L￨,￨O￨- quarantined￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- delays￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dS￨L￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨A Add￨U￨VB￨O￨- a￨L￨DT￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- sigma￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- b￨L￨NN￨O￨- d￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dR￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- p￨L￨NN￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- delay￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- f￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- f￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- The￨U￨DT￨O￨- linear￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Case￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- false￨L￨JJ￨O￨- ,￨L￨,￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- reduces￨L￨VBZ￨O￨- to￨L￨TO￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨A m￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Obviously￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- holds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- roots￨L￨NNS￨O￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- must￨L￨MD￨O￨- have￨L￨VB￨O￨- negative￨L￨JJ￨O￨- real￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- Equality￨U￨NNP￨O￨- tau￨L￨FW￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Add￨U￨VB￨O￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨A m￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- lambda￨L￨NN￨ORGANIZATION￨- 3￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- bigl￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- lambda￨L￨NN￨ORGANIZATION￨- 3￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Let￨U￨VB￨O￨- Equality￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- omega￨L￨FW￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- StrictGreaterThan￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- sin￨L￨NN￨O￨- Mul￨U￨NN￨O￨- omega￨L￨JJ￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Add￨U￨VB￨O￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- cos￨L￨NNS￨O￨- Mul￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- m￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 4￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- get￨L￨VB￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 4￨L￨CD￨NUMBER￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 6￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 8￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- Let￨U￨VB￨O￨- Equality￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Define￨U￨VB￨O￨- The￨U￨DT￨O￨- discussion￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- roots￨L￨NNS￨O￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Existence￨U￨NN￨O￨- of￨L￨IN￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcationAccording￨L￨NNP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- computation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨PERSON￨- Pow￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- 4￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- d￨L￨NN￨O￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨A Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- d￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨MISC￨- Pow￨U￨NNP￨MISC￨- A￨U￨NNP￨MISC￨- 2￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- equilibriums￨L￨NNS￨O￨- where￨L￨WRB￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- d￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Let￨U￨VB￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- general￨L￨JJ￨TITLE￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- formulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- gamma￨L￨NN￨O￨A Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- R￨U￨NNP￨O￨- Tuple￨U￨NNP￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- mu￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Lambda￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NNP￨O￨- mu￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- gamma￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Asymptotic￨U￨JJ￨MISC￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- global￨L￨JJ￨O￨- positive￨L￨JJ￨O￨A solution￨L￨NN￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- media￨L￨NNS￨O￨- coverageMiaochan￨L￨NN￨O￨- Zhao1￨U￨NN￨O￨- and￨L￨CC￨O￨- Huitao￨U￨NN￨O￨- Zhao1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2016:149￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- media￨L￨NNS￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- positivity￨L￨NN￨O￨- and￨L￨CC￨O￨- boundedness￨L￨NN￨O￨- of￨L￨IN￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- within￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- environment￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- asymptotical￨L￨JJ￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibria￨L￨NNS￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A .￨L￨.￨O￨- +Secondly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- global￨L￨JJ￨O￨- positive￨L￨JJ￨O￨A solution￨L￨NN￨O￨A and￨L￨CC￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- solution￨L￨NN￨O￨- oscillates￨L￨VBZ￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibria￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- certain￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- and￨L￨CC￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stage-structured￨L￨JJ￨O￨- predator-prey￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- prey￨L￨NN￨O￨A impulsively￨L￨RB￨O￨- diffusing￨L￨VBG￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- patches￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- triangle￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- triangle￨L￨NN￨O￨- y￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- triangle￨L￨NN￨O￨- y￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- suppose￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- patches￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- and￨L￨CC￨O￨- occupied￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- species￨L￨NNS￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ith￨L￨NN￨O￨- patch￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- biological￨L￨JJ￨O￨- pest￨L￨NN￨O￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- pest￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- program￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- releases￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- yield￨L￨NN￨O￨- of￨L￨IN￨O￨- predators￨L￨NNS￨O￨- that￨L￨WDT￨O￨- prey￨L￨VBP￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- pest￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Illustrative￨U￨JJ￨O￨- example￨L￨NN￨O￨- is￨L￨VBZ￨O￨- included￨L￨VBN￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- validity￨L￨NN￨O￨- and￨L￨CC￨O￨- applicability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- operational￨L￨JJ￨O￨- matrices.Mathematics￨L￨NNS￨O￨- Subject￨U￨JJ￨O￨- Classification65C30￨U￨NN￨O￨- 60H35￨L￨NN￨O￨- 65C20￨L￨NN￨O￨- 60H20￨L￨NN￨O￨- 37N25￨L￨CD￨NUMBER￨- Open￨U￨NNP￨MISC￨- image￨L￨NN￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- window￨L￨NN￨O￨- Download￨U￨VB￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- article￨L￨NN￨O￨- textReferences1.Babolian￨L￨NN￨MISC￨- E.￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Mokhtari￨U￨NNP￨PERSON￨- R.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Salmani￨U￨NNP￨PERSON￨- M.￨U￨NNP￨O￨- :￨L￨:￨O￨- Using￨U￨VBG￨O￨- direct￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- solving￨L￨VBG￨O￨- variational￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- via￨L￨IN￨O￨- triangular￨L￨JJ￨O￨- orthogonal￨L￨JJ￨O￨- functions￨L￨NNS￨O￨A .￨L￨.￨O￨- +201￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 452￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 456￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- MathSciNetzbMATHGoogle￨U￨NNP￨O￨- Scholar3.Babolian￨U￨NNP￨O￨- E.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Masouri￨U￨NNP￨O￨- Z.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Hatamzadeh-Varmazyarb￨U￨NNP￨O￨- S.￨U￨NNP￨O￨- :￨L￨:￨O￨- Numerical￨U￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- Volterra￨U￨NNP￨CITY￨- –￨L￨:￨O￨- Fredholm￨U￨NNP￨PERSON￨- integro-differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- via￨L￨IN￨O￨- direct￨L￨JJ￨O￨- method￨L￨NN￨O￨- using￨L￨VBG￨O￨- triangular￨L￨JJ￨O￨- functions￨L￨NNS￨O￨A .￨L￨.￨O￨- +58￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 239￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 247￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2009￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- MathSciNetCrossRefzbMATHGoogle￨U￨NNP￨O￨- Scholar4.Babolian￨U￨NNP￨O￨- E.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Maleknejad￨U￨NNP￨PERSON￨- K.￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Roodaki￨U￨NNP￨O￨- M.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Almasieh￨U￨NNP￨O￨- H.￨U￨NNP￨O￨- :￨L￨:￨O￨- Two-dimensional￨U￨JJ￨O￨- triangular￨L￨JJ￨O￨- functions￨L￨NNS￨O￨A and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- nonlinear￨L￨JJ￨O￨- 2D￨L￨NN￨O￨- Volterra￨U￨NNP￨CITY￨- –￨L￨:￨O￨- Fredholm￨U￨NNP￨PERSON￨- integral￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +191￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 206￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 217￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- MathSciNetzbMATHGoogle￨U￨NNP￨O￨- Scholar2.Babolian￨U￨NNP￨O￨- E.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Marzban￨U￨NNP￨PERSON￨- H.R.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Salmani￨U￨NNP￨PERSON￨- M.￨U￨NNP￨O￨- :￨L￨:￨O￨- Using￨U￨VBG￨O￨- triangular￨L￨JJ￨O￨- orthogonal￨L￨JJ￨O￨- functions￨L￨NNS￨O￨A for￨L￨IN￨O￨- solving￨L￨VBG￨O￨- Fredholm￨U￨NNP￨PERSON￨- integral￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- kind￨L￨NN￨O￨- .￨L￨.￨O￨- +60￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1711￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1722￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- MathSciNetCrossRefzbMATHGoogle￨U￨NNP￨O￨- Scholar5.Deb￨U￨NNP￨O￨- A.￨U￨NN￨O￨- ,￨L￨,￨O￨- Dasgupta￨U￨NNP￨PERSON￨- A.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Sarkar￨U￨NNP￨PERSON￨- G.￨U￨NNP￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- new￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- orthogonal￨L￨JJ￨O￨- functions￨L￨NNS￨O￨A and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- application￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Meng￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Chen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- vertical￨L￨JJ￨O￨- and￨L￨CC￨O￨- horizontal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- analyzed￨L￨VBD￨O￨- some￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- infection-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨- ,￨L￨,￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- obtained￨L￨VBN￨O￨- some￨L￨DT￨O￨- important￨L￨JJ￨O￨- qualitative￨L￨JJ￨O￨- properties.Recently￨L￨NN￨O￨- ,￨L￨,￨O￨- pulse￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- against￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Hethcote￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- problem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IVP￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- vital￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- GreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- N￨U￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨- rate￨L￨NN￨O￨- constant￨L￨JJ￨O￨- γ￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- constant￨L￨JJ￨O￨- μ￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨A constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Dynamics￨U￨NNP￨MISC￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- pulse￨L￨NN￨O￨A vaccinationAiren￨L￨NN￨O￨- Zhou1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Pairote￨U￨NNP￨O￨- Sattayatham1￨U￨NNP￨O￨- and￨L￨CC￨O￨- Jianjun￨U￨NNP￨PERSON￨- Jiao2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2016:140￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractPulse￨U￨NNP￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- pulse￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- pulse￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- related￨L￨JJ￨O￨- research￨L￨NN￨O￨- works￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- pulse￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- also￨L￨RB￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- references￨L￨NNS￨O￨- therein.Looking￨L￨VBG￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- existing￨L￨VBG￨O￨- researches￨L￨VBZ￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- vector-borne￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- with￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Of￨U￨IN￨O￨- course￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- also￨L￨RB￨O￨- used￨L￨VBD￨O￨- to￨L￨TO￨O￨- discuss￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rules￨L￨NNS￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- vector-borne￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- references￨L￨NNS￨O￨A therein.Recently￨L￨RB￨O￨- ,￨L￨,￨O￨- vaccines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- animals￨L￨NNS￨O￨- from￨L￨IN￨O￨- Rift￨U￨NNP￨O￨- Valley￨U￨NNP￨O￨- Fever￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Modelling￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- Rift￨U￨NNP￨O￨- Valley￨U￨NNP￨O￨- Fever￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- transmissionChen-Xia￨L￨JJ￨O￨- Yang1￨U￨NN￨O￨- and￨L￨CC￨O￨- Lin-Fei￨U￨JJ￨MISC￨- Nie1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2016:134￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- vector-bone￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Rift￨U￨NNP￨O￨- Valley￨U￨NNP￨O￨- Fever￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- RVF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- ruminants￨L￨NNS￨O￨- and￨L￨CC￨O￨- mosquitoes￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- impulsive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ruminants￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- RVFV￨U￨NN￨O￨- with￨L￨IN￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- computed￨L￨VBD￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- threshold￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- for￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibria￨L￨NNS￨O￨- .￨L￨.￨O￨- +d’Onofrio￨L￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- pulse￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- eradication￨L￨NN￨O￨- solution￨L￨NN￨O￨- are￨L￨VBP￨O￨- analyzed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- Lyapunov￨U￨NN￨PERSON￨- function￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- LessThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable.Consider￨L￨NN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- continuous￨L￨JJ￨O￨- SEIRS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Some￨U￨DT￨O￨- particular￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- calculated￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- established￨L￨VBN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- verify￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- open￨L￨JJ￨O￨- problem￨L￨NN￨O￨- that￨L￨WDT￨O￨- when￨L￨WRB￨O￨- Mul￨U￨NN￨PERSON￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- SEIRS￨U￨NN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- globally￨L￨RB￨O￨- attractive.Keywordsdiscrete￨L￨JJ￨O￨- SEIRS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelnonlinear￨L￨NN￨O￨- incidencebasic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numberglobal￨L￨JJ￨O￨- attractivitypermanenceMSC37M9939A1192D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionAs￨U￨NNPS￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- possess￨L￨VBP￨O￨- a￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Hepatitis￨U￨NNP￨O￨- ,￨L￨,￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- SARS￨U￨NNP￨O￨- ,￨L￨,￨O￨- Ebola￨U￨NNP￨O￨- ,￨L￨,￨O￨- MERS￨U￨NNP￨O￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- and￨L￨CC￨O￨- important￨L￨JJ￨O￨- research￨L￨NN￨O￨- subjects￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- computing￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- thresholds￨L￨NNS￨O￨- values￨L￨NNS￨O￨- and￨L￨CC￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- ,￨L￨,￨O￨- permanence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- bifurcations￨L￨NNS￨O￨- and￨L￨CC￨O￨- chaos￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- when￨L￨WRB￨O￨- some￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- vary￨L￨VBP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- Mul￨U￨NN￨PERSON￨- R￨U￨NN￨PERSON￨- mathcal￨L￨NN￨PERSON￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- permanent￨L￨JJ￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- degenerates￨L￨VBZ￨O￨- into￨L￨IN￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- Mul￨U￨NN￨PERSON￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- To￨U￨TO￨O￨- demonstrate￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- among￨L￨IN￨O￨- people￨L￨NNS￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- multi-strain￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- a￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- strain￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- every￨L￨DT￨O￨- individual￨L￨JJ￨O￨- randomly￨L￨RB￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- One￨U￨CD￨NUMBER￨- common￨L￨JJ￨O￨- observation￨L￨NN￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- multi-strain￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- strain￨L￨NN￨O￨A oscillate￨L￨VBP￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- so-called￨L￨JJ￨O￨- Epidemic￨U￨JJ￨O￨- cycling￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Compared￨U￨VBN￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- strain￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- strain￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- presented￨L￨VBN￨O￨- here￨L￨RB￨O￨- can￨L￨MD￨O￨- generate￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- cycling￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- much￨L￨JJ￨O￨- wider￨L￨JJR￨O￨- parameter￨L￨NN￨O￨- range￨L￨NN￨O￨- that￨L￨WDT￨O￨- covers￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Zhang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Yang￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIRS￨U￨NN￨O￨- worm￨L￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- zeta￨L￨NN￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dS￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- q￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- b￨L￨NN￨O￨- p￨L￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Add￨U￨VB￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dE￨L￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varepsilon￨L￨NN￨O￨A E￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- q￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- eta￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dI￨L￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- zeta￨L￨NN￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dR￨L￨NN￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- in￨L￨IN￨O￨- states￨L￨NNS￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Local￨U￨JJ￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- Hopf￨U￨NNP￨O￨- bifurcationAccording￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨PERSON￨- Pow￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- Add￨U￨VB￨PERSON￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- gamma￨L￨NN￨O￨- d￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨A -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- dp￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- dq￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- b￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- q￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- The￨U￨DT￨O￨- Jacobian￨U￨JJ￨MISC￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- is￨L￨VBZ￨O￨- J￨U￨NNP￨O￨- where￨L￨WRB￨O￨- Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Case￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- false￨L￨JJ￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- H21￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- holds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- root￨L￨NN￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- v￨L￨LS￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- purely￨L￨RB￨O￨- imaginary￨L￨JJ￨O￨- roots￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- pm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- omega￨L￨FW￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- pm￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- i￨L￨FW￨ORGANIZATION￨- Pow￨U￨FW￨ORGANIZATION￨- v￨L￨LS￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Rational￨U￨NNP￨O￨- .￨L￨.￨O￨- +Equation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Multiplying￨U￨VBG￨O￨- by￨L￨IN￨O￨- Pow￨U￨NN￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- equation￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Let￨U￨VB￨O￨- Equality￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- omega￨L￨FW￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- StrictGreaterThan￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- us￨L￨PRP￨O￨- denote￨L￨VB￨O￨- by￨L￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A against￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- antibiotics￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- A￨U￨DT￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- concentration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- i-th￨L￨JJ￨O￨- antibiotic￨L￨JJ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t.￨L￨NN￨O￨- Also￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- interacts￨L￨VBZ￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- generalised￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- bacterial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- urinary￨L￨JJ￨O￨- tract￨L￨NN￨O￨- ,￨L￨,￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- wound￨L￨NN￨O￨- infection.During￨L￨VBG￨O￨- the￨L￨DT￨O￨- administration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- i￨L￨FW￨O￨- th￨L￨DT￨O￨- antibiotic￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- to￨L￨TO￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- showed￨L￨VBN￨O￨- up￨L￨IN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- mutations￨L￨NNS￨O￨- of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- sensitive￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- to￨L￨TO￨O￨- such￨L￨JJ￨O￨- antibiotic￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- this￨L￨DT￨O￨- situation￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- Mul￨U￨NN￨O￨- overline￨L￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- A￨U￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- overline￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mutation￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- i￨L￨FW￨O￨- th￨L￨DT￨O￨- antibiotic￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- reactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- different￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- response￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- host.In￨L￨NN￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- relations￨L￨NNS￨O￨- among￨L￨IN￨O￨- antibiotics￨L￨NNS￨O￨- ,￨L￨,￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- cells￨L￨NNS￨O￨- and￨L￨CC￨O￨- bacteria￨L￨NNS￨O￨A are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection.Mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- significant￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- possible￨L￨JJ￨O￨- reinfection￨L￨NN￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- defining￨L￨VBG￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- produced￨L￨VBD￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- bacteria￨L￨NNS￨O￨A by￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- bacteria￨L￨NNS￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- multiple￨L￨JJ￨O￨- antibiotics￨L￨NNS￨O￨- synchronically￨L￨RB￨O￨- ,￨L￨,￨O￨- presuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- resistance￨L￨NN￨O￨- is￨L￨VBZ￨O￨- gained￨L￨VBN￨O￨- through￨L￨IN￨O￨- mutations￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- antibiotic￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- respect￨L￨NN￨O￨- ,￨L￨,￨O￨- understanding￨L￨NN￨O￨- and￨L￨CC￨O￨- anticipating￨L￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- load￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bacteria￨L￨NNS￨O￨A and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- cells￨L￨NNS￨O￨- by￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- crucial￨L￨JJ￨O￨- in￨L￨IN￨O￨- selecting￨L￨VBG￨O￨- effective￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- results￨L￨VBZ￨O￨- on￨L￨IN￨O￨- reproduction￨L￨NN￨O￨- of￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A to￨L￨TO￨O￨- antibiotics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- Austin￨U￨NNP￨CITY￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- point￨L￨NN￨O￨- solutions￨L￨NNS￨O￨- ,￨L￨,￨O￨- periodic￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- identified￨L￨VBN￨O￨- and￨L￨CC￨O￨- conditions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- were￨L￨VBD￨O￨- derived￨L￨VBN￨O￨- analytically.KeywordsSchelling￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- Agent￨U￨NNP￨O￨- based￨L￨VBN￨O￨- State￨U￨NNP￨ORGANIZATION￨- equation￨L￨NN￨O￨- Discrete￨U￨NNP￨O￨- map￨L￨NN￨O￨- IntroductionWe￨U￨NN￨O￨- frequently￨L￨RB￨O￨- find￨L￨VBP￨O￨- social￨L￨JJ￨O￨- or￨L￨CC￨O￨- natural￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- composed￨L￨VBN￨O￨A of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- :￨L￨:￨O￨- cities￨L￨NNS￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- races￨L￨NNS￨O￨- ,￨L￨,￨O￨- ecological￨L￨JJ￨O￨- system￨L￨NN￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- opinions￨L￨NNS￨O￨- ,￨L￨,￨O￨- cultures￨L￨NNS￨O￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +Open￨U￨VB￨O￨- image￨L￨NN￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- window￨L￨NN￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Two-room￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- aspatial￨L￨JJ￨O￨- version￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- Schelling￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- To￨U￨TO￨O￨- understand￨L￨VB￨O￨- these￨L￨DT￨O￨- phenomena￨L￨NNS￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- in￨L￨IN￨O￨- use￨L￨NN￨O￨- :￨L￨:￨O￨- state￨L￨NN￨O￨- equation-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- and￨L￨CC￨O￨- agent-based￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 35￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 43￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asA￨L￨NN￨O￨- state￨L￨NN￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Schelling￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- segregation￨L￨NN￨O￨- modelAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsJae￨L￨NNP￨O￨- Kyun￨U￨NNP￨PERSON￨- ShinHiroki￨U￨NNP￨PERSON￨- SayamaSeung￨U￨NNP￨PERSON￨- Ryul￨U￨NNP￨PERSON￨- ChoiOpen￨U￨NNP￨PERSON￨- AccessOriginal￨U￨NNP￨O￨- ArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractAn￨U￨NN￨O￨- aspatial￨L￨JJ￨O￨- version￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- famous￨L￨JJ￨O￨- Schelling￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- segregation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- format￨L￨NN￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- Schelling￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- ,￨L￨,￨O￨- state￨L￨NN￨O￨- equation￨L￨NN￨O￨- version￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- Schelling￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- indirect￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- where￨L￨WRB￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- organisms￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- well-mixed￨L￨JJ￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- linearly￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- shed￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- shedding￨L￨VBG￨O￨A pathogens￨L￨NNS￨O￨- several￨L￨JJ￨O￨- orders￨L￨NNS￨O￨- of￨L￨IN￨O￨- magnitude￨L￨NN￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- would￨L￨MD￨O￨- drive￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- by￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- order￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- precise￨L￨JJ￨O￨- contribution￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- producing￨L￨VBG￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- concentration￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- poorly￨L￨RB￨O￨- understood.If￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- host-to-host￨L￨JJ￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- with￨L￨IN￨O￨- all￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- being￨L￨VBG￨O￨- effective￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- every￨L￨DT￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- results￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- capped￨L￨VBN￨O￨- by￨L￨IN￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨O￨- Impact￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- shedding￨L￨VBG￨O￨A level￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- persistent￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Mycobacterium￨U￨NN￨O￨- avium￨L￨NN￨O￨- subspecies￨L￨NNS￨O￨- paratuberculosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MAP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Noa￨U￨NN￨O￨- Slater1￨U￨NN￨O￨- ,￨L￨,￨O￨- Rebecca￨U￨NNP￨PERSON￨- Mans￨U￨NNP￨PERSON￨- Mitchell2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Robert￨U￨NNP￨PERSON￨- H.￨U￨NNP￨PERSON￨- Using￨U￨VBG￨PERSON￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- routes￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- indirect￨L￨JJ￨O￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- background￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- linear￨L￨JJ￨O￨- mass-action￨L￨NN￨O￨- functional￨L￨JJ￨O￨- response￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ecoepidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- takes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- t￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- prey￨L￨NN￨O￨A ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- predator￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- K￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- conversion￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- on￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- and￨L￨CC￨O￨- δ￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- and￨L￨CC￨O￨- predators￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively.The￨L￨NN￨O￨- authors￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- detail￨L￨NN￨O￨- that￨L￨WDT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equilibria￨L￨NNS￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- System￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- around￨L￨IN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- parametric￨L￨JJ￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- around￨L￨IN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictLessThan￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- K￨U￨NNP￨O￨- theta￨L￨IN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- around￨L￨IN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictLessThan￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mu￨L￨NN￨O￨- theta￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- theta￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- K￨U￨NN￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- K￨U￨NN￨O￨- lambda￨L￨NN￨O￨- r￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- around￨L￨IN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- lambda￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mu￨L￨NN￨O￨- theta￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- unstable￨L￨JJ￨O￨- around￨L￨IN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- parametric￨L￨JJ￨O￨- values.However￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- environmental￨L￨JJ￨O￨- noise￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- neglected￨L￨VBN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- studied￨L￨VBN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- ecoepidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- system￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- ranges￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- different￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- predicted￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- prey￨L￨NN￨O￨A ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- predators￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keeping￨U￨VBG￨O￨- this￨L￨DT￨O￨- in￨L￨IN￨O￨- mind￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- modified￨L￨VBN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- randomly￨L￨RB￨O￨- fluctuating￨L￨VBG￨O￨- and￨L￨CC￨O￨- stochastically￨L￨RB￨O￨- perturbed￨L￨VBD￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- λ￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- lambda￨L￨NN￨O￨A Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- B￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Brownian￨U￨JJ￨MISC￨- motion￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- sigma￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- author￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- studied￨L￨VBD￨O￨- an￨L￨DT￨O￨- SI￨U￨NNP￨O￨- or￨L￨CC￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨A when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨- and￨L￨CC￨O￨- prey￨L￨NN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- predators￨L￨NNS￨O￨- eat￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +Further￨U￨RB￨O￨- ,￨L￨,￨O￨- interpreting￨L￨VBG￨O￨- the￨L￨DT￨O￨- edge￨L￨NN￨O￨- weights￨L￨NNS￨O￨- as￨L￨IN￨O￨- time￨L￨NN￨O￨- or￨L￨CC￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- vertices￨L￨NNS￨O￨A can￨L￨MD￨O￨- also￨L￨RB￨O￨- correspond￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- it￨L￨PRP￨O￨- takes￨L￨VBZ￨O￨- for￨L￨IN￨O￨- information￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- vertex￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- vertices.We￨L￨NNP￨O￨- say￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- events￨L￨NNS￨O￨- happens￨L￨VBZ￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- probability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- w.h.p.￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- Limit￨U￨NN￨O￨- Mul￨U￨NN￨O￨- P￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- n￨L￨NN￨O￨- -￨L￨:￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- holds￨L￨VBZ￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- weight￨L￨NN￨O￨- path￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- Mul￨U￨NN￨O￨- P￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Theorem￨U￨NNP￨O￨- 1.1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Typical￨U￨JJ￨O￨- distances￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- Let￨U￨VB￨O￨- U￨U￨NNP￨O￨- ,￨L￨,￨O￨- V￨U￨NNP￨O￨- be￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- uniformly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- vertices￨L￨NNS￨O￨A in￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- write￨L￨VBP￨O￨- Mul￨U￨JJ￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- W￨U￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- realization￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- random￨L￨JJ￨O￨- graph.We￨L￨NN￨O￨- define￨L￨VB￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- vertices￨L￨NNS￨O￨A in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- W￨U￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- weights￨L￨NNS￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- weight￨L￨NN￨O￨- path￨L￨NN￨O￨- connecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- vertices￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- circle￨L￨NN￨O￨- with￨L￨IN￨O￨- circumference￨L￨NN￨O￨- n￨L￨NN￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- cycle￨L￨NN￨O￨- on￨L￨IN￨O￨- n￨L￨NN￨O￨- many￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- added￨L￨VBD￨O￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- rho￨L￨VBG￨O￨- Mul￨U￨NN￨O￨- P￨U￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- o￨L￨NN￨O￨- many￨L￨JJ￨O￨- 0-length￨L￨JJ￨O￨- shortcuts￨L￨NNS￨O￨- at￨L￨IN￨O￨- locations￨L￨NNS￨O￨- chosen￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- measure￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- circle￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- worm￨L￨NN￨O￨- repeatedly￨L￨RB￨O￨- infected￨L￨VBN￨O￨- the￨L￨DT￨O￨- internal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Norwegian￨U￨JJ￨NATIONALITY￨- bank￨L￨NN￨O￨- ,￨L￨,￨O￨- illustrates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- reinfections￨L￨NNS￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- networks.The￨L￨NN￨O￨- stochastic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- first￨L￨RB￨ORDINAL￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- immunize￨L￨VB￨O￨- unknown￨L￨JJ￨O￨- hubs￨L￨NNS￨O￨- on￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- inhomogeneous￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spreading￨L￨NN￨O￨A process￨L￨NN￨O￨- was￨L￨VBD￨O￨- completely￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- configuration￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- types￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- seeds￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- malware￨L￨NN￨O￨- ’s￨L￨POS￨O￨- spreading￨L￨NN￨O￨A network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- undirected￨L￨JJ￨O￨- graph￨L￨NN￨O￨- with￨L￨IN￨O￨- M￨U￨NN￨O￨- edges￨L￨NNS￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- .￨L￨.￨O￨- +Any￨U￨DT￨O￨- spreading￨L￨VBG￨O￨A network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- L￨U￨NN￨O￨- different￨L￨JJ￨O￨- node￨L￨NN￨O￨- types￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- l￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- le￨L￨DT￨O￨- Mul￨U￨NN￨O￨- L￨U￨NN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- ll￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- applications￨L￨NNS￨O￨- are￨L￨VBP￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- biology￨L￨NN￨O￨- ,￨L￨,￨O￨- finance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- physics￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- cover￨L￨VB￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- or￨L￨CC￨O￨- decay￨L￨NN￨O￨A ,￨L￨,￨O￨- interacting￨L￨VBG￨O￨- predator-prey￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- compound￨L￨NN￨O￨- interest￨L￨NN￨O￨- and￨L￨CC￨O￨- inflation￨L￨NN￨O￨- ,￨L￨,￨O￨- radioactive￨L￨JJ￨O￨- decay￨L￨NN￨O￨- ,￨L￨,￨O￨- chemical￨L￨NN￨O￨- and￨L￨CC￨O￨- biochemical￨L￨JJ￨O￨- reaction￨L￨NN￨O￨- ,￨L￨,￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- cooling￨L￨NN￨O￨- of￨L￨IN￨O￨- objects￨L￨NNS￨O￨- ,￨L￨,￨O￨- compaction￨L￨NN￨O￨- of￨L￨IN￨O￨- geological￨L￨JJ￨O￨- media￨L￨NNS￨O￨- ,￨L￨,￨O￨- pressure￨L￨NN￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- atmosphere￨L￨NN￨O￨- ,￨L￨,￨O￨- viscoelastic￨L￨JJ￨O￨- response￨L￨NN￨O￨- in￨L￨IN￨O￨- materials￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- air￨L￨NN￨O￨- resistance￨L￨NN￨O￨- on￨L￨IN￨O￨- falling￨L￨VBG￨O￨- or￨L￨CC￨O￨- rising￨L￨VBG￨O￨- bodies.Before￨L￨NN￨O￨- we￨L￨PRP￨O￨- turn￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- applications￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- take￨L￨VBP￨O￨- a￨L￨DT￨O￨- brief￨L￨JJ￨O￨- look￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- technique￨L￨NN￨O￨- of￨L￨IN￨O￨- scaling￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- so￨L￨RB￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- .4.1￨L￨CD￨NUMBER￨- ScalingReal￨U￨NNP￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- Equality￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- u￨L￨NN￨O￨- prime￨L￨JJ￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- u￨L￨NN￨O￨- b￨L￨NN￨O￨- will￨L￨MD￨O￨- often￨L￨RB￨O￨- involve￨L￨VB￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- expressions￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- .￨L￨.￨O￨- +4.1.1￨L￨CD￨NUMBER￨- Dimensionless￨U￨JJ￨O￨- VariablesScaling￨U￨NN￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- function￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- u￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- bar￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- bar￨L￨NN￨ORGANIZATION￨- u￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- Pow￨U￨NN￨ORGANIZATION￨- u￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- u￨L￨FW￨O￨- Mul￨U￨FW￨O￨- -1￨L￨CD￨NUMBER￨- u￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- um￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨A value￨L￨NN￨O￨- of￨L￨IN￨O￨- u￨L￨NN￨O￨- ,￨L￨,￨O￨- uc￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- u￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- tc￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- t￨L￨NN￨O￨- where￨L￨WRB￨O￨- u￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- significant￨L￨JJ￨O￨- variation￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- structural￨L￨JJ￨O￨- interdependencies￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- examined￨L￨VBN￨O￨- with￨L￨IN￨O￨- measures￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- science.KeywordsComplex￨L￨NN￨O￨- network￨L￨NN￨O￨- Supply￨U￨NN￨O￨- Manufacturing￨U￨NNP￨O￨- Robustness￨U￨NNP￨O￨- This￨U￨DT￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- focus￨L￨NN￨O￨- collection￨L￨NN￨O￨- on￨L￨IN￨O￨- “￨L￨``￨O￨- Robust￨U￨JJ￨O￨- Manufacturing￨U￨NNP￨O￨- Control￨U￨NNP￨O￨- :￨L￨:￨O￨- Robustness￨U￨NNP￨O￨- and￨L￨CC￨O￨- Resilience￨U￨NNP￨O￨- in￨L￨IN￨O￨- Global￨U￨NNP￨O￨- Manufacturing￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- ”￨L￨''￨O￨- .1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- and￨L￨CC￨O￨- backgroundA￨L￨NN￨O￨- supply￨L￨NN￨O￨A network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- created￨L￨VBN￨O￨- when￨L￨WRB￨O￨- companies￨L￨NNS￨O￨- buy￨L￨VBP￨O￨- and￨L￨CC￨O￨- sell￨L￨VBP￨O￨- goods￨L￨NNS￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- ,￨L￨,￨O￨- transferring￨L￨VBG￨O￨- necessary￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- downstream￨L￨JJ￨O￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨- a￨L￨DT￨O￨- final￨L￨JJ￨O￨- product￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- studies￨L￨NNS￨O￨- examined￨L￨VBD￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- supply￨L￨NN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- complex￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- their￨L￨PRP$￨O￨- robustness￨L￨NN￨O￨A properties￨L￨NNS￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- find￨L￨VB￨O￨- empirical￨L￨JJ￨O￨- consensus￨L￨NN￨O￨- on￨L￨IN￨O￨- universal￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Brintrup￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Nair￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Vidal￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- examined￨L￨VBD￨O￨- robustness￨L￨NN￨O￨A against￨L￨IN￨O￨- disruptions￨L￨NNS￨O￨- under￨L￨IN￨O￨- random￨L￨JJ￨O￨- ,￨L￨,￨O￨- small-world￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨- topologies￨L￨NNS￨O￨- using￨L￨VBG￨O￨- multi-agent￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A throughout￨L￨IN￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- imposed￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- ignorant￨L￨JJ￨O￨- users￨L￨NNS￨O￨- and￨L￨CC￨O￨- stifle￨L￨VBP￨O￨- users￨L￨NNS￨O￨- usually￨L￨RB￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- spatial-temporal￨L￨JJ￨O￨- models￨L￨NNS￨O￨- will￨L￨MD￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- insight￨L￨NN￨O￨- to￨L￨TO￨O￨- research￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks.It￨L￨NN￨O￨- is￨L￨VBZ￨O￨- worth￨L￨JJ￨O￨- noting￨L￨VBG￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- works￨L￨NNS￨O￨- mentioned￨L￨VBN￨O￨- above￨L￨IN￨O￨- on￨L￨IN￨O￨- rumor￨L￨NN￨O￨- propagation￨L￨NN￨O￨- modeling￨L￨NN￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- over￨L￨IN￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- users￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- ignorants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- those￨L￨DT￨O￨- not￨L￨RB￨O￨- aware￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- spreaders￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- spreading￨L￨VBG￨O￨- it￨L￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- stiflers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- know￨L￨VBP￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- but￨L￨CC￨O￨- have￨L￨VBP￨O￨- ceased￨L￨VBN￨O￨- communicating￨L￨VBG￨O￨- it￨L￨PRP￨O￨- after￨L￨IN￨O￨- meeting￨L￨VBG￨O￨- somebody￨L￨NN￨O￨- already￨L￨RB￨O￨- informed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Dynamic￨U￨NNP￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- rumor￨L￨NN￨O￨A propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- delayChunru￨L￨NN￨O￨- Li1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Zujun￨U￨NN￨O￨- Ma3￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2015:364￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- reaction-diffusion￨L￨NN￨O￨- rumor￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- government￨L￨NN￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- diffusive￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- DL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- spatial-temporal￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- terms￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- propagation￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- online￨L￨JJ￨O￨A social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Consider￨U￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- discontinuous￨L￨JJ￨O￨A treatment￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Equality￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- I￨U￨PRP￨O￨- Equality￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- gamma￨L￨NN￨O￨- h￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Λ￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- naturally￨L￨RB￨O￨- leaving￨L￨VBG￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- stage￨L￨NN￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- stage￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- Lyapunov￨U￨NNP￨PERSON￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- discontinuous￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- on￨L￨IN￨O￨- non-smooth￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- sharp￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- which￨L￨WDT￨O￨- completely￨L￨RB￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- there￨L￨EX￨O￨- only￨L￨RB￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- function￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- h￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- I￨U￨PRP￨O￨- phi￨L￨NN￨O￨- I￨U￨PRP￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨A rate￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- wild￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- in￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨A ZVL￨U￨NNP￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- Latin￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- Amazons￨U￨NNP￨O￨- and￨L￨CC￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- crab-eating￨L￨JJ￨O￨- fox￨L￨NN￨O￨- ,￨L￨,￨O￨- spiny￨L￨JJ￨O￨- rat￨L￨NN￨O￨- ,￨L￨,￨O￨- common￨L￨JJ￨O￨- opossum￨L￨NN￨O￨- and￨L￨CC￨O￨- black￨L￨JJ￨O￨- rat￨L￨NN￨O￨- in￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 32￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 661￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 673￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asExamining￨L￨VBG￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨A potential￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- species￨L￨NNS￨O￨- for￨L￨IN￨O￨- Mul￨U￨NN￨O￨- varvec￨L￨NN￨O￨- Mul￨U￨NN￨O￨- textit￨L￨NN￨O￨- Mul￨U￨NN￨O￨- L￨U￨NN￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- s￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- h￨L￨NN￨O￨- Mul￨U￨NN￨O￨- m￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨ORGANIZATION￨- n￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- f￨L￨FW￨O￨- Mul￨U￨FW￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- m￨L￨NN￨O￨- u￨L￨NN￨O￨- infectionAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsRyutaro￨L￨NN￨O￨- FukamiHiroshi￨U￨NN￨MISC￨- NishiuraOpen￨U￨NN￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- Paper￨U￨NNP￨MISC￨- Area￨U￨NNP￨MISC￨- 3First￨L￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractLeishamaniasis￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- parasitic￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- sandfly￨L￨NN￨O￨- Phlebotomus￨U￨NN￨O￨- spp￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- animal￨L￨NN￨O￨- species￨L￨NNS￨O￨- other￨L￨JJ￨O￨- than￨L￨IN￨O￨- canine￨L￨JJ￨O￨- play￨L￨NN￨O￨- important￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨A transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Leishmania￨U￨NN￨LOCATION￨- infantum￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- conventional￨L￨JJ￨O￨- wisdom￨L￨NN￨O￨- that￨L￨WDT￨O￨- centered￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- canine￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Summary￨U￨NNP￨O￨- of￨L￨IN￨O￨- notation￨L￨NN￨O￨- Notation￨U￨NN￨O￨- Explanation￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Rate￨U￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Pow￨U￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- Pow￨U￨NN￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- ,￨L￨,￨O￨- Pow￨U￨NN￨O￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- Nature￨U￨NN￨O￨- mortality￨L￨NN￨O￨- of￨L￨IN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- compartments￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨A ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- Lambda￨U￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Recruitment￨U￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Fatality￨U￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Recovery￨U￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Removed￨U￨VBN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Positive￨U￨JJ￨O￨- parameter￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- throughout￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- their￨L￨PRP$￨O￨- paper￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Gao￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Hethcote￨U￨NNP￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- logistic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- N￨U￨NNP￨O￨- Tuple￨U￨NNP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- biggl￨L￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- N￨U￨NN￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- biggl￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- biggr￨L￨NN￨O￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- convex￨L￨NN￨O￨- combination￨L￨NN￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- and￨L￨CC￨O￨- μ￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NN￨O￨- r￨L￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- K￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +mention￨L￨VB￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- logistic￨L￨JJ￨O￨- birth￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- Here￨U￨RB￨O￨- Equality￨U￨NN￨O￨- N￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NN￨O￨- beta￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨MISC￨- delta￨L￨NN￨MISC￨- Add￨U￨VB￨MISC￨- mu￨L￨NN￨MISC￨A Add￨U￨VB￨MISC￨- alpha￨L￨NN￨O￨- gamma￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- non-negative￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- prevail￨L￨VB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨A rate￨L￨NN￨O￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- limited.Keywordsstochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- modellogistic￨L￨JJ￨O￨- birthdisease-free￨L￨JJ￨O￨- equilibriumendemic￨L￨JJ￨O￨- equilibriumstochastic￨L￨JJ￨O￨- Lyapunov￨U￨NN￨O￨- functionasymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionFrom￨U￨NNP￨O￨- the￨L￨DT￨O￨- pioneering￨L￨JJ￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Kermack￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Mckendrick￨U￨NNP￨PERSON￨- on￨L￨IN￨O￨- SIR￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- have￨L￨VBP￨O￨- descended￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- carry￨L￨VBP￨O￨- out￨L￨RP￨O￨- the￨L￨DT￨O￨- globally￨L￨RB￨O￨- asymptotical￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨A through￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- Lyapunov￨U￨NNP￨PERSON￨- functional￨L￨JJ￨O￨- method￨L￨NN￨O￨- if￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- le￨L￨DT￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- StrictGreaterThan￨U￨NNP￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- system￨L￨NN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- will￨L￨MD￨O￨- oscillate￨L￨VB￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- summarized￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- list￨L￨NN￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- input￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- members￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ;￨L￨:￨O￨- q￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- new-borns￨L￨NNS￨O￨- ;￨L￨:￨O￨- β￨L￨NN￨O￨- :￨L￨:￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- ;￨L￨:￨O￨- μ￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨A rate￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- V￨U￨NNP￨O￨- compartments￨L￨NNS￨O￨- ;￨L￨:￨O￨- p￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- proportionality￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ;￨L￨:￨O￨- γ￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- ε￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- losing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- immunity￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- α￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- disease-caused￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals.All￨L￨NN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- nonnegative￨L￨JJ￨O￨- and￨L￨CC￨O￨- mu￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- system￨L￨NN￨O￨- has￨L￨VBZ￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- mu￨L￨NN￨O￨- p￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- A￨U￨DT￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Here￨U￨RB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨A the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- members￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disease-related￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- are￨L￨VBP￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- persist￨L￨VB￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- measured￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- LessThan￨U￨JJ￨O￨- R￨U￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- decays￨L￨NNS￨O￨- exponentially￨L￨RB￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- A￨U￨DT￨O￨- delayed￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rateLuju￨L￨NN￨O￨- Liu1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2015:329￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractAn￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- an￨L￨DT￨O￨- incubation￨L￨NN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A and￨L￨CC￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- logistic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- vector￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- incubation￨L￨NN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A and￨L￨CC￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- with￨L￨IN￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- K￨U￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- host￨L￨NN￨TITLE￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- bilinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- vector￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- McCluskey￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- discussed￨L￨VBD￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibria￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- extended￨L￨VBD￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- vector￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- ,￨L￨,￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- meanings￨L￨NNS￨O￨- as￨L￨IN￨O￨- that￨L￨DT￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- GreaterThan￨U￨NNP￨O￨- alpha￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- saturation￨L￨NN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- applying￨L￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- bifurcation￨L￨NN￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- absolutely￨L￨RB￨O￨- stable￨L￨JJ￨O￨- or￨L￨CC￨O￨- conditionally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- established￨L￨VBN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨O￨- HAT￨U￨NN￨O￨- elimination￨L￨NN￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- feasible￨L￨JJ￨O￨- under￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- interventions￨L￨NNS￨O￨- or￨L￨CC￨O￨- if￨L￨IN￨O￨- complementary￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- considered.We￨L￨NN￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- HAT￨U￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- that￨L￨WDT￨O￨- ongoing￨L￨JJ￨O￨- vector￨L￨NN￨O￨A control￨L￨NN￨O￨A ,￨L￨,￨O￨- active￨L￨JJ￨O￨- screening￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- could￨L￨MD￨O￨- eliminate￨L￨VB￨O￨- Gambian￨U￨JJ￨NATIONALITY￨- HAT￨U￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- HAT￨U￨NN￨O￨- elimination￨L￨NN￨O￨- goal￨L￨NN￨O￨- seeks￨L￨VBZ￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨A Gambian￨U￨JJ￨NATIONALITY￨- HAT￨U￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- problem￨L￨NN￨O￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- 10,000￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- in￨L￨IN￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- foci￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- target￨L￨NN￨O￨- in￨L￨IN￨O￨- Boffa￨U￨NNP￨CITY￨- prefecture￨L￨NN￨O￨- in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- prevalences￨L￨NNS￨O￨- for￨L￨IN￨O￨- HAT￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- where￨L￨WRB￨O￨- vector￨L￨NN￨O￨A control￨L￨NN￨O￨A measures￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- screen￨L￨NN￨O￨- and￨L￨CC￨O￨- treat￨L￨VB￨O￨- strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- renewed￨L￨VBN￨O￨- control￨L￨NN￨O￨- activities￨L￨NNS￨O￨- that￨L￨WDT￨O￨- centered￨L￨VBD￨O￨- around￨L￨IN￨O￨- case￨L￨NN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- Gambian￨U￨JJ￨NATIONALITY￨- HAT￨U￨NN￨O￨- fell￨L￨VBD￨O￨- by￨L￨IN￨O￨- 75￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- 27,862￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 6,984￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- multi-state￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- visceral￨L￨JJ￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- going￨L￨VBG￨O￨- on￨L￨IN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- clinical￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatically￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- develop￨L￨VBP￨O￨- clinical￨L￨JJ￨O￨- visceral￨L￨JJ￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- estimated￨L￨VBN￨O￨- average￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- symptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- are￨L￨VBP￨O￨- 147￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- 130￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 166￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- 140￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- 123￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 160￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- significantly￨L￨RB￨O￨- longer￨L￨JJR￨O￨- than￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- reported￨L￨VBN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Clinical￨U￨JJ￨O￨- and￨L￨CC￨O￨- laboratory￨L￨JJ￨O￨- diagnostics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- imprecise￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- partly￨L￨RB￨O￨- because￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- develop￨L￨VBP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- alone￨L￨RB￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- diagnostic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- partly￨L￨RB￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- clinical￨L￨JJ￨O￨A features￨L￨NNS￨O￨- of￨L￨IN￨O￨- VL￨U￨NN￨O￨- overlap￨L￨VBP￨O￨- with￨L￨IN￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- hyperreactive￨L￨JJ￨O￨- malarial￨L￨JJ￨O￨- splenomegaly￨L￨NN￨O￨- ,￨L￨,￨O￨- typhoid￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- disseminated￨L￨VBN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- presentation￨L￨NN￨O￨- alone￨L￨RB￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- diagnostic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Extended￨U￨JJ￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- visceral￨L￨JJ￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- depends￨L￨VBZ￨O￨- critically￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- symptomatic￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- sandflies￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- address￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- issues￨L￨NNS￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- their￨L￨PRP$￨O￨- biological￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- precise￨L￨JJ￨O￨- information￨L￨NN￨O￨- as￨L￨IN￨O￨- regards￨L￨VBZ￨O￨- the￨L￨DT￨O￨- domains￨L￨NNS￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- sets￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- sets￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- domains￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Poincaré￨U￨NNP￨O￨- map￨L￨NN￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- point￨L￨NN￨O￨- series￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- order-1￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- boundary￨L￨NN￨O￨- order-1￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- order-2￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- and￨L￨CC￨O￨- non-existence￨L￨NN￨O￨- of￨L￨IN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- with￨L￨IN￨O￨- order￨L￨NN￨O￨- no￨L￨RB￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- problem￨L￨NN￨O￨- listed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- order-2￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- order-2￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- and￨L￨CC￨O￨- order-1￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- precise￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- finite￨L￨JJ￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- actions￨L￨NNS￨O￨- ,￨L￨,￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- designing￨L￨VBG￨O￨- threshold￨L￨NN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- attractors￨L￨NNS￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- basins￨L￨NNS￨O￨- of￨L￨IN￨O￨- attraction￨L￨NN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- phase￨L￨NN￨O￨- sets￨L￨NNS￨O￨- and￨L￨CC￨O￨- interior￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- of￨L￨IN￨O￨- horseshoe-like￨L￨JJ￨O￨- attractors￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- any￨L￨DT￨O￨- trajectory￨L￨NN￨O￨- initiating￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- set￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- free￨L￨JJ￨O￨- from￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- after￨L￨IN￨O￨- finite￨L￨JJ￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- actions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- order-k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GreaterThan￨U￨NN￨O￨- k￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨A do￨L￨VBP￨O￨- not￨L￨RB￨O￨- exist￨L￨VB￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- integrated￨L￨VBN￨O￨- pest￨L￨NN￨O￨- management￨L￨NN￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- pest￨L￨NN￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- ,￨L￨,￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- GreaterThan￨U￨NNP￨O￨- tau￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Pow￨U￨NN￨O￨- p￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- if￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- theta￨L￨IN￨O￨A 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- biological￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- ,￨L￨,￨O￨- sufficient￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- enemies￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- released￨L￨VBN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- pest￨L￨JJS￨O￨- population￨L￨NN￨O￨- exceeding￨L￨VBG￨O￨- V￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- L￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- StrictLessThan￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- theta￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- if￨L￨IN￨O￨- Equality￨U￨NN￨O￨- tau￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Denoting￨U￨VBG￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- level￨L￨NN￨O￨- as￨L￨IN￨O￨- V￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- L￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- state-dependent￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- y￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- omega￨L￨JJ￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- x￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- pests￨L￨NNS￨O￨- and￨L￨CC￨O￨- natural￨L￨JJ￨O￨- enemies￨L￨NNS￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- applied￨L￨VBD￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- x￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- pest￨L￨NN￨O￨- and￨L￨CC￨O￨- natural￨L￨JJ￨O￨- enemy￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- reasonable￨L￨JJ￨O￨- to￨L￨TO￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- x￨L￨NN￨O￨- could￨L￨MD￨O￨- grow￨L￨VB￨O￨- exponentially￨L￨RB￨O￨- before￨L￨IN￨O￨- reaching￨L￨VBG￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- level￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- let￨L￨VB￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨A y￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- omega￨L￨JJ￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- Equality￨U￨NN￨O￨- b￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- r￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- stated￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- may￨L￨MD￨O￨- purposely￨L￨RB￨O￨- lay￨L￨VB￨O￨- dormant￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- prior￨L￨JJ￨O￨- to￨L￨TO￨O￨- infecting￨L￨VBG￨O￨- other￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A for￨L￨IN￨O￨- stealth￨L￨NN￨O￨- reasons￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- to￨L￨TO￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- these￨L￨DT￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ability￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t.￨L￨NN￨O￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- incorporate￨L￨VBP￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- delay￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- into￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- eta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- varepsilon￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- E￨U￨NNP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- delay￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- external￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- eta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- and￨L￨CC￨O￨- external￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +[￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- may￨L￨MD￨O￨- purposely￨L￨RB￨O￨- lay￨L￨VB￨O￨- dormant￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- prior￨L￨JJ￨O￨- to￨L￨TO￨O￨- infecting￨L￨VBG￨O￨- other￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A for￨L￨IN￨O￨- stealth￨L￨NN￨O￨- reasons￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- deals￨L￨VBZ￨O￨- both￨L￨CC￨O￨- with￨L￨IN￨O￨- classical￨L￨JJ￨O￨- and￨L￨CC￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- removed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- extracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- reports￨L￨NNS￨O￨- periodically￨L￨RB￨O￨- published￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- March￨U￨NNP￨DATE￨- 27￨L￨CD￨DATE￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- physical￨L￨JJ￨O￨- meaning￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- in￨L￨IN￨O￨- fractional￨L￨JJ￨O￨- derivatives￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- index￨L￨NN￨O￨- of￨L￨IN￨O￨- memory￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- seems￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- exist￨L￨VBP￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨A to￨L￨TO￨O￨- predict￨L￨VB￨O￨- its￨L￨PRP$￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- previous￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- or￨L￨CC￨O￨- using￨L￨VBG￨O￨- restricted￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- persons￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- variable￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- On￨U￨IN￨O￨- a￨L￨DT￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- modelIvan￨L￨NN￨O￨- Area1￨U￨NN￨O￨- ,￨L￨,￨O￨- Hanan￨U￨NNP￨PERSON￨- Batarfi2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jorge￨U￨NNP￨PERSON￨- Losada3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Juan￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Nieto2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Wafa￨U￨NNP￨ORGANIZATION￨- Shammakh2￨U￨NNP￨O￨- and￨L￨CC￨O￨- Ángela￨U￨NNP￨MISC￨- Torres4￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 2015:278￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractEbola￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- world￨L￨NN￨O￨- health￨L￨NN￨O￨- problem￨L￨NN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨ORGANIZATION￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- reports￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- classical￨L￨JJ￨O￨- and￨L￨CC￨O￨- fractional￨L￨JJ￨O￨A SEIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- latency￨L￨NN￨O￨A :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- varphi￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- net￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immature￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- varphi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- varphi￨L￨FW￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- b￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- b￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- Pow￨U￨NN￨O￨- d￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- populationBaodan￨L￨NN￨O￨- Tian1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yunguo￨U￨NNP￨O￨- Jin2￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Shouming￨U￨VBG￨O￨- Zhong2￨U￨NN￨O￨- and￨L￨CC￨O￨- Ning￨U￨NN￨MISC￨- Chen1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2015:260￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- latency￨L￨NN￨O￨A spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- call￨L￨NN￨O￨- data￨L￨NN￨O￨- records￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- CDRs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- needed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨- operators￨L￨NNS￨O￨- for￨L￨IN￨O￨- billing￨L￨NN￨O￨- purposes￨L￨NNS￨O￨- ,￨L￨,￨O￨- contain￨L￨VBP￨O￨- an￨L￨DT￨O￨- enormous￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- whom￨L￨WP￨O￨- we￨L￨PRP￨O￨- communicate.In￨L￨VBP￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- ,￨L￨,￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- mostly￨L￨RB￨O￨- done￨L￨VBN￨O￨- by￨L￨IN￨O￨- surveys￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- participants￨L￨NNS￨O￨- ranges￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- around￨L￨RB￨O￨- 1,000￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- were￨L￨VBD￨O￨- biased￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- subjectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- participants￨L￨NNS￨O￨- ’￨L￨POS￨O￨- answers￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- survey￨L￨VBP￨O￨- the￨L￨DT￨O￨- contributions￨L￨NNS￨O￨- made￨L￨VBN￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- constructed￨L￨VBN￨O￨- with￨L￨IN￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- personal￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- ,￨L￨,￨O￨- geographical￨L￨JJ￨O￨- partitioning￨L￨NN￨O￨- ,￨L￨,￨O￨- urban￨L￨JJ￨O￨- planning￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- help￨L￨VB￨O￨- towards￨L￨IN￨O￨- development￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- security￨L￨NN￨O￨- and￨L￨CC￨O￨- privacy￨L￨NN￨O￨- issues.Keywordsmobile￨L￨NN￨O￨- phone￨L￨NN￨O￨- datasetsbig￨L￨NN￨O￨- data￨L￨NNS￨O￨- analysisdata￨L￨NN￨O￨- miningsocial￨L￨JJ￨O￨- networkstemporal￨L￨JJ￨O￨- networksgeographical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionAs￨U￨NNPS￨O￨- the￨L￨DT￨O￨- Internet￨U￨NN￨MISC￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- technological￨L￨JJ￨O￨- breakthrough￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- ’90s￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- mobile￨L￨JJ￨TITLE￨A phones￨L￨NNS￨O￨- have￨L￨VBP￨O￨- changed￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- communication￨L￨NN￨O￨- habits￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- first￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- twenty-first￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Ricker￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- Equality￨U￨NNP￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- e￨L￨SYM￨O￨- Add￨U￨VB￨O￨- r￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Hassell￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- x￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- rich￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behavior.There￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- increasing￨L￨VBG￨O￨- interest￨L￨NN￨O￨- and￨L￨CC￨O￨- more￨L￨JJR￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- discrete￨L￨JJ￨O￨A time￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- recently￨L￨RB￨DATE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theoretical￨L￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- discrete￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- computation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 14￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- using￨L￨VBG￨O￨- discrete￨L￨JJ￨O￨A mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- latent￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- The￨U￨DT￨O￨- discrete￨L￨JJ￨O￨A tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individualsHui￨L￨NN￨O￨- Cao1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Hongwu￨U￨NN￨O￨- Tan1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2015:165￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractA￨U￨NNP￨O￨- discrete￨L￨JJ￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- direct￨L￨JJ￨O￨- progression￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- determined￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- successful￨L￨JJ￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +171￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 143￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 154￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2001￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Scholar4.Brauer￨U￨NNP￨O￨- ,￨L￨,￨O￨- F.￨U￨NNP￨O￨- ;￨L￨:￨O￨- van￨L￨NNP￨O￨- den￨L￨NN￨O￨A Driessche￨U￨NNP￨O￨- ,￨L￨,￨O￨- P.￨U￨NNP￨O￨- ;￨L￨:￨O￨- Wu￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- J.￨U￨NNP￨O￨- :￨L￨:￨O￨- Mathematical￨U￨JJ￨O￨- Epidemiology￨U￨NNP￨O￨- ,￨L￨,￨O￨- Springer￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Berlin￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Scholar5.Capasso￨U￨NNP￨O￨- V.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Serio￨U￨NNP￨O￨- G.￨U￨NNP￨O￨- :￨L￨:￨O￨- A￨U￨NNP￨O￨- generalization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Kermack￨U￨NNP￨O￨- –￨L￨:￨O￨- McKendrick￨U￨NNP￨PERSON￨- deterministic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +42￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 41￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 61￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1978￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- CrossRefMathSciNetGoogle￨U￨NNP￨O￨- Scholar6.Carletti￨U￨NNP￨O￨- M.￨U￨NNP￨O￨- :￨L￨:￨O￨- Mean-square￨U￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- bacteriophage￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨- .￨L￨.￨O￨- +33￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 250￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 260￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1995￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- CrossRefzbMATHMathSciNetGoogle￨U￨NNP￨O￨- Scholar2.Beretta￨U￨NNP￨O￨- E.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Kolmanovskii￨U￨NNP￨PERSON￨- V.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Shaikhet￨U￨NNP￨O￨- L.￨U￨NNP￨O￨- :￨L￨:￨O￨- Stability￨U￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- ifluenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- perturbations￨L￨NNS￨O￨- .￨L￨.￨O￨- +45￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 269￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 277￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1998￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- CrossRefzbMATHMathSciNetGoogle￨U￨NNP￨O￨- Scholar3.Brauer￨U￨NNP￨O￨- ,￨L￨,￨O￨- F.￨U￨NNP￨O￨- ;￨L￨:￨O￨- van￨L￨NNP￨O￨- den￨L￨NN￨O￨A Driessche￨U￨NNP￨O￨- ,￨L￨,￨O￨- P.￨U￨NNP￨O￨- :￨L￨:￨O￨- Models￨U￨NNS￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- immigration￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- periodic￨L￨JJ￨O￨- forced￨L￨JJ￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- beta￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- mu￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- fractions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- death￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- seasonally-dependent￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- T-periodic￨U￨JJ￨MISC￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- decreasing￨L￨VBG￨O￨- piecewise￨L￨NN￨O￨- smooth￨L￨JJ￨O￨- factor￨L￨NN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- coverage￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- influences￨L￨NNS￨O￨- ,￨L￨,￨O￨- σ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- Leray-Schauder￨U￨JJ￨O￨- degree￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨- new￨L￨JJ￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- positive￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- seasonally￨L￨RB￨O￨- forced￨L￨VBN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- Mul￨U￨NN￨O￨- equiv￨L￨FW￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Katriel￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- got￨L￨VBD￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- periodically￨L￨RB￨O￨- forced￨L￨VBN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- Leray-Schauder￨U￨NNP￨O￨- degree￨L￨NN￨O￨- theory￨L￨NN￨O￨- provided￨L￨VBN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- .￨L￨.￨O￨- +2015Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- periodic￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- seasonally￨L￨RB￨O￨- forced￨L￨VBN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Periodic￨U￨JJ￨MISC￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- seasonally￨L￨RB￨O￨- forced￨L￨VBN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- coverageJian￨L￨NN￨O￨- Zu1￨U￨NN￨O￨- and￨L￨CC￨O￨- Lin￨U￨NNP￨O￨- Wang2￨U￨NNP￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2015:136￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Zu￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Wang￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- experimental￨L￨JJ￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- features￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- feature￨L￨NN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- latent￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- nodes.KeywordsEpidemicsInformation￨L￨NN￨O￨- cascadesInformation￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- IntroductionNetworks￨U￨NNS￨O￨- are￨L￨VBP￨O￨- underlying￨L￨VBG￨O￨- mediums￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- rumors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- evaluate￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- classifiers￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Naive￨U￨JJ￨LOCATION￨- Bayes￨U￨NNS￨LOCATION￨- ,￨L￨,￨O￨- Naive￨U￨JJ￨O￨- Bayes￨U￨NNS￨PERSON￨- with￨L￨IN￨O￨- kernel￨L￨NN￨O￨- density￨L￨NN￨O￨- estimation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- decision￨L￨NN￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- with￨L￨IN￨O￨- features￨L￨NNS￨O￨- including￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨A and￨L￨CC￨O￨- different￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +2015Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractAlgorithms￨U￨NNP￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- and￨L￨CC￨O￨- containing￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- cascades￨L￨NNS￨O￨A .￨L￨.￨O￨- +Determining￨U￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- states￨L￨NNS￨O￨A of￨L￨IN￨O￨- network￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- to￨L￨TO￨O￨- taking￨L￨VBG￨O￨- corrective￨L￨JJ￨O￨- or￨L￨CC￨O￨- preventive￨L￨JJ￨O￨- action￨L￨NN￨O￨- to￨L￨TO￨O￨- stop￨L￨VB￨O￨- or￨L￨CC￨O￨- slow￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stability￨U￨NN￨MISC￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- observer￨L￨NN￨O￨- design￨L￨NN￨O￨A for￨L￨IN￨O￨- discrete-time￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelsAsier￨L￨NN￨O￨- Ibeas1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Manuel￨U￨NNP￨O￨- de￨L￨FW￨O￨- la￨L￨FW￨O￨- Sen2￨U￨NN￨O￨- ,￨L￨,￨O￨- Santiago￨U￨NNP￨CITY￨- Alonso-Quesada2￨U￨NN￨O￨- and￨L￨CC￨O￨- Iman￨U￨NN￨O￨- Zamani3￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2015:122￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Ibeas￨U￨NNPS￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- observer￨L￨NN￨O￨- design￨L￨NN￨O￨A is￨L￨VBZ￨O￨- faced￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- implicit￨L￨JJ￨O￨- way￨L￨NN￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨- first￨L￨RB￨ORDINAL￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- novelty￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- presented￨L￨VBN￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Afterwards￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- state￨L￨NN￨O￨- observer￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- tackled￨L￨VBN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- theoretical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- lambda￨L￨NN￨O￨A _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- StrictLessThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- lambda￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- lambda￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- .￨L￨.￨O￨- +Classical￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- revealed￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- lambda￨L￨NN￨O￨A _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- below￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- die￨L￨VB￨O￨- out￨L￨RP￨O￨- ;￨L￨:￨O￨- otherwise￨L￨RB￨O￨- there￨L￨EX￨O￨- will￨L￨MD￨O￨- exist￨L￨VB￨O￨- a￨L￨DT￨O￨- persistence￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- apart￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- external￨L￨JJ￨O￨- environment￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- vector￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- mosquitoes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- play￨L￨VB￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +2015Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIRS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- not￨L￨RB￨O￨- containing￨L￨VBG￨O￨- the￨L￨DT￨O￨- permanent￨L￨JJ￨O￨- acquired￨L￨VBN￨O￨- immunity￨L￨NN￨O￨- with￨L￨IN￨O￨- non-linear￨L￨JJ￨O￨- generalized￨L￨VBN￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- preventive￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stable￨L￨JJ￨O￨- locally￨L￨RB￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- globally￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨JJ￨O￨A and￨L￨CC￨O￨- an￨L￨DT￨O￨- unstable￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- for￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- SEIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- non-linear￨L￨JJ￨O￨- generalized￨L￨VBN￨O￨- incidences￨L￨NNS￨O￨- and￨L￨CC￨O￨- preventive￨L￨JJ￨O￨A vaccinationMuhammad￨L￨NNP￨O￨- Altaf￨U￨NNP￨PERSON￨- Khan1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Qaisar￨U￨NNP￨PERSON￨- Badshah1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Saeed￨U￨NNP￨PERSON￨- Islam1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ilyas￨U￨NNP￨PERSON￨- Khan2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Sharidan￨U￨NNP￨O￨- Shafie3Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Sher￨U￨NNP￨O￨- Afzal￨U￨NNP￨O￨- Khan4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2015:88￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Khan￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stable￨L￨JJ￨O￨- both￨L￨CC￨O￨- locally￨L￨RB￨O￨- and￨L￨CC￨O￨- globally￨L￨RB￨O￨- when￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- global￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- completely￨L￨RB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- vaccine-induced￨L￨JJ￨O￨- protection￨L￨NN￨O￨- equivalent￨L￨NN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- annual￨L￨JJ￨SET￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- students￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- alternative￨L￨NN￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- routine￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- of￨L￨IN￨O￨- infants￨L￨NNS￨O￨A able￨L￨JJ￨O￨- to￨L￨TO￨O￨- trigger￨L￨VB￨O￨- a￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- and￨L￨CC￨O￨- persistent￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- infant￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- 35.6￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- versus￨L￨CC￨O￨- 41.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- explicitly￨L￨RB￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- socio-demographic￨L￨JJ￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- RSV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- rural￨L￨JJ￨O￨- setting￨L￨NN￨O￨- of￨L￨IN￨O￨- Kenya￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨A population￨L￨NN￨O￨- targets￨L￨NNS￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- RSV￨U￨NN￨O￨- infant￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Evaluating￨U￨VBG￨MISC￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- reducing￨L￨VBG￨O￨A infant￨L￨NN￨O￨- respiratory￨L￨JJ￨O￨- syncytial￨L￨NN￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- low-income￨L￨JJ￨O￨- settingsPiero￨L￨NN￨O￨- Poletti1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Stefano￨U￨NNP￨PERSON￨- Merler2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marco￨U￨NNP￨PERSON￨- Ajelli2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Piero￨U￨NNP￨O￨- Manfredi3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Patrick￨U￨NNP￨PERSON￨- K￨U￨NNP￨PERSON￨- Munywoki4￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- D￨U￨NN￨O￨- James￨U￨NNP￨PERSON￨- Nokes4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Alessia￨U￨NNP￨PERSON￨- Melegaro1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 13:49￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Poletti￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨O￨- Central￨U￨NNP￨O￨- .￨L￨.￨O￨- +Interestingly￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- pregnant￨L￨JJ￨O￨- women￨L￨NNS￨O￨- boosts￨L￨VBZ￨O￨- maternal￨L￨JJ￨O￨- antibody￨L￨NN￨O￨- protection￨L￨NN￨O￨- in￨L￨IN￨O￨- infants￨L￨NNS￨O￨A by￨L￨IN￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- 4￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- RSV￨U￨NN￨O￨- infant￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- 31.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- household￨L￨NN￨O￨A transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- 39￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- infant￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- school-age￨L￨JJ￨O￨- children￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨- ,￨L￨,￨O￨- causing￨L￨VBG￨O￨- around￨L￨IN￨O￨- 55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- ergodic.Throughout￨L￨JJ￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- Ω￨U￨NNP￨O￨- ,￨L￨,￨O￨- F￨U￨NN￨O￨- ,￨L￨,￨O￨- {￨L￨-LRB-￨O￨- F￨U￨NN￨O￨- t￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- probability￨L￨NN￨O￨- space￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- filtration￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- F￨U￨NN￨O￨- t￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- satisfying￨L￨VBG￨O￨- the￨L￨DT￨O￨- usual￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- right￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- and￨L￨CC￨O￨- F￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- contains￨L￨VBZ￨O￨- all￨L￨DT￨O￨- P-null￨U￨JJ￨MISC￨- sets￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- takes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Ideally￨U￨RB￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficients￨L￨NNS￨O￨A beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- should￨L￨MD￨O￨- suffer￨L￨VB￨O￨- from￨L￨IN￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- global￨L￨JJ￨O￨- positive￨L￨JJ￨O￨A solution￨L￨NN￨O￨- and￨L￨CC￨O￨- establish￨L￨VB￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants.Since￨L￨NN￨O￨- gonorrhea￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- essence￨L￨NN￨O￨- a￨L￨DT￨O￨- nonseasonal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- 10￨L￨CD￨PERCENT￨- percent￨L￨NN￨PERCENT￨- seasonal￨L￨JJ￨O￨- component￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- give￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- time-independent￨L￨JJ￨O￨- coefficients￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- interdisciplinary￨L￨JJ￨O￨- ,￨L￨,￨O￨- combining￨L￨VBG￨O￨- anthropological￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨- with￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- archaeological￨L￨JJ￨O￨- parallels￨L￨NNS￨O￨- in￨L￨IN￨O￨- regards￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- findings.KeywordsSIRS￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- Periodic￨U￨JJ￨O￨- forcing￨L￨VBG￨O￨- Social￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- Nonlinear￨U￨JJ￨O￨- dynamics￨L￨NNS￨O￨- Sabbath￨U￨NNP￨O￨- Cultural￨U￨NNP￨O￨- anthropology￨L￨NNP￨O￨- Electronic￨U￨NNP￨O￨- supplementary￨L￨JJ￨O￨A materialThe￨L￨NN￨O￨- online￨L￨NN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- doi￨L￨FW￨O￨- :￨L￨:￨O￨- 10.1007￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- s10867-014-9373-9￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- contains￨L￨VBZ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- authorized￨L￨VBN￨O￨- users￨L￨NNS￨O￨- .1￨L￨VBP￨NUMBER￨- IntroductionEspecially￨U￨RB￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- proven￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- important￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- shedding￨L￨VBG￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- complex￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- culture￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- communications￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- investigating￨L￨VBG￨O￨- topical￨L￨JJ￨O￨- anthropological￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- approach￨L￨NN￨O￨- takes￨L￨VBZ￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- analogy￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- transgression￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- here￨L￨RB￨O￨- as￨L￨IN￨O￨- violation￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨A norms￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- society.Interestingly￨L￨NN￨O￨- ,￨L￨,￨O￨- similar￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- formulated￨L￨VBN￨O￨- to￨L￨TO￨O￨- express￨L￨VB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- acquired￨L￨VBN￨O￨- by￨L￨IN￨O￨- learning￨L￨VBG￨O￨- from￨L￨IN￨O￨- others￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- vein￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- demonstrates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- may￨L￨MD￨O￨- help￨L￨VB￨O￨- understand￨L￨VB￨O￨- justice￨L￨NN￨O￨- administration￨L￨NN￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- societies￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- social￨L￨JJ￨O￨A organization￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- institution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Sabbath￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- appearance￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- Israel￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- work￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- a￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- Sabbath￨U￨NNP￨O￨- could￨L￨MD￨O￨- in￨L￨IN￨O￨- theory￨L￨NN￨O￨- enhance￨L￨VBP￨O￨- social￨L￨JJ￨O￨A resilience￨L￨NN￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- assembly￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- natural￨L￨JJ￨O￨- and￨L￨CC￨O￨- longer￨L￨JJR￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- say￨L￨VBP￨O￨- between￨L￨IN￨O￨- New￨U￨NNP￨LOCATION￨- Moon￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Full￨U￨JJ￨O￨- Moon￨U￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- mathematical￨L￨JJ￨O￨- examination￨L￨NN￨O￨- points￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- cultural￨L￨JJ￨O￨A ,￨L￨,￨O￨- civic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- Sabbath￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Sabbath￨U￨NNP￨MISC￨- institution￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- deviation￨L￨NN￨O￨- from￨L￨IN￨O￨- social￨L￨JJ￨O￨- norms￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- latency￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- case￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- backward￨L￨RB￨O￨A Euler￨U￨NNP￨PERSON￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- obtained￨L￨VBD￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- plentiful￨L￨JJ￨O￨- and￨L￨CC￨O￨- complex￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- including￨L￨VBG￨O￨- bifurcations.In￨L￨NN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- backward￨L￨RB￨O￨A Euler￨U￨NNP￨PERSON￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- discretize￨L￨VB￨O￨- a￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- plant￨L￨NN￨O￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- roguing￨L￨NN￨O￨- and￨L￨CC￨O￨- replanting￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- A￨U￨DT￨O￨- discrete￨L￨JJ￨O￨- plant￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- roguing￨L￨NN￨O￨- and￨L￨CC￨O￨- replantingYueli￨L￨NN￨O￨- Luo1￨U￨NN￨O￨- ,￨L￨,￨O￨- Shujing￨U￨VBG￨O￨- Gao1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Dehui￨U￨NNP￨O￨- Xie1￨U￨NN￨O￨- and￨L￨CC￨O￨- Yanfei￨U￨NN￨MISC￨- Dai1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2015:12￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Luo￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- plant￨L￨NN￨O￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- roguing￨L￨NN￨O￨- and￨L￨CC￨O￨- replanting￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- case￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- backward￨L￨RB￨O￨A Euler￨U￨NNP￨PERSON￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- applying￨L￨VBG￨O￨- analytic￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- and￨L￨CC￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨A Lyapunov￨U￨NN￨PERSON￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- if￨L￨IN￨O￨- LessThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- permanent￨L￨JJ￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨A SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- principles￨L￨NNS￨O￨- discussed￨L￨VBN￨O￨- herein￨L￨RB￨O￨- will￨L￨MD￨O￨- help￨L￨VB￨O￨- organizations￨L￨NNS￨O￨A and￨L￨CC￨O￨- investigators￨L￨NNS￨O￨- document￨L￨VBP￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- ranaviruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- identify￨L￨VBP￨O￨- hotspots￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- determine￨L￨VB￨O￨- factors￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- emergence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- collect￨L￨VB￨O￨- data￨L￨NNS￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- practical￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies.KeywordsDetection￨L￨NN￨O￨- Probability￨U￨NN￨O￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- Prevalence￨U￨NN￨O￨- Require￨U￨VB￨O￨- Sample￨U￨NNP￨O￨- Size￨U￨NN￨O￨- Captive￨U￨NNP￨O￨- Population￨U￨NNP￨O￨- Wood￨U￨NNP￨O￨- Frog￨U￨NNP￨O￨- These￨U￨DT￨O￨- keywords￨L￨NNS￨O￨- were￨L￨VBD￨O￨- added￨L￨VBN￨O￨- by￨L￨IN￨O￨- machine￨L￨NN￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- chapter￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- surveillance￨L￨NN￨O￨- studies￨L￨NNS￨O￨- for￨L￨IN￨O￨- ranavirus￨L￨NN￨O￨- ,￨L￨,￨O￨- required￨L￨VBN￨O￨- sample￨L￨NN￨O￨A sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- statistical￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- that￨L￨DT￨O￨- adequate￨L￨JJ￨O￨- sample￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- ranavirus￨L￨NN￨O￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- precise￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A prevalence￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- high￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- >￨L￨JJR￨O￨- 60￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- laboratory￨L￨NN￨O￨- expenses￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- ranavirus￨L￨NN￨O￨- testing￨L￨NN￨O￨- are￨L￨VBP￨O￨- substantial￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- organizations￨L￨NNS￨O￨A that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- ranaviruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- take￨L￨VB￨O￨- several￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- document￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- ranaviruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- identify￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- hotspots￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- implement￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- thwart￨L￨VBP￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- ranavirus￨L￨NN￨O￨- or￨L￨CC￨O￨- reduce￨L￨VB￨O￨- its￨L￨PRP$￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- prevalence￨L￨NN￨O￨A of￨L￨IN￨O￨- ranavirus￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- uninfected￨L￨JJ￨O￨- area￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- possible￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- modified￨L￨VBN￨O￨- metapopulation￨L￨NN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- produce￨L￨VBP￨O￨- a￨L￨DT￨O￨- discontinuous￨L￨JJ￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- jump￨L￨NN￨O￨- at￨L￨IN￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- modified￨L￨VBN￨O￨- metapopulation￨L￨NN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- produce￨L￨VBP￨O￨- a￨L￨DT￨O￨- discontinuous￨L￨JJ￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- their￨L￨PRP$￨O￨- broad￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- ranges￨L￨NNS￨O￨- ,￨L￨,￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- high￨L￨JJ￨O￨- virulence￨L￨NN￨O￨- ,￨L￨,￨O￨- multiple￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- frequent￨L￨JJ￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- amphibians￨L￨NNS￨O￨- ,￨L￨,￨O￨- fish￨L￨NN￨O￨- and￨L￨CC￨O￨- reptiles￨L￨NNS￨O￨- in￨L￨IN￨O￨- global￨L￨JJ￨O￨- trade￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- appears￨L￨VBZ￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- ranaviruses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- significantly￨L￨RB￨O￨- impact￨L￨VB￨O￨- host￨L￨NN￨TITLE￨A populations￨L￨NNS￨O￨A and￨L￨CC￨O￨- even￨L￨RB￨O￨- cause￨L￨VB￨O￨- extinctions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- wild.KeywordsLargemouth￨L￨NNP￨O￨- Bass￨U￨NNP￨O￨- Wood￨U￨NNP￨O￨- Frog￨U￨NNP￨O￨- Tiger￨U￨NNP￨O￨- Salamander￨U￨NNP￨O￨- Ectothermic￨U￨NNP￨O￨- Vertebrate￨U￨NNP￨O￨- Pallid￨U￨NNP￨O￨- Sturgeon￨U￨NNP￨O￨- These￨U￨DT￨O￨- keywords￨L￨NNS￨O￨- were￨L￨VBD￨O￨- added￨L￨VBN￨O￨- by￨L￨IN￨O￨- machine￨L￨NN￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Generally￨U￨RB￨O￨- ,￨L￨,￨O￨- ranaviruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- locally￨L￨RB￨O￨- adapted￨L￨VBN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨A populations￨L￨NNS￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- over￨L￨IN￨O￨- long￨L￨JJ￨O￨- distances￨L￨NNS￨O￨- can￨L￨MD￨O￨- disrupt￨L￨VB￨O￨- these￨L￨DT￨O￨- associations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Ranavirus￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨A populations￨L￨NNS￨O￨A ,￨L￨,￨O￨- from￨L￨IN￨O￨- apparently￨L￨RB￨O￨- benign￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- mass￨L￨NN￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- extirpation￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- view￨L￨NN￨O￨- changed￨L￨VBD￨O￨- with￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- evidence￨L￨NN￨O￨A that￨L￨IN￨O￨- ranaviruses￨L￨NNS￨O￨- were￨L￨VBD￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- widespread￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- in￨L￨IN￨O￨- several￨L￨JJ￨O￨- fishes￨L￨NNS￨O￨- and￨L￨CC￨O￨- later￨L￨RB￨O￨- amphibians￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- virulence￨L￨NN￨O￨A of￨L￨IN￨O￨- ranaviruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- captive￨L￨JJ￨O￨- fish￨L￨NN￨O￨- and￨L￨CC￨O￨- amphibian￨L￨NN￨O￨- populations￨L￨NNS￨O￨- raised￨L￨VBD￨O￨- for￨L￨IN￨O￨- production￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- summarized￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- list￨L￨NN￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- births￨L￨NNS￨O￨- and￨L￨CC￨O￨- immigration￨L￨NN￨O￨- ;￨L￨:￨O￨- β￨L￨NN￨O￨- :￨L￨:￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- ;￨L￨:￨O￨- μ￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- per￨L￨FW￨O￨- capita￨L￨NN￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- δ￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- leaving￨L￨VBG￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- compartment￨L￨NN￨O￨A I￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- quarantine￨L￨NN￨O￨- compartment￨L￨NN￨O￨- Q￨U￨NNP￨O￨- ;￨L￨:￨O￨- γ￨L￨NN￨O￨- :￨L￨:￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- ε￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- return￨L￨VBP￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- S￨U￨NN￨O￨- from￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- Q￨U￨NNP￨O￨- ;￨L￨:￨O￨- α￨L￨NN￨O￨- :￨L￨:￨O￨- disease-caused￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals.In￨L￨NN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- P￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- P￨U￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- ∗￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨A under￨L￨IN￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- condition￨L￨NN￨O￨- in￨L￨IN￨O￨- invariant￨L￨JJ￨O￨- set￨L￨NN￨O￨- Γ.In￨U￨NN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- inevitably￨L￨RB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- component￨L￨NN￨O￨- in￨L￨IN￨O￨- realism￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- realism￨L￨NN￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- deterministic￨L￨JJ￨O￨- counterparts￨L￨NNS￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- obtain￨L￨VB￨O￨- if￨L￨IN￨O￨- β￨L￨NN￨O￨- <￨L￨JJR￨O￨- γ￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- μ￨L￨NN￨O￨- −￨L￨NN￨O￨- σ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stochastically￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- and￨L￨CC￨O￨- exponentially￨L￨RB￨O￨- mean-square￨L￨JJ￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- stochastic￨L￨JJ￨O￨- version￨L￨NN￨O￨- corresponding￨L￨VBG￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- takes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- μ￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- σ￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- β￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- σ￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- δ￨L￨JJ￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- This￨U￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- discuss￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIQS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ˙￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- μ￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ˙￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- ˙￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- δ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- parameters￨L￨NNS￨O￨- A￨U￨DT￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- δ￨L￨NN￨O￨- are￨L￨VBP￨O￨- non-negative￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- complemented￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- selection￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨A networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Value￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Information￨U￨NN￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- VoI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- reporting￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- subnetworks￨L￨NNS￨O￨- of￨L￨IN￨O￨- mobility￨L￨NN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- food￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- species￨L￨NNS￨O￨- move￨L￨VBP￨O￨- .￨L￨.￨O￨- +Surveillance￨U￨NN￨O￨- network￨L￨NN￨O￨- topologies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- selected￨L￨VBN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- integrated￨L￨VBN￨O￨- network￨L￨NN￨O￨- resilience￨L￨NN￨O￨- expressing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rewiring￨L￨NN￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- report￨L￨VB￨O￨- outbreak￨L￨NN￨O￨- information￨L￨NN￨O￨A even￨L￨RB￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- destruction￨L￨NN￨O￨- or￨L￨CC￨O￨- missing￨L￨VBG￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- functioning￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨A networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- rapid￨L￨JJ￨O￨- response￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- possibly￨L￨RB￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- respond￨L￨VB￨O￨- to￨L￨TO￨O￨- emerging/re-emerging￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- unprepared￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- surveillance￨L￨NN￨O￨A network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- variable￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- in￨L￨IN￨O￨- maximizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- source￨L￨NN￨O￨- detections￨L￨NNS￨O￨- while￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- detection￨L￨NN￨O￨- error￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Optimal￨U￨JJ￨MISC￨- surveillance￨L￨NN￨O￨A network￨L￨NN￨O￨- design￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- modelMatteo￨L￨NN￨O￨- Convertino1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yang￨U￨NNP￨PERSON￨- Liu1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Haejin￨U￨NN￨O￨- Hwang1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2:6￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Convertino￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- attacking￨L￨VBG￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- worms￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A network￨L￨NN￨O￨- and￨L￨CC￨O￨- considering￨L￨VBG￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- similarity￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- software￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- spread￨L￨VBN￨O￨- among￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- devices￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- Mishra￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Keshri￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIRS-V￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- p￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- sensor￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- in￨L￨IN￨O￨- states￨L￨NNS￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBD￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- above￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- considering￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- sensor￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- need￨L￨VBP￨O￨- some￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- worms￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨- network￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- sensor￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- period￨L￨NN￨O￨- after￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- again￨L￨RB￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- incorporate￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- delays￨L￨NNS￨O￨- into￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- delayed￨L￨VBN￨O￨- SEIRS-V￨U￨NN￨O￨- system￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- worms￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨- network￨L￨NN￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- μ￨L￨SYM￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- δ￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- p￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- μ￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- η￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- sensor￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- worms￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- and￨L￨CC￨O￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- period￨L￨NN￨O￨- after￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- again￨L￨RB￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Local￨U￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨A and￨L￨CC￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- Hopf￨U￨NNP￨O￨- bifurcationIt￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- verify￨L￨VB￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- η￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- D￨U￨NN￨O￨- ∗￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- R￨U￨NNP￨O￨- ∗￨L￨NNP￨O￨- ,￨L￨,￨O￨- V￨U￨NNP￨O￨- ∗￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- α￨L￨NN￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- =￨L￨JJ￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- η￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- δ￨L￨NN￨O￨- γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Jacobian￨U￨JJ￨MISC￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- D￨U￨NN￨O￨- ∗￨L￨NN￨O￨- is￨L￨VBZ￨O￨- J￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- ∗￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨JJ￨O￨- −￨L￨NN￨O￨- a￨L￨DT￨O￨- 11￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- a￨L￨DT￨O￨- 13￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- b￨L￨NN￨O￨- 14￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨FW￨O￨- τ￨L￨FW￨O￨- −￨L￨FW￨O￨- b￨L￨NN￨O￨- 15￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨FW￨O￨- τ￨L￨FW￨O￨- −￨L￨FW￨O￨- a￨L￨DT￨O￨- 21￨L￨CD￨NUMBER￨- λ￨L￨NN￨O￨- −￨L￨VBD￨O￨- a￨L￨DT￨O￨- 22￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- a￨L￨DT￨O￨- 23￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- a￨L￨DT￨O￨- 32￨L￨CD￨NUMBER￨- λ￨L￨NN￨O￨- −￨L￨VBD￨O￨- a￨L￨DT￨O￨- 33￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- b￨L￨NN￨O￨- 33￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨SYM￨O￨- τ￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- b￨L￨NN￨O￨- 43￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨FW￨O￨- τ￨L￨FW￨O￨- λ￨L￨FW￨O￨- −￨L￨FW￨O￨- a￨L￨DT￨O￨- 44￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- b￨L￨NN￨O￨- 44￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨NN￨O￨- τ￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- a￨L￨DT￨O￨- 51￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- λ￨L￨NN￨O￨- −￨L￨VBD￨O￨- a￨L￨DT￨O￨- 55￨L￨CD￨NUMBER￨A −￨L￨NN￨O￨- b￨L￨NN￨O￨- 55￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨FW￨O￨- τ￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- 11￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- ∗￨L￨NN￨O￨- +￨L￨CC￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 13￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 21￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 22￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 23￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 32￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 33￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 44￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 51￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 55￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 14￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- δ￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 15￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- η￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 33￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 43￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 44￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- δ￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 55￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- η￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- SParSE￨U￨VBP￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- ,￨L￨,￨O￨- efficient￨L￨JJ￨O￨- ,￨L￨,￨O￨- event-oriented￨L￨JJ￨O￨- parameter￨L￨NN￨O￨A estimation￨L￨NN￨O￨A method￨L￨NN￨O￨- for￨L￨IN￨O￨- computing￨L￨VBG￨O￨- parametric￨L￨JJ￨O￨- configurations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- readily￨L￨RB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- obeying￨L￨VBG￨O￨- chemical￨L￨JJ￨O￨- master￨L￨NN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CME￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- parameter￨L￨NN￨O￨A estimation￨L￨NN￨O￨A algorithm￨L￨NN￨O￨- —￨L￨:￨O￨- Stochastic￨U￨NNP￨O￨- Parameter￨U￨NNP￨O￨- Search￨U￨VB￨O￨- for￨L￨IN￨O￨- Events￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- SParSE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- —￨L￨:￨O￨- that￨L￨IN￨O￨- automatically￨L￨RB￨O￨- computes￨L￨VBZ￨O￨- parameter￨L￨NN￨O￨- configurations￨L￨NNS￨O￨- for￨L￨IN￨O￨- propagating￨L￨VBG￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- an￨L￨DT￨O￨- event￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- user-specified￨L￨JJ￨O￨- success￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- error￨L￨NN￨O￨- tolerance￨L￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- parameter￨L￨NN￨O￨A estimation￨L￨NN￨O￨A algorithms￨L￨NNS￨O￨- in￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- chemical￨L￨NN￨O￨- kinetics￨L￨NNS￨O￨- setting￨L￨VBG￨O￨- take￨L￨VB￨O￨- time-series￨L￨JJ￨O￨- data￨L￨NNS￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- input￨L￨NN￨O￨- and￨L￨CC￨O￨- compute￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- reaction￨L￨NN￨O￨- rate￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- closely￨L￨RB￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- novel￨L￨JJ￨O￨- heuristic￨L￨NN￨O￨- for￨L￨IN￨O￨- handling￨L￨VBG￨O￨- over-perturbing￨L￨JJ￨O￨- parameter￨L￨NN￨O￨A sets￨L￨NNS￨O￨- enables￨L￨VBZ￨O￨- SParSE￨U￨NNP￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- biasing￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- rare￨L￨JJ￨O￨- events￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- amenable￨L￨JJ￨O￨- to￨L￨TO￨O￨- current￨L￨JJ￨DATE￨- algorithms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- importance￨L￨NN￨O￨- sampling￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- may￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- fractional￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- models.Keywordsfractional￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- modelKermack-McKendrick￨L￨NN￨O￨- modelnonlinear￨L￨NN￨O￨- incidenceexistence￨L￨NN￨O￨- of￨L￨IN￨O￨- solutionswellposedness￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- pioneering￨L￨JJ￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Kermack￨U￨NNP￨O￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- interesting￨L￨JJ￨O￨- and￨L￨CC￨O￨- useful￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Kermack-McKendrick￨U￨NNP￨LOCATION￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- fractional￨L￨JJ￨O￨A derivative￨L￨JJ￨O￨- order￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- of￨L￨IN￨O￨- Caputo￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Kermack-McKendrick￨U￨NN￨LOCATION￨- with￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A function￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Some￨U￨DT￨MISC￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Kermack-McKendrick￨U￨NNP￨LOCATION￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A derivative￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- incidenceEmile￨L￨NNP￨O￨- Franc￨U￨NNP￨O￨- Doungmo￨U￨NNP￨O￨- Goufo1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Riëtte￨U￨NNP￨O￨- Maritz1￨U￨NN￨O￨- and￨L￨CC￨O￨- Justin￨U￨NNP￨PERSON￨- Munganga1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2014:278￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Doungmo￨U￨NNP￨O￨- Goufo￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- monotonic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fractional￨L￨JJ￨O￨A derivative￨L￨JJ￨O￨- order￨L￨NN￨O￨- α￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- α￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- saw￨L￨VBD￨O￨- a￨L￨DT￨O￨- weak￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- testing￨L￨NN￨O￨- positive￨L￨JJ￨O￨- -￨L￨:￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- test￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- moved￨L￨VBD￨O￨- to￨L￨TO￨O￨- units￨L￨NNS￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- centrality￨L￨NN￨O￨- measured￨L￨VBN￨O￨- as￨L￨IN￨O￨- degree￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- units￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- care￨L￨NN￨O￨- episodes￨L￨NNS￨O￨- became￨L￨VBD￨O￨- longer￨L￨RBR￨O￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨O￨- Access￨U￨NN￨O￨- The￨U￨DT￨O￨- network￨L￨NN￨O￨- positions￨L￨NNS￨O￨- of￨L￨IN￨O￨- methicillin￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- Staphylococcus￨U￨FW￨O￨- aureus￨L￨FW￨O￨- affected￨L￨VBN￨O￨- units￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- regional￨L￨JJ￨O￨- healthcare￨L￨NN￨O￨- systemJan￨L￨NN￨O￨- Ohst1￨U￨NN￨O￨- ,￨L￨,￨O￨- Fredrik￨U￨NNP￨PERSON￨- Liljeros2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mikael￨U￨NNP￨PERSON￨- Stenhem4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Petter￨U￨NNP￨PERSON￨- Holme3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 3:29￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Ohst￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- dataset￨L￨NN￨O￨- of￨L￨IN￨O￨- care￨L￨NN￨O￨- episodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- regional￨L￨JJ￨O￨- Swedish￨U￨JJ￨NATIONALITY￨- hospital￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- this￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- characterized￨L￨VBD￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- network￨L￨NN￨O￨- position￨L￨NN￨O￨- of￨L￨IN￨O￨- units￨L￨NNS￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- methicillin￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- Staphylococcus￨U￨FW￨MISC￨- aureus￨L￨FW￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- ’s￨L￨POS￨O￨- location￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- changed￨L￨VBN￨O￨- upon￨L￨IN￨O￨- testing￨L￨NN￨O￨- positive￨L￨JJ￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- simplify￨L￨VB￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- flow￨L￨NN￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- represented￨L￨VBD￨O￨- it￨L￨PRP￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- units￨L￨NNS￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- two￨L￨CD￨NUMBER￨- units￨L￨NNS￨O￨- were￨L￨VBD￨O￨- connected￨L￨VBN￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- patient￨L￨NN￨O￨- moved￨L￨VBD￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- unit￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- visiting￨L￨VBG￨O￨- a￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- unit￨L￨NN￨O￨- in￨L￨IN￨O￨- between￨L￨IN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- for￨L￨IN￨O￨- e.g.￨L￨FW￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- -￨L￨:￨O￨- the￨L￨DT￨O￨- topic￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- -￨L￨:￨O￨- healthcare￨L￨NN￨O￨A associated￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- HAI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- version￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- perform￨L￨VBP￨O￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- also￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨A by￨L￨IN￨O￨- measuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- time-averaged￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- problem￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- -￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- snapshot￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given.While￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- -￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- answered￨L￨VBD￨O￨- some￨L￨DT￨O￨- basic￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- about￨L￨IN￨O￨- information￨L￨NN￨O￨- source￨L￨NN￨O￨- detection￨L￨NN￨O￨- in￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- snapshot￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- real-world￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- hundreds￨L￨NNS￨O￨- of￨L￨IN￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- expensive￨L￨JJ￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- adopt￨L￨VBP￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- path-based￨L￨JJ￨O￨- estimator￨L￨NN￨O￨A developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Zhu￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ying￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- arXiv￨L￨NNP￨O￨- :￨L￨:￨O￨- 1206.5421￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- prove￨L￨VB￨O￨- that￨L￨DT￨O￨- on￨L￨IN￨O￨- infinite￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- path-based￨L￨JJ￨O￨- estimator￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Jordan￨U￨NNP￨CITY￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- center￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- estimator￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- source￨L￨NN￨O￨- is￨L￨VBZ￨O￨- upper￨L￨JJ￨O￨- bounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- probability￨L￨NN￨O￨- on￨L￨IN￨O￨- infinite￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- other￨L￨JJ￨O￨- words￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- path-based￨L￨JJ￨O￨- estimator￨L￨NN￨O￨A minimizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- observed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- piece￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A spreads￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- said￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- receives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- removes￨L￨VBZ￨O￨- or￨L￨CC￨O￨- hides￨L￨VBZ￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- historical￨L￨JJ￨O￨- ,￨L￨,￨O￨- experimental￨L￨JJ￨O￨- mosquito-transmitted￨L￨JJ￨O￨- human￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Bayesian￨U￨JJ￨O￨- estimation￨L￨NN￨O￨- with￨L￨IN￨O￨- non-informative￨L￨JJ￨O￨- priors￨L￨NNS￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- parametric￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- readily￨L￨RB￨O￨- implemented￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨A period￨L￨NN￨O￨- and￨L￨CC￨O￨- time-to-first￨L￨JJ￨O￨- relapse￨L￨NN￨O￨- in￨L￨IN￨O￨- P.￨U￨NNP￨O￨- Results￨U￨NNS￨O￨- Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- Deviance￨U￨NNP￨O￨- Information￨U￨NNP￨O￨- Criteria￨U￨NNP￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- parameterizations￨L￨NNS￨O￨- ,￨L￨,￨O￨- experimental￨L￨JJ￨O￨- incubation￨L￨NN￨O￨- periods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- closely￨L￨RB￨O￨- modeled￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- shifted￨L￨VBN￨O￨- log-logistic￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- log-logistic￨L￨JJ￨O￨- mixture￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- fit￨L￨NN￨O￨- for￨L￨IN￨O￨- incubations￨L￨NNS￨O￨- in￨L￨IN￨O￨- observational￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- incubation￨L￨NN￨O￨A and￨L￨CC￨O￨- relapse￨L￨NN￨O￨- times￨L￨NNS￨O￨- in￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- human￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasite￨L￨NN￨O￨- Plasmodium￨U￨NN￨O￨- vivax￨L￨NN￨O￨- Andrew￨U￨NNP￨O￨- A￨U￨NNP￨O￨- Lover1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Xiahong￨U￨NNP￨O￨- Zhao1￨U￨NN￨O￨- ,￨L￨,￨O￨- Zheng￨U￨NNP￨PERSON￨- Gao2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Richard￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Coker1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Alex￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- Cook1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 14:539￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Lover￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- incubation￨L￨NN￨O￨- and￨L￨CC￨O￨- relapse￨L￨NN￨O￨- periods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- key￨L￨JJ￨O￨- components￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasite￨L￨NN￨O￨- Plasmodium￨U￨NN￨O￨- vivax￨L￨NN￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- detailed￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- based￨L￨VBN￨O￨- upon￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- lacking￨L￨VBG￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- future￨L￨JJ￨DATE￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- log-logistic￨L￨JJ￨O￨- and￨L￨CC￨O￨- Gompertz￨U￨NNP￨PERSON￨- distributions￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- utilized￨L￨VBN￨O￨- for￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- incubation￨L￨NN￨O￨A periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- relapse￨L￨NN￨O￨- times￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- region-specific￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- model￨L￨VB￨O￨- and￨L￨CC￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- important￨L￨JJ￨O￨- human￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- These￨U￨DT￨O￨- results￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- and￨L￨CC￨O￨- gamma￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- incubation￨L￨NN￨O￨A periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- relapse￨L￨NN￨O￨- times￨L￨NNS￨O￨- inadequately￨L￨RB￨O￨- capture￨L￨VBP￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- event￨L￨NN￨O￨- times￨L￨NNS￨O￨- in￨L￨IN￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- semi-automated￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- quality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- language￨L￨NN￨O￨A of￨L￨IN￨O￨- influence￨L￨NN￨O￨- using￨L￨VBG￨O￨- semantic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- singular￨L￨JJ￨O￨- value￨L￨NN￨O￨- decomposition￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- middle￨L￨JJ￨O￨- ground￨L￨NN￨O￨- between￨L￨IN￨O￨- high-level￨L￨JJ￨O￨- abstract￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- simple￨L￨JJ￨O￨- word￨L￨NN￨O￨- counting.We￨L￨NN￨O￨- then￨L￨RB￨O￨- apply￨L￨VB￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- intelligence￨L￨NN￨O￨- application￨L￨NN￨O￨- :￨L￨:￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- language￨L￨NN￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- jihadist￨L￨NN￨O￨- magazines￨L￨NNS￨O￨- Inspire￨U￨NNP￨O￨- and￨L￨CC￨O￨- Azan￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- enables￨L￨VBZ￨O￨- model￨L￨NN￨TITLE￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- documents￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- compared￨L￨VBN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- magazines￨L￨NNS￨O￨- across￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hypotheses￨L￨NNS￨O￨- about￨L￨IN￨O￨- expected￨L￨VBN￨O￨- language￨L￨NN￨O￨A use￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- validated￨L￨VBN￨O￨- or￨L￨CC￨O￨- falsified￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- textual￨L￨JJ￨O￨- content￨L￨NN￨O￨- of￨L￨IN￨O￨- issues￨L￨NNS￨O￨A of￨L￨IN￨O￨- Azan￨U￨NNP￨PERSON￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- between￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- four￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- longer￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- textual￨L￨JJ￨O￨- content￨L￨NN￨O￨- of￨L￨IN￨O￨- issues￨L￨NNS￨O￨- of￨L￨IN￨O￨- Inspire￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- issues￨L￨NNS￨O￨- are￨L￨VBP￨O￨- appearing￨L￨VBG￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- often￨L￨RB￨O￨- so￨L￨IN￨O￨- their￨L￨PRP$￨O￨- author/editor￨L￨NN￨O￨- is￨L￨VBZ￨O￨- noticeably￨L￨RB￨O￨- more￨L￨RBR￨O￨- productive.The￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- magazines￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- judge￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Issues￨U￨NNS￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- product￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- ,￨L￨,￨O￨- editors.The￨L￨JJ￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- Inspire￨U￨NNP￨O￨- appears￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- to￨L￨TO￨O￨- motivate￨L￨VB￨O￨- lone-wolf￨L￨JJ￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Western￨U￨JJ￨MISC￨- countries￨L￨NNS￨O￨- by￨L￨IN￨O￨- diaspora￨L￨NN￨O￨- jihadists￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Language￨U￨NN￨MISC￨- use￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- Jihadist￨U￨NNP￨MISC￨- magazines￨L￨NNS￨O￨- inspire￨L￨VB￨O￨- and￨L￨CC￨O￨- AzanDavid￨U￨NN￨O￨- B￨U￨NN￨O￨- Skillicorn1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Edna￨U￨NNP￨PERSON￨- F￨U￨NN￨O￨- Reid2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 3:9￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Skillicorn￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Reid￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨MISC￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- some￨L￨DT￨O￨- recent￨L￨JJ￨O￨- results.By￨L￨NN￨O￨- a￨L￨DT￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- δ￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- ≤￨L￨VBP￨O￨- I￨U￨PRP￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- I￨U￨PRP￨O￨- ≥￨L￨VBP￨O￨- I￨U￨PRP￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- δ￨L￨NN￨O￨- I￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- ;￨L￨:￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- newborns￨L￨NNS￨O￨- and￨L￨CC￨O￨- immigrants￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- recovered￨L￨VBN￨O￨- ;￨L￨:￨O￨- ε￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-related￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- positive￨L￨JJ￨O￨- numbers.Thus￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- ≤￨L￨VBP￨O￨- I￨U￨PRP￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- implies￨L￨VBZ￨O￨- {￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- I￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- δ￨L￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +Steady￨U￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- satisfy￨L￨VBP￨O￨A the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- easily￨L￨RB￨O￨- see￨L￨VBP￨O￨- that￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A P￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- I￨U￨PRP￨O￨- >￨L￨JJR￨O￨- I￨U￨PRP￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- implies￨L￨VBZ￨O￨A {￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- k￨L￨NN￨O￨- .￨L￨.￨O￨- +2014Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractTo￨U￨NNP￨O￨- facilitate￨L￨VB￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- control￨L￨NN￨O￨- plane￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- C-plane￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- user￨L￨NN￨O￨- plane￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- U-plane￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- decoupled￨L￨JJ￨O￨- architecture￨L￨NN￨O￨A is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- considered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- fifth￨L￨JJ￨ORDINAL￨- generation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5G￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- wireless￨L￨JJ￨O￨- communication￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- relatively￨L￨RB￨O￨- crucial￨L￨JJ￨O￨- C-plane￨U￨NN￨MISC￨- is￨L￨VBZ￨O￨- expanded￨L￨VBN￨O￨- and￨L￨CC￨O￨- kept￨L￨VBN￨O￨- at￨L￨IN￨O￨- dependable￨L￨JJ￨O￨- lower￨L￨JJR￨O￨- frequency￨L￨NN￨O￨- bands￨L￨NNS￨O￨- to￨L￨TO￨O￨- guarantee￨L￨VB￨O￨- transmission￨L￨NN￨O￨- reliability￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- U-plane￨U￨NN￨MISC￨- is￨L￨VBZ￨O￨- moved￨L￨VBN￨O￨- to￨L￨TO￨O￨- available￨L￨JJ￨O￨- higher￨L￨JJR￨O￨- frequency￨L￨NN￨O￨- bands￨L￨NNS￨O￨- to￨L￨TO￨O￨- boost￨L￨VB￨O￨- capacity￨L￨NN￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- reflect￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- C-plane￨U￨NN￨O￨- ,￨L￨,￨O￨- conventional￨L￨JJ￨O￨- outage￨L￨NN￨O￨- probability￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- properly￨L￨RB￨O￨- indicate￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- reliability￨L￨NN￨O￨- of￨L￨IN￨O￨- C/U-plane￨U￨NN￨O￨- decoupled￨L￨VBN￨O￨- architecture￨L￨NN￨O￨A whose￨L￨WP$￨O￨- primary￨L￨JJ￨O￨- design￨L￨NN￨O￨- consideration￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- C-plane￨U￨NN￨MISC￨- more￨L￨RBR￨O￨- heavily￨L￨RB￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- reliability￨L￨NN￨O￨- thereby￨L￨RB￨O￨- being￨L￨VBG￨O￨- kept￨L￨VBN￨O￨- at￨L￨IN￨O￨- dependable￨L￨JJ￨O￨- lower￨L￨JJR￨O￨- frequency￨L￨NN￨O￨- bands￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- appropriately￨L￨RB￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- reliability￨L￨NN￨O￨- of￨L￨IN￨O￨- C/U-plane￨U￨NN￨O￨- decoupled￨L￨VBN￨O￨- architecture￨L￨NN￨O￨A is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Reliability￨U￨NN￨MISC￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- 5G￨L￨NN￨O￨- C/U-plane￨U￨NN￨O￨- decoupled￨L￨VBN￨O￨- architecture￨L￨NN￨O￨A for￨L￨IN￨O￨- high-speed￨L￨JJ￨O￨- railwayLi￨L￨NNP￨O￨- Yan￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Xuming￨U￨NN￨O￨- Fang￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- †￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2014:127￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Yan￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Fang￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- some￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- realize￨L￨VB￨O￨- the￨L￨DT￨O￨- genetic￨L￨JJ￨O￨- switching￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- GATA-PU.1￨U￨NN￨O￨- regulatory￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- d￨L￨NN￨O￨- x￨L￨CC￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- a￨L￨DT￨O￨- 3￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- 4￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- 5￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- 6￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- 7￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- z￨L￨SYM￨O￨- −￨L￨SYM￨O￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- y￨L￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- b￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- b￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- b￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- b￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- +￨L￨CC￨O￨- b￨L￨NN￨O￨- 5￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- +￨L￨CC￨O￨- b￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- z￨L￨SYM￨O￨- −￨L￨SYM￨O￨- k￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- z￨L￨SYM￨O￨- d￨L￨FW￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- c￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- c￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- 5￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- z￨L￨SYM￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- 7￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- z￨L￨SYM￨O￨- −￨L￨SYM￨O￨- k￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- and￨L￨CC￨O￨- z￨L￨SYM￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- TFs￨U￨NNS￨MISC￨- GATA-1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- GATA-2￨U￨NN￨O￨- and￨L￨CC￨O￨- PU￨U￨NN￨O￨- .1￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- c￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- expression￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨- GATA-1￨U￨NN￨O￨- ,￨L￨,￨O￨- GATA-2￨U￨NN￨O￨- and￨L￨CC￨O￨- PU￨U￨NN￨O￨- .1￨L￨CD￨NUMBER￨- auto-regulated￨L￨JJ￨O￨- by￨L￨IN￨O￨- itself￨L￨PRP￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expression￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- gene￨L￨NN￨O￨- GATA-1￨U￨NN￨O￨- regulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- TF￨U￨NN￨O￨- GATA-2￨U￨NN￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- k￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- degradation￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- TFs￨U￨NNS￨MISC￨- GATA-1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- GATA-2￨U￨NN￨O￨- and￨L￨CC￨O￨- PU￨U￨NN￨O￨- .1￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- An￨U￨DT￨O￨- NSFD￨U￨NN￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategyQianqian￨L￨NN￨O￨- Cui1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jiabo￨U￨NNP￨O￨- Xu3￨U￨NN￨O￨- ,￨L￨,￨O￨- Qiang￨U￨NNP￨PERSON￨- Zhang2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Kai￨U￨NNP￨MISC￨- Wang4￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 2014:172￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Cui￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- construct￨L￨VBP￨O￨- a￨L￨DT￨O￨- nonstandard￨L￨JJ￨O￨- finite￨L￨JJ￨O￨- difference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NSFD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- are￨L￨VBP￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- μ￨L￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- R￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- p￨L￨NN￨O￨- A￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- μ￨L￨NN￨O￨- R￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- noted￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- equations￨L￨NNS￨O￨A ,￨L￨,￨O￨- if￨L￨IN￨O￨- added￨L￨VBN￨O￨- together￨L￨RB￨O￨- ,￨L￨,￨O￨- satisfies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- conservation￨L￨NN￨O￨- law￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- d￨L￨NN￨O￨- N￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- μ￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- easy￨L￨JJ￨O￨- to￨L￨TO￨O￨- verify￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- domain￨L￨NN￨O￨- D￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- 3￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- ≤￨L￨NN￨O￨- A￨U￨NN￨O￨- /￨L￨:￨O￨- μ￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- compact￨L￨JJ￨O￨- ,￨L￨,￨O￨- positively￨L￨RB￨O￨A invariant￨L￨JJ￨O￨- set￨L￨NN￨O￨- for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- illustrating￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- theoretical￨L￨JJ￨O￨- conclusions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- give￨L￨VBP￨O￨- some￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- examples.For￨L￨NN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- and￨L￨CC￨O￨- more￨L￨JJR￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A of￨L￨IN￨O￨- map￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- should￨L￨MD￨O￨- refer￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- references￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- cited￨L￨VBN￨O￨- therein.We￨L￨NN￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- deterministic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- studied￨L￨VBN￨O￨- by￨L￨IN￨O￨- Allen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- α￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- N￨U￨NN￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- β￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- N￨U￨NN￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- represent￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- isolated￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- subgroups￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- n￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- Δt￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨DURATION￨- hour￨L￨NN￨DURATION￨- or￨L￨CC￨O￨- 1￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- deaths￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- vertical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- all￨L￨DT￨O￨- new-born￨L￨JJ￨O￨- members￨L￨NNS￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- recovery￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- immunity.In￨L￨NN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- discuss￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- easily￨L￨RB￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- preliminary￨L￨JJ￨O￨- transformations￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- hereafter.Dividing￨L￨VBG￨O￨- both￨L￨DT￨O￨- sides￨L￨NNS￨O￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- performing￨L￨VBG￨O￨- a￨L￨DT￨O￨- scaling￨L￨NN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- →￨L￨NN￨O￨- α￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- →￨L￨NN￨O￨- β￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- →￨L￨NN￨O￨- γ￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- →￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- n￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- write￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨A {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- α￨L￨NN￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- n￨L￨NN￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- α￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- pay￨L￨VBP￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- structural￨L￨JJ￨O￨- stabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- under￨L￨IN￨O￨- certain￨L￨JJ￨O￨- restrictive￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- of￨L￨IN￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- <￨L￨JJR￨O￨- s￨L￨NNS￨O￨- ≤￨L￨VBP￨O￨- 0￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- map￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- s￨L￨NNS￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- ∗￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- =￨L￨JJ￨O￨- s￨L￨NNS￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- s￨L￨NNS￨O￨- α￨L￨VBP￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIRI￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨A :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- b￨L￨NN￨O￨- −￨L￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- k￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- μ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- μ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- proportionality￨L￨NN￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- temporarily￨L￨RB￨O￨- immune￨L￨JJ￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- class￨L￨NN￨O￨- revert￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- saturated￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- h￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- parameters.For￨L￨NN￨O￨- convenience￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- transform￨L￨VB￨O￨- the￨L￨DT￨O￨- three-dimensional￨L￨JJ￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +Moreira￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIRI￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- φ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- derived￨L￨VBN￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibria￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- elementary￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- Lienard￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- equation￨L￨NN￨O￨- and￨L￨CC￨O￨- Lyapunov￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- direct￨L￨JJ￨O￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +2014Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIRI￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨A ,￨L￨,￨O￨- namely￨L￨RB￨O￨- k￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- psychological￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- certain￨L￨JJ￨O￨- serious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- getting￨L￨VBG￨O￨- larger￨L￨JJR￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- delay￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A function￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- =￨L￨JJ￨O￨- k￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- stability￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 611￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 625￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asStochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- maternal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- vertical￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- horizontal￨L￨JJ￨O￨A )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- appraisal￨L￨NN￨O￨- of￨L￨IN￨O￨- preventive￨L￨JJ￨O￨- strategiesAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsHui-Fang￨L￨JJ￨O￨- HungYa-Chuan￨U￨JJ￨MISC￨- WangAmy￨U￨NNP￨MISC￨- Ming-Fang￨U￨NNP￨MISC￨- YenHsiu-Hsi￨U￨NNP￨MISC￨- ChenOpen￨U￨NNP￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- PaperFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1.5￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 5￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractElucidating￨U￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- Hepatitis￨U￨NNP￨CAUSE_OF_DEATH￨- B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HBV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- provides￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- useful￨L￨JJ￨O￨- information￨L￨NN￨O￨- for￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- a￨L￨DT￨O￨- bedrock￨L￨NN￨O￨- for￨L￨IN￨O￨- economic￨L￨JJ￨O￨- appraisal￨L￨NN￨O￨- of￨L￨IN￨O￨- population-based￨L￨JJ￨O￨- preventive￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- universal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- linking￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- established￨L￨VBN￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- sequelae￨L￨NN￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- chronic￨L￨JJ￨O￨- hepatitis￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- liver￨L￨NN￨O￨- cirrhosis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hepatocelluar￨L￨JJ￨O￨- carcinoma￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- cycle￨L￨NN￨O￨- decision￨L￨NN￨O￨- tree￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- population-based￨L￨JJ￨O￨- preventive￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- maternal￨L￨JJ￨O￨- lamivudine￨L￨NN￨O￨- use￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- began￨L￨VBD￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- two-state￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- further￨L￨JJ￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- five-state￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- latent￨L￨JJ￨O￨- phase￨L￨NN￨O￨- ,￨L￨,￨O￨- active￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- replication￨L￨NN￨O￨- ,￨L￨,￨O￨- carrier￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- states￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- allowances￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- mixed￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- vertical￨L￨JJ￨O￨- and￨L￨CC￨O￨- horizontal￨L￨JJ￨O￨A transmissions￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- active￨L￨JJ￨O￨- virus￨L￨NN￨O￨- replication￨L￨NN￨O￨A and￨L￨CC￨O￨- finally￨L￨RB￨O￨- to￨L￨TO￨O￨- recovery￨L￨NN￨O￨- state￨L￨NN￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- carrier￨L￨NN￨O￨- state￨L￨NN￨O￨- through￨L￨IN￨O￨- both￨L￨DT￨O￨- routes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- directly￨L￨RB￨O￨- observable￨L￨JJ￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- therefore￨L￨RB￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- quantitatively￨L￨RB￨O￨- elucidate￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- five-state￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- horizontal￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- contribute￨L￨VB￨O￨- more￨L￨JJR￨O￨- to￨L￨TO￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- than￨L￨IN￨O￨- vertical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- northern￨L￨JJ￨O￨- area￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 59￨L￨CD￨NUMBER￨- vs.￨L￨CC￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibria￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Jacobian￨U￨JJ￨MISC￨- matrix￨L￨NN￨O￨- method￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- Lyapunov￨U￨NN￨MISC￨- function￨L￨NN￨O￨- and￨L￨CC￨O￨- employing￨L￨VBG￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- competitive￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- are￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- plant￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- effects.Although￨L￨NN￨O￨- early￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- plant￨L￨NN￨O￨- pathogens￨L￨NNS￨O￨- seldom￨L￨RB￨O￨- included￨L￨VBD￨O￨- the￨L￨DT￨O￨- demographics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- replenishment￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- common￨L￨JJ￨O￨- in￨L￨IN￨O￨- those￨L￨DT￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- plant￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- disappear￨L￨VB￨O￨- eventually￨L￨RB￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- plant￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- persist￨L￨VB￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- formula￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- generation￨L￨NN￨O￨- matrix￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- discussed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Invasion￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Salmonella￨U￨FW￨LOCATION￨- Kentucky￨U￨NNP￨STATE_OR_PROVINCE￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- adult￨L￨JJ￨O￨- dairy￨L￨NN￨O￨- herd￨L￨NN￨O￨- using￨L￨VBG￨O￨- approximate￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- computationZhao￨L￨NN￨O￨- Lu1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Rebecca￨U￨NNP￨PERSON￨- M￨U￨NNP￨O￨- Mitchell1￨U￨NN￨O￨- ,￨L￨,￨O￨- Rebecca￨U￨NNP￨PERSON￨- L￨U￨NNP￨PERSON￨- Smith1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Jeffrey￨U￨NNP￨PERSON￨- S￨U￨NN￨PERSON￨- Karns2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Jo￨U￨NNP￨PERSON￨- Ann￨U￨NNP￨PERSON￨- S￨U￨NN￨PERSON￨- van￨L￨NN￨PERSON￨- Kessel2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- Wolfgang3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ynte￨U￨NNP￨PERSON￨- H￨U￨NNP￨PERSON￨- Schukken1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Yrjo￨U￨NN￨PERSON￨- T￨U￨NN￨O￨- Grohn1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 9:245￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Lu￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- An￨U￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- Salmonella￨U￨FW￨LOCATION￨- Kentucky￨U￨NNP￨STATE_OR_PROVINCE￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- sustained￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- was￨L￨VBD￨O￨- recently￨L￨RB￨DATE￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- adult￨L￨JJ￨O￨- dairy￨L￨NN￨O￨- herd￨L￨NN￨O￨- enrolled￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- longitudinal￨L￨JJ￨O￨A study￨L￨NN￨O￨- involving￨L￨VBG￨O￨- intensive￨L￨JJ￨O￨- fecal￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approximate￨L￨JJ￨O￨- Bayesian￨U￨JJ￨MISC￨- computation￨L￨NN￨O￨- technique￨L￨NN￨O￨- was￨L￨VBD￨O￨- applied￨L￨VBN￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- shape￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- gamma￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- shedding￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- susceptible-infectious-recovered-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- compartment￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- gamma￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨A period￨L￨NN￨O￨A .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- results￨L￨NNS￨O￨- report￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- 0.417￨L￨CD￨NUMBER￨- month-1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- median￨L￨NN￨O￨- :￨L￨:￨O￨- 0.417￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨A %￨L￨NN￨PERCENT￨- credible￨L￨JJ￨O￨- interval￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 0.406￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0.429￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- γ-1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- 7.95￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- median￨L￨NN￨O￨- :￨L￨:￨O￨- 7.95￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- credible￨L￨JJ￨O￨- interval￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 7.70￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8.22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- shape￨L￨NN￨O￨- parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- gamma￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 242￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- median￨L￨NN￨O￨- :￨L￨:￨O￨- 182￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- credible￨L￨JJ￨O￨- interval￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- 2.91￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- median￨L￨NN￨O￨- :￨L￨:￨O￨- 2.91￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- credible￨L￨JJ￨O￨- interval￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 2.83￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3.00￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- This￨U￨DT￨O￨- study￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- Salmonella￨U￨FW￨LOCATION￨- Kentucky￨U￨NNP￨STATE_OR_PROVINCE￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- herd￨L￨NN￨O￨- was￨L￨VBD￨O￨- of￨L￨IN￨O￨- mild￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- and￨L￨CC￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- together￨L￨RB￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- explanation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- prevalence￨L￨NN￨O￨- pattern￨L￨NN￨O￨- after￨L￨IN￨O￨- invasion￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨A ability￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- Salmonella￨U￨FW￨LOCATION￨- Kentucky￨U￨NNP￨STATE_OR_PROVINCE￨- in￨L￨IN￨O￨- dairy￨L￨NN￨O￨- cattle￨L￨NNS￨O￨- ,￨L￨,￨O￨- accurate￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- longitudinal￨L￨JJ￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- offers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- feasible￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- community￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- valuable￨L￨JJ￨O￨- for￨L￨IN￨O￨- designing￨L￨VBG￨O￨- and￨L￨CC￨O￨- optimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- defense￨L￨NN￨O￨- systems.KeywordsDynamic￨L￨JJ￨O￨- networkPropagation￨L￨NN￨O￨- powerVirus￨L￨NN￨O￨- restraintBasic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨A structure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Three￨U￨CD￨NUMBER￨- basic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- structures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- quantified￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A in￨L￨IN￨O￨- different￨L￨JJ￨O￨- network￨L￨NN￨O￨- structures￨L￨NNS￨O￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- smart￨L￨JJ￨O￨- devices￨L￨NNS￨O￨- can￨L￨MD￨O￨- greatly￨L￨RB￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A even￨L￨RB￨O￨- if￨L￨IN￨O￨- most￨L￨JJS￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- remain￨L￨VBP￨O￨- still￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- and￨L￨CC￨O￨- restrain￨L￨VB￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A by￨L￨IN￨O￨- proposing￨L￨VBG￨O￨- the￨L￨DT￨O￨- concepts￨L￨NNS￨O￨- of￨L￨IN￨O￨- propagation￨L￨NN￨O￨- power￨L￨NN￨O￨- and￨L￨CC￨O￨- propagation￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A and￨L￨CC￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- explored￨L￨VBN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 58￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NNP￨O￨- 15￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 1818￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1831￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asExploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- SARS￨U￨NNP￨O￨- in-out￨L￨JJ￨O￨- flow￨L￨NN￨O￨- in￨L￨IN￨O￨- mainland￨L￨NN￨O￨- ChinaAuthorsAuthors￨U￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsBiSong￨L￨NNP￨O￨- HuJianHua￨U￨NNP￨MISC￨- GongJun￨U￨NNP￨MISC￨- SunJiePing￨U￨NNP￨MISC￨- ZhouOpen￨U￨NNP￨MISC￨- AccessArticle￨U￨NNP￨MISC￨- GeographyFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 612￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractThe￨U￨NNP￨O￨- changing￨L￨VBG￨O￨- spatiotemporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- susceptible-infected-symptomatic-treated-recovered￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- /￨L￨:￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2003￨L￨CD￨DATE￨A Severe￨U￨JJ￨O￨- Acute￨U￨JJ￨O￨- Respiratory￨U￨JJ￨O￨- Syndrome￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SARS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemiological￨L￨JJ￨O￨- investigation￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- mainland￨L￨NN￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- three￨L￨CD￨NUMBER￨- typical￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- working￨L￨VBG￨O￨- unit/home￨L￨NN￨O￨- address￨L￨NN￨O￨- ,￨L￨,￨O￨- onset￨L￨NN￨O￨- location￨L￨NN￨O￨- and￨L￨CC￨O￨- reporting￨L￨VBG￨O￨- unit￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- define￨L￨VB￨O￨- the￨L￨DT￨O￨- in-out￨L￨JJ￨O￨- flow￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SARS￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemiology￨U￨NNP￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- SARS￨U￨NNP￨O￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2003￨L￨CD￨DATE￨A epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 3215￨L￨CD￨DATE￨- –￨L￨:￨O￨- 3221CrossRefGoogle￨L￨NN￨O￨- Scholar7.Cao￨U￨NN￨O￨- Z￨U￨NN￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- Zeng￨U￨NN￨PERSON￨- D￨U￨NN￨PERSON￨- J￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Zheng￨U￨NN￨PERSON￨- X￨U￨NN￨O￨- L￨U￨NN￨O￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 1017￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1028CrossRefGoogle￨L￨JJ￨O￨- Scholar8.Fang￨U￨NN￨O￨- L￨U￨NN￨O￨- Q￨U￨NNP￨O￨- ,￨L￨,￨O￨- de￨L￨FW￨PERSON￨- Vlas￨U￨FW￨PERSON￨- S￨U￨NN￨PERSON￨- J￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Feng￨U￨NN￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +Remark￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- For￨U￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- easily￨L￨RB￨O￨- see￨L￨VB￨O￨- that￨L￨DT￨O￨- when￨L￨WRB￨O￨- β￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- describes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- type￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- courses￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- y￨L￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- i￨L￨FW￨O￨- th￨L￨DT￨O￨A course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- β￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- describes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- SEIRS￨U￨NN￨O￨- type￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- courses￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- y￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- exposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- i￨L￨FW￨O￨- th￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease.Remark￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- term￨L￨NN￨O￨- is￨L￨VBZ￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- ∑￨L￨NN￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- β￨L￨NN￨O￨- i￨L￨FW￨O￨- y￨L￨FW￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 58￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 741￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 749￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asInfluence￨L￨NN￨O￨- of￨L￨IN￨O￨- extreme￨L￨JJ￨O￨- weather￨L￨NN￨O￨- and￨L￨CC￨O￨- meteorological￨L￨JJ￨O￨- anomalies￨L￨NNS￨O￨- on￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- AuthorsAuthors￨U￨NNPS￨ORGANIZATION￨- and￨L￨CC￨O￨- affiliationsHong￨L￨NNP￨O￨- XiaoHuaiYu￨U￨NNP￨O￨- TianXiaoLing￨U￨NNP￨O￨- LinLiDong￨U￨NNP￨O￨- GaoXiangYu￨U￨NNP￨O￨- DaiXiXing￨U￨NNP￨O￨- ZhangBiYun￨U￨NNP￨MISC￨- ChenJian￨U￨NNP￨MISC￨- ZhaoJingZhe￨U￨NNP￨MISC￨- XuOpen￨U￨NNP￨MISC￨- AccessArticle￨U￨NNP￨MISC￨- Preventive￨U￨NNP￨MISC￨- Medicine￨U￨NNP￨MISC￨- &￨L￨CC￨O￨- HygienicsFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 834￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨O￨- 10￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractBiological￨U￨JJ￨O￨- experiments￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- evidence￨L￨NN￨O￨A indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- environment￨L￨NN￨O￨- have￨L￨VBP￨O￨- important￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 2211￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2218CrossRefGoogle￨L￨JJ￨O￨- Scholar7.Barry￨U￨NN￨O￨- J￨U￨NN￨O￨- M￨U￨NN￨O￨- ,￨L￨,￨O￨- Viboud￨U￨NN￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- Simonsen￨U￨NNP￨ORGANIZATION￨- L.￨U￨NNP￨ORGANIZATION￨- Citation￨U￨NNP￨ORGANIZATION￨- –￨L￨:￨O￨- 1919￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- :￨L￨:￨O￨- Epidemiological￨U￨JJ￨O￨- evidence￨L￨NN￨O￨A from￨L￨IN￨O￨- US￨U￨NNP￨ORGANIZATION￨- Army￨U￨NNP￨ORGANIZATION￨- camps￨L￨NNS￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- Britain￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 7313￨L￨CD￨DATE￨- –￨L￨:￨O￨- 7314CrossRefGoogle￨L￨JJ￨O￨- Scholar3.Webster￨U￨NN￨O￨- R￨U￨NN￨O￨- G￨U￨NN￨O￨- ,￨L￨,￨O￨- Bean￨U￨NNP￨O￨- W￨U￨NNP￨O￨- J￨U￨NNP￨O￨- ,￨L￨,￨O￨- Gorman￨U￨NNP￨PERSON￨- O￨U￨NNP￨O￨- T￨U￨NN￨O￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22CrossRefGoogle￨L￨JJ￨O￨- Scholar6.Murray￨U￨NN￨O￨- C￨U￨NN￨O￨- J￨U￨NN￨O￨- L￨U￨NN￨O￨- ,￨L￨,￨O￨- Lopez￨U￨NNP￨PERSON￨- A￨U￨NNP￨O￨- D￨U￨NNP￨O￨- ,￨L￨,￨O￨- Chin￨U￨NNP￨PERSON￨- B￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- research￨L￨NN￨O￨- works￨L￨VBZ￨O￨- on￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- concern￨L￨NN￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- equilibria￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- flip￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨- and￨L￨CC￨O￨- Hopf￨U￨NN￨PERSON￨- bifurcation￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- are￨L￨VBP￨O￨- quite￨L￨RB￨O￨- few￨L￨JJ￨O￨- for￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- enough￨L￨JJ￨O￨- effective￨L￨JJ￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- discrete￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- complicated￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- than￨L￨IN￨O￨- its￨L￨PRP$￨O￨- corresponding￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- model.We￨L￨NN￨O￨- will￨L￨MD￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- get￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨A SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelXia￨L￨NN￨O￨- Ma1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yicang￨U￨NNP￨O￨- Zhou1￨U￨NN￨O￨- and￨L￨CC￨O￨- Hui￨U￨NNP￨O￨- Cao2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2013:42￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Ma￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- discrete￨L￨JJ￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- Λ￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- μ￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- μ￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Λ￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- when￨L￨WRB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- A￨U￨NNP￨O￨- low-cost￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaksTimo￨L￨NN￨O￨- Smieszek1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Marcel￨U￨NNP￨O￨- Salathé1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 11:35￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Smieszek￨U￨NNP￨O￨- and￨L￨CC￨O￨- Salathé￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Infectious￨U￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- communities￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- early￨L￨JJ￨O￨A detection￨L￨NN￨O￨A and￨L￨CC￨O￨- effective￨L￨JJ￨O￨- prevention￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- low-cost￨L￨JJ￨O￨- method￨L￨NN￨O￨- -￨L￨:￨O￨- called￨L￨VBN￨O￨- collocation￨L￨NN￨O￨- ranking￨L￨NN￨O￨- -￨L￨:￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- individual￨L￨JJ￨O￨- importance￨L￨NN￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨A detection￨L￨NN￨O￨A and￨L￨CC￨O￨- targeted￨L￨VBN￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- easily￨L￨RB￨O￨- implementable￨L￨JJ￨O￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- computationally￨L￨RB￨O￨- validate￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- method￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- school￨L￨NN￨O￨- setting￨L￨NN￨O￨- by￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- against￨L￨IN￨O￨- computational￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- high-resolution￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Assessing￨U￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- importance￨L￨NN￨O￨A of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- community￨L￨NN￨O￨- member￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- processes￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- detailed￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨A is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- individual￨L￨JJ￨O￨- collocation￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- readily￨L￨RB￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- community￨L￨NN￨O￨- settings￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- offices￨L￨NNS￨O￨- ,￨L￨,￨O￨- hospitals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +Analysis￨U￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- shared￨L￨JJ￨O￨- access￨L￨NN￨O￨- achieves￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- throughput￨L￨NN￨O￨- of￨L￨IN￨O￨- open￨L￨JJ￨O￨- access￨L￨NN￨O￨- while￨L￨IN￨O￨- also￨L￨RB￨O￨- satisfying￨L￨VBG￨O￨- rate￨L￨NN￨O￨- requirements￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- closed￨L￨JJ￨O￨- access￨L￨NN￨O￨- fails￨L￨VBZ￨O￨- for￨L￨IN￨O￨- cellular￨L￨JJ￨O￨- users￨L￨NNS￨O￨- and￨L￨CC￨O￨- open￨L￨JJ￨O￨- access￨L￨NN￨O￨- fails￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- home￨L￨NN￨O￨A user.KeywordsNetwork￨L￨NN￨MISC￨- ThroughputComplementary￨U￨NNP￨MISC￨- Cumulative￨U￨NNP￨MISC￨- Distribution￨U￨NN￨MISC￨- FunctionMacrocell￨U￨NNP￨MISC￨- Base￨U￨NNP￨MISC￨- StationCellular￨U￨NNP￨MISC￨- UserHome￨U￨NNP￨MISC￨- User￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionFemtocells￨U￨NNS￨O￨- are￨L￨VBP￨O￨- small￨L￨JJ￨O￨- form-factor￨L￨JJ￨O￨- base￨L￨NN￨O￨- stations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- installed￨L￨VBN￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- existing￨L￨VBG￨O￨- cellular￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Closed￨U￨JJ￨O￨- access￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- only￨L￨RB￨O￨- specified￨L￨VBN￨O￨- registered￨L￨VBN￨O￨- home￨L￨NN￨O￨A users￨L￨NNS￨O￨- can￨L￨MD￨O￨- communicate￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- femtocell￨L￨NN￨O￨- access￨L￨NN￨O￨- point￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FAP￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- appears￨L￨VBZ￨O￨- attractive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- home￨L￨NN￨O￨- user￨L￨NN￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- severe￨L￨JJ￨O￨- cross-tier￨L￨JJ￨O￨- interference￨L￨NN￨O￨- from￨L￨IN￨O￨- nearby￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- users￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- uplink￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Figure1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- nearby￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- users￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- downlink￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- average￨L￨JJ￨O￨- sum￨L￨NN￨O￨- throughput￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- any￨L￨DT￨O￨- other￨L￨JJ￨O￨- SINR-based￨U￨JJ￨MISC￨- metric￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- home￨L￨NN￨O￨A users￨L￨NNS￨O￨- and￨L￨CC￨O￨- cellular￨L￨JJ￨O￨- users￨L￨NNS￨O￨- under￨L￨IN￨O￨- open￨L￨JJ￨O￨- and￨L￨CC￨O￨- closed￨L￨JJ￨O￨- access￨L￨NN￨O￨- can￨L￨MD￨O￨- readily￨L￨RB￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- expressions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Such￨U￨PDT￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- BS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- appears￨L￨VBZ￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨- outage/throughput￨L￨JJ￨O￨- averaged￨L￨VBD￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- throughput￨L￨NN￨O￨- of￨L￨IN￨O￨- open￨L￨JJ￨O￨- ,￨L￨,￨O￨- closed￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- shared￨L￨VBD￨O￨A access￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- femtocell￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- distance￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- MBS￨U￨NNP￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- uplink￨L￨NN￨O￨- throughput￨L￨NN￨O￨- of￨L￨IN￨O￨- registered￨L￨VBN￨O￨- home￨L￨NN￨O￨A users￨L￨NNS￨O￨- ,￨L￨,￨O￨- open￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- shared￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- access￨L￨NN￨O￨- reduces￨L￨VBZ￨O￨- interference￨L￨NN￨O￨- by￨L￨IN￨O￨- handing￨L￨VBG￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- loud￨L￨JJ￨O￨- neighbor￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- expense￨L￨NN￨O￨- of￨L￨IN￨O￨- FAP￨U￨NN￨ORGANIZATION￨- resource￨L￨NN￨O￨- sharing￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- advantage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- discrete-time￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- easier￨L￨JJR￨O￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- than￨L￨IN￨O￨- continuous-time￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- easier￨L￨JJR￨O￨- to￨L￨TO￨O￨- derive.The￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- ,￨L￨,￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- extinction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- constraints￨L￨NNS￨O￨- for￨L￨IN￨O￨- guaranteeing￨L￨VBG￨O￨- the￨L￨DT￨O￨- positivity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- boundedness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- generate￨L￨VBP￨O￨- an￨L￨DT￨O￨- oscillatory￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- objectives￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- about￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- positivity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- eradication￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- under￨L￨IN￨O￨- feedback￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- laws￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- properties￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- convergence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- errors￨L￨NNS￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- time￨L￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- are￨L￨VBP￨O￨- investigated.KeywordsSEIR￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelsvaccinationnonlinear￨L￨NN￨O￨- controlstabilitypositivitynonlinear￨L￨NN￨O￨- observers￨L￨NNS￨O￨- design￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionA￨U￨NN￨O￨- relevant￨L￨JJ￨O￨- area￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Concretely￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- exhaustively￨L￨RB￨O￨- analyses￨L￨NNS￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- state￨L￨NN￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨- law￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- the￨L￨DT￨O￨- controller￨L￨NN￨TITLE￨- gains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- An￨U￨DT￨O￨- observer-based￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- control￨L￨NN￨O￨- law￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- feedback￨L￨NN￨O￨- linearization￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- for￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- systemsS￨L￨NN￨O￨- Alonso-Quesada1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- De￨U￨NNP￨O￨- la￨L￨NNP￨O￨- Sen1￨U￨NN￨O￨- ,￨L￨,￨O￨- RP￨U￨NN￨MISC￨- Agarwal2￨U￨NN￨MISC￨- and￨L￨CC￨O￨- A￨U￨DT￨O￨- Ibeas3￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2012:161￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Alonso-Quesada￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- fighting￨L￨VBG￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- higher￨L￨JJR￨O￨- in￨L￨IN￨O￨- pre-weaning￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- post-weaning￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- which￨L￨WDT￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- age-related￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sow￨L￨VB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NN￨O￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- longitudinal￨L￨JJ￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- Danish￨U￨JJ￨NATIONALITY￨- and￨L￨CC￨O￨- four￨L￨CD￨NUMBER￨- Dutch￨U￨JJ￨NATIONALITY￨- pig￨L￨NN￨O￨- herds￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NN￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- within￨L￨IN￨O￨- pig￨L￨NN￨O￨- herds￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- factors￨L￨NNS￨O￨- affecting￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Longitudinal￨U￨JJ￨MISC￨- study￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NN￨O￨- within￨L￨IN￨O￨- pig￨L￨NN￨O￨A herdsEls￨L￨NNS￨O￨- M￨U￨NN￨O￨- Broens1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Carmen￨U￨NNP￨PERSON￨- Espinosa-Gongora3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Elisabeth￨U￨NNP￨PERSON￨- AM￨U￨NNP￨PERSON￨- Graat1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Nadia￨U￨NNP￨PERSON￨- Vendrig1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Peter￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Der￨U￨NNP￨PERSON￨- Wolf4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Luca￨U￨NNP￨PERSON￨- Guardabassi3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Patrick￨U￨NNP￨PERSON￨- Butaye5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jens￨U￨NNP￨PERSON￨- Peter￨U￨NNP￨PERSON￨- Nielsen7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Mart￨U￨NNP￨O￨- CM￨U￨NN￨O￨- De￨U￨NNP￨O￨- Jong1￨U￨NNP￨O￨- and￨L￨CC￨O￨- Arjen￨U￨NNP￨PERSON￨- W￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- De￨U￨NNP￨PERSON￨- Giessen2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 8:58￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- 2012￨L￨CD￨DATE￨- Broens￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Since￨U￨IN￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- emerged￨L￨VBN￨O￨- in￨L￨IN￨O￨- livestock￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +Transmission￨U￨NNP￨O￨- rates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- higher￨L￨JJR￨O￨- in￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A treated￨L￨VBN￨O￨- with￨L￨IN￨O￨- tetracyclins￨L￨NNS￨O￨- and￨L￨CC￨O￨- β-lactams￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- untreated￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- implying￨L￨VBG￨O￨- a￨L￨DT￨O￨- selective￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NN￨O￨- when￨L￨WRB￨O￨- these￨L￨DT￨O￨- antimicrobials￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- distinct￨L￨JJ￨O￨- clone￨L￨NN￨O￨- of￨L￨IN￨O￨- methicillin￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- Staphylococcus￨U￨FW￨O￨- aureus￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- livestock-associated￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- LA￨U￨NNP￨CITY￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A and￨L￨CC￨O￨- in￨L￨IN￨O￨- people￨L￨NNS￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- Spray￨U￨NN￨O￨- and￨L￨CC￨O￨- Wait￨U￨VB￨O￨- protocols￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- H￨U￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- hop￨L￨NN￨O￨- forwarding￨L￨NN￨O￨- mode￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- better￨L￨JJR￨O￨- performance￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- delivery￨L￨NN￨O￨A delay￨L￨NN￨O￨- and￨L￨CC￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- copies.Keywordsintermittently￨L￨NN￨O￨- connectedmobile￨L￨NN￨O￨- ad￨L￨NN￨O￨- hoc￨L￨FW￨O￨- and￨L￨CC￨O￨- sensor￨L￨NN￨O￨- networksepidemic￨L￨JJ￨O￨- theoryforwardingMarkov￨L￨NN￨O￨- chain￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionThanks￨U￨NNPS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- devices￨L￨NNS￨O￨- with￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- capabilities￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- communication￨L￨NN￨O￨- without￨L￨IN￨O￨- network￨L￨NN￨O￨- infrastructure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- becoming￨L￨VBG￨O￨- a￨L￨DT￨O￨- reality￨L￨NN￨O￨- .￨L￨.￨O￨- +2012Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- intermittently￨L￨RB￨O￨- connected￨L￨JJ￨O￨- mobile￨L￨JJ￨TITLE￨- ad￨L￨NN￨O￨- hoc￨L￨FW￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- guarantee￨L￨VB￨O￨- the￨L￨DT￨O￨- packet￨L￨NN￨O￨- delivery￨L￨NN￨O￨A ratio￨L￨NN￨O￨- and￨L￨CC￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- delay￨L￨NN￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- researchers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Epidemic￨U￨JJ￨MISC￨- theory￨L￨NN￨O￨- based￨L￨VBN￨O￨- H￨U￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- hop￨L￨NN￨O￨- forwarding￨L￨NN￨O￨- for￨L￨IN￨O￨- intermittently￨L￨RB￨O￨- connected￨L￨VBN￨O￨- mobile￨L￨JJ￨TITLE￨- ad￨L￨NN￨O￨A hoc￨L￨FW￨O￨A networksXin￨L￨FW￨O￨- Guan1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Min￨U￨NN￨DURATION￨- Chen2￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Tomoaki￨U￨NNP￨PERSON￨- Ohtsuki1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2012:76￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Guan￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- utilize￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- recovered￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- relay￨L￨NN￨O￨- node￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- epidemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- delivery￨L￨NN￨O￨A delay￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- large-scale￨L￨JJ￨O￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- simulations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- visualize￨L￨VB￨O￨- and￨L￨CC￨O￨- interpret￨L￨VB￨O￨- these￨L￨DT￨O￨- phenomena￨L￨NNS￨O￨- explicitly.Keywordsprisoner￨L￨NNP￨O￨- ’s￨L￨POS￨O￨- dilemma￨L￨NN￨O￨- game￨L￨NN￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- cooperation￨L￨NN￨O￨A size￨L￨NN￨O￨- of￨L￨IN￨O￨- interaction￨L￨NN￨O￨- neighborhood￨L￨NN￨O￨- This￨U￨DT￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- published￨L￨VBN￨O￨- with￨L￨IN￨O￨- open￨L￨JJ￨O￨- access￨L￨NN￨O￨- at￨L￨IN￨O￨- Download￨U￨VB￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- article￨L￨NN￨O￨- textReferences1.Hamilton￨L￨NN￨O￨- W￨U￨NN￨O￨- D.￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 1390￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1396CrossRefGoogle￨L￨NN￨O￨- Scholar4.Wang￨U￨NN￨O￨- Z￨U￨NN￨O￨- ,￨L￨,￨O￨- Du￨U￨NNP￨O￨- W￨U￨NNP￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- Cao￨U￨NNP￨PERSON￨- X￨U￨NN￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 57￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 724￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 728￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asSpatial￨L￨JJ￨O￨- prisoner￨L￨NN￨O￨- ’s￨L￨POS￨O￨- dilemma￨L￨NN￨O￨- games￨L￨NNS￨O￨- with￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- neighborhood￨L￨NN￨O￨- on￨L￨IN￨O￨- regular￨L￨JJ￨O￨- latticesAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsJuan￨L￨JJ￨MISC￨- WangChengYi￨U￨NN￨MISC￨- XiaYiLing￨U￨NN￨MISC￨- WangShuai￨U￨NNP￨MISC￨- DingJunQing￨U￨NNP￨MISC￨- SunOpen￨U￨NNP￨MISC￨- AccessArticle￨U￨NNP￨MISC￨- Statistical￨U￨NNP￨MISC￨- PhysicsFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- cooperation￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- prisoner￨L￨NN￨O￨- ’s￨L￨POS￨O￨- dilemma￨L￨NN￨O￨- game￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- square￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- neighborhood￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +Integrating￨U￨VBG￨O￨- neighborhoods￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- fitness￨L￨NN￨O￨- promotes￨L￨VBZ￨O￨- cooperation￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- prisoner￨L￨NN￨O￨- ’s￨L￨POS￨O￨- dilemma￨L￨NN￨O￨- game￨L￨NN￨O￨- .￨L￨.￨O￨- +Volunteering￨U￨VBG￨O￨- as￨L￨IN￨O￨- red￨L￨JJ￨O￨- queen￨L￨NN￨TITLE￨- mechanism￨L￨NN￨O￨- for￨L￨IN￨O￨- cooperation￨L￨NN￨O￨A in￨L￨IN￨O￨- public￨L￨JJ￨O￨- goods￨L￨NNS￨O￨- game￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 35￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asGetting￨L￨NN￨O￨- a￨L￨DT￨O￨- free￨L￨JJ￨O￨- ride￨L￨NN￨O￨- on￨L￨IN￨O￨- poultry￨L￨NN￨O￨- farms￨L￨NNS￨O￨- :￨L￨:￨O￨- how￨L￨WRB￨O￨- highly￨L￨RB￨O￨- pathogenic￨L￨JJ￨O￨- avian￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A may￨L￨MD￨O￨- persist￨L￨VB￨O￨- in￨L￨IN￨O￨- spite￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- virulenceAuthorsAuthors￨L￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsGiulio￨L￨NNP￨O￨- Alessandro￨U￨NNP￨PERSON￨- De￨U￨NNP￨PERSON￨- LeoLuca￨U￨NNP￨PERSON￨- BolzoniOpen￨U￨NNP￨PERSON￨- AccessOriginal￨U￨NNP￨O￨- paperFirst￨L￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 864￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- 3￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractIt￨U￨NN￨O￨- is￨L￨VBZ￨O￨- well-known￨L￨JJ￨O￨- that￨L￨IN￨O￨- highly￨L￨RB￨O￨- pathogenic￨L￨JJ￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- HPAI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- strains￨L￨NNS￨O￨- can￨L￨MD￨O￨- arise￨L￨VB￨O￨- from￨L￨IN￨O￨- low￨L￨JJ￨O￨- pathogenic￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- LPAI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- during￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨- farms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- that￨L￨IN￨O￨- partial￨L￨JJ￨O￨- cross-immunity￨L￨NN￨O￨- triggered￨L￨VBN￨O￨- by￨L￨IN￨O￨- previous￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- LPAI￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- may￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- pathogenicity￨L￨NN￨O￨- of￨L￨IN￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- enhance￨L￨VBP￨O￨- its￨L￨PRP$￨O￨- persistence￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- generally￨L￨RB￨O￨- overlooked￨L￨VBN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- avian￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- interacting￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- LPAI￨U￨NNP￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- small-scale￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- farms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- simulations￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- troughs￨L￨NNS￨O￨- between￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- deep￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- existing￨L￨VBG￨O￨- flocks￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- strain￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- ran￨L￨VBD￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- natural￨L￨JJ￨O￨- fade-out￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- strain￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 56￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NNP￨O￨- 34￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 3683￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3688￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asModeling￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- with￨L￨IN￨O￨- white￨L￨JJ￨O￨A Gaussian￨U￨JJ￨MISC￨- noiseAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsJiao￨L￨NNP￨O￨- GuZongMao￨U￨NNP￨MISC￨- GaoWei￨U￨NNP￨MISC￨- LiOpen￨U￨NNP￨MISC￨- AccessArticle￨U￨NNP￨O￨- Statistical￨U￨NNP￨O￨- Physics￨U￨NN￨O￨- and￨L￨CC￨O￨- Mathematics￨U￨NN￨O￨- for￨L￨IN￨O￨- Complex￨U￨NN￨O￨- SystemsFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 02￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 605￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- 3￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractMotivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- damping￨L￨VBG￨O￨- effect￨L￨NN￨O￨- in￨L￨IN￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- build￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- variant￨L￨JJ￨O￨- coefficients￨L￨NNS￨O￨- and￨L￨CC￨O￨- white￨L￨JJ￨O￨- Gaussian￨U￨JJ￨MISC￨- noise￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Spreading￨U￨VBG￨O￨- speed￨L￨NN￨O￨- and￨L￨CC￨O￨- traveling￨L￨VBG￨O￨A waves￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- multi-type￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +J￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 270￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 296CrossRefGoogle￨L￨JJ￨O￨- Scholar4.Han￨U￨NN￨O￨- X￨U￨NN￨O￨- P.￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 2168￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2170CrossRefGoogle￨L￨JJ￨O￨- Scholar8.Chen￨U￨NN￨O￨- H￨U￨NN￨O￨- L.￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 2677￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2683CrossRefGoogle￨L￨JJ￨O￨- Scholar10.Cao￨U￨NN￨O￨- C￨U￨NN￨O￨- X￨U￨NN￨O￨- ,￨L￨,￨O￨- Xu￨U￨NN￨O￨- M￨U￨NN￨O￨- ,￨L￨,￨O￨- Chang￨U￨NNP￨PERSON￨- C￨U￨NNP￨O￨- Y￨U￨NN￨O￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- both￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- and￨L￨CC￨O￨- static￨L￨JJ￨O￨A small￨L￨JJ￨O￨- worlds￨L￨NNS￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- suppression￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- dependence￨L￨NN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- finite-size￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- known￨L￨VBN￨O￨- for￨L￨IN￨O￨- regular￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- result￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨A small￨L￨JJ￨O￨- world￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- shortcuts￨L￨NNS￨O￨- increased￨L￨VBN￨O￨- by￨L￨IN￨O￨- 20.7￨L￨CD￨PERCENT￨- ±￨L￨CD￨PERCENT￨- 1.4￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- qualitative￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- stays￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 373￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asShift￨L￨NN￨O￨- of￨L￨IN￨O￨- percolation￨L￨NN￨O￨- thresholds￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- between￨L￨IN￨O￨- static￨L￨JJ￨O￨A and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- small-world￨L￨JJ￨O￨- networksAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsJ￨L￨NN￨O￨- .￨L￨.￨O￨- +F.￨U￨NNP￨O￨- GóraOpen￨U￨NNP￨O￨- AccessInterdisciplinary￨U￨NNP￨O￨- PhysicsFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 269￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- 4￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractThe￨U￨NNP￨O￨- study￨L￨NN￨O￨- compares￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- static￨L￨JJ￨O￨A and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- small-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- other￨L￨JJ￨O￨- many￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- :￨L￨:￨O￨- constant￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- impulsive￨L￨JJ￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- discrete-time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- forth￨L￨RB￨O￨- ,￨L￨,￨O￨- incorporating￨L￨VBG￨O￨- point￨L￨NN￨O￨- or￨L￨CC￨O￨- distributed￨L￨VBN￨O￨- delays￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- oscillatory￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- forth￨L￨RB￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- well-known￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- SVEIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- incorporate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- "￨L￨``￨O￨- infected￨L￨JJ￨O￨- "￨L￨''￨O￨- population￨L￨NN￨O￨- without￨L￨IN￨O￨- external￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR-type￨U￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- replaced￨L￨VBN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- "￨L￨``￨O￨- exposed￨L￨VBN￨O￨- "￨L￨''￨O￨- population￨L￨NN￨O￨- subject￨L￨JJ￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- discusses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A points￨L￨NNS￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- SVEIRS￨U￨NN￨O￨- propagation￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- potentially￨L￨RB￨O￨- involves￨L￨VBZ￨O￨- a￨L￨DT￨O￨- regular￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A policies￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- isolation￨L￨NN￨O￨- only￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- only￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- combined￨L￨JJ￨O￨- isolation￨L￨NN￨O￨- –￨L￨:￨O￨- vaccination￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- mixed￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Oxford￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- Publications￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- OxfordGoogle￨U￨NNP￨O￨- ScholarBehncke￨U￨NNP￨O￨- H￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- Optimal￨U￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Springer-Verlag￨U￨NNP￨O￨- ,￨L￨,￨O￨- New￨U￨NNP￨O￨- YorkGoogle￨U￨NNP￨O￨- ScholarGreenhalgh￨U￨NNP￨O￨- D￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 1988￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Some￨U￨DT￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A applied￨L￨VBD￨O￨- to￨L￨TO￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +J￨U￨NNP￨PERSON￨- Appl￨U￨NNP￨PERSON￨- Probab￨U￨NNP￨PERSON￨- 10￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- 247￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 262zbMATHCrossRefMathSciNetGoogle￨L￨JJ￨O￨- ScholarAbakuks￨U￨NNPS￨O￨- A￨U￨DT￨O￨- (￨L￨-LRB-￨O￨- 1974￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Optimal￨U￨JJ￨O￨- immunization￨L￨NN￨O￨- policies￨L￨NNS￨O￨A for￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- discusses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- time-varying￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- propagation￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- subject￨L￨NN￨O￨- to￨L￨TO￨O￨- delays￨L￨NNS￨O￨A which￨L￨WDT￨O￨- potentially￨L￨RB￨O￨- involves￨L￨VBZ￨O￨- mixed￨L￨JJ￨O￨- regular￨L￨JJ￨O￨- and￨L￨CC￨O￨- impulsive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- rules￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- takes￨L￨VBZ￨O￨- also￨L￨RB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- population￨L￨NN￨O￨- growing￨L￨VBG￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mortality￨L￨NN￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- endemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- lost￨L￨VBN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- of￨L￨IN￨O￨- newborns￨L￨NNS￨O￨A .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- time-varying￨L￨JJ￨O￨- point￨L￨NN￨O￨- delays￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- coupled￨L￨VBN￨O￨- dynamics￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- removed-by-immunity￨L￨NN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- regular￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- control￨L￨NN￨O￨- objective￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- tracking￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- prescribed￨L￨VBN￨O￨- suited￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- trajectory￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- given￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- cutting-plane￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- mixed￨L￨JJ￨O￨- 0-1￨L￨CD￨NUMBER￨- stochastic￨L￨JJ￨O￨- integer￨L￨NN￨O￨A programs￨L￨NNS￨O￨- .￨L￨.￨O￨- +CrossRefGoogle￨U￨NNP￨O￨- Scholar￨U￨NNP￨TITLE￨- Dyer￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- M.￨U￨NNP￨O￨- ,￨L￨,￨O￨- &￨L￨CC￨O￨- Stougie￨U￨NNP￨O￨- ,￨L￨,￨O￨- L.￨U￨NNP￨O￨- Integer￨U￨NNP￨O￨- programming￨L￨NN￨O￨- and￨L￨CC￨O￨- combinatorial￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- pp￨L￨NN￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Existence￨U￨NN￨MISC￨- of￨L￨IN￨MISC￨- a￨L￨DT￨MISC￨- Nonautonomous￨U￨JJ￨MISC￨- SIR￨U￨NN￨MISC￨- Epidemic￨U￨JJ￨MISC￨- Model￨U￨NNP￨TITLE￨- with￨L￨IN￨O￨- Age￨U￨NNP￨MISC￨- StructureJunyuan￨U￨NNP￨MISC￨- Yang1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Xiaoyan￨U￨NNP￨MISC￨- Wang2￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 2010:212858￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- J.￨U￨NNP￨O￨- 2010Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractA￨U￨NN￨O￨- nonautonomous￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- age￨L￨NN￨O￨A structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- integro-differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- point￨L￨NN￨O￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨A and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨O￨- Access￨U￨NN￨O￨- Identification￨U￨NN￨O￨- of￨L￨IN￨O￨- expressed￨L￨VBN￨O￨- genes￨L￨NNS￨O￨A during￨L￨IN￨O￨- compatible￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- stripe￨L￨NN￨O￨- rust￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Puccinia￨U￨NN￨O￨- striiformis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- wheat￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- cDNA￨L￨NN￨O￨- libraryJinbiao￨L￨NN￨O￨- Ma1￨U￨NN￨O￨- ,￨L￨,￨O￨- Xueling￨U￨VBG￨O￨- Huang2￨U￨NN￨O￨- ,￨L￨,￨O￨- Xiaojie￨U￨NN￨O￨- Wang2￨U￨NN￨O￨- ,￨L￨,￨O￨- Xianming￨U￨VBG￨O￨- Chen3￨U￨NN￨O￨- ,￨L￨,￨O￨- Zhipeng￨U￨NN￨O￨- Qu2￨U￨NN￨O￨- ,￨L￨,￨O￨- Lili￨U￨NNP￨PERSON￨- Huang2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Zhensheng￨U￨NNP￨PERSON￨- Kang1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 10:586￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Ma￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2009Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Wheat￨U￨NNP￨O￨- stripe￨L￨NN￨O￨- rust￨L￨NN￨O￨- ,￨L￨,￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- Puccinia￨U￨NN￨O￨- striiformis￨L￨NN￨O￨- f.￨L￨NN￨O￨- To￨U￨TO￨O￨- establish￨L￨VB￨O￨- compatibility￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Pst￨U￨NN￨O￨- forms￨L￨NNS￨O￨- special￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- structures￨L￨NNS￨O￨- to￨L￨TO￨O￨- invade￨L￨VB￨O￨- the￨L￨DT￨O￨- plant￨L￨NN￨O￨- with￨L￨IN￨O￨- minimal￨L￨JJ￨O￨- damage￨L￨NN￨O￨- to￨L￨TO￨O￨- host￨L￨NN￨TITLE￨- cells￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Total￨U￨JJ￨O￨- RNA￨U￨NN￨O￨- ,￨L￨,￨O￨- extracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- wheat￨L￨NN￨O￨- leaves￨L￨VBZ￨O￨- harvested￨L￨VBN￨O￨- at￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 8￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- post￨L￨JJ￨O￨- inoculation￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- dpi￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨- a￨L￨DT￨O￨- cDNA￨L￨NN￨O￨- library￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- 5,793￨L￨CD￨NUMBER￨- ESTs￨U￨NNS￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- quality￨L￨NN￨O￨- were￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- and￨L￨CC￨O￨- clustered￨L￨VBN￨O￨- into￨L￨IN￨O￨- 583￨L￨CD￨NUMBER￨- contigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- 2,160￨L￨CD￨NUMBER￨- singletons￨L￨NNS￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- 2,743￨L￨CD￨NUMBER￨- unisequences￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- GenBank￨U￨NN￨ORGANIZATION￨- accessions￨L￨NNS￨O￨- :￨L￨:￨O￨- GR302385￨U￨NN￨O￨- to￨L￨TO￨O￨- GR305127￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +About￨U￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ESTs￨U￨NNS￨O￨- were￨L￨VBD￨O￨- significantly￨L￨RB￨O￨- homologous￨L￨JJ￨O￨- to￨L￨TO￨O￨- genes￨L￨NNS￨O￨A encoding￨L￨VBG￨O￨- proteins￨L￨NNS￨O￨- with￨L￨IN￨O￨- known￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- ;￨L￨:￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- were￨L￨VBD￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- genes￨L￨NNS￨O￨- encoding￨L￨VBG￨O￨- proteins￨L￨NNS￨O￨- with￨L￨IN￨O￨- unknown￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- and￨L￨CC￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- significant￨L￨JJ￨O￨- homology￨L￨NN￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- sequence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- database￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- an￨L￨DT￨O￨- EST￨U￨NN￨MISC￨- database￨L￨NN￨O￨- of￨L￨IN￨O￨- wheat￨L￨NN￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- Pst￨U￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- transcription￨L￨NN￨O￨- profiles￨L￨NNS￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨A involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- compatible￨L￨JJ￨O￨- wheat-Pst￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- .￨L￨.￨O￨- +Dividing￨U￨VBG￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- into￨L￨IN￨O￨- regions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- continents￨L￨NNS￨O￨- ,￨L￨,￨O￨- countries￨L￨NNS￨O￨- etc￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- eradication￨L￨NN￨O￨A properties￨L￨NNS￨O￨- as￨L￨IN￨O￨- more￨L￨JJR￨O￨- complex￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- predicts￨L￨VBZ￨O￨- eradication￨L￨NN￨O￨A or￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- world￨L￨NN￨O￨- scale￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- eradicated￨L￨VBN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- region￨L￨NN￨O￨- independently￨L￨RB￨O￨- ,￨L￨,￨O￨- travel/immigration￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨A could￨L￨MD￨O￨- still￨L￨RB￨O￨- sustain￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Volume￨U￨NN￨O￨- 9￨L￨CD￨NUMBER￨- Supplement￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- OptAIDS￨U￨NN￨O￨- project￨L￨NN￨O￨A :￨L￨:￨O￨- towards￨L￨IN￨O￨- global￨L￨JJ￨O￨- halting￨L￨VBG￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NNP￨MISC￨- Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Can￨U￨MD￨MISC￨- we￨L￨PRP￨O￨- spend￨L￨VB￨O￨- our￨L￨PRP$￨O￨- way￨L￨NN￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- ?￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- Latin￨U￨JJ￨O￨- hypercube￨L￨NN￨O￨- sampling￨L￨NN￨O￨- scheme￨L￨NN￨O￨- ,￨L￨,￨O￨- parameters￨L￨NNS￨O￨- governing￨L￨VBG￨O￨- killing￨L￨NN￨O￨A ,￨L￨,￨O￨- diverting￨L￨VBG￨O￨- and￨L￨CC￨O￨- personal￨L￨JJ￨O￨- protection￨L￨NN￨O￨- of￨L￨IN￨O￨- net￨L￨JJ￨O￨- users￨L￨NNS￨O￨- were￨L￨VBD￨O￨- evaluated￨L￨VBN￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- containing￨L￨VBG￨O￨- mosquito￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- entomological￨L￨JJ￨O￨- inoculation￨L￨NN￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- EIRs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +Consistent￨U￨JJ￨O￨- with￨L￨IN￨O￨- early￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- from￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- plausible￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- profiles￨L￨NNS￨O￨- were￨L￨VBD￨O￨- tested￨L￨VBN￨O￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- transmissibility￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- max￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- 1.5￨L￨CD￨NUMBER￨- was￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- whereas￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- max￨L￨NN￨O￨- ,￨L￨,￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- 2.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- chosen￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- two-wave￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- dynamic￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Southern￨U￨NNP￨MISC￨- hemisphere￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- max￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- city￨L￨NN￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- 1.5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- mean￨L￨NN￨O￨- generation￨L￨NN￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- extrapolation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- up￨L￨RP￨O￨- to￨L￨TO￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- implemented￨L￨VBD￨O￨- 6￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- may￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- 91￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- low￨L￨JJ￨O￨- transmissible￨L￨JJ￨O￨- strain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- max￨L￨NN￨O￨A =￨L￨JJ￨O￨- 1.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- at￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- global￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- S-OIV￨U￨NN￨O￨- pandemic￨L￨JJ￨O￨A flu￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- attempted￨L￨VBD￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A across￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- 52￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +No￨U￨DT￨O￨- suboptimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- treatment￨L￨NN￨O￨- provided￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- age-dependent￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- found￨L￨VBN￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- remarkably￨L￨RB￨O￨- reduce￨L￨VB￨O￨- both￨L￨DT￨O￨- clinical￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- antiviral￨L￨JJ￨O￨A drugs￨L￨NNS￨CRIMINAL_CHARGE￨- needs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- though￨L￨IN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- largely￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- excess￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Age-prioritized￨U￨JJ￨MISC￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- antivirals￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemicStefano￨L￨NN￨O￨- Merler1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Marco￨U￨NNP￨PERSON￨- Ajelli1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Caterina￨U￨NNP￨MISC￨- Rizzo3￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 9:117￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Merler￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2009Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- WHO￨U￨WP￨ORGANIZATION￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- governments￨L￨NNS￨O￨- stockpile￨L￨VBP￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- preparations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- sufficient￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- antiviral￨L￨JJ￨O￨A drugs￨L￨NNS￨CRIMINAL_CHARGE￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- approximately￨L￨RB￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- two-fold￨L￨JJ￨O￨- :￨L￨:￨O￨- first￨L￨RB￨ORDINAL￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- the￨L￨DT￨O￨- antiviral￨L￨JJ￨O￨A stockpile￨L￨NN￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- below￨L￨IN￨O￨- this￨L￨DT￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- search￨L￨VBP￨O￨- for￨L￨IN￨O￨- suboptimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- treatment￨L￨NN￨O￨- provided￨L￨VBD￨O￨- only￨L￨RB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- age-dependent￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- antiviral￨L￨JJ￨O￨A stockpile￨L￨NN￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ranges￨L￨VBZ￨O￨- from￨L￨IN￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- to￨L￨TO￨O￨- 35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- for￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- 1.4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- systematically￨L￨RB￨O￨- test￨L￨NN￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- differs￨L￨VBZ￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- types￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨A ,￨L￨,￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- clustering￨L￨NN￨O￨- and￨L￨CC￨O￨- varying￨L￨VBG￨O￨- proportions￨L￨NNS￨O￨- of￨L￨IN￨O￨- repetitive￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Models￨U￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- :￨L￨:￨O￨- when￨L￨WRB￨O￨- contact￨L￨NN￨O￨- repetition￨L￨NN￨O￨- and￨L￨CC￨O￨- clustering￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- includedTimo￨L￨JJ￨O￨- Smieszek1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Lena￨U￨NNP￨PERSON￨- Fiebig2￨U￨NNP￨O￨- and￨L￨CC￨O￨- Roland￨U￨NNP￨O￨- W￨U￨NNP￨O￨- Scholz1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 6:11￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Smieszek￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2009Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 05￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- biological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- arrangement￨L￨NN￨O￨- of￨L￨IN￨O￨- potentially￨L￨RB￨O￨- contagious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨A .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- simulation￨L￨NN￨O￨- runs￨L￨VBZ￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- constellations￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- results￨L￨NNS￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- both￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- types￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- highest￨L￨JJS￨O￨- for￨L￨IN￨O￨- low￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨A and￨L￨CC￨O￨- low￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Repetitiveness￨U￨NNP￨O￨- and￨L￨CC￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨A are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- relevant￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- droplet￨L￨NN￨O￨- or￨L￨CC￨O￨- contact￨L￨NN￨O￨- transmitted￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Rotavirus￨U￨NNP￨O￨- vaccination￨L￨NN￨O￨- would￨L￨MD￨O￨- not￨L￨RB￨O￨- completely￨L￨RB￨O￨- protect￨L￨VB￨O￨- young￨L￨JJ￨O￨A children￨L￨NNS￨O￨- against￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- partial￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- would￨L￨MD￨O￨- effectively￨L￨RB￨O￨- reduce￨L￨VB￨O￨- severe￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- gastroenteritis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- outpatient￨L￨NN￨O￨- visits￨L￨NNS￨O￨- ,￨L￨,￨O￨- hospitalizations￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- about￨L￨IN￨O￨- 67￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- life￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- broad￨L￨JJ￨O￨- qualitative￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- vaccines￨L￨NNS￨O￨- into￨L￨IN￨O￨- low-income￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- several￨L￨JJ￨O￨- features￨L￨NNS￨O￨A of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- varying￨L￨VBG￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- severity￨L￨NN￨O￨- and￨L￨CC￨O￨- age-dependency￨L￨NN￨O￨- of￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- manifestation￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- model-based￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Cost-effectiveness￨U￨NN￨MISC￨- of￨L￨IN￨MISC￨- Rotavirus￨U￨NNP￨MISC￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- VietnamSun-Young￨U￨NNP￨O￨- Kim1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Sue￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Goldie1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Joshua￨U￨NNP￨PERSON￨- A￨U￨NNP￨PERSON￨- Salomon1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 9:29￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Kim￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2009Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Rotavirus￨U￨NNP￨MISC￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- diarrhea￨L￨NN￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- hospitalization￨L￨NN￨O￨- or￨L￨CC￨O￨- disease-specific￨L￨JJ￨O￨- death￨L￨NN￨O￨- among￨L￨IN￨O￨- young￨L￨JJ￨O￨A children￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extend￨L￨VBP￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- to￨L￨TO￨O￨- reflect￨L￨VB￨O￨- additional￨L￨JJ￨O￨- features￨L￨NNS￨O￨A of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- reinfection￨L￨NN￨O￨- and￨L￨CC￨O￨- varying￨L￨VBG￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- partial￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- conferred￨L￨VBD￨O￨- by￨L￨IN￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- features￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Software￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Multi-agent￨U￨JJ￨MISC￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- for￨L￨IN￨O￨- computational￨L￨JJ￨O￨A biology￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmissionBenjamin￨L￨NN￨O￨- Roche1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Jean-François￨U￨NNP￨O￨- Guégan1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- François￨U￨NNP￨O￨- Bousquet3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 9:435￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Roche￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2008Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Computational￨U￨NNP￨O￨- biology￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- or￨L￨CC￨O￨- genomic￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +So￨U￨RB￨O￨- far￨L￨RB￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- ecological￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- implicit￨L￨JJ￨O￨- standard￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨A .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- systems￨L￨NNS￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨A of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- computational￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- context￨L￨NN￨O￨- .￨L￨.￨O￨- +Statistical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- climate￨L￨NN￨O￨A indexes￨L￨NNS￨O￨- work￨L￨VBP￨O￨- well￨L￨RB￨O￨- in￨L￨IN￨O￨- Niger￨U￨NNP￨COUNTRY￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- variance￨L￨NN￨O￨- from￨L￨IN￨O￨- year-to-year￨L￨JJ￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- country￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- winter￨L￨NN￨DATE￨- climate￨L￨NN￨O￨- but￨L￨CC￨O￨- fail￨L￨VBP￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- accurately￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- Burkina￨U￨NNP￨COUNTRY￨- Faso￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- A￨U￨DT￨O￨- statistical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- annual￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- MCM￨U￨NN￨O￨- and￨L￨CC￨O￨- climatic￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- performed￨L￨VBN￨O￨- to￨L￨TO￨O￨- highlight￨L￨VB￨O￨- the￨L￨DT￨O￨- relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- climate￨L￨NN￨O￨A and￨L￨CC￨O￨- MCM￨U￨NN￨O￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- highly￨L￨RB￨O￨- afflicted￨L￨VBD￨O￨- countries￨L￨NNS￨O￨- :￨L￨:￨O￨- Niger￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Burkina￨U￨NNP￨COUNTRY￨- Faso￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Relationships￨U￨NNPS￨MISC￨- between￨L￨IN￨O￨- climate￨L￨NN￨O￨A and￨L￨CC￨O￨- year-to-year￨L￨JJ￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- meningitis￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- Burkina￨U￨NNP￨COUNTRY￨- Faso￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- NigerPascal￨U￨NNP￨O￨- Yaka1￨U￨NN￨O￨- ,￨L￨,￨O￨- Benjamin￨U￨NNP￨PERSON￨- Sultan2Email￨U￨NNP￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Hélène￨U￨NN￨O￨- Broutin3￨U￨NN￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Serge￨U￨NNP￨PERSON￨- Janicot2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Solenne￨U￨NNP￨O￨- Philippon1￨U￨NN￨O￨- and￨L￨CC￨O￨- Nicole￨U￨NNP￨MISC￨- Fourquet1￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 7:34￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Yaka￨U￨FW￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2008Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 02￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 02￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Every￨U￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- is￨L￨VBZ￨O￨- afflicted￨L￨VBN￨O￨- with￨L￨IN￨O￨- Meningococcal￨U￨JJ￨O￨- Meningitis￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- MCM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resurgence￨L￨NN￨O￨- in￨L￨IN￨O￨- Niger￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- Burkina￨U￨NNP￨COUNTRY￨- Faso￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- partly￨L￨RB￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- winter￨L￨NN￨DATE￨- climate￨L￨NN￨O￨A through￨L￨IN￨O￨- enhanced￨L￨VBN￨O￨- Harmattan￨U￨NNP￨MISC￨- winds￨L￨NNS￨O￨- .￨L￨.￨O￨- +MCM￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- worldwide￨L￨JJ￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- incidence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- "￨L￨``￨O￨- meningitis￨L￨NN￨CAUSE_OF_DEATH￨- belt￨L￨NN￨O￨- "￨L￨''￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- stretching￨L￨VBG￨O￨- from￨L￨IN￨O￨- Senegal￨U￨NNP￨COUNTRY￨- to￨L￨TO￨O￨- Ethiopia￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Clinically￨U￨RB￨MISC￨- immune￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- refuge￨L￨NN￨O￨- for￨L￨IN￨O￨- drug-sensitive￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasitesEili￨L￨NN￨O￨- Y￨U￨NN￨O￨- Klein1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- L￨U￨NNP￨PERSON￨- Smith3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Maciej￨U￨NNP￨PERSON￨- F￨U￨NN￨PERSON￨- Boni1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Ramanan￨U￨NNP￨PERSON￨- Laxminarayan1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 7:67￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Klein￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2008Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Mutations￨U￨NNS￨O￨- in￨L￨IN￨O￨- Plasmodium￨U￨NN￨LOCATION￨- falciparum￨L￨NN￨O￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- first-line￨L￨JJ￨O￨- antimalarial￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- have￨L￨VBP￨O￨- spread￨L￨VBN￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- independent￨L￨JJ￨RELIGION￨- foci￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- located￨L￨JJ￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- likely￨L￨JJ￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- low￨L￨JJ￨O￨- or￨L￨CC￨O￨- unstable￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Simulations￨U￨NNS￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- clinical￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- can￨L￨MD￨O￨- significantly￨L￨RB￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- fitness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- parasite￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- thereby￨L￨RB￨O￨- impact￨L￨NN￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- parasite￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- parasite￨L￨NN￨O￨- as￨L￨IN￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- increases￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- reconsiders￨L￨VBZ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- antimalarial￨L￨JJ￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A have￨L￨VBP￨O￨- generally￨L￨RB￨O￨- ignored￨L￨VBN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- fitness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- constructed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- two-stage￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A that￨L￨WDT￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- build￨L￨VBP￨O￨- up￨L￨RP￨O￨- clinical￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- In￨U￨IN￨O￨- WT￨U￨JJ￨O￨- mice￨L￨NNS￨O￨A ,￨L￨,￨O￨- CpG-ODN￨U￨NN￨O￨- induced￨L￨VBD￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- pulmonary￨L￨JJ￨O￨- NFκB￨U￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- pulmonary￨L￨JJ￨O￨- TNF-α￨U￨NN￨O￨- and￨L￨CC￨O￨- IL-1β￨U￨NN￨O￨- mRNA/protein￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Clinical￨U￨JJ￨O￨- manifestation￨L￨NN￨O￨- of￨L￨IN￨O￨- inflammation￨L￨NN￨O￨- Clinical￨U￨JJ￨O￨- symptoms￨L￨NNS￨O￨- of￨L￨IN￨O￨- inflammation￨L￨NN￨O￨- were￨L￨VBD￨O￨- monitored￨L￨VBN￨O￨- after￨L￨IN￨O￨- CpG-ODN￨U￨NN￨O￨- application￨L￨NN￨O￨- in￨L￨IN￨O￨- WT￨U￨NNP￨O￨- and￨L￨CC￨O￨- TLR9-D￨U￨NN￨O￨- mice￨L￨NNS￨O￨A .￨L￨.￨O￨- +Increased￨U￨VBN￨O￨- pulmonary￨L￨JJ￨O￨- content￨L￨NN￨O￨- of￨L￨IN￨O￨- lung￨L￨NN￨O￨- myeloperoxidase￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MPO￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- documented￨L￨VBN￨O￨- in￨L￨IN￨O￨- WT￨U￨NNP￨O￨- mice￨L￨NNS￨O￨A following￨L￨VBG￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- CpG-ODN￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- CpG-ODN-induced￨U￨JJ￨O￨- inflammatory￨L￨JJ￨O￨- response￨L￨NN￨O￨- was￨L￨VBD￨O￨- abolished￨L￨VBN￨O￨- in￨L￨IN￨O￨- TLR9-D￨U￨NN￨O￨- mice￨L￨NNS￨O￨A .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Wild-type￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- WT￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- TLR9-deficient￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- TLR9-D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- mice￨L￨NNS￨O￨A received￨L￨VBD￨O￨- CpG-ODN￨U￨NN￨O￨- intraperitoneally￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- 1668-Thioat￨L￨NN￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- nmol/g￨L￨NN￨O￨- BW￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- were￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- up￨L￨RB￨DURATION￨- to￨L￨TO￨DURATION￨- 6￨L￨CD￨DURATION￨- hrs￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- A￨U￨NNP￨O￨- rationale￨L￨NN￨O￨- for￨L￨IN￨O￨- continuing￨L￨VBG￨O￨- mass￨L￨NN￨O￨- antibiotic￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- for￨L￨IN￨O￨- trachomaKathryn￨L￨NN￨O￨- J￨U￨NN￨O￨- Ray1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Travis￨U￨NNP￨O￨- C￨U￨NNP￨O￨- Porco1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kevin￨U￨NNP￨PERSON￨- C￨U￨NNP￨O￨- Hong1￨U￨NN￨O￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- C￨U￨NNP￨PERSON￨- Lee1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Wondu￨U￨NNP￨PERSON￨- Alemayehu4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Muluken￨U￨JJ￨O￨- Melese4￨U￨NN￨O￨- ,￨L￨,￨O￨- Takele￨U￨NNP￨O￨- Lakew4￨U￨NN￨O￨- ,￨L￨,￨O￨- Elizabeth￨U￨NNP￨PERSON￨- Yi1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jenafir￨U￨NNP￨O￨- House1￨U￨NN￨O￨- ,￨L￨,￨O￨- Jaya￨U￨NNP￨PERSON￨- D￨U￨NNP￨O￨- Chidambaram1￨U￨NN￨O￨- ,￨L￨,￨O￨- John￨U￨NNP￨PERSON￨- P￨U￨NN￨PERSON￨- Whitcher1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Bruce￨U￨NNP￨PERSON￨- D￨U￨NNP￨PERSON￨- Gaynor1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Thomas￨U￨NNP￨PERSON￨- M￨U￨NN￨PERSON￨- Lietman1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 7:91￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Ray￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2007Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨A Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- recommends￨L￨VBZ￨O￨- periodic￨L￨JJ￨O￨- mass￨L￨NN￨O￨- antibiotic￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- ocular￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨- that￨L￨WDT￨O￨- cause￨L￨VBP￨O￨- trachoma￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- 's￨L￨POS￨O￨- leading￨L￨VBG￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- blindness￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- eliminated￨L￨VBN￨O￨- in￨L￨IN￨O￨- every￨L￨DT￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- gradually￨L￨RB￨O￨- return￨L￨VB￨O￨- back￨L￨RB￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- often￨L￨RB￨O￨- repeated￨L￨VBN￨O￨A treatments￨L￨NNS￨O￨- are￨L￨VBP￨O￨- necessary￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- treatment￨L￨NN￨O￨A programs￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- that￨L￨IN￨O￨- repeated￨L￨VBN￨O￨A antibiotic￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- can￨L￨MD￨O￨- eliminate￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Simulations￨U￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- villages￨L￨NNS￨O￨- progressively￨L￨RB￨O￨- decreases￨L￨VBZ￨O￨- after￨L￨IN￨O￨- each￨L￨DT￨O￨- treatment￨L￨NN￨O￨A ,￨L￨,￨O￨- as￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- and￨L￨CC￨O￨- coverage￨L￨NN￨O￨- of￨L￨IN￨O￨- antibiotics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- high￨L￨JJ￨O￨- enough￨L￨RB￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- find￨L￨VB￨O￨- that￨L￨DT￨O￨- :￨L￨:￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- eliminated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- within￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- effective￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨A diversity￨L￨NN￨O￨A increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- R0￨U￨NN￨O￨- or￨L￨CC￨O￨- peaks￨L￨VBZ￨O￨- at￨L￨IN￨O￨- intermediate￨L￨JJ￨O￨- R0￨U￨NN￨O￨- levels￨L￨NNS￨O￨- ;￨L￨:￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- expected￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- neutral￨L￨JJ￨IDEOLOGY￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- scale￨L￨NN￨O￨- free￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- low￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- a￨L￨DT￨O￨- distortion￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- neutral￨L￨JJ￨IDEOLOGY￨- mutation￨L￨NN￨O￨- frequency￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- ;￨L￨:￨O￨- highly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- hubs￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- show￨L￨VBP￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- diversity￨L￨NN￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- poorly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- higher￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- ,￨L￨,￨O￨- lower￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- differentiation￨L￨NN￨O￨- and￨L￨CC￨O￨- larger￨L￨JJR￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- Tajima￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- D.￨U￨NNP￨O￨- Furthermore￨U￨RB￨O￨- for￨L￨IN￨O￨- low￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- very￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- contact￨L￨NN￨O￨- structures￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- lower￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- diversity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- agent￨L￨NN￨O￨- variation￨L￨NN￨O￨- can￨L￨MD￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- certain￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- ,￨L￨,￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- history￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- agent￨L￨NN￨O￨- genetic￨L￨JJ￨O￨A structure￨L￨NN￨O￨- may￨L￨MD￨O￨- reflect￨L￨VB￨O￨- its￨L￨PRP$￨O￨- evolutionary￨L￨JJ￨O￨- potential￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- study￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- levels￨L￨NNS￨O￨- and￨L￨CC￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A diversity￨L￨NN￨O￨A in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- .￨L￨.￨O￨- +KeywordsInfectious￨U￨NNP￨MISC￨- AgentInfected￨U￨NNP￨MISC￨- HostContact￨U￨NNP￨MISC￨- StructureScale￨U￨NNP￨MISC￨- Free￨U￨NNP￨MISC￨- NetworkContact￨U￨NNP￨MISC￨- Network￨U￨NNP￨MISC￨- BackgroundPatterns￨U￨NNP￨MISC￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A diversity￨L￨NN￨O￨A in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- contain￨L￨VBP￨O￨- important￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- their￨L￨PRP$￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- like￨L￨IN￨O￨- pharmaceutical￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- antiviral￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- non-pharmaceutical￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- implemented.The￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨A during￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- seems￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- choice￨L￨NN￨O￨- at￨L￨IN￨O￨- present￨L￨JJ￨DATE￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- all￨L￨DT￨O￨- countries￨L￨NNS￨O￨- can￨L￨MD￨O￨- afford￨L￨VB￨O￨- stockpiling￨L￨NN￨O￨- enough￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- how￨L￨WRB￨O￨- intervention￨L￨NN￨O￨- schedules￨L￨NNS￨O￨- ,￨L￨,￨O￨- restricted￨L￨JJ￨O￨- stockpiles￨L￨NNS￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- reduction￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨- measures￨L￨NNS￨O￨- and￨L￨CC￨O￨- isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- wave￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- A￨U￨DT￨O￨- timely￨L￨JJ￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨A combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- quick￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- reduction￨L￨NN￨O￨- measures￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- substantially￨L￨RB￨O￨- protract￨L￨VB￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- reduce￨L￨VB￨O￨- its￨L￨PRP$￨O￨- height￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- freely￨L￨RB￨O￨- available￨L￨JJ￨O￨- planning￨L￨NN￨O￨- tool￨L￨NN￨O￨- InfluSim￨U￨NNP￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- pharmaceutical￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-pharmaceutical￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- can￨L￨MD￨O￨- mitigate￨L￨VB￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨A .￨L￨.￨O￨- +An￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- can￨L￨NN￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- mitigated￨L￨VBN￨O￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- contact￨L￨NN￨O￨A rates￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- initiated￨L￨VBD￨O￨- replicate￨L￨VB￨O￨- longitudinal￨L￨JJ￨O￨- host-schistosome￨L￨JJ￨O￨- co-selection￨L￨NN￨O￨- trials￨L￨NNS￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- genotype￨L￨NN￨O￨- combinations￨L￨NNS￨O￨- :￨L￨:￨O￨- Schistosoma￨U￨NN￨O￨- mansoni￨L￨NN￨O￨- parasite￨L￨NN￨O￨- lines￨L￨NNS￨O￨A were￨L￨VBD￨O￨- co-selected￨L￨VBN￨O￨- with￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- previously￨L￨RB￨DATE￨- resistant-selected￨L￨JJ￨O￨- Biomphalaria￨U￨NN￨O￨- glabrata￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- genotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- unselected￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- B.￨U￨NNP￨O￨- KeywordsParasite￨U￨NNP￨O￨- InfectivityIntermediate￨U￨NNP￨O￨- HostSimian￨U￨NNP￨O￨- Immunodeficiency￨U￨NN￨O￨- VirusDefinitive￨U￨JJ￨O￨- HostUnweighted￨U￨NNP￨O￨- Pair￨U￨NNP￨O￨- Group￨U￨NNP￨O￨- Method￨U￨NNP￨O￨- With￨U￨IN￨O￨- Arithmetic￨U￨NNP￨O￨- BackgroundHost-parasite￨U￨NNP￨O￨- coevolution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- reciprocal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- resistance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- infectivity￨L￨NN￨O￨- and/or￨L￨CC￨O￨- virulence￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Appendix￨U￨NNP￨O￨- for￨L￨IN￨O￨- definitions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Host-parasite￨U￨JJ￨O￨- coevolution￨L￨NN￨O￨A requires￨L￨VBZ￨O￨- additive￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- traits￨L￨NNS￨O￨- ,￨L￨,￨O￨- reciprocal￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- fitness￨L￨NN￨O￨- traits￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host-parasite￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- genotypes￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- .￨L￨.￨O￨- +Sources￨U￨NNS￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- C￨U￨NN￨O￨- assumed￨L￨VBD￨O￨- ,￨L￨,￨O￨- D￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- Table￨U￨NNP￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- to￨L￨TO￨O￨- 5960￨L￨CD￨DATE￨- and￨L￨CC￨O￨- olderHospitalized￨L￨VBN￨O￨- fraction￨L￨NN￨O￨- h￨L￨NN￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- of￨L￨IN￨O￨- untreated￨L￨JJ￨O￨- severe￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- low￨L￨JJ￨O￨- risk￨L￨NN￨O￨- group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- r￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 0.187￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 2.339￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 3.560￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- r￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 1.333￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 2.762￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 7.768￨L￨CD￨NUMBER￨- se￨L￨FW￨O￨- fatality￨L￨NN￨O￨- d￨L￨NN￨O￨- a￨L￨DT￨O￨- of￨L￨IN￨O￨- hospitalized￨L￨VBN￨O￨- cases5￨L￨NN￨O￨- .541￨L￨CD￨PERCENT￨- .5319.505￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Independent￨U￨NNP￨RELIGION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- a￨L￨DT￨O￨- and￨L￨CC￨O￨- risk￨L￨VB￨O￨- group￨L￨NN￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- c￨L￨NN￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 33￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- c￨L￨NN￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- M￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 33.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- become￨L￨VBN￨O￨- moderately￨L￨RB￨O￨- sick￨L￨JJ￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- fraction￨L￨NN￨O￨- develops￨L￨VBZ￨O￨- severe￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Software￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨JJ￨O￨- preparedness￨L￨NN￨O￨- planning￨L￨NN￨O￨A tool￨L￨NN￨O￨- InfluSim￨U￨NNP￨O￨- Martin￨U￨NNP￨O￨- Eichner1￨U￨NN￨O￨- ,￨L￨,￨O￨- Markus￨U￨NNP￨PERSON￨- Schwehm1Email￨U￨NNP￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Hans-Peter￨U￨NNP￨PERSON￨- Duerr1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Stefan￨U￨NNP￨PERSON￨- O￨U￨NNP￨O￨- Brockmann2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:17￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Eichner￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2007Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Planning￨U￨NNP￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- responses￨L￨NNS￨O￨- against￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- predictive￨L￨JJ￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- evaluated￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- minimum￨L￨NN￨O￨- requirement￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- planning￨L￨NN￨O￨A tool￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- structure￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- time-dependent￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- like￨L￨IN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- height￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨- ,￨L￨,￨O￨- antiviral￨L￨JJ￨O￨- availability￨L￨NN￨O￨- etc￨L￨NN￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 4￨L￨CD￨NUMBER￨- Sojourn￨U￨NNP￨O￨- times￨L￨NNS￨O￨- Periodaverage￨U￨JJ￨O￨- durationstagescoefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- variationLatent￨L￨JJ￨O￨- period￨L￨NN￨O￨- D￨U￨NN￨O￨- E￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1.9￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨A A￨U￨DT￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 737.8￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- A￨U￨NN￨O￨- Fully￨U￨RB￨O￨- contagious￨L￨JJ￨O￨- period￨L￨NN￨O￨- asymptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- moderately￨L￨RB￨O￨- sick￨L￨JJ￨O￨- adults4￨L￨NN￨O￨- .1￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- A￨U￨DT￨O￨- m￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1922.9￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- A￨U￨NN￨O￨- others7￨L￨NN￨O￨- .0￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- B￨U￨NN￨O￨- m￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1922.9￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- C￨U￨NN￨O￨- Period￨U￨NN￨O￨- of￨L￨IN￨O￨- convalescence￨L￨NN￨O￨- D￨U￨NN￨O￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- 5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- D￨U￨NN￨O￨- j￨L￨NN￨O￨- =￨L￨JJ￨O￨- 933.3￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- C￨U￨NN￨O￨- Distribution￨U￨NN￨O￨- of￨L￨IN￨O￨- sojourn￨L￨NN￨O￨- times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- early￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- average￨L￨JJ￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- D￨U￨NN￨O￨- L￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0.5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Source￨U￨NN￨O￨- :￨L￨:￨O￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- Table￨U￨NNP￨ORGANIZATION￨- 3￨L￨CD￨NUMBER￨- WAIFW￨U￨NN￨ORGANIZATION￨- matrix￨L￨NN￨O￨A 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 56￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 1213￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1920￨L￨CD￨DATE￨- –￨L￨:￨O￨- 3940￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5960￨L￨CD￨NUMBER￨- +0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5169.1431.4717.7634.5015.8311.476￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 1231.47274.5132.3134.8620.6111.5013￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 1917.7632.31224.2550.7537.5214.9620￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3934.5034.8650.7575.6649.4525.0840￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5915.8320.6137.5249.4561.2632.9960￨L￨CD￨NUMBER￨- +11.4711.5014.9625.0832.9954.23￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- who-acquires-infection-from-whom￨L￨NN￨O￨- matrix￨L￨NN￨O￨- K￨U￨NN￨O￨- a￨L￨DT￨O￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- i￨L￨FW￨O￨- @￨L￨SYM￨O￨- @￨L￨SYM￨O￨- +￨L￨CC￨O￨- =￨L￨JJ￨O￨- feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY￨L￨NN￨O￨- =￨L￨JJ￨O￨- wiFfYdH8Gipec8Eeeu0xXdbba9frFj0￨L￨NN￨O￨- =￨L￨JJ￨O￨- OqFfea0dXdd9vqai￨U￨NN￨O￨- =￨L￨JJ￨O￨- hGuQ8kuc9pgc9s8qqaq￨L￨NN￨O￨- =￨L￨JJ￨O￨- dirpe0xb9q8qiLsFr0￨L￨NN￨O￨- =￨L￨JJ￨O￨- vr0￨L￨NN￨O￨- =￨L￨JJ￨O￨- @￨L￨SYM￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- per￨L￨IN￨O￨- week￨L￨NN￨DURATION￨- per￨L￨IN￨O￨- person￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- classes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Comparative￨U￨JJ￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- ESTs￨U￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- grape￨L￨NN￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- Xylella￨U￨NNP￨LOCATION￨- fastidiosa￨L￨FW￨O￨- infectionHong￨L￨NNP￨O￨- Lin￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Harshavardhan￨U￨NNP￨O￨- Doddapaneni￨U￨NNP￨O￨- †￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yuri￨U￨NNP￨PERSON￨- Takahashi2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- M￨U￨NN￨O￨- Andrew￨U￨NNP￨O￨- Walker2￨U￨NNP￨O￨- †￨L￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:8￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Lin￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2007Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨A Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- gram-negative￨L￨JJ￨O￨- bacterium￨L￨NN￨O￨- Xylella￨U￨NNP￨O￨- fastidiosa￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Xf￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- causal￨L￨JJ￨O￨- agent￨L￨NN￨O￨- of￨L￨IN￨O￨- Pierce￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- PD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- grape￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- fruit￨L￨NN￨O￨- and￨L￨CC￨O￨- ornamental￨L￨JJ￨O￨- plants￨L￨NNS￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- resistance￨L￨NN￨O￨A genes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- directly￨L￨RB￨O￨- introduce￨L￨VB￨O￨- resistance￨L￨NN￨O￨- into￨L￨IN￨O￨- elite￨L￨JJ￨O￨- wine￨L￨NN￨O￨- grape￨L￨NN￨O￨- cultivars￨L￨NNS￨O￨- by￨L￨IN￨O￨- transgenic￨L￨JJ￨O￨- technologies.Systemic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- studies￨L￨NNS￨O￨- under￨L￨IN￨O￨- greenhouse￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- differential￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- X.￨U￨NNP￨O￨- +Results￨U￨NNS￨O￨- Basic￨U￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- possible￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- ranged￨L￨VBD￨O￨A between￨L￨IN￨O￨- 1.3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 3.1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- corresponding￨L￨JJ￨O￨- average￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- ranged￨L￨VBD￨O￨- between￨L￨IN￨O￨- 0.7￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 1.3￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 0.2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 0.3￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A pandemic￨L￨JJ￨O￨A estimated￨L￨VBN￨O￨- by￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- modellingGabriel￨L￨NN￨O￨- Sertsou1￨U￨NN￨O￨- ,￨L￨,￨O￨- Nick￨U￨NNP￨PERSON￨- Wilson1Email￨U￨NN￨PERSON￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Michael￨U￨NNP￨PERSON￨- Baker1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Peter￨U￨NNP￨PERSON￨- Nelson1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Mick￨U￨NNP￨PERSON￨- G￨U￨NNP￨O￨- Roberts2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 3:38￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Sertsou￨U￨FW￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2006Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Aim￨U￨NNP￨O￨- To￨U￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- institutional￨L￨JJ￨O￨- setting￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- These￨U￨DT￨O￨- R0￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A pandemic￨L￨NN￨O￨A and￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- particularly￨L￨RB￨O￨- large￨L￨JJ￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Methodology￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Stochastic￨U￨JJ￨MISC￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A of￨L￨IN￨O￨- childhood￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- before￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccinationHelen￨L￨NN￨O￨- Trottier1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Pierre￨U￨NNP￨PERSON￨- Philippe1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Roch￨U￨NNP￨O￨- Roy2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 3:9￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Trottier￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2006Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- .￨L￨.￨O￨- +Canadian￨U￨JJ￨NATIONALITY￨- chronological￨L￨JJ￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- mumps￨L￨NNS￨O￨- ,￨L￨,￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- rubella￨L￨NN￨O￨A ,￨L￨,￨O￨- before￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- analyzed￨L￨VBN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- enables￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dependency￨L￨NN￨O￨- structure￨L￨NN￨O￨- embedded￨L￨VBN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A data￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- potential￨L￨JJ￨O￨- research￨L￨NN￨O￨- applications￨L￨NNS￨O￨- in￨L￨IN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- biologically￨L￨RB￨O￨- different￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨A structure￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- univariate￨L￨JJ￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- mumps￨L￨NNS￨O￨- ,￨L￨,￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- rubella￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Box-Jenkins￨U￨NNS￨MISC￨- or￨L￨CC￨MISC￨- AutoRegressive￨U￨NNP￨MISC￨- Integrated￨U￨NNP￨MISC￨- Moving￨U￨VBG￨MISC￨- Average￨U￨JJ￨MISC￨- (￨L￨-LRB-￨O￨- ARIMA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- modeling￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- For￨U￨IN￨O￨- practical￨L￨JJ￨O￨- emergency￨L￨NN￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- ring-like￨L￨JJ￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- oral￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- favourable￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- at￨L￨IN￨O￨- all￨L￨DT￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spatial-explicit￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- fox￨L￨NN￨O￨- group￨L￨NN￨O￨- home-ranges￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- facilitates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A spread￨L￨VBD￨O￨- to￨L￨TO￨O￨- larger￨L￨JJR￨O￨- areas￨L￨NNS￨O￨- relevant￨L￨JJ￨O￨- to￨L￨TO￨O￨- management￨L￨NN￨O￨- .￨L￨.￨O￨- +Worldwide￨U￨NNP￨O￨- efforts￨L￨NNS￨O￨- to￨L￨TO￨O￨- combat￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- oral￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- reservoirs￨L￨NNS￨O￨- have￨L￨VBP￨O￨- managed￨L￨VBN￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- wildlife￨L￨NN￨O￨- rabies￨L￨NNP￨O￨A in￨L￨IN￨O￨- large￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- of￨L￨IN￨O￨- central￨L￨JJ￨O￨- Europe￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- North-America￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- then￨L￨RB￨O￨- as￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A is￨L￨VBZ￨O￨- eliminated￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- circle￨L￨NN￨O￨- area￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- respective￨L￨JJ￨O￨- ring￨L￨NN￨O￨- area￨L￨NN￨O￨- fails￨L￨VBZ￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- non-controlled￨L￨JJ￨O￨- inner￨L￨JJ￨O￨- part￨L￨NN￨O￨- .￨L￨.￨O￨- diff --git a/test/inputall.txt b/test/inputall.txt new file mode 100644 index 0000000..6bce44d --- /dev/null +++ b/test/inputall.txt @@ -0,0 +1,11204 @@ +C.￨U￨NNP￨O￨- Gomesb￨U￨NNP￨O￨- aCentro￨L￨NNP￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- Te´orica￨U￨NNP￨O￨- e￨L￨SYM￨O￨- Computacional￨U￨NNP￨O￨- and￨L￨CC￨O￨- Departamento￨U￨NNP￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- ,￨L￨,￨O￨- Faculdade￨U￨NNP￨O￨- de￨L￨IN￨O￨- Ciˆencias￨U￨NNP￨O￨- da￨L￨NNP￨O￨A Universidade￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Lisboa￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- P-1649-003￨U￨NNP￨O￨- Lisboa￨U￨NNP￨ORGANIZATION￨- Codex￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Portugal￨U￨NNP￨COUNTRY￨- bDepartamento￨L￨NNP￨O￨- de￨L￨IN￨O￨- Biologia￨U￨NNP￨O￨- Vegetal￨U￨NNP￨O￨- ,￨L￨,￨O￨- Faculdade￨U￨NNP￨O￨- de￨L￨IN￨O￨- Ciˆencias￨U￨NNP￨O￨- da￨L￨NNP￨O￨- Universidade￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Lisboa￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Campo￨U￨NNP￨CITY￨- Grande￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- 1749-016￨L￨CD￨NUMBER￨- Lisboa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Portugal￨U￨NNP￨COUNTRY￨- ∗￨L￨NNP￨O￨- Corresponding￨U￨VBG￨O￨- author￨L￨NN￨TITLE￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- investigated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infective-Recovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- unforced￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- provide￨L￨VBP￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- slightly￨L￨RB￨O￨- irregular￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- realistic￨L￨JJ￨O￨A amplitudes￨L￨NNS￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- term￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spatial￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- were￨L￨VBD￨O￨- analysed￨L￨VBN￨O￨- quantitatively￨L￨RB￨O￨- by￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Exposed-Infective-Recovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Both￨U￨CC￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- coherence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A are￨L￨VBP￨O￨- well￨L￨RB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- unforced￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- complicated￨L￨JJ￨O￨- question￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- related￨L￨JJ￨O￨- question￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- :￨L￨:￨O￨- what￨L￨WP￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- newly￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- what￨L￨WDT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- ?￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- two-type￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- ;￨L￨:￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- ;￨L￨:￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- infector￨L￨NN￨O￨- ;￨L￨:￨O￨- continuous-time￨L￨JJ￨O￨- Reed-Frost￨U￨JJ￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- Markov￨U￨NNP￨PERSON￨- models￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- For￨U￨IN￨O￨- many￨L￨JJ￨O￨- known￨L￨JJ￨O￨- human￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- extent￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- idea￨L￨NN￨O￨- about￨L￨IN￨O￨- their￨L￨PRP$￨O￨- clinical￨L￨JJ￨O￨- features￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨A incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- common￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- current￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- considers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- following￨L￨VBG￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- →￨L￨NN￨O￨- Exposed￨U￨VBN￨O￨- →￨L￨SYM￨O￨- Infectious￨U￨JJ￨O￨- →￨L￨NN￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- structure￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨A and￨L￨CC￨O￨- asymptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- latter￨L￨JJ￨O￨- fraction￨L￨NN￨O￨A only￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- type-specific￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- former￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- ρ￨L￨NN￨O￨- also￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- their￨L￨PRP$￨O￨- means￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- following￨L￨VBG￨O￨- question￨L￨NN￨O￨- is￨L￨VBZ￨O￨- addressed￨L￨VBN￨O￨- :￨L￨:￨O￨- what￨L￨WP￨O￨- fraction￨L￨NN￨O￨- ρ￨L￨NN￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- getting￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- asymptomatic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- cases￨L￨NNS￨O￨- ?￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- Epidemics￨U￨NNS￨O￨- with￨L￨IN￨O￨- Seasonality￨U￨NN￨O￨- and￨L￨CC￨O￨- Noise￨U￨NN￨O￨- ,￨L￨,￨O￨- Model￨U￨NNP￨TITLE￨- Reduction￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- As￨U￨IN￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- noise￨L￨NN￨O￨A increasingly￨L￨RB￨O￨- plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- when￨L￨WRB￨O￨- using￨L￨VBG￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- and￨L￨CC￨O￨- predict￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- method￨L￨NN￨O￨- produces￨L￨VBZ￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- dimensional￨L￨JJ￨O￨A stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- amplitude￨L￨NN￨O￨- and￨L￨CC￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- recurrent￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- dimensional￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- seasonal￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- method￨L￨NN￨O￨- enables￨L￨VBZ￨O￨- a￨L￨DT￨O￨- data-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- unobserved￨L￨JJ￨O￨- exposed￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨- over￨L￨IN￨O￨- very￨L￨RB￨O￨- long￨L￨JJ￨O￨- times￨L￨NNS￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- pro￨L￨JJ￨O￨- jection￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- analytically￨L￨RB￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- dimensional￨L￨JJ￨O￨A manifold￨L￨NN￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- correctly￨L￨RB￨O￨- interact￨L￨VBP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨A Susceptible-Exposed-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- that￨L￨WDT￨O￨- fluctuates￨L￨VBZ￨O￨- seasonally￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- programmes￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- several￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- of￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- :￨L￨:￨O￨- control￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ;￨L￨:￨O￨- minimize￨L￨VB￨O￨- exposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- infected￨L￨VBN￨O￨- ;￨L￨:￨O￨- reduce￨L￨VB￨O￨- Ebola￨U￨NN￨MISC￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- education￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- precisely￨L￨RB￨O￨- ,￨L￨,￨O￨- Mathematics￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- spreads￨L￨NNS￨O￨- by￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- policy-makers￨L￨NNS￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- programmes￨L￨NNS￨O￨A or￨L￨CC￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- more￨L￨JJR￨O￨- efficient￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- –￨L￨:￨O￨- Exposed￨U￨VBN￨O￨- –￨L￨:￨O￨- Infective￨U￨JJ￨O￨- –￨L￨:￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- optimal￨L￨JJ￨O￨A strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNPS￨O￨- Mathematical￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- ·￨L￨NN￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A ·￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- ·￨L￨NN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- ·￨L￨CD￨NUMBER￨- 2014￨L￨CD￨DATE￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- low-dimensional￨L￨JJ￨O￨- system￨L￨NN￨O￨- are￨L￨VBP￨O￨- discussed￨L￨VBN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- system￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- center￨L￨NN￨O￨- manifold￨L￨NN￨O￨A analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- system￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- normal￨L￨JJ￨O￨- form￨L￨NN￨O￨- coordinate￨L￨JJ￨O￨- transform￨L￨VB￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- this￨L￨DT￨O￨- latter￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- construction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- normal￨L￨JJ￨O￨- form￨L￨NN￨O￨- coordinate￨L￨JJ￨O￨- transform￨L￨VB￨O￨- more￨L￨JJR￨O￨- transparent￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- the￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- stochastic￨L￨JJ￨O￨- center￨L￨NN￨O￨- manifold￨L￨NN￨O￨A equation￨L￨NN￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- normal￨L￨JJ￨O￨- form￨L￨NN￨O￨- coordinate￨L￨JJ￨O￨- transform￨L￨VB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- analytically￨L￨RB￨O￨- derive￨L￨VB￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- center￨L￨NN￨O￨- manifold￨L￨NN￨O￨A along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- associated￨L￨VBN￨O￨- ,￨L￨,￨O￨- reduced￨L￨VBN￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Rigorous￨U￨JJ￨O￨- theoretical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- normal￨L￨JJ￨O￨- form￨L￨NN￨O￨- coordinate￨L￨JJ￨O￨- transformations￨L￨NNS￨O￨- for￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- center￨L￨NN￨O￨- manifold￨L￨NN￨O￨A reduction￨L￨NN￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Refs￨U￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- reduction￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- normal￨L￨JJ￨O￨- form￨L￨NN￨O￨- coordinate￨L￨JJ￨O￨- transform￨L￨VB￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- build￨L￨VBP￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- neighborhood￨L￨NN￨O￨- based￨L￨VBN￨O￨- peers￨L￨NNS￨O￨- for￨L￨IN￨O￨- 16￨L￨CD￨NUMBER￨- randomly￨L￨RB￨O￨- selected￨L￨VBN￨O￨- neighborhoods￨L￨NNS￨O￨- in￨L￨IN￨O￨- Las￨U￨NNP￨CITY￨- Vegas￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- test￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- peer￨L￨VBP￨O￨- based￨L￨VBN￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- WSL￨U￨NNP￨O￨- participation￨L￨NN￨O￨A by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Susceptible-Exposed-Infected-Recovered￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- home￨L￨NN￨O￨- can￨L￨MD￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- via￨L￨IN￨O￨- autoinfection￨L￨NN￨O￨- or￨L￨CC￨O￨- through￨L￨IN￨O￨- contagion￨L￨NN￨O￨- from￨L￨IN￨O￨- its￨L￨PRP$￨O￨- infected￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- stimulates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- research￨L￨NN￨O￨- question￨L￨NN￨O￨- :￨L￨:￨O￨- can￨L￨MD￨O￨- we￨L￨PRP￨O￨- observe￨L￨VB￨O￨- neighborhood￨L￨NN￨O￨- based￨L￨VBN￨O￨- peer￨L￨VBP￨O￨- effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- household￨L￨NN￨O￨- participation￨L￨NN￨O￨A in￨L￨IN￨O￨- Las￨U￨NNP￨CITY￨- Vegas￨U￨NNP￨CITY￨- ’￨L￨POS￨O￨- Water￨U￨NN￨O￨- Smart￨U￨NNP￨O￨- Landscapes￨U￨NNP￨O￨- program￨L￨NN￨O￨- ?￨L￨.￨O￨- +We￨U￨PRP￨O￨- test￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- neighborhood￨L￨NN￨O￨- based￨L￨VBN￨O￨- peer￨L￨VBP￨O￨- effect￨L￨NN￨O￨- around￨L￨IN￨O￨- participation￨L￨NN￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- incentive￨L￨NN￨O￨- based￨L￨VBN￨O￨- conservation￨L￨NN￨O￨- program￨L￨NN￨O￨- called￨L￨VBN￨O￨- ‘￨L￨``￨O￨- Water￨U￨NNP￨O￨- Smart￨U￨NNP￨O￨- Landscapes￨U￨NNP￨O￨- ’￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- WSL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨- of￨L￨IN￨O￨- Las￨U￨NNP￨CITY￨- Vegas￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Nevada￨U￨NNP￨STATE_OR_PROVINCE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- this￨L￨DT￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- test￨L￨VB￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- mediated￨L￨VBN￨O￨- peer￨L￨VBP￨O￨- effect￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- WSL￨U￨NNP￨O￨- participation￨L￨NN￨O￨A likelihood￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- unforced￨L￨JJ￨O￨- Susceptible-Exposed-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- amplitudes￨L￨NNS￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- ingredients￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- prevaccination￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- on￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- for￨L￨IN￨O￨- life￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- screening￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- may￨L￨MD￨O￨- strongly￨L￨RB￨O￨- enhance￨L￨VB￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- setting￨L￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- small-world￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- short￨L￨JJ￨O￨A term￨L￨NN￨O￨A and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- term￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Early￨U￨RB￨O￨- numerical￨L￨JJ￨O￨- and￨L￨CC￨O￨- analytical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- focussed￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- short￨L￨JJ￨O￨- term￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- bursts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- small￨L￨JJ￨O￨A world￨L￨NN￨O￨A networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Watts￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Strogatz￨U￨NNP￨PERSON￨- type￨L￨NN￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- Re￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- index￨L￨NN￨O￨A case￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- and￨L￨CC￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- affected￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A cases￨L￨NNS￨O￨A and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- from￨L￨IN￨O￨- EBOV￨U￨NN￨ORGANIZATION￨- continue￨L￨VBP￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- are￨L￨VBP￨O￨- 1.51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨A %￨L￨NN￨PERCENT￨- confidence￨L￨NN￨O￨- interval￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- CI￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- :￨L￨:￨O￨- 1.50-1.52￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- 2.53￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- :￨L￨:￨O￨- 2.41-2.67￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- 1.59￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- :￨L￨:￨O￨- 1.57-1.60￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- EBOV￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptibleexposedinfectious-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- fit￨L￨NN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- repor￨L￨NN￨O￨- ted￨L￨VBD￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A cases￨L￨NNS￨O￨A and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Liberia￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- SI￨U￨NNP￨O￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIRI￨U￨NN￨ORGANIZATION￨- spreading￨L￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- mild￨L￨JJ￨O￨- technical￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Jordan￨U￨NNP￨CITY￨- center￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- path￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- tree￨L￨NN￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- finding￨L￨VBG￨O￨- a￨L￨DT￨O￨- source￨L￨NN￨O￨A estimator￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- applic￨L￨JJ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- various￨L￨JJ￨O￨- spreading￨L￨VBG￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- Susceptible-Infected￨U￨JJ￨MISC￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- SusceptibleInfectedRecoveredInfected￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SIRI￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- k￨L￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- sources￨L￨NNS￨O￨- ,￨L￨,￨O￨- generalize￨L￨VB￨O￨- the￨L￨DT￨O￨- Jordan￨U￨NNP￨CITY￨- center￨L￨NN￨O￨- de￨L￨IN￨O￨- finition￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- Jordan￨U￨NNP￨CITY￨- center￨L￨NN￨O￨- set￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A set￨L￨VBN￨O￨- estimator￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- tree￨L￨NN￨O￨- network￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +E-mail￨U￨NN￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A estimation￨L￨NN￨O￨- ,￨L￨,￨O￨- universal￨L￨JJ￨O￨- source￨L￨NN￨O￨- estimator￨L￨NN￨O￨- ,￨L￨,￨O￨- Jordan￨U￨NNP￨PERSON￨- center￨L￨NN￨O￨- ,￨L￨,￨O￨- SIRI￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- sample￨L￨NN￨O￨- path￨L￨NN￨O￨- based￨L￨VBN￨O￨- approach￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- estimator￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- source￨L￨NN￨O￨- is￨L￨VBZ￨O￨- chosen￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- root￨L￨NN￨O￨- node￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- path￨L￨NN￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- likely￨L￨JJ￨O￨- leads￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- snapshot￨L￨NN￨O￨A .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- a￨L￨DT￨O￨- snapshot￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- all￨L￨DT￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- distinguish￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- source￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- snapshot￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +6￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- This￨U￨DT￨O￨- paper￨L￨NN￨O￨- studies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- source￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- follows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- popular￨L￨JJ￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- initially￨L￨RB￨O￨- except￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- source￨L￨NN￨O￨A which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- for￨L￨IN￨O￨- infinite-trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- estimator￨L￨NN￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- that￨L￨WDT￨O￨- minimizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Extending￨U￨VBG￨O￨- the￨L￨DT￨O￨- elementary￨L￨JJ￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- convergence￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- process￨L￨NN￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- Armbruster￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Beck￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2016￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- convergence￨L￨NN￨O￨- using￨L￨VBG￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- ODEs￨U￨NNS￨MISC￨- ,￨L￨,￨O￨- simple￨L￨JJ￨O￨- probabilistic￨L￨JJ￨O￨- inequalities￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- basic￨L￨JJ￨O￨- ODE￨U￨NN￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- O￨U￨NN￨O￨- belongs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infinite￨L￨NN￨O￨- open￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- equation￨L￨NN￨O￨- x￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λx￨L￨FW￨O￨- λ￨L￨FW￨O￨- open￨L￨JJ￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- dimension￨L￨NN￨O￨- d￨L￨NN￨O￨- grows￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- bond￨L￨NN￨O￨A percolation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- Zd￨U￨NN￨O￨- where￨L￨WRB￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- is￨L￨VBZ￨O￨- C￨U￨NN￨O￨- O￨U￨NN￨O￨- =￨L￨JJ￨O￨- ∅￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ∀￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Pλ￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨PRP￨O￨- O￨U￨NN￨O￨- =￨L￨JJ￨O￨- ∅￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ∀￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- increasing￨L￨VBG￨O￨- with￨L￨IN￨O￨- 2d￨L￨NN￨O￨- with￨L￨IN￨O￨- λ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Address￨U￨NN￨O￨- :￨L￨:￨O￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Beijing￨U￨NNP￨ORGANIZATION￨- Jiaotong￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Beijing￨U￨NNP￨CITY￨- 100044￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- X1￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- :￨L￨:￨O￨- C￨U￨NN￨O￨- ⊆￨L￨CD￨NUMBER￨- Zd￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- Ct￨U￨NN￨O￨- \￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- x￨L￨CC￨O￨- }￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- transition￨L￨NN￨O￨- rate￨L￨NN￨O￨- function￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Ct￨U￨NN￨O￨- ∪￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- Ct￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- λ￨L￨NN￨O￨- 2d￨L￨NN￨O￨- y￨L￨NN￨O￨- :￨L￨:￨O￨- y￨L￨VB￨O￨- ∼￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Ct￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- x￨L￨CC￨O￨- ∈￨L￨SYM￨O￨- Ct￨U￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- x￨L￨CC￨O￨- ∈￨L￨SYM￨O￨- Ct￨U￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- called￨L￨VBN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- 1A￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- indicator￨L￨NN￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- A.￨U￨NN￨MISC￨- Let￨U￨NNP￨MISC￨- O￨U￨NNP￨MISC￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨- of￨L￨IN￨O￨- Zd￨U￨NN￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- C￨U￨NN￨O￨- O￨U￨NN￨O￨- I￨U￨PRP￨O￨- O￨U￨VBP￨O￨- then￨L￨RB￨O￨- λE￨L￨VB￨O￨- ρ￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- ∅￨L￨NN￨O￨- ,￨L￨,￨O￨- ∀￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- ∅￨L￨NN￨O￨- ,￨L￨,￨O￨- ∀￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- lim￨L￨NN￨O￨A lim￨L￨NN￨O￨- d￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨SYM￨O￨- Pλ￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- d￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨SYM￨O￨- Pλ￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- λE￨L￨NN￨O￨- ρ￨L￨NN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- λ￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Eρ￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- E￨U￨NN￨O￨- ρ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expectation￨L￨NN￨O￨- of￨L￨IN￨O￨- ρ￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- dimension￨L￨NN￨O￨A d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- likely￨L￨JJ￨O￨- that￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- will￨L￨MD￨O￨- cluster￨L￨VB￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- |￨L￨SYM￨O￨- Ct￨U￨NNP￨O￨- |￨L￨SYM￨O￨- decreases￨L￨VBZ￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- |￨L￨CD￨NUMBER￨- Ct￨U￨NN￨O￨- |￨L￨NN￨O￨- and￨L￨CC￨O￨- increases￨L￨NNS￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- approximate￨L￨JJ￨O￨- to￨L￨TO￨O￨- x￨L￨CC￨O￨- ∈￨L￨SYM￨O￨- Ct￨U￨FW￨O￨- y￨L￨FW￨O￨- :￨L￨:￨O￨- y￨L￨VB￨O￨- ∼￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≈￨L￨SYM￨O￨- λ￨L￨SYM￨O￨- |￨L￨SYM￨O￨- Ct￨U￨FW￨O￨- |￨L￨FW￨O￨- E￨U￨NN￨O￨- ρ￨L￨NN￨O￨- λ￨L￨NN￨O￨- 2d￨L￨VBD￨O￨- |￨L￨SYM￨O￨- Ct￨U￨NNP￨O￨- |￨L￨SYM￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- .￨L￨.￨O￨- +lim￨L￨NN￨O￨A d￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨SYM￨O￨- Pλ￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- Similar￨U￨JJ￨O￨- result￨L￨NN￨O￨- with￨L￨IN￨O￨- that￨L￨DT￨O￨- in￨L￨IN￨O￨- Theorem￨U￨NNP￨O￨- 2.1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- identical￨L￨JJ￨O￨- ,￨L￨,￨O￨- mix￨L￨NN￨O￨- homogeneously￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- threshold￨L￨NN￨O￨- property￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- vaccinating￨L￨VBG￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- 1/R0￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- chosen￨L￨VBN￨O￨- uniformly￨L￨RB￨O￨A at￨L￨IN￨O￨- random￨L￨JJ￨O￨- –￨L￨:￨O￨- or￨L￨CC￨O￨- ,￨L￨,￨O￨- equivalently￨L￨RB￨O￨- ,￨L￨,￨O￨- isolating￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- before￨L￨IN￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- further￨L￨RB￨O￨- –￨L￨:￨O￨- is￨L￨VBZ￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- critical￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- depends￨L￨VBZ￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- fraction￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- 1/R0￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- chosen￨L￨VBN￨O￨- uniformly￨L￨RB￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- perfect￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- without￨L￨IN￨O￨- social￨L￨JJ￨O￨A structure￨L￨NN￨O￨A ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- insufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- large￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Consider￨U￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- graph￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Section￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Section￨U￨NN￨O￨- 2.1￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- vertices￨L￨NNS￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- ordered￨L￨VBN￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- ,￨L￨,￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- say￨L￨VB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- directed￨L￨JJ￨O￨- edge￨L￨NN￨O￨- from￨L￨IN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- i￨L￨FW￨O￨- with￨L￨IN￨O￨- i￨L￨FW￨O￨- initially￨L￨RB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- infective￨L￨JJ￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- remainder￨L￨NN￨O￨- of￨L￨IN￨O￨- if￨L￨IN￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- makes￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Special￨U￨JJ￨O￨- focus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- put￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- exponential-growth-associated￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Rr￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- loosely￨L￨RB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- obtained￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨A structure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- ignored￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- briefly￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- →￨L￨NN￨O￨- infective￨L￨JJ￨O￨A →￨L￨NN￨O￨- recovered￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- population￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- manner￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨- is￨L￨VBZ￨O￨- quite￨L￨RB￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- coupled￨L￨VBN￨O￨A disease-behavior￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- [￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- Letter￨U￨NN￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- coupled￨L￨VBN￨O￨- disease-behavior￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- dividing￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- U-state￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- without￨L￨IN￨O￨- evident￨L￨JJ￨O￨A clinical￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- labelled￨L￨VBN￨O￨- as￨L￨IN￨O￨- U￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I-state￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- evident￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- labelled￨L￨VBN￨O￨- as￨L￨IN￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- noticed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- U-state￨U￨NN￨O￨- is￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- E-state￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- E-state￨U￨NN￨O￨- is￨L￨VBZ￨O￨- asymptomatic￨L￨JJ￨O￨A but￨L￨CC￨O￨- not￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- U-state￨U￨NN￨O￨- is￨L￨VBZ￨O￨- asymptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- coupled￨L￨VBN￨O￨- disease-behavior￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- analytic￨L￨JJ￨O￨- results￨L￨NNS￨O￨- quantitatively￨L￨RB￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- awareness￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- forth￨L￨RB￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- .￨L￨.￨O￨- +–￨L￨:￨O￨- Many￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- enhance￨L￨VB￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- often￨L￨RB￨O￨- established￨L￨VBN￨O￨- with￨L￨IN￨O￨- static￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- modified￨L￨JJ￨O￨A metapopulation￨L￨NN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- produce￨L￨VBP￨O￨- a￨L￨DT￨O￨- discontinuous￨L￨JJ￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- jump￨L￨NN￨O￨- at￨L￨IN￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- modified￨L￨JJ￨O￨A metapopulat￨L￨NN￨O￨- ion￨L￨NN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- produce￨L￨VBP￨O￨- a￨L￨DT￨O￨- discontinuous￨L￨JJ￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- stage￨L￨NN￨O￨- spread￨L￨VBD￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- seriously￨L￨RB￨O￨- ill￨L￨JJ￨O￨- stage￨L￨NN￨O￨- and￨L￨CC￨O￨- never￨L￨RB￨O￨- recover￨L￨VB￨O￨- directly￨L￨RB￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- makes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- recovery￨L￨NN￨O￨A rate￨L￨NN￨O￨A smaller￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- given￨L￨VBN￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- group￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- recovered￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- group￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Later￨U￨RB￨O￨- on￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- wide￨L￨JJ￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- intrinsic￨L￨JJ￨O￨- heterogeneous￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- started￨L￨VBD￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- microstructure￨L￨NN￨O￨- on￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- more￨L￨JJR￨O￨- detailed￨L￨JJ￨O￨- perspectives￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- appearing￨L￨VBG￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- shell￨L￨NN￨O￨A decomposition￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- for￨L￨IN￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- link￨L￨NN￨O￨- salience￨L￨NN￨O￨- skeleton￨L￨NN￨O￨- correlated￨L￨VBD￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- ’s￨L￨POS￨O￨- appearance￨L￨NN￨O￨- in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- hierarchies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- weak￨L￨JJ￨O￨- ties￨L￨NNS￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- significant￨L￨JJ￨O￨- for￨L￨IN￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- SIR￨U￨NN￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- to￨L￨TO￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- influence￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- indicator￨L￨NN￨O￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- shell￨L￨NN￨O￨A can￨L￨MD￨O￨- better￨L￨RBR￨O￨- identify￨L￨VB￨O￨- highly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- outperforming￨L￨VBG￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨- and￨L￨CC￨O￨- PageRank￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- influence￨L￨NN￨O￨- have￨L￨VBP￨O￨- no￨L￨DT￨O￨- clear￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- ,￨L￨,￨O￨- degree￨L￨NN￨O￨- performs￨L￨VBZ￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- among￨L￨IN￨O￨- considered￨L￨VBN￨O￨- topological￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A can￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- given￨L￨VBN￨O￨- same￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- will￨L￨MD￨O￨- not￨L￨RB￨O￨- deterministically￨L￨RB￨O￨- affect￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +Identifying￨U￨VBG￨O￨- highly￨L￨RB￨O￨A susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- significance￨L￨NN￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- infinite￨L￨JJ￨O￨- population￨L￨NN￨O￨- limit￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨- analytically￨L￨RB￨O￨- scaling￨L￨VBG￨O￨A rules￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- time-dependent￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- functions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- characterize￨L￨VBP￨O￨- the￨L￨DT￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- sub-populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Theoretical￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- framework￨L￨NN￨O￨- is￨L￨VBZ￨O￨- challenging￨L￨JJ￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨JJS￨O￨- basic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- processes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- many￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- concerning￨L￨VBG￨O￨- finite-size￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- and￨L￨CC￨O￨- extremal￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- functions￨L￨NNS￨O￨A remain￨L￨VBP￨O￨- unanswered￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A outbreaks￨L￨NNS￨O￨A at￨L￨IN￨O￨- or￨L￨CC￨O￨- near￨L￨IN￨O￨- the￨L￨DT￨O￨- threshThe￨L￨NN￨O￨- overall￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- times￨L￨NNS￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- heuristic￨L￨NN￨O￨- arguments￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- obtain￨L￨VB￨O￨- scaling￨L￨VBG￨O￨- laws￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A outbreaks￨L￨NNS￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- focus￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- processes￨L￨NNS￨O￨- balance￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- time-evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- steady￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨A susceptible-infected-recovered-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- one-and￨L￨JJ￨O￨- two-dimensional￨L￨JJ￨O￨- lattices￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- time￨L￨NN￨O￨A evolution￨L￨NN￨O￨A of￨L￨IN￨O￨- these￨L￨DT￨O￨- variables￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- at￨L￨IN￨O￨- site￨L￨NN￨O￨- i￨L￨FW￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- probability￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- λ￨L￨NN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- neighboring￨L￨VBG￨O￨- site￨L￨NN￨O￨- j￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- PA￨U￨NN￨STATE_OR_PROVINCE￨- approximation￨L￨NN￨O￨A was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- Durrett￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Levin￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- simpler￨L￨JJR￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- immediately￨L￨RB￨O￨- become￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- again￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- solve￨L￨VB￨O￨A the￨L￨DT￨O￨- PA￨U￨NN￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- MFA￨U￨NN￨ORGANIZATION￨- models￨L￨NNS￨O￨- analytically￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- numerically￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- square￨L￨JJ￨O￨- lattice￨L￨NN￨O￨A Tˆania￨U￨NNP￨O￨- Tom￨U￨NNP￨O￨- ´￨L￨POS￨O￨- e1￨L￨NN￨O￨- and￨L￨CC￨O￨- Robert￨U￨NNP￨PERSON￨- M.￨U￨NNP￨PERSON￨- Ziff2￨U￨NNP￨PERSON￨- 1￨L￨CD￨NUMBER￨- Instituto￨U￨NNP￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- ,￨L￨,￨O￨- Universidade￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- S˜ao￨U￨NNP￨ORGANIZATION￨- Paulo￨U￨NNP￨ORGANIZATION￨- Caixa￨U￨NNP￨ORGANIZATION￨- Postal￨U￨NNP￨ORGANIZATION￨- 66138￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 05315-970￨L￨CD￨NUMBER￨- S˜ao￨U￨NNP￨O￨- Paulo￨U￨NNP￨O￨- SP￨U￨NN￨O￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- 2Michigan￨L￨NNP￨O￨- Center￨U￨NNP￨O￨- for￨L￨IN￨O￨- Theoretical￨U￨NNP￨O￨- Physics￨U￨NN￨O￨- and￨L￨CC￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Chemical￨U￨NNP￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Michigan￨U￨NNP￨ORGANIZATION￨- Ann￨U￨NNP￨ORGANIZATION￨- Arbor￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- MI￨U￨NNP￨STATE_OR_PROVINCE￨- 48109-2136￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- By￨U￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- asynchronous￨L￨JJ￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- square￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- c0￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.1765005￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- a￨L￨DT￨O￨- chosen￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- site￨L￨NN￨O￨- spontaneously￨L￨RB￨O￨- recovers￨L￨VBZ￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infection/recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- λc￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- This￨U￨DT￨O￨- point￨L￨NN￨O￨- corresponds￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- c0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- 3c0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0.538410￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- falls￨L￨VBZ￨O￨- the￨L￨DT￨O￨- site￨L￨NN￨O￨- and￨L￨CC￨O￨- bond￨L￨NN￨O￨- thresholds￨L￨NNS￨O￨- .￨L￨.￨O￨- +I.￨U￨NN￨O￨- INTRODUCTION￨U￨NNP￨O￨- The￨U￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- non-equilibrium￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨A phenomena￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 24￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- asynchronous-update￨L￨JJ￨O￨- lattice￨L￨NN￨O￨A version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- lattice￨L￨NN￨O￨- sites￨L￨NNS￨O￨- are￨L￨VBP￨O￨- updated￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Removed-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- stochastic￨L￨JJ￨O￨- lattice￨L￨NN￨O￨A gas￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- recent￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- changes￨L￨VBZ￨O￨- structure￨L￨NN￨O￨- dynamically￨L￨RB￨O￨A according￨L￨VBG￨O￨- to￨L￨TO￨O￨- rules￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- epidemic￨L￨JJ￨O￨- status￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Infections￨U￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- reduced￨L￨VBN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- phenomenon￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- :￨L￨:￨O￨- for￨L￨IN￨O￨- appropriate￨L￨JJ￨O￨- choices￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- bistability￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨A state￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rewiring￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- infective￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- links￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- combine￨L￨VB￨O￨A Monte￨U￨NNP￨LOCATION￨- Carlo￨U￨NNP￨LOCATION￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- mean￨L￨NN￨O￨- field￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- on￨L￨IN￨O￨- evolving￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Degree￨U￨NN￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- altered￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- distance￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- nearest￨L￨JJS￨O￨- infective￨L￨JJ￨O￨A increases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Distinct￨U￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- two￨L￨CD￨NUMBER￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- models￨L￨NNS￨O￨- first￨L￨VBP￨O￨- assume￨L￨VB￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- propagation￨L￨NN￨O￨A parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- relate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- global￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- without￨L￨IN￨O￨- knowing￨L￨VBG￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- local￨L￨JJ￨O￨- details￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- SIS￨U￨NN￨O￨- setting￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- review￨L￨VBP￨O￨- a￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- novel￨L￨JJ￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- computation￨L￨NN￨O￨- and￨L￨CC￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- above￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- present￨L￨JJ￨DATE￨- alternative￨L￨JJ￨O￨- proofs￨L￨NNS￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- SIR￨U￨NN￨O￨- setting￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- novel￨L￨JJ￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- transient￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- threshold￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- stability￨L￨NN￨O￨- properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- asymptotic￨L￨JJ￨O￨- convergence￨L￨NN￨O￨- .￨L￨.￨O￨- +Scalar￨U￨NNP￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- propagation￨L￨NN￨O￨A phenomena￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- studied￨L￨VBN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- survey￨L￨NN￨O￨- by￨L￨IN￨O￨- Hethcote￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- on￨L￨IN￨O￨- scalar￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- FastSIR￨U￨NN￨O￨- algorithm￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- novel￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- average￨L￨JJ￨O￨- case￨L￨NN￨O￨- running￨L￨VBG￨O￨A time￨L￨NN￨O￨- by￨L￨IN￨O￨- constant￨L￨JJ￨O￨- factor￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- probability￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Naive￨U￨JJ￨O￨- SIR￨U￨NN￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- uses￨L￨VBZ￨O￨- data￨L￨NNS￨O￨- structures￨L￨NNS￨O￨- efficiently￨L￨RB￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- running￨L￨VBG￨O￨A time￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- propose￨L￨VBP￨O￨- novel￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- FastSIR￨U￨NN￨O￨- algorithm￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- better￨L￨JJR￨O￨- average￨L￨JJ￨O￨- case￨L￨NN￨O￨- running￨L￨VBG￨O￨A time￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- Naive￨U￨JJ￨O￨- SIR￨U￨NN￨O￨- algorithm￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- FastSIR￨U￨NN￨O￨- algorithm￨L￨NN￨O￨A does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- follow￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- still￨L￨RB￨O￨- captures￨L￨VBZ￨O￨- all￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- transfers￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A on￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- Infected￨U￨JJ￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- compartment￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- empirically￨L￨RB￨O￨- examines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- betweenness￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- shell￨L￨NN￨O￨- number￨L￨NN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- spreaders￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- conduct￨L￨VBP￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨A on￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- real-world￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- data-sets￨L￨NNS￨O￨- from￨L￨IN￨O￨- various￨L￨JJ￨O￨- domains￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e-mail￨L￨NN￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- blogging￨L￨NN￨O￨- ,￨L￨,￨O￨- power￨L￨NN￨O￨- ,￨L￨,￨O￨- autonomous￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- collaboration￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- empirically￨L￨RB￨O￨- study￨L￨VB￨O￨- how￨L￨WRB￨O￨- well￨L￨RB￨O￨- various￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨A perform￨L￨VBP￨O￨- at￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- spreaders￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- shell￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- β￨L￨VB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- will￨L￨MD￨O￨- transmit￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- problem￨L￨NN￨O￨- relating￨L￨VBG￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- when￨L￨WRB￨O￨- considering￨L￨VBG￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- will￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- greatest￨L￨JJS￨O￨A portion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- expectation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- also￨L￨RB￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- provided￨L￨VBN￨O￨- various￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨A that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- heuristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- their￨L￨PRP$￨O￨- mathematical￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- xyz￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- McKendrick￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Kermack￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- nonlinear￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- dx￨L￨NNP￨O￨- dt￨L￨NN￨O￨A =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- βx￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- dy￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- βx￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- γ￨L￨FW￨O￨- y￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- dz￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N1￨U￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N2￨U￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- z￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N3￨U￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ni￨U￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- ℜ￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- γ￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- general￨L￨JJ￨TITLE￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Abel￨U￨NNP￨O￨- equation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- perturbative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- series￨L￨NN￨O￨- form￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vital￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- exact￨L￨JJ￨O￨- parametric￨L￨JJ￨O￨A form￨L￨NN￨O￨- .￨L￨.￨O￨- +K.￨U￨NNP￨PERSON￨- Mak￨U￨NNP￨PERSON￨- ‡￨L￨NNP￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- parametric￨L￨JJ￨O￨A form￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- generalization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- births￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨A equations￨L￨NNS￨O￨A ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- Abel￨U￨NNP￨PERSON￨- type￨L￨NN￨O￨- equation￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- exact￨L￨JJ￨O￨A solution￨L￨NN￨O￨- ;￨L￨:￨O￨- Abel￨U￨NNP￨PERSON￨- equation￨L￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- 1￨L￨CD￨DATE￨- 4￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- ∗￨L￨NN￨O￨- Electronic￨U￨JJ￨O￨- address￨L￨NN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- INTRODUCTION￨U￨NNP￨O￨- Most￨U￨JJS￨O￨- real-world￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- represent￨L￨VBP￨O￨A such￨L￨JJ￨O￨- entities￨L￨NNS￨O￨- as￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- companies￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- computers￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- two-layer￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- an￨L￨DT￨O￨- isolation￨L￨NN￨O￨A parameter￨L￨NN￨O￨- w￨L￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- quarantining￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- layers￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- isolation￨L￨NN￨O￨- period￨L￨NN￨O￨- tw￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- link￨L￨NN￨O￨- percolation￨L￨NN￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- isolation￨L￨NN￨O￨A increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- configuration￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- almost￨L￨RB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- research￨L￨NN￨O￨- the￨L￨DT￨O￨- isolation￨L￨NN￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- disregarded￨L￨VBN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- isolation￨L￨NN￨O￨A period￨L￨NN￨O￨- is￨L￨VBZ￨O￨- maximum￨L￨JJ￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- w￨L￨NN￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- never￨L￨RB￨O￨- becomes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +•￨L￨SYM￨O￨- That￨U￨IN￨O￨- the￨L￨DT￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- confer￨L￨VB￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- cured￨L￨VBN￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- so￨L￨IN￨O￨- they￨L￨PRP￨O￨- go￨L￨VBP￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- rate￨L￨NN￨O￨- •￨L￨SYM￨O￨- That￨U￨DT￨O￨- people￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- compartment￨L￨NN￨O￨A have￨L￨VBP￨O￨- equal￨L￨JJ￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- β￨L￨NN￨O￨- •￨L￨SYM￨O￨- That￨U￨DT￨O￨- all￨L￨DT￨O￨- newborns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- uninfected￨L￨JJ￨O￨- by￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- join￨L￨VB￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- immunized￨L￨VBN￨O￨- compartment￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- vaccinated￨L￨VBN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- •￨L￨SYM￨O￨- That￨U￨DT￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- immigrants￨L￨NNS￨O￨- and￨L￨CC￨O￨- emigrants￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- state￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- totally￨L￨RB￨O￨- be￨L￨VB￨O￨- eradicated￨L￨VBN￨O￨- if￨L￨IN￨O￨- effort￨L￨NN￨O￨- is￨L￨VBZ￨O￨- made￨L￨VBN￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- actively￨L￨RB￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- must￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- considerations￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- immunized￨L￨VBN￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- latent￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +keywords￨L￨NNS￨O￨- :￨L￨:￨O￨- Hepatitis￨U￨NNP￨CAUSE_OF_DEATH￨- B￨U￨NNP￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HBV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Disease-free￨U￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ;￨L￨:￨O￨- Endermic￨U￨JJ￨O￨- equilibrium￨L￨NN￨O￨- state￨L￨NN￨O￨- ;￨L￨:￨O￨- Stability￨U￨NN￨O￨- analysis￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Hepatitis￨U￨NNP￨CAUSE_OF_DEATH￨- B￨U￨NNP￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- potentially￨L￨RB￨O￨- life-threatening￨L￨JJ￨O￨- liver￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HBV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- born￨L￨VBN￨O￨- babies￨L￨NNS￨O￨- against￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- latently￨L￨RB￨O￨- and￨L￨CC￨O￨- actively￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- are￨L￨VBP￨O￨- factored￨L￨JJ￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- con￨L￨VBP￨O￨- firm￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- measure￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- awry￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- bimodal￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- near￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨A thresholds￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- accurately￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- variability￨L￨NN￨O￨- .￨L￨.￨O￨- +0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 4￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- CONTENTS￨U￨NNP￨O￨- Contents￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- An￨U￨DT￨O￨- effective￨L￨JJ￨O￨- simulated￨L￨JJ￨O￨A identi￨L￨NNS￨O￨- fication￨L￨NN￨O￨- measure￨L￨NN￨O￨- Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- identi￨L￨NNS￨O￨- fication￨L￨NN￨O￨- measure￨L￨NN￨O￨- near￨L￨IN￨O￨- the￨L￨DT￨O￨- crit￨L￨NN￨O￨- ical￨L￨JJ￨O￨- point￨L￨NN￨O￨- 3.1￨L￨CD￨NUMBER￨- 3.2￨L￨CD￨NUMBER￨- Comparison￨U￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- Effectiveness￨U￨NN￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- identi￨L￨NNS￨O￨- fication￨L￨NN￨O￨- measure￨L￨NN￨O￨- unde￨L￨NN￨O￨- r￨L￨NN￨O￨- cutoff￨L￨NN￨O￨- hypothesis￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- Applications￨U￨NNS￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- identi￨L￨NNS￨O￨- fication￨L￨NN￨O￨- method￨L￨NN￨O￨- 4.1￨L￨CD￨NUMBER￨- 4.2￨L￨CD￨NUMBER￨- Comparison￨U￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- in￨L￨IN￨O￨- classic￨L￨JJ￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- various￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨A identification￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- o￨L￨NN￨O￨- n￨L￨NN￨O￨- finite-size￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- verify￨L￨VB￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- theoretical￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- mean￨L￨NN￨O￨- -￨L￨:￨O￨- field￨L￨NN￨O￨- theory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HMF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- quenched￨L￨VBN￨O￨- mean￨L￨NN￨O￨- -￨L￨:￨O￨- field￨L￨NN￨O￨- theory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- QMF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- y￨L￨NN￨O￨- comparing￨L￨VBG￨O￨- them￨L￨PRP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨A threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨- measure￨L￨NN￨O￨- .￨L￨.￨O￨- +Reduced￨U￨VBN￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨A suppresses￨L￨VBZ￨O￨- but￨L￨CC￨O￨- lengthens￨L￨VBZ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- biased￨L￨VBN￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- Genki￨U￨NNP￨PERSON￨- Ichinose￨U￨NNP￨PERSON￨- ∗￨L￨NNP￨O￨- Department￨U￨NNP￨O￨- of￨L￨IN￨O￨- Mathematical￨U￨NNP￨O￨- and￨L￨CC￨O￨- Systems￨U￨NNP￨O￨- Engineering￨U￨NNP￨O￨- ,￨L￨,￨O￨- Shizuoka￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hamamatsu￨U￨NNP￨CITY￨- 432-8561￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨ORGANIZATION￨- Yoshiki￨U￨NNP￨ORGANIZATION￨- Satotani￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Information￨U￨NNP￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Okayama￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Okayama￨U￨NNP￨LOCATION￨- 700-8530￨L￨CD￨NUMBER￨- Japan￨U￨NNP￨ORGANIZATION￨- Hiroki￨U￨NNP￨ORGANIZATION￨- Sayama￨U￨NNP￨ORGANIZATION￨- Center￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Col￨U￨NNP￨ORGANIZATION￨- lective￨L￨JJ￨ORGANIZATION￨- Dynamics￨U￨NNPS￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Complex￨U￨JJ￨ORGANIZATION￨- Systems￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Industrial￨U￨NNP￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Binghamton￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- State￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- New￨U￨NNP￨ORGANIZATION￨- York￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Binghamton￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- NY￨U￨NNP￨STATE_OR_PROVINCE￨- 13902-6000￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Commerce￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Waseda￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Tokyo￨U￨NNP￨CITY￨- 169-8050￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨ORGANIZATION￨- Takashi￨U￨NNP￨ORGANIZATION￨- Nagatani￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mechanical￨U￨JJ￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Shizuoka￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hamamatsu￨U￨NNP￨ORGANIZATION￨- 432-8561￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- September￨U￨NNP￨DATE￨- 9￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Various￨U￨JJ￨O￨- theoretical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- 2D￨L￨NN￨O￨- continuous￨L￨JJ￨O￨- space￨L￨NN￨O￨- where￨L￨WRB￨O￨- agents￨L￨NNS￨O￨A tend￨L￨VBP￨O￨- to￨L￨TO￨O￨- move￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- direction￨L￨NN￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- random￨L￨JJ￨O￨- movement￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨A lengthened￨L￨VBD￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- progressed￨L￨VBD￨O￨- slowly￨L￨RB￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- people￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- movement￨L￨NN￨O￨A activity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- greatly￨L￨RB￨O￨- reduced￨L￨VBN￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- physically￨L￨RB￨O￨- weakened￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- conducting￨L￨VBG￨O￨- extensive￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- limited￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- .￨L￨.￨O￨- +Where￨U￨WRB￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- survivors￨L￨NNS￨O￨- was￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- soon￨L￨RB￨O￨- to￨L￨TO￨O￨- carry￨L￨VB￨O￨- out￨L￨RP￨O￨- Meta￨U￨NNP￨O￨- Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- to￨L￨TO￨O￨- verify￨L￨VB￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- conditions￨L￨VBZ￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- excellent￨L￨JJ￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- fictitious￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨A ones￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- from￨L￨IN￨O￨- real￨L￨JJ￨O￨A social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- real￨L￨JJ￨O￨- or￨L￨CC￨O￨- fictitious￨L￨JJ￨O￨- study￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Scale-Free￨U￨JJ￨O￨- SF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 6￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Smal￨U￨JJ￨O￨- l￨L￨NN￨O￨- World￨U￨NN￨O￨- SW￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 7￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +A.￨U￨NN￨O￨- Theoretical￨U￨NNP￨O￨- bases￨L￨NNS￨O￨- A￨U￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- relations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- bonds￨L￨NNS￨O￨- or￨L￨CC￨O￨- edges￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- defined￨L￨JJ￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- elements￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- vertices￨L￨NNS￨O￨A or￨L￨CC￨O￨- actors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Formally￨U￨RB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- triada￨L￨NN￨O￨- G￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- V￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨A ,￨L￨,￨O￨- E￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- and￨L￨CC￨O￨- g￨L￨NN￨O￨- :￨L￨:￨O￨- E￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- w￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- form￨L￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- histogram￨L￨NN￨O￨- of￨L￨IN￨O￨- rows￨L￨NNS￨O￨- also￨L￨RB￨O￨- named￨L￨VBD￨O￨A prestige￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- actor￨L￨NN￨TITLE￨- who￨L￨WP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graphs￨L￨NNS￨O￨- agrees￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- histogram￨L￨NN￨O￨- of￨L￨IN￨O￨- columns￨L￨NNS￨O￨- or￨L￨CC￨O￨- popularity￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- actor￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- par￨L￨JJ￨O￨- ticular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- graph￨L￨NN￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- takes￨L￨VBZ￨O￨- on￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- forms￨L￨NNS￨O￨- :￨L￨:￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- it￨L￨PRP￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- unique￨L￨JJ￨O￨- fixed￨L￨JJ￨O￨A point￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- tie￨L￨VBP￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- results￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- true￨L￨JJ￨O￨- ”￨L￨''￨O￨- underlying￨L￨VBG￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- tightest￨L￨JJS￨O￨- upper-bound￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- involves￨L￨VBZ￨O￨- only￨L￨RB￨O￨- marginals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- an￨L￨DT￨O￨- upper-bound￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- does￨L￨VBZ￨O￨- provide￨L￨VB￨O￨- an￨L￨DT￨O￨- upper-bound￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- chain￨L￨NN￨O￨- not￨L￨RB￨O￨- being￨L￨VBG￨O￨- absorbed￨L￨VBN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- fixed￨L￨JJ￨O￨- point￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨A has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- log￨L￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- mixing￨L￨VBG￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- quickly￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- n-dimensional￨L￨JJ￨O￨- non-linear￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- corresponding￨L￨JJ￨O￨- linearization￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- fixed￨L￨JJ￨O￨A point￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- “￨L￨``￨O￨- deterministic￨L￨JJ￨O￨- ”￨L￨''￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- even￨L￨RB￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- entirety￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- n￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- yields￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨A with￨L￨IN￨O￨- 2n￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- sometimes￨L￨RB￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- stochastic￨L￨JJ￨O￨- ”￨L￨''￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +38￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- D-01187￨U￨CD￨LOCATION￨- Dresden￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Germany￨U￨NNP￨COUNTRY￨- E-mail￨U￨NN￨O￨- :￨L￨:￨O￨- 4Mathematics￨L￨NNS￨O￨- Department￨U￨NNP￨O￨- ,￨L￨,￨O￨- Faculty￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Education￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- El-Arish￨U￨NNP￨LOCATION￨- 45111￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Egypt￨U￨NNP￨COUNTRY￨- A￨U￨NNP￨O￨- modified￨L￨VBD￨O￨A version￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible-infected-recovered-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- foot-and-mouth￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- FMD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- small-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- ring￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- programme￨L￨NN￨O￨- is￨L￨VBZ￨O￨- included￨L￨VBN￨O￨- .￨L￨.￨O￨- +Ring￨U￨NN￨O￨- vaccination￨L￨NN￨O￨A is￨L￨VBZ￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- eradicating￨L￨VBG￨O￨- FMD￨U￨NNP￨ORGANIZATION￨- provided￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- enough￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible-infective-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨A graph￨L￨NN￨O￨A chosen￨L￨VBN￨O￨- uniformly￨L￨RB￨O￨- sub￨L￨JJ￨O￨- ject￨L￨NN￨O￨- to￨L￨TO￨O￨- having￨L￨VBG￨O￨- given￨L￨VBN￨O￨- vertex￨L￨NN￨O￨- degrees￨L￨NNS￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- families￨L￨NNS￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨A graph￨L￨NN￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Erd˝os￨U￨NNS￨O￨- –￨L￨:￨O￨- R´enyi￨U￨NN￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- graphs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- local￨L￨JJ￨O￨- household￨L￨NN￨O￨- structure￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- clustering￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- survey￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- random￨L￨JJ￨O￨A graph￨L￨NN￨O￨A with￨L￨IN￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨- sequence￨L￨NN￨O￨- ,￨L￨,￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- infinite￨L￨JJ￨O￨- population￨L￨NN￨O￨- limit￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compute￨L￨VBP￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- asymptotic￨L￨JJ￨O￨- results￨L￨NNS￨O￨- apply￨L￨VBP￨O￨- to￨L￨TO￨O￨- more￨L￨JJR￨O￨- general￨L￨JJ￨TITLE￨- multiple-type￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- branching￨L￨VBG￨O￨A processes￨L￨NNS￨O￨A .￨L￨.￨O￨- +II￨U￨CD￨NUMBER￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- multiple-type￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨- and￨L￨CC￨O￨- derive￨L￨VB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infinite￨L￨JJ￨O￨- population￨L￨NN￨O￨- limit￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relatively￨L￨RB￨O￨- slow￨L￨JJ￨O￨- early￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- clustering￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- many￨L￨JJ￨O￨- short￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- super￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- people￨L￨NNS￨O￨- infecting￨L￨VBG￨O￨- many￨L￨JJ￨O￨- more￨L￨RBR￨O￨- others￨L￨NNS￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- person￨L￨NN￨O￨- do￨L￨VBP￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- attributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- broad￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- degree￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- distances￨L￨NNS￨O￨- in￨L￨IN￨O￨- isolated￨L￨VBN￨O￨- components￨L￨NNS￨O￨- ,￨L￨,￨O￨- weighted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- component￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- predictor￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- Susceptible￨U￨NNP￨O￨- –￨L￨:￨O￨- Infectious￨U￨JJ￨O￨- –￨L￨:￨O￨- Recovered￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- happens￨L￨VBZ￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- per-contact￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- characterize￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- extinction￨L￨NN￨O￨A time￨L￨NN￨O￨A in￨L￨IN￨O￨- SIR￨U￨NN￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- think￨L￨VBP￨O￨- ,￨L￨,￨O￨- understudied￨L￨VBD￨O￨- topic￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- to￨L￨TO￨O￨- die￨L￨VB￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨A time￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- spreading￨L￨NN￨O￨- influences￨L￨NNS￨O￨A can￨L￨MD￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- hindering￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- or￨L￨CC￨O￨- accelerating￨L￨VBG￨O￨- the￨L￨DT￨O￨- innovation￨L￨NN￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- similar￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- further￨L￨JJ￨O￨- applied￨L￨VBN￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- influential￨L￨JJ￨O￨- spreader￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- scientists￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- publicat￨L￨NN￨O￨- ions￨L￨NNS￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- injection￨L￨NN￨O￨- points￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- microfinance￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- predicting￨L￨VBG￨O￨- essential￨L￨JJ￨O￨- proteins￨L￨NNS￨O￨- in￨L￨IN￨O￨- protein￨L￨NN￨O￨- interaction￨L￨NN￨O￨- networks￨L￨NNS￨O￨- 13￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- scientists￨L￨NNS￨O￨- argued￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- important￨L￨JJ￨O￨- than￨L￨IN￨O￨- its￨L￨PRP$￨O￨- immediate￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- proposed￨L￨VBN￨O￨- k-shell￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- index￨L￨NN￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 15￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- variants￨L￨NNS￨O￨- 16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- indicators￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- influences￨L￨NNS￨O￨A .￨L￨.￨O￨- +Locating￨U￨VBG￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- via￨L￨IN￨O￨- dynamics-sensitive￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- Jian-Hong￨U￨NNP￨O￨- Lin1￨U￨NN￨O￨- ,￨L￨,￨O￨- Qiang￨U￨NNP￨PERSON￨- Guo1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jian-Guo￨U￨NNP￨O￨- Liu1￨U￨NNP￨O￨- *￨L￨SYM￨O￨- Tao￨U￨NNP￨O￨- Zhou2￨U￨NNP￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- *￨L￨SYM￨O￨- September￨U￨NNP￨DATE￨- 25￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 93￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- PR￨U￨NN￨STATE_OR_PROVINCE￨- China￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- 2CompleX￨L￨NNP￨O￨- Lab￨U￨NNP￨O￨- ,￨L￨,￨O￨- Web￨U￨NN￨O￨- Sciences￨U￨NNP￨O￨- Center￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electronic￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Chengdu￨U￨NNP￨CITY￨- 611731￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- PR￨U￨NN￨STATE_OR_PROVINCE￨- China￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Big￨U￨NNP￨ORGANIZATION￨- Data￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- Center￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electronic￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Chengdu￨U￨NNP￨CITY￨- 611731￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- PR￨U￨NN￨STATE_OR_PROVINCE￨- China￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- great￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- and￨L￨CC￨O￨- practical￨L￨JJ￨O￨- signi￨L￨NN￨O￨- ficance￨L￨NN￨O￨- ,￨L￨,￨O￨- locatin￨L￨NN￨O￨- g￨L￨NN￨O￨- in￨L￨IN￨O￨- fluential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨A of￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- promising￨L￨JJ￨O￨- issues￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- adopt￨L￨VBP￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- path￨L￨NN￨O￨- based￨L￨VBN￨O￨- estimator￨L￨NN￨O￨A developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- on￨L￨IN￨O￨- infinite￨L￨NN￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- path￨L￨NN￨O￨- based￨L￨VBN￨O￨- estimator￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Jordan￨U￨NNP￨CITY￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- center￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- estimator￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- source￨L￨NN￨O￨- is￨L￨VBZ￨O￨- upper￨L￨JJ￨O￨- bounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- probability￨L￨NN￨O￨- on￨L￨IN￨O￨- infinite￨L￨NN￨O￨- trees￨L￨NNS￨O￨- .￨L￨.￨O￨- +Surprisingly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- path￨L￨NN￨O￨- based￨L￨VBN￨O￨- estimator￨L￨NN￨O￨A is￨L￨VBZ￨O￨- robust￨L￨JJ￨O￨- to￨L￨TO￨O￨- network￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- other￨L￨JJ￨O￨- words￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- path￨L￨NN￨O￨- based￨L￨VBN￨O￨- estimator￨L￨NN￨O￨A minimizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- observed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- piece￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- spreads￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A are￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +Central￨U￨NNP￨O￨- limit￨L￨NN￨O￨A theorems￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- susceptibles￨L￨NNS￨O￨- that￨L￨WDT￨O￨- become￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- such￨L￨PDT￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- n￨L￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- explicit￨L￨JJ￨O￨- ,￨L￨,￨O￨- easy￨L￨JJ￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- expressions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- variance￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- proved￨L￨VBN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- degrees￨L￨NNS￨O￨- are￨L￨VBP￨O￨- bounded￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- central￨L￨JJ￨O￨- limit￨L￨NN￨O￨A theorems￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- graphs￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +the￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- converges￨L￨NNS￨O￨- In￨U￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- limit￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- conditional￨L￨JJ￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- more￨L￨RBR￨O￨- precisely￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- theorems￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- limit￨L￨NN￨O￨- log￨L￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- central￨L￨JJ￨O￨- limit￨L￨NN￨O￨A theorems￨L￨NNS￨O￨- cover￨L￨VBP￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- it￨L￨PRP￨O￨- initial￨L￨JJ￨O￨- infectives￨L￨NNS￨O￨- either￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- held￨L￨VBN￨O￨- fixed￨L￨VBN￨O￨- as￨L￨IN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- configuration￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A graphs￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- as￨L￨IN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- either￨L￨CC￨O￨- reproduction￨L￨NN￨O￨- rule￨L￨NN￨O￨- RN￨U￨NN￨O￨- or￨L￨CC￨O￨- R￨U￨NN￨O￨- ∞￨L￨NN￨O￨- ,￨L￨,￨O￨- particle￨L￨NN￨O￨- motion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- nearest￨L￨JJS￨O￨- neighbor￨L￨NN￨O￨- random￨L￨JJ￨O￨- walk1￨L￨NN￨O￨- on￨L￨IN￨O￨- Zd￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- holding￨L￨VBG￨O￨- probability￨L￨NN￨O￨- In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨- at￨L￨IN￨O￨- site￨L￨NN￨O￨- x￨L￨NN￨O￨- has￨L￨VBZ￨O￨- k￨L￨NN￨O￨- offspring￨L￨NN￨O￨A ,￨L￨,￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- offspring￨L￨NN￨O￨- independently￨L￨RB￨O￨- chooses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- neighboring￨L￨VBG￨O￨- site￨L￨NN￨O￨- y￨L￨NN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- law￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2d￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- P1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2d￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- |￨L￨SYM￨O￨- y￨L￨SYM￨O￨- −￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- |￨L￨SYM￨O￨- ≤￨L￨SYM￨O￨- 1￨L￨LS￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- branching￨L￨VBG￨O￨- envelope￨L￨NN￨O￨- evolves￨L￨VBZ￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Any￨U￨DT￨O￨- particle￨L￨NN￨O￨- located￨L￨JJ￨O￨- at￨L￨IN￨O￨- site￨L￨NN￨O￨- x￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- lives￨L￨VBZ￨O￨- for￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- unit￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- reproduces￨L￨VBZ￨O￨- ,￨L￨,￨O￨- placing￨L￨VBG￨O￨- random￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- ξy￨L￨NN￨O￨- of￨L￨IN￨O￨- offspring￨L￨NN￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- sites￨L￨NNS￨O￨- y￨L￨VBP￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- |￨L￨SYM￨O￨- y￨L￨SYM￨O￨- −￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- |￨L￨SYM￨O￨- ≤￨L￨SYM￨O￨- 1￨L￨LS￨NUMBER￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- N￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- site￨L￨NN￨O￨A x￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Zd￨U￨NN￨O￨- may￨L￨MD￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- be￨L￨VB￨O￨- either￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- .￨L￨.￨O￨- +Contrasting￨U￨VBG￨O￨- Effects￨U￨NNS￨MISC￨- of￨L￨IN￨MISC￨- Strong￨U￨JJ￨MISC￨- Ties￨U￨NNPS￨MISC￨- on￨L￨IN￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- Processes￨U￨NNS￨O￨- in￨L￨IN￨O￨- Temporal￨U￨JJ￨O￨- Networks￨U￨NNP￨O￨- Kaiyuan￨U￨NNP￨PERSON￨- Sun￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Andrea￨U￨NNP￨PERSON￨- Baronchelli￨U￨NNP￨PERSON￨- ,2￨L￨NN￨O￨- and￨L￨CC￨O￨- Nicola￨U￨NN￨MISC￨- Perra1￨U￨NN￨O￨- 1Laboratory￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Modeling￨U￨NN￨O￨- of￨L￨IN￨O￨- Biological￨U￨JJ￨O￨- and￨L￨CC￨O￨- Socio-technical￨U￨JJ￨MISC￨- Systems￨U￨NNPS￨MISC￨- ,￨L￨,￨O￨- Northeastern￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Boston￨U￨NNP￨ORGANIZATION￨- MA￨U￨NNP￨ORGANIZATION￨- 02115￨L￨CD￨DATE￨- USA￨U￨NNP￨COUNTRY￨- 2Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Mathematics￨U￨NNP￨O￨- ,￨L￨,￨O￨- City￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- London￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Northampton￨U￨NNP￨LOCATION￨- Square￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- London￨U￨NNP￨CITY￨- EC1V￨U￨NN￨O￨- 0HB￨L￨NN￨O￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- March￨U￨NNP￨DATE￨- 20￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Most￨U￨JJS￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- connectivity￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- that￨L￨WDT￨O￨- evolve￨L￨VBP￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- following￨L￨VBG￨O￨- complex￨L￨NN￨O￨- ,￨L￨,￨O￨- non-Markovian￨L￨JJ￨MISC￨- ,￨L￨,￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- ubiquitous￨L￨JJ￨O￨- feature￨L￨NN￨O￨- by￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- activity￨L￨NN￨O￨- driven￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- memory￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- Markovian￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- non-Markovian￨L￨JJ￨MISC￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- SIS￨U￨NN￨O￨- processes￨L￨NNS￨O￨- instead￨L￨RB￨O￨- ,￨L￨,￨O￨- memory￨L￨NN￨O￨A reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ’￨L￨POS￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +All￨U￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- phenomena￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- affected￨L￨VBN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- ordering￨L￨VBG￨O￨- ,￨L￨,￨O￨- concurrence￨L￨NN￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- activities￨L￨NNS￨O￨- and￨L￨CC￨O￨- connectivity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 36￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- memory￨L￨NN￨O￨A inhibits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- shifting￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- to￨L￨TO￨O￨- larger￨L￨JJR￨O￨- values￨L￨NNS￨O￨- and￨L￨CC￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- help￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- approximation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- ever￨L￨RB￨O￨- get￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- minor￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- final￨L￨JJ￨O￨A state￨L￨NN￨O￨- hence￨L￨RB￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- let￨L￨VBD￨O￨- Z￨U￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- by￨L￨IN￨O￨- then￨L￨RB￨O￨- recovered￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- excluding￨L￨VBG￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Z￨U￨NN￨O￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +1.1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- stochastic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨A homogeneous￨L￨JJ￨O￨- community￨L￨NN￨O￨- 1.1.1￨L￨CD￨NUMBER￨- Model￨U￨NNP￨TITLE￨- definition￨L￨NN￨O￨- Consider￨U￨VB￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- initially￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +STOCHASTIC￨U￨JJ￨O￨- EPIDEMIC￨U￨NN￨O￨- MODELS￨U￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- specified￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- often￨L￨RB￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨A case￨L￨NN￨O￨A and￨L￨CC￨O￨- thought￨L￨NN￨O￨- of￨L￨IN￨O￨- as￨L￨IN￨O￨- being￨L￨VBG￨O￨- externally￨L￨RB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- being￨L￨VBG￨O￨- susceptible￨L￨JJ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denote￨L￨VBP￨O￨A the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- so￨L￨RB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Much￨U￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨A work￨L￨NN￨O￨A gives￨L￨VBZ￨O￨- explicit￨L￨JJ￨O￨- consideration￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- or￨L￨CC￨O￨- disease-transmitting￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- attendant￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- interacting￨L￨VBG￨O￨- pair￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- would￨L￨MD￨O￨- like￨L￨VB￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- their￨L￨PRP$￨O￨- probability￨L￨NN￨O￨A of￨L￨IN￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- Susceptible￨U￨JJ￨O￨- →￨L￨NN￨O￨- Infected￨U￨JJ￨O￨- →￨L￨NN￨O￨- Recovered￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Kermack￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- provides￨L￨VBZ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- strict￨L￨JJ￨O￨- lower￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- suscpetibles￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- strict￨L￨JJ￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- recoveries￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨A stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Y￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- transition￨L￨NN￨O￨A rates￨L￨NNS￨O￨A as￨L￨IN￨O￨- in￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- constraint￨L￨NN￨O￨- that￨L￨WDT￨O￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- y￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- denote￨L￨VBP￨O￨- possible￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Y￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +J.￨U￨NNP￨PERSON￨- Sharkey￨U￨NNP￨PERSON￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- Population-level￨U￨JJ￨O￨- transition￨L￨NN￨O￨A rates￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- From￨U￨IN￨O￨- To￨U￨TO￨O￨- Rate￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- x￨L￨CC￨O￨- −￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- βxy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- γ￨L￨FW￨O￨- y￨L￨FW￨O￨- makes￨L￨VBZ￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- other￨L￨JJ￨O￨- given￨L￨VBN￨O￨- individual￨L￨JJ￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- all￨L￨DT￨O￨- such￨L￨JJ￨O￨- Poisson￨U￨NNP￨PERSON￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- General￨U￨NNP￨TITLE￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ;￨L￨:￨O￨- deterministic￨L￨JJ￨O￨- general￨L￨JJ￨TITLE￨A epidemic￨L￨JJ￨O￨- ;￨L￨:￨O￨- SIR￨U￨NN￨O￨- ;￨L￨:￨O￨- Kermack-McKendrick￨U￨NNP￨O￨- ;￨L￨:￨O￨- message￨L￨NN￨O￨- passing￨L￨NN￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Mathematics￨U￨NNP￨O￨- Sub￨U￨NN￨O￨- ject￨L￨NN￨O￨- Classification￨U￨NN￨O￨- :￨L￨:￨O￨- Primary￨U￨JJ￨O￨- 92D30￨L￨NN￨O￨- Secondary￨U￨JJ￨O￨- 60J27￨L￨NN￨O￨- ;￨L￨:￨O￨- 60J22￨L￨NN￨O￨- ;￨L￨:￨O￨- 05C80￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- so-called￨L￨JJ￨O￨- general￨L￨JJ￨TITLE￨A stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- →￨L￨NN￨O￨- Infected￨U￨JJ￨O￨- →￨L￨NN￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Chapter￨U￨NNP￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- generalized￨L￨VBN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- latency￨L￨NN￨O￨A ,￨L￨,￨O￨- incubation￨L￨NN￨O￨- and￨L￨CC￨O￨- variable￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Phase￨U￨NN￨O￨- transitions￨L￨NNS￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨A are￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- quantity￨L￨NN￨O￨- U￨U￨NNP￨O￨- P￨U￨NN￨O￨- ,￨L￨,￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- U￨U￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- moment￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- squared￨L￨VBN￨O￨- first￨L￨JJ￨O￨- moment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- multiplied￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- parameter￨L￨NN￨O￨- P￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- square￨L￨JJ￨O￨A system￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- universal￨L￨JJ￨O￨- value￨L￨NN￨O￨- 1.0167￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- as￨L￨IN￨O￨- for￨L￨IN￨O￨- site￨L￨NN￨O￨- and￨L￨CC￨O￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨- ,￨L￨,￨O￨- confirming￨L￨VBG￨O￨- further￨L￨RBR￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- order￨L￨NN￨O￨- parameter￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- several￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- will￨L￨MD￨O￨- then￨L￨RB￨O￨- start￨L￨VB￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- a￨L￨DT￨O￨- multivariate￨L￨JJ￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- joint￨L￨JJ￨O￨- probability￨L￨NN￨O￨- function￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- As￨U￨IN￨O￨- previously￨L￨RB￨DATE￨- stated￨L￨VBN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- time-dependent￨L￨JJ￨O￨- expectation￨L￨NN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observables￨L￨NNS￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- configuration￨L￨NN￨O￨- probability￨L￨NN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- The￨U￨DT￨O￨- probabilistic￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- normalization￨L￨NN￨O￨- condition￨L￨NN￨O￨- At￨U￨IN￨O￨- this￨L￨DT￨O￨- point￨L￨NN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- worth￨L￨JJ￨O￨- to￨L￨TO￨O￨- note￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- configurations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- entirely￨L￨RB￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- occupation￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- calls￨L￨VBZ￨O￨- indeed￨L￨RB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- representation￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- second-quantized￨L￨JJ￨O￨- bosonic￨L￨JJ￨O￨- operators￨L￨NNS￨O￨- which￨L￨WDT￨O￨- then￨L￨RB￨O￨- lead￨L￨VBP￨O￨- 1￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- will￨L￨MD￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A C￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- interest￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- this￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- what￨L￨WP￨O￨- follows￨L￨VBZ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- above￨L￨IN￨O￨- mentioned￨L￨VBN￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- an￨L￨DT￨O￨- SIR-inspired￨U￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A C￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- and￨L￨CC￨O￨- chronically￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- whose￨L￨WP$￨O￨- total￨L￨JJ￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- allowed￨L￨VBN￨O￨- to￨L￨TO￨O￨- change￨L￨VB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- that￨L￨DT￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIR-inspired￨U￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A C￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- and￨L￨CC￨O￨- chronically￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- whose￨L￨WP$￨O￨- total￨L￨JJ￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- allowed￨L￨VBN￨O￨- to￨L￨TO￨O￨- change￨L￨VB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨- and￨L￨CC￨O￨- multilayer￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- can￨L￨MD￨O￨- become￨L￨VB￨O￨- endemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨- network￨L￨NN￨O￨- also￨L￨RB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- layers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- form￨L￨VBP￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- could￨L￨MD￨O￨- not￨L￨RB￨O￨- possibly￨L￨RB￨O￨- sustain￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- isolation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- effect￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- fully￨L￨RB￨O￨- accounted￨L￨VBN￨O￨- NumericCitation￨U￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨A network￨L￨NN￨O￨- perspective￨L￨NN￨O￨- by￨L￨IN￨O￨- coupling￨L￨NN￨O￨- two￨L￨CD￨NUMBER￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- SIS-like￨U￨JJ￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- awarenessunawareness-awareness￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- online￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨- in￨L￨IN￨O￨- multilayer￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- So￨U￨RB￨O￨- far￨L￨RB￨O￨- several￨L￨JJ￨O￨- works￨L￨NNS￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Suceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- on￨L￨IN￨O￨- multilayer￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- multilayer￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- layers￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- notable￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨A network￨L￨NN￨O￨- framework￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- also￨L￨RB￨O￨- successfully￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- modular￨L￨JJ￨O￨A time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Matthieu￨U￨NNP￨ORGANIZATION￨- Nadini￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mechanical￨U￨JJ￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Aerospace￨U￨NNP￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- New￨U￨NNP￨ORGANIZATION￨- York￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Tandon￨U￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Brooklyn￨U￨NNP￨CITY￨- NY￨U￨NNP￨STATE_OR_PROVINCE￨- 11201￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- USA￨U￨NNP￨ORGANIZATION￨- Dipartimento￨U￨NNP￨ORGANIZATION￨- di￨L￨NNP￨ORGANIZATION￨- Elettronica￨U￨NNP￨ORGANIZATION￨- e￨L￨SYM￨O￨- Telecomunicazioni￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Politecnico￨U￨NNP￨ORGANIZATION￨- di￨L￨NNP￨ORGANIZATION￨- Torino￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Corso￨U￨NNP￨PERSON￨- Duca￨U￨NNP￨PERSON￨- degli￨L￨NNP￨O￨- Abruzzi￨U￨NNP￨ORGANIZATION￨- 24￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10129￨L￨CD￨NUMBER￨- Torino￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- Kaiyuan￨U￨NNP￨CITY￨- Sun￨U￨NNP￨LOCATION￨- Laboratory￨U￨NNP￨LOCATION￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Modeling￨U￨NN￨O￨- of￨L￨IN￨O￨- Biological￨U￨JJ￨O￨- and￨L￨CC￨O￨- Socio-technical￨U￨JJ￨MISC￨- Systems￨U￨NNPS￨MISC￨- ,￨L￨,￨O￨- Northeastern￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Boston￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- USA￨U￨NNP￨ORGANIZATION￨- Enrico￨U￨NNP￨ORGANIZATION￨- Ubaldi￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Scientific￨U￨NNP￨ORGANIZATION￨- Interchange￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- ISI￨U￨NNP￨ORGANIZATION￨- Foundation￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Turin￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- Michele￨U￨NNP￨PERSON￨- Starnini￨U￨NNP￨PERSON￨- Departament￨U￨NNP￨PERSON￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- Fondamental￨U￨NNP￨O￨- ,￨L￨,￨O￨- Universitat￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Barcelona￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Mart￨U￨NNP￨ORGANIZATION￨- ´￨L￨POS￨O￨- ı￨L￨NN￨O￨- i￨L￨FW￨O￨- Franqu`es￨U￨FW￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 08028￨L￨CD￨NUMBER￨- Barcelona￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- Universitat￨U￨NNP￨O￨- de￨L￨IN￨O￨- Barcelona￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Complex￨U￨JJ￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- UBICS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Universitat￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Barcelona￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Barcelona￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- Alessandro￨U￨NNP￨PERSON￨- Rizzo￨U￨NNP￨PERSON￨- Dipartimento￨U￨NNP￨PERSON￨- di￨L￨NNP￨PERSON￨- Elettronica￨U￨NNP￨PERSON￨- e￨L￨SYM￨O￨- Telecomunicazioni￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Politecnico￨U￨NNP￨ORGANIZATION￨- di￨L￨NNP￨ORGANIZATION￨- Torino￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Corso￨U￨NNP￨PERSON￨- Duca￨U￨NNP￨PERSON￨- degli￨L￨NNP￨O￨- Abruzzi￨U￨NNP￨ORGANIZATION￨- 24￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10129￨L￨CD￨NUMBER￨- Torino￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- Nicola￨U￨NNP￨O￨- Perra￨U￨NNP￨O￨- ∗￨L￨NNP￨O￨- Centre￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Business￨U￨NNP￨ORGANIZATION￨- Network￨U￨NNP￨ORGANIZATION￨- Analysis￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Greenwich￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- London￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 5￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- modular￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- that￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- modular￨L￨JJ￨O￨A structures￨L￨NNS￨O￨- induce￨L￨VBP￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- without￨L￨IN￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mapping￨U￨NN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- Master￨U￨NN￨O￨- equation￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- quantum￨L￨NN￨O￨- formulation￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- spin￨L￨NN￨O￨- operators￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- hierarchy￨L￨NN￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- equations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- solved￨L￨VBN￨O￨- exactly￨L￨RB￨O￨- for￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- initial￨L￨JJ￨O￨A conditions￨L￨NNS￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- chain￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- exact￨L￨JJ￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- ensemble￨L￨NN￨O￨- averaged￨L￨VBD￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- are￨L￨VBP￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- for￨L￨IN￨O￨- single￨L￨JJ￨O￨- realizations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- with￨L￨IN￨O￨- standard￨L￨JJ￨O￨- mean￨L￨NN￨O￨A field￨L￨NN￨O￨A theory￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- valid￨L￨JJ￨O￨- on￨L￨IN￨O￨- large￨L￨JJ￨O￨- fully-connected￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- uncorrelated￨L￨JJ￨O￨- random￨L￨JJ￨O￨- initial￨L￨JJ￨O￨A conditions￨L￨NNS￨O￨A the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- analytically￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- susceptible-infectious-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨A of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- sub￨L￨JJ￨O￨- ject￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- this￨L￨DT￨O￨- hidden￨L￨JJ￨O￨A SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- implementing￨L￨VBG￨O￨- particle￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- sample￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- entire￨L￨JJ￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- treated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- hidden￨L￨JJ￨O￨A Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- hidden￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- states￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- states￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- reported￨L￨VBD￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- successfully￨L￨RB￨O￨- predict￨L￨VB￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- weeks￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A cases￨L￨NNS￨O￨- increases￨L￨VBZ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- notification￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- timely￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- implement￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- which￨L￨WDT￨O￨- simultaneously￨L￨RB￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Susceptible-Infected-Recovered-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- predictive￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- predictors￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨A programs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- are￨L￨VBP￨O￨- very￨L￨RB￨O￨- efficient￨L￨JJ￨O￨- in￨L￨IN￨O￨- providing￨L￨VBG￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- decreases￨L￨VBZ￨O￨- considerably￨L￨RB￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- probability￨L￨NN￨O￨- ω￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- controlled￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- drastically￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- efficiently￨L￨RB￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- manuscript￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- local￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- considering￨L￨VBG￨O￨- limited￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨A .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- immunized￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- reaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- VL￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨A stops￨L￨VBZ￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- which￨L￨WDT￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- susceptibles￨L￨NNS￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- vaccinated￨L￨VBN￨O￨- -￨L￨:￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨A ω￨L￨SYM￨O￨- -￨L￨:￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- get￨L￨VB￨O￨- infected￨L￨JJ￨O￨- -￨L￨:￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +Severe￨U￨JJ￨O￨- population￨L￨NN￨O￨- collapses￨L￨NNS￨O￨- and￨L￨CC￨O￨- species￨L￨NNS￨O￨A extinctions￨L￨NNS￨O￨- in￨L￨IN￨O￨- multi-host￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- Sergei￨U￨NNP￨PERSON￨- Maslov￨U￨NNP￨PERSON￨- ∗￨L￨NNP￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Bioengineering￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- Carl￨U￨NNP￨ORGANIZATION￨- R.￨U￨NNP￨ORGANIZATION￨- Woese￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Genomic￨U￨JJ￨ORGANIZATION￨- Biology￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Il￨U￨NNP￨ORGANIZATION￨- linois￨L￨VBZ￨O￨- at￨L￨IN￨O￨- Urbana-Champaign￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Urbana￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- IL￨U￨NN￨STATE_OR_PROVINCE￨- 61801￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- USA￨U￨NNP￨ORGANIZATION￨- Kim￨U￨NNP￨ORGANIZATION￨- Sneppen￨U￨NNP￨ORGANIZATION￨- †￨L￨NNP￨ORGANIZATION￨- Center￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Models￨U￨NNS￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Life￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Niels￨U￨NNP￨ORGANIZATION￨- Bohr￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Copenhagen￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 2100￨L￨CD￨DATE￨- Copenhagen￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Denmark￨U￨NNP￨COUNTRY￨- Most￨U￨JJS￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- including￨L￨VBG￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- half￨L￨NN￨O￨- of￨L￨IN￨O￨- known￨L￨JJ￨O￨- human￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- restricted￨L￨JJ￨O￨- to￨L￨TO￨O￨- just￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- much￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- species￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- two-species￨L￨NNS￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- post-epidemic￨L￨JJ￨O￨- collapses￨L￨NNS￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- initial￨L￨JJ￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- times￨L￨NNS￨O￨- individuals￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- conclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- could￨L￨MD￨O￨- drive￨L￨VB￨O￨- a￨L￨DT￨O￨- species￨L￨NNS￨O￨A with￨L￨IN￨O￨- high￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- local￨L￨JJ￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- global￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- provided￨L￨VBD￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- co-infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- abundant￨L￨JJ￨O￨- species￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- propagating￨L￨VBG￨O￨- in￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- species￨L￨NNS￨O￨A and￨L￨CC￨O￨- compare￨L￨VB￨O￨- and￨L￨CC￨O￨- contrast￨L￨VB￨O￨- it￨L￨PRP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- an￨L￨DT￨O￨- edge-based￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- approach￨L￨NN￨O￨- and￨L￨CC￨O￨- percolation￨L￨NN￨O￨A tools￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- time-dependent￨L￨JJ￨O￨- quantity￨L￨NN￨O￨- ΦS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- neighbor￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- void￨L￨NN￨O￨- percolation￨L￨NN￨O￨- process￨L￨NN￨O￨- involving￨L￨VBG￨O￨- those￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- not-reached￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reproduce￨L￨VBP￨O￨- seasonal￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- influenza￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- sub￨L￨NN￨O￨- ject￨L￨NN￨O￨- of￨L￨IN￨O￨- extensive￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- and￨L￨CC￨O￨- numerical￨L￨JJ￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨A networks￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- preserve￨L￨VB￨O￨- a￨L￨DT￨O￨- macroscopic￨L￨JJ￨O￨- connected￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- composed￨L￨VBN￨O￨- by￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- which￨L￨WDT￨O￨- guarantee￨L￨VBP￨O￨A its￨L￨PRP$￨O￨- functionality￨L￨NN￨O￨- ,￨L￨,￨O￨- any￨L￨DT￨O￨- mitigation￨L￨NN￨O￨- strategy￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- before￨L￨IN￨O￨- this￨L￨DT￨O￨- critical￨L￨JJ￨O￨- time￨L￨NN￨O￨- tc￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- process￨L￨NN￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- its￨L￨PRP$￨O￨- discrete￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨A step￨L￨NN￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- susceptible￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- recover￨L￨VB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- time￨L￨NN￨O￨- tr￨L￨NN￨O￨- since￨L￨IN￨O￨- they￨L￨PRP￨O￨- were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- recovery￨L￨NN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Recovery￨U￨NN￨O￨- rate￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A with￨L￨IN￨O￨- synchronous￨L￨JJ￨O￨- updating￨L￨VBG￨O￨- Panpan￨U￨NNP￨PERSON￨- Shu￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Wei￨U￨NNP￨PERSON￨- Wang￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ∗￨L￨CD￨NUMBER￨- Ming￨U￨NNP￨O￨- Tang￨U￨NNP￨O￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- †￨L￨CD￨NUMBER￨- Pengcheng￨U￨NNP￨PERSON￨- Zhao￨U￨NNP￨PERSON￨- ,4￨L￨NN￨O￨- and￨L￨CC￨O￨- Yi-Cheng￨U￨JJ￨O￨- Zhang5￨U￨NN￨O￨- 1Web￨L￨NNP￨O￨- Sciences￨U￨NNP￨O￨- Center￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electronic￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Chengdu￨U￨NNP￨CITY￨- 610054￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 2￨L￨CD￨NUMBER￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Xi’an￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Xi’an￨U￨NNP￨LOCATION￨- 710054￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 3Big￨L￨NNP￨O￨- data￨L￨NNS￨O￨- research￨L￨NN￨O￨- center￨L￨NN￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electronic￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Chengdu￨U￨NNP￨CITY￨- 610054￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 4￨L￨CD￨NUMBER￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Optoelectronic￨U￨NNP￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Xidian￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Xi’an￨U￨NNP￨LOCATION￨- 710071￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 5Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Fribourg￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Chemin￨U￨NNP￨PERSON￨- du￨L￨NNP￨PERSON￨- Mus￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- ee￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1700￨L￨CD￨DATE￨- Fribourg￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- August￨U￨NNP￨DATE￨- 10￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Accurate￨U￨NNP￨O￨- identi￨L￨NNS￨O￨- fication￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- essential￨L￨JJ￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- effective￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A and￨L￨CC￨O￨- final￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- based￨L￨VBN￨O￨- o￨L￨NN￨O￨- n￨L￨NN￨O￨- the￨L￨DT￨O￨- edge-based￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- systematically￨L￨RB￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- recovery￨L￨NN￨O￨A rate￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- asynchronous￨L￨JJ￨O￨- updating￨L￨VBG￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨A rate￨L￨NN￨O￨A does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- provides￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- socalled￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- ful￨L￨JJ￨O￨- ly￨L￨NN￨O￨- connected￨L￨VBN￨O￨- mean-field￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- species￨L￨NNS￨O￨- evolve￨L￨VBP￨O￨- with￨L￨IN￨O￨- dS/dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- ;￨L￨:￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- coupled￨L￨VBN￨O￨- nonlinear￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- dI￨L￨NN￨O￨- /￨L￨:￨O￨- dt￨L￨NN￨O￨A =￨L￨JJ￨O￨- β￨L￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- and￨L￨CC￨O￨- dR/dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- assessed￨L￨VBN￨O￨- by￨L￨IN￨O￨- computing￨L￨VBG￨O￨- the￨L￨DT￨O￨- convex￨L￨NN￨O￨A hull￨L￨NN￨O￨- enclosing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemics￨U￨NNS￨O￨- |￨L￨SYM￨O￨- Branching￨U￨VBG￨O￨- Brownian￨U￨JJ￨MISC￨- motion￨L￨NN￨O￨- |￨L￨SYM￨O￨- Convex￨U￨NNP￨O￨- hull￨L￨NN￨O￨- M￨U￨NN￨O￨- odels￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- traditionally￨L￨RB￨O￨A consider￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- susceptibles￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- explodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- invades￨L￨VBZ￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- goes￨L￨VBZ￨O￨A to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- case￨L￨NN￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- constant￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- perimeter￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- convex￨L￨NN￨O￨A hull￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- them￨L￨PRP￨O￨- with￨L￨IN￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- identical￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- Rui￨U￨NNP￨PERSON￨- Yang￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Bing-Hong￨U￨NNP￨PERSON￨- Wang￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jie￨U￨NNP￨PERSON￨- Ren￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Wen-Jie￨U￨NNP￨PERSON￨- Bai￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Zhi-Wen￨U￨NNP￨PERSON￨- Shi￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Wen-Xu￨U￨NNP￨PERSON￨- Wang￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Tao￨U￨NNP￨O￨- Zhou￨U￨NNP￨O￨- ∗￨L￨NNP￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Modern￨U￨NNP￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Nonlinear￨U￨JJ￨ORGANIZATION￨- Science￨U￨NN￨ORGANIZATION￨- Center￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hefei￨U￨NNP￨CITY￨- 230026￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- PR￨U￨NN￨STATE_OR_PROVINCE￨- China￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- February￨U￨NNP￨DATE￨- 2￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- modified￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assigned￨L￨VBN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- identical￨L￨JJ￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- A￨U￨DT￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨A step￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- standard￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- style￨L￨NN￨O￨- contains￨L￨VBZ￨O￨- some￨L￨DT￨O￨- unexpected￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- while￨L￨IN￨O￨- being￨L￨VBG￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- networks￨L￨NNS￨O￨- directly￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- potential￨L￨JJ￨O￨- infection-activity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- infectivity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- its￨L￨PRP$￨O￨- possibly￨L￨RB￨O￨- maximal￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- process￨L￨NN￨O￨- within￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- time￨L￨NN￨O￨A step￨L￨NN￨O￨A ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- strictly￨L￨RB￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- degree￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨A model￨L￨NN￨TITLE￨A shows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- extensively￨L￨RB￨O￨A studied￨L￨VBN￨O￨A recently￨L￨RB￨DATE￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- the￨L￨DT￨O￨- highly￨L￨RB￨O￨A connected￨L￨VBN￨O￨A hubs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- reached￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pervades￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- progressive￨L￨JJ￨IDEOLOGY￨- cascade￨L￨NN￨O￨- across￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- degree￨L￨NN￨O￨- classes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- allow￨L￨VBP￨O￨- the￨L￨DT￨O￨- campaigner￨L￨NN￨O￨- to￨L￨TO￨O￨- adjust￨L￨VB￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A rate￨L￨NN￨O￨A by￨L￨IN￨O￨- incentivizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- recruitment￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- time￨L￨NN￨O￨- varying￨L￨VBG￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨A rate￨L￨NN￨O￨A in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- formulation￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- changing￨L￨VBG￨O￨- interest￨L￨NN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- campaign￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- deadline￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reached￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- situation￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- problem￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- using￨L￨VBG￨O￨- Pontryagin￨U￨NNP￨O￨- ’s￨L￨POS￨O￨- Maximum￨U￨NNP￨O￨- Principle￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- prescribes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- campaign￨L￨NN￨O￨A .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Information￨U￨NNP￨O￨- Epidemics￨U￨NNP￨O￨- ,￨L￨,￨O￨- Optimal￨U￨JJ￨O￨- Control￨U￨NN￨O￨- ,￨L￨,￨O￨- Pontryagin￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- Maximum￨U￨NNP￨O￨- principle￨L￨NN￨O￨A ,￨L￨,￨O￨- Social￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- ,￨L￨,￨O￨- Susceptible-Infected-Recovered￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨PERSON￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- small￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- γ￨L￨NN￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- phase￨L￨NN￨O￨A boundary￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- black￨L￨JJ￨O￨- solid￨L￨JJ￨O￨- line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- supercritical￨L￨JJ￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nontrivial￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- missed￨L￨VBN￨O￨- in￨L￨IN￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- phase￨L￨NN￨O￨- diagram￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- PA￨U￨NN￨STATE_OR_PROVINCE￨- SIRS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 4￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- plotted￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 1a￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Susceptible-Infected-Recovered￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- Euclidean￨U￨JJ￨MISC￨- network￨L￨NN￨O￨- Abdul￨U￨NNP￨O￨- Khaleque1￨U￨NN￨O￨- ,￨L￨,￨O￨- ∗￨L￨NN￨O￨- and￨L￨CC￨O￨- Parongama￨U￨NN￨O￨- Sen1￨U￨NN￨O￨- ,￨L￨,￨O￨- †￨L￨SYM￨O￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Calcutta￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 92￨L￨CD￨NUMBER￨- APC￨U￨NN￨O￨- Road￨U￨NNP￨O￨- ,￨L￨,￨O￨- Kolkata￨U￨NNP￨LOCATION￨- 700009￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- India￨U￨NNP￨COUNTRY￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Euclidean￨U￨JJ￨MISC￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- dimension￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- distance￨L￨NN￨O￨- l￨L￨NN￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- l￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∝￨L￨CD￨NUMBER￨- l￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- δ￨L￨NN￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- nearest￨L￨JJS￨O￨A neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- threshold￨L￨NN￨O￨- behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- δ￨L￨VB￨O￨- up￨L￨RP￨O￨- to￨L￨TO￨O￨- δ￨L￨VB￨O￨- ≈￨L￨SYM￨O￨- 2.0￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- above￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨A q￨L￨NN￨O￨- =￨L￨JJ￨O￨- qc￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- saturation￨L￨NN￨O￨- value￨L￨NN￨O￨- Rsat￨U￨NN￨O￨- attains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- value￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- changes￨L￨NNS￨O￨- as￨L￨IN￨O￨- δ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- varied￨L￨JJ￨O￨A and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- Rsat￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- τ￨L￨NN￨O￨- show￨L￨VBP￨O￨- scaling￨L￨VBG￨O￨- behavior￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨A system￨L￨NN￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- ;￨L￨:￨O￨- Rsat￨U￨NNP￨O￨- ∼￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- /￨L￨:￨O￨- ˜ν￨L￨JJ￨O￨- g1￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- q￨L￨JJ￨O￨- −￨L￨NN￨O￨- qc￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- ˜ν￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- τ￨L￨NN￨O￨- ∼￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- µ￨L￨NN￨O￨- /￨L￨:￨O￨- ˜ν￨L￨JJ￨O￨- g2￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- q￨L￨JJ￨O￨- −￨L￨NN￨O￨- qc￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- ˜ν￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Starting￨U￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- and￨L￨CC￨O￨- simulations￨L￨NNS￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- rewiring￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- quarantine￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- threshold￨L￨NN￨O￨- wc￨L￨NN￨O￨- separating￨L￨VBG￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- w￨L￨NN￨O￨- <￨L￨JJR￨O￨- wc￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- reaches￨L￨VBZ￨O￨A a￨L￨DT￨O￨- large￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- w￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- wc￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- spread￨L￨VBN￨O￨- out￨L￨RP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- purpose￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- quarantine￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- protect￨L￨VBP￨O￨- themselves￨L￨PRP￨O￨- by￨L￨IN￨O￨- disconnecting￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- links￨L￨NNS￨O￨- to￨L￨TO￨O￨- infected￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨A with￨L￨IN￨O￨- probability￨L￨NN￨O￨- w￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reconnecting￨L￨VBG￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- chosen￨L￨VBN￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- s￨L￨NNS￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- get￨L￨VB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- with￨L￨IN￨O￨- rewiring￨L￨VBG￨O￨- probability￨L￨NN￨O￨- w￨L￨VBD￨O￨- it￨L￨PRP￨O￨- disconnects￨L￨VBZ￨O￨- its￨L￨PRP$￨O￨- link￨L￨NN￨O￨- from￨L￨IN￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- reconnects￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- susceptible￨L￨JJ￨O￨A node￨L￨NN￨O￨A ,￨L￨,￨O￨- different￨L￨NN￨O￨- from￨L￨IN￨O￨- its￨L￨PRP$￨O￨- present￨L￨JJ￨DATE￨- neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- estimate￨L￨VB￨O￨- wc￨L￨NN￨O￨- we￨L￨PRP￨O￨- start￨L￨VBP￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- tree￨L￨NN￨O￨- structure￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- out￨L￨RP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- seed￨L￨NN￨O￨- and￨L￨CC￨O￨- reaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨A node￨L￨NN￨O￨A s￨L￨NNS￨O￨- through￨L￨IN￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- i.￨L￨VBP￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- strategy￨L￨NN￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- unit￨L￨NN￨O￨- ,￨L￨,￨O￨- every￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨A i￨L￨FW￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- tries￨L￨VBZ￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- neighbor￨L￨NN￨O￨- s￨L￨NNS￨O￨- with￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +Myers￨U￨NNP￨ORGANIZATION￨- Laboratory￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Atomic￨U￨JJ￨ORGANIZATION￨- and￨L￨CC￨O￨- Solid￨U￨JJ￨ORGANIZATION￨- State￨U￨NN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Biotechnology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Cornel￨U￨NNP￨ORGANIZATION￨- l￨L￨NN￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Ithaca￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- MY￨U￨NNP￨O￨- 14853￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- quasi-neutral￨L￨JJ￨O￨- competition￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- competition￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- apply￨L￨VB￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- fixation￨L￨NN￨O￨- of￨L￨IN￨O￨- competing￨L￨VBG￨O￨- strains￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- strains￨L￨NNS￨O￨- are￨L￨VBP￨O￨- identical￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infinite￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- approaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- point￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- coexistence￨L￨NN￨O￨- line￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- CL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- straight￨L￨JJ￨O￨- line￨L￨NN￨O￨- of￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- points￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- space￨L￨NN￨O￨- of￨L￨IN￨O￨- sub-population￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- argue￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- slow￨L￨JJ￨O￨- strain￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- competitive￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- for￨L￨IN￨O￨- mathematically￨L￨RB￨O￨- “￨L￨``￨O￨- typical￨L￨JJ￨O￨- ”￨L￨''￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fast￨L￨JJ￨O￨- strain￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- win￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- situation￨L￨NN￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- infectives￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- strains￨L￨NNS￨O￨A are￨L￨VBP￨O￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- continues￨L￨VBZ￨O￨- this￨L￨DT￨O￨- line￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- by￨L￨IN￨O￨- studying￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- competition￨L￨NN￨O￨A between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- strains￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- population￨L￨NN￨O￨- turnover￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- two-strain￨L￨JJ￨O￨- generalization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- population￨L￨NN￨O￨- turnover￨L￨NN￨O￨A ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- Susceptible￨U￨JJ￨O￨- individual￨L￨NN￨O￨- can￨L￨MD￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- get￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- his￨L￨PRP$￨O￨- opinion￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- totally￨L￨RB￨O￨- in￨L￨IN￨O￨- favor￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- get￨L￨VB￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- β￨L￨NN￨O￨- if￨L￨IN￨O￨- he￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- neighbor￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- successful￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- his￨L￨PRP$￨O￨- opinion￨L￨NN￨O￨A from￨L￨IN￨O￨- extremist￨L￨NN￨O￨- positive￨L￨JJ￨O￨- to￨L￨TO￨O￨- totally￨L￨RB￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +Vaccinated￨U￨VBN￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- extremist￨L￨NN￨O￨- positive￨L￨JJ￨O￨- opinion￨L￨NN￨O￨A that￨L￨WDT￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- change￨L￨VB￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- below￨L￨IN￨O￨- β￨L￨NN￨O￨- ∗￨L￨NN￨O￨- and￨L￨CC￨O￨- above￨L￨IN￨O￨- ω￨L￨NN￨O￨- ∗￨L￨IN￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- never￨L￨RB￨O￨- becomes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- varies￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- opinion￨L￨NN￨O￨A parameter￨L￨NN￨O￨- r￨L￨NN￨O￨- .￨L￨.￨O￨- +o￨L￨NN￨O￨- i￨L￨FW￨O￨- b￨L￨SYM￨O￨- -￨L￨:￨O￨- q￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- 2￨L￨CD￨NUMBER￨- 0￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 3￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 5￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- /￨L￨:￨O￨- o￨L￨NN￨O￨- i￨L￨FW￨O￨- b￨L￨SYM￨O￨- -￨L￨:￨O￨- q￨L￨NN￨O￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- SARS￨U￨NN￨O￨- ’￨L￨''￨O￨- average￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 1.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- value￨L￨NN￨O￨- quite￨L￨RB￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- computed￨L￨VBD￨O￨A for￨L￨IN￨O￨- some￨L￨DT￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- of￨L￨IN￨O￨- April￨U￨NNP￨DATE￨- 17th￨L￨JJ￨DATE￨- ,￨L￨,￨O￨- Canada￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- location￨L￨NN￨O￨- outside￨L￨IN￨O￨A of￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- seen￨L￨VBN￨O￨- deaths￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- SARS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- global￨L￨JJ￨O￨- and￨L￨CC￨O￨- regional￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- SARS￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- conjunction￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨A ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- ,￨L￨,￨O￨- diagnosed￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- 5￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- M￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- T￨U￨NN￨O￨- O￨U￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- individual￨L￨JJ￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- SARS￨U￨NNP￨O￨- may￨L￨MD￨O￨- become￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- after￨L￨IN￨O￨- an￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- 7￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨A (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- longer￨L￨JJR￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- being￨L￨VBG￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- February￨U￨NNP￨DATE￨- 26￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2003￨L￨CD￨DATE￨A officials￨L￨NNS￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- reported￨L￨VBD￨O￨- their￨L￨PRP$￨O￨- first￨L￨NN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- SARS￨U￨NNP￨O￨- and￨L￨CC￨O￨- no￨L￨RB￨O￨- later￨L￨RB￨O￨- than￨L￨IN￨O￨- March￨U￨NNP￨DATE￨- 14th￨L￨JJ￨DATE￨- of￨L￨IN￨DATE￨- this￨L￨DT￨DATE￨- year￨L￨NN￨DATE￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- reached￨L￨VBD￨O￨- Canada￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Various￨U￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- simpler￨L￨JJR￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- network￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- including￨L￨VBG￨O￨- grouping￨L￨VBG￨O￨- vertices￨L￨NNS￨O￨- by￨L￨IN￨O￨- degree￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- effective￨L￨JJ￨O￨- degree￨L￨NN￨O￨- ”￨L￨''￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- considering￨L￨VBG￨O￨- stationary￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- for￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- limiting￨L￨VBG￨O￨- system￨L￨NN￨O￨- elucidates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- of￨L￨IN￨O￨- edge￨L￨NN￨O￨A activation￨L￨NN￨O￨- and￨L￨CC￨O￨- deactivation￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- illustrated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- two-layer￨L￨JJ￨O￨- network￨L￨NN￨O￨- example￨L￨NN￨O￨- with￨L￨IN￨O￨- edge￨L￨NN￨O￨- types￨L￨NNS￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- community￨L￨NN￨O￨- and￨L￨CC￨O￨- healthcare￨L￨NN￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨A configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- edges￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- layers￨L￨NNS￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- potentially￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- .￨L￨.￨O￨- +5￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 6￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- The￨U￨DT￨O￨- large￨L￨JJ￨O￨- graph￨L￨NN￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- multilayer￨L￨JJ￨O￨A network￨L￨NN￨O￨- Karly￨U￨NNP￨O￨- A￨U￨NNP￨O￨- .￨L￨.￨O￨- +Memory￨U￨NN￨O￨- effects￨L￨NNS￨O￨A on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- M.￨U￨NN￨O￨- Ausloos5￨U￨NN￨O￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- Shahid￨U￨NNP￨ORGANIZATION￨- Beheshti￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- G.C.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2Physics￨L￨NNP￨O￨- Department￨U￨NNP￨O￨- ,￨L￨,￨O￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Advanced￨U￨NNP￨ORGANIZATION￨- Studies￨U￨NNPS￨ORGANIZATION￨- 3School￨L￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Biological￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- 4Center￨L￨NNP￨O￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨ORGANIZATION￨- Fundamental￨U￨JJ￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- in￨L￨IN￨O￨- Basic￨U￨NNP￨O￨- Sciences￨U￨NNPS￨O￨- ,￨L￨,￨O￨- 45195-1159￨L￨CD￨NUMBER￨- Zanjan￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- Network￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- Central￨U￨NNP￨ORGANIZATION￨- European￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- H-1051￨U￨NN￨O￨- ,￨L￨,￨O￨- Budapest￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Hungary￨U￨NNP￨COUNTRY￨- 5GRAPES￨L￨NNP￨O￨- ,￨L￨,￨O￨- la￨L￨NNP￨O￨- Bel￨U￨NNP￨O￨- le￨L￨DT￨O￨- Jardini`ere￨U￨NNP￨O￨- 483￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- B-4031￨U￨NN￨O￨- ,￨L￨,￨O￨- Angleur￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Belgium￨U￨NNP￨COUNTRY￨- rue￨L￨FW￨O￨- de￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- IPM￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Tehran￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Iran￨U￨NNP￨ORGANIZATION￨- Iran￨U￨NNP￨ORGANIZATION￨- Iran￨U￨NNP￨ORGANIZATION￨- 6￨L￨CD￨NUMBER￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Management￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Leicester￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨LOCATION￨- Road￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Leicester￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- LE1￨U￨NN￨O￨- 7RH￨L￨NN￨O￨- ,￨L￨,￨O￨- United￨U￨NNP￨ORGANIZATION￨- Kingdom￨U￨NNP￨ORGANIZATION￨- 7￨L￨CD￨NUMBER￨- eHumanities￨L￨NNS￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- Royal￨U￨NNP￨ORGANIZATION￨- Netherlands￨U￨NNP￨ORGANIZATION￨- Academy￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Arts￨U￨NNS￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Joan￨U￨NNP￨PERSON￨- Muyskenweg￨U￨NNP￨PERSON￨- 25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1096￨L￨CD￨DATE￨- CJ￨U￨NNP￨O￨- ,￨L￨,￨O￨- Amsterdam￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- The￨U￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- March￨U￨NNP￨DATE￨- 10￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Memory￨U￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- great￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- process￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- societies￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- decay￨L￨NN￨O￨- of￨L￨IN￨O￨- long-range￨L￨JJ￨O￨- memory￨L￨NN￨O￨A ,￨L￨,￨O￨- taken￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- power-law￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- directly￨L￨RB￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fractional￨L￨JJ￨O￨- derivatives￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨- fractional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- evolutio￨L￨NN￨O￨- 7￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- M￨U￨NN￨O￨- 9￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- h￨L￨NN￨O￨- p￨L￨NN￨O￨- -￨L￨:￨O￨- c￨L￨NN￨O￨- o￨L￨NN￨O￨- s￨L￨NNS￨O￨- .￨L￨.￨O￨- +3￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 7￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- exact￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- in￨L￨IN￨O￨- Markovian￨U￨JJ￨MISC￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 30￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 34￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- few￨L￨JJ￨O￨- works￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- devoted￨L￨VBN￨O￨A to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- nonMarkovian￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Including￨U￨VBG￨O￨- memory￨L￨NN￨O￨A effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- seems￨L￨VBZ￨O￨- very￨L￨RB￨O￨- appropriate￨L￨JJ￨O￨- for￨L￨IN￨O￨- such￨L￨PDT￨O￨- an￨L￨DT￨O￨- investigation￨L￨NN￨O￨- .￨L￨.￨O￨- +APS/123-QED￨U￨JJ￨O￨- Modelling￨U￨NN￨O￨- of￨L￨IN￨O￨- SARS￨U￨NNP￨O￨- for￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- Pengliang￨U￨NNP￨LOCATION￨- Shi￨U￨NNP￨O￨- ∗￨L￨NNP￨O￨- and￨L￨CC￨O￨- Michael￨U￨NNP￨ORGANIZATION￨- Small￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electronic￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Information￨U￨NNP￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- The￨U￨DT￨O￨- Hong￨U￨NNP￨ORGANIZATION￨- Kong￨U￨NNP￨ORGANIZATION￨- Polytechnic￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hung￨U￨NNP￨PERSON￨- Hom￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Kow￨U￨NNP￨O￨- loon￨L￨NN￨O￨- ,￨L￨,￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 30￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- simplified￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- small-world￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨A of￨L￨IN￨O￨- Severe￨U￨JJ￨O￨- Acute￨U￨JJ￨O￨- Respiratory￨U￨JJ￨O￨- Syndrome￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SARS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- predict￨L￨VBP￨O￨- that￨L￨IN￨O￨- SARS￨U￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- June￨U￨NNP￨DATE￨- and￨L￨CC￨O￨- nearly￨L￨RB￨O￨A 1700￨L￨CD￨NUMBER￨- persons￨L￨NNS￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨JJ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- theoretical￨L￨JJ￨O￨- support￨L￨NN￨O￨- for￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- strategies￨L￨NNS￨O￨- and￨L￨CC￨O￨- achieve￨L￨VB￨O￨- more￨L￨JJR￨O￨- efficient￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- SARS￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- control￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- promoted￨L￨VBN￨O￨- here￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- work￨L￨NN￨O￨- aims￨L￨VBZ￨O￨A to￨L￨TO￨O￨- model￨L￨VB￨O￨- SARS￨U￨NNP￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- HK￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- where￨L￨WRB￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infectiousness￨L￨NN￨O￨- and￨L￨CC￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- his/her￨L￨NN￨O￨- “￨L￨``￨O￨- age￨L￨NN￨O￨A ”￨L￨''￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- power￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fluctuations￨L￨NNS￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- computed￨L￨VBD￨O￨- analytically￨L￨RB￨O￨- using￨L￨VBG￨O￨- van￨L￨NN￨O￨- Kampen￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- expansion￨L￨NN￨O￨- has￨L￨VBZ￨O￨- well￨L￨RB￨O￨- defined￨L￨JJ￨O￨- resonant￨L￨JJ￨O￨- like￨L￨IN￨O￨- peaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- moderate￨L￨JJ￨O￨- system￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- demographic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- will￨L￨MD￨O￨- generate￨L￨VB￨O￨- sustained￨L￨JJ￨O￨- noisy￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- dubbed￨L￨VBN￨O￨- stochastic￨L￨JJ￨O￨- amplification￨L￨NN￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- first￨L￨JJ￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- ecological￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Deterministic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- stochasticity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- merely￨L￨RB￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- making￨L￨VBG￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- switch￨L￨NN￨O￨- between￨L￨IN￨O￨- coexisting￨L￨VBG￨O￨- attractors￨L￨NNS￨O￨- ,￨L￨,￨O￨- successfully￨L￨RB￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- for￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- fail￨L￨VBP￨O￨- conspicuously￨L￨RB￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- exhibit￨L￨VBP￨O￨- non-seasonal￨L￨JJ￨O￨- sustained￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨A on￨L￨IN￨O￨- several￨L￨JJ￨O￨- long￨L￨JJ￨O￨- term￨L￨NN￨O￨- data￨L￨NNS￨O￨- records￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- fluctuations￨L￨NNS￨O￨A power￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- periodically￨L￨RB￨O￨- forced￨L￨VBN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- seasonality￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- nonlinearities￨L￨NNS￨O￨- and￨L￨CC￨O￨- intrinsic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- power￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A around￨L￨IN￨O￨- the￨L￨DT￨O￨- attractors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨- limit￨L￨NN￨O￨- is￨L￨VBZ￨O￨- computed￨L￨VBN￨O￨- analytically￨L￨RB￨O￨- and￨L￨CC￨O￨- validated￨L￨VBN￨O￨- by￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- for￨L￨IN￨O￨- large￨L￨JJ￨O￨- system￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- failure￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- addressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- by￨L￨IN￨O￨- claiming￨L￨VBG￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- different￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- more￨L￨JJR￨O￨- realistic￨L￨JJ￨O￨- latent￨L￨NN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- show￨L￨VB￨O￨- up￨L￨RP￨O￨- as￨L￨IN￨O￨- noisy￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨A with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- frequency￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- damped￨L￨VBN￨O￨- oscillations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- system￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- useful￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- and￨L￨CC￨O￨- simulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vital￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- demographic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- induced￨L￨VBN￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A problem￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- while￨L￨IN￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A is￨L￨VBZ￨O￨- analysed￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Infected￨U￨JJ￨O￨- ,￨L￨,￨O￨- Recovered￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- being￨L￨VBG￨O￨- identified￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- epidemiological￨L￨JJ￨O￨- language￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- coupled￨L￨VBN￨O￨- Susceptible-Infective-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- ;￨L￨:￨O￨- empty￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- sites￨L￨NNS￨O￨- are￨L￨VBP￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- host￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- secondary￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- parasite￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Court￨U￨NNP￨O￨- ,￨L￨,￨O￨- Blythe￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Allen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- hierarchical￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- Their￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- concerns￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fate￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- coevolving￨L￨VBG￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- lattice￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- parasites￨L￨NNS￨O￨- ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- restricted￨L￨JJ￨O￨- to￨L￨TO￨O￨- sites￨L￨NNS￨O￨- currently￨L￨RB￨DATE￨- occupied￨L￨VBN￨O￨- by￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- both￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- follow￨L￨VBP￨O￨- the￨L￨DT￨O￨- Susceptible-Infective-Recovered￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- survive￨L￨VB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- evolve￨L￨VB￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- timescale￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- closely￨L￨RB￨O￨- matched￨L￨VBN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A on￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- depends￨L￨VBZ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- sparse￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- mapped￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- time-sensitive￨L￨JJ￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- primary￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- currently￨L￨RB￨DATE￨- carrying￨L￨VBG￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- primary￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +0￨L￨CD￨NUMBER￨- eP￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ds￨L￨JJ￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨A β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- Condition￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- d￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ln￨L￨NN￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- dt￨L￨NN￨O￨- >￨L￨JJR￨O￨- −￨L￨CD￨NUMBER￨- ν￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- decay￨L￨NN￨O￨- too￨L￨RB￨O￨- fast￨L￨RB￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Recovery￨U￨NN￨O￨- algorithm￨L￨NN￨O￨A We￨U￨PRP￨O￨- now￨L￨RB￨DATE￨- turn￨L￨VBP￨O￨- the￨L￨DT￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- theorem￨L￨NN￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- to￨L￨TO￨O￨- recover￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NN￨O￨- set￨L￨NN￨O￨- .￨L￨.￨O￨- +Check￨U￨VB￨O￨- condition￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- T￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- eP￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ds￨L￨JJ￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- T￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- cast￨L￨VBD￨O￨- this￨L￨DT￨O￨- graphical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A problem￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- penalized￨L￨VBN￨O￨- likelihood￨L￨NN￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- convex￨L￨NN￨O￨- program￨L￨NN￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- convex￨L￨NN￨O￨- optimization￨L￨NN￨O￨- solvers￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- topology￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- outperform￨L￨VBP￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- random￨L￨JJ￨O￨- field￨L￨NN￨O￨- graphical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A using￨L￨VBG￨O￨- 1￨L￨LS￨NUMBER￨- -￨L￨:￨O￨- regularized￨L￨VBN￨O￨- logistic￨L￨JJ￨O￨- regression￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- framework￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- partial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- realization￨L￨NN￨O￨- and￨L￨CC￨O￨- involves￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- contagion￨L￨NN￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- source￨L￨NN￨O￨A locations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- base￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- inference￨L￨NN￨O￨- study￨L￨NN￨O￨- on￨L￨IN￨O￨- rather￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- assumptions￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- relaxed￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- observed￨L￨VBD￨O￨- partial￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- realization￨L￨NN￨O￨- is￨L￨VBZ￨O￨- de￨L￨IN￨O￨- fined￨L￨VBN￨O￨- by￨L￨IN￨O￨- complete￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- node￨L￨NN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- probabilities￨L￨NNS￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- in￨L￨IN￨O￨- advance￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨A inference￨L￨NN￨O￨A framework￨L￨NN￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- contagion￨L￨NN￨O￨- source￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- partially￨L￨RB￨O￨- observed￨L￨VBN￨O￨- contagion￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- cast￨L￨VBD￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨A inference￨L￨NN￨O￨A framework￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- realization￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- likelihood￨L￨NN￨O￨- estimators￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- observing￨L￨VBG￨O￨- partial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- realization￨L￨NN￨O￨- with￨L￨IN￨O￨- particular￨L￨JJ￨O￨- source￨L￨NN￨O￨A location￨L￨NN￨O￨- candidates￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- external￨L￨JJ￨O￨- driving￨L￨NN￨O￨- rate￨L￨NN￨O￨- approaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- above￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A point￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- scaling￨L￨NN￨O￨- laws￨L￨NNS￨O￨- bifurcate￨L￨VBP￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- regimes￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- is￨L￨VBZ￨O￨- characteristic￨L￨JJ￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- power-law￨L￨NN￨O￨- scaling￨L￨NN￨O￨A in￨L￨IN￨O￨- various￨L￨JJ￨O￨- statistics￨L￨NNS￨O￨- characterizing￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- finite-size￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- laws￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- well￨L￨RB￨O￨- un-In￨L￨JJ￨O￨- this￨L￨DT￨O￨- system￨L￨NN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A point￨L￨NN￨O￨A as￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- derstood￨L￨NN￨O￨- and￨L￨CC￨O￨- characterized￨L￨VBN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- epidemiology￨L￨NN￨O￨- —￨L￨:￨O￨- zoonoses￨L￨NNS￨O￨- —￨L￨:￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- —￨L￨:￨O￨- scaling￨L￨VBG￨O￨- laws￨L￨NNS￨O￨A —￨L￨:￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- —￨L￨:￨O￨- queueing￨L￨VBG￨O￨- theory￨L￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- realistic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- of￨L￨IN￨O￨- continuity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SusceptibleInfected-Recovered-Susceptible￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- connects￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- temporally￨L￨RB￨O￨- immune￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- kinetic￨L￨JJ￨O￨- scheme￨L￨NN￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨PRP￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- →￨L￨CD￨NUMBER￨- 2I￨L￨NN￨O￨- τ￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- →￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- θ￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- →￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reaction￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- time-dependent￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- temperature￨L￨NN￨O￨- variations￨L￨NNS￨O￨A ;￨L￨:￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- characteristic￨L￨JJ￨O￨- times￨L￨NNS￨O￨- τ￨L￨NN￨O￨- and￨L￨CC￨O￨- θ￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- goals￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- are￨L￨VBP￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- analytically￨L￨RB￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- background￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- resonance￨L￨NN￨O￨- basing￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- ODE￨U￨NN￨O￨- system￨L￨NN￨O￨- corresponding￨L￨JJ￨O￨- 3￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- kinetic￨L￨JJ￨O￨- scheme￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- its￨L￨PRP$￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- flu￨L￨NN￨O￨- activity￨L￨NN￨O￨- using￨L￨VBG￨O￨- actual￨L￨JJ￨O￨- meteorological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- important￨L￨JJ￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- finding￨L￨NN￨O￨- that￨L￨WDT￨O￨- large￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- are￨L￨VBP￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- dynamical￨L￨JJ￨O￨- resonance￨L￨NN￨O￨- of￨L￨IN￨O￨- intrinsic￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨- and￨L￨CC￨O￨- sinusoidal￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Dushoff￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- work￨L￨NN￨O￨- opens￨L￨VBZ￨O￨- the￨L￨DT￨O￨- perspectives￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- instant￨L￨JJ￨O￨- short-time￨L￨JJ￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- normal￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- flu￨L￨NN￨O￨- activity￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- weather￨L￨NN￨O￨- forecast￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- allow￨L￨VB￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- a￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- epidemic￨L￨JJ￨O￨- level￨L￨NN￨O￨- more￨L￨RBR￨O￨- precisely￨L￨RB￨O￨- .￨L￨.￨O￨- +Besides￨U￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- papers￨L￨NNS￨O￨- ,￨L￨,￨O￨- artificial￨L￨JJ￨O￨- or￨L￨CC￨O￨- too￨L￨RB￨O￨- averaged￨L￨VBD￨O￨- parameter￨L￨NN￨O￨- variations￨L￨NNS￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- that￨L￨IN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- allow￨L￨VB￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- detailed￨L￨JJ￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- microstructure￨L￨NN￨O￨- of￨L￨IN￨O￨- flu￨L￨NN￨O￨- and￨L￨CC￨O￨- temperature￨L￨NN￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- .￨L￨.￨O￨- +Namely￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- events￨L￨NNS￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- extended￨L￨JJ￨O￨- Hawkes￨U￨NN￨PERSON￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- identical￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SusceptibleInfected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- after￨L￨IN￨O￨- marginalizing￨L￨VBG￨O￨- out￨L￨RP￨O￨- recovery￨L￨NN￨O￨- events￨L￨NNS￨O￨- –￨L￨:￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- unobserved￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Hawkes￨U￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 7￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- ABSTRACT￨U￨NN￨O￨- Among￨U￨IN￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- online￨L￨JJ￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨A models￨L￨NNS￨O￨A and￨L￨CC￨O￨- Hawkes￨U￨NN￨PERSON￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- popular￨L￨JJ￨O￨- choices￨L￨NNS￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- cascade￨L￨NN￨O￨A sizes￨L￨NNS￨O￨- for￨L￨IN￨O￨- HawkesN￨U￨NN￨O￨- ,￨L￨,￨O￨- inspired￨L￨VBN￨O￨- by￨L￨IN￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- R0￨U￨NN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- size-biased￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- degree￨L￨NN￨O￨A times￨L￨NNS￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨- takes￨L￨VBZ￨O￨- place￨L￨NN￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- recovers￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Critical￨U￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- for￨L￨IN￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- complete￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- studying￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- graph￨L￨NN￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Erd˝os￨U￨NN￨O￨- -￨L￨:￨O￨- R´enyi￨U￨NN￨O￨- graph￨L￨NN￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- near-critical￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptibleinfectiverecovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- multi￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- graph￨L￨NN￨O￨A on￨L￨IN￨O￨- n￨L￨NN￨O￨- vertices￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨- sequence￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- require￨L￨VBP￨O￨- basic￨L￨JJ￨O￨- regularity￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A sequences￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- moment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- stays￨L￨VBZ￨O￨- uniformly￨L￨RB￨O￨- bounded￨L￨VBN￨O￨- as￨L￨IN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- binomial￨L￨JJ￨O￨- case￨L￨NN￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨A G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- regime￨L￨NN￨O￨- where￨L￨WRB￨O￨- R0￨U￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- for￨L￨IN￨O￨- constant￨L￨JJ￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- b.￨L￨IN￨O￨- +Using￨U￨VBG￨O￨- extensive￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- our￨L￨PRP$￨O￨- analytical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- we￨L￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- ceteris￨L￨FW￨O￨- paribus￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- elongation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- plot/field￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- distributed￨L￨VBN￨O￨- makes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- more￨L￨RBR￨O￨- resilient￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- elongation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rectangle￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A propagation￨L￨NN￨O￨A taking￨L￨VBG￨O￨- place￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- rectangular￨L￨JJ￨O￨- graph￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RRG￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- SusceptibleInfectedSusceptible￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- geometric￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- RGG￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- consideration￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A propagation￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A propagation￨L￨NN￨O￨A on￨L￨IN￨O￨- populations￨L￨NNS￨O￨- introduces￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- elements￨L￨NNS￨O￨- of￨L￨IN￨O￨- reality￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- results￨L￨NNS￨O￨- agree￨L￨VBP￨O￨- with￨L￨IN￨O￨- accumulated￨L￨VBN￨O￨- empirical￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- and￨L￨CC￨O￨- simulation￨L￨NN￨O￨- results￨L￨VBZ￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨A of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- plants￨L￨NNS￨O￨- in￨L￨IN￨O￨- plots/fields￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- area￨L￨NN￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- shapes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Belief￨U￨NN￨O￨- Propagation￨U￨NN￨O￨- gives￨L￨VBZ￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- prediction￨L￨NN￨O￨- that￨L￨IN￨O￨- direct￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- quality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- quantity￨L￨NN￨O￨- under￨L￨IN￨O￨- study￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- marginals￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- extinction-time￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨A time￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Holme￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- recently￨L￨RB￨DATE￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- situation￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- all￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interpersonal￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- relevant￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨A time￨L￨NN￨O￨A ,￨L￨,￨O￨- very￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Belief￨U￨NNP￨O￨- Propagation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- BP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- very￨L￨RB￨O￨- reliable￨L￨JJ￨O￨- and￨L￨CC￨O￨- efficient￨L￨JJ￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- also￨L￨RB￨O￨- makes￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- easily￨L￨RB￨O￨- reconstruct￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- marginals￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- states￨L￨NNS￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- exploiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- causality￨L￨NN￨O￨- relations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- generated￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- using￨L￨VBG￨O￨- Belief￨U￨NNP￨O￨- Propagation￨U￨NN￨O￨- are￨L￨VBP￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- direct￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- regular￨L￨JJ￨O￨- and￨L￨CC￨O￨- power-law￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- graphs￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- observation￨L￨NN￨O￨A methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- use￨L￨VB￨O￨- BP￨U￨NNP￨ORGANIZATION￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- network￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- partial￨L￨JJ￨O￨- observation￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Interplay￨U￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- information￨L￨NN￨O￨- based￨L￨VBN￨O￨- behavioral￨L￨JJ￨O￨- responses￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Can￨U￨MD￨O￨- Liu￨U￨NNP￨O￨- ,1￨L￨CD￨NUMBER￨- Jia-Rong￨U￨NNP￨PERSON￨- Xie￨U￨NNP￨PERSON￨- ,2￨L￨CD￨NUMBER￨- Han-Shuang￨U￨NNP￨PERSON￨- Chen￨U￨NNP￨PERSON￨- ,3￨L￨CD￨NUMBER￨- Hai-Feng￨U￨NNP￨PERSON￨- Zhang￨U￨NNP￨PERSON￨- ,1￨L￨NN￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Ming￨U￨VBG￨PERSON￨- Tang6￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- School￨U￨NN￨O￨- of￨L￨IN￨O￨- Mathematical￨U￨JJ￨O￨- Science￨U￨NN￨O￨- ,￨L￨,￨O￨- Anhui￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hefei￨U￨NNP￨CITY￨- 230601￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P.￨U￨NNP￨PERSON￨- R.￨U￨NNP￨PERSON￨- China￨U￨NNP￨PERSON￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Department￨U￨NNP￨O￨- of￨L￨IN￨O￨- Modern￨U￨NNP￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hefei￨U￨NNP￨CITY￨- 230026￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- School￨U￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- and￨L￨CC￨O￨- Material￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- Anhui￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hefei￨U￨NNP￨CITY￨- 230601￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Center￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Information￨U￨NN￨ORGANIZATION￨- Support￨U￨NN￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Assurance￨U￨NNP￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Anhui￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hefei￨U￨NNP￨CITY￨- 230601￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Communication￨U￨NNP￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- North￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Taiyuan￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Shan￨U￨NNP￨PERSON￨- ’￨L￨POS￨O￨- xi￨L￨NN￨O￨- 030051￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Web￨U￨NN￨O￨- Sciences￨U￨NNPS￨O￨- Center￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electronic￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Chengdu￨U￨NNP￨CITY￨- 611731￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- trigger￨L￨VB￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- role￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- F￨U￨NN￨O￨- state￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- that￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- take￨L￨VBP￨O￨- self-initiate￨L￨JJ￨O￨- protective￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- to￨L￨TO￨O￨- lower￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- may￨L￨MD￨O￨- go￨L￨VB￨O￨- to￨L￨TO￨O￨- S￨U￨NN￨O￨- F￨U￨NN￨O￨- state￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- response￨L￨NN￨O￨- rate￨L￨NN￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨A when￨L￨WRB￨O￨- contacting￨L￨VBG￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- neighbor￨L￨NN￨O￨- .￨L￨.￨O￨- +responses￨L￨NNS￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- F￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- finding￨L￨JJ￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨A rate￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- enhanced￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +Commonly￨U￨RB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- describe￨L￨VBP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- via￨L￨IN￨O￨- subgroups￨L￨NNS￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- seen￨L￨VBN￨O￨A in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1A￨L￨NN￨O￨- these￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modified￨L￨VBN￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Epidemic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- combined￨L￨VBN￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- biological￨L￨JJ￨O￨- system￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- and￨L￨CC￨O￨- control￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- seen￨L￨VBN￨O￨A in￨L￨IN￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- influenza￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- .￨L￨.￨O￨- +Unlike￨U￨IN￨O￨- Munz￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 2009￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- include￨L￨VBP￨O￨- data￨L￨NNS￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- specific￨L￨NN￨O￨- depictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- zombies￨L￨NNS￨O￨- in￨L￨IN￨O￨- popular￨L￨JJ￨O￨- culture￨L￨NN￨O￨A films￨L￨NNS￨O￨- and￨L￨CC￨O￨- apply￨L￨VB￨O￨- Markov￨U￨NNP￨PERSON￨- Chain￨U￨NNP￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- MCMC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- methods￨L￨NNS￨O￨- on￨L￨IN￨O￨- improved￨L￨VBN￨O￨- dynamical￨L￨JJ￨O￨- representations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- offer￨L￨VBP￨O￨- significant￨L￨JJ￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- and￨L￨CC￨O￨- controlling￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- generally￨L￨RB￨O￨- follow￨L￨VBP￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- standard￨L￨JJ￨O￨- modifications￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- generating￨L￨VBG￨O￨- homogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- equal￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- and￨L￨CC￨O￨- quantify￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- structural￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- dynamics￨L￨NNS￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- computationally￨L￨RB￨O￨- how￨L￨WRB￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- higher-order￨L￨JJ￨O￨- structure￨L￨NN￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- prevalence￨L￨NN￨O￨- levels￨L￨NNS￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- networks￨L￨NNS￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- having￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- equal￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A ,￨L￨,￨O￨- exhibit￨L￨VBP￨O￨- different￨L￨JJ￨O￨- higher-order￨L￨JJ￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- overlapping￨L￨VBG￨O￨- triangles￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- order-four￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- network￨L￨NN￨O￨- motif￨L￨NN￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- structures￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- examine￨L￨VB￨O￨- existing￨L￨VBG￨O￨- clustered￨L￨VBN￨O￨- network￨L￨NN￨O￨- generating￨L￨VBG￨O￨- algorithms￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- otherwise￨L￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- higher-order￨L￨JJ￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- which￨L￨WDT￨O￨- sometimes￨L￨RB￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- by-product￨L￨NN￨O￨- of￨L￨IN￨O￨- generating￨L￨VBG￨O￨- low-order￨L￨JJ￨O￨- structure￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- preclude￨L￨VB￨O￨- a￨L￨DT￨O￨- correct￨L￨JJ￨O￨- interpretation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- clustering￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- go￨L￨VB￨O￨- beyond￨L￨IN￨O￨- open￨L￨JJ￨O￨- and￨L￨CC￨O￨- closed￨L￨VBD￨O￨- triples￨L￨NNS￨O￨- and￨L￨CC￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- comprehensive￨L￨JJ￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- higher-order￨L￨JJ￨O￨- structure￨L￨NN￨O￨- frequency￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- specifically￨L￨RB￨O￨A order-four￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- distribution￨L￨NN￨O￨- around￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Clustering￨U￨NN￨O￨- ,￨L￨,￨O￨- motif￨L￨NN￨O￨- counting￨L￨NN￨O￨- ,￨L￨,￨O￨- loops￨L￨NNS￨O￨- ,￨L￨,￨O￨- networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIRWS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- dividing￨L￨VBG￨O￨- each￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- age-classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- 6￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- each￨L￨DT￨O￨- and￨L￨CC￨O￨- further￨L￨JJ￨O￨- classifying￨L￨VBG￨O￨- immune￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- hosts￨L￨NNS￨O￨- with￨L￨IN￨O￨- waning￨L￨VBG￨O￨A immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- W￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- suggest￨L￨VB￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- waning￨L￨VBG￨O￨A immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- boosting￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- sole￨L￨JJ￨O￨- waning￨L￨VBG￨O￨A immunity￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- chosen￨L￨VBN￨O￨- delay￨L￨NN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- DDEs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- or￨L￨CC￨O￨- distributed￨L￨VBN￨O￨- delay￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Wodarz￨U￨JJ￨PERSON￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ODEs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- only￨L￨RB￨O￨- at￨L￨IN￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- defining￨L￨VBG￨O￨- compartments￨L￨NNS￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨A and￨L￨CC￨O￨- introducing￨L￨VBG￨O￨- transitions￨L￨NNS￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- compartments￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Martcheva￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Pilyugin￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- suggest￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- infective￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- hosts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- structured￨L￨VBN￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- immune￨L￨JJ￨O￨A status￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- overcomplete￨L￨JJ￨O￨- dictionary￨L￨NN￨O￨- of￨L￨IN￨O￨- feasible￨L￨JJ￨O￨- realizations￨L￨NNS￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- solutions￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- blindly￨L￨RB￨O￨- partition￨L￨NN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- representing￨L￨VBG￨O￨A the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- individual￨L￨JJ￨O￨- components￨L￨NNS￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- method￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- bridge￨L￨NN￨O￨- between￨L￨IN￨O￨- theoretical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- data-driven￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨O￨A and￨L￨CC￨O￨- other￨L￨JJ￨O￨- similar￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- extends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- higher￨L￨JJR￨O￨- dimensions￨L￨NNS￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- specific￨L￨NN￨O￨- threshold￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- fixed￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- underlying￨L￨VBG￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨A has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- log￨L￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- mixing￨L￨VBG￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- quickly￨L￨RB￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- condition￨L￨NN￨O￨- is￨L￨VBZ￨O￨- violated￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- second￨L￨JJ￨ORDINAL￨- fixed￨L￨JJ￨O￨- point￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- an￨L￨DT￨O￨- interesting￨L￨JJ￨O￨- connection￨L￨NN￨O￨- with￨L￨IN￨O￨- its￨L￨PRP$￨O￨- 2n-state￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨- “￨L￨``￨O￨- mean-field￨L￨JJ￨O￨- ”￨L￨''￨O￨- approximation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- latter￨L￨NN￨O￨- ’s￨L￨POS￨O￨- corresponding￨L￨JJ￨O￨- linear￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- .￨L￨.￨O￨- +3￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 5￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SusceptibleInfectedRecovered-Susceptible￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- over￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- exact￨L￨JJ￨O￨- 3n￨L￨NN￨O￨- -￨L￨:￨O￨- state￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- scenarios￨L￨NNS￨O￨- —￨L￨:￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- positive￨L￨JJ￨O￨- degree-degree￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- eigenvector￨L￨JJ￨O￨- localized￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- k-core￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- clustering￨L￨NN￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- th￨L￨DT￨O￨- e￨L￨SYM￨O￨- MFL￨U￨NNP￨ORGANIZATION￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- uses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- input￨L￨NN￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- performs￨L￨VBZ￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- 56￨L￨CD￨NUMBER￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- DMP￨U￨NN￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- closer￨L￨RBR￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- incorporates￨L￨VBZ￨O￨- full￨L￨JJ￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A they￨L￨PRP￨O￨- often￨L￨RB￨O￨- produce￨L￨VBP￨O￨- differing￨L￨VBG￨O￨- results￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- accuracy￨L￨NN￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- uncorrelated￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- networks￨L￨NNS￨O￨- the￨L￨DT￨O￨- MFL￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- DMP￨U￨NN￨O￨- methods￨L￨NNS￨O￨- yield￨L￨VBP￨O￨- identic￨L￨JJ￨O￨- al￨L￨NNP￨O￨- predictions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- larger￨L￨JJR￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- QMF￨U￨NN￨O￨- method￨L￨NN￨O￨A .￨L￨.￨O￨- +Infection￨U￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨NNS￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- to￨L￨TO￨O￨- healthy￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- addition￨L￨NN￨O￨- that￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- recover￨L￨VB￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- remain￨L￨VBP￨O￨- connected￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- pre-defined￨L￨JJ￨O￨- central￨L￨JJ￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- path￨L￨NN￨O￨- that￨L￨WDT￨O￨- contains￨L￨VBZ￨O￨- only￨L￨RB￨O￨- healthy￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- mapping￨L￨NN￨O￨- reveals￨L￨VBZ￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- models￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- second-order￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨A being￨L￨VBG￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨A insights￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- transition￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- regime￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- clusters￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨A will￨L￨MD￨O￨- absorb￨L￨VB￨O￨- their￨L￨PRP$￨O￨- non-infected￨L￨JJ￨O￨- interior￨L￨NN￨O￨- because￨L￨IN￨O￨- no￨L￨DT￨O￨- path￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- node￨L￨NN￨O￨- and￨L￨CC￨O￨- encapsulated￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- simultaneous￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- give￨L￨VB￨O￨- rise￨L￨VB￨O￨- to￨L￨TO￨O￨- discontinuous￨L￨JJ￨O￨- jumps￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- failed￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨A .￨L￨.￨O￨- +More￨U￨RBR￨O￨- precisely￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- view￨L￨VBP￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- economy￨L￨NN￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- countries￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- economic￨L￨JJ￨O￨A relations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- International￨U￨NNP￨ORGANIZATION￨- Trade￨U￨NNP￨ORGANIZATION￨- Network￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- ITN￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- CHELEM￨U￨NN￨O￨- database￨L￨NN￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- Bureau￨U￨NNP￨ORGANIZATION￨- Van￨U￨NNP￨ORGANIZATION￨- Dijk￨U￨NNP￨ORGANIZATION￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- contains￨L￨VBZ￨O￨- detailed￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- international￨L￨JJ￨O￨- trade￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- GDP￨U￨NNP￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- 82￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨A in￨L￨IN￨O￨- million￨L￨CD￨NUMBER￨- US￨U￨NNP￨COUNTRY￨- dollars￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- crisis￨L￨NN￨O￨- by￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- economic￨L￨JJ￨O￨A network￨L￨NN￨O￨- and￨L￨CC￨O￨- applying￨L￨VBG￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- variable￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- today￨L￨NN￨DATE￨- ’s￨L￨POS￨O￨- global￨L￨JJ￨O￨- economy￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- strong￨L￨JJ￨O￨- economic￨L￨JJ￨O￨A relations￨L￨NNS￨O￨- between￨L￨IN￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- a￨L￨DT￨O￨- crisis￨L￨NN￨O￨- propagates￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- of￨L￨IN￨O￨- origin￨L￨NN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- crisis￨L￨NN￨O￨- which￨L￨WDT￨O￨- originates￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- country￨L￨NN￨O￨A ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- USA￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- globally￨L￨RB￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- crisis￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- effective￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- vaccinations￨L￨NNS￨O￨A through￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- popular￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- in￨L￨IN￨O￨- rural￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- those￨L￨DT￨O￨- groups￨L￨NNS￨O￨- and￨L￨CC￨O￨- locations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- and￨L￨CC￨O￨- targeted￨L￨VBN￨O￨- vaccinations￨L￨NNS￨O￨A using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Susceptible-Exposed-Infected-Recovered￨U￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- create￨L￨VBP￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- rural￨L￨JJ￨O￨A community￨L￨NN￨O￨- in￨L￨IN￨O￨- Kansas￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- collecting￨L￨VBG￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- computing￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- among￨L￨IN￨O￨- a￨L￨DT￨O￨- sampled￨L￨VBN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- visiting￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- popular￨L￨JJ￨O￨- locations￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- randomly￨L￨RB￨O￨- vaccinated￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- 19￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- coupling￨L￨NN￨O￨- argument￨L￨NN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- all￨L￨DT￨O￨- households￨L￨NNS￨O￨- and￨L￨CC￨O￨- schools￨L￨NNS￨O￨A have￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- easier￨L￨JJR￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- stochastically￨L￨RB￨O￨- larger￨L￨JJR￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- independent￨L￨JJ￨RELIGION￨- partition￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- unstructured￨L￨JJ￨O￨- homogeneously￨L￨RB￨O￨A mixing￨L￨VBG￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- every￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- makes￨L￨VBZ￨O￨- contacts￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- approximations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- will￨L￨MD￨O￨- occur￨L￨VB￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- →￨L￨NN￨O￨- Infectious￨U￨JJ￨O￨- →￨L￨NN￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- structured￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- schools￨L￨NNS￨O￨A and￨L￨CC￨O￨- households￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- independent￨L￨JJ￨RELIGION￨- partition￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- partitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- schools￨L￨NNS￨O￨A and￨L￨CC￨O￨- households￨L￨NNS￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- types￨L￨NNS￨O￨A ,￨L￨,￨O￨- every￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- school￨L￨NN￨O￨- and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- household￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- quite￨L￨RB￨O￨- drastic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- patient￨L￨NN￨O￨- unlikely￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- even￨L￨RB￨O￨- with￨L￨IN￨O￨- prompt￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- argued￨L￨VBN￨O￨- that￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 7￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- varying￨L￨VBG￨O￨- among￨L￨IN￨O￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- poses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- lesser￨L￨JJR￨O￨- contagion￨L￨NN￨O￨A threat￨L￨NN￨O￨- than￨L￨IN￨O￨- faster￨L￨JJR￨O￨- spreading￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- small￨L￨JJ￨O￨- pox￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- widespread￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- placed￨L￨VBD￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- communities￨L￨NNS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- contracting￨L￨VBG￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- acting￨L￨VBG￨O￨- as￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- coupled￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- connectivity￨L￨NN￨O￨A graph￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- measured￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- impact￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- change￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- local￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- with￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- short-range￨L￨JJ￨O￨- and￨L￨CC￨O￨- long-range￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- .￨L￨.￨O￨- +Classical￨U￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- capture￨L￨VBP￨O￨- well￨L￨RB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- accurately￨L￨RB￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨A of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- 1.1￨L￨CD￨NUMBER￨- Background￨U￨NN￨O￨- to￨L￨TO￨O￨- Ebola￨U￨NNP￨O￨- and￨L￨CC￨O￨- modeling￨L￨NN￨O￨- The￨U￨DT￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- prognosis￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- contagious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨A of￨L￨IN￨O￨- approaches￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- peaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- separated￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- exceeds￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- progresses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- characterized￨L￨VBN￨O￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨A results￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Results￨U￨NNS￨O￨- we￨L￨PRP￨O￨- compute￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨A size￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- regimes￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- and￨L￨CC￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- most￨L￨RBS￨O￨- significantly￨L￨RB￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- if￨L￨IN￨O￨- r0￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- dI/dt￨L￨NN￨O￨- <￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- will￨L￨MD￨O￨- decline￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- seed￨L￨NN￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨SYM￨O￨- I0￨U￨NN￨O￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- will￨L￨MD￨O￨- occur￨L￨VB￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- :￨L￨:￨O￨- Figure￨U￨NNP￨O￨- A￨U￨NNP￨O￨- illustrates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨A size￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- various￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- r0￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compute￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- non-interacting￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨A case￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- side￨L￨JJ￨O￨- information￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- if￨L￨IN￨O￨- any￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- times￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- prior￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- state-space￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- utilizing￨L￨VBG￨O￨- a￨L￨DT￨O￨- state￨L￨NN￨O￨- propagation￨L￨NN￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- an￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- source￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- HISS￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- estimator￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- HISS￨U￨NNP￨O￨- estimator￨L￨NN￨O￨A uses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- states￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- elapsed￨L￨JJ￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- unknown￨L￨JJ￨O￨- .￨L￨.￨O￨- +0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 4￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- ABSTRACT￨U￨NN￨O￨- We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Daley￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Kendall￨U￨NNP￨PERSON￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- variant￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infectious-Removed￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- rumors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- Vespignani￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Pastor-Satorras￨U￨NNP￨LOCATION￨- examined￨L￨VBD￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨- of￨L￨IN￨O￨- systemic￨L￨JJ￨O￨- failure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- internet￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- Jeffs￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- used￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨A and￨L￨CC￨O￨- decline￨L￨NN￨O￨- of￨L￨IN￨O￨- political￨L￨JJ￨O￨- parties￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- irSIR￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- always￨L￨RB￨O￨- predicts￨L￨VBZ￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- construct￨L￨VBP￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- matches￨L￨VBZ￨O￨- the￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- irSIR￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- while￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- run￨L￨NN￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Cannarella￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Spechler￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- Ribiero￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- separately￨L￨RB￨O￨- developed￨L￨VBD￨O￨- ODE￨U￨NNP￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- OSN￨U￨NN￨O￨- membership￨L￨NN￨O￨- with￨L￨IN￨O￨- inspiration￨L￨NN￨O￨- from￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨A epidemiology￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- Susceptible-Infective-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- renewal￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- demographic￨L￨JJ￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- ring￨L￨NN￨O￨- with￨L￨IN￨O￨- next￨L￨JJ￨O￨- nearest￨L￨JJS￨O￨- neighbour￨L￨NN￨O￨A interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- correlated￨L￨VBN￨O￨- pair￨L￨NN￨O￨- approximations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- CPA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- parametrized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- contributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- loops￨L￨NNS￨O￨- and￨L￨CC￨O￨- open￨L￨JJ￨O￨- triplets￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sites￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- performed￨L￨VBN￨O￨- computer￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- CPA￨U￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- parameter￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibria￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- diagram￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- to￨L￨TO￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- demographic￨L￨JJ￨O￨A rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- highlighted￨L￨VBD￨O￨- additional￨L￨JJ￨O￨- unexpected￨L￨JJ￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- delayed￨L￨VBN￨O￨- also￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- switching￨L￨NN￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- no￨L￨DT￨O￨- control￨L￨NN￨O￨- to￨L￨TO￨O￨- maximum￨L￨NN￨O￨- control￨L￨NN￨O￨- can￨L￨MD￨O￨- even￨L￨RB￨O￨- occur￨L￨VB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- reached￨L￨VBN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- result￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- with￨L￨IN￨O￨- previous￨L￨JJ￨O￨- findings￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- unconstrained￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- of￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- burden￨L￨NN￨O￨- over￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- control￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- time-optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨A problem￨L￨NN￨O￨- in￨L￨IN￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SusceptibleInfectedRecovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- different￨L￨NN￨O￨- control￨L￨NN￨O￨- policies￨L￨NNS￨O￨- :￨L￨:￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- culling￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- a￨L￨DT￨O￨- switch￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- delay￨L￨VB￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨A action￨L￨NN￨O￨- some￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- apply￨L￨VB￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- remainder￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Minimum￨U￨NNP￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- Bang-bang￨U￨JJ￨O￨- control￨L￨NN￨O￨A ,￨L￨,￨O￨- Delayed￨U￨VBN￨O￨- intervention￨L￨NN￨O￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Deterministic￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ∗￨L￨NN￨O￨- Corresponding￨U￨VBG￨O￨- author￨L￨NN￨TITLE￨- Email￨U￨VB￨O￨- address￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- Luca￨U￨NNP￨PERSON￨- Bolzoni￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- Preprint￨U￨NNP￨ORGANIZATION￨- submitted￨L￨VBD￨O￨- to￨L￨TO￨O￨- Mathematical￨U￨NNP￨O￨- Biosciences￨U￨NNP￨O￨- June￨U￨NNP￨DATE￨- 15￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2017￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- employing￨L￨VBG￨O￨- the￨L￨DT￨O￨- Wentzel-Kramers-Brillouin￨U￨NNP￨O￨- approximation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- zero-energy￨L￨JJ￨O￨- tra￨L￨NN￨O￨- jectories￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- Hamiltonian￨U￨JJ￨IDEOLOGY￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- extinction￨L￨NN￨O￨A time￨L￨NN￨O￨- hT￨L￨NN￨O￨- i￨L￨FW￨O￨- depends￨L￨VBZ￨O￨- exponentially￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- associated￨L￨VBN￨O￨- action￨L￨NN￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- hT￨L￨NN￨O￨- i￨L￨FW￨O￨- ∼￨L￨FW￨O￨- exp￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- reactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- mI￨L￨NN￨O￨- I￨U￨PRP￨O￨- λ￨L￨VBP￨O￨- →￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- µ￨L￨VBP￨O￨- →￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- The￨U￨DT￨O￨- first￨L￨JJ￨O￨- reaction￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- S￨U￨NN￨O￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- when￨L￨WRB￨O￨- contacting￨L￨VBG￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- m￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- I￨U￨PRP￨O￨- simultaneously￨L￨RB￨O￨A with￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- one￨L￨CD￨NUMBER￨- refers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- I￨U￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- µ￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- qualitatively￨L￨RB￨O￨- different￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨- features￨L￨NNS￨O￨- between￨L￨IN￨O￨- m￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- m￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- calculate￨L￨VBP￨O￨- independently￨L￨RB￨O￨- the￨L￨DT￨O￨- MET￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- exponentially￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- action￨L￨NN￨O￨- S￨U￨NN￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- extinction￨L￨NN￨O￨A path￨L￨NN￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨A of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- when￨L￨WRB￨O￨- contacting￨L￨VBG￨O￨- m￨L￨NN￨O￨- infective￨L￨JJ￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- simultaneously￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- spontaneously￨L￨RB￨O￨- recovers￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- µ￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- dynamical￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- stochastic￨L￨JJ￨O￨- lattice￨L￨NN￨O￨A gas￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- line￨L￨NN￨O￨- of￨L￨IN￨O￨- critical￨L￨JJ￨O￨- points￨L￨NNS￨O￨- separating￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- phases￨L￨NNS￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- absorbing￨L￨VBG￨O￨- phase￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- lattice￨L￨NN￨O￨- is￨L￨VBZ￨O￨- completely￨L￨RB￨O￨- full￨L￨JJ￨O￨- of￨L￨IN￨O￨- S￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- phase￨L￨NN￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- coexist￨L￨VBP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- or￨L￨CC￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- present￨L￨VB￨DATE￨- population￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- lattice￨L￨NN￨O￨A gas￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- here￨L￨RB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- separated￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- states￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- composed￨L￨VBN￨O￨- by￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨A :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- socalled￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- which￨L￨WDT￨O￨- occurs￨L￨VBZ￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- smaller￨L￨JJR￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- lifetime￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- analyzed￨L￨VBN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- description￨L￨NN￨O￨- :￨L￨:￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- lattice￨L￨NN￨O￨A gas￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- birth￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Assign￨U￨VB￨O￨- independent￨L￨JJ￨RELIGION￨- and￨L￨CC￨O￨- identically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- i.i.d.￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- weights￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Ai￨U￨NNS￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- random￨L￨JJ￨O￨- variable￨L￨NN￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- independently￨L￨RB￨O￨- ,￨L￨,￨O￨- i.i.d.￨L￨NN￨O￨- weights￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Bj￨U￨NNP￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- verin￨L￨NN￨O￨- V￨U￨NN￨O￨- ′￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- distributed￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- nonnegative￨L￨JJ￨O￨A random￨L￨JJ￨O￨- variable￨L￨JJ￨O￨- B￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- Ω￨U￨NN￨O￨- ,￨L￨,￨O￨- F￨U￨NN￨O￨- ,￨L￨,￨O￨- ν￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- probability￨L￨NN￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Ω￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- ×￨L￨CD￨NUMBER￨- Let￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- product￨L￨NN￨O￨- space￨L￨NN￨O￨- of￨L￨IN￨O￨- nonnegative￨L￨JJ￨O￨- real-valued￨L￨JJ￨O￨- infinite￨L￨NN￨O￨A sequences￨L￨NNS￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- Ai￨U￨NN￨O￨- and￨L￨CC￨O￨- L￨U￨NN￨O￨- ′￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- P￨U￨NN￨O￨- ⌊￨L￨CD￨NUMBER￨- αn￨L￨NN￨O￨- ⌋￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Ai￨U￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- Bj￨U￨NNP￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Consider￨U￨VB￨O￨- two￨L￨CD￨NUMBER￨- infinite￨L￨JJ￨O￨A sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- V￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- vi￨L￨LS￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- v￨L￨LS￨O￨- ′￨L￨SYM￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Vertices￨U￨NNS￨O￨- vi￨L￨LS￨O￨A ∈￨L￨SYM￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- v￨L￨LS￨O￨- ′￨L￨SYM￨O￨- share￨L￨VBP￨O￨- a￨L￨DT￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- AiBj￨U￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- µn￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Remark￨U￨NNP￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- particles￨L￨NNS￨O￨A perform￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- random￨L￨JJ￨O￨- walks￨L￨VBZ￨O￨- with￨L￨IN￨O￨- jump￨L￨NN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- respective￨L￨JJ￨O￨- accessible￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- an￨L￨DT￨O￨- exponentially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- time￨L￨NN￨O￨- with￨L￨IN￨O￨- mean￨L￨JJ￨O￨- β￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨- at￨L￨IN￨O￨- y￨L￨NN￨O￨- with￨L￨IN￨O￨- home￨L￨NN￨O￨- location￨L￨NN￨O￨- x￨L￨CC￨O￨- jumps￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- site￨L￨NN￨O￨- in￨L￨IN￨O￨- Ny￨U￨NN￨O￨- scribing￨L￨VBG￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- random￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- initial￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- particles￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- site￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- particle￨L￨NN￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- accessible￨L￨JJ￨O￨- region￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- it￨L￨PRP￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- Rx￨U￨NN￨O￨- and￨L￨CC￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- sites￨L￨NNS￨O￨A within￨L￨IN￨O￨- L1￨U￨NN￨O￨- -￨L￨:￨O￨- distance￨L￨NN￨O￨- at￨L￨IN￨O￨- most￨L￨JJS￨O￨- k￨L￨NN￨O￨- <￨L￨JJR￨O￨- ∞￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- its￨L￨PRP$￨O￨- home￨L￨NN￨O￨- location￨L￨NN￨O￨- .￨L￨.￨O￨- +Write￨U￨VB￨O￨- Sλ￨U￨NNP￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- or￨L￨CC￨O￨- particles￨L￨NNS￨O￨A at￨L￨IN￨O￨- infinitely￨L￨RB￨O￨- large￨L￨JJ￨O￨- times￨L￨NNS￨O￨- .￨L￨.￨O￨- +Particles￨U￨NNS￨O￨- and￨L￨CC￨O￨- sites￨L￨NNS￨O￨A recover￨L￨VB￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- become￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- again￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- given￨L￨VBN￨O￨- value￨L￨NN￨O￨A of￨L￨IN￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- survives￨L￨VBZ￨O￨- indefinitely￨L￨RB￨O￨- if￨L￨IN￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- given￨L￨VBN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- if￨L￨IN￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- enough￨L￨RB￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 3￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ˜s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ˜i￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ˜r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- exp￨L￨NN￨O￨A t￨L￨NN￨O￨- N￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- ν￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ν￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ˜s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ˜i￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ˜r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VB￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- exp￨L￨NN￨O￨- t￨L￨NN￨O￨- N￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- ν￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ν￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- +￨L￨CC￨O￨- exp￨L￨NN￨O￨- t￨L￨NN￨O￨- N￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- ν￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ν￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- ˙s￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ˙i￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- N￨U￨NN￨O￨- ν￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- ν￨L￨SYM￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ˙r￨L￨NN￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- equation￨L￨NN￨O￨- d￨L￨NN￨O￨- dt￨L￨NN￨O￨A s￨L￨VBZ￨O￨- i￨L￨FW￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- β￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ν￨L￨NN￨O￨- ν￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- ν￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ν￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- i￨L￨FW￨O￨- r￨L￨NN￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- us￨L￨PRP￨O￨- rewrite￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- like￨L￨IN￨O￨A ˙S￨L￨NN￨O￨- S￨U￨NN￨O￨- ˙I￨L￨NN￨O￨- I￨U￨PRP￨O￨- ˙R￨L￨VBP￨O￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- N￨U￨NN￨O￨- I￨U￨NN￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- N￨U￨NN￨O￨- ν￨L￨NN￨O￨- N￨U￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- ν￨L￨NN￨O￨- N￨U￨NN￨O￨- R￨U￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- we￨L￨PRP￨O￨- set￨L￨VBD￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- es￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ei￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- er￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- ˙s￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- N￨U￨NN￨O￨- ei￨L￨FW￨O￨- ˙i￨L￨FW￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- N￨U￨NN￨O￨- ν￨L￨NN￨O￨- es￨L￨VBZ￨O￨- −￨L￨CD￨NUMBER￨- ν￨L￨NN￨O￨- N￨U￨NN￨O￨- er￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ˙r￨L￨NN￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- ei￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- use￨L￨VBP￨O￨- Bayesian￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- averaging￨L￨VBG￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- ensemble￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- short-term￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- incidence￨L￨NN￨O￨- under￨L￨IN￨O￨- varying￨L￨VBG￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ensemble￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- predicts￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- burden￨L￨NN￨O￨A of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- rotavirus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- 2.9￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 4.1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- 2-dose￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- schedule￨L￨NN￨O￨- achieving￨L￨VBG￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- coverage￨L￨NN￨O￨- could￨L￨MD￨O￨- reduce￨L￨VB￨O￨- burden￨L￨NN￨O￨- by￨L￨IN￨O￨- 37-43￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- are￨L￨VBP￨O￨- critical￨L￨JJ￨O￨- both￨L￨CC￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- current￨L￨JJ￨DATE￨- burden￨L￨NN￨O￨A from￨L￨IN￨O￨- imperfect￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- potential￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Rotavirus￨U￨NNP￨O￨- ,￨L￨,￨O￨- Vaccine￨U￨NNP￨O￨- ,￨L￨,￨O￨- Niger￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Susceptible-Infectious-Recovered￨U￨NNP￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- Bayesian￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- averaging￨L￨VBG￨O￨- ∗￨L￨SYM￨O￨- Email￨U￨VB￨O￨- addresses￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- J.￨U￨NNP￨O￨- Observation￨U￨NNP￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨A of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- limited￨L￨VBN￨O￨- both￨L￨CC￨O￨- by￨L￨IN￨O￨- non-specific￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- under-reporting￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- use￨L￨VBP￨O￨- this￨L￨DT￨O￨- technique￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- fronts￨L￨NNS￨O￨- propagating￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- one-dimensional￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- of￨L￨IN￨O￨- interconnected￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- –￨L￨:￨O￨- representing￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- chain￨L￨NN￨O￨- of￨L￨IN￨O￨- coupled￨L￨VBN￨O￨- population￨L￨NN￨O￨- centers￨L￨NNS￨O￨A –￨L￨:￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- first￨L￨JJ￨O￨- step￨L￨NN￨O￨- in￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- how￨L￨WRB￨O￨- macro-scale￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- micro-scale￨L￨JJ￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- expand￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- possible￨L￨JJ￨O￨- avenue￨L￨NN￨O￨- for￨L￨IN￨O￨- addressing￨L￨VBG￨O￨- this￨L￨DT￨O￨- question￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- multitype￨L￨JJ￨O￨- generalization￨L￨NN￨O￨A of￨L￨IN￨O￨- random￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- with￨L￨IN￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- meta-level￨L￨JJ￨O￨- topology￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- multitype￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- framework￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- studying￨L￨VBG￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- where￨L￨WRB￨O￨- most￨L￨RBS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- in￨L￨IN￨O￨- localized￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- transported￨L￨VBN￨O￨- on￨L￨IN￨O￨- larger￨L￨JJR￨O￨- scales￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- traveling￨L￨VBG￨O￨- among￨L￨IN￨O￨- population￨L￨NN￨O￨- centers￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- formalism￨L￨NN￨O￨- of￨L￨IN￨O￨- front￨L￨JJ￨O￨- propagation￨L￨NN￨O￨A into￨L￨IN￨O￨- unstable￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- transport￨L￨NN￨O￨- coefficients￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- :￨L￨:￨O￨- asymptotic￨L￨JJ￨O￨- speed￨L￨NN￨O￨- ,￨L￨,￨O￨- characteristic￨L￨JJ￨O￨- wavelength￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- diffusion￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- leading￨L￨VBG￨O￨- edge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pulled￨L￨VBN￨O￨- fronts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- dependence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- graph￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨VBD￨O￨- present￨L￨JJ￨DATE￨- a￨L￨DT￨O￨- generalization￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- Volz-Miller￨U￨NNP￨O￨- mean-field￨L￨NN￨O￨- approximation￨L￨NN￨O￨- for￨L￨IN￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- multitype￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- carefully￨L￨RB￨O￨- examine￨L￨VBP￨O￨- some￨L￨DT￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- moment￨L￨NN￨O￨A closures￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- maximum￨L￨NN￨O￨- entropy￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- approximating￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- reconstructing￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- over￨L￨IN￨O￨- triplets￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- those￨L￨DT￨O￨- over￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- derive￨L￨VBP￨O￨- a￨L￨DT￨O￨- simpler￨L￨JJR￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- intuitive￨L￨JJ￨O￨- proof￨L￨NN￨O￨- than￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- available￨L￨JJ￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- known￨L￨JJ￨O￨- result￨L￨NN￨O￨- that￨L￨IN￨O￨- pair-based￨L￨JJ￨O￨- moment￨L￨NN￨O￨A closure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- exact￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Markovian￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- tree-like￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- under￨L￨IN￨O￨- pure￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- explore￨L￨VB￨O￨- numerically￨L￨RB￨O￨- the￨L￨DT￨O￨- exactness￨L￨NN￨O￨- of￨L￨IN￨O￨- moment￨L￨NN￨O￨A closures￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- larger￨L￨JJR￨O￨- motifs￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- gaining￨L￨VBG￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- introduce￨L￨VBP￨O￨- errors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- approximations￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- overlapping￨L￨VBG￨O￨- triangles￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Moment-closure￨U￨NN￨O￨- techniques￨L￨NNS￨O￨- are￨L￨VBP￨O￨- commonly￨L￨RB￨O￨A used￨L￨VBN￨O￨A to￨L￨TO￨O￨- generate￨L￨VB￨O￨- low-dimensional￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- extend￨L￨VBP￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- Markovian￨U￨NNP￨O￨- and￨L￨CC￨O￨- non-Markovian￨L￨JJ￨MISC￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- susceptibles￨L￨NNS￨O￨- escape￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- independently￨L￨RB￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- infected￨L￨JJ￨O￨- neighbour￨L￨NN￨O￨A and￨L￨CC￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- infectives￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- re￨L￨VB￨O￨- -￨L￨:￨O￨- 5￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 2￨L￨CD￨DATE￨- y￨L￨NN￨O￨- a￨L￨DT￨O￨- M￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- providing￨L￨VBG￨O￨- exact￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- quite￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- large￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A formulation￨L￨NN￨O￨- also￨L￨RB￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- results￨L￨NNS￨O￨- concerning￨L￨VBG￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- rigorous￨L￨JJ￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- results￨L￨VBZ￨O￨- for￨L￨IN￨O￨- late-time￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- results￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- ensembles￨L￨NNS￨O￨- .￨L￨.￨O￨- +Newman1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Michigan￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Ann￨U￨NNP￨PERSON￨- Arbor￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- MI￨U￨NNP￨STATE_OR_PROVINCE￨- 48109￨L￨CD￨NUMBER￨- 2Center￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Study￨U￨NN￨O￨- of￨L￨IN￨O￨- Complex￨U￨JJ￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Michigan￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Ann￨U￨NNP￨CITY￨- Arbor￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- MI￨U￨NNP￨STATE_OR_PROVINCE￨- 48109￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- most￨L￨JJS￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probabilities￨L￨NNS￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨A time￨L￨NN￨O￨A of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- from￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- implying￨L￨VBG￨O￨- exponential￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨A times￨L￨NNS￨O￨- .￨L￨.￨O￨- +Standard￨U￨NNP￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reformulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- time-dependent￨L￨JJ￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A calculation￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- modeling￨L￨NN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- most￨L￨RBS￨O￨- victims￨L￨NNS￨O￨- recover￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- typically￨L￨RB￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- probability￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨A time￨L￨NN￨O￨A of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- edge-based￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- EBCM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- generating￨L￨VBG￨O￨A function￨L￨NN￨O￨A formalism￨L￨NN￨O￨- ,￨L￨,￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- which￨L￨WDT￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- giant￨L￨JJ￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- GSC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- pandemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- SARS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- H1N1￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- promoted￨L￨VBN￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A to￨L￨TO￨O￨- slow￨L￨VB￨O￨- down￨L￨RP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- used￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- represents￨L￨VBZ￨O￨- these￨L￨DT￨O￨- recent￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- propagates￨L￨VBZ￨O￨- on￨L￨IN￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A until￨L￨IN￨O￨- it￨L￨PRP￨O￨- reaches￨L￨VBZ￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨RB￨O￨- more￨L￨RBR￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- systems￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- between￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- proximity￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- identify￨L￨VB￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- spatial￨L￨JJ￨O￨- arrangement￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- morphology￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- efficiency￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- net￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- upon￨L￨IN￨O￨- contact￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- analysing￨L￨VBG￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- several￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- configurational￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨A is￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- overlap￨L￨VBP￨O￨- between￨L￨IN￨O￨- neighbouring￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- morphological￨L￨JJ￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- shape￨L￨NN￨O￨- anisotropy￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- obtain￨L￨VBP￨O￨- general￨L￨JJ￨TITLE￨- analytical￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- minimally￨L￨RB￨O￨- safe￨L￨JJ￨O￨- bounds￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨A and￨L￨CC￨O￨- then￨L￨RB￨O￨- illustrate￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- validity￨L￨NN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- branching￨L￨VBG￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- salamander￨L￨NN￨O￨- retinal￨L￨JJ￨O￨- ganglion￨L￨NN￨O￨- cells￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- stochasticity￨L￨NN￨O￨- and￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- simplistic￨L￨JJ￨O￨- way￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- phenomenological￨L￨JJ￨O￨- probability￨L￨NN￨O￨- densities￨L￨NNS￨O￨- for￨L￨IN￨O￨- relevant￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- not￨L￨RB￨O￨- linking￨L￨VBG￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- morphology￨L￨NN￨O￨- and￨L￨CC￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- analysed￨L￨VBN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- realistically￨L￨RB￨O￨- complex￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- morphology￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- invasion￨L￨NN￨O￨A and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- comprehensive￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- coherent￨L￨JJ￨O￨A picture￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- which￨L￨WDT￨O￨- unifies￨L￨VBZ￨O￨- past￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- which￨L￨WDT￨O￨- also￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- oscillations￨L￨NNS￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- whooping￨L￨JJ￨O￨- cough￨L￨NN￨O￨- and￨L￨CC￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time-dependent￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨A using￨L￨VBG￨O￨- analytic￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- which￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- disentangle￨L￨VB￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- of￨L￨IN￨O￨- stochasticity￨L￨NN￨O￨- and￨L￨CC￨O￨- external￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- forcing￨L￨VBG￨O￨A induces￨L￨VBZ￨O￨- a￨L￨DT￨O￨- limit￨L￨NN￨O￨- cycle￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fluctuations￨L￨NNS￨O￨- about￨L￨IN￨O￨- this￨L￨DT￨O￨- time-dependent￨L￨JJ￨O￨- solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- decomposed￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- corrections￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- expansion￨L￨NN￨O￨- in￨L￨IN￨O￨- inverse￨L￨JJ￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- applied￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- cycle￨L￨NN￨O￨A is￨L￨VBZ￨O￨- annual￨L￨JJ￨SET￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- period-doubling￨L￨JJ￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- biennial￨L￨JJ￨O￨- .￨L￨.￨O￨- +general￨L￨JJ￨TITLE￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- node￨L￨NN￨O￨- spreading￨L￨NN￨O￨- influence￨L￨NN￨O￨A via￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacent￨L￨JJ￨O￨- matrix￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨NN￨O￨- rate￨L￨NN￨O￨- Jian-Hong￨U￨NNP￨PERSON￨- Lin￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Jian-Guo￨U￨NNP￨PERSON￨- Liu￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Qiang￨U￨NNP￨PERSON￨- Guo1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 93￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P.￨U￨NNP￨PERSON￨- R.￨U￨NNP￨PERSON￨- China￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- With￨U￨IN￨O￨- great￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- and￨L￨CC￨O￨- practical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- ,￨L￨,￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- spreading￨L￨NN￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- promising￨L￨JJ￨O￨- domains￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- build￨L￨VBP￨O￨- up￨L￨RP￨O￨- the￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- method￨L￨NN￨O￨- by￨L￨IN￨O￨- combining￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- spreading￨L￨NN￨O￨- influence￨L￨NN￨O￨A .￨L￨.￨O￨- +So￨U￨RB￨O￨- far￨L￨RB￨O￨- ,￨L￨,￨O￨- various￨L￨JJ￨O￨- topology-based￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- spreading￨L￨NN￨O￨- influence￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- spreading￨L￨NN￨O￨- influence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +proposed￨L￨VBN￨O￨- a￨L￨DT￨O￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- shell￨L￨NN￨O￨A decomposition￨L￨NN￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- shell￨L￨NN￨O￨- have￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- influence￨L￨NN￨O￨- and￨L￨CC￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- higher￨L￨JJR￨O￨- shells￨L￨NNS￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- more￨L￨JJR￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- recent￨L￨JJ￨O￨- researches￨L￨VBZ￨O￨- have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- shell￨L￨NN￨O￨A often￨L￨RB￨O￨- have￨L￨VBP￨O￨- distinct￨L￨JJ￨O￨- influences￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- may￨L￨MD￨O￨- fail￨L￨VB￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- networks￨L￨NNS￨O￨- without￨L￨IN￨O￨- core-like￨L￨JJ￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Baras￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- asi-Albert￨L￨JJ￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- centrality￨L￨NN￨O￨- methods13￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- eigenvector￨L￨NN￨O￨- centrality14￨L￨NN￨O￨- ,￨L￨,￨O￨- closeness￨L￨NN￨O￨- centrality15￨L￨NN￨O￨- and￨L￨CC￨O￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- shell￨L￨NN￨O￨- decomposition16￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- neighbors￨L￨NNS￨O￨- ’￨L￨POS￨O￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- core￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- Lin￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 20￨L￨CD￨NUMBER￨- proposed￨L￨VBD￨O￨- an￨L￨DT￨O￨- improved￨L￨VBN￨O￨- neighbors￨L￨NNS￨O￨- ’￨L￨POS￨O￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- core￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- INK￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- influential￨L￨NN￨O￨A a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- core￨L￨NN￨O￨- values￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- improved￨L￨VBN￨O￨- iterative￨L￨JJ￨O￨A resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IIRA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- centrality￨L￨NN￨O￨- information￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- target￨L￨NN￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +Iterative￨U￨JJ￨O￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- propagation￨L￨NN￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- Lin-Feng￨U￨NNP￨PERSON￨- Zhong￨U￨NNP￨PERSON￨- ,1￨L￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Jian-Guo￨U￨NNP￨PERSON￨- Liu￨U￨NNP￨PERSON￨- ,3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Ming-Sheng￨U￨JJ￨O￨- Shang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Web￨U￨NN￨O￨- Science￨U￨NNP￨O￨- Center￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electronic￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Chengdu￨U￨NNP￨CITY￨- 611731￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +Comparing￨U￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible￨U￨NNP￨O￨- Infected￨U￨JJ￨O￨- Recovered￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- IIRA￨U￨NN￨O￨- method￨L￨NN￨O￨- could￨L￨MD￨O￨- identify￨L￨VB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- tradition￨L￨NN￨O￨- IRA￨U￨NNP￨ORGANIZATION￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- bond￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- site￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- percolation￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- p￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- occupied￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- removed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- MMP￨U￨NN￨O￨- theory￨L￨NN￨O￨- improves￨L￨VBZ￨O￨- significantly￨L￨RB￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- MP￨U￨NN￨O￨- for￨L￨IN￨O￨- percolation￨L￨NN￨O￨A on￨L￨IN￨O￨- synthetic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- limited￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- on￨L￨IN￨O￨- several￨L￨JJ￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- pk￨L￨NN￨O￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- bond￨L￨NN￨O￨A percolation￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- accurately￨L￨RB￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- quantity￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- is￨L￨VBZ￨O￨- S￨U￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- fractional￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- giant￨L￨JJ￨O￨- component￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- infinitely￨L￨RB￨O￨- large￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- percolating￨L￨VBG￨O￨- cluster￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- coexisting￨L￨VBG￨O￨- percolating￨L￨VBG￨O￨- clusters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- CPCs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- emerge￨L￨VBP￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- limited￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- interlinks￨L￨NNS￨O￨- between￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- modules￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- report￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- simply￨L￨RB￨O￨- yet￨L￨RB￨O￨- effectively￨L￨JJ￨O￨- iterative￨L￨JJ￨O￨- method￨L￨NN￨O￨- named￨L￨VBN￨O￨- VoteRank￨U￨NNP￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- decentralized￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨A with￨L￨IN￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- spreading￨L￨NN￨O￨- ability￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simple￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- choose￨L￨VB￨O￨- top-r￨L￨JJ￨O￨- ranked￨L￨VBD￨O￨- nodes￨L￨NNS￨O￨- as￨L￨IN￨O￨- spreaders￨L￨NNS￨O￨A according￨L￨VBG￨O￨- to￨L￨TO￨O￨- influence￨L￨NN￨O￨- ranking￨L￨NN￨O￨- method￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- PageRank￨U￨NN￨O￨- ,￨L￨,￨O￨- ClusterRank￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- shell￨L￨NN￨O￨- decomposition￨L￨NN￨O￨- .￨L￨.￨O￨- +Experimental￨U￨JJ￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- under￨L￨IN￨O￨- Susceptible-Infected-Recovered￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Susceptible-Infected￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- VoteRank￨U￨NNP￨O￨- outperforms￨L￨VBZ￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- benchmark￨L￨NN￨O￨- methods￨L￨NNS￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- spreading￨L￨VBG￨O￨A rate￨L￨NN￨O￨A and￨L￨CC￨O￨- final￨L￨JJ￨O￨- affected￨L￨JJ￨O￨- scale￨L￨NN￨O￨- .￨L￨.￨O￨- +Identifying￨U￨VBG￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- effective￨L￨JJ￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- vote￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- spreader￨L￨NN￨TITLE￨A in￨L￨IN￨O￨- each￨L￨DT￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- voting￨L￨NN￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- elected￨L￨VBN￨O￨- spreader￨L￨NN￨TITLE￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- decreased￨L￨VBN￨O￨- in￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- turn￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- Continuous￨U￨JJ￨O￨- Time￨U￨NNP￨O￨- Markov￨U￨NNP￨O￨- Chain￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- CTMC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Infectious￨U￨JJ￨O￨- Salmon￨U￨NNS￨O￨- Anemia￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- patches￨L￨NNS￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- CTMC￨U￨NN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- patch￨L￨NN￨O￨A and￨L￨CC￨O￨- companion￨L￨NN￨TITLE￨- multitype￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MTBP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Multitype￨U￨JJ￨O￨- branching￨L￨VBG￨O￨A processes￨L￨NNS￨O￨- allow￨L￨VBP￨O￨- for￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- latterly￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- metapopulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- extinction￨L￨NN￨O￨A is￨L￨VBZ￨O￨- computed￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- CTMC￨U￨NNP￨ORGANIZATION￨- via￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- MTBP￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- supercritical￨L￨JJ￨O￨- regime￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Simulations￨U￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- yield￨L￨NN￨O￨- high-level￨L￨JJ￨O￨- ,￨L￨,￨O￨- qualitative￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- on￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- intervention￨L￨NN￨O￨A policies￨L￨NNS￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- policy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- when￨L￨WRB￨O￨- considering￨L￨VBG￨O￨- a￨L￨DT￨O￨- five-year￨L￨JJ￨O￨- time￨L￨NN￨O￨- horizon￨L￨NN￨O￨- than￨L￨IN￨O￨- when￨L￨WRB￨O￨- considering￨L￨VBG￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- year￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- that￨L￨WDT￨O￨- interventions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨- policy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- selecting￨L￨VBG￨O￨- different￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- for￨L￨IN￨O￨- wet￨L￨JJ￨O￨- climates￨L￨NNS￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- density￨L￨NN￨O￨- than￨L￨IN￨O￨- for￨L￨IN￨O￨- dry￨L￨JJ￨O￨- climates￨L￨NNS￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- less￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- at￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- wet￨L￨JJ￨O￨- climates￨L￨NNS￨O￨- when￨L￨WRB￨O￨- attainable￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- or￨L￨CC￨O￨- lower￨L￨JJR￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- allocating￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A interventions￨L￨NNS￨O￨- across￨L￨IN￨O￨- geographic￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- sub￨L￨NN￨O￨- ject￨L￨NN￨O￨- to￨L￨TO￨O￨- budget￨L￨NN￨O￨- constraints￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- person-days￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- one-size-fits-all￨L￨JJ￨O￨- campaign￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- cost-effective￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- better￨L￨JJR￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- geographic￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- and￨L￨CC￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- when￨L￨WRB￨O￨- determining￨L￨VBG￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- produces￨L￨VBZ￨O￨- an￨L￨DT￨O￨- intervention￨L￨NN￨O￨A plan￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- identifying￨L￨VBG￨O￨- which￨L￨WDT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- region￨L￨NN￨O￨- and￨L￨CC￨O￨- year￨L￨NN￨DURATION￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- five-year￨L￨JJ￨O￨- planning￨L￨NN￨O￨- horizon￨L￨NN￨O￨- .￨L￨.￨O￨- +Concerning￨U￨VBG￨O￨- vector￨L￨NN￨O￨- transmitted￨L￨VBD￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A including￨L￨VBG￨O￨- dengue￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- different￨L￨JJ￨O￨- schemes￨L￨NNS￨O￨- and￨L￨CC￨O￨- approaches￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- probabilistic￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- automata￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- techniques￨L￨NNS￨O￨- and￨L￨CC￨O￨- approaches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmitted￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A NumericCitation￨U￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- cellular￨L￨JJ￨O￨- automata￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- a￨L￨DT￨O￨- description￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- master￨L￨JJ￨O￨- equation￨L￨NN￨O￨- defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- lattice￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- direct￨L￨JJ￨O￨- transmitted￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- explored￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vector-borne￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨NN￨O￨- dengue￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Newton￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Reiter￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- Citation￨U￨NNP￨ORGANIZATION￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- susceptible-exposed-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- structure￨L￨NN￨O￨- for￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- susceptible-exposed-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- structure￨L￨NN￨O￨- for￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquitoes￨L￨NNS￨O￨- die￨L￨VBP￨O￨- before￨L￨IN￨O￨- being￨L￨VBG￨O￨- removed￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- follows￨L￨VBZ￨O￨A a￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- type￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- population￨L￨NN￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- type￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- control￨L￨NN￨O￨- objective￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- asymptotically￨L￨RB￨O￨- tracking￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- removed-by-immunity￨L￨JJ￨O￨- population￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- while￨L￨IN￨O￨- achieving￨L￨VBG￨O￨- simultaneously￨L￨RB￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- susceptible￨L￨JJ￨O￨- plus￨L￨CC￨O￨A infected￨L￨JJ￨O￨- plus￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- asymptotically￨L￨RB￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vaccination-based￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- plus￨L￨CC￨O￨A infected￨L￨JJ￨O￨- plus￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- plus￨L￨CC￨O￨- removed￨L￨VBD￨O￨- populations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- propagation￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- Important￨U￨JJ￨O￨- control￨L￨NN￨O￨- problems￨L￨NNS￨O￨- nowadays￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- Life￨U￨NNP￨O￨- Sciences￨U￨NNPS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- ecological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- evolution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Beverton-Holt￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Hassell￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Ricker￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- etc.￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- online￨L￨JJ￨O￨- adjustment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- species￨L￨NNS￨O￨- environment￨L￨NN￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- or￨L￨CC￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- regulated￨L￨VBN￨O￨- harvesting￨L￨NN￨O￨- quota￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- via￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A control￨L￨NN￨O￨- .￨L￨.￨O￨- +Control￨U￨NN￨O￨- parameters￨L￨NNS￨O￨- influence￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- In￨U￨IN￨O￨- one￨L￨CD￨NUMBER￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- e￨L￨SYM￨O￨- xperiments￨L￨VBZ￨O￨- a￨L￨DT￨O￨- pea￨L￨NN￨O￨- k￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨A population￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- 12￨L￨CD￨NUMBER￨- th￨L￨DT￨O￨- day￨L￨NN￨DURATION￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- control￨L￨NN￨O￨- law￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- from￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- control￨L￨NN￨O￨- law￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ma￨L￨NN￨O￨- kes￨L￨NN￨O￨- t￨L￨NN￨O￨- he￨L￨PRP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- reaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- pea￨L￨NN￨O￨- k￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- 5￨L￨CD￨NUMBER￨- th￨L￨DT￨O￨- day￨L￨NN￨DURATION￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- 5.4￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨A population￨L￨NN￨O￨A is￨L￨VBZ￨O￨- infectious￨L￨JJ￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- from￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Example￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- An￨U￨DT￨O￨- example￨L￨NN￨O￨- ba￨L￨FW￨O￨- se￨L￨FW￨O￨- d￨L￨NN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- outbrea￨L￨NN￨O￨- k￨L￨NN￨O￨- of￨L￨IN￨O￨- mea￨L￨NN￨O￨- sle￨L￨NN￨O￨- s￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- total￨L￨JJ￨O￨A population￨L￨NN￨O￨A of￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- M￨U￨NN￨O￨- U￨U￨NNP￨O￨- L￨U￨NNP￨O￨- A￨U￨NNP￨O￨- T￨U￨NN￨O￨- I￨U￨PRP￨O￨- O￨U￨VBP￨O￨- E￨U￨NN￨O￨- S￨U￨NN￨O￨- U￨U￨NNP￨O￨- L￨U￨NNP￨O￨- T￨U￨NN￨O￨- S￨U￨NN￨O￨- a￨L￨DT￨O￨- i￨L￨FW￨O￨- x￨L￨CC￨O￨- a￨L￨DT￨O￨- m￨L￨NN￨O￨- p￨L￨NN￨O￨- l￨L￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- o￨L￨NN￨O￨- l￨L￨NN￨O￨- l￨L￨NN￨O￨- u￨L￨NN￨O￨- s￨L￨VBZ￨O￨- t￨L￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- t￨L￨NN￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- h￨L￨NN￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- e￨L￨SYM￨O￨- o￨L￨NN￨O￨- r￨L￨NN￨O￨- e￨L￨SYM￨O￨- t￨L￨NN￨O￨- i￨L￨FW￨O￨- c￨L￨NN￨O￨- a￨L￨DT￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- u￨L￨FW￨O￨- l￨L￨NN￨O￨- t￨L￨NN￨O￨- p￨L￨NN￨O￨- r￨L￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- e￨L￨SYM￨O￨- n￨L￨NN￨O￨- t￨L￨NN￨O￨- e￨L￨SYM￨O￨- h￨L￨NN￨O￨- a￨L￨DT￨O￨- p￨L￨NN￨O￨- e￨L￨SYM￨O￨- r￨L￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- c￨L￨NN￨O￨- r￨L￨NN￨O￨- i￨L￨FW￨O￨- b￨L￨NN￨O￨- e￨L￨SYM￨O￨- h￨L￨NN￨O￨- i￨L￨FW￨O￨- s￨L￨VBZ￨O￨- e￨L￨SYM￨O￨- c￨L￨NN￨O￨- t￨L￨NN￨O￨- i￨L￨FW￨O￨- o￨L￨NN￨O￨- n￨L￨NN￨O￨- 4.1.1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +PGFs￨U￨NNS￨O￨- help￨L￨VBP￨O￨- predict￨L￨VB￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- properties￨L￨NNS￨O￨- about￨L￨RB￨O￨- early￨L￨RB￨O￨- outbreak￨L￨NN￨O￨- behavior￨L￨NN￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- effectively￨L￨JJ￨O￨- infinite￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- after￨L￨IN￨O￨- some￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- generations￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- non-epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Remarkably￨U￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- acquiring￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- interact￨L￨VBP￨O￨- with￨L￨IN￨O￨- unequal￨L￨JJ￨O￨- frequency￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- always￨L￨RB￨O￨- exist￨L￨VBP￨O￨- a￨L￨DT￨O￨- cross￨L￨JJ￨O￨- point￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- ,￨L￨,￨O￨- below￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A hinders￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- expedites￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- analytical￨L￨JJ￨O￨- arguments￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- extensive￨L￨JJ￨O￨- computer￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A can￨L￨MD￨O￨- either￨L￨RB￨O￨- impede￨L￨VB￨O￨- or￨L￨CC￨O￨- accelerate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- pattern￨L￨NN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Generally￨U￨RB￨O￨- ,￨L￨,￨O￨- catching￨L￨VBG￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- complex￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- great￨L￨JJ￨O￨- difference￨L￨NN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- forth￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- most￨L￨JJS￨O￨- classical￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- identical￨L￨JJ￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- acquire￨L￨VBP￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- probability￨L￨NN￨O￨- whenever￨L￨WRB￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- all￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- recover￨L￨VB￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- go￨L￨VB￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- being￨L￨VBG￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- rate￨L￨NN￨O￨A .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- 1￨L￨CD￨DATE￨- 3￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- a￨L￨DT￨O￨- susceptible-vaccinated￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SVIR￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- epidemic-spreading￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- focus￨L￨NN￨O￨- lies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- is￨L￨VBZ￨O￨- taken￨L￨VBN￨O￨- keeping￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- otherwise￨L￨RB￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- immigration￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- fixed￨L￨VBD￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- quotient￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- lifetime￨L￨NN￨O￨- tends￨L￨VBZ￨O￨A to￨L￨TO￨O￨- 0￨L￨CD￨NUMBER￨- faster￨L￨JJR￨O￨- than￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- log￨L￨NN￨O￨- n.￨L￨NN￨O￨- Under￨U￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- regime￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- short￨L￨JJ￨O￨- ,￨L￨,￨O￨- having￨L￨VBG￨O￨- duration￨L￨NN￨O￨- that￨L￨WDT￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- 0￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- probability￨L￨NN￨O￨- as￨L￨IN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- situation￨L￨NN￨O￨- treated￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- where￨L￨WRB￨O￨- n￨L￨NN￨O￨- →￨L￨SYM￨O￨- ∞￨L￨SYM￨O￨- ,￨L￨,￨O￨- keeping￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- importation￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- fixed￨L￨VBD￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- quotient￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- lifetime￨L￨NN￨O￨- tends￨L￨VBZ￨O￨A to￨L￨TO￨O￨- 0￨L￨CD￨NUMBER￨- faster￨L￨JJR￨O￨- than￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- log￨L￨NN￨O￨- n￨L￨NN￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- each￨L￨DT￨O￨- cycle￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- S￨U￨NN￨O￨- makes￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- down￨L￨IN￨O￨- jump￨L￨NN￨O￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- ma￨L￨FW￨O￨- jor￨L￨FW￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- except￨L￨IN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- increases￨L￨VBZ￨O￨- deterministically￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- minor￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- no￨L￨DT￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- ¯￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨A as￨L￨IN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- follow￨L￨VBP￨O￨- the￨L￨DT￨O￨- edge-based￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- equations￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- -￨L￨:￨O￨- infected￨L￨JJ￨O￨- -￨L￨:￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- through￨L￨IN￨O￨- this￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨A network￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Existing￨U￨VBG￨O￨- multiplex￨L￨JJ￨O￨A modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- single-layer￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- or￨L￨CC￨O￨- aggregations￨L￨NNS￨O￨- of￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- accurate￨L￨JJ￨O￨- enough￨L￨JJ￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- further￨L￨RB￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨- network￨L￨NN￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- layers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- below￨L￨IN￨O￨- their￨L￨PRP$￨O￨- respective￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamic￨L￨JJ￨O￨- network￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨A describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transient￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- makes￨L￨NNS￨O￨- with￨L￨IN￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- wider￨L￨JJR￨O￨- population￨L￨NN￨O￨- by￨L￨IN￨O￨- imposing￨L￨VBG￨O￨- constant￨L￨JJ￨O￨- edge￨L￨NN￨O￨- rewiring￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- incorporate￨L￨VBP￨O￨- the￨L￨DT￨O￨- aforementioned￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- a￨L￨DT￨O￨- dual-layer￨L￨JJ￨O￨- static-dynamic￨L￨JJ￨O￨- multiplex￨L￨JJ￨O￨A network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- altering￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- multiplex￨L￨JJ￨O￨A network￨L￨NN￨O￨- attributes￨L￨VBZ￨O￨- on￨L￨IN￨O￨- resultant￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- compartment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- analogous￨L￨JJ￨O￨- to￨L￨TO￨O￨- OSN￨U￨NN￨O￨- users￨L￨NNS￨O￨A :￨L￨:￨O￨- potential￨L￨JJ￨O￨- OSN￨U￨NN￨O￨- users￨L￨NNS￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- joining￨L￨VBG￨O￨- the￨L￨DT￨O￨- OSN￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- S0￨U￨NN￨O￨- R0￨U￨NN￨O￨- <￨L￨JJR￨O￨- γ￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Similar￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- Equation￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- this￨L￨DT￨O￨- criterion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- satisfied￨L￨JJ￨O￨- then￨L￨RB￨O￨- I￨U￨PRP￨O￨- can￨L￨MD￨O￨- never￨L￨RB￨O￨- increase￨L￨VB￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- publicly￨L￨RB￨O￨- available￨L￨JJ￨O￨- Google￨U￨NNP￨ORGANIZATION￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- search￨L￨NN￨O￨A query￨L￨NN￨O￨- Myspace￨U￨NNP￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- poor￨L￨JJ￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relatively￨L￨RB￨O￨- poor￨L￨JJ￨O￨A fit￨L￨NN￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- given￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- assumption￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- intuitively￨L￨RB￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- adoption￨L￨NN￨O￨- and￨L￨CC￨O￨- abandonment￨L￨NN￨CRIMINAL_CHARGE￨- dynamics￨L￨NNS￨O￨- 6￨L￨CD￨NUMBER￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Having￨U￨VBG￨O￨- validated￨L￨VBN￨O￨- the￨L￨DT￨O￨- irSIR￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- OSN￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- search￨L￨NN￨O￨A query￨L￨NN￨O￨- Myspace￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- then￨L￨RB￨O￨- applied￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Google￨U￨NNP￨ORGANIZATION￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- search￨L￨NN￨O￨- query￨L￨NN￨O￨- Facebook￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- and￨L￨CC￨O￨- analytical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A becomes￨L￨VBZ￨O￨- intense￨L￨JJ￨O￨- and￨L￨CC￨O￨- wide￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- delivery￨L￨NN￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- average￨L￨JJ￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- homogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- constantly￨L￨RB￨O￨- spread￨L￨VBD￨O￨- some￨L￨DT￨O￨- infected￨L￨JJ￨O￨- packets￨L￨NNS￨O￨- by￨L￨IN￨O￨- biased￨L￨VBN￨O￨- random￨L￨JJ￨O￨- walks￨L￨VBZ￨O￨A to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- neighbor￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- causing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- receive￨L￨VBP￨O￨- the￨L￨DT￨O￨- packets￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- biased￨L￨VBN￨O￨- random￨L￨JJ￨O￨- walks￨L￨VBZ￨O￨A on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- corresponding￨L￨VBG￨O￨- optimal￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- instantaneously￨L￨RB￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A process￨L￨NN￨O￨- covers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- biased￨L￨VBN￨O￨- random￨L￨JJ￨O￨- walks￨L￨VBZ￨O￨A ,￨L￨,￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨A in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- Francisco￨U￨NNP￨PERSON￨- Herrer￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- ıas-Azcu￨L￨NN￨O￨- ´￨L￨''￨O￨- e1￨L￨NN￨O￨- ,￨L￨,￨O￨- *￨L￨SYM￨O￨- and￨L￨CC￨O￨- Tobias￨U￨NNP￨PERSON￨- Galla1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- +￨L￨CC￨O￨- 1Theoretical￨L￨JJ￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Astronomy￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- The￨U￨NNP￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Manchester￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Manchester￨U￨NNP￨ORGANIZATION￨- M13￨U￨NNP￨O￨- 9PL￨L￨NN￨O￨- ,￨L￨,￨O￨- United￨U￨NNP￨COUNTRY￨- Kingdom￨U￨NNP￨COUNTRY￨- *￨L￨SYM￨O￨- +￨L￨CC￨O￨- ABSTRACT￨U￨NN￨O￨- Models￨U￨NNS￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- noise￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- cycles￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- population￨L￨NN￨O￨- averages￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptibilities￨L￨NNS￨O￨- and￨L￨CC￨O￨- infectivities￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- that￨L￨IN￨O￨- their￨L￨PRP$￨O￨- amplitude￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- higher-order￨L￨JJ￨O￨- moments￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- variant￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infective-recovered￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- both￨L￨DT￨O￨- agent-to-agent￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨A and￨L￨CC￨O￨- intrinsic￨L￨JJ￨O￨- noise￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨A ,￨L￨,￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- stochasticity￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- how￨L￨WRB￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptibilities￨L￨NNS￨O￨- and￨L￨CC￨O￨- propensities￨L￨NNS￨O￨- to￨L￨TO￨O￨- pass￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- affects￨L￨NNS￨O￨- these￨L￨DT￨O￨- quasi-cycles￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- synchronisation￨L￨NN￨O￨- properties￨L￨NNS￨O￨- and￨L￨CC￨O￨- phase￨L￨NN￨O￨- lag￨L￨NN￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨A groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Instead￨U￨RB￨O￨- of￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- recovery￨L￨NN￨O￨A rate￨L￨NN￨O￨A for￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- to￨L￨TO￨O￨- allocate￨L￨VB￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- δi￨L￨NN￨O￨- for￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- indegree￨L￨NN￨O￨- and￨L￨CC￨O￨- outdegree-δi￨L￨JJ￨O￨- ∼￨L￨NN￨O￨- kαin￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- out￨L￨RB￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- finite￨L￨JJ￨O￨- average￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- hδi￨L￨NN￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- resources￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- The￨U￨DT￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- communication￨L￨NN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- possibly￨L￨RB￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- equipped￨L￨VBN￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- recovery￨L￨NN￨O￨A resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- recover￨L￨VB￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- neighbor￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- recovered￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- again￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨A rate￨L￨NN￨O￨A δ￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- directed￨L￨VBN￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- indegree￨L￨NN￨O￨- and￨L￨CC￨O￨- outdegree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- directionality￨L￨NN￨O￨- ξ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- unidirectional￨L￨JJ￨O￨- links￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- linear￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- coef￨L￨NN￨O￨- ficients￨L￨NNS￨O￨- ρ￨L￨VBP￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- indegree￨L￨NN￨O￨- and￨L￨CC￨O￨- outdegree￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- directed￨L￨VBN￨O￨A scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Asymptotic￨U￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A ,￨L￨,￨O￨- degree￨L￨NN￨O￨- correlation￨L￨NN￨O￨- and￨L￨CC￨O￨- clustering￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- ma￨L￨FW￨O￨- jor￨L￨FW￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨PDT￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2001￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- defines￨L￨VBZ￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- or￨L￨CC￨O￨- less￨L￨JJR￨O￨- arbitrary￨L￨JJ￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A FD￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbours￨L￨NNS￨O￨- D￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨- selected￨L￨VBN￨O￨- node￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- context￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- tunable￨L￨JJ￨O￨- ,￨L￨,￨O￨- quite￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- clustering￨L￨NN￨O￨- ,￨L￨,￨O￨- degree￨L￨NN￨O￨- correlation￨L￨NN￨O￨- and￨L￨CC￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- contagions￨L￨NNS￨O￨- over￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- monoplex￨L￨JJ￨O￨- pro￨L￨JJ￨O￨- jections￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- ignoring￨L￨VBG￨O￨- link￨L￨NN￨O￨- types￨L￨NNS￨O￨- and￨L￨CC￨O￨- aggregating￨L￨VBG￨O￨- network￨L￨NN￨O￨- layers￨L￨NNS￨O￨A may￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- inaccurate￨L￨JJ￨O￨- conclusions￨L￨NNS￨O￨- about￨L￨IN￨O￨- contagion￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- degrees￨L￨NNS￨O￨- between￨L￨IN￨O￨- layers￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contagion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- general￨L￨JJ￨TITLE￨- enough￨L￨JJ￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- content-dependent￨L￨JJ￨O￨- linear￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- link￨L￨NN￨O￨- type￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- weight￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- influence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- content￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- product￨L￨NN￨O￨- ,￨L￨,￨O￨- rumor￨L￨NN￨O￨- ,￨L￨,￨O￨- political￨L￨JJ￨O￨- view￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- spread￨L￨VBN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- widely￨L￨RB￨O￨- studied￨L￨VBN￨O￨- problems￨L￨NNS￨O￨- include￨L￨VBP￨O￨- cascading￨L￨VBG￨O￨- failures￨L￨NNS￨O￨- in￨L￨IN￨O￨- interdependent￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- simple￨L￨JJ￨O￨- contagions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- animal￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- complex￨L￨JJ￨O￨- contagions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨- ,￨L￨,￨O￨- beliefs￨L￨NNS￨O￨- ,￨L￨,￨O￨- norms￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- innovations￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Generally￨U￨RB￨O￨- speaking￨L￨VBG￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- findings￨L￨NNS￨O￨- reveal￨L￨VBP￨O￨- that￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- clustering￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- having￨L￨VBG￨O￨- global￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- this￨L￨DT￨O￨- tendency￨L￨NN￨O￨A changes￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- inactive￨L￨JJ￨O￨- node￨L￨NN￨O￨- with￨L￨IN￨O￨- mi￨L￨FW￨O￨- neighbors￨L￨NNS￨O￨A and￨L￨CC￨O￨- di￨L￨FW￨O￨- −￨L￨FW￨O￨- mi￨L￨FW￨O￨- inactive￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- via￨L￨IN￨O￨- type-i￨L￨JJ￨O￨- links￨L￨NNS￨O￨- turns￨L￨VBZ￨O￨- active￨L￨JJ￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- active￨L￨JJ￨O￨- i￨L￨FW￨O￨- cimi￨L￨FW￨O￨- i￨L￨FW￨O￨- cidi￨L￨FW￨O￨- ≥￨L￨FW￨O￨- τ￨L￨FW￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- threshold￨L￨NN￨O￨- drawn￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- Ben-Naim￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Krapivsky￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- BN-K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- statistics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SusceptibleInfected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- near￨L￨IN￨O￨- its￨L￨PRP$￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- recover￨L￨VBP￨O￨- the￨L￨DT￨O￨- scaling￨L￨NN￨O￨A results￨L￨NNS￨O￨- of￨L￨IN￨O￨- Ben-Naim￨U￨NNP￨O￨- and￨L￨CC￨O￨- Krapivsky￨U￨NNP￨PERSON￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- maximal￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- scales￨L￨NNS￨O￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- 2/3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- 1/3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- form￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- scaling￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +BN-K￨U￨NN￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- at￨L￨IN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨A average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- affected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- N￨U￨NN￨O￨- 1/3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- essentially￨L￨RB￨O￨- no￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- which￨L￨WDT￨O￨- infect￨L￨VBP￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- N￨U￨NN￨O￨- 2/3￨L￨CD￨NUMBER￨- victims￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- N￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- are￨L￨VBP￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- subclasses￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- pool￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨A S￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- I￨U￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- no￨L￨RB￨O￨- longer￨L￨RBR￨O￨- infectible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- R.￨U￨NNP￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- total￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- .￨L￨.￨O￨- +Experimental￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- several￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- demonstrates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- LH-index￨U￨NN￨MISC￨- method￨L￨NN￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- h-index￨L￨NN￨O￨- centrality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LH-index￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- and￨L￨CC￨O￨- rank￨L￨VB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- LH-index￨U￨NN￨MISC￨- method￨L￨NN￨O￨- simultaneously￨L￨RB￨O￨- takes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- of￨L￨IN￨O￨- h-index￨L￨NN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- itself￨L￨PRP￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- idea￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- connecting￨L￨VBG￨O￨- to￨L￨TO￨O￨- more￨L￨JJR￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A will￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- influential￨L￨JJ￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A ,￨L￨,￨O￨- local￨L￨JJ￨O￨- h-index￨L￨NN￨O￨- centrality￨L￨NN￨O￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- modular￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- has￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨A :￨L￨:￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- influence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- community￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- through￨L￨IN￨O￨- its￨L￨PRP$￨O￨- intra-community￨L￨JJ￨O￨- links￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- influence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- through￨L￨IN￨O￨- its￨L￨PRP$￨O￨- inter-community￨L￨JJ￨O￨- links￨L￨NNS￨O￨- .￨L￨.￨O￨- +Influential￨U￨JJ￨O￨- nodes￨L￨NNS￨O￨- ·￨L￨VBP￨O￨- Centrality￨U￨NNP￨O￨- measures￨L￨NNS￨O￨- ·￨L￨NNP￨O￨- Community￨U￨NNP￨O￨- Structure￨U￨NN￨O￨- ·￨L￨NN￨O￨- SIR￨U￨NN￨O￨- Keywords￨U￨NNS￨O￨- model￨L￨NN￨TITLE￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Identifying￨U￨VBG￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- gained￨L￨VBN￨O￨- much￨L￨JJ￨O￨- attention￨L￨NN￨O￨- among￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- many￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- idea￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- to￨L￨TO￨O￨- extend￨L￨VB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨- to￨L￨TO￨O￨- modular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- measures￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- have￨L￨VBP￨O￨- emerged￨L￨VBN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- years￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Betweenness￨U￨NNP￨O￨- ,￨L￨,￨O￨- Closeness￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Eigenvalue￨U￨NNP￨O￨- centrality￨L￨NN￨O￨- .￨L￨.￨O￨- +Its￨U￨PRP$￨O￨- first￨L￨JJ￨O￨- component￨L￨NN￨O￨- quantifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- influence￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- community￨L￨NN￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- component￨L￨NN￨O￨- quantifies￨L￨VBZ￨O￨- its￨L￨PRP$￨O￨- global￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 8￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- aspects￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- for￨L￨IN￨O￨- characterizing￨L￨VBG￨O￨- topologies￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- path￨L￨NN￨O￨- distance￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- core￨L￨NN￨O￨- decomposition￨L￨NN￨O￨- ,5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- motif￨L￨NN￨O￨- tification￨L￨NN￨O￨- ,8￨L￨CD￨NUMBER￨- community￨L￨NN￨O￨- identification￨L￨NN￨O￨- .9￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- 10￨L￨CD￨NUMBER￨- Spreading￨U￨VBG￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- ubiquitous￨L￨JJ￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- knowledge￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- idene.g.￨L￨NN￨O￨- ,￨L￨,￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- particular￨L￨JJ￨O￨- focus￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- put￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreaders￨L￨NNS￨O￨- ,18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- relevancy￨L￨NN￨O￨- localizing￨L￨VBG￨O￨- these￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- as￨L￨IN￨O￨- for￨L￨IN￨O￨- designing￨L￨VBG￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- decelerate￨L￨VB￨O￨- or￨L￨CC￨O￨- stop￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- accelerate￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- knowledge￨L￨NN￨O￨- dissemination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- L￨U￨NN￨O￨- :￨L￨:￨O￨- G0￨U￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- G1￨U￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- G2￨U￨NN￨O￨- ≥￨L￨SYM￨O￨- ·￨L￨SYM￨O￨- ·￨L￨SYM￨O￨- ·￨L￨SYM￨O￨- ≥￨L￨SYM￨O￨- Gk￨U￨NNP￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- D-chain￨U￨NN￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨A t￨L￨NN￨O￨- of￨L￨IN￨O￨- G.￨U￨NNP￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- shall￨L￨MD￨O￨- make￨L￨VB￨O￨- explicit￨L￨JJ￨O￨- the￨L￨DT￨O￨- mapping￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- established￨L￨JJ￨O￨- Multi-strain￨U￨JJ￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- onto￨L￨IN￨O￨- the￨L￨DT￨O￨- TW￨U￨NNP￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- can￨L￨MD￨O￨- persist￨L￨VB￨O￨- in￨L￨IN￨O￨- RQS￨U￨NNP￨O￨- if￨L￨IN￨O￨- cross-immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- long-ranged￨L￨JJ￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- adaptation￨L￨NN￨O￨A .￨L￨.￨O￨- +Shraiman1￨U￨NN￨O￨- 1Kavli￨L￨NNS￨O￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Theoretical￨U￨NNP￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- UC￨U￨NN￨ORGANIZATION￨- Santa￨U￨NNP￨ORGANIZATION￨- Barbara￨U￨NNP￨ORGANIZATION￨- 2Biozentrum￨L￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Basel￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 30￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Rapidly￨U￨RB￨O￨- evolving￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- like￨L￨IN￨O￨- influenza￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- can￨L￨MD￨O￨- persist￨L￨VB￨O￨- by￨L￨IN￨O￨- accumulating￨L￨VBG￨O￨- antigenic￨L￨JJ￨O￨A novelty￨L￨NN￨O￨- fast￨L￨RB￨O￨- enough￨L￨RB￨O￨- to￨L￨TO￨O￨- evade￨L￨VB￨O￨- the￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- without￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- accumulation￨L￨NN￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- Red￨U￨JJ￨O￨- Queen￨U￨NNP￨TITLE￨- States￨U￨NNPS￨O￨- (￨L￨-LRB-￨O￨- RQS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- adaptation￨L￨NN￨O￨A in￨L￨IN￨O￨- large￨L￨JJ￨O￨- rapidly￨L￨RB￨O￨- mutating￨L￨VBG￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- understood￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- Traveling￨U￨VBG￨O￨- Wave￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- TW￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- theories￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- .￨L￨.￨O￨- +range￨L￨NN￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- TW￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- antigenic￨L￨JJ￨O￨A advance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- lead￨L￨NN￨O￨- strains￨L￨NNS￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- co-circulating￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- oscillate￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- state￨L￨NN￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- speciation￨L￨NN￨O￨- ”￨L￨''￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨A divergence￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- cross-inhibition￨L￨NN￨O￨- .￨L￨.￨O￨- +Starting￨U￨VBG￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- graph￨L￨NN￨O￨- with￨L￨IN￨O￨- N￨U￨NN￨O￨- +￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- verthe￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- graph￨L￨NN￨O￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- tices￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stopping￨L￨VBG￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- when￨L￨WRB￨O￨- one￨L￨CD￨NUMBER￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- disappears￨L￨VBZ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- tending￨L￨VBG￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- tends￨L￨VBZ￨O￨A to￨L￨TO￨O￨- 1/2￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- λ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- no￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- tends￨L￨VBZ￨O￨A to￨L￨TO￨O￨- 0￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨CD￨NUMBER￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- λ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- was￨L￨VBD￨O￨- no￨L￨DT￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- shape￨L￨NN￨O￨- theorem￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- higher￨L￨JJR￨O￨- dimensions￨L￨NNS￨O￨- ,￨L￨,￨O￨- until￨L￨IN￨O￨- Chabot￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1998￨L￨CD￨DATE￨- ,￨L￨,￨O￨- unpublished￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- proved￨L￨VBD￨O￨- it￨L￨PRP￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- nearest￨L￨JJS￨O￨- neighbor￨L￨NN￨O￨- contamination￨L￨NN￨O￨- rule￨L￨NN￨O￨- in￨L￨IN￨O￨- dimension￨L￨NN￨O￨- d￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- restriction￨L￨NN￨O￨- to￨L￨TO￨O￨- deterministic￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- case￨L￨NN￨O￨- the￨L￨DT￨O￨- oriented￨L￨VBN￨O￨- percolation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- comparable￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- non-oriented￨L￨JJ￨O￨- Bernoulli￨U￨NNP￨O￨- percolation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- Z2￨U￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- extinction￨L￨NN￨O￨- ,￨L￨,￨O￨- Cox￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- Durrett￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 1988￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- a￨L￨DT￨O￨- shape￨L￨NN￨O￨A theorem￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- contamination￨L￨NN￨O￨- rule￨L￨NN￨O￨- is￨L￨VBZ￨O￨- nearest￨L￨JJS￨O￨- neighbor￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- durations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- a￨L￨DT￨O￨- shape￨L￨NN￨O￨A theorem￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- Zd￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Analyzing￨U￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- d￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- required￨L￨VBN￨O￨- heavier￨L￨JJR￨O￨- techniques￨L￨NNS￨O￨- than￨L￨IN￨O￨- before￨L￨IN￨O￨- :￨L￨:￨O￨- Chabot￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1998￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- used￨L￨VBN￨O￨- results￨L￨NNS￨O￨- from￨L￨IN￨O￨- Antal￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Pisztora￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 1996￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Grimmett￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Marstrand￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- 1990￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- non-oriented￨L￨JJ￨O￨- Bernoulli￨U￨NNP￨O￨- percolation￨L￨NN￨O￨A to￨L￨TO￨O￨- derive￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- exponential￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- subcritical￨L￨JJ￨O￨- case￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- estimates￨L￨VBZ￨O￨- using￨L￨VBG￨O￨- percolation￨L￨NN￨O￨- on￨L￨IN￨O￨- slabs￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- .￨L￨.￨O￨- +Shape￨U￨VBG￨O￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- first￨L￨JJ￨O￨- passage￨L￨NN￨O￨- locally￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- renormalization￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- constant￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 8-9￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- impulsive￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- discrete￨L￨JJ￨O￨- –￨L￨:￨O￨- time￨L￨NN￨O￨- etc.￨L￨FW￨O￨- ,￨L￨,￨O￨- incorporating￨L￨VBG￨O￨- point￨L￨NN￨O￨- or￨L￨CC￨O￨- distributed￨L￨VBN￨O￨- delays￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 12-13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- oscillatory￨L￨JJ￨O￨- behaviours￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- coupled￨L￨VBN￨O￨- partial￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- require￨L￨VBP￨O￨- very￨L￨RB￨O￨- close￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- ,￨L￨,￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- positivity￨L￨NN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- required￨L￨VBN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨A ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 22-23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- continuous-time￨L￨JJ￨O￨- linear￨L￨JJ￨O￨- vaccination-based￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- plus￨L￨CC￨O￨A infected￨L￨JJ￨O￨- plus￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- plus￨L￨CC￨O￨- removed￨L￨VBD￨O￨- populations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- propagation￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- observer￨L￨NN￨O￨- ,￨L￨,￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- stability￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- when￨L￨WRB￨O￨- τI￨L￨NN￨O￨- <￨L￨JJR￨O￨- τR￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- unlike￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- models￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- separate￨L￨JJ￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- phase￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- phase￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- τI￨L￨NN￨O￨- and￨L￨CC￨O￨- τR￨L￨NN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- critical￨L￨JJ￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A λ1￨L￨NN￨O￨- and￨L￨CC￨O￨- λ2￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- epidemic￨L￨JJ￨O￨- persists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- between￨L￨IN￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- persistent￨L￨JJ￨O￨- when￨L￨WRB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- support￨L￨VBP￨O￨- those￨L￨DT￨O￨- results￨L￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- Model￨U￨NNP￨TITLE￨- Description￨U￨NN￨O￨- The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- if￨L￨IN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- dimensional￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- behavior￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- deduce￨L￨VB￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- enough￨L￨RB￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- any￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- infects￨L￨VBZ￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- during￨L￨IN￨O￨- its￨L￨PRP$￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A time￨L￨NN￨O￨A ,￨L￨,￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- evolves￨L￨VBZ￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- become￨L￨VBN￨O￨- susceptible￨L￨JJ￨O￨- .￨L￨.￨O￨- +e.￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A time￨L￨NN￨O￨A τI￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λ1￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λ2￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Infected￨U￨JJ￨O￨- node￨L￨NN￨O￨- pass￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- refractory￨L￨JJ￨O￨- state￨L￨NN￨O￨- after￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A time￨L￨NN￨O￨A τI￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- this￨L￨DT￨O￨- framework￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- state￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- rewiring￨L￨VBG￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Phase￨U￨NN￨O￨- transition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨A networks￨L￨NNS￨O￨A Guillaume￨U￨NNP￨PERSON￨- St-Onge￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- ∗￨L￨NNP￨O￨- Jean-Gabriel￨U￨NNP￨PERSON￨- Young￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Edward￨U￨NNP￨PERSON￨- Laurence￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Charles￨U￨NNP￨PERSON￨- Murphy￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Louis￨U￨NNP￨PERSON￨- J.￨U￨NNP￨PERSON￨- Dub￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- e￨L￨SYM￨O￨- †￨L￨SYM￨O￨- D´epartement￨U￨NNP￨O￨- de￨L￨IN￨O￨- Physique￨U￨NNP￨O￨- ,￨L￨,￨O￨- de￨L￨FW￨O￨- G´enie￨U￨FW￨O￨- Physique￨U￨NN￨O￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨- d’Optique￨L￨FW￨O￨- ,￨L￨,￨O￨- Universit￨U￨NNP￨ORGANIZATION￨- ´￨L￨POS￨O￨- e￨L￨SYM￨O￨- Laval￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Qu´ebec￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Qu´ebec￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Canada￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- G1V￨U￨NN￨O￨- 0A6￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Dated￨U￨VBN￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 18￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- degree-based￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- rewired￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- our￨L￨PRP$￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- appears￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- phenomenon￨L￨NN￨O￨A :￨L￨:￨O￨- observables￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- degree￨L￨NN￨O￨- classes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- scaling￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- phenomenon￨L￨NN￨O￨A is￨L￨VBZ￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- successive￨L￨JJ￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- classes￨L￨NNS￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- obtain￨L￨VB￨O￨- more￨L￨JJR￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- such￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- strating￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨- equation￨L￨NN￨O￨- formulation￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- van￨L￨NN￨PERSON￨- Kampen￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 1992￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- field￨L￨JJ￨O￨- theoretic￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- with￨L￨IN￨O￨- creation￨L￨NN￨O￨- and￨L￨CC￨O￨- annihilation￨L￨NN￨O￨- operators￨L￨NNS￨O￨A giving￨L￨VBG￨O￨- a￨L￨DT￨O￨- Schr￨U￨JJ￨O￨- ¨￨L￨NN￨O￨- odinger￨L￨NN￨O￨- like￨L￨IN￨O￨- operator￨L￨NN￨TITLE￨- equation￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- ,￨L￨,￨O￨- first￨L￨NN￨O￨- in￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- Doi￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 1976￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- subsequently￨L￨RB￨O￨- elaborated￨L￨VBD￨O￨- [￨L￨-LRB-￨O￨- Grassberger￨U￨NN￨O￨- and￨L￨CC￨O￨- de￨L￨IN￨O￨- la￨L￨DT￨O￨- Torre￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1979￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Grassberger￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Scheunert￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1980￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Peliti￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1985￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- recently￨L￨RB￨DATE￨- used￨L￨VBN￨O￨- e.g.￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- models￨L￨NNS￨O￨- Pauli￨U￨JJ￨O￨- matrices￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- spin￨L￨NN￨O￨- 1/2￨L￨CD￨NUMBER￨- ladder￨L￨NN￨O￨- operators￨L￨NNS￨O￨- which￨L￨WDT￨O￨- serve￨L￨VBP￨O￨- as￨L￨IN￨O￨- creation￨L￨NN￨O￨- and￨L￨CC￨O￨- annihilation￨L￨NN￨O￨- operators￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨- equation￨L￨NN￨O￨- in￨L￨IN￨O￨- vector￨L￨NN￨O￨- notation￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- Hinrichsen￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- generalize￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SIRI￨U￨NNP￨ORGANIZATION￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- ladder￨L￨NN￨O￨- operators￨L￨NNS￨O￨A as￨L￨IN￨O￨- creation￨L￨NN￨O￨- and￨L￨CC￨O￨- annihilation￨L￨NN￨O￨- operators￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Gell-Mann￨U￨NNP￨MISC￨- matrices￨L￨NNS￨O￨- ,￨L￨,￨O￨- normally￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- quantum￨L￨NN￨O￨- chromodynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Then￨U￨RB￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- master￨L￨JJ￨O￨- equation￨L￨NN￨O￨- d￨L￨NN￨O￨- dt￨L￨NN￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I1￨U￨NN￨O￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- IN￨U￨IN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- Xi￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- wIi￨L￨NN￨O￨- ,1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- Ii￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I1￨U￨NN￨O￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- Ii￨U￨NN￨O￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- IN￨U￨IN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- Xi￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- w1￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- Ii￨U￨NN￨O￨- ,￨L￨,￨O￨- Ii￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I1￨U￨NN￨O￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- Ii￨U￨NN￨O￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- IN￨U￨IN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- Ii￨U￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- transition￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- vector￨L￨NN￨O￨- notation￨L￨NN￨O￨- by￨L￨IN￨O￨- wIi￨L￨NNP￨O￨- ,1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- Ii￨U￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- w1￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- Ii￨U￨NN￨O￨- ,￨L￨,￨O￨- Ii￨U￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- N￨U￨NN￨O￨- Xj￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- Xj￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- Jij￨U￨NN￨O￨- Ij￨U￨NN￨O￨- ·￨L￨NN￨O￨- Ii￨U￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- ·￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- Ii￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Jij￨U￨NN￨O￨- Ij￨U￨NN￨O￨- ·￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- Ii￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- ·￨L￨NN￨O￨- Ii￨U￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- dt￨L￨NN￨O￨- |￨L￨SYM￨O￨- Ψ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- L￨U￨NN￨O￨- |￨L￨SYM￨O￨- Ψ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- Liouville￨U￨NN￨LOCATION￨- operator￨L￨NN￨TITLE￨- L￨U￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- generalize￨L￨VBP￨O￨- the￨L￨DT￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- susceptibles￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- spatial￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- creation￨L￨NN￨O￨- and￨L￨CC￨O￨- annihilation￨L￨NN￨O￨- operators￨L￨NNS￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- reinfection￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- including￨L￨VBG￨O￨- recovered￨L￨VBN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reinfected￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SIRI￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- ladder￨L￨NN￨O￨- operators￨L￨NNS￨O￨- constructed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Gell-Mann￨U￨NNP￨O￨- matrices￨L￨NNS￨O￨- known￨L￨VBN￨O￨- in￨L￨IN￨O￨- quantum￨L￨NN￨O￨- chromodynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- every￨L￨DT￨O￨- T￨U￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- sup￨L￨NN￨O￨- ,￨L￨,￨O￨- G￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- ZTd￨U￨NN￨O￨- ui￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dr￨L￨NN￨O￨A where￨L￨WRB￨O￨- u0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- u1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- t￨L￨NN￨O￨- ∈￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- π￨L￨NN￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- ε￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- G￨U￨NN￨O￨- ∈￨L￨NN￨O￨- C￨U￨NN￨O￨- Td￨U￨NN￨O￨- P￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- →￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- →￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ∂￨L￨SYM￨O￨- ∂￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- u0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- J￨U￨NN￨O￨- ∗￨L￨CD￨NUMBER￨- u1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- u0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∂￨L￨CD￨NUMBER￨- ∂￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- u1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- J￨U￨NN￨O￨- ∗￨L￨CD￨NUMBER￨- u1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- u0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- u1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- u0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ρ0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- u1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ρ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- following￨L￨VBG￨O￨- theorem￨L￨NN￨O￨- guarantees￨L￨VBZ￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hydrodynamic￨L￨JJ￨O￨- limit￨L￨NN￨O￨- for￨L￨IN￨O￨- large￨L￨JJ￨O￨- times￨L￨NNS￨O￨- .￨L￨.￨O￨- +Suppose￨U￨VB￨O￨- that￨L￨DT￨O￨- be￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- π￨L￨NN￨O￨- γ￨L￨NN￨O￨- ,0￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- initial￨L￨JJ￨O￨- density￨L￨NN￨O￨- profiles￨L￨NNS￨O￨- from￨L￨IN￨O￨- Td￨U￨NN￨O￨- to￨L￨TO￨O￨- NumericCitation￨U￨NNP￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- dr￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- π￨L￨NN￨O￨- γ￨L￨NN￨O￨- ,1￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dr￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- 0￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- →￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- lim￨L￨NN￨O￨- inf￨L￨NN￨O￨- for￨L￨IN￨O￨- al￨L￨NNP￨O￨- l￨L￨NN￨O￨- ε￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- π￨L￨NN￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- G￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- ZTd￨U￨NN￨O￨- ρi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dr￨L￨NN￨O￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- G￨U￨NN￨O￨- ∈￨L￨NN￨O￨- C￨U￨NN￨O￨- Td￨U￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- π￨L￨NN￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- π￨L￨NN￨O￨- γ￨L￨NN￨O￨- ,0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dr￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- whose￨L￨WP$￨O￨- hydrodynamic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- theorem￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ρ0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ρ0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ρ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- β￨L￨NN￨O￨- J￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ′￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ′￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dr￨L￨NN￨O￨A ′￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- J￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ′￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- intensity￨L￨NN￨O￨- at￨L￨IN￨O￨- r￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individual￨L￨NN￨O￨- at￨L￨IN￨O￨- r￨L￨NN￨O￨- ′￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- J￨U￨NN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- in￨L￨IN￨O￨- ∈￨L￨CD￨NUMBER￨- L￨U￨NN￨O￨- ∞￨L￨CD￨NUMBER￨- Rd￨U￨NN￨O￨- ×￨L￨CD￨NUMBER￨- Rd￨U￨NN￨O￨- ;￨L￨:￨O￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- ,￨L￨,￨O￨- homogeneus￨L￨NN￨O￨- in￨L￨IN￨O￨- space￨L￨NN￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- solution￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fol￨L￨NN￨O￨- lowing￨L￨NN￨O￨- properties￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- u0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- decreasing￨L￨VBG￨O￨- in￨L￨IN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- moreover￨L￨RB￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- u0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨SYM￨O￨- u1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- u0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- lim￨L￨NN￨O￨A t￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- u0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- u1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- satisfies￨L￨NNS￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ρ0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- β￨L￨SYM￨O￨- [￨L￨-LRB-￨O￨- ρ0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ρ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- J￨U￨NN￨O￨- ∗￨L￨CD￨NUMBER￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Theorem￨U￨NNP￨O￨- 2.2￨L￨CD￨NUMBER￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- u0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≥￨L￨CD￨NUMBER￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≥￨L￨SYM￨O￨- ρ0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ρ0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ρ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- t￨L￨NN￨O￨- ∈￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- infective￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- at￨L￨IN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- define￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A value￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- infective￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- die￨L￨VBP￨O￨- out￨L￨RP￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- o￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2dp￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- d￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dimension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- lattice￨L￨NN￨O￨- and￨L￨CC￨O￨- p￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- edge￨L￨NN￨O￨- is￨L￨VBZ￨O￨- open￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- any￨L￨DT￨O￨- ω￨L￨NN￨O￨- ∈￨L￨NN￨O￨- Yd￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- denote￨L￨VBP￨O￨A by￨L￨IN￨O￨- P￨U￨NN￨O￨- ω￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- St￨U￨NNP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- environment￨L￨NN￨O￨- on￨L￨IN￨O￨- Zd￨U￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- {￨L￨-LRB-￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ω￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- {￨L￨-LRB-￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- e￨L￨SYM￨O￨- ∈￨L￨SYM￨O￨- Ed￨U￨NNP￨O￨- λ￨L￨VBD￨O￨- the￨L￨DT￨O￨- expectation￨L￨NN￨O￨- operator￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- under￨L￨IN￨O￨- It￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- e￨L￨SYM￨O￨- ∈￨L￨SYM￨O￨- Ed￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- reasonable￨L￨JJ￨O￨- to￨L￨TO￨O￨- define￨L￨VB￨O￨- λc￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- sup￨L￨NN￨O￨- λ￨L￨NN￨O￨- :￨L￨:￨O￨- Pλ￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- It￨U￨PRP￨O￨- 6￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- ∅￨L￨NN￨O￨- ,￨L￨,￨O￨- ∀￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- say￨L￨VB￨O￨- ,￨L￨,￨O￨- λc￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- d￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrary￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- for￨L￨IN￨O￨- life￨L￨NN￨O￨- :￨L￨:￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- again￨L￨RB￨O￨- 4￨L￨CD￨NUMBER￨- Parameter￨U￨NN￨O￨- β￨L￨NN￨O￨- a￨L￨DT￨O￨- p￨L￨NN￨O￨- B￨U￨NN￨O￨- v1￨L￨NN￨O￨- v2￨L￨NN￨O￨- q1￨L￨NN￨O￨- q2￨L￨NN￨O￨- Description￨U￨NN￨O￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- Recovery￨U￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- Death￨U￨NN￨O￨- rate￨L￨NN￨O￨- Birth￨U￨NN￨O￨- rate￨L￨NN￨O￨- Fraction￨U￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨A newborns￨L￨NNS￨O￨- Vaccination￨U￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- Conversion￨U￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- Conversion￨U￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Parameters￨U￨NNP￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Abstract￨U￨JJ￨O￨- This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- SIRV￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- study￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- containing￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- 4-tiered￨L￨JJ￨O￨- population￨L￨NN￨O￨- compartment￨L￨NN￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBD￨O￨A agents￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- inserted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- editor￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- Epidemiological￨U￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- waning￨L￨VBG￨O￨- immunization￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨A population￨L￨NN￨O￨- Ewa￨U￨NNP￨PERSON￨- Grela￨U￨NNP￨PERSON￨- ·￨L￨NNP￨O￨- Michael￨U￨NNP￨PERSON￨- Stich￨U￨NNP￨PERSON￨- ·￨L￨NNP￨O￨- Amit￨U￨NNP￨PERSON￨- K￨U￨NNP￨PERSON￨- Chattopadhyay￨U￨NNP￨PERSON￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Infectious￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- routinely￨L￨RB￨O￨- highlighted￨L￨VBN￨O￨- when￨L￨WRB￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- deadly￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- or￨L￨CC￨O￨- MERS￨U￨NNP￨O￨- occur￨L￨VBP￨O￨- .￨L￨.￨O￨- +with￨L￨IN￨O￨- rate￨L￨NN￨O￨- q1￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccinated￨L￨VBN￨O￨A ones￨L￨NNS￨O￨- with￨L￨IN￨O￨- rate￨L￨NN￨O￨- q2￨L￨NN￨O￨- ,￨L￨,￨O￨- yielding￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- dS￨L￨NN￨O￨- dt￨L￨NN￨O￨- dI￨L￨NN￨O￨- dt￨L￨NN￨O￨- dR￨L￨NN￨O￨- dt￨L￨NN￨O￨- dV￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- v1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- v2S￨L￨NN￨O￨- +￨L￨CC￨O￨- q1R￨L￨NN￨O￨- +￨L￨CC￨O￨- q2V￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- pS￨L￨NN￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- aI￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- pI￨L￨NN￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- aI￨L￨NN￨O￨- −￨L￨NN￨O￨- q1R￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- pR￨L￨NN￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- v1B￨L￨NN￨O￨- +￨L￨CC￨O￨- v2S￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- q2V￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- pV￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- –￨L￨:￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- deaths￨L￨NNS￨O￨- from￨L￨IN￨O￨- causes￨L￨NNS￨O￨- unrelated￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- losing￨L￨VBG￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- constant￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- per￨L￨IN￨O￨- unity￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- being￨L￨VBG￨O￨- I￨U￨PRP￨O￨- N￨U￨NN￨O￨- t￨L￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- infective￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- constraint￨L￨NN￨O￨- :￨L￨:￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- E￨U￨NN￨O￨- S￨U￨NN￨O￨- tR￨L￨NN￨O￨- t￨L￨NN￨O￨- I￨U￨PRP￨O￨- tE￨L￨VBP￨O￨- tS￨L￨NN￨O￨- N￨U￨NN￨O￨- N￨U￨NN￨O￨- ;￨L￨:￨O￨- 0R￨L￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- implying￨L￨VBG￨O￨- directly￨L￨RB￨O￨A :￨L￨:￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- E￨U￨NN￨O￨- S￨U￨NN￨O￨- tR￨L￨NN￨O￨- t￨L￨NN￨O￨- I￨U￨PRP￨O￨- tE￨L￨VBP￨O￨- tS￨L￨NN￨O￨- ;￨L￨:￨O￨- 0R￨L￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- holds￨L￨VBZ￨O￨- directly￨L￨RB￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- since￨L￨IN￨O￨- summing-up￨L￨NN￨O￨- the￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- right-sides￨L￨NNS￨O￨- yields￨L￨NNS￨O￨- zero￨L￨VBP￨NUMBER￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Consider￨U￨VB￨O￨- the￨L￨DT￨O￨- SEIR-type￨U￨JJ￨MISC￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- tV￨L￨NN￨O￨- N￨U￨NN￨O￨- I￨U￨PRP￨O￨- N￨U￨NN￨O￨- t￨L￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- tR￨L￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- tE￨L￨NN￨O￨- I￨U￨PRP￨O￨- N￨U￨NN￨O￨- t￨L￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- tE￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- tE￨L￨NN￨O￨- t￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- tVN￨L￨NN￨O￨- t￨L￨NN￨O￨- I￨U￨PRP￨O￨- tR￨L￨VBP￨O￨- tR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨A 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- R￨U￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- constraint￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- R￨U￨NN￨O￨- :￨L￨:￨O￨- V￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- data￨L￨NNS￨O￨- consist￨L￨VBP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- adult￨L￨JJ￨O￨A hospitalization￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- and￨L￨CC￨O￨- fatalities￨L￨NNS￨O￨- recorded￨L￨VBN￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- state￨L￨NN￨O￨- hospitals￨L￨NNS￨O￨- serving￨L￨VBG￨O￨- an￨L￨DT￨O￨- adult￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- about￨L￨IN￨O￨- 1.5-2￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- fatalities￨L￨NNS￨O￨- and￨L￨CC￨O￨- hospitalizations￨L￨NNS￨O￨A occur￨L￨VBP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- shift￨L￨NN￨O￨- of￨L￨IN￨O￨- 9￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportionality￨L￨NN￨O￨- constant￨L￨NN￨O￨- is￨L￨VBZ￨O￨- δ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.0537￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- -￨L￨:￨O￨- Citation￨U￨NNP￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- hospitalizations￨L￨NNS￨O￨A and￨L￨CC￨O￨- fatalities￨L￨NNS￨O￨- being￨L￨VBG￨O￨- respectively￨L￨RB￨O￨- 869￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 46￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +A/H1N1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- -￨L￨:￨O￨- Citation￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- analyzed￨L￨VBN￨O￨A with￨L￨IN￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Exposed-Infected-Removed￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ultimate￨L￨JJ￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Western￨U￨JJ￨MISC￨- African￨U￨JJ￨NATIONALITY￨- and￨L￨CC￨O￨- identify￨L￨VB￨O￨- useful￨L￨JJ￨O￨- metrics￨L￨NNS￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- which￨L￨WDT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- affected￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- would￨L￨MD￨O￨- benefit￨L￨VB￨O￨- most￨L￨RBS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- additional￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- new￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- facilities￨L￨NNS￨O￨A or￨L￨CC￨O￨- greater￨L￨JJR￨O￨- manpower￨L￨NN￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- proper￨L￨JJ￨O￨- burials￨L￨NNS￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- hospitalization￨L￨NN￨O￨A and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- does￨L￨VBZ￨O￨- improve￨L￨VB￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- patient￨L￨NN￨O￨- ’s￨L￨POS￨O￨- chances￨L￨NNS￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- though￨L￨IN￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- between￨L￨IN￨O￨- hospitalized￨L￨VBN￨O￨- patients￨L￨NNS￨O￨- and￨L￨CC￨O￨- non-hospitalized￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- medical￨L￨JJ￨O￨- facilities￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- can￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- damage￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- include￨L￨VBP￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨- metrics￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- hospitalization￨L￨NN￨O￨A and￨L￨CC￨O￨- proper￨L￨JJ￨O￨- burial￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- hospitalization￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- with￨L￨IN￨O￨- deceased￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- parameters￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- fit￨L￨NN￨O￨A to￨L￨TO￨O￨- recent￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- deceased￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- nation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- possible￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- several￨L￨JJ￨O￨- attributes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- originating￨L￨VBG￨O￨- vertices￨L￨NNS￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- Erd￨U￨NNP￨O￨- ¨￨L￨SYM￨O￨- os-R￨L￨NN￨O￨- ´￨L￨''￨O￨- enyi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ER￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Barab￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- asi-Albert￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- BA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- random￨L￨JJ￨O￨- geometric￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- RGG￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨ORGANIZATION￨- Air￨U￨NNP￨ORGANIZATION￨- Transportation￨U￨NNP￨ORGANIZATION￨- Network￨U￨NNP￨ORGANIZATION￨- that￨L￨WDT￨O￨- comprises￨L￨VBZ￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- 500￨L￨CD￨NUMBER￨- busiest￨L￨JJS￨O￨- airports￨L￨NNS￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- inter-connections￨L￨NNS￨O￨- .￨L￨.￨O￨- +Initially￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- achieved￨L￨VBN￨O￨- considering￨L￨VBG￨O￨A the￨L￨DT￨O￨- RGG￨U￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- analytically￨L￨RB￨O￨- derive￨L￨VBP￨O￨- an￨L￨DT￨O￨- expression￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- rates￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- established￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- such￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- decay￨L￨NN￨O￨- exponentially￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- that￨L￨WDT￨O￨- separates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- accessibility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- network￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ;￨L￨:￨O￨- epidemic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- ;￨L￨:￨O￨- random￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨A ,￨L￨,￨O￨- networks￨L￨NNS￨O￨- I.￨U￨NN￨O￨- +Our￨U￨PRP$￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- general￨L￨JJ￨TITLE￨- Poisson￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- constant-rate￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- stochastically￨L￨RB￨O￨- exact￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- multiple￨L￨JJ￨O￨- orders￨L￨NNS￨O￨- of￨L￨IN￨O￨- magnitude￨L￨NN￨O￨- faster￨L￨RBR￨O￨A than￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- rejection￨L￨NN￨O￨- sampling￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- empirical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨- is￨L￨VBZ￨O￨- here￨L￨RB￨O￨- typically￨L￨RB￨O￨- from￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 100￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- faster￨L￨JJR￨O￨A than￨L￨IN￨O￨- rejection￨L￨NN￨O￨- sampling￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- fixed￨L￨JJ￨O￨- point￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- remarkably￨L￨RB￨O￨- simple￨L￨JJ￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- non-trivial￨L￨JJ￨O￨- fixed￨L￨JJ￨O￨- point￨L￨NN￨O￨- always￨L￨RB￨O￨- exists￨L￨VBZ￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- feature￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- city￨L￨NN￨O￨A irrespective￨L￨RB￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +J.￨U￨NNP￨O￨- McKane1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- 1Centro￨L￨NNP￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- da￨L￨NNP￨O￨A Mat￨U￨NNP￨O￨- ´￨L￨POS￨O￨- eria￨L￨NN￨O￨- Condensada￨U￨NN￨O￨- and￨L￨CC￨O￨- Departamento￨U￨NNP￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- ,￨L￨,￨O￨- Faculdade￨U￨NNP￨O￨- de￨L￨IN￨O￨- Ciˆencias￨U￨NNP￨O￨- da￨L￨NNP￨O￨- Universidade￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Lisboa￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- P-1649-003￨U￨NNP￨O￨- Lisboa￨U￨NNP￨ORGANIZATION￨- Codex￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Portugal￨U￨NNP￨COUNTRY￨- 2Theoretical￨L￨NNP￨O￨- Physics￨U￨NN￨O￨- Division￨U￨NNP￨O￨- ,￨L￨,￨O￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Astronomy￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Manchester￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Manchester￨U￨NNP￨ORGANIZATION￨- M13￨U￨NNP￨O￨- 9PL￨L￨NN￨O￨- ,￨L￨,￨O￨- United￨U￨NNP￨COUNTRY￨- Kingdom￨U￨NNP￨COUNTRY￨- We￨U￨PRP￨O￨- carry￨L￨VBP￨O￨- out￨L￨RP￨O￨- an￨L￨DT￨O￨- analytic￨L￨JJ￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- cities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Starting￨U￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- valid￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- city￨L￨NN￨O￨A is￨L￨VBZ￨O￨- infinite￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- recovered￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- fjk￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- from￨L￨IN￨O￨- city￨L￨NN￨O￨A k￨L￨NN￨O￨- commute￨L￨NN￨O￨- to￨L￨TO￨O￨- city￨L￨NN￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- infect￨L￨VB￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- ,￨L￨,￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- opinion￨L￨NN￨O￨A formation￨L￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- usually￨L￨RB￨O￨- tend￨L￨VBP￨O￨- to￨L￨TO￨O￨- rewire￨L￨VB￨O￨- or￨L￨CC￨O￨- break￨L￨VB￨O￨- their￨L￨PRP$￨O￨- links￨L￨NNS￨O￨- with￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- opinions￨L￨NNS￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- fragmentation￨L￨NN￨O￨- into￨L￨IN￨O￨- components￨L￨NNS￨O￨- or￨L￨CC￨O￨- clusters￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- all￨L￨DT￨O￨- members￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- opinion￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Similarly￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- widely￨L￨RB￨O￨- studied￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- adaptive￨L￨JJ￨O￨A processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- intermittent￨L￨JJ￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A strategy￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A strategy￨L￨NN￨O￨- there￨L￨RB￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- cutoff￨L￨NN￨O￨- threshold￨L￨NN￨O￨- σc￨L￨NN￨O￨- beyond￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- phase￨L￨NN￨O￨- disappears￨L￨VBZ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- local￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- interrupts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- σ￨L￨NN￨O￨- and￨L￨CC￨O￨- restores￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- time￨L￨NN￨O￨- tb￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +a￨L￨DT￨O￨- generalization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- obtained￨L￨VBN￨O￨- with￨L￨IN￨O￨- quenched￨L￨VBN￨O￨- mean-field￨L￨JJ￨O￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- static￨L￨JJ￨O￨A PACS￨U￨NNS￨O￨- numbers￨L￨NNS￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- annealed￨L￨JJ￨O￨- network￨L￨NN￨O￨- regime￨L￨NN￨O￨A when￨L￨WRB￨O￨- the￨L￨DT￨O￨- rewiring￨L￨NN￨O￨- is￨L￨VBZ￨O￨- much￨L￨JJ￨O￨- faster￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ω￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +ciency￨L￨NN￨O￨- of￨L￨IN￨O￨- prompt￨L￨JJ￨O￨- quarantine￨L￨NN￨O￨A measures￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- Takehisa￨U￨NNP￨PERSON￨- Hasegawa1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- ∗￨L￨NN￨O￨- and￨L￨CC￨O￨- Ko￨U￨NNP￨PERSON￨- ji￨L￨NN￨O￨- Nemoto2￨U￨NN￨O￨- ,￨L￨,￨O￨- †￨L￨SYM￨O￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Mathematics￨U￨NNS￨O￨- and￨L￨CC￨O￨- Informatics￨U￨NNS￨O￨- ,￨L￨,￨O￨- Ibaraki￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 2-1-1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Bunkyo￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Mito￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 310-8512￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- 2Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- Hokkaido￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Kita￨U￨NNP￨PERSON￨- 10￨L￨CD￨NUMBER￨- Nishi￨U￨NNP￨ORGANIZATION￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kita-ku￨U￨NN￨O￨- ,￨L￨,￨O￨- Sapporo￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Hokkaido￨U￨NNP￨O￨- ,￨L￨,￨O￨- 060-0810￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- This￨U￨DT￨O￨- study￨L￨NN￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- investigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- manner￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- prompt￨L￨JJ￨O￨- quarantine￨L￨NN￨O￨- measure￨L￨NN￨O￨- suppresses￨L￨VBZ￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- simulations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- prompt￨L￨JJ￨O￨- quarantine￨L￨NN￨O￨A measure￨L￨NN￨O￨- outperforms￨L￨VBZ￨O￨- random￨L￨JJ￨O￨- and￨L￨CC￨O￨- acquaintance￨L￨NN￨O￨- preventive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- analytically￨L￨RB￨O￨- derived￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- quarantine￨L￨NN￨O￨A measure￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- findings￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- prompt￨L￨JJ￨O￨- executions￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- quarantines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- containing￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simple￨L￨JJ￨O￨- and￨L￨CC￨O￨- ideal￨L￨JJ￨O￨- quarantine￨L￨NN￨O￨A measure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- detected￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- immediately￨L￨RB￨O￨- after￨L￨IN￨O￨- it￨L￨PRP￨O￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- detected￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- promptly￨L￨RB￨O￨- isolated￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- quarantine￨L￨NN￨O￨A in￨L￨IN￨O￨- suppressing￨L￨VBG￨O￨- a￨L￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- tested￨L￨VBN￨O￨- in￨L￨IN￨O￨- random￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- and￨L￨CC￨O￨- uncorrelated￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- note￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- comment￨L￨VB￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- communicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- Cator￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Van￨U￨NNP￨PERSON￨- Mieghem￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- stated￨L￨VBN￨O￨A that￨L￨IN￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- any￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- non-negative￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Markovian￨U￨JJ￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- review￨L￨VBP￨O￨- the￨L￨DT￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨ORGANIZATION￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- through￨L￨IN￨O￨- its￨L￨PRP$￨O￨- graphical￨L￨JJ￨O￨- construction￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- briefly￨L￨VBP￨O￨- present￨L￨JJ￨DATE￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- idea￨L￨NN￨O￨- behind￨L￨IN￨O￨- the￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- construction￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- fail￨L￨VBP￨O￨- into￨L￨IN￨O￨- try￨L￨NN￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- the￨L￨DT￨O￨- FKG￨U￨NN￨O￨- inequality￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Rev.￨U￨NNP￨TITLE￨- E￨U￨NNP￨O￨- 89￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 052802￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- stated￨L￨VBD￨O￨A that￨L￨IN￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- any￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- non-negative￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Markovian￨U￨JJ￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- counter-example￨L￨NN￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- graph￨L￨NN￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- nodal￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- negatively￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨A Markovian￨U￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- positively￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- if￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- encoding￨L￨VBG￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- arguments￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- rely￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- graphical￨L￨JJ￨O￨- construction￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- elegant￨L￨JJ￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- FKG￨U￨NN￨O￨- inequality￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Individual-based￨U￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨A Luis￨U￨NNP￨PERSON￨- E￨U￨NNP￨O￨- C￨U￨NNP￨O￨- Rocha￨U￨NNP￨O￨- ∗￨L￨NNP￨O￨- Department￨U￨NNP￨O￨- of￨L￨IN￨O￨- Mathematics￨U￨NNPS￨O￨- and￨L￨CC￨O￨- naXys￨L￨NNPS￨O￨- ,￨L￨,￨O￨- Universit￨U￨NNP￨O￨- ´￨L￨POS￨O￨- e￨L￨SYM￨O￨- de￨L￨FW￨O￨- Namur￨U￨FW￨LOCATION￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- Rempart￨U￨NNP￨ORGANIZATION￨- de￨L￨FW￨ORGANIZATION￨- la￨L￨FW￨ORGANIZATION￨- Vierge￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- B-5000￨U￨NNP￨O￨- Namur￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Belgium￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Karolinska￨U￨NNP￨ORGANIZATION￨- Institutet￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 18A￨L￨NNP￨O￨- Tomtebodav￨U￨NNP￨O￨- ¨￨L￨NN￨O￨- agen￨L￨NN￨O￨- ,￨L￨,￨O￨- S-17177￨U￨NN￨O￨- Stockholm￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Sweden￨U￨NNP￨COUNTRY￨- Naoki￨U￨NNP￨PERSON￨- Masuda￨U￨NNP￨PERSON￨- Department￨U￨NNP￨O￨- of￨L￨IN￨O￨- Engineering￨U￨NNP￨O￨- Mathematics￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Bristol￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Woodland￨U￨NNP￨CITY￨- Road￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Bristol￨U￨NNP￨CITY￨- BS8￨U￨NN￨O￨- 1UB￨L￨NN￨O￨- ,￨L￨,￨O￨- United￨U￨NNP￨COUNTRY￨- Kingdom￨U￨NNP￨COUNTRY￨- The￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- often￨L￨RB￨O￨- occur￨L￨VBP￨O￨- on￨L￨IN￨O￨- comparable￨L￨JJ￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- arbitrary￨L￨JJ￨O￨A dynamic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- real-life￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨A network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- overestimates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- but￨L￨CC￨O￨- underestimates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- super-spreading￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +potential￨L￨JJ￨O￨- These￨U￨DT￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨A are￨L￨VBP￨O￨- characterised￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- connectivity￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- timings￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- events3￨L￨NN￨O￨- ,5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- π￨L￨NN￨O￨- is￨L￨VBZ￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- effects￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- requirement￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infecting￨L￨VBG￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- recover￨L￨VB￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- reinfection￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- simultaneously￨L￨RB￨O￨- try￨L￨VBP￨O￨- to￨L￨TO￨O￨- reinfect￨L￨VB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- ancestor￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A Roni￨U￨NNP￨PERSON￨- Parshani￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Shai￨U￨NNP￨PERSON￨- Carmi￨U￨NNP￨PERSON￨- ,1￨L￨NN￨O￨- and￨L￨CC￨O￨- Shlomo￨U￨NNP￨PERSON￨- Havlin1￨U￨NNP￨O￨- 1Minerva￨L￨NNP￨O￨- Center￨U￨NNP￨O￨- &￨L￨CC￨O￨- Department￨U￨NNP￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- Bar-Ilan￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Ramat￨U￨NNP￨ORGANIZATION￨- Gan￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Israel￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- August￨U￨NNP￨DATE￨- 27￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- expression￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- rc￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infectious-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- N￨U￨NN￨O￨- network￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- initially￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- they￨L￨PRP￨O￨- currently￨L￨RB￨DATE￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- might￨L￨MD￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- later￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- for￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- obtain￨L￨VB￨O￨- rc￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨VBP￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- reinfection￨L￨NN￨O￨A ,￨L￨,￨O￨- π￨L￨NN￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- reinfect￨L￨VB￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- that￨L￨WDT￨O￨- had￨L￨VBD￨O￨- earlier￨L￨JJR￨O￨- infected￨L￨JJ￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- was￨L￨VBD￨O￨- recently￨L￨RB￨DATE￨- demonstrated￨L￨VBN￨O￨- for￨L￨IN￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- couple￨L￨NN￨O￨- recombination￨L￨NN￨O￨- can￨L￨MD￨O￨- compensate￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- extent￨L￨NN￨O￨- the￨L￨DT￨O￨- instantaneous￨L￨JJ￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ’s￨L￨POS￨O￨- interaction￨L￨NN￨O￨- pattern￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- possibly￨L￨RB￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- otherwise￨L￨RB￨O￨- confined￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- recombination￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- couples￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ’s￨L￨POS￨O￨- interaction￨L￨NN￨O￨- pattern￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- specific￨L￨NN￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- never￨L￨RB￨O￨- propagates￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- where￨L￨WRB￨O￨- sexual￨L￨JJ￨O￨- partnership￨L￨NN￨O￨A is￨L￨VBZ￨O￨- confined￨L￨VBN￨O￨- within￨L￨IN￨O￨- stable￨L￨JJ￨O￨- couples￨L￨NNS￨O￨- or￨L￨CC￨O￨- small￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Zanette1￨U￨NN￨O￨- ∗￨L￨SYM￨O￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infectious￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- an￨L￨DT￨O￨- agent￨L￨NN￨O￨- population￨L￨NN￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- instant￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- fully￨L￨RB￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- couples￨L￨NNS￨O￨- of￨L￨IN￨O￨- agents￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- couple￨L￨NN￨O￨- recombination￨L￨NN￨O￨- can￨L￨MD￨O￨- compensate￨L￨VB￨O￨- the￨L￨DT￨O￨- instantaneous￨L￨JJ￨O￨- disconnection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- pattern￨L￨NN￨O￨A and￨L￨CC￨O￨- thus￨L￨RB￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infective-Removed￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- random￨L￨JJ￨O￨- vertex￨L￨NN￨O￨A weights￨L￨NNS￨O￨- on￨L￨IN￨O￨- Erd˝os￨U￨NNS￨O￨- -￨L￨:￨O￨- R´enyi￨U￨NN￨O￨- graph￨L￨NN￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Law￨U￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- random￨L￨JJ￨O￨- vertex￨L￨NN￨O￨A weights￨L￨NNS￨O￨- on￨L￨IN￨O￨- Erd˝os￨U￨NNS￨O￨- -￨L￨:￨O￨- R´enyi￨U￨NN￨O￨- graph￨L￨NN￨O￨- Xiaofeng￨U￨NNP￨PERSON￨- Xue￨U￨NNP￨PERSON￨- ∗￨L￨NNP￨O￨- Beijing￨U￨NNP￨CITY￨- Jiaotong￨U￨NNP￨LOCATION￨- University￨U￨NNP￨LOCATION￨- Abstract￨U￨NNP￨LOCATION￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- random￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- weights￨L￨NNS￨O￨- on￨L￨IN￨O￨- Erd˝os￨U￨NNS￨O￨- -￨L￨:￨O￨- R´enyi￨U￨NN￨O￨- graph￨L￨NN￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- give￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- deterministic￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- HS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ψt￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- HV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ψt￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- t￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- HS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ψt￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- and￨L￨CC￨O￨- HV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ψt￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨- vertex￨L￨NN￨O￨A to￨L￨TO￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- susceptible￨L￨JJ￨O￨- neighbor￨L￨NN￨O￨- at￨L￨IN￨O￨- moment￨L￨NN￨O￨- t￨L￨NN￨O￨- as￨L￨IN￨O￨- n￨L￨NN￨O￨- grows￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- at￨L￨IN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- removed￨L￨VBN￨O￨- vertex￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Bernoulli￨U￨JJ￨MISC￨- distribution￨L￨NN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- arbitrary￨L￨JJ￨O￨A time-independent￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨- passing￨L￨VBG￨O￨- formalism￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- pair-based￨L￨JJ￨O￨- moment￨L￨NN￨O￨- closure￨L￨NN￨O￨- equations￨L￨NNS￨O￨- also￨L￨RB￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- rigorous￨L￨JJ￨O￨- lower￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- at￨L￨IN￨O￨- all￨L￨DT￨O￨- times￨L￨NNS￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- Karrer￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Newman￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ordered-pairwise￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- functions￨L￨NNS￨O￨- fij￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- ∀￨L￨SYM￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- A￨U￨DT￨O￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- j￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨- to￨L￨TO￨O￨- i￨L￨FW￨O￨- within￨L￨IN￨O￨- time￨L￨NN￨O￨A period￨L￨NN￨O￨A t￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- fij￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dτ￨L￨NN￨O￨- .￨L￨.￨O￨- +SUSCEPTIBLE-INFECTED-RECOVERED￨U￨JJ￨O￨- DYNAMICS￨U￨NN￨O￨- ON￨U￨IN￨O￨- TREE￨U￨NN￨O￨- NETWORKS￨U￨NNS￨O￨- We￨U￨PRP￨O￨- define￨L￨VBP￨O￨A an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- directed￨L￨VBN￨O￨- graph￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- digraph￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- D￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- V￨U￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- arc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨NN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- contacts￨L￨NNS￨O￨- to￨L￨TO￨O￨- j￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- V￨U￨NN￨O￨- is￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- receives￨L￨VBZ￨O￨- an￨L￨DT￨O￨- The￨U￨DT￨O￨- time￨L￨NN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- takes￨L￨VBZ￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- from￨L￨IN￨O￨- i￨L￨FW￨O￨- permanently￨L￨RB￨O￨- cease￨L￨VB￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- distributed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- individual-specific￨L￨JJ￨O￨- probability￨L￨NN￨O￨A density￨L￨NN￨O￨A function￨L￨NN￨O￨- ri￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- will￨L￨MD￨O￨- also￨L￨RB￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- fij￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- hij￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- ∞￨L￨CD￨NUMBER￨- rj￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- ′￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dτ￨L￨NN￨O￨- ′￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- hij￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dτ￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- j￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- any￨L￨DT￨O￨- contact￨L￨NN￨O￨- to￨L￨TO￨O￨- i￨L￨FW￨O￨- within￨L￨IN￨O￨- time￨L￨NN￨O￨A period￨L￨NN￨O￨A t￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- seed￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- namely￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- patch￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- cycle￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- varying￨L￨VBG￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- population￨L￨NN￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- randomly￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- refractory￨L￨JJ￨O￨A and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- sustained￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- facilitates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- de-synchronization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- phases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- observe￨L￨VBP￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- uniform￨L￨JJ￨O￨- ,￨L￨,￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A progression￨L￨NN￨O￨A ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- seed￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- persist￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- persistent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- patch￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A progression￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- another￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- any￨L￨DT￨O￨- instant￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- τi￨L￨NNS￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨SYM￨O￨- τI￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- at￨L￨IN￨O￨- site￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- ;￨L￨:￨O￨- then￨L￨RB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- phase￨L￨NN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- refractory￨L￨JJ￨O￨A stage￨L￨NN￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- witnessed￨L￨VBN￨O￨- a￨L￨DT￨O￨- tremendous￨L￨JJ￨O￨- advance￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- eigenvalues￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- curing￨L￨VBG￨O￨- policies￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cut-width￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- optimization￨L￨NN￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨A epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- new￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- frameworks￨L￨NNS￨O￨- for￨L￨IN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- over￨L￨IN￨O￨- multilayer￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- time-varying￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- adaptive￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- networked￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- resorting￨L￨VBG￨O￨- to￨L￨TO￨O￨- mean-field￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- convex￨L￨NN￨O￨- optimization￨L￨NN￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨A the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- accumulated￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +3￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 6￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- This￨U￨DT￨O￨- paper￨L￨NN￨O￨- introduces￨L￨VBZ￨O￨- a￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨A and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- question￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- interest￨L￨NN￨O￨- :￨L￨:￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- resources￨L￨NNS￨O￨- that￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- partial￨L￨JJ￨O￨- protection￨L￨NN￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- should￨L￨MD￨O￨- one￨L￨PRP￨NUMBER￨- distribute￨L￨VB￨O￨- these￨L￨DT￨O￨- resources￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- cost-optimal￨L￨JJ￨O￨- manner￨L￨NN￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨A the￨L￨DT￨O￨- spread￨L￨NN￨O￨- ?￨L￨.￨O￨- +Most￨U￨JJS￨O￨- existing￨L￨VBG￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- healthy￨L￨JJ￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GA￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- only￨L￨RB￨O￨- steps￨L￨VBZ￨O￨- that￨L￨IN￨O￨- change￨L￨NN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- numerical￨L￨JJ￨O￨- recipes￨L￨NNS￨O￨- and￨L￨CC￨O￨- describe￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- computer￨L￨NN￨O￨- implementations￨L￨NNS￨O￨- for￨L￨IN￨O￨- statistically￨L￨RB￨O￨- exact￨L￨JJ￨O￨- and￨L￨CC￨O￨- computationally￨L￨RB￨O￨- efficient￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- generic￨L￨JJ￨O￨- Markovian￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- aiming￨L￨VBG￨O￨- at￨L￨IN￨O￨- highly￨L￨RB￨O￨A heterogeneous￨L￨JJ￨O￨A and￨L￨CC￨O￨- large￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transitions￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- occur￨L￨VBP￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- automata￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- :￨L￨:￨O￨- •￨L￨SYM￨O￨- If￨U￨IN￨O￨- individual￨L￨JJ￨O￨- j￨L￨NN￨O￨- is￨L￨VBZ￨O￨- Infected￨U￨JJ￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- Susceptible￨U￨JJ￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- α￨L￨NN￨O￨- ;￨L￨:￨O￨- •￨L￨SYM￨O￨- If￨U￨IN￨O￨- ,￨L￨,￨O￨- otherwise￨L￨RB￨O￨- ,￨L￨,￨O￨- individual￨L￨JJ￨O￨- j￨L￨NN￨O￨- is￨L￨VBZ￨O￨- Susceptible￨U￨JJ￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- λ￨L￨VBP￨O￨- it￨L￨PRP￨O￨- becomes￨L￨VBZ￨O￨- Infected￨U￨JJ￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- Infected￨U￨JJ￨O￨- individual￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- ;￨L￨:￨O￨- •￨L￨SYM￨O￨- Each￨U￨DT￨O￨- individual￨L￨JJ￨O￨- j￨L￨NN￨O￨- starts￨L￨VBZ￨O￨- with￨L￨IN￨O￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- λ0￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- λ￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- times￨L￨NNS￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- was￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- before￨L￨RB￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- j￨L￨NN￨O￨- performed￨L￨VBD￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- I￨U￨PRP￨O￨- →￨L￨VBP￨O￨- S￨U￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- time￨L￨NN￨O￨A step￨L￨NN￨O￨A t￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- updated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ǫ￨L￨NN￨O￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- ǫ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- less￨L￨RBR￨O￨- than￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- that￨L￨WDT￨O￨- controls￨L￨VBZ￨O￨- the￨L￨DT￨O￨- decaying￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- regular￨L￨JJ￨O￨- lattices￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- regime￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- above-mentioned￨L￨JJ￨O￨- modification￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- undergoes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- at￨L￨IN￨O￨- critical￨L￨JJ￨O￨A values￨L￨NNS￨O￨- ǫc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- l￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- separating￨L￨VBG￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- reaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ǫ￨L￨NN￨O￨- >￨L￨JJR￨O￨- ǫc￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- spread￨L￨VBN￨O￨- out￨L￨RP￨O￨- (￨L￨-LRB-￨O￨- ǫ￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- ǫc￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- decaying￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- j￨L￨NN￨O￨- that￨L￨WDT￨O￨- recovers￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- state￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- time￨L￨NN￨O￨A step￨L￨NN￨O￨A t￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- his￨L￨PRP$￨O￨- probability￨L￨NN￨O￨- to￨L￨TO￨O￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- again￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- λj￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ǫ￨L￨NN￨O￨- λj￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- ǫ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- upper￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- Critical￨U￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time-dependent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A 3￨L￨CD￨NUMBER￨- dimension￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +3￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Critical￨U￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time-dependent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Phase￨U￨NN￨O￨- transition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- random￨L￨JJ￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- on￨L￨IN￨O￨- complete￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- Xiaofeng￨U￨NNP￨O￨- Xue￨U￨NNP￨O￨- ∗￨L￨NNP￨O￨- Beijing￨U￨NNP￨ORGANIZATION￨- Jiaotong￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Abstract￨U￨NNP￨ORGANIZATION￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infective-Removed￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- random￨L￨JJ￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- on￨L￨IN￨O￨- complete￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- Cn￨U￨NN￨MISC￨- with￨L￨IN￨O￨- n￨L￨NN￨O￨- vertices￨L￨NNS￨O￨A .￨L￨.￨O￨- +When￨U￨WRB￨O￨- λ￨L￨NN￨O￨- <￨L￨JJR￨O￨- λc￨L￨CD￨NUMBER￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- ever￨L￨RB￨O￨- been￨L￨VBN￨O￨- infective￨L￨JJ￨O￨- converges￨L￨NNS￨O￨- to￨L￨TO￨O￨- 0￨L￨CD￨NUMBER￨- weakly￨L￨RB￨O￨- as￨L￨IN￨O￨- n￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- while￨L￨IN￨O￨- when￨L￨WRB￨O￨- λ￨L￨NN￨O￨- >￨L￨JJR￨O￨- λc￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exist￨L￨VBP￨O￨- c￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- n￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- b￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- ever￨L￨RB￨O￨- been￨L￨VBN￨O￨- infective￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- c￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- ξ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vertex￨L￨NN￨O￨- j￨L￨NN￨O￨- while￨L￨IN￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- weight￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- edge￨L￨NN￨O￨A e￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- any￨L￨DT￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- integer￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- i￨L￨FW￨O￨- ≤￨L￨FW￨O￨- n￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- denote￨L￨VBP￨O￨- by￨L￨IN￨O￨- ηt￨L￨NN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- at￨L￨IN￨O￨- moment￨L￨NN￨O￨A t￨L￨NN￨O￨- and￨L￨CC￨O￨- ηt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spin￨L￨NN￨O￨- on￨L￨IN￨O￨- i￨L￨FW￨O￨- at￨L￨IN￨O￨- moment￨L￨NN￨O￨- t.￨L￨IN￨O￨- +For￨U￨IN￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- i￨L￨FW￨O￨- 6￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- j￨L￨NN￨O￨- ≤￨L￨NN￨O￨- n￨L￨NN￨O￨- −￨L￨VBG￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- e￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- denote￨L￨VB￨O￨- the￨L￨DT￨O￨- edge￨L￨NN￨O￨A connecting￨L￨VBG￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- j￨L￨FW￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- quite￨L￨RB￨O￨- well￨L￨RB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- periods￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- captures￨L￨VBZ￨O￨A the￨L￨DT￨O￨- essentials￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- considered￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- involve￨L￨VBP￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨A properties￨L￨NNS￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- quasi-stationary￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- using￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SEIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- two-dimensional￨L￨JJ￨O￨- Watts-Strogatz-type￨U￨JJ￨O￨- dynamical￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- finally￨L￨RB￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- goodness￨L￨NN￨O￨- and￨L￨CC￨O￨- limitations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- parameters￨L￨NNS￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨A studied￨L￨VBN￨O￨A .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- several￨L￨JJ￨O￨- publications￨L￨NNS￨O￨- ,￨L￨,￨O￨- always￨L￨RB￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- very￨L￨RB￨O￨- few￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Measles￨U￨NNP￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- exception￨L￨NN￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- parsimonious￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- accepted￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- urban￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- adequately￨L￨RB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- seasonally￨L￨RB￨O￨A forced￨L￨VBN￨O￨- well-mixed￨L￨JJ￨O￨- susceptible-infective-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- susceptibleexposedinfective-recovered￨L￨JJ￨O￨- based￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compare￨L￨VBP￨O￨- five￨L￨NN￨O￨- minimal￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- seasonally￨L￨RB￨O￨A forced￨L￨VBN￨O￨- ,￨L￨,￨O￨- well-mixed￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- susceptible-infective-recovered￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- power￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- seasonally￨L￨RB￨O￨A forced￨L￨VBN￨O￨- well-mixed￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- modifications￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- reflect￨L￨VBP￨O￨- different￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- induced￨L￨VBD￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- successful￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- sets￨L￨NNS￨O￨A of￨L￨IN￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- records￨L￨NNS￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- closed￨L￨VBN￨O￨- the￨L￨DT￨O￨- discussion￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- determinants￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- power￨L￨NN￨O￨A spectra￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- output￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- characterize￨L￨VBP￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- term￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- provably￨L￨RB￨O￨- guarantees￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- rate￨L￨NN￨O￨- have￨L￨VBP￨O￨- only￨L￨RB￨O￨- been￨L￨VBN￨O￨- established￨L￨VBN￨O￨- for￨L￨IN￨O￨- tree￨L￨NN￨O￨- networks￨L￨NNS￨O￨- except￨L￨IN￨O￨- ∗￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- ‡￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- paper￨L￨NN￨O￨- by￨L￨IN￨O￨- Zhu￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ying￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- Short-Fat￨U￨NNP￨O￨- Tree￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SFT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- algorithm￨L￨NN￨O￨- and￨L￨CC￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- single-source￨L￨NN￨O￨- ,￨L￨,￨O￨- homogeneous￨L￨JJ￨O￨- Independent-Cascade￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- IC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- SFT￨U￨NN￨O￨- locates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- source￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- Erd￨U￨NNP￨O￨- ˝os￨L￨SYM￨O￨- -￨L￨:￨O￨- Rényi￨U￨NN￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- asymptotically￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- increases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- snapshot￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- turns￨L￨VBZ￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- candidate￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- to￨L￨TO￨O￨- select￨L￨VB￨O￨- source￨L￨NN￨O￨- candidates￨L￨NNS￨O￨- from￨L￨IN￨O￨- unobserved￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- but￨L￨CC￨O￨- only￨L￨RB￨O￨- use￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- computing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- eccentricity￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- algorithm￨L￨NN￨O￨- first￨L￨JJ￨O￨- extracts￨L￨NNS￨O￨- a￨L￨DT￨O￨- subgraph￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- candidate￨L￨NN￨TITLE￨- select￨L￨JJ￨O￨- ion￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- that￨L￨WDT￨O￨- selects￨L￨VBZ￨O￨- source￨L￨NN￨O￨- candidates￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- neighborhoods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- partial￨L￨JJ￨O￨- snapshot￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sources￨L￨NNS￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- report￨L￨VB￨O￨- their￨L￨PRP$￨O￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- as￨L￨IN￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- form￨L￨VB￨O￨- a￨L￨DT￨O￨- connected￨L￨JJ￨O￨- component￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- incorporates￨L￨VBZ￨O￨- individual￨L￨JJ￨O￨- memory￨L￨NN￨O￨A of￨L￨IN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- entity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- rumor￨L￨NN￨O￨- or￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- variable￨L￨JJ￨O￨- magnitudes￨L￨NNS￨O￨- of￨L￨IN￨O￨- exposure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dose￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- belong￨L￨VB￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- these￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- memory￨L￨NN￨O￨A length￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- exposures￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- simulation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- recover￨L￨VB￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- immediately￨L￨RB￨O￨- become￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- again￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- analogous￨L￨JJ￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +DESCRIPTON￨U￨NNP￨O￨- OF￨U￨IN￨O￨- MODEL￨U￨NNP￨TITLE￨- Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- brief￨L￨JJ￨O￨A elsewhere￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- comprises￨L￨VBZ￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- occupy￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- what￨L￨WP￨O￨- follows￨L￨VBZ￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- notation￨L￨NN￨O￨- :￨L￨:￨O￨- •￨L￨SYM￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- •￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- represent￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- from￨L￨IN￨O￨- strain￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- strain￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- •￨L￨SYM￨O￨- 12￨L￨CD￨NUMBER￨A represents￨L￨VBZ￨O￨- co-infected￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- •￨L￨SYM￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- •￨L￨SYM￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birthrate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- •￨L￨SYM￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- •￨L￨SYM￨O￨- •￨L￨SYM￨O￨- •￨L￨SYM￨O￨- •￨L￨SYM￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- strain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- coinfection￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- strain￨L￨NN￨O￨- getting￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- co-infected￨L￨JJ￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- follows￨L￨VBZ￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- lose￨L￨VBP￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- stability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- picture￨L￨NN￨O￨- drastically￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- small￨L￨JJ￨O￨- perturbations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- case￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- relations￨L￨NNS￨O￨- between￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- denote￨L￨VBP￨O￨- with￨L￨IN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- )￨L￨-RRB-￨O￨- ⋅￨L￨RB￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- +￨L￨CC￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ⎛￨L￨CD￨NUMBER￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎝￨L￨SYM￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- )￨L￨-RRB-￨O￨- 3￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ⎞￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎠￨L￨SYM￨O￨- =￨L￨SYM￨O￨- ⎛￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎝￨L￨SYM￨O￨- −￨L￨SYM￨O￨- +￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ⎞￨L￨CD￨NUMBER￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎠￨L￨SYM￨O￨- =￨L￨SYM￨O￨- ⎛￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎝￨L￨SYM￨O￨- −￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 3￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 2￨L￨CD￨DATE￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ⎞￨L￨CD￨NUMBER￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎠￨L￨SYM￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- ⎛￨L￨CD￨NUMBER￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎜￨L￨SYM￨O￨- ⎝￨L￨SYM￨O￨- ⎞￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎟￨L￨SYM￨O￨- ⎠￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 4￨L￨CD￨NUMBER￨- Samia￨U￨NNP￨PERSON￨- Ghersheen￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Vladimir￨U￨NNP￨PERSON￨- Kozlov￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Vladimir￨U￨NNP￨PERSON￨- Tkachev￨U￨NNP￨PERSON￨- Uno￨U￨NNP￨PERSON￨- Wennergren￨U￨NNP￨PERSON￨- A￨U￨NNP￨O￨- point￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- an￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- The￨U￨DT￨O￨- following￨L￨JJ￨O￨- ratios￨L￨NNS￨O￨- play￨L￨VBP￨O￨- an￨L￨DT￨O￨- essential￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨SYM￨O￨- ≤￨L￨SYM￨O￨- 3￨L￨LS￨NUMBER￨- .￨L￨.￨O￨- +3￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Samia￨U￨NNP￨PERSON￨- Ghersheen￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Vladimir￨U￨NNP￨PERSON￨- Kozlov￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Vladimir￨U￨NNP￨PERSON￨- Tkachev￨U￨NNP￨PERSON￨- Uno￨U￨NNP￨O￨- Wennergren￨U￨NNP￨O￨- The￨U￨NNP￨O￨- corresponding￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- ODE￨U￨NN￨O￨- system￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- ߰￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- 12￨L￨CD￨NUMBER￨A −￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ߰￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 12￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ߰￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- 12￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ߰￨L￨CD￨NUMBER￨- 12￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ߰￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- 3￨L￨CD￨NUMBER￨- 12￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- ߰￨L￨SYM￨O￨- 4￨L￨LS￨NUMBER￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- to￨L￨TO￨O￨- SIS￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- Epidemic￨U￨JJ￨O￨- processes￨L￨NNS￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- approximately￨L￨RB￨O￨- describe￨L￨VB￨O￨- an￨L￨DT￨O￨- amazingly￨L￨RB￨O￨- large￨L￨JJ￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- digital￨L￨JJ￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- message￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- on-line￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- emotion￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- failure￨L￨NN￨O￨- or￨L￨CC￨O￨- an￨L￨DT￨O￨- innovation￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- competing￨L￨VBG￨O￨- opinions￨L￨NNS￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- universal￨L￨JJ￨O￨- curve￨L￨NN￨O￨- also￨L￨RB￨O￨- applies￨L￨VBZ￨O￨- to￨L￨TO￨O￨- various￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- Susceptible-Infected-Removed￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- processes￨L￨NNS￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- both￨L￨DT￨O￨- homogenous￨L￨JJ￨O￨- and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- characteristics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- curing￨L￨VBG￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- disconnected￨L￨VBD￨O￨- graphs￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- SIS￨U￨NN￨O￨- processes￨L￨NNS￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- self-infections￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- dates￨L￨NNS￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- great￨L￨JJ￨O￨- Bernoulli￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- graph￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- process￨L￨NN￨O￨- was￨L￨VBD￨O￨- only￨L￨RB￨O￨- initiated￨L￨VBN￨O￨- 15￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- ago￨L￨RB￨DATE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- seminal￨L￨JJ￨O￨- paper￨L￨NN￨O￨- of￨L￨IN￨O￨- PastorSatorras￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Vespignani￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relatively￨L￨RB￨O￨- new￨L￨JJ￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- science￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- graph￨L￨NN￨O￨- .￨L￨.￨O￨- +Key￨U￨NN￨O￨- words￨L￨NNS￨O￨- :￨L￨:￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- migration￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- ;￨L￨:￨O￨- ourbreak￨L￨JJ￨O￨- time￨L￨NN￨O￨- 92D30￨L￨NN￨O￨- ,￨L￨,￨O￨- 91D25￨L￨CD￨NUMBER￨- AMS￨U￨NNS￨O￨- subject￨L￨JJ￨O￨- classi￨L￨NN￨O￨- fication￨L￨NN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- classical￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- qualitatively￨L￨RB￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- directly￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- populated￨L￨JJ￨O￨- center￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- remains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- building￨L￨NN￨O￨- block￨L￨NN￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- ,￨L￨,￨O￨- more￨L￨RBR￨O￨- complicated￨L￨JJ￨O￨- applied￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- previous￨L￨JJ￨O￨- works￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- small￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- approximation￨L￨NN￨O￨- was￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- every￨L￨DT￨O￨- population￨L￨NN￨O￨- center￨L￨NN￨O￨- is￨L￨VBZ￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- initially￨L￨RB￨O￨- infectives￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- start￨L￨VBP￨O￨- with￨L￨IN￨O￨- consideration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- only￨L￨RB￨O￨- two￨L￨CD￨NUMBER￨- interacting￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- centra￨L￨NNS￨O￨- and￨L￨CC￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- the￨L￨DT￨O￨- migration￨L￨NN￨O￨A processes￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- in￨L￨IN￨O￨- fluence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- like￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fast￨L￨JJ￨O￨- migration￨L￨NN￨O￨A time￨L￨NN￨O￨- approximation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Rn￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- infectives￨L￨NNS￨O￨A and￨L￨CC￨O￨- removed￨L￨VBN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- node￨L￨NN￨O￨- n￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t.￨L￨IN￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- network￨L￨NN￨O￨- structures￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- approximation￨L￨NN￨O￨- onto￨L￨IN￨O￨- a￨L￨DT￨O￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨A problem￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- edge-based￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- degree￨L￨NN￨O￨- approach￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- pair￨L￨NN￨O￨- approximation￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- succeeded￨L￨VBN￨O￨- in￨L￨IN￨O￨- describing￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- transition￨L￨NN￨O￨- points￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- seeds￨L￨NNS￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- increases￨L￨NNS￨O￨- epidemic￨L￨JJ￨O￨- clusters￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- seed￨L￨NN￨O￨A percolate￨L￨NN￨O￨- before￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- seed￨L￨NN￨O￨- can￨L￨MD￨O￨- induce￨L￨VB￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- first￨L￨JJ￨O￨- applied￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- well-mixed￨L￨JJ￨O￨- population￨L￨NN￨O￨- for￨L￨IN￨O￨- computation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- eventually￨L￨RB￨O￨- removed￨L￨VBD￨O￨A (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨- having￨L￨VBG￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- pk￨L￨NN￨O￨- ∝￨L￨NN￨O￨- k￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- degree-based￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- node￨L￨NN￨O￨A i￨L￨FW￨O￨- linking￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- j￨L￨NN￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- kj￨L￨NN￨O￨- at￨L￨IN￨O￨- distance￨L￨NN￨O￨- dij￨L￨NN￨O￨- from￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- kA￨L￨NN￨O￨- ij￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- governing￨L￨VBG￨O￨- preferential￨L￨JJ￨O￨- attachment￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- node-node￨L￨JJ￨O￨- distance￨L￨NN￨O￨- .￨L￨.￨O￨- +Mendes1￨U￨NN￨O￨- ∗￨L￨SYM￨O￨- 1Departamento￨L￨FW￨O￨- de￨L￨FW￨O￨- F´ısica￨U￨FW￨O￨- da￨L￨NN￨O￨A Universidade￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Aveiro￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 3810-19￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- Aveiro￨U￨NNP￨O￨- ,￨L￨,￨O￨- Portugal￨U￨NNP￨COUNTRY￨- 2￨L￨CD￨NUMBER￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Theoretical￨U￨NNP￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Lanzhou￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Lanzhou￨U￨NNP￨CITY￨- Gansu￨U￨NNP￨STATE_OR_PROVINCE￨- 730000￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- November￨U￨NNP￨DATE￨- 17￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- preference￨L￨NN￨O￨- and￨L￨CC￨O￨- geography￨L￨NN￨O￨- on￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- network￨L￨NN￨O￨- grows￨L￨VBZ￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- random￨L￨JJ￨O￨- node￨L￨NN￨O￨A with￨L￨IN￨O￨- m￨L￨NN￨O￨- links￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Euclidean￨U￨JJ￨MISC￨- space￨L￨NN￨O￨- at￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- both￨L￨DT￨O￨- ingredients￨L￨NNS￨O￨- are￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- simultaneously￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- robust￨L￨JJ￨O￨A to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- larger￨L￨JJR￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- smaller￨L￨JJR￨O￨- B￨U￨NN￨O￨- .￨L￨.￨O￨- +System￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- classical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- studied￨L￨VBN￨O￨A by￨L￨IN￨O￨- Brauer￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- has￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- recovery￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- nonfatal￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- yield￨L￨VB￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Basic￨U￨JJ￨O￨- results￨L￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- section￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- some￨L￨DT￨O￨- definitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- stated￨L￨VBN￨O￨- theorems￨L￨NNS￨O￨- which￨L￨WDT￨O￨- shall￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- section￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- phase￨L￨NN￨O￨- portraits￨L￨NNS￨O￨- of￨L￨IN￨O￨- finite￨L￨NN￨O￨- and￨L￨CC￨O￨- infinite￨L￨NN￨O￨A singularities￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- finite￨L￨NN￨O￨- and￨L￨CC￨O￨- infinite￨L￨NN￨O￨A singular￨L￨JJ￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- done￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- three￨L￨CD￨NUMBER￨- invariant￨L￨JJ￨O￨- straight￨L￨JJ￨O￨- lines￨L￨NNS￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Particularly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- first-order￨L￨NN￨O￨- ODE￨U￨NN￨O￨- ˙x￨L￨NN￨O￨- ˙y￨L￨NN￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- bxy￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- mx￨L￨NN￨COUNTRY￨- +￨L￨CC￨O￨- cy￨L￨NN￨O￨- +￨L￨CC￨O￨- mk￨L￨NN￨O￨- ,￨L￨,￨O￨- bxy￨L￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- x￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- represent￨L￨VBP￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- portion￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- already￨L￨RB￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨A described￨L￨VBN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- differential￨L￨JJ￨O￨- system￨L￨NN￨O￨- ˙x￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- bxy￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- mx￨L￨NN￨COUNTRY￨- +￨L￨CC￨O￨- cy￨L￨NN￨O￨- +￨L￨CC￨O￨- mk￨L￨NN￨O￨- ,￨L￨,￨O￨- ˙y￨L￨NN￨O￨- =￨L￨JJ￨O￨- bxy￨L￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- are￨L￨VBP￨O￨- real￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- with￨L￨IN￨O￨- b￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Appendix￨U￨NN￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- S0￨U￨NN￨O￨- >￨L￨JJR￨O￨- Sc￨U￨NN￨O￨- ≡￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- /￨L￨:￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- any￨L￨DT￨O￨- I0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- will￨L￨MD￨O￨- trigger￨L￨VB￨O￨- a￨L￨DT￨O￨- traveling￨L￨VBG￨O￨A wave￨L￨NN￨O￨- ,￨L￨,￨O￨- leaving￨L￨VBG￨O￨- behind￨L￨IN￨O￨- a￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- S1￨U￨NN￨O￨- <￨L￨JJR￨O￨- Sc￨U￨NN￨O￨- <￨L￨JJR￨O￨- S0￨U￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- a￨L￨DT￨O￨- non-trivial￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- velocity￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- shape￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- rough￨L￨JJ￨O￨- geometry￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- displacement￨L￨NN￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- front￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- disorder￨L￨NN￨O￨A approaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- quenched￨L￨JJ￨O￨- disorder￨L￨NN￨O￨A thus￨L￨RB￨O￨- completely￨L￨RB￨O￨- protects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- positions￨L￨NNS￨O￨- where￨L￨WRB￨O￨- βr￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- occurring￨L￨VBG￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- diffusive￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- those￨L￨DT￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- extended￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- fronts￨L￨NNS￨O￨- advancing￨L￨VBG￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨A uniform￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- by￨L￨IN￨O￨- solving￨L￨VBG￨O￨- numerically￨L￨RB￨O￨- a￨L￨DT￨O￨- diffusive￨L￨JJ￨O￨- Kermack￨U￨NNP￨PERSON￨- McKendrick￨U￨NNP￨PERSON￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- dichotomous￨L￨JJ￨O￨- spatially￨L￨RB￨O￨- random￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- dimensions￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- similar￨L￨JJ￨O￨- traveling￨L￨VBG￨O￨- wave￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- observed￨L￨VBN￨O￨- at￨L￨IN￨O￨- moderate￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- disorder￨L￨NN￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Likewise￨U￨RB￨O￨- ,￨L￨,￨O￨- local￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- can￨L￨MD￨O￨- allow￨L￨VB￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- remain￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- age￨L￨VBP￨O￨- into￨L￨IN￨O￨- their￨L￨PRP$￨O￨- childbearing￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 1985 1990 1995 2000￨L￨CD￨NUMBER￨- 200￨L￨CD￨NUMBER￨- 400￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- n￨L￨NN￨O￨- o￨L￨NN￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- l￨L￨NN￨O￨- y￨L￨NN￨O￨- c￨L￨NN￨O￨- a￨L￨DT￨O￨- s￨L￨NNS￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- 0￨L￨CD￨NUMBER￨- 1925 1930 1935 1940￨L￨CD￨NUMBER￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- yr￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- 1945 1950 1955 1500￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 1982￨L￨CD￨DATE￨- 3000￨L￨CD￨NUMBER￨- w￨L￨NN￨O￨- e￨L￨SYM￨O￨- e￨L￨SYM￨O￨- k￨L￨NN￨O￨- l￨L￨NN￨O￨- y￨L￨NN￨O￨- c￨L￨NN￨O￨- a￨L￨DT￨O￨- s￨L￨NNS￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- 1987 1992 1997￨L￨CD￨NUMBER￨- 5￨L￨CD￨NUMBER￨- 10￨L￨CD￨NUMBER￨- w￨L￨NN￨O￨- e￨L￨SYM￨O￨- e￨L￨SYM￨O￨- p￨L￨NN￨O￨- e￨L￨SYM￨O￨- k￨L￨NN￨O￨- l￨L￨NN￨O￨- c￨L￨NN￨O￨- y￨L￨NN￨O￨- c￨L￨NN￨O￨- a￨L￨DT￨O￨- n￨L￨NN￨O￨- s￨L￨VBZ￨O￨- c￨L￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- r￨L￨NN￨O￨- i￨L￨FW￨O￨- l￨L￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Mexico￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Hidalgo￨U￨NNP￨CITY￨- Japan￨U￨NNP￨COUNTRY￨- Canada￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Ontario￨U￨NNP￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0.5￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 1.5￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- 3￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 2￨L￨CD￨DATE￨- 0.5￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- 1.5￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- 2￨L￨CD￨DATE￨- o￨L￨NN￨O￨- p￨L￨NN￨O￨- w￨L￨NN￨O￨- e￨L￨SYM￨O￨- r￨L￨NN￨O￨- s￨L￨NNS￨O￨- e￨L￨SYM￨O￨- p￨L￨NN￨O￨- c￨L￨NN￨O￨- t￨L￨NN￨O￨- r￨L￨NN￨O￨- u￨L￨NN￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0.5￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 1.5￨L￨CD￨NUMBER￨- frequency￨L￨NN￨O￨- ,￨L￨,￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- yr￨L￨NN￨DURATION￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- Color￨U￨NNP￨O￨- online￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Time￨U￨NN￨ORGANIZATION￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- rubella￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- spectrum￨L￨NN￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- Hidalgo￨U￨NNP￨CITY￨- district￨L￨NN￨O￨- ,￨L￨,￨O￨- Mexico￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Japan￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- province￨L￨NN￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- Canada￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- approach￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- coherent￨L￨JJ￨O￨- picture￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- rubella￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- explaining￨L￨VBG￨O￨- essential￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- recurrent￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- exhibited￨L￨VBD￨O￨- by￨L￨IN￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- during￨L￨IN￨O￨- early￨L￨JJ￨O￨- pregnancy￨L￨NN￨O￨- may￨L￨MD￨O￨- cause￨L￨VB￨O￨- spontaneous￨L￨JJ￨O￨A abortion￨L￨NN￨O￨- or￨L￨CC￨O￨- Congenital￨U￨JJ￨MISC￨- Rubella￨U￨NNP￨MISC￨- Syndrome￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- CRS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- entail￨L￨VB￨O￨- a￨L￨DT￨O￨- varitic￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- around￨L￨IN￨O￨- stable￨L￨JJ￨O￨- attractors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- corety￨L￨NN￨O￨- of￨L￨IN￨O￨- birth￨L￨NN￨O￨- defects￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- responding￨L￨VBG￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- them￨L￨PRP￨O￨- with￨L￨IN￨O￨- spectra￨L￨NNS￨O￨- from￨L￨IN￨O￨- full￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- seasonally￨L￨RB￨O￨- forced￨L￨VBN￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- determinants￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- illustrate￨L￨VBP￨O￨- patterns￨L￨NNS￨O￨- by￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- that￨L￨WDT￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- rubella￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- systems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- rumor￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- etc.￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨A [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- —￨L￨:￨O￨- in￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- stand￨L￨VBP￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- each￨L￨DT￨O￨- edge￨L￨NN￨O￨- connecting￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- describes￨L￨VBZ￨O￨- potential￨L￨JJ￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨A including￨L￨VBG￨O￨A variable￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- degree-related￨L￨JJ￨O￨- imperfect￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- quarantine￨L￨NN￨O￨- on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Epidemic￨U￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- attracted￨L￨VBN￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- attention￨L￨NN￨O￨- from￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- since￨L￨IN￨O￨- Barab￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- asi￨L￨NN￨O￨- and￨L￨CC￨O￨- Albert￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∗￨L￨CD￨NUMBER￨- Corresponding￨U￨VBG￨O￨- author￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +showed￨L￨VBD￨O￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- and￨L￨CC￨O￨- numerical￨L￨JJ￨O￨- study￨L￨NN￨O￨- on￨L￨IN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- found￨L￨VBD￨O￨- similar￨L￨JJ￨O￨- conclusions￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A .￨L￨.￨O￨- +–￨L￨:￨O￨- We￨U￨PRP￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- efficiently￨L￨RB￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- initially-infected￨L￨JJ￨O￨- node￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- counting￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- walks￨L￨VBZ￨O￨A of￨L￨IN￨O￨- various￨L￨JJ￨O￨- lengths￨L￨NNS￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A sharing￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- SIR￨U￨NN￨O￨- centers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- tf￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- functional￨L￨JJ￨O￨- Q￨U￨NNP￨O￨- =￨L￨JJ￨O￨- tf￨L￨NN￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- migration￨L￨NN￨O￨- fluxes￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- mumps￨L￨NNS￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Optimality￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- minimization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- lost￨L￨VBN￨O￨- working￨L￨VBG￨O￨- days￨L￨NNS￨DURATION￨- during￨L￨IN￨O￨- where￨L￨WRB￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- stands￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explain￨L￨VBP￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- available￨L￨JJ￨O￨- V￨U￨NN￨O￨- .￨L￨.￨O￨- +I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- mumps￨L￨NNS￨O￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- and￨L￨CC￨O￨- optimal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A for￨L￨IN￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- well-known￨L￨JJ￨O￨- that￨L￨IN￨O￨- international￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- traffic￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- significantly￨L￨RB￨O￨- influence￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemics￨L￨NNS￨O￨A ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- integrating￨L￨VBG￨O￨- these￨L￨DT￨O￨- factors￨L￨NNS￨O￨- into￨L￨IN￨O￨- relatively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- greatly￨L￨RB￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemics￨L￨NNS￨O￨A considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- regions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- validate￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- hybrid￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- carrying￨L￨VBG￨O￨- out￨L￨RP￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- -2003￨L￨CD￨NUMBER￨- using￨L￨VBG￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- traffic￨L￨NN￨O￨- networks￨L￨NNS￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- introduces￨L￨VBZ￨O￨- a￨L￨DT￨O￨- hybrid￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- pandemics￨L￨NNS￨O￨A considering￨L￨VBG￨O￨- both￨L￨CC￨O￨- global￨L￨JJ￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- different￨L￨JJ￨O￨A rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- population￨L￨NN￨O￨- densities￨L￨NNS￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- policies￨L￨NNS￨O￨- of￨L￨IN￨O￨- variable￨L￨JJ￨O￨- strength￨L￨NN￨O￨- and￨L￨CC￨O￨- coordination￨L￨NN￨O￨- .￨L￨.￨O￨- +Modeling￨U￨VBG￨O￨- Super-spreading￨U￨JJ￨O￨- Events￨U￨NNS￨O￨- for￨L￨IN￨O￨- Infectious￨U￨JJ￨O￨- Diseases￨U￨NNS￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- Case￨U￨NNP￨O￨- Study￨U￨NNP￨O￨- SARS￨U￨NNP￨O￨- Thembinkosi￨U￨NNP￨PERSON￨- Mkhatshwa￨U￨NNP￨PERSON￨- ∗￨L￨NNP￨O￨- Anna￨U￨NNP￨PERSON￨- Mummert￨U￨NNP￨PERSON￨- †￨L￨NNP￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- Super-spreading￨U￨JJ￨O￨- events￨L￨NNS￨O￨A for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- occur￨L￨VBP￨O￨- when￨L￨WRB￨O￨- some￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- small-scale￨L￨JJ￨O￨- SARS￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- Amoy￨U￨NNP￨ORGANIZATION￨- Gardens￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- Special￨U￨JJ￨LOCATION￨- Administrative￨U￨JJ￨LOCATION￨- Region￨U￨NN￨LOCATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- problem￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- mass-action￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- some￨L￨DT￨O￨- simulation￨L￨NN￨O￨- results￨L￨VBZ￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- an￨L￨DT￨O￨- autonomous￨L￨JJ￨O￨A and￨L￨CC￨O￨- corresponding￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- controlled￨L￨JJ￨O￨- versus￨L￨CC￨O￨- uncontrolled￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Optimal￨U￨JJ￨O￨- control￨L￨NN￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- tool￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- strategies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +doi￨L￨FW￨O￨A :￨L￨:￨O￨- 10.3934￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- dcdss￨L￨JJ￨O￨- .2018067￨L￨CD￨NUMBER￨- OPTIMAL￨U￨JJ￨O￨- CONTROL￨U￨NNP￨O￨- OF￨U￨IN￨O￨- NON-AUTONOMOUS￨U￨NNP￨O￨- SEIRS￨U￨NNP￨O￨- MODELS￨U￨NNPS￨O￨- WITH￨U￨IN￨O￨- VACCINATION￨U￨NNPS￨O￨- AND￨U￨CC￨O￨- TREATMENT￨U￨NNP￨O￨- Joaquim￨U￨NNP￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- epidemiological￨L￨JJ￨O￨- interpretation￨L￨NN￨O￨- and￨L￨CC￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- generalizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- single-stage￨L￨JJ￨O￨- case￨L￨NN￨O￨- K￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- natural￨L￨JJ￨O￨- to￨L￨TO￨O￨- interpret￨L￨VB￨O￨A this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- D￨U￨NN￨O￨- E￨U￨NN￨O￨- PA￨U￨NN￨STATE_OR_PROVINCE￨- RTM￨U￨NN￨O￨- E￨U￨NN￨O￨- N￨U￨NN￨O￨- T￨U￨NN￨O￨- O￨U￨NN￨O￨- F￨U￨NN￨O￨- M￨U￨NN￨O￨- ATH￨U￨NN￨ORGANIZATION￨- EM￨U￨NN￨ORGANIZATION￨- AT￨U￨IN￨ORGANIZATION￨- IC￨U￨NN￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- C￨U￨NN￨ORGANIZATION￨- OM￨U￨NN￨ORGANIZATION￨- PU￨U￨NN￨O￨- T￨U￨NN￨O￨- E￨U￨NN￨O￨- R￨U￨NN￨O￨- S￨U￨NN￨O￨- C￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- E￨U￨NN￨O￨- N￨U￨NN￨O￨- C￨U￨NN￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- I￨U￨PRP￨O￨- N￨U￨NN￨O￨- D￨U￨NN￨O￨- H￨U￨NN￨O￨- OV￨U￨NN￨O￨- E￨U￨NN￨O￨- N￨U￨NN￨O￨- UN￨U￨NNP￨ORGANIZATION￨- I￨U￨NN￨O￨- V￨U￨NN￨O￨- E￨U￨NN￨O￨- R￨U￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- T￨U￨NN￨O￨- Y￨U￨NN￨O￨- O￨U￨NN￨O￨- F￨U￨NN￨O￨- T￨U￨NN￨O￨- E￨U￨NN￨O￨- CH￨U￨NN￨COUNTRY￨- N￨U￨NN￨O￨- O￨U￨NN￨O￨- L￨U￨NN￨O￨- O￨U￨NN￨O￨- G￨U￨NN￨O￨- Y￨U￨NN￨O￨- ,￨L￨,￨O￨- P.O.￨U￨NNP￨O￨- BOX￨U￨NNP￨O￨- 5￨L￨CD￨NUMBER￨- 1￨L￨CD￨DATE￨- 3￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- 6￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- M￨U￨NN￨O￨- B￨U￨NN￨O￨- E￨U￨NN￨O￨- I￨U￨PRP￨O￨- N￨U￨NN￨O￨- D￨U￨NN￨O￨- H￨U￨NN￨O￨- OV￨U￨NN￨O￨- E￨U￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- H￨U￨NN￨O￨- E￨U￨NN￨O￨- N￨U￨NN￨O￨- E￨U￨NN￨O￨- TH￨U￨NN￨O￨- E￨U￨NN￨O￨- R￨U￨NN￨O￨- L￨U￨NN￨O￨- AN￨U￨DT￨O￨- D￨U￨NN￨O￨- S￨U￨NN￨O￨- E-mail￨U￨NN￨O￨- address￨L￨NN￨O￨- :￨L￨:￨O￨- .￨L￨.￨O￨- +Namely￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- toy￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- at￨L￨IN￨O￨- initial￨L￨JJ￨O￨- moment￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- A￨U￨NN￨O￨- started￨L￨VBD￨O￨- challenging￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- X￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- B￨U￨NN￨O￨- supported￨L￨VBD￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- C￨U￨NN￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- neither￨L￨CC￨O￨- B￨U￨NN￨O￨- nor￨L￨CC￨O￨- C￨U￨NN￨O￨- change￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- supportive￨L￨JJ￨O￨- and￨L￨CC￨O￨- neutral￨L￨JJ￨IDEOLOGY￨A ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- neighbourhoods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- host￨L￨NN￨TITLE￨- B￨U￨NN￨O￨- is￨L￨VBZ￨O￨- supportive￨L￨JJ￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- C￨U￨NN￨O￨- is￨L￨VBZ￨O￨- neutral￨L￨JJ￨IDEOLOGY￨A )￨L￨-RRB-￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- note￨L￨VB￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- epidemic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- It￨U￨PRP￨O￨- then￨L￨RB￨O￨- turns￨L￨VBZ￨O￨- out￨L￨RP￨O￨- stochastic￨L￨JJ￨O￨- and￨L￨CC￨O￨- deterministic￨L￨JJ￨O￨A models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- attained￨L￨VBN￨O￨- at￨L￨IN￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- In￨U￨IN￨O￨- epidemic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨A and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- use￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- to￨L￨TO￨O￨- know￨L￨VB￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Stochastic￨U￨NNP￨O￨- Model￨U￨NNP￨TITLE￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- Epidemic￨U￨JJ￨O￨- Modelling￨U￨NN￨O￨- Kurnia￨U￨NN￨O￨- Susvitasari1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- School￨U￨NNP￨O￨- of￨L￨IN￨O￨- Mathematical￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Nottingham￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mathematics￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Indonesia￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Indonesia￨U￨NNP￨COUNTRY￨- ARTICLE￨U￨NN￨O￨- HISTORY￨U￨NN￨O￨- Compiled￨U￨VBN￨O￨- March￨U￨NNP￨DATE￨- 6￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- ABSTRACT￨U￨NN￨O￨- Threshold￨U￨NN￨O￨- theorem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- probably￨L￨RB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- successfully￨L￨RB￨O￨- showed￨L￨VBN￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- deterministic￨L￨JJ￨O￨A and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- performed￨L￨VBD￨O￨- similar￨L￨JJ￨O￨- results￨L￨NNS￨O￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- minor￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- always￨L￨RB￨O￨- occurs￨L￨VBZ￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- otherwise￨L￨RB￨O￨- the￨L￨DT￨O￨- ma￨L￨NN￨O￨- jor￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- occurs￨L￨VBZ￨O￨- also￨L￨RB￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- computed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- maximised￨L￨VBN￨O￨- if￨L￨IN￨O￨- all￨L￨DT￨O￨- weights￨L￨NNS￨O￨A are￨L￨VBP￨O￨- equal￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- equally￨L￨RB￨O￨- matched￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- weight￨L￨NN￨O￨- distribution￨L￨NN￨O￨- give￨L￨VBP￨O￨- rise￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- R0￨U￨NN￨O￨- value￨L￨NN￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- models￨L￨NNS￨O￨- start￨L￨VBP￨O￨- from￨L￨IN￨O￨- non-weighted￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- topology￨L￨NN￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- link￨L￨NN￨O￨- weights￨L￨NNS￨O￨A in￨L￨IN￨O￨- either￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- random￨L￨JJ￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- fixed/deterministic￨L￨JJ￨O￨- way￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptibleinfected-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- undirected￨L￨JJ￨O￨- ,￨L￨,￨O￨- weighted￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- pairwisetype￨L￨NN￨O￨- approximate￨L￨JJ￨O￨- models￨L￨NNS￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- individual-based￨L￨JJ￨O￨- network￨L￨NN￨O￨- simulation￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- pairwise￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- formulated￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- discrete￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- weights￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- then￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- conjunction￨L￨NN￨O￨- with￨L￨IN￨O￨- network￨L￨NN￨O￨- simulation￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- weight￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- theoretical/synthetic￨L￨JJ￨O￨- weighted￨L￨JJ￨O￨A network￨L￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- weakly-coupled￨L￨JJ￨O￨- network￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mixed￨L￨JJ￨O￨- phase￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- below￨L￨IN￨O￨- βc￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coupled￨L￨JJ￨O￨A network￨L￨NN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- occurs￨L￨VBZ￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- network￨L￨NN￨O￨- but￨L￨CC￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- spread￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- coupled￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- disease-spreading￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- n￨L￨NN￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- interconnected￨L￨JJ￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- complicated￨L￨JJ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- cause￨L￨VB￨O￨A an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- coupling￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨A and￨L￨CC￨O￨- human￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- several￨L￨JJ￨O￨- crucial￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- ,￨L￨,￨O￨- most￨L￨RBS￨O￨- importantly￨L￨RB￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- human￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- human-to-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- subcritical￨L￨JJ￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- long￨L￨JJ￨O￨- times￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- characterize￨L￨VBP￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- human￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- show￨L￨VBP￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- dependence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- animal￨L￨NN￨O￨A population￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- early￨L￨JJ￨O￨- timescales￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- solve￨L￨VBP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- spillover￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- animal￨L￨NN￨O￨A population￨L￨NN￨O￨- at￨L￨IN￨O￨- spillover￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- epidemiology￨L￨NN￨O￨- —￨L￨:￨O￨- zoonoses￨L￨NNS￨O￨- —￨L￨:￨O￨- metapopulation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- —￨L￨:￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- —￨L￨:￨O￨- epidemic￨L￨JJ￨O￨- probability￨L￨NN￨O￨- —￨L￨:￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- I.￨U￨NN￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨A ,￨L￨,￨O￨- stability￨L￨NN￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- relapse￨L￨NN￨O￨- ∗￨L￨CD￨NUMBER￨- Principal￨U￨NN￨TITLE￨- Corresponding￨U￨VBG￨O￨- Author￨U￨NN￨TITLE￨- ∗￨L￨SYM￨O￨- ∗￨L￨SYM￨O￨- Tel.￨U￨NNP￨O￨- :￨L￨:￨O￨- +91 40 2388 4388￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- Fax.￨U￨NNP￨O￨- :￨L￨:￨O￨- +91 40 2388 4437￨L￨CD￨NUMBER￨- Email￨U￨VB￨O￨- address￨L￨NN￨O￨- :￨L￨:￨O￨- 1This￨L￨NN￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- dedicated￨L￨VBN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- (￨L￨-LRB-￨O￨- M.￨U￨NN￨O￨- Mathematical￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- tool￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- popularly￨L￨RB￨O￨- employed￨L￨VBN￨O￨- in￨L￨IN￨O￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- severe￨L￨JJ￨O￨- acute￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SARS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- infection/acquired￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- deficiency￨L￨NN￨O￨- syndrome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HIV/AIDS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- H5N1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- avian￨L￨JJ￨O￨- flu￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- H1N1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- swine￨L￨NNS￨O￨- flu￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- has￨L￨VBZ￨O￨- clearly￨L￨RB￨O￨- brought￨L￨VBN￨O￨- out￨L￨RP￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- treatment￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨A would￨L￨MD￨O￨- contain￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- popular￨L￨JJ￨O￨- belief￨L￨NN￨O￨- that￨L￨WDT￨O￨- eradication￨L￨NN￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- be￨L￨VB￨O￨- done￨L￨VBN￨O￨- through￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- spread￨L￨VBN￨O￨- having￨L￨VBG￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- study￨L￨VB￨O￨- its￨L￨PRP$￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- incubation￨L￨NN￨O￨- delays￨L￨NNS￨O￨A and￨L￨CC￨O￨- relapse￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨A are￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +is￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- statics￨L￨NNS￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- mapped￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- percolation￨L￨NN￨O￨A problem￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- T￨U￨NN￨O￨- which￨L￨WDT￨O￨- plays￨L￨VBZ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- p￨L￨NN￨O￨- in￨L￨IN￨O￨- percolation￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crossover￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- regime￨L￨NN￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- logarithmic￨L￨JJ￨O￨- regime￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disorder￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨A ,￨L￨,￨O￨- depends￨L￨VBZ￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- T￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- tr￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dβ￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- δ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- β0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- constant￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- there￨L￨EX￨O￨- exist￨L￨VBP￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- Tc￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- It￨U￨PRP￨O￨- was￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- pc￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- percolation￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- nonzero￨L￨NN￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- biggest￨L￨JJS￨O￨- cluster￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- ∼￨L￨JJ￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- that￨L￨IN￨O￨- not￨L￨RB￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- interact￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- way￨L￨NN￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +Inferring￨U￨VBG￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- message-passing￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- Andrey￨U￨NNP￨PERSON￨- Y.￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- July￨U￨NNP￨DATE￨- 3￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- :￨L￨:￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- snapshot￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- article￨L￨NN￨O￨- we￨L￨PRP￨O￨- address￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- patient￨L￨NN￨O￨- zero￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨- -￨L￨:￨O￨- in￨L￨IN￨O￨- what￨L￨WP￨O￨- follows￨L￨VBZ￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- terms￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- alternately￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- snapshot￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨- .￨L￨.￨O￨- +Assuming￨U￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A spread￨L￨NN￨O￨A follows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- usual￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- an￨L￨DT￨O￨- inference￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- message-passing￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- significant￨L￨JJ￨O￨- improvement￨L￨NN￨O￨- of￨L￨IN￨O￨- performance￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- existing￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- .￨L￨.￨O￨- +Whereas￨U￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- attracted￨L￨VBN￨O￨- a￨L￨DT￨O￨- considerable￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- works￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- see￨L￨VB￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- origin￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- mathematically￨L￨RB￨O￨- formulated￨L￨VBN￨O￨- only￨L￨RB￨O￨- recently￨L￨RB￨DATE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- burst￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- practically￨L￨RB￨O￨- important￨L￨JJ￨O￨- problem￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Parameter￨U￨NN￨O￨- Biological￨U￨JJ￨O￨- meaning￨L￨NN￨O￨- ¯￨L￨NN￨O￨- ν￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- r0￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- k1￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- k2￨L￨NN￨O￨- ¯￨L￨NN￨O￨- γ￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- µ1￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- µ2￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- µ3￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- β1￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- β2￨L￨NN￨O￨- ¯￨L￨NN￨O￨- σ￨L￨NN￨O￨- ¯￨L￨NN￨O￨- D￨U￨NN￨O￨- advection￨L￨NN￨O￨- coefficient￨L￨JJ￨O￨- intrinsic￨L￨JJ￨O￨- oviposition￨L￨NN￨O￨- rate￨L￨NN￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- winged￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨A form￨L￨VBP￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- aquatic￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- form￨L￨VBP￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- maturation￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- aquatic￨L￨JJ￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- to￨L￨TO￨O￨- winged￨L￨JJ￨O￨- form￨L￨NN￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- winged￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- sub-population￨L￨NN￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- aquatic￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- sub-population￨L￨NN￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- from￨L￨IN￨O￨- humans￨L￨NNS￨O￨- to￨L￨TO￨O￨- mosquitoes￨L￨NNS￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- from￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- diffusion￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- winged￨L￨JJ￨O￨- population￨L￨NN￨O￨- 2.1￨L￨CD￨NUMBER￨- Previous￨U￨JJ￨O￨- models￨L￨NNS￨O￨- Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- recall￨L￨VBP￨O￨- previous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- influenced￨L￨VBD￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- section￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- Malthusian￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- a￨L￨DT￨O￨- division￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- classification￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquitoes￨L￨NNS￨O￨A are￨L￨VBP￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- female￨L￨JJ￨O￨- winged￨L￨JJ￨O￨- non-infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- aquatic￨L￨JJ￨O￨- sub-populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +2010￨L￨CD￨DATE￨- AMS￨U￨NNP￨MISC￨- Mathematics￨U￨NNP￨MISC￨- Classification￨U￨NNP￨MISC￨- numbers￨L￨NNS￨O￨- :￨L￨:￨O￨- 34D20￨L￨NN￨O￨- ,￨L￨,￨O￨- 35B35￨L￨NN￨O￨- ,￨L￨,￨O￨- 76M60￨L￨NN￨O￨- ,￨L￨,￨O￨- 92Bxx￨L￨NN￨O￨- Key￨U￨NN￨O￨- words￨L￨NNS￨O￨- :￨L￨:￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- dengue￨L￨NN￨O￨- ,￨L￨,￨O￨- Lie￨U￨NN￨O￨- symmetries￨L￨NNS￨O￨- ,￨L￨,￨O￨- qualitative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- applied￨L￨VBD￨O￨- mathematics￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- Aedes￨U￨NNPS￨O￨- aegypti￨L￨NNS￨O￨- mosquito￨L￨NN￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- vector￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- dengue￨L￨NN￨O￨- and￨L￨CC￨O￨- Zika￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- name￨L￨VB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- picture￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- constitutive￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- we￨L￨PRP￨O￨- look￨L￨VBP￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- point￨L￨NN￨O￨- symmetries￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- section￨L￨NN￨O￨A 3￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- Lie￨U￨NN￨O￨- point￨L￨NN￨O￨- symmetries￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- theirs￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- provides￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- the￨L￨DT￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- instability￨L￨NN￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- offspring￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- perform￨L￨VBP￨O￨- mean￨L￨VB￨O￨- field￨L￨JJ￨O￨- calculations￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨A the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- occupied￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- quadratic￨L￨JJ￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- QCP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- well￨L￨RB￨O￨- studied￨L￨VBN￨O￨- linear￨L￨JJ￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- where￨L￨WRB￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- neighbors￨L￨NNS￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- recover￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- →￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- QCP￨U￨NN￨O￨- –￨L￨:￨O￨- vertex￨L￨NN￨O￨- centered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- VQCP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- edge￨L￨NN￨O￨A centered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- EQCP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- birth￨L￨NN￨O￨- events￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- →￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- →￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- ‘￨L￨``￨O￨- −￨L￨SYM￨O￨- ’￨L￨''￨O￨- represents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Traveling￨U￨VBG￨O￨- waves￨L￨NNS￨O￨- ;￨L￨:￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- Schauder￨U￨NNP￨O￨- fixed￨L￨VBD￨O￨- point￨L￨NN￨O￨- theorem￨L￨NN￨O￨- ;￨L￨:￨O￨- Laplace￨U￨NNP￨CITY￨- transform￨L￨VB￨O￨A AMS￨U￨NNP￨O￨- Sub￨U￨NN￨O￨- ject￨L￨NN￨O￨- Classification￨U￨NN￨O￨- :￨L￨:￨O￨- 92D30￨L￨NN￨O￨- ;￨L￨:￨O￨- 35K57￨L￨NN￨O￨- ;￨L￨:￨O￨- 34B40￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Kermack-McKendrick￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- standard￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- Compartmental￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- communicable￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- various￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- many￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- emerging￨L￨VBG￨O￨- fields￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- socio-biological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- media￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- speed￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- traveling￨L￨VBG￨O￨A waves￨L￨NNS￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- three-dimensional￨L￨JJ￨O￨- non-monotonic￨L￨JJ￨O￨- system￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- its￨L￨PRP$￨O￨- linearizaion￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- The￨U￨DT￨O￨- proof￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Schauder￨U￨NNP￨O￨- fixed￨L￨VBD￨O￨- point￨L￨NN￨O￨- theorem￨L￨NN￨O￨- and￨L￨CC￨O￨- Laplace￨U￨NNP￨CITY￨- transform￨L￨VB￨O￨- and￨L￨CC￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- promising￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- dimensional￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- rich￨L￨JJ￨O￨- literature￨L￨NN￨O￨- on￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- delays￨L￨NNS￨O￨- or￨L￨CC￨O￨- integral￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- brief￨L￨JJ￨O￨- review￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- previous￨L￨JJ￨O￨- works￨L￨NNS￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- traveling￨L￨VBG￨O￨A wave￨L￨NN￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- basic￨L￨JJ￨O￨- diffusive￨L￨JJ￨O￨- Kermack-McKendrick￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 1.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1.6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aid￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- shooting￨L￨NN￨CAUSE_OF_DEATH￨- technique￨L￨NN￨O￨- and￨L￨CC￨O￨- invariant￨L￨JJ￨O￨- manifold￨L￨NN￨O￨- theory￨L￨NN￨O￨- developed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Dunbar￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Hosono￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ilyas￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- βS￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- /￨L￨:￨O￨- γ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- c￨L￨NN￨O￨- ≥￨L￨NN￨O￨- c￨L￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- 2pd2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- βS￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ∞￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.5-1.6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- traveling￨L￨VBG￨O￨A wave￨L￨NN￨O￨- solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- ct￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- ct￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- satisfying￨L￨VBG￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- −￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- −￨L￨SYM￨O￨- ∞￨L￨SYM￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- ±￨L￨SYM￨O￨- ∞￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ∞￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- ∞￨L￨NN￨O￨- <￨L￨JJR￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +Wang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wu￨U￨NNP￨PERSON￨- proved￨L￨VBD￨O￨A a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- result￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- diffusive￨L￨JJ￨O￨- Kermack-McKendrick￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- standard￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- ∂￨L￨SYM￨O￨- tS￨L￨NN￨O￨- =￨L￨JJ￨O￨- d1￨L￨NN￨O￨- ∂￨L￨NN￨O￨- xxS￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ∂￨L￨NN￨O￨- t￨L￨NN￨O￨- I￨U￨NN￨O￨- =￨L￨JJ￨O￨- d2￨L￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- xxI￨L￨NN￨O￨- +￨L￨CC￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨PRP￨O￨- ;￨L￨:￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- arrive￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- expression￨L￨NN￨O￨- for￨L￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- R0R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- but￨L￨CC￨O￨- no￨L￨DT￨O￨- removed￨L￨VBN￨O￨- sub￨L￨NN￨O￨- jects￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- i0￨L￨NN￨O￨A ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- i0￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- V￨U￨NN￨O￨- ∗￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- non-Poisson￨L￨JJ￨MISC￨- spreading￨L￨NN￨O￨A processes￨L￨NNS￨O￨A letting￨L￨VBG￨O￨- us￨L￨PRP￨O￨- capture￨L￨VB￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- complicated￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- than￨L￨IN￨O￨- existing￨L￨VBG￨O￨- works￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- information￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- works￨L￨VBZ￨O￨A to￨L￨TO￨O￨- consider￨L￨VB￨O￨- a￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- over￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- contact￨L￨NN￨O￨- graphs￨L￨NNS￨O￨- using￨L￨VBG￨O￨- mean￨L￨JJ￨O￨- field￨L￨JJ￨O￨- theory￨L￨NN￨O￨- is￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- provides￨L￨VBZ￨O￨- conditions￨L￨NNS￨O￨- on￨L￨IN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- show￨L￨VB￨O￨- how￨L￨WRB￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- spreading￨L￨VBG￨O￨A processes￨L￨NNS￨O￨A that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- n’t￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- evolve￨L￨VB￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- overwhelming￨L￨JJ￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- studied￨L￨VBN￨O￨- assume￨L￨VB￨O￨- that￨L￨DT￨O￨- transitions￨L￨NNS￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- state￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- recovering￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨O￨- process￨L￨NN￨O￨- that￨L￨WDT￨O￨- follows￨L￨VBZ￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨A distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +9￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 5￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- spreading￨L￨VBG￨O￨A processes￨L￨NNS￨O￨A we￨L￨PRP￨O￨- call￨L￨VBP￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- V￨U￨NN￨O￨- ∗￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- bottom￨L￨NN￨O￨- up￨L￨RP￨O￨- approach￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- parametric￨L￨JJ￨O￨A heterogeneity￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- description￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- used￨L￨VBN￨O￨- without￨L￨IN￨O￨- a￨L￨DT￨O￨- firm￨L￨NN￨O￨- mechanistic￨L￨JJ￨O￨- basis￨L￨NN￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- transmission￨L￨NN￨O￨- function￨L￨NN￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- gamma￨L￨NN￨O￨- distributed￨L￨VBN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- distributed￨L￨VBN￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- closed￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- suited￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- suggested￨L￨VBN￨O￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- unified￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- parametric￨L￨JJ￨O￨A heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- describe￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- as￨L￨IN￨O￨- having￨L￨VBG￨O￨- specific￨L￨NN￨O￨- parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- trait￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- values￨L￨NNS￨O￨- that￨L￨WDT￨O￨- vary￨L￨VBP￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- known￨L￨VBN￨O￨- results￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- distributed￨L￨VBN￨O￨- susceptibility￨L￨NN￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨A or￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- k￨L￨NN￨O￨- both￨L￨CC￨O￨- models￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- an￨L￨DT￨O￨- oscillatory￨L￨JJ￨O￨A phase￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- that￨L￨WDT￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- weak￨L￨JJ￨O￨- driving￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- inserted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- editor￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- Population￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- :￨L￨:￨O￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- analytical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- Ganna￨U￨NNP￨PERSON￨- Rozhnova￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ana￨U￨NNP￨PERSON￨- Nunes￨U￨NNP￨PERSON￨- Centro￨U￨NNP￨PERSON￨- de￨L￨IN￨PERSON￨- F´ısica￨U￨NNP￨PERSON￨- da￨L￨NNP￨O￨A Mat￨U￨NNP￨O￨- ´￨L￨POS￨O￨- eria￨L￨NN￨O￨- Condensada￨U￨NN￨O￨- and￨L￨CC￨O￨- Departamento￨U￨NNP￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- ,￨L￨,￨O￨- Faculdade￨U￨NNP￨O￨- de￨L￨IN￨O￨- Ciˆencias￨U￨NNP￨O￨- da￨L￨NNP￨O￨- Universidade￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Lisboa￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- P-1649-003￨U￨NNP￨O￨- Lisboa￨U￨NNP￨ORGANIZATION￨- Codex￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Portugal￨U￨NNP￨COUNTRY￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- date￨L￨NN￨O￨- /￨L￨:￨O￨- Revised￨U￨VBN￨O￨- version￨L￨NN￨O￨- :￨L￨:￨O￨- date￨L￨NN￨O￨- Abstract￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- major￨L￨JJ￨O￨- find￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A fever￨L￨NN￨CAUSE_OF_DEATH￨A epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- eradicated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- immunizing￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- because￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- directed￨L￨VBN￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- enough￨L￨RB￨O￨- to￨L￨TO￨O￨- halt￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- Macdonald￨U￨NNP￨PERSON￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- creation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- Ross-Macdonald￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- two￨L￨CD￨NUMBER￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨A structure￨L￨NN￨O￨A of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +Even￨U￨RB￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- eliminated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- cause￨L￨VBP￨O￨- dengue￨L￨JJ￨O￨A fever￨L￨NN￨CAUSE_OF_DEATH￨A to￨L￨TO￨O￨- reappear￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- importance￨L￨NN￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- us￨L￨PRP￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- interfering￨L￨VBG￨O￨- with￨L￨IN￨O￨- its￨L￨PRP$￨O￨- spreading￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- proposition￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- attempt￨L￨NN￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- the￨L￨DT￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨- mosquito￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- proposals￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- are￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- formulate￨L￨VBP￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨- partial￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- features￨L￨VBZ￨O￨- short-term￨L￨JJ￨O￨- immigration￨L￨NN￨O￨A effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- approach￨L￨NN￨O￨- with￨L￨IN￨O￨- age-structure￨L￨NN￨O￨- that￨L￨WDT￨O￨- takes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- short-term￨L￨JJ￨O￨- immigration￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- age-structured￨L￨JJ￨O￨- models￨L￨NNS￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- term￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- equilibria￨L￨NNS￨O￨- and￨L￨CC￨O￨- strategies￨L￨NNS￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- normal￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- die￨L￨VB￨O￨- out￨L￨RP￨O￨- ,￨L￨,￨O￨- unless￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- other￨L￨JJ￨O￨- influencing￨L￨NN￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- coming￨L￨VBG￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- via￨L￨IN￨O￨- immigration￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- usually￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- compartment￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- rather￨L￨RB￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- studying￨L￨VBG￨O￨- them￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- in￨L￨IN￨O￨- gaining￨L￨VBG￨O￨- important￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- spread￨L￨VBN￨O￨- out￨L￨RP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨A programs￨L￨NNS￨O￨A in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- mathematician￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- epidemiology￨L￨NN￨O￨A provides￨L￨VBZ￨O￨- new￨L￨JJ￨O￨- and￨L￨CC￨O￨- exciting￨L￨JJ￨O￨- branches￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiologist￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- offers￨L￨NNS￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- research￨L￨NN￨O￨- tool￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- simplest￨L￨JJS￨O￨- epidemiologic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- composed￨L￨VBN￨O￨- by￨L￨IN￨O￨- mutually￨L￨RB￨O￨- exclusive￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- a￨L￨DT￨O￨- reality￨L￨NN￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- about￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- had￨L￨VBN￨O￨- a￨L￨DT￨O￨- great￨L￨JJ￨O￨- influence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨A models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- differential￨L￨JJ￨O￨A equations￨L￨NNS￨O￨A ,￨L￨,￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- intuition￨L￨NN￨O￨- behind￨L￨IN￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- person￨L￨NN￨O￨- has￨L￨VBZ￨O￨- multiple￨L￨JJ￨O￨- potential￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- In￨U￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- serial￨L￨NN￨O￨- interval￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- symptom￨L￨NN￨O￨- onset￨L￨NN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- person￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- symptom￨L￨NN￨O￨- onset￨L￨NN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- his￨L￨PRP$￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- j￨L￨NN￨O￨- given￨L￨VBN￨O￨- m￨L￨NN￨O￨- potential￨L￨JJ￨O￨- infectors￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- specify￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- prove￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- generation￨L￨NN￨O￨- interval￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- susceptible￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- are￨L￨VBP￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A contact￨L￨NN￨O￨A from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NNP￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- argue￨L￨VBP￨O￨- that￨L￨IN￨O￨- hazards￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A contact￨L￨NN￨O￨A should￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- generation￨L￨NN￨O￨- or￨L￨CC￨O￨- serial￨L￨NN￨O￨- interval￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- hazard￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- infectors￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- defining￨L￨VBG￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- most￨L￨JJS￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- generation￨L￨NN￨O￨- interval￨L￨JJ￨O￨A contraction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- phenomenon￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- person￨L￨NN￨O￨- i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- he￨L￨PRP￨O￨- or￨L￨CC￨O￨- she￨L￨PRP￨O￨- makes￨L￨VBZ￨O￨- infectious￨L￨JJ￨O￨A contact￨L￨NN￨O￨A with￨L￨IN￨O￨- person￨L￨NN￨O￨- j￨L￨NN￨O￨- after￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨- interval￨L￨NN￨O￨- τij￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- wherein￨L￨WRB￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- they￨L￨PRP￨O￨- name￨L￨VBP￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- ,￨L￨,￨O￨- people￨L￨NNS￨O￨- they￨L￨PRP￨O￨- had￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- named￨L￨VBN￨O￨- undiagnosed￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- being￨L￨VBG￨O￨- traced￨L￨VBN￨O￨- and￨L￨CC￨O￨- prevented￨L￨VBN￨O￨- from￨L￨IN￨O￨- making￨L￨VBG￨O￨- further￨L￨JJ￨O￨- potentially￨L￨RB￨O￨- infectious￨L￨JJ￨O￨A contacts￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- isolation￨L￨NN￨O￨- or￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- probability￨L￨NN￨O￨- a￨L￨DT￨O￨- traced￨L￨VBN￨O￨- individual￨L￨JJ￨O￨- then￨L￨RB￨O￨- also￨L￨RB￨O￨- names￨L￨NNS￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- increased￨L￨VBN￨O￨- realism￨L￨NN￨O￨- ,￨L￨,￨O￨- incorporating￨L￨VBG￨O￨- a￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- may￨L￨MD￨O￨- make￨L￨VB￨O￨- it￨L￨PRP￨O￨- possible￨L￨JJ￨O￨- for￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- traced￨L￨VBN￨O￨- while￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- before￨L￨IN￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- any￨L￨DT￨O￨- infectious￨L￨JJ￨O￨A contacts￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- such￨L￨JJ￨O￨- this￨L￨DT￨O￨- can￨L￨MD￨O￨- enhance￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- .￨L￨.￨O￨- +Numerical￨U￨JJ￨O￨- illustrations￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- latent￨L￨JJ￨O￨A periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- delays￨L￨NNS￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- delays￨L￨NNS￨O￨- experienced￨L￨VBN￨O￨- by￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- individual￨L￨NN￨O￨- are￨L￨VBP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- or￨L￨CC￨O￨- independent￨L￨JJ￨RELIGION￨- length￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- little￨L￨JJ￨O￨- difference￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- →￨L￨NN￨O￨- exposed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- =￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- →￨L￨SYM￨O￨- infective￨L￨JJ￨O￨- →￨L￨NN￨O￨- removed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- scheme￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- name￨L￨VB￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- infectious￨L￨JJ￨O￨A contacts￨L￨NNS￨O￨A ,￨L￨,￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- then￨L￨RB￨O￨- removed￨L￨VBN￨O￨- if￨L￨IN￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- already￨L￨RB￨O￨- after￨L￨IN￨O￨- some￨L￨DT￨O￨- tracing￨L￨VBG￨O￨- delay￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- stop￨L￨VBP￨O￨- short￨L￨JJ￨O￨- of￨L￨IN￨O￨- providing￨L￨VBG￨O￨- insights￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A centrality￨L￨NN￨O￨- estimator￨L￨NN￨O￨- in￨L￨IN￨O￨- more￨L￨JJR￨O￨- general￨L￨JJ￨TITLE￨- settings￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- irregular￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- SI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- non-exponential￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- times￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- overcomes￨L￨VBZ￨O￨- this￨L￨DT￨O￨- limitation￨L￨NN￨O￨- and￨L￨CC￨O￨- establishes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A centrality￨L￨NN￨O￨- for￨L￨IN￨O￨- source￨L￨NN￨O￨- detection￨L￨NN￨O￨- for￨L￨IN￨O￨- generic￨L￨JJ￨O￨- random￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- SI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- time￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- graph￨L￨NN￨O￨- increases￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- path￨L￨NN￨O￨- graph￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2-regular￨L￨JJ￨O￨- tree￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- source￨L￨NN￨O￨- detection￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- 0￨L￨CD￨NUMBER￨- while￨L￨IN￨O￨- for￨L￨IN￨O￨- d-regular￨L￨JJ￨O￨- trees￨L￨NNS￨O￨A with￨L￨IN￨O￨- d￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- detection￨L￨NN￨O￨- ,￨L￨,￨O￨- say￨L￨VBP￨O￨- αd￨L￨NN￨O￨- ,￨L￨,￨O￨- remains￨L￨VBZ￨O￨- bounded￨L￨VBN￨O￨- away￨L￨RB￨O￨- from￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- than￨L￨IN￨O￨- 1/2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- establish￨L￨VBP￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- estimator￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- popular￨L￨JJ￨O￨- Susceptible￨U￨NNP￨O￨- Infected￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- times￨L￨NNS￨O￨- for￨L￨IN￨O￨- regular￨L￨JJ￨O￨- trees￨L￨NNS￨O￨A .￨L￨.￨O￨- +Finding￨U￨NNP￨O￨- Rumor￨U￨NNP￨O￨- Sources￨U￨NNS￨O￨- on￨L￨IN￨O￨- Random￨U￨NNP￨ORGANIZATION￨- Trees￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electrical￨U￨JJ￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Computer￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Massachusetts￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Cambridge￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- MA￨U￨NNP￨STATE_OR_PROVINCE￨- 02139￨L￨CD￨DATE￨- ,￨L￨,￨O￨- Sloan￨U￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Management￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Massachusetts￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Cambridge￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- MA￨U￨NNP￨STATE_OR_PROVINCE￨- 02139￨L￨CD￨DATE￨- ,￨L￨,￨O￨- Tauhid￨U￨NNP￨PERSON￨- Zaman￨U￨NNP￨PERSON￨- Devavrat￨U￨NNP￨PERSON￨- Shah￨U￨NNP￨PERSON￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- rumor￨L￨NN￨O￨A which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- spread￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- using￨L￨VBG￨O￨- only￨L￨RB￨O￨- observations￨L￨NNS￨O￨- about￨L￨IN￨O￨- which￨L￨WDT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- information￨L￨NN￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- when￨L￨WRB￨O￨- these￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- became￨L￨VBD￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- concerns￨L￨NNS￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- of￨L￨IN￨O￨- households￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- varies￨L￨VBZ￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- we￨L￨PRP￨O￨- restrict￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- having￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- mild￨L￨JJ￨O￨A and￨L￨CC￨O￨- severe￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- whether￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- which￨L￨WDT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- underlying￨L￨VBG￨O￨- explanations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- causing￨L￨VBG￨O￨- the￨L￨DT￨O￨- varying￨L￨VBG￨O￨- response￨L￨NN￨O￨- when￨L￨WRB￨O￨- given￨L￨VBN￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- household￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- containing￨L￨VBG￨O￨- mild￨L￨JJ￨O￨A and￨L￨CC￨O￨- severe￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Large￨U￨JJ￨O￨- population￨L￨NN￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- focus￨L￨NN￨O￨- being￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- mild￨L￨JJ￨O￨A and￨L￨CC￨O￨- severe￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- household￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- becomes￨L￨VBZ￨O￨- established￨L￨VBN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- →￨L￨NN￨O￨- infected￨L￨JJ￨O￨- →￨L￨NN￨O￨- removed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- household￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- response￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- either￨L￨CC￨O￨- mild￨L￨JJ￨O￨A or￨L￨CC￨O￨- severe￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- response￨L￨NN￨O￨- also￨L￨RB￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- infectiousness￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Household￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- infector￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- severity￨L￨NN￨O￨- ,￨L￨,￨O￨- Kullback-Leibler￨U￨NN￨O￨- divergence￨L￨NN￨O￨- ,￨L￨,￨O￨- multitype￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- varying￨L￨VBG￨O￨- response￨L￨NN￨O￨A ,￨L￨,￨O￨- final￨L￨JJ￨O￨- outcome￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- knocking￨L￨VBG￨O￨- out￨L￨RP￨O￨- gap￨L￨NN￨O￨- junctions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- electrical￨L￨JJ￨O￨- synapses￨L￨NNS￨O￨- among￨L￨IN￨O￨- neurons￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- substantial￨L￨JJ￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- retinal￨L￨JJ￨O￨- ganglion￨L￨NN￨O￨- cells￨L￨NNS￨O￨- of￨L￨IN￨O￨- mammals￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- range￨L￨NN￨O￨- and￨L￨CC￨O￨- sensitivity￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- exponent￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- any￨L￨DT￨O￨- dimension￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- range￨L￨NN￨O￨- and￨L￨CC￨O￨- sensitivity￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- function￨L￨NN￨O￨- are￨L￨VBP￨O￨- maximized￨L￨VBN￨O￨- precisely￨L￨RB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- nonequilibrium￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- to￨L￨TO￨O￨- self-sustained￨L￨JJ￨O￨- activity￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- reasoning￨L￨NN￨O￨- recently￨L￨RB￨DATE￨- proposed￨L￨VBD￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Stevens￨U￨NNP￨PERSON￨- ’￨L￨POS￨O￨- exponent￨L￨NN￨O￨- m￨L￨NN￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- range￨L￨NN￨O￨- and￨L￨CC￨O￨- sensitivity￨L￨NN￨O￨A of￨L￨IN￨O￨- psychophysical￨L￨JJ￨O￨- response￨L￨NN￨O￨- functions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- ≃￨L￨CD￨NUMBER￨- 0.6￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- smell￨L￨NN￨O￨- of￨L￨IN￨O￨- heptane￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- response￨L￨NN￨O￨A function￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- mean￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- ρ￨L￨VBP￨O￨- versus￨L￨CC￨O￨- h￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- via￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- d￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- mean-field￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- single-site￨L￨JJ￨O￨- and￨L￨CC￨O￨- pair￨L￨NN￨O￨- levels￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ∀￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Electrical￨U￨JJ￨O￨- coupling￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- excite￨L￨VB￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- might￨L￨MD￨O￨- have￨L￨VB￨O￨- the￨L￨DT￨O￨- functional￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- augmenting￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- dynamic￨L￨JJ￨O￨- range￨L￨NN￨O￨- and￨L￨CC￨O￨- sensitivity￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- generating￨L￨VBG￨O￨- function￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PGF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- formalism￨L￨NN￨O￨- for￨L￨IN￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- makes￨L￨VBZ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- network-centric￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- well-defined￨L￨JJ￨O￨- category￨L￨NN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- node-centric￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infecteds￨L￨NNS￨O￨- or￨L￨CC￨O￨- susceptibles￨L￨NNS￨O￨- .￨L￨.￨O￨- +Random￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- specified￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- as￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamically￨L￨RB￨O￨- modeling￨L￨NN￨O￨- SIR-type￨U￨JJ￨MISC￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- random￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A remains￨L￨VBZ￨O￨- complex￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- dramatic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A plays￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- spreads￨L￨VBZ￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- inserted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- editor￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- Erik￨U￨NNP￨PERSON￨- Volz￨U￨NNP￨PERSON￨- SIR￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- random￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- Received￨U￨VBN￨O￨- :￨L￨:￨O￨- January￨U￨NNP￨DATE￨- 17￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2007￨L￨CD￨DATE￨- –￨L￨:￨O￨- c￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- reaction-diffusion￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- treated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨A distribution￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- SHIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- discontinuous￨L￨JJ￨O￨- jump￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- shows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- transition￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expected￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨A susceptible￨L￨JJ￨O￨A population￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Final￨U￨JJ￨O￨- size￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨A SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SHIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- simulated￨L￨JJ￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- modified￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨A Susceptible-Infected-Removed￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- call￨L￨VBP￨O￨- the￨L￨DT￨O￨- SHIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Outbreaks￨U￨NNS￨O￨- of￨L￨IN￨O￨- coinfections￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- role￨L￨NN￨O￨A of￨L￨IN￨O￨- cooperativity￨L￨NN￨O￨- Li￨U￨NNP￨PERSON￨- Chen￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Fakhteh￨U￨NNP￨PERSON￨- Ghanbarnejad￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Weiran￨U￨NNP￨PERSON￨- Cai￨U￨NNP￨PERSON￨- ,2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Peter￨U￨NNP￨PERSON￨- Grassberger1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- 1Max￨L￨NN￨O￨- Planck￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- the￨L￨DT￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Complex￨U￨JJ￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Dresden￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Germany￨U￨NNP￨COUNTRY￨- 2Faculty￨L￨NNP￨O￨- of￨L￨IN￨O￨- Electrical￨U￨JJ￨O￨- and￨L￨CC￨O￨- Computer￨U￨NNP￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- TU￨U￨NNP￨LOCATION￨- Dresden￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Dresden￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Germany￨U￨NNP￨COUNTRY￨- 3￨L￨CD￨NUMBER￨- JSC￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- FZ￨U￨NNP￨O￨- J￨U￨NNP￨O￨- ¨￨L￨NNP￨O￨- ulich￨L￨NN￨O￨- ,￨L￨,￨O￨- D-52425￨U￨NN￨O￨- J￨U￨NN￨O￨- ¨￨L￨CD￨NUMBER￨- ulich￨L￨NN￨O￨- ,￨L￨,￨O￨- Germany￨U￨NNP￨COUNTRY￨- ∗￨L￨NNP￨O￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 29￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Modeling￨U￨VBG￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- studying￨L￨VBG￨O￨- how￨L￨WRB￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- spread￨L￨VBN￨O￨- ,￨L￨,￨O￨- predicting￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- future￨L￨JJ￨DATE￨- course￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- designing￨L￨VBG￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +Apart￨U￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- phase￨L￨NN￨O￨A transition￨L￨NN￨O￨A for￨L￨IN￨O￨- single-disease￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- continuous￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- where￨L￨WRB￨O￨- both￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- must￨L￨MD￨O￨- coexist￨L￨VB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- discontinuous￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- already￨L￨RB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- both￨L￨CC￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- passes￨L￨VBZ￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- relative￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- size￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- gradually￨L￨RB￨O￨- from￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- implying￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- second￨L￨JJ￨ORDINAL￨- order￨L￨NN￨O￨- ”￨L￨''￨O￨- phase￨L￨NN￨O￨A transition￨L￨NN￨O￨A .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- thus￨L￨RB￨O￨- extremely￨L￨RB￨O￨A important￨L￨JJ￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- pioneering￨L￨JJ￨O￨- work￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- direction￨L￨NN￨O￨A was￨L￨VBD￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- by￨L￨IN￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- Susceptible-Infective-Removed￨U￨NNP￨O￨- ’￨L￨''￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- compartments￨L￨NNS￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- non-monotonic￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- intervene￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- fundamentally￨L￨RB￨O￨- new￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- change￨L￨VB￨O￨A the￨L￨DT￨O￨- network￨L￨NN￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- unexpectedly-high￨L￨JJ￨O￨- virulence￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- SIR-like￨U￨JJ￨MISC￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- give￨L￨VB￨O￨- an￨L￨DT￨O￨- elementary￨L￨JJ￨O￨- proof￨L￨NN￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- network￨L￨NN￨O￨- increasing￨L￨VBG￨O￨A the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +Contact￨U￨NN￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- significantly￨L￨RB￨O￨- change￨L￨VB￨O￨A the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- 2FleeSIR￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- non-monotonic￨L￨JJ￨O￨- :￨L￨:￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨A transmissibility￨L￨NN￨O￨- actually￨L￨RB￨O￨- decreases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- extent￨L￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- this￨L￨DT￨O￨- dependence￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨A are￨L￨VBP￨O￨- not￨L￨RB￨O￨- contingent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- probably￨L￨RB￨O￨- predictable￨L￨JJ￨O￨- based￨L￨VBN￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- interesting￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- cooperation￨L￨NN￨O￨- can￨L￨MD￨O￨- change￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- transition￨L￨NN￨O￨A from￨L￨IN￨O￨- being￨L￨VBG￨O￨- continuous￨L￨JJ￨O￨- to￨L￨TO￨O￨- abrupt￨L￨JJ￨O￨- when￨L￨WRB￨O￨- external￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- vary￨L￨VBP￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- slightly￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- removed￨L￨VBN￨O￨A (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- type￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- mutually￨L￨RB￨O￨- cooperative￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- already￨L￨RB￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- getting￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- NumericCitation￨U￨NNP￨O￨- Newman￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ferrario￨U￨NNP￨PERSON￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- co-infection￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- removed￨L￨VBN￨O￨A (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- diffusing￨L￨VBG￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- moment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- finite￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- transition￨L￨NN￨O￨A is￨L￨VBZ￨O￨- continuous￨L￨JJ￨O￨- for￨L￨IN￨O￨- low￨L￨JJ￨O￨- cooperativity￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- discontinuous￨L￨JJ￨O￨- when￨L￨WRB￨O￨- cooperativity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- high￨L￨JJ￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- G0￨U￨NN￨O￨- above￨L￨IN￨O￨- correctly￨L￨RB￨O￨- generates￨L￨VBZ￨O￨- tribution￨L￨NN￨O￨- of￨L￨IN￨O￨- degrees￨L￨NNS￨O￨A of￨L￨IN￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- vertices￨L￨NNS￨O￨- the￨L￨DT￨O￨- disin￨L￨NN￨O￨- our￨L￨PRP$￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- generating￨L￨NN￨O￨- function￨L￨NN￨O￨- is￨L￨VBZ￨O￨- needed￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- reached￨L￨VBN￨O￨- by￨L￨IN￨O￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- edge￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- degrees￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- vertices￨L￨NNS￨O￨- reached￨L￨VBN￨O￨- by￨L￨IN￨O￨- following￨L￨VBG￨O￨- edges￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- kpk￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- the￨L￨DT￨O￨- generating￨L￨VBG￨O￨- function￨L￨NN￨O￨- for￨L￨IN￨O￨- those￨L￨DT￨O￨- degrees￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- Pk￨U￨NN￨O￨- kpk￨L￨NN￨O￨- xk￨L￨NN￨O￨- Pk￨U￨NN￨O￨- kpk￨L￨NN￨O￨- In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ways￨L￨NNS￨O￨- =￨L￨JJ￨O￨- x￨L￨CC￨O￨- G￨U￨NN￨O￨- ′￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- G￨U￨NN￨O￨- ′￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- also￨L￨RB￨O￨- need￨L￨VB￨O￨- generating￨L￨VBG￨O￨A functions￨L￨NNS￨O￨- G0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ;￨L￨:￨O￨- T￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- G1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ;￨L￨:￨O￨- T￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- occupied￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- attached￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- vertex￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- T￨U￨NN￨O￨- .￨L￨.￨O￨- +Now￨U￨RB￨DATE￨- imagine￨L￨VB￨O￨- watching￨L￨VBG￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- starts￨L￨VBZ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- 3￨L￨CD￨NUMBER￨- 4￨L￨CD￨NUMBER￨- Higher￨U￨JJR￨O￨- moments￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨- from￨L￨IN￨O￨- higher￨L￨JJR￨O￨- derivatives￨L￨NNS￨O￨- also￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- consider￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- structured￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨VBN￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨A divided￨L￨VBN￨O￨A into￨L￨IN￨O￨- men￨L￨NNS￨O￨- and￨L￨CC￨O￨- women￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- traditional￨L￨JJ￨O￨- inference￨L￨NN￨O￨A may￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- poor￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- fitted￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- capture￨L￨VB￨O￨- important￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Observations￨U￨NNS￨O￨- on￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- space-time￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- becoming￨L￨VBG￨O￨- increasingly￨L￨RB￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨A for￨L￨IN￨O￨- unknown￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- traditional￨L￨JJ￨O￨- likelihood-based￨L￨JJ￨O￨- inference￨L￨NN￨O￨A for￨L￨IN￨O￨- many￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- challenging￨L￨JJ￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- expensive￨L￨JJ￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- likelihood-based￨L￨JJ￨O￨- inference￨L￨NN￨O￨- computationally￨L￨RB￨O￨- intractable￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- via￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- computationally￨L￨RB￨O￨- expedient￨L￨JJ￨O￨- ,￨L￨,￨O￨- provides￨L￨VBZ￨O￨- accurate￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- inference￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- fit￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- multi-patch￨L￨JJ￨O￨- and￨L￨CC￨O￨- multi-group￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- structured￨L￨VBN￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- groups￨L￨NNS￨O￨- and￨L￨CC￨O￨- interacts￨L￨VBZ￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- patches￨L￨NNS￨O￨A where￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- takes￨L￨VBZ￨O￨- place￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- patches￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- mobility￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- patches￨L￨NNS￨O￨A and￨L￨CC￨O￨- mobility￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- on￨L￨IN￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- are￨L￨VBP￨O￨- explored￨L￨VBN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- framework￨L￨NN￨O￨- is￨L￨VBZ￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- SEIRS￨U￨NN￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- .￨L￨.￨O￨- +Mathematics￨U￨NNP￨O￨- Sub￨U￨NN￨O￨- ject￨L￨NN￨O￨A Classification￨U￨NN￨O￨- :￨L￨:￨O￨- 92D25￨L￨NN￨O￨- ,￨L￨,￨O￨- 92D30￨L￨NN￨O￨- Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Multi-Patch￨U￨NNP￨O￨- ,￨L￨,￨O￨- Multi-Group￨U￨NNP￨O￨- ,￨L￨,￨O￨- Mobility￨U￨NN￨O￨- ,￨L￨,￨O￨- Heterogeneity￨U￨NN￨O￨- ,￨L￨,￨O￨- Residence￨U￨NNP￨ORGANIZATION￨- Times￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Global￨U￨NNP￨O￨- Stability￨U￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- particles￨L￨NNS￨O￨A representing￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- are￨L￨VBP￨O￨- distributed￨L￨VBN￨O￨- randomly￨L￨RB￨O￨- and￨L￨CC￨O￨- independently￨L￨RB￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- cells￨L￨NNS￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Lh￨U￨NNP￨O￨- ,￨L￨,￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- probabilities￨L￨NNS￨O￨- given￨L￨VBN￨O￨- Published￨U￨VBN￨O￨- in￨L￨IN￨O￨- "￨L￨``￨O￨- Discrete￨U￨NNP￨MISC￨- Dynamics￨U￨NNP￨MISC￨- in￨L￨IN￨MISC￨- Nature￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- Society￨U￨NNP￨O￨- "￨L￨''￨O￨- ,￨L￨,￨O￨- vol￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- lattice￨L￨NN￨O￨- gas￨L￨NN￨O￨- cellular￨L￨JJ￨O￨- automaton￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LGCA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- type￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- inhomogeneities￨L￨NNS￨O￨- in￨L￨IN￨O￨- initial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- populations￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- type￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- initial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- particles￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- at￨L￨IN￨O￨- most￨L￨JJS￨O￨- six￨L￨CD￨NUMBER￨- particles￨L￨NNS￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- type￨L￨NN￨O￨- ,￨L￨,￨O￨- per￨L￨IN￨O￨- cell￨L￨NN￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- four￨L￨CD￨NUMBER￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- cells￨L￨NNS￨O￨- are￨L￨VBP￨O￨- squares￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- very￨L￨RB￨O￨- unrealistic￨L￨JJ￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- endemic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- relaying￨L￨VBG￨O￨- on￨L￨IN￨O￨- very￨L￨RB￨O￨- small￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- named￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- in￨L￨IN￨O￨- "￨L￨``￨O￨- Discrete￨U￨NNP￨MISC￨- Dynamics￨U￨NNP￨MISC￨- in￨L￨IN￨MISC￨- Nature￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- Society￨U￨NNP￨O￨- "￨L￨''￨O￨- ,￨L￨,￨O￨- vol￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- expanding￨L￨VBG￨O￨- user-generated￨L￨JJ￨O￨- content￨L￨NN￨O￨- in￨L￨IN￨O￨- Sina￨U￨NNP￨PERSON￨- Weibo￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- micro-blog￨L￨NN￨O￨- site￨L￨NN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- find￨L￨NN￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- popular￨L￨JJ￨O￨A messages￨L￨NNS￨O￨- often￨L￨RB￨O￨- follow￨L￨VBP￨O￨- a￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- that￨L￨WDT￨O￨- differs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- that￨L￨DT￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- common￨L￨JJ￨O￨- believe￨L￨VBP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- involve￨L￨VBP￨O￨- analyzing￨L￨VBG￨O￨- large￨L￨JJ￨O￨- amounts￨L￨NNS￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- others￨L￨NNS￨O￨- formulate￨L￨VBP￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- popular￨L￨JJ￨O￨A a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- piece￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- will￨L￨MD￨O￨- become￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- overloaded￨L￨VBN￨O￨- with￨L￨IN￨O￨- excess￨L￨JJ￨O￨- information￨L￨NN￨O￨A feeds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- either￨L￨CC￨O￨- reaches￨L￨VBZ￨O￨- out￨L￨RP￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- above￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- it￨L￨PRP￨O￨- would￨L￨MD￨O￨- never￨L￨RB￨O￨- be￨L￨VB￨O￨- well￨L￨RB￨O￨- received￨L￨VBN￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- handful￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- contents￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- widely￨L￨RB￨O￨- spread￨L￨VBN￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- the￨L￨DT￨O￨- greater￨L￨JJR￨O￨A the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- friends￨L￨NNS￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- greater￨L￨JJR￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- repeated￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- competition￨L￨NN￨O￨- for￨L￨IN￨O￨- attention￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- FSIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨A that￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- activity-based￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- approach￨L￨NN￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- limit￨L￨NN￨O￨- ,￨L￨,￨O￨- analytical￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- activities￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- memory￨L￨NN￨O￨A effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- introduced￨L￨VBN￨O￨- activity-driven￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- memory￨L￨NN￨O￨A .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- memory￨L￨NN￨O￨A reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- for￨L￨IN￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- favouring￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- Spreading￨U￨NN￨O￨- and￨L￨CC￨O￨- Aging￨U￨NN￨O￨- in￨L￨IN￨O￨- Temporal￨U￨JJ￨O￨- Networks￨U￨NNP￨O￨- with￨L￨IN￨O￨- Memory￨U￨NN￨O￨- Michele￨U￨NNP￨PERSON￨- Tizzani￨U￨NNP￨PERSON￨- ,1￨L￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Simone￨U￨NNP￨PERSON￨- Lenti￨U￨NNP￨PERSON￨- ,3￨L￨CD￨NUMBER￨- Enrico￨U￨NNP￨PERSON￨- Ubaldi￨U￨NNP￨PERSON￨- ,4￨L￨NN￨O￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- Alessandro￨U￨NNP￨PERSON￨- Vezzani￨U￨NNP￨PERSON￨- ,6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- Claudio￨U￨NNP￨PERSON￨- Castellano￨U￨NNP￨PERSON￨- ,7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Raffaella￨U￨NNP￨MISC￨- Burioni1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- 1Dipartimento￨L￨NN￨O￨- di￨L￨FW￨O￨A Scienze￨U￨FW￨O￨- Matematiche￨U￨FW￨O￨- ,￨L￨,￨O￨- Fisiche￨U￨NNP￨PERSON￨- e￨L￨SYM￨O￨- Informatiche￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Università￨U￨NNP￨O￨- degli￨L￨NNS￨O￨- Studi￨U￨NNP￨PERSON￨- di￨L￨NNP￨O￨- Parma￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Parco￨U￨NNP￨ORGANIZATION￨- Area￨U￨NNP￨ORGANIZATION￨- del￨L￨NNP￨O￨- le￨L￨DT￨O￨- Scienze￨U￨NNP￨O￨- ,￨L￨,￨O￨- 7/A￨L￨NNP￨O￨- 43124￨L￨CD￨NUMBER￨- Parma￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- 2￨L￨CD￨NUMBER￨- INFN￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Gruppo￨U￨NNP￨ORGANIZATION￨- Col￨U￨NNP￨ORGANIZATION￨- legato￨L￨NNP￨ORGANIZATION￨- di￨L￨NNP￨ORGANIZATION￨- Parma￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Parco￨U￨NNP￨ORGANIZATION￨- Area￨U￨NNP￨ORGANIZATION￨- del￨L￨NNP￨O￨- le￨L￨DT￨O￨- Scienze￨U￨NNP￨O￨- 7/A￨L￨NNP￨O￨- ,￨L￨,￨O￨- 43124￨L￨CD￨NUMBER￨- Parma￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- 3Dipartimento￨L￨NN￨O￨- di￨L￨FW￨O￨- Fisica￨U￨FW￨O￨- ,￨L￨,￨O￨- "￨L￨``￨O￨- Sapienza￨U￨NNP￨O￨- ”￨L￨''￨O￨- Università￨U￨NNP￨ORGANIZATION￨- di￨L￨NNP￨ORGANIZATION￨- Roma￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- P.le￨U￨NNP￨O￨- A￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- Birth-Death￨U￨NNP￨MISC￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BDSIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- gene￨L￨NN￨O￨- genealogy￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- phylogeny￨L￨NN￨O￨- connecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- sampled￨L￨VBN￨O￨A sequences￨L￨NNS￨O￨- ,￨L￨,￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- transmission￨L￨NN￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- note￨L￨NN￨O￨- that￨L￨IN￨O￨- of￨L￨IN￨O￨- course￨L￨NN￨O￨- this￨L￨DT￨O￨- transmission￨L￨NN￨O￨- history￨L￨NN￨O￨- is￨L￨VBZ￨O￨- incomplete￨L￨JJ￨O￨- as￨L￨IN￨O￨- many￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- sampled￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- here￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- birth-death￨L￨JJ￨O￨- skyline￨L￨NN￨O￨- plot￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- parametrized￨L￨VBN￨O￨- to￨L￨TO￨O￨- enable￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- classic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- changing￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- composition￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- Stadler￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- birth-death-sampling￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- birth-death￨L￨JJ￨O￨- skyline￨L￨NN￨O￨- plot￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- BDSKY￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- serially￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- rate￨L￨NN￨O￨- changes￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- phylodynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- simultaneously￨L￨RB￨O￨- estimates￨L￨VBZ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- reconstructs￨L￨VBZ￨O￨- phylogenetic￨L￨JJ￨O￨- history￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- BDSIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- self-limited￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- outbreak￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- identical￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- small￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- out-components￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- giant￨L￨JJ￨O￨A strongly-connected￨L￨JJ￨O￨- component￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- occurs￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- giant￨L￨JJ￨O￨- in-component￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- contained￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- giant￨L￨JJ￨O￨- out-component￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- M.E.J.￨U￨NNP￨PERSON￨- Newman￨U￨NNP￨PERSON￨- claimed￨L￨VBD￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- network-based￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- Susceptible-Infectious-Removed￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- isomorphic￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- bond￨L￨NN￨O￨A percolation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- bonds￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- bond￨L￨NN￨O￨- occupation￨L￨NN￨O￨- probability￨L￨NN￨O￨- is￨L￨VBZ￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- marginal￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- neighbor￨L￨NN￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- these￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- Newman￨U￨NNP￨PERSON￨- claimed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- exactly￨L￨RB￨O￨- isomorphic￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- bond￨L￨NN￨O￨A percolation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- bond￨L￨NN￨O￨- occupation￨L￨NN￨O￨- probability￨L￨NN￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- any￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- connected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- considered￨L￨VBN￨O￨- by￨L￨IN￨O￨- Newman￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- percolation￨L￨NN￨O￨- network￨L￨NN￨O￨- predicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- mean￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- bond￨L￨NN￨O￨A percolation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- bond￨L￨NN￨O￨A percolation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- fails￨L￨VBZ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- correct￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nondegenerate￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- cases￨L￨NNS￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- initially￨L￨RB￨O￨- infected￨L￨VBN￨O￨- :￨L￨:￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- evolves￨L￨VBZ￨O￨- in￨L￨IN￨O￨- essentially￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- manner￨L￨NN￨O￨- as￨L￨IN￨O￨- its￨L￨PRP$￨O￨- branching￨L￨VBG￨O￨A envelope￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- evolves￨L￨VBZ￨O￨- like￨L￨IN￨O￨- a￨L￨DT￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- size-dependent￨L￨JJ￨O￨- drift￨L￨NN￨O￨- .￨L￨.￨O￨- +55￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 167￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 178￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.1214￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 074921707000000346￨L￨CD￨NUMBER￨- Critical￨U￨JJ￨O￨- scaling￨L￨NN￨O￨A of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ∗￨L￨VBP￨O￨- Steven￨U￨NNP￨PERSON￨- P.￨U￨NNP￨PERSON￨- Abstract￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- from￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- population￨L￨NN￨O￨- by￨L￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- p￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- coin￨L￨NN￨O￨- tosses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- and￨L￨CC￨O￨- phrases￨L￨NNS￨O￨- :￨L￨:￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- Feller￨U￨NNP￨PERSON￨- diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- branching￨L￨VBG￨O￨A random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- ,￨L￨,￨O￨- Dawson-Watanabe￨U￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- critical￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- .￨L￨.￨O￨- +Scaling￨U￨VBG￨O￨- laws￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- parameter￨L￨NN￨O￨- p￨L￨NN￨O￨- is￨L￨VBZ￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- critical￨L￨JJ￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- spatial￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- henceforth￨L￨RB￨O￨- call￨L￨VB￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- −￨L￨NN￨O￨- d￨L￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Assume￨U￨VB￨O￨- that￨L￨DT￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- lattice￨L￨NN￨O￨- point￨L￨NN￨O￨- x￨L￨CC￨O￨- ∈￨L￨SYM￨O￨- Zd￨U￨NN￨O￨- as￨L￨IN￨O￨- SPATIAL￨U￨JJ￨O￨- EPIDEMICS￨U￨NNS￨O￨- :￨L￨:￨O￨- CRITICAL￨U￨NNP￨O￨- BEHAVIOR￨U￨NNP￨O￨- IN￨U￨IN￨O￨- ONE￨U￨CD￨NUMBER￨- DIMENSION￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- tossing￨L￨VBG￨O￨- a￨L￨DT￨O￨- p￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- coin￨L￨NN￨O￨- for￨L￨IN￨O￨- every￨L￨DT￨O￨- pair￨L￨NN￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- drawing￨L￨VBG￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- between￨L￨IN￨O￨- x￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- coin￨L￨NN￨O￨- toss￨L￨VBP￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Head￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- Erd￨U￨NNP￨MISC￨- ¨￨L￨SYM￨MISC￨- os-Renyi￨L￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- random￨L￨JJ￨O￨A graph￨L￨NN￨O￨A determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- these￨L￨DT￨O￨- edges￨L￨NNS￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- set￨L￨VBN￨O￨- Y1￨U￨NN￨O￨- of￨L￨IN￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +R.￨U￨NNP￨PERSON￨- Dolgoarshinnykh￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- author￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- that￨L￨IN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- there￨L￨EX￨O￨- critical￨L￨JJ￨O￨A threshold￨L￨NN￨O￨- effect￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- here￨L￨RB￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- J0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- N￨U￨NN￨O￨- 1/3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- distribution￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- involves￨L￨VBZ￨O￨- first￨L￨JJ￨O￨- passage￨L￨NN￨O￨- times￨L￨NNS￨O￨- by￨L￨IN￨O￨- N￨U￨NN￨O￨- 1/2￨L￨CD￨NUMBER￨- Ornstein-Uhlenbeck￨U￨NNP￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨A graph￨L￨NN￨O￨A ,￨L￨,￨O￨- simulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- generations￨L￨NNS￨O￨- Yn￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR-d￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- rule￨L￨NN￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- case￨L￨NN￨O￨- :￨L￨:￨O￨- For￨U￨IN￨O￨- each￨L￨DT￨O￨- generation￨L￨NN￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- set￨L￨VBN￨O￨- Yn￨U￨NN￨O￨- +1￨L￨NN￨NUMBER￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- vertices￨L￨NNS￨O￨- x￨L￨CC￨O￨- 6￨L￨CD￨NUMBER￨- ∈￨L￨NN￨O￨- ∪￨L￨NN￨O￨- j￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- Yj￨U￨NN￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- Yn￨U￨NN￨O￨- .￨L￨.￨O￨- +Branching￨U￨VBG￨O￨- envelopes￨L￨NNS￨O￨- of￨L￨IN￨O￨- or￨L￨CC￨O￨- SIR￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- branching￨L￨VBG￨O￨A random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- Any￨U￨DT￨O￨- particle￨L￨NN￨O￨- located￨L￨JJ￨O￨- at￨L￨IN￨O￨- site￨L￨NN￨O￨- x￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- lives￨L￨VBZ￨O￨- for￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- unit￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Spatial￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- branching￨L￨VBG￨O￨A random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- ,￨L￨,￨O￨- Dawson-Watanabe￨U￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- critical￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- various￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- action￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- both￨L￨DT￨O￨- household-based￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- chosen￨L￨VBN￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- households￨L￨NNS￨O￨A in￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- reside￨L￨VBP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- acquaintance￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- targets￨L￨VBZ￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- →￨L￨NN￨O￨- infected￨L￨JJ￨O￨- →￨L￨NN￨O￨- removed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- for￨L￨IN￨O￨- amongst￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- partitioned￨L￨VBN￨O￨- into￨L￨IN￨O￨- households￨L￨NNS￨O￨A .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- Bollob￨U￨FW￨PERSON￨- ´￨L￨''￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1980￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Newman￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Strogatz￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Watts￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- 2001￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Newman￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2002￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- partitioned￨L￨VBN￨O￨- into￨L￨IN￨O￨- households￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- Ball￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- both￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A scheme￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- few￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- infectives￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- parameter￨L￨NN￨O￨- which￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- such￨L￨JJ￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Branching￨U￨VBG￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- configuration￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- threshold￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- considers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- →￨L￨NN￨O￨- infective￨L￨JJ￨O￨- →￨L￨NN￨O￨- removed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- make￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- ways￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- within￨L￨IN￨O￨- ‘￨L￨``￨O￨- households￨L￨NNS￨O￨A ’￨L￨''￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- for￨L￨IN￨O￨- ease￨L￨NN￨O￨- of￨L￨IN￨O￨- exposition￨L￨NN￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- equal￨L￨JJ￨O￨- size￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- describing￨L￨VBG￨O￨- additional￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- σ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- D￨U￨NN￨O￨- <￨L￨JJR￨O￨- ∞￨L￨CD￨NUMBER￨- ensures￨L￨VBZ￨O￨- that￨L￨IN￨O￨- as￨L￨IN￨O￨- m￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- imperfections￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- global￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- converges￨L￨VBZ￨O￨- in￨L￨IN￨O￨- distribution￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨PERSON￨- random￨L￨JJ￨O￨- variable￨L￨JJ￨O￨- whose￨L￨WP$￨O￨- mean￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µD￨L￨NN￨O￨- ,￨L￨,￨O￨- σ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- households￨L￨NNS￨O￨A as￨L￨IN￨O￨- macro-individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Theorem￨U￨NNP￨O￨- 3.1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Email￨U￨VB￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Keywords￨U￨NNPS￨O￨- Branching￨U￨VBG￨O￨- processes￨L￨NNS￨O￨- ;￨L￨:￨O￨- coupling￨L￨NN￨O￨- ;￨L￨:￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ;￨L￨:￨O￨- final￨L￨JJ￨O￨- outcome￨L￨NN￨O￨- ;￨L￨:￨O￨- households￨L￨NNS￨O￨A ;￨L￨:￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ;￨L￨:￨O￨- random￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- ;￨L￨:￨O￨- susceptibility￨L￨NN￨O￨- set￨L￨NN￨O￨- ;￨L￨:￨O￨- threshold￨L￨NN￨O￨- theorem￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Model￨U￨NNP￨TITLE￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- m￨L￨NN￨O￨- households￨L￨NNS￨O￨A ,￨L￨,￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- construct￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- global￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ’￨L￨''￨O￨- (￨L￨-LRB-￨O￨- as￨L￨RB￨O￨- in￨L￨IN￨O￨- Durrett￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2006￨L￨CD￨DATE￨- ,￨L￨,￨O￨- Chapter￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- assign￨L￨VB￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- half-edges￨L￨NNS￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- being￨L￨VBG￨O￨- independent￨L￨JJ￨RELIGION￨- realisations￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨A variable￨L￨NN￨O￨A D￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- =￨L￨JJ￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- pk￨L￨NN￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- asymmetry￨L￨NN￨O￨- in￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- communication￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- scarceness￨L￨NN￨O￨- of￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- open￨L￨JJ￨O￨- research￨L￨NN￨O￨- issues￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- techniques￨L￨NNS￨O￨- which￨L￨WDT￨O￨- enable￨L￨VBP￨O￨- high￨L￨JJ￨O￨- resource￨L￨NN￨O￨- availability￨L￨NN￨O￨- in￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨A peer￨L￨VBP￨O￨- to￨L￨TO￨O￨- peer￨L￨VB￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- replicated￨L￨VBN￨O￨- file￨L￨NN￨O￨- chunks￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- efficiently￨L￨RB￨O￨- disseminated￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- enable￨L￨VB￨O￨- resource￨L￨NN￨O￨- availability￨L￨NN￨O￨- on-demand￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨A users￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- resources￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- aggravated￨L￨VBN￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- for￨L￨IN￨O￨- availability￨L￨NN￨O￨A or￨L￨CC￨O￨- node￨L￨NN￨O￨- flooding￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- requested￨L￨VBN￨O￨- replicated￨L￨VBN￨O￨- file￨L￨NN￨O￨- chunks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Gossip-based￨U￨JJ￨MISC￨- stateful￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- enforces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨A nodes￨L￨NNS￨O￨- whether￨L￨IN￨O￨- to￨L￨TO￨O￨- host￨L￨VB￨O￨- a￨L￨DT￨O￨- file￨L￨NN￨O￨- chunk￨L￨NN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- or￨L￨CC￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- no￨L￨RB￨O￨- longer￨L￨RB￨O￨- a￨L￨DT￨O￨- chunk￨L￨NN￨O￨- is￨L￨VBZ￨O￨- needed￨L￨VBN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- purge￨L￨VB￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- few￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- researches￨L￨VBZ￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- dynamically￨L￨RB￨O￨- contacting￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- rewiring￨L￨NN￨O￨A strategy￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- this￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- property￨L￨NN￨O￨- and￨L￨CC￨O￨- study￨L￨VB￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- rewiring￨L￨NN￨O￨A strategy￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Fermi￨U￨NNP￨O￨- function￨L￨NN￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- results￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- time￨L￨NN￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- would￨L￨MD￨O￨- spread￨L￨VB￨O￨- more￨L￨RBR￨O￨- faster￨L￨RBR￨O￨- and￨L￨CC￨O￨- broader￨L￨JJR￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- rewiring￨L￨NN￨O￨A strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- shed￨L￨VB￨O￨- some￨L￨DT￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- in-depth￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A spreading￨L￨NN￨O￨A on￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Realizing￨U￨VBG￨O￨- the￨L￨DT￨O￨- challenges￨L￨NNS￨O￨- of￨L￨IN￨O￨- immunization￨L￨NN￨O￨- in￨L￨IN￨O￨- containing￨L￨VBG￨O￨- viral￨L￨JJ￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- large￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- instead￨L￨RB￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- partition￨L￨NN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- graph￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- small￨L￨JJ￨O￨- islands￨L￨NNS￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- deploy￨L￨VB￨O￨- message￨L￨NN￨O￨- sanitization￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- the￨L￨DT￨O￨- sanity￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- messages￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- delivered￨L￨VBN￨O￨- across￨L￨IN￨O￨- islands￨L￨NNS￨O￨- .￨L￨.￨O￨- +Viral￨U￨JJ￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- large￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨A has￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- real-life￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- malware￨L￨NN￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- computer￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- rumor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- misinformation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- Twitter-like￨U￨JJ￨MISC￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- challenge￨L￨NN￨O￨- of￨L￨IN￨O￨- containing￨L￨VBG￨O￨- viral￨L￨JJ￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- large￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- common￨L￨JJ￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- malware￨L￨NN￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- computer￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- misinformation￨L￨NN￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Consider￨U￨VB￨O￨- an￨L￨DT￨O￨- undirected￨L￨JJ￨O￨- graph￨L￨NN￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- V￨U￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- E￨U￨NN￨O￨- contains￨L￨VBZ￨O￨- all￨L￨DT￨O￨- friendships￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- users￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- proposed￨L￨VBN￨O￨- algorithms￨L￨NNS￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- network￨L￨NN￨O￨A topologies￨L￨NNS￨O￨A and￨L￨CC￨O￨- different￨L￨JJ￨O￨- edge￨L￨NN￨O￨- weight￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- very￨L￨RB￨O￨- successful￨L￨JJ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- context￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- in￨L￨IN￨O￨- economy￨L￨NN￨O￨- ,￨L￨,￨O￨- sociology￨L￨NN￨O￨- and￨L￨CC￨O￨- informatics￨L￨NNS￨O￨- .5￨L￨CD￨NUMBER￨- It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- diverse￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- k￨L￨NN￨O￨- links￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- used￨L￨JJ￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +∗￨L￨SYM￨O￨- Also￨U￨RB￨O￨- at￨L￨IN￨O￨- Center￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Polymer￨U￨NNP￨ORGANIZATION￨- Studies￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Boston￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- CPS￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 590￨L￨CD￨NUMBER￨- Commonwealth￨U￨NNP￨ORGANIZATION￨- Av￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Boston￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Massachusetts￨U￨NNP￨STATE_OR_PROVINCE￨- 02215￨L￨CD￨DATE￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- September￨U￨NNP￨DATE￨- 26￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- 19:8￨L￨CD￨NUMBER￨- WSPC￨U￨SYM￨ORGANIZATION￨- -￨L￨:￨O￨- Proceedings￨U￨NNP￨O￨- Trim￨U￨NNP￨O￨- Size￨U￨NN￨O￨- :￨L￨:￨O￨- 9in￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- 6in￨L￨CD￨NUMBER￨- vbmb￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- simplest￨L￨JJS￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- mimics￨L￨VBZ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- acquire￨L￨VBP￨O￨- permanent￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- pioneer￨L￨NN￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- healthy￨L￨JJ￨O￨A individual￨L￨NN￨O￨- who￨L￨WP￨O￨- has￨L￨VBZ￨O￨- no￨L￨DT￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- non-healthy￨L￨JJ￨O￨- individual￨L￨NN￨O￨- and￨L￨CC￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- who￨L￨WP￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- propagate￨L￨VB￨O￨- anymore￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- because￨L￨IN￨O￨- he￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- immune￨L￨JJ￨O￨- or￨L￨CC￨O￨- dead￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- give￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- outlook￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- link￨L￨NN￨O￨- percolation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- introduce￨L￨VB￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- void￨L￨NN￨O￨- percolation￨L￨NN￨O￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- dilution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- composed￨L￨VBN￨O￨- by￨L￨IN￨O￨- healthy￨L￨JJ￨O￨A individual￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- sustain￨L￨VBP￨O￨- the￨L￨DT￨O￨- functionality￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- society￨L￨NN￨O￨- .￨L￨.￨O￨- +Above￨U￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- T￨U￨NN￨O￨- =￨L￨JJ￨O￨- Tc￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- becomes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- for￨L￨IN￨O￨- T￨U￨NN￨O￨- <￨L￨JJR￨O￨- Tc￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- reaches￨L￨VBZ￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- fraction￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- outbreaks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- random￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- possible￨L￨JJ￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- through￨L￨IN￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +September￨U￨NNP￨DATE￨- 26￨L￨CD￨DATE￨A ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- 19:8￨L￨CD￨NUMBER￨- WSPC￨U￨SYM￨ORGANIZATION￨- -￨L￨:￨O￨- Proceedings￨U￨NNP￨O￨- Trim￨U￨NNP￨O￨- Size￨U￨NN￨O￨- :￨L￨:￨O￨- 9in￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- 6in￨L￨CD￨NUMBER￨- vbmb￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Social￨U￨NNP￨O￨- distancing￨L￨VBG￨O￨- strategies￨L￨NNS￨O￨- against￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- L￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- progress￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- recently￨L￨RB￨DATE￨- made￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- authors￨L￨NNS￨O￨- who￨L￨WP￨O￨- were￨L￨VBD￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- write￨L￨VB￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- cavity-like￨L￨JJ￨O￨- arguments￨L￨NNS￨O￨- ,￨L￨,￨O￨- tractable￨L￨JJ￨O￨- asymptotically-exact￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨A equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- several￨L￨JJ￨O￨- models￨L￨NNS￨O￨- defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- locally￨L￨RB￨O￨- tree-like￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- zero-temperature￨L￨JJ￨O￨- random￨L￨JJ￨O￨- field￨L￨NN￨O￨- Ising￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- RFIM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨A cavity￨L￨NN￨O￨- method￨L￨NN￨O￨- on￨L￨IN￨O￨- time￨L￨NN￨O￨- tra￨L￨NN￨O￨- jectories￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- construct￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- procedure￨L￨NN￨O￨- for￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- message-passing￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- unidirectional￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- zero-temperature￨L￨JJ￨O￨- random￨L￨JJ￨O￨- field￨L￨NN￨O￨- Ising￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +All￨U￨DT￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- share￨L￨VBP￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- property￨L￨NN￨O￨- :￨L￨:￨O￨- they￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- unidirectional￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- transition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- active￨L￨JJ￨O￨- state￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- correct￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- closed-form￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- guess￨L￨VB￨O￨- the￨L￨DT￨O￨- right￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- that￨L￨WDT￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- more￨L￨RBR￨O￨- complicated￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- involving￨L￨VBG￨O￨- a￨L￨DT￨O￨- larger￨L￨JJR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- several￨L￨JJ￨O￨- non-trivial￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- procedure￨L￨NN￨O￨- for￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨A message-passing￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DMP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- unidirectional￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- ar￨L￨SYM￨O￨- -￨L￨:￨O￨- bitrary￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- states￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Ref￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- the￨L￨DT￨O￨- research￨L￨NN￨O￨- concentrated￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- partially￨L￨RB￨O￨- overlapped￨L￨VBD￨O￨- multilayer￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- layers￨L￨NNS￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- society￨L￨NN￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- impact￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- also￨L￨RB￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- as￨L￨IN￨O￨- q￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- small￨L￨JJ￨O￨- overlapping￨L￨VBG￨O￨- fraction￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- dominated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- heterogeneous￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- effect￨L￨NN￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- important￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- mitigation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- layers￨L￨NNS￨O￨A and￨L￨CC￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- overlapping￨L￨VBG￨O￨- fraction￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- immunization￨L￨NN￨O￨- strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- studied￨L￨VBN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- tr￨L￨NN￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- overlapping￨L￨VBG￨O￨- layers￨L￨NNS￨O￨A in￨L￨IN￨O￨- which￨L￨WDT￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- q￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- act￨L￨VB￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- layers￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- partial￨L￨JJ￨O￨- ly￨L￨NN￨O￨- overlapped￨L￨VBD￨O￨- multiplex￨L￨JJ￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- shared￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- layers￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- case￨L￨NN￨O￨- we￨L￨PRP￨O￨- analytically￨L￨RB￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- age￨L￨NN￨O￨- distribution￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- colony￨L￨NN￨O￨- and￨L￨CC￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- determining￨L￨VBG￨O￨A the￨L￨DT￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- determining￨L￨VBG￨O￨A the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- age-structured￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- partial￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- honey￨L￨NN￨O￨- bee￨L￨NN￨O￨- colony￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- age￨L￨NN￨O￨A distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- decline￨L￨NN￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- agriculture￨L￨NN￨O￨- and￨L￨CC￨O￨- economics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- question￨L￨NN￨O￨- clearly￨L￨RB￨O￨- hinges￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- honey￨L￨NN￨O￨- bee￨L￨NN￨O￨- colony￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- expression￨L￨NN￨O￨- for￨L￨IN￨O￨- R0￨U￨NN￨O￨- has￨L￨VBZ￨O￨- potential￨L￨JJ￨O￨- uses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tracking￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A within￨L￨IN￨O￨- a￨L￨DT￨O￨- bee￨L￨NN￨O￨- colony￨L￨NN￨O￨- .￨L￨.￨O￨- +Cost-efficient￨U￨JJ￨O￨- vaccination￨L￨NN￨O￨- protocols￨L￨NNS￨O￨A for￨L￨IN￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- Petter￨U￨NNP￨PERSON￨- Holme1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Nelly￨U￨NNP￨PERSON￨- Litvak2￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Innovative￨U￨JJ￨ORGANIZATION￨- Research￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Tokyo￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Tokyo￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- 2Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Applied￨U￨NNP￨O￨- Mathematics￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Twente￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Enschede￨U￨NNP￨O￨- ,￨L￨,￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- —￨L￨:￨O￨- i.e.￨L￨FW￨O￨- removing￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- that￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- hindered￨L￨VBN￨O￨- as￨L￨RB￨O￨- much￨L￨RB￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- —￨L￨:￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- cost-efficiency￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- generic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- making￨L￨VBG￨O￨- patients￨L￨NNS￨O￨- immune￨L￨JJ￨O￨- upon￨L￨IN￨O￨- recovery￨L￨NN￨O￨- —￨L￨:￨O￨- as￨L￨IN￨O￨- our￨L￨PRP$￨O￨- disease-spreading￨L￨NN￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- outbreaks￨L￨NNS￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- and￨L￨CC￨O￨- model￨L￨JJ￨TITLE￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +Any￨U￨DT￨O￨- real￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- protocols￨L￨NNS￨O￨A would￨L￨MD￨O￨- come￨L￨VB￨O￨- with￨L￨IN￨O￨- costs￨L￨NNS￨O￨- related￨L￨VBN￨O￨- both￨L￨CC￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- itself￨L￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- gathering￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- premises￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨A epidemiology￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- —￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- most￨L￨RBS￨O￨- active￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- being￨L￨VBG￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- exploit￨L￨VB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- other￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- protocols￨L￨NNS￨O￨A designed￨L￨VBN￨O￨- for￨L￨IN￨O￨- query-efficient￨L￨JJ￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- largest￨L￨JJS￨O￨- degrees￨L￨NNS￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- efficient￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- shift￨L￨NN￨O￨- in￨L￨IN￨O￨- perspective￨L￨NN￨O￨- from￨L￨IN￨O￨- node-to￨L￨JJ￨O￨- edge-centric￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- allows￨L￨VBZ￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- model￨L￨VB￨O￨- Markovian￨U￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- on￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- loop-free￨L￨JJ￨O￨- underlying￨L￨VBG￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +Contact-based￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A Andreas￨U￨NNP￨PERSON￨- Koher￨U￨NNP￨PERSON￨- ∗￨L￨NNP￨O￨- Institut￨U￨NNP￨O￨- f￨L￨FW￨O￨- ¨￨L￨FW￨O￨- ur￨L￨NN￨O￨- Theoretische￨U￨NNP￨O￨- Physik￨U￨NNP￨O￨- ,￨L￨,￨O￨- Technische￨U￨NNP￨O￨- Universit￨U￨NNP￨O￨- ¨￨L￨NN￨O￨- at￨L￨IN￨O￨- Berlin￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Hardenbergstraße￨U￨NNP￨O￨- 36￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10623￨L￨CD￨NUMBER￨- Berlin￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Germany￨U￨NNP￨COUNTRY￨- Hartmut￨U￨NNP￨PERSON￨- H.￨U￨NNP￨PERSON￨- Gleeson￨U￨NNP￨PERSON￨- MACSI￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Department￨U￨NNP￨O￨- of￨L￨IN￨O￨- Mathematics￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Statistics￨U￨NNPS￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Limerick￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Ireland￨U￨NNP￨COUNTRY￨- Philipp￨U￨NNP￨LOCATION￨- H￨U￨NN￨O￨- ¨￨L￨CD￨NUMBER￨- ovel￨L￨NN￨O￨- School￨U￨NN￨O￨- of￨L￨IN￨O￨- Mathematical￨U￨JJ￨O￨- Science￨U￨NN￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- Col￨U￨NNP￨ORGANIZATION￨- lege￨L￨VBD￨ORGANIZATION￨- Cork￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Cork￨U￨NNP￨PERSON￨- T12￨U￨NNP￨TIME￨- XF64￨U￨NN￨O￨- ,￨L￨,￨O￨- Ireland￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Institut￨U￨NNP￨ORGANIZATION￨- f￨L￨LS￨O￨- ¨￨L￨SYM￨O￨- ur￨L￨NN￨O￨- Theoretische￨U￨NNP￨O￨- Physik￨U￨NNP￨O￨- ,￨L￨,￨O￨- Technische￨U￨NNP￨O￨- Universit￨U￨NNP￨O￨- ¨￨L￨NN￨O￨- at￨L￨IN￨O￨- Berlin￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Hardenbergstraße￨U￨NNP￨O￨- 36￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10623￨L￨CD￨NUMBER￨- Berlin￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Germany￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- November￨U￨NNP￨DATE￨- 15￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- contact-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- extending￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- message￨L￨NN￨O￨- passing￨L￨VBG￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +I.￨U￨NN￨O￨- INTRODUCTION￨U￨NNP￨O￨- Accurate￨U￨NNP￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- are￨L￨VBP￨O￨- valuable￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- institutions￨L￨NNS￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- allow￨L￨VBP￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- origins￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- vulnerability￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- potentially￨L￨RB￨O￨- ,￨L￨,￨O￨- containment￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- early￨L￨JJ￨O￨- stage￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- R0￨U￨NN￨O￨- calculation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨A network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- timescales￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- two￨L￨CD￨NUMBER￨- limiting￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- recovered￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- case￨L￨NN￨O￨- when￨L￨WRB￨O￨- network￨L￨NN￨O￨- evolution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- slow￨L￨JJ￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- homogeneous￨L￨JJ￨O￨- random￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- evolution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- rapid￨L￨JJ￨O￨- .￨L￨.￨O￨- +Kiss1￨U￨NN￨O￨- 1School￨L￨NN￨O￨- of￨L￨IN￨O￨- Mathematical￨U￨JJ￨O￨- and￨L￨CC￨O￨- Physical￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mathematics￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Sussex￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Brighton￨U￨NNP￨CITY￨- BN1￨U￨NN￨O￨- 9QH￨L￨NN￨O￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- 2Centre￨L￨NNP￨O￨- for￨L￨IN￨O￨- Computational￨U￨NNP￨ORGANIZATION￨- Neuroscience￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Robotics￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Sussex￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Brighton￨U￨NNP￨CITY￨- BN1￨U￨NN￨O￨- 9QH￨L￨NN￨O￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- type￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- spreading￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- random￨L￨JJ￨O￨- link￨L￨NN￨O￨- activation￨L￨NN￨O￨A and￨L￨CC￨O￨- deletion￨L￨NN￨O￨- where￨L￨WRB￨O￨- link￨L￨NN￨O￨- activation￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- locally￨L￨RB￨O￨- constrained￨L￨VBN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- move￨L￨VBP￨O￨- away￨L￨RB￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨A network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- link￨L￨NN￨O￨- activation-deletion￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Chlamydia￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- our￨L￨PRP$￨O￨- dynamic￨L￨JJ￨O￨A network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- refined￨L￨VBN￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- constraint￨L￨NN￨O￨- on￨L￨IN￨O￨- link￨L￨NN￨O￨- activation￨L￨NN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- dynamic￨L￨JJ￨O￨A network￨L￨NN￨O￨A coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- analysed￨L￨VBN￨O￨- and￨L￨CC￨O￨- discussed￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- results￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- transition￨L￨NN￨O￨- rules￨L￨NNS￨O￨- iterated￨L￨VBD￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Susceptible￨U￨JJ￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨- i￨L￨FW￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Ni￨U￨NN￨MISC￨- and￨L￨CC￨O￨- Ii￨U￨NN￨O￨- denote￨L￨VBP￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- Ii￨U￨NN￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- Ni￨U￨NNS￨MISC￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨A )￨L￨-RRB-￨O￨- Infected￨U￨JJ￨O￨- individuals￨L￨NNS￨O￨- transition￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- µ￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- compartment￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- state￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- –￨L￨:￨O￨- here￨L￨RB￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- complete￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- eventually￨L￨RB￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- lose￨L￨VB￨O￨- their￨L￨PRP$￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- get￨L￨VB￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- persistence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- ecological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- like￨L￨IN￨O￨- seasonality￨L￨NN￨O￨A ,￨L￨,￨O￨- interaction￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- circulating￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- such￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- multiple￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- and￨L￨CC￨O￨- population-level￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- pathogen￨L￨NN￨O￨- ’s￨L￨POS￨O￨- epidemiological￨L￨JJ￨O￨- traits￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- transmissibility￨L￨NN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- seasonality￨L￨NN￨O￨A ,￨L￨,￨O￨- interaction￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- circulating￨L￨VBG￨O￨- strains￨L￨NNS￨O￨- and￨L￨CC￨O￨- hosts￨L￨NNS￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- fragmentation￨L￨NN￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- mix￨L￨VBP￨O￨- homogeneously￨L￨RB￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- called￨L￨VBN￨O￨- subpopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- patches￨L￨NNS￨O￨- or￨L￨CC￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- system￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- level￨L￨NN￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- sub-populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- travel￨L￨VBP￨O￨- along￨L￨IN￨O￨- mobility￨L￨NN￨O￨A connections￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- measles￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- may￨L￨MD￨O￨- impact￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- persistence￨L￨NN￨O￨A and￨L￨CC￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- community￨L￨NN￨O￨- size￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- threshold￨L￨NN￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨A reproductive￨L￨JJ￨O￨A number￨L￨NN￨O￨- ,￨L￨,￨O￨- Rt￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- MCMC￨U￨NN￨ORGANIZATION￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- posterior￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single-strain￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨A using￨L￨VBG￨O￨- aggregated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨A ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- AR￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- morbidity￨L￨NN￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- divided￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- circulating￨L￨VBG￨O￨- virus￨L￨NN￨O￨- type￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- before￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨TIME￨- November￨U￨NNP￨DATE￨- 20￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- 10:22￨L￨CD￨TIME￨- Proceedings￨U￨NNP￨O￨- Trim￨U￨NNP￨O￨- Size￨U￨NN￨O￨- :￨L￨:￨O￨- 9in￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- 6in￨L￨CD￨NUMBER￨- vbmat05arxiv￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- human￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- mean-field￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- still￨L￨RB￨O￨- capture￨L￨VBP￨O￨- most￨L￨RBS￨O￨- static￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- typical￨L￨JJ￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A including￨L￨VBG￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- age￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- acquired￨L￨VBN￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- far￨L￨RB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- serious￨L￨JJ￨O￨- shortcoming￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- minima￨L￨NN￨O￨- often￨L￨RB￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- falls￨L￨VBZ￨O￨- below￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨A −￨L￨CD￨NUMBER￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- would￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- enough￨L￨JJ￨O￨- to￨L￨TO￨O￨- sustain￨L￨VB￨O￨- recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +International￨U￨NNP￨ORGANIZATION￨- Journal￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Computer￨U￨NNP￨ORGANIZATION￨- Networks￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Communications￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- IJCNC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- Vol￨U￨NNP￨O￨- .5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- No.￨U￨NN￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- GENERAL￨U￨NNP￨TITLE￨- STOCHASTIC￨U￨NNP￨O￨- INFORMATION￨U￨NNP￨O￨- DIFFUSION￨U￨NNP￨O￨- MODEL￨U￨NNP￨TITLE￨- IN￨U￨IN￨O￨- SOCIAL￨U￨NNP￨O￨- NETWORKS￨U￨NNP￨O￨- BASED￨U￨NN￨O￨- ON￨U￨IN￨O￨- EPIDEMIC￨U￨NNP￨O￨- DISEASES￨U￨NNP￨CAUSE_OF_DEATH￨- Hamidreza￨U￨NNP￨O￨- Sotoodeh1￨U￨NN￨O￨- ,￨L￨,￨O￨- Farshad￨U￨NNP￨PERSON￨- Safaei2￨U￨NNP￨O￨- ,3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Arghavan￨U￨JJ￨O￨- Sanei3￨U￨NN￨O￨- and￨L￨CC￨O￨- Elahe￨U￨NNP￨PERSON￨- Daei1￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Computer￨U￨NNP￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Qazvin￨U￨NNP￨ORGANIZATION￨- Islamic￨U￨NNP￨ORGANIZATION￨- Azad￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Qazvin￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- IRAN￨U￨NNP￨ORGANIZATION￨- 2￨L￨CD￨NUMBER￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Computer￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨ORGANIZATION￨- Fundamental￨U￨JJ￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- IPM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- {￨L￨-LRB-￨O￨- hr.sotoodeh￨L￨NN￨O￨- ,￨L￨,￨O￨- e.daei￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- P.o.￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 5-5746￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Tehran￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- IRAN￨U￨NNP￨ORGANIZATION￨- 3￨L￨CD￨NUMBER￨- Faculty￨U￨NNP￨O￨- of￨L￨IN￨O￨- ECE￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Shahid￨U￨NNP￨ORGANIZATION￨- Beheshti￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- G.C.￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- 963113￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Tehran￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- IRAN￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- ABSTRACT￨U￨NN￨O￨- Social￨U￨NNP￨O￨- networks￨L￨NNS￨O￨A are￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- infrastructure￨L￨NN￨O￨- for￨L￨IN￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- viruses￨L￨NNS￨O￨- and￨L￨CC￨O￨- innovations￨L￨NNS￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A are￨L￨VBP￨O￨- abstraction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- ;￨L￨:￨O￨- many￨L￨JJ￨O￨- social￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Dealing￨U￨VBG￨O￨- with￨L￨IN￨O￨- all￨L￨DT￨O￨- kind￨L￨NN￨O￨A of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.5121￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- ijcnc￨L￨JJ￨O￨- .2013.5512￨L￨NN￨O￨- 161￨L￨CD￨NUMBER￨- International￨U￨NNP￨ORGANIZATION￨- Journal￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Computer￨U￨NNP￨ORGANIZATION￨- Networks￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Communications￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- IJCNC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- Vol￨U￨NNP￨O￨- .5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- No.￨U￨NN￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- society￨L￨NN￨O￨- ,￨L￨,￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- issue￨L￨NN￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- calculate￨L￨VB￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- transaction￨L￨NN￨O￨- between￨L￨IN￨O￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- predicting￨L￨VBG￨O￨A value￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +KEYWORDS￨U￨NNP￨O￨- Information￨U￨NNP￨O￨- diffusion￨L￨NNP￨O￨A ,￨L￨,￨O￨- Social￨U￨NNP￨ORGANIZATION￨- Network￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- DTMC￨U￨NNP￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Very￨U￨RB￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- psychological￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- Li￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network-based￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonmonotone￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- dSk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A dIk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- λkSk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Θ￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- Ik￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- λkSk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Θ￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- Ik￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ·￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- λ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- when￨L￨WRB￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- .￨L￨.￨O￨- +Inspired￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- works￨L￨NNS￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- nonmonotone￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- dSk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A dIk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- dRk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- λkSk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Θ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- αΘ2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- δRk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µSk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- λkSk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Θ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- αΘ2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- Ik￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- Ik￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- δRk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- µSk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ·￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ,￨L￨,￨O￨- n.￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Positivity￨U￨NN￨O￨- of￨L￨IN￨O￨- solutions￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- From￨U￨IN￨O￨- a￨L￨DT￨O￨- practical￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- satisfy￨L￨VBP￨O￨- Ik￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Rk￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Sk￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- Ik￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- Rk￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- function￨L￨NN￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Θ￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- reflect￨L￨VB￨O￨- the￨L￨DT￨O￨- psychological￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- thus￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- Θ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- kP￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Ik￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- kP￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- hki￨L￨NN￨O￨- Pn￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- mentioned￨L￨VBN￨O￨- above￨L￨IN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- λkSk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Θ￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- λkSk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Θ￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- αΘ2￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- α￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +Sk￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Ik￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨A networks￨L￨NNS￨O￨A with￨L￨IN￨O￨- maximum￨L￨JJ￨O￨- degree￨L￨NN￨O￨- n￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- multitype￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- demography￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨A scale￨L￨NN￨O￨A ·￨L￨NN￨O￨- continuous-time￨L￨JJ￨O￨- multitype￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- ·￨L￨VBP￨O￨- Markovian￨U￨JJ￨O￨- process￨L￨NN￨O￨- ·￨L￨NN￨O￨- major￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- probability￨L￨NN￨O￨- ·￨L￨NN￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ·￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨- network￨L￨NN￨O￨- ·￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- time￨L￨NN￨O￨- ·￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- total￨L￨JJ￨O￨- size￨L￨NN￨O￨- ·￨L￨NN￨O￨- endemicity￨L￨NN￨O￨- ·￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Animal￨U￨NN￨O￨- movements￨L￨NNS￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- between￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- holdings￨L￨NNS￨O￨- at￨L￨IN￨O￨- large￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- and￨L￨CC￨O￨- study￨L￨VBP￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- –￨L￨:￨O￨- Infected￨U￨JJ￨O￨- –￨L￨:￨O￨- Removed￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- cattle￨L￨NNS￨O￨- trade￨L￨VBP￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨A scale￨L￨NN￨O￨A .￨L￨.￨O￨- +Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- exhibit￨L￨VBP￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- lower￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨A time￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- stable￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- case￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- scaling￨L￨NN￨O￨- parameter￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- using￨L￨VBG￨O￨- results￨L￨NNS￨O￨- inspired￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Freidlin-Wentzell￨U￨NNP￨MISC￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- deviations￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +5￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 8￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- cattle￨L￨NNS￨O￨- trade￨L￨VBP￨O￨- network￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨A scale￨L￨NN￨O￨A .￨L￨.￨O￨- +Standard￨U￨NNP￨O￨- branching￨L￨VBG￨O￨- approximation￨L￨NN￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- are￨L￨VBP￨O￨- first￨L￨JJ￨O￨- given￨L￨VBN￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- computation￨L￨NN￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- vaccination￨L￨NN￨O￨- control￨L￨NN￨O￨- u1￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨A control￨L￨NN￨O￨- u2￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- optimally￨L￨RB￨O￨- combine￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- considering￨L￨VBG￨O￨- both￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨A in￨L￨IN￨O￨- finding￨L￨VBG￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- implementing￨L￨VBG￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- controls￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨A function￨L￨NN￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- u2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ru2￨L￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- bu2￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- clearly￨L￨RB￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- I￨U￨NN￨O￨- and￨L￨CC￨O￨- u2￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- supply￨L￨NN￨O￨- of￨L￨IN￨O￨- medical￨L￨JJ￨O￨- resource￨L￨NN￨O￨- is￨L￨VBZ￨O￨- r￨L￨NN￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- because￨L￨IN￨O￨- T￨U￨NN￨O￨- decreases￨L￨VBZ￨O￨- as￨L￨IN￨O￨- b￨L￨NN￨O￨- increases￨L￨NNS￨O￨- and￨L￨CC￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- cure￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Mathematics￨U￨NNP￨O￨- Subject￨U￨NNP￨O￨- Classification￨U￨NNP￨O￨- :￨L￨:￨O￨- 37N25￨L￨CD￨NUMBER￨- .34￨L￨CD￨NUMBER￨- C23￨U￨NN￨O￨- .49￨L￨CD￨NUMBER￨- J15￨U￨NN￨O￨- .92￨L￨CD￨NUMBER￨- D30￨U￨NN￨O￨- Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Inhibitory￨U￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- Non-hyperbolic￨U￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- Centre￨U￨NNP￨O￨- manifold￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- Transcritical￨U￨JJ￨O￨- bifurcation￨L￨NN￨O￨A ,￨L￨,￨O￨- Backward￨U￨RB￨O￨- bifurcation￨L￨NN￨O￨- ,￨L￨,￨O￨- Optimal￨U￨JJ￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- Efficiency￨U￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- researchers￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- only￨L￨RB￨O￨- vaccination￨L￨NN￨O￨- control￨L￨NN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- used￨L￨VBD￨O￨- only￨L￨JJ￨O￨- treatment￨L￨NN￨O￨A control￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 9-10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- models￨L￨NNS￨O￨- grant￨L￨VBP￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- include￨L￨VBP￨O￨- birth-death￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- coalescent￨L￨JJ￨O￨A approaches￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- Kingman￨U￨NNP￨CITY￨- ’s￨L￨POS￨O￨- coalescent￨L￨JJ￨O￨- theory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- coalescent￨L￨JJ￨O￨A models￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- juxtapose￨L￨VB￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- with￨L￨IN￨O￨- BDSIR￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- birth-death-sampling￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- inference￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- structures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- the￨L￨DT￨O￨- small-world￨L￨JJ￨O￨- effect￨L￨NN￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- reach￨L￨VB￨O￨- any￨L￨DT￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- node￨L￨NN￨O￨- through￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- links￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- high-clustering￨L￨JJ￨O￨- effect￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- chosen￨L￨VBN￨O￨- node￨L￨NN￨O￨- have￨L￨VBP￨O￨- high￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- having￨L￨VBG￨O￨- links￨L￨NNS￨O￨- among￨L￨IN￨O￨- themselves￨L￨PRP￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- well-defined￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aging￨L￨NN￨O￨- effect￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- introduced￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- ti￨L￨NN￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- aging￨L￨NN￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ti￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- β￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- newly￨L￨RB￨O￨- added￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- growing￨L￨VBG￨O￨- network￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- preferential￨L￨JJ￨O￨- attachment￨L￨NN￨O￨- scheme￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- popularity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- representative￨L￨JJ￨TITLE￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- small-world￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Watts￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Strogatz￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- growing￨L￨VBG￨O￨A network￨L￨NN￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Barab￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- asi￨L￨NN￨O￨- and￨L￨CC￨O￨- Albert￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- BA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +SIR￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- p￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨A removed￨L￨VBD￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- related￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- normalization￨L￨NN￨O￨- condition￨L￨NN￨O￨- The￨U￨DT￨O￨- following￨L￨VBG￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obeyed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- :￨L￨:￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- dS￨L￨NN￨O￨- dt￨L￨NN￨O￨A =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- dI￨L￨NNP￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- µI￨L￨NN￨O￨- +￨L￨CC￨O￨- q￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- dR￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- µI￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- made￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- agent￨L￨NN￨O￨- based￨L￨VBN￨O￨- Susceptible-Infected-Removed￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Euclidean￨U￨JJ￨MISC￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- distance￨L￨NN￨O￨- l￨L￨NN￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- l￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∝￨L￨CD￨NUMBER￨- l￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- δ￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- nearest￨L￨JJS￨O￨A neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- cumulative￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- total￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- here￨L￨RB￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- a￨L￨DT￨O￨- exp￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- t/T￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- exp￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t/T￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- δ￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- q￨L￨NN￨O￨- .￨L￨.￨O￨- +Comparing￨U￨VBG￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- one￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- population￨L￨NN￨O￨A susceptible￨L￨JJ￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Euclidean￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- choose￨L￨VB￨O￨- δ￨L￨NN￨O￨- and￨L￨CC￨O￨- q￨L￨NN￨O￨- values￨L￨NNS￨O￨- which￨L￨WDT￨O￨- reproduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- qualitatively￨L￨RB￨O￨A .￨L￨.￨O￨- +Discontinuous￨U￨JJ￨O￨- nonequilibrium￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinearly￨L￨JJ￨O￨- pulse-coupled￨L￨JJ￨O￨- excitable￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- Vladimir￨U￨NNP￨PERSON￨- R.￨U￨NNP￨PERSON￨- For￨U￨IN￨PERSON￨- weak￨L￨JJ￨O￨- nonlinearity￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- nonequilibrium￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- between￨L￨IN￨O￨- an￨L￨DT￨O￨- absorbing￨L￨NN￨O￨A and￨L￨CC￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- phase￨L￨NN￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- usual￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- [￨L￨-LRB-￨O￨- Joo￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Lebowitz￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Phys￨U￨NNP￨O￨- .￨L￨.￨O￨- +Increasing￨U￨VBG￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- undergoes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- nonequilibrium￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- absorbing￨L￨VBG￨O￨A to￨L￨TO￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- phase￨L￨NN￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- nonzero￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- discussed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Risau-Gusman￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Abramson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- sometimes￨L￨RB￨O￨- appear￨L￨VBP￨O￨- as￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨- in￨L￨IN￨O￨- single￨L￨JJ￨O￨- runs￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- but￨L￨CC￨O￨- disappear￨L￨VBP￨O￨- in￨L￨IN￨O￨- tra￨L￨NN￨O￨- jectories￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- averaged￨L￨VBN￨O￨- lattice￨L￨NN￨O￨A activity￨L￨NN￨O￨- and￨L￨CC￨O￨- analytical￨L￨JJ￨O￨- descriptions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- usually￨L￨RB￨O￨- mean-field￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- thereof￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- at￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- modelling￨L￨NN￨O￨- methodologies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- pairwise/stochastic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- Susceptible-Infectious-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Susceptible-Exposed-Infectious-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- preventive￨L￨JJ￨O￨- rewiring￨L￨NN￨O￨A among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- so￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rewiring￨L￨VBG￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- between￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ’s￨L￨POS￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- rewire￨L￨VB￨O￨- away￨L￨RB￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- at￨L￨IN￨O￨- some￨L￨DT￨O￨- rate￨L￨NN￨O￨- ω￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- reconnect￨L￨VB￨O￨- to￨L￨TO￨O￨- non-infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- α￨L￨NN￨O￨- or￨L￨CC￨O￨- else￨L￨RB￨O￨- simply￨L￨RB￨O￨- drop￨L￨VB￨O￨- the￨L￨DT￨O￨- edge￨L￨NN￨O￨- if￨L￨IN￨O￨- α￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- so-called￨L￨JJ￨O￨- preventive￨L￨JJ￨O￨- rewiring￨L￨NN￨O￨A .￨L￨.￨O￨- +Without￨U￨IN￨O￨- rewiring￨L￨VBG￨O￨A of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- approaches￨L￨NNS￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- DI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- being￨L￨VBG￨O￨- very￨L￨RB￨O￨- close￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- degree￨L￨NN￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- over￨L￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Urban￨U￨NNP￨O￨- contact￨L￨NN￨O￨- structures￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- :￨L￨:￨O￨- Correcting￨U￨VBG￨O￨- biases￨L￨NNS￨O￨- in￨L￨IN￨O￨- data-driven￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- Zhanwei￨U￨NNP￨O￨- Du1￨U￨NN￨O￨- ,￨L￨,￨O￨- Chao￨U￨NNP￨PERSON￨- Gao2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Yuan￨U￨NNP￨O￨- Bai3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Yongjian￨U￨NNP￨PERSON￨- Yang3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Petter￨U￨NNP￨PERSON￨- Holme4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- *￨L￨SYM￨O￨- Integrative￨U￨NNP￨O￨- Biology￨U￨NNP￨O￨- ,￨L￨,￨O￨- The￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Texas￨U￨NNP￨ORGANIZATION￨- at￨L￨IN￨O￨- Austin￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Austin￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Texas￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- 78712￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- of￨L￨IN￨O￨- 1Depar￨L￨JJ￨O￨- tment￨L￨NN￨O￨- of￨L￨IN￨O￨- America￨U￨NNP￨COUNTRY￨- 2College￨L￨NN￨O￨- of￨L￨IN￨O￨- Computer￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Information￨U￨NN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- College￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Software￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Southwest￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Chongqing￨U￨NNP￨CITY￨- 400715￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 3College￨L￨NNP￨O￨- of￨L￨IN￨O￨- Computer￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Jilin￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Changchun￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- 130012￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 4￨L￨CD￨NUMBER￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Innovative￨U￨JJ￨ORGANIZATION￨- Research￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Tokyo￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Kanagawa￨U￨NNP￨LOCATION￨- 226-8503￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- *￨L￨SYM￨O￨- ABSTRACT￨U￨NN￨O￨- Epidemics￨U￨NNS￨O￨- are￨L￨VBP￨O￨- emergent￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- and￨L￨CC￨O￨- movement￨L￨NN￨O￨A of￨L￨IN￨O￨- people￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- different￨L￨JJ￨O￨- effective￨L￨JJ￨O￨- contract￨L￨NN￨O￨- matrices￨L￨NNS￨O￨- ,￨L￨,￨O￨- constructed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- transit￨L￨NN￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- mobile￨L￨JJ￨TITLE￨A phones￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- advance￨L￨VB￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- using￨L￨VBG￨O￨- public￨L￨JJ￨O￨- transit￨L￨NN￨O￨- trips￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- more￨L￨JJR￨O￨- accurate￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- movement￨L￨NN￨O￨A using￨L￨VBG￨O￨- mobile￨L￨JJ￨TITLE￨- phones￨L￨NNS￨O￨- traces￨L￨NNS￨O￨- .￨L￨.￨O￨- +Public￨U￨NNP￨O￨- transit￨L￨NN￨O￨- systems￨L￨NNS￨O￨- have￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- much￨L￨JJ￨O￨- impor￨L￨NN￨O￨- tant￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨A of￨L￨IN￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- other￨L￨JJ￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- transpor￨L￨NN￨O￨- tation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- bicycle￨L￨NN￨O￨- and￨L￨CC￨O￨- private￨L￨JJ￨O￨- car￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- invisible￨L￨JJ￨O￨- to￨L￨TO￨O￨- public￨L￨JJ￨O￨- transit￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- discrepancy￨L￨NN￨O￨- can￨L￨MD￨O￨- induce￨L￨VB￨O￨A a￨L￨DT￨O￨- bias￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- mispredictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- peak￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- CA￨U￨NNP￨STATE_OR_PROVINCE￨- or￨L￨CC￨O￨- AB￨U￨NNP￨STATE_OR_PROVINCE￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cells￨L￨NNS￨O￨- or￨L￨CC￨O￨- agents￨L￨NNS￨O￨A are￨L￨VBP￨O￨- each￨L￨DT￨O￨- individually￨L￨RB￨O￨- assessing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- surrounding￨L￨JJ￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- potentially￨L￨RB￨O￨- moving￨L￨VBG￨O￨- or￨L￨CC￨O￨- changing￨L￨VBG￨O￨- state￨L￨NN￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- increment￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- rules￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 2.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- detail￨L￨NN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- a￨L￨DT￨O￨- Global￨U￨JJ￨O￨- Recurrence￨U￨NN￨O￨- Rule￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- GRR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- agents￨L￨NNS￨O￨A in￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- when￨L￨WRB￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- cell￨L￨NN￨O￨- ’s￨L￨POS￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- movement￨L￨NN￨O￨- are￨L￨VBP￨O￨- solely￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- cell￨L￨NN￨O￨- ’s￨L￨POS￨O￨- current￨L￨JJ￨DATE￨- status￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- long￨L￨JJ￨O￨- term￨L￨NN￨O￨- behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨A solutions￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- states￨L￨NNS￨O￨- using￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- GRR￨U￨NN￨O￨- have￨L￨VBP￨O￨- good￨L￨JJ￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- prove￨L￨VB￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- regular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- extensions￨L￨NNS￨O￨- to￨L￨TO￨O￨- SIS￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- on￨L￨IN￨O￨- more￨L￨JJR￨O￨- exotic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- exhibiting￨L￨VBG￨O￨- degree￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- directed￨L￨VBN￨O￨- and/or￨L￨CC￨O￨- weighted￨L￨VBN￨O￨- links￨L￨NNS￨O￨- and￨L￨CC￨O￨- clustering￨L￨NN￨O￨- .￨L￨.￨O￨- +Focusing￨U￨VBG￨O￨- on￨L￨IN￨O￨- SIR￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- regular￨L￨JJ￨O￨- but￨L￨CC￨O￨- clustered￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- even￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- complex￨L￨JJ￨O￨- closure￨L￨NN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A as￨L￨IN￨O￨- an￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- expansion￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- do￨L￨VBP￨O￨- this￨L￨DT￨O￨- by￨L￨IN￨O￨- exploiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- fast￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- specified￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- technique￨L￨NN￨O￨- carries￨L￨VBZ￨O￨- over￨L￨IN￨O￨- to￨L￨TO￨O￨- pairwise￨L￨JJ￨O￨A models￨L￨NNS￨O￨A with￨L￨IN￨O￨- other￨L￨JJ￨O￨- closures￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- note￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- dependent￨L￨JJ￨O￨- .￨L￨.￨O￨- +Pairwise￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- widely￨L￨RB￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨A are￨L￨VBP￨O￨- discussed￨L￨VBN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- pointed￨L￨VBN￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- usual￨L￨JJ￨O￨- moment-closure￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- erroneous￨L￨JJ￨O￨- conclusions￨L￨NNS￨O￨- if￨L￨IN￨O￨- applied￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infective-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨A .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- explicit￨L￨JJ￨O￨- form￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- widely￨L￨RB￨O￨- used￨L￨JJ￨O￨- power￨L￨NN￨O￨- transmission￨L￨NN￨O￨- function￨L￨NN￨O￨- is￨L￨VBZ￨O￨- deduced￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- gamma-distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- general￨L￨JJ￨TITLE￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A populations￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +Leveraging￨U￨VBG￨O￨- percolation￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- single￨L￨VB￨O￨- out￨L￨RP￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- Filippo￨U￨NNP￨ORGANIZATION￨- Radicchi￨U￨NNP￨ORGANIZATION￨- Center￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Complex￨U￨JJ￨ORGANIZATION￨- Networks￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Systems￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Indiana￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Bloomington￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- USA￨U￨NNP￨ORGANIZATION￨- ∗￨L￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Informatics￨U￨NNPS￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Computing￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Claudio￨U￨NNP￨PERSON￨- Castellano￨U￨NNP￨PERSON￨- Istituto￨U￨NNP￨PERSON￨- dei￨L￨FW￨PERSON￨- Sistemi￨U￨NNP￨PERSON￨- Complessi￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- ISC-CNR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Via￨U￨NNP￨O￨- dei￨L￨FW￨O￨- Taurini￨U￨NNP￨O￨- 19￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 00185￨L￨CD￨NUMBER￨- Roma￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Dipartimento￨U￨NNP￨ORGANIZATION￨- di￨L￨NNP￨ORGANIZATION￨- Fisica￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Sapienza￨U￨NNP￨ORGANIZATION￨- Universit￨U￨NNP￨ORGANIZATION￨- `￨L￨``￨O￨- a￨L￨DT￨O￨- di￨L￨FW￨O￨- Roma￨U￨FW￨ORGANIZATION￨- ,￨L￨,￨O￨- Roma￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- Among￨U￨IN￨O￨- the￨L￨DT￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disordered￨L￨VBN￨O￨- interaction￨L￨NN￨O￨- topology￨L￨NN￨O￨- underlying￨L￨VBG￨O￨- many￨L￨JJ￨O￨- social￨L￨JJ￨O￨- ,￨L￨,￨O￨- technological￨L￨JJ￨O￨- and￨L￨CC￨O￨- biological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- particularly￨L￨RB￨O￨- important￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- just￨L￨RB￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- position￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- disproportionate￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- mediated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- pattern￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- synthetic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- extensive￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Non-Backtracking￨U￨JJ￨O￨- centrality￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- reliable￨L￨JJ￨O￨- metric￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- top￨L￨JJ￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨- also￨L￨RB￨O￨- in￨L￨IN￨O￨- generic￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- not￨L￨RB￨O￨- embedded￨L￨VBN￨O￨- in￨L￨IN￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- noncritical￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- exploiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- mapping￨L￨NN￨O￨- between￨L￨IN￨O￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- introduced￨L￨VBN￨O￨- Non-Backtracking￨U￨JJ￨O￨- centrality￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- criterion￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- locally￨L￨RB￨O￨- tree-like￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- at￨L￨IN￨O￨- criticality￨L￨NN￨O￨- .￨L￨.￨O￨- +Probably￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- universal￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- perfectly￨L￨RB￨O￨- single￨L￨JJ￨O￨- out￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- for￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- exist￨L￨VB￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- large￨L￨JJ￨O￨- interest￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- recently￨L￨RB￨DATE￨- devoted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- often￨L￨RB￨O￨- called￨L￨VBN￨O￨- super-spreaders￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- chosen￨L￨VBN￨O￨- as￨L￨IN￨O￨- initiators￨L￨NNS￨O￨- ,￨L￨,￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- date￨L￨VB￨O￨- the￨L￨DT￨O￨- influences￨L￨NNS￨O￨- of￨L￨IN￨O￨- most￨L￨JJS￨O￨- structural￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- include￨L￨VBP￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨- coefficient￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- degree￨L￨NN￨O￨- correlations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +4￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 8￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨A years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- much￨L￨JJ￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- clustered￨L￨VBN￨O￨A bond￨L￨NN￨O￨- percolation-type￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- PGF-based￨U￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- consider￨L￨VB￨O￨- specific￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- clustering￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- non-overlapping￨L￨JJ￨O￨- triangles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- usually￨L￨RB￨O￨- work￨L￨VBP￨O￨- best￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- clustering￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ‘￨L￨``￨O￨- randomly￨L￨RB￨O￨- ’￨L￨''￨O￨- distributed￨L￨VBN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- when￨L￨WRB￨O￨- using￨L￨VBG￨O￨- rewiring￨L￨VBG￨O￨- algorithms￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- big-V￨L￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- precludes￨L￨VBZ￨O￨- certain￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- clustering￨L￨NN￨O￨- and￨L￨CC￨O￨- degree￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simulation￨L￨NN￨O￨- study￨L￨NN￨O￨- comparing￨L￨VBG￨O￨- alternative￨L￨JJ￨O￨- ODE￨U￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- performed￨L￨VBN￨O￨- for￨L￨IN￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- –￨L￨:￨O￨- Infected￨U￨JJ￨O￨- –￨L￨:￨O￨- Removed￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- test￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- conjectured￨L￨JJ￨O￨- error￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- novel￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- than￨L￨IN￨O￨- existing￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- .￨L￨.￨O￨- +Degree￨U￨NN￨O￨- or￨L￨CC￨O￨- contact￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- degree-based￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- accounted￨L￨VBN￨O￨- for￨L￨IN￨O￨- in￨L￨IN￨O￨- existing￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- clustered￨L￨VBN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- where￨L￨WRB￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- neighbour￨L￨NN￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- neigbours￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pose￨L￨VBP￨O￨- more￨L￨JJR￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- challenge￨L￨NN￨O￨- .￨L￨.￨O￨- +Consistent￨U￨JJ￨O￨- Approximation￨U￨NN￨O￨- of￨L￨IN￨O￨- Epidemic￨U￨NNP￨MISC￨- Dynamics￨U￨NNP￨MISC￨- on￨L￨IN￨MISC￨- Degree-heterogeneous￨U￨JJ￨MISC￨- Clustered￨U￨NNP￨MISC￨- Networks￨U￨NNP￨MISC￨- A.￨U￨NNP￨MISC￨- To￨U￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- joint￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- network￨L￨NN￨O￨- properties￨L￨NNS￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- degree￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Lindquist￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- analytically￨L￨RB￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- order￨L￨NN￨O￨- moments￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- enter￨L￨VBP￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- three￨L￨CD￨NUMBER￨- moments￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- are￨L￨VBP￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- specify￨L￨VB￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- fully￨L￨RB￨O￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- skewness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Simple￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- interact￨L￨VBP￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- that￨L￨DT￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- every￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- equal￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- contracting￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- any￨L￨DT￨O￨- infectious￨L￨JJ￨O￨A individual￨L￨NN￨O￨A .￨L￨.￨O￨- +There￨U￨EX￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- many￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- using￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- review￨L￨NN￨O￨- papers￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- compare￨L￨VB￨O￨- several￨L￨JJ￨O￨- different￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- network￨L￨NN￨O￨- modelling￨L￨NN￨O￨- .￨L￨.￨O￨- +Soon￨U￨RB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- realized￨L￨VBN￨O￨- that￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- Send￨U￨VB￨O￨- offprint￨L￨NN￨O￨- requests￨L￨NNS￨O￨- to￨L￨TO￨O￨- :￨L￨:￨O￨- Y.Moreno￨U￨NN￨O￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- immunization￨L￨NN￨O￨A ,￨L￨,￨O￨- while￨L￨IN￨O￨- worth￨L￨JJ￨O￨- taking￨L￨VBG￨O￨- for￨L￨IN￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- topologies￨L￨NNS￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- useless￨L￨JJ￨O￨- in￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- verify￨L￨VB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immunization￨L￨NN￨O￨A strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- implement￨L￨VBP￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Removed￨U￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- on￨L￨IN￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Internet￨U￨NN￨MISC￨- maps￨L￨VBZ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- Autonomous￨U￨NNP￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- AS￨U￨JJ￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- router￨L￨NN￨TITLE￨- levels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- targeted￨L￨VBN￨O￨- and￨L￨CC￨O￨- random￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- findings￨L￨NNS￨O￨- are￨L￨VBP￨O￨- supported￨L￨VBN￨O￨- with￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Removed￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- communication￨L￨NN￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- immune￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- identified￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- covering￨L￨VBG￨O￨- algorithm￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- an￨L￨DT￨O￨- immunization￨L￨NN￨O￨A strategy￨L￨NN￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- works￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- as￨L￨RB￨O￨- good￨L￨JJ￨O￨- as￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- immunization￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- using￨L￨VBG￨O￨- only￨L￨RB￨O￨- local￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- digitized￨L￨JJ￨O￨- images￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three-dimensional￨L￨JJ￨O￨- ,￨L￨,￨O￨- branching￨L￨VBG￨O￨- structures￨L￨NNS￨O￨- for￨L￨IN￨O￨- root￨L￨NN￨O￨A systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- bean￨L￨NN￨O￨- seedlings￨L￨NNS￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- analytical￨L￨JJ￨O￨- and￨L￨CC￨O￨- numerical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- map￨L￨VBP￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- ’￨L￨''￨O￨- SIR￨U￨NN￨O￨- ’￨L￨''￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- onto￨L￨IN￨O￨- the￨L￨DT￨O￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- spatially-correlated￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- structures￨L￨NNS￨O￨- of￨L￨IN￨O￨- plant￨L￨NN￨O￨- roots￨L￨NNS￨O￨- affect￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- efficiencies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨- criterion￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- soil-borne￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- spreads￨L￨VBZ￨O￨- through￨L￨IN￨O￨- ensembles￨L￨NNS￨O￨- of￨L￨IN￨O￨- morphologically￨L￨RB￨O￨- complex￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transition￨L￨NN￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- regimes￨L￨NNS￨O￨- occurs￨L￨VBZ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- point￨L￨NN￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- universality￨L￨NN￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- directed￨L￨VBN￨O￨- or￨L￨CC￨O￨- isotropic￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A for￨L￨IN￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- ´￨L￨''￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- inherent￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmissibilities￨L￨NNS￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- correlations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- overlap￨L￨VBP￨O￨- between￨L￨IN￨O￨- neighbouring￨L￨JJ￨O￨- plants￨L￨NNS￨O￨- ,￨L￨,￨O￨- render￨L￨VBP￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- root￨L￨NN￨O￨A systems￨L￨NNS￨O￨- less￨L￨RBR￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- invasion￨L￨NN￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- homogeneous￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- advance￨L￨VBP￨O￨- the￨L￨DT￨O￨- analyses￨L￨NNS￨O￨- to￨L￨TO￨O￨- 3d￨L￨VB￨O￨- morphologically￨L￨RB￨O￨- complex￨L￨JJ￨O￨- and￨L￨CC￨O￨- anisotropic￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- plant￨L￨NN￨O￨- root￨L￨NN￨O￨A systems￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- high￨L￨JJ￨O￨- anisotropy￨L￨NN￨O￨- in￨L￨IN￨O￨- 3d￨L￨JJ￨O￨- root￨L￨NN￨O￨- systems￨L￨NNS￨O￨- can￨L￨MD￨O￨- bring￨L￨VB￨O￨- non-negligible￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- in￨L￨IN￨O￨- pair-wise￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- roots￨L￨NNS￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- analytically￨L￨RB￨O￨- only￨L￨RB￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- :￨L￨:￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- devoted￨L￨VBN￨O￨- to￨L￨TO￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- non-overlapping￨L￨JJ￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- belongs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- community￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- and￨L￨CC￨O￨- investigate￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- deterministic￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- reasons￨L￨NNS￨O￨- referred￨L￨VBD￨O￨- to￨L￨TO￨O￨- above￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- new￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- clear￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- show￨L￨VBP￨O￨- marked￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- strong￨L￨JJ￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- property￨L￨NN￨O￨- has￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- been￨L￨VBN￨O￨- ignored￨L￨VBN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- ubiquitous￨L￨JJ￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- few￨L￨JJ￨O￨- works￨L￨NNS￨O￨- exploit￨L￨VBP￨O￨- this￨L￨DT￨O￨- topological￨L￨JJ￨O￨- property￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- first￨L￨JJ￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- invasion￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- fungal￨L￨JJ￨O￨- plant￨L￨NN￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- Rhizoctonia￨U￨NNP￨O￨- solani￨L￨NNS￨O￨- ,￨L￨,￨O￨- spreads￨L￨NNS￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- nutrient￨L￨NN￨O￨- sites￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- prediction￨L￨NN￨O￨A analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- test￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- experiments￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- spreading￨L￨VBG￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- arranged￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- regular￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- methodologies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- first￨L￨JJ￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- experimentally￨L￨RB￨O￨- observed￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- :￨L￨:￨O￨- invasion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fungal￨L￨JJ￨O￨- plant￨L￨NN￨O￨A pathogen￨L￨NN￨O￨- Rhizoctonia￨U￨NN￨O￨- solani￨L￨NNS￨O￨- in￨L￨IN￨O￨- replicated￨L￨VBN￨O￨- host￨L￨NN￨TITLE￨- microcosms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- devoted￨L￨VBN￨O￨- to￨L￨TO￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Methods￨U￨NNS￨O￨- The￨U￨DT￨O￨- methods￨L￨NNS￨O￨- follow￨L￨VBP￨O￨- four￨L￨CD￨NUMBER￨- steps￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- basic￨L￨JJ￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- scientifically￨L￨RB￨O￨- meaningful￨L￨JJ￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Observation￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- tobs￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- an￨L￨DT￨O￨- interesting￨L￨JJ￨O￨- phase￨L￨NN￨O￨- diagram￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- plane￨L￨NN￨O￨- β￨L￨NN￨O￨- −￨L￨NN￨O￨- ω￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- composed￨L￨VBN￨O￨A by￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- non-epidemic￨L￨JJ￨O￨- phases￨L￨NNS￨O￨- ,￨L￨,￨O￨- separated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- line￨L￨NN￨O￨- βc￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- q￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- people￨L￨NNS￨O￨- become￨L￨VBP￨O￨- aware￨L￨JJ￨O￨- that￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- contacts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thereby￨L￨RB￨O￨- get￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨A with￨L￨IN￨O￨- probability￨L￨NN￨O￨- ω￨L￨NN￨O￨- ,￨L￨,￨O￨- before￨L￨IN￨O￨- having￨L￨VBG￨O￨- physical￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- any￨L￨DT￨O￨- infected￨L￨JJ￨O￨- patient￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- the￨L￨DT￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨- network￨L￨NN￨O￨- composed￨L￨VBN￨O￨A by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- q￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- acts￨L￨VBZ￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- q￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨A ,￨L￨,￨O￨- βc￨L￨NN￨O￨- increases￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- overlap￨L￨VBP￨O￨- decreases￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- disconnected￨L￨VBN￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- more￨L￨RBR￨O￨- virulent￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Exploiting￨U￨VBG￨O￨- this￨L￨DT￨O￨- structural￨L￨JJ￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- yields￨L￨VBZ￨O￨- some￨L￨DT￨O￨- natural￨L￨JJ￨O￨- closures￨L￨NNS￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- state￨L￨NN￨O￨- can￨L￨MD￨O￨- typically￨L￨RB￨O￨- be￨L￨VB￨O￨- exactly￨L￨RB￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- or￨L￨CC￨O￨- pro￨L￨JJ￨O￨- jected￨L￨JJ￨O￨- sates￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- subnetworks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cut-vertex￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- findings￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- lead￨L￨VB￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- generalisation￨L￨NN￨O￨- of￨L￨IN￨O￨- closures￨L￨NNS￨O￨A that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- partitioning￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- around￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- cut-vertices￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- breaking￨L￨VBG￨O￨- down￨L￨RP￨O￨- into￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- two￨L￨CD￨NUMBER￨- disjointed￨L￨JJ￨O￨- components￨L￨NNS￨O￨- or￨L￨CC￨O￨- subnetworks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proved￨L￨VBD￨O￨- the￨L￨DT￨O￨- exactness￨L￨NN￨O￨- of￨L￨IN￨O￨- closures￨L￨NNS￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- triples￨L￨NNS￨O￨- for￨L￨IN￨O￨- Markovian￨U￨JJ￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- tree-like￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- byproduct￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- probabilistic￨L￨JJ￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exactness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- closures￨L￨NNS￨O￨A for￨L￨IN￨O￨- tree-like￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- Sharkey￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- closures￨L￨NNS￨O￨A where￨L￨WRB￨O￨- the￨L￨DT￨O￨- loops￨L￨NNS￨O￨- are￨L￨VBP￨O￨- kept￨L￨VBN￨O￨- intact￨L￨JJ￨O￨- are￨L￨VBP￨O￨- exact￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- simplified￨L￨VBN￨O￨- and￨L￨CC￨O￨- numerically￨L￨RB￨O￨- solvable￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ODEs￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- ordinary-differential-equations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- follow￨L￨VBP￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- explicit￨L￨JJ￨O￨- criteria￨L￨NNS￨O￨- for￨L￨IN￨O￨- strong￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- non-autonomous￨L￨JJ￨O￨- setting￨L￨NN￨O￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- particular￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- autonomous￨L￨JJ￨O￨A and￨L￨CC￨O￨- asymptotically￨L￨RB￨O￨- autonomous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- periodic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- non-autonomous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Michaelis-Menten￨U￨JJ￨PERSON￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +NON-AUTONOMOUS￨U￨NN￨O￨- SEIRS￨U￨NNP￨O￨- MODEL￨U￨NNP￨TITLE￨- WITH￨U￨IN￨O￨- GENERAL￨U￨NNP￨TITLE￨- INCIDENCE￨U￨NNP￨O￨- RATE￨U￨NNP￨O￨- JOAQUIM￨U￨NNP￨O￨- P.￨U￨NNP￨O￨- Namely￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- consider￨L￨VB￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- S￨U￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- Λ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ϕ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- E￨U￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ϕ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ǫ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- I￨U￨PRP￨O￨- ′￨L￨VBP￨O￨- =￨L￨JJ￨O￨- ǫ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- E￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- denote￨L￨VBP￨O￨- respectively￨L￨RB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- infected￨L￨JJ￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- infective￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- compartments￨L￨NNS￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- Λ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ϕ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨A into￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- class￨L￨NN￨O￨- Date￨U￨NN￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 3￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- .￨L￨.￨O￨- +Notation￨U￨NN￨O￨- and￨L￨CC￨O￨- Preliminaries￨U￨NNPS￨O￨- We￨U￨PRP￨O￨- will￨L￨MD￨O￨- assume￨L￨VB￨O￨- that￨L￨DT￨O￨- Λ￨U￨NN￨O￨- ,￨L￨,￨O￨- µ￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- ,￨L￨,￨O￨- ǫ￨L￨NN￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- are￨L￨VBP￨O￨- continuous￨L￨JJ￨O￨- bounded￨L￨VBN￨O￨- and￨L￨CC￨O￨- nonnegative￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- on￨L￨IN￨O￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- ϕ￨L￨VBP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- bounded￨L￨VBN￨O￨- and￨L￨CC￨O￨- nonnegative￨L￨JJ￨O￨- function￨L￨NN￨O￨- on￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- ωµ￨L￨NN￨O￨- ,￨L￨,￨O￨- ωΛ￨L￨NN￨O￨- ,￨L￨,￨O￨- ωβ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 3￨L￨CD￨NUMBER￨- µ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ωµ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Λ￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- ωΛ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ωβ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- notation￨L￨NN￨O￨A h￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ω￨L￨NN￨O￨- =￨L￨JJ￨O￨- lim￨L￨NN￨O￨- inf￨L￨NN￨O￨- t￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ω￨L￨NN￨O￨- Z￨U￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ds￨L￨JJ￨O￨- and￨L￨CC￨O￨- h￨L￨NN￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- =￨L￨JJ￨O￨- lim￨L￨NN￨O￨- sup￨L￨NN￨O￨- t￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ω￨L￨NN￨O￨- Z￨U￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ds￨L￨JJ￨O￨- ,￨L￨,￨O￨- A￨U￨DT￨O￨- NON-AUTONOMOUS￨U￨NN￨O￨- SEIRS￨U￨NNP￨O￨- MODEL￨U￨NNP￨TITLE￨- WITH￨U￨IN￨O￨- GENERAL￨U￨NNP￨TITLE￨- INCIDENCE￨U￨NNP￨O￨- RATE￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- keep￨L￨VB￨O￨- on￨L￨IN￨O￨- using￨L￨VBG￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +Namely￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- our￨L￨PRP$￨O￨- conditions￨L￨NNS￨O￨- determine￨L￨VBP￨O￨- extinction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- respectively￨L￨RB￨O￨- strong￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- replace￨L￨VBP￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- ,￨L￨,￨O￨- ǫ￨L￨NN￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- functions￨L￨NNS￨O￨- sufficiently￨L￨RB￨O￨- close￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- C￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- topology￨L￨NN￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- replace￨L￨VB￨O￨- ϕ￨L￨NN￨O￨- by￨L￨IN￨O￨- some￨L￨DT￨O￨- sufficiently￨L￨RB￨O￨- close￨L￨JJ￨O￨- incidence￨L￨NN￨O￨A function￨L￨NN￨O￨- we￨L￨PRP￨O￨- still￨L￨RB￨O￨- have￨L￨VBP￨O￨- extinction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- respectively￨L￨RB￨O￨- strong￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨A SEIRS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- fairly￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- parameter￨L￨NN￨O￨- for￨L￨IN￨O￨- persistence￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- section￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- adapt￨L￨VBP￨O￨- the￨L￨DT￨O￨- arguments￨L￨NNS￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- prove￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨A is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- persistent￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A R0￨U￨NN￨O￨- Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- generalize￨L￨VBP￨O￨- the￨L￨DT￨O￨- ones￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨A of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- under￨L￨IN￨O￨- initial￨L￨JJ￨O￨- continuity￨L￨NN￨O￨- of￨L￨IN￨O￨- solution￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- at￨L￨IN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- t￨L￨NN￨O￨- <￨L￨JJR￨O￨- t0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- INTRODUCTION￨U￨NNP￨O￨- We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨A the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIRS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- µN￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- δR￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- =￨L￨JJ￨O￨- σE￨L￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- =￨L￨JJ￨O￨- µN￨L￨NN￨O￨- p￨L￨NN￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- variable￨L￨JJ￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- more￨L￨RBR￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- mathematically￨L￨RB￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- variable￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- The￨U￨DT￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A using￨L￨VBG￨O￨- Lyapunov￨U￨NNP￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- total￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- in￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DFE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- domain￨L￨NN￨O￨- minus￨L￨CC￨O￨- the￨L￨DT￨O￨- stable￨L￨JJ￨O￨- manifold￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- DFE￨U￨NNP￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- using￨L￨VBG￨O￨- phase￨L￨NN￨O￨- plane￨L￨NN￨O￨- methods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Poincar￨U￨NN￨O￨- ´￨L￨''￨O￨- e-Birkhoff￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Lyapunov￨U￨NNP￨PERSON￨- functions￨L￨VBZ￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Nonlinear￨U￨JJ￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A ,￨L￨,￨O￨- Lyapunov￨U￨NNP￨PERSON￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- and￨L￨CC￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- RS￨U￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- differential￨L￨JJ￨O￨A mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- and￨L￨CC￨O￨- discuss￨L￨VB￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- SEIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- they￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- make￨L￨VBP￨O￨- sense￨L￨NN￨O￨- .￨L￨.￨O￨- +ANALYSIS￨U￨NN￨O￨- ,￨L￨,￨O￨- SIMULATION￨U￨NN￨O￨- AND￨U￨CC￨O￨- OPTIMAL￨U￨JJ￨O￨- CONTROL￨U￨NNP￨O￨- OF￨U￨IN￨O￨- A￨U￨DT￨O￨- SEIR￨U￨NNP￨O￨- MODEL￨U￨NNP￨TITLE￨- FOR￨U￨IN￨O￨- EBOLA￨U￨NNP￨MISC￨- VIRUS￨U￨NNP￨O￨- WITH￨U￨IN￨O￨- DEMOGRAPHIC￨U￨NNP￨O￨- EFFECTS￨U￨NNP￨O￨- AMIRA￨U￨NNP￨O￨- RACHAH￨U￨NNPS￨O￨- AND￨U￨CC￨O￨- DELFIM￨U￨NNP￨O￨- F.￨U￨NNP￨O￨- By￨U￨IN￨O￨- using￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- latest￨L￨JJS￨O￨- ma￨L￨NN￨O￨- jor￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- added￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- demographic￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- equilibria￨L￨NNS￨O￨- with￨L￨IN￨O￨- vital￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Ebola￨U￨NNP￨MISC￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- spread￨L￨VBN￨O￨- by￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- blood￨L￨NN￨O￨- and￨L￨CC￨O￨- secretions￨L￨NNS￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- via￨L￨IN￨O￨- direct￨L￨JJ￨O￨A contact￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- through￨L￨IN￨O￨- broken￨L￨VBN￨O￨- skin￨L￨NN￨O￨- or￨L￨CC￨O￨- mucous￨L￨JJ￨O￨- membranes￨L￨NNS￨O￨- in￨L￨IN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- eyes￨L￨NNS￨O￨- ,￨L￨,￨O￨- nose￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- mouth￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- or￨L￨CC￨O￨- fluids￨L￨NNS￨O￨- on￨L￨IN￨O￨- clothing￨L￨NN￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- surfaces￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- needles￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- experimental￨L￨JJ￨O￨- results￨L￨NNS￨O￨- using￨L￨VBG￨O￨- machine￨L￨NN￨O￨- learning￨L￨NN￨O￨- algorithms￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- Betweenness￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- feature￨L￨NN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- latent￨L￨JJ￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A .￨L￨.￨O￨- +Classifying￨U￨VBG￨O￨- Latent￨U￨JJ￨O￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- States￨U￨NNS￨O￨- in￨L￨IN￨O￨- Complex￨U￨NN￨MISC￨- Networks￨U￨NNP￨MISC￨- Yeon-sup￨U￨NNP￨MISC￨- Lim￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Massachusetts￨U￨NNP￨ORGANIZATION￨- Amherst￨U￨NNP￨ORGANIZATION￨- Bruno￨U￨NNP￨ORGANIZATION￨- Ribeiro￨U￨NNP￨ORGANIZATION￨- Carnegie￨U￨NNP￨ORGANIZATION￨- Mellon￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Don￨U￨NNP￨ORGANIZATION￨- Towsley￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Massachusetts￨U￨NNP￨ORGANIZATION￨- Amherst￨U￨NNP￨ORGANIZATION￨- ABSTRACT￨U￨NN￨ORGANIZATION￨- Algorithms￨U￨NNS￨ORGANIZATION￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- and￨L￨CC￨O￨- containing￨L￨VBG￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- missing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- –￨L￨:￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- most￨L￨JJS￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A time￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- –￨L￨:￨O￨- poses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenge￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨- .￨L￨.￨O￨- +Often￨U￨RB￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨A have￨L￨VBP￨O￨- a￨L￨DT￨O￨- known￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +9￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- ABSTRACT￨U￨NN￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A based￨L￨VBN￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- SusceptibleInfected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- works￨L￨VBZ￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A identification￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- consid￨L￨VBD￨O￨- er￨L￨NN￨O￨- a￨L￨DT￨O￨- Susceptible-Infected￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- may￨L￨MD￨O￨- get￨L￨VB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- recover￨L￨VB￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- minimum￨L￨JJ￨O￨- distance￨L￨NN￨O￨- centrality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DC￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- estimator￨L￨NN￨O￨- was￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- all￨L￨DT￨O￨- these￨L￨DT￨O￨- examples￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- may￨L￨MD￨O￨- want￨L￨VB￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- or￨L￨CC￨O￨- estimate￨L￨VB￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- that￨L￨IN￨O￨- first￨L￨NN￨O￨A started￨L￨VBD￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Index￨U￨NNP￨O￨- Terms￨U￨NNS￨O￨- —￨L￨:￨O￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A estimation￨L￨NN￨O￨- ,￨L￨,￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- security￨L￨NN￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- for￨L￨IN￨O￨- years￨L￨NNS￨DURATION￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- the￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- approach￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- homogeneous￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- may￨L￨MD￨O￨- get￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- neighbor￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rates￨L￨NNS￨O￨A between￨L￨IN￨O￨- different￨L￨JJ￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- different￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- average￨L￨JJ￨O￨- fraction￨L￨NN￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- y￨L￨VBP￨O￨- ∞￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ∗￨L￨NN￨MISC￨- Faculty￨U￨NN￨MISC￨- of￨L￨IN￨MISC￨- Electrical￨U￨JJ￨MISC￨- Engineering￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Mathematics￨U￨NNP￨O￨- and￨L￨CC￨O￨- Computer￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- Delft￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- The￨U￨DT￨O￨- Netherlands￨U￨NNPS￨COUNTRY￨- ;￨L￨:￨O￨- email￨L￨NN￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- B.Qu￨U￨NN￨O￨- ,￨L￨,￨O￨- H.Wang￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- metastable￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- indicates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- severe￨L￨JJ￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- larger￨L￨JJR￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- y￨L￨NN￨O￨- ∞￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- severely￨L￨RB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- actual￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- NIMFA￨U￨NNP￨ORGANIZATION￨- performs￨L￨VBZ￨O￨- better￨L￨RBR￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- i.i.d.￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rates￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- smaller￨L￨JJR￨O￨- (￨L￨-LRB-￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unchanged￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- nodal￨L￨JJ￨O￨- degree￨L￨NN￨O￨- is￨L￨VBZ￨O￨- positive￨L￨JJ￨O￨- .￨L￨.￨O￨- +NIMFA￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- ,￨L￨,￨O￨- turns￨L￨VBZ￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- precise￨L￨JJ￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rates￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- while￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- DBMF￨U￨NN￨MISC￨- approximation￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A ,￨L￨,￨O￨- NIMFA￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- i.i.d.￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- nodal￨L￨JJ￨O￨- degree￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- out￨L￨IN￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rates￨L￨NNS￨O￨A on￨L￨IN￨O￨- average￨L￨JJ￨O￨- retards￨L￨VBZ￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- larger￨L￨JJR￨O￨- even-order￨L￨NN￨O￨- moment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- smaller￨L￨JJR￨O￨- average￨L￨NN￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- odd-order￨L￨JJ￨O￨- moments￨L￨NNS￨O￨- contribute￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- opposite￨L￨JJ￨O￨- way￨L￨NN￨O￨- ;￨L￨:￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- may￨L￨MD￨O￨- die￨L￨VB￨O￨- out￨L￨RP￨O￨- or￨L￨CC￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- may￨L￨MD￨O￨- enhance￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- out￨L￨IN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- studies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- τ￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- y￨L￨NN￨O￨- ∞￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A or￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- contamination￨L￨NN￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- recovery￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Employing￨U￨VBG￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- benchmark￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- independently￨L￨RB￨O￨- identically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rates￨L￨NNS￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- metastable￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rates￨L￨NNS￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- y￨L￨NN￨O￨- ∞￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- way￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- N￨U￨NN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- δ￨L￨NN￨O￨- but￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rates￨L￨NNS￨O￨A βij￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- =￨L￨JJ￨O￨- βj￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- i￨L￨FW￨O￨- 6￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- node￨L￨NN￨O￨- j￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infectious-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A model￨L￨NN￨TITLE￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- simple￨L￨JJ￨O￨- formulae￨L￨NNS￨O￨- giving￨L￨VBG￨O￨- the￨L￨DT￨O￨- leading-order￨L￨NN￨O￨- asymptotic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- persistence￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- our￨L￨PRP$￨O￨- asymptotic￨L￨JJ￨O￨- formulae￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- such￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- reduce￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- to￨L￨TO￨O￨- leading￨L￨VBG￨O￨- order￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- persistence￨L￨NN￨O￨A time￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- homogeneous￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- greater￨L￨JJR￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- quickly￨L￨RB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- die￨L￨VB￨O￨- out￨L￨RP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- discrete￨L￨JJ￨O￨- state-space￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- persistence￨L￨NN￨O￨A time￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- endemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- quasi-stationarity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- rate￨L￨NN￨O￨- matrix￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- describing￨L￨VBG￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- either￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨A in￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- susceptibility￨L￨NN￨O￨- and/or￨L￨CC￨O￨- infectiousness￨L￨NN￨O￨- ;￨L￨:￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- directed￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +7￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 3-7￨L￨CD￨NUMBER￨- ISSN￨U￨NNP￨O￨- :￨L￨:￨O￨- 2244-7423￨L￨CD￨DURATION￨- Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR-SEI￨U￨NN￨O￨- four-strain￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- dengue￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- primary￨L￨JJ￨O￨- and￨L￨CC￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- Raúl￨U￨NN￨ORGANIZATION￨- Isea￨U￨NN￨ORGANIZATION￨- Fundación￨U￨NNP￨ORGANIZATION￨- Instituto￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Estudios￨U￨NNP￨ORGANIZATION￨- Avanzados￨U￨NNP￨ORGANIZATION￨- Hoyo￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- la￨L￨DT￨ORGANIZATION￨- Puerta￨U￨NNP￨ORGANIZATION￨- Baruta￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- República￨U￨NNP￨PERSON￨- Bolivariana￨U￨NNP￨PERSON￨- de￨L￨IN￨O￨- Venezuela￨U￨NNP￨COUNTRY￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- SEI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- four-strain￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- primary￨L￨JJ￨O￨- and￨L￨CC￨O￨- secondary￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- Asian￨U￨JJ￨NATIONALITY￨- strain￨L￨NN￨O￨A of￨L￨IN￨O￨- Dengue￨U￨JJ￨MISC￨- serotype-II￨L￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- complete￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Predicting￨U￨VBG￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨A Joel￨U￨NNP￨ORGANIZATION￨- C.￨U￨NNP￨ORGANIZATION￨- Miller￨U￨NNP￨ORGANIZATION￨- Mathematical￨U￨NNP￨ORGANIZATION￨- Modeling￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Analysis￨U￨NNP￨ORGANIZATION￨- Group￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- Center￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Nonlinear￨U￨NNP￨ORGANIZATION￨- Studies￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- MS￨U￨NN￨STATE_OR_PROVINCE￨- B284￨U￨NN￨O￨- ,￨L￨,￨O￨- Los￨U￨NNP￨ORGANIZATION￨- Alamos￨U￨NNP￨ORGANIZATION￨- National￨U￨NNP￨ORGANIZATION￨- Laboratory￨U￨NNP￨ORGANIZATION￨- ∗￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Dated￨U￨VBN￨O￨- :￨L￨:￨O￨- July￨U￨NNP￨DATE￨- 6￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- analytically￨L￨RB￨O￨- address￨L￨VBP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmissibility￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- transmits￨L￨VBZ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- network-dependent￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- zero￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- order￨L￨NN￨O￨- phase￨L￨NN￨O￨- transistion￨L￨NN￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- may￨L￨MD￨O￨- happen￨L￨VB￨O￨- and￨L￨CC￨O￨- below￨L￨IN￨O￨- which￨L￨WDT￨O￨- epidemics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- found￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- generating￨L￨VBG￨O￨- function￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- how￨L￨WRB￨O￨- heterogeneity￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- occurs￨L￨VBZ￨O￨A and￨L￨CC￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- occurs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmissibility￨L￨NN￨O￨- Tuv￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- u￨L￨NN￨O￨- causes￨L￨VBZ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- u￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨A of￨L￨IN￨O￨- v￨L￨LS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨A solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- SEIRS￨U￨NN￨O￨- models￨L￨NNS￨O￨- contained￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- already￨L￨RB￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +EXISTENCE￨U￨NN￨O￨- OF￨U￨IN￨O￨- PERIODIC￨U￨NNP￨O￨- SOLUTIONS￨U￨NNPS￨O￨- OF￨U￨IN￨O￨- A￨U￨DT￨O￨- PERIODIC￨U￨JJ￨O￨- SEIRS￨U￨NNP￨O￨- MODEL￨U￨NNP￨TITLE￨- WITH￨U￨IN￨O￨- GENERAL￨U￨NNP￨TITLE￨- INCIDENCE￨U￨NNP￨O￨- JOAQUIM￨U￨NNP￨O￨- P.￨U￨NNP￨O￨- For￨U￨IN￨O￨- a￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨A SEIRS￨U￨NN￨ORGANIZATION￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- endemic￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- orbit￨L￨NN￨O￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- main￨L￨JJ￨O￨- result￨L￨NN￨O￨- establishes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- sharp￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- between￨L￨IN￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- non-existence￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨A orbits￨L￨NNS￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- disease-free￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨A orbit￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- nonlinear￨L￨JJ￨O￨- prediction￨L￨NN￨O￨A ,￨L￨,￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- chaos￨L￨NN￨O￨- theory￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- decades￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- to￨L￨TO￨O￨- classify￨L￨VB￨O￨- and￨L￨CC￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- maxima￨L￨NNS￨O￨- -￨L￨:￨O￨- or￨L￨CC￨O￨- ’￨L￨''￨O￨- Peak-to-Peak￨U￨NNP￨MISC￨- Dynamics￨U￨NNP￨MISC￨- ’￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- PPD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- -￨L￨:￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- at￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- maxima￨L￨NNS￨O￨- values￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- variables￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- in-between￨L￨JJ￨O￨- time￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- maxima￨L￨NNS￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- R￨U￨NN￨O￨- ¨￨L￨NN￨O￨- ossler￨L￨NN￨O￨- hyperchaotic￨L￨JJ￨O￨- system￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- prediction￨L￨NN￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- maxima￨L￨NNS￨O￨- are￨L￨VBP￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- predictability￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- biological￨L￨JJ￨O￨A systems￨L￨NNS￨O￨A and￨L￨CC￨O￨- specifically￨L￨RB￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- maxima￨L￨NNS￨O￨- incidents￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- incidents￨L￨NNS￨O￨- where￨L￨WRB￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- state￨L￨NN￨O￨- variable￨L￨NN￨O￨- has￨L￨VBZ￨O￨- maximum￨L￨JJ￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- of￨L￨IN￨O￨- primary￨L￨JJ￨O￨- concern￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- maxima￨L￨NNS￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- already￨L￨RB￨O￨- been￨L￨VBN￨O￨- discussed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- illustration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coevolution￨L￨NN￨O￨- of￨L￨IN￨O￨- agents￨L￨NNS￨O￨A and￨L￨CC￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- inspired￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- contagion￨L￨NN￨O￨- probability￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- per￨L￨IN￨O￨- infected￨L￨JJ￨O￨- neighbour￨L￨NN￨O￨A is￨L￨VBZ￨O￨- ρ￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- S-agent￨U￨JJ￨O￨- with￨L￨IN￨O￨- kI￨L￨NN￨O￨- infected￨L￨JJ￨O￨- neighbours￨L￨NNS￨O￨- becomes￨L￨VBZ￨O￨- itself￨L￨PRP￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- pIdt￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- ρ￨L￨NN￨O￨- dt￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- kI￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- kIρ￨L￨NN￨O￨- dt￨L￨NN￨O￨- interval￨L￨NN￨O￨- dt￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- joins￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- agents￨L￨NNS￨O￨A ,￨L￨,￨O￨- contagion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- when￨L￨WRB￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- his￨L￨PRP$￨O￨- neighbour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- .￨L￨.￨O￨- +Susceptible￨U￨JJ￨O￨- agents￨L￨NNS￨O￨A are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- opportunity￨L￨NN￨O￨- of￨L￨IN￨O￨- breaking￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- links￨L￨NNS￨O￨- with￨L￨IN￨O￨- infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemiological￨L￨JJ￨O￨- process￨L￨NN￨O￨- where￨L￨WRB￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- fractional￨L￨JJ￨O￨A derivative￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- generalised￨L￨JJ￨O￨- master￨L￨NN￨O￨- equations￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- through￨L￨IN￨O￨- SIR￨U￨NN￨O￨- compartments￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- power-law￨L￨NN￨O￨- function￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- issue￨L￨NN￨O￨- that￨L￨WDT￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- addressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- modelling￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- processes￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- coupled￨L￨VBN￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- differential￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- equations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- matching￨L￨VBG￨O￨- dimensions￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- with￨L￨IN￨O￨- fractional￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- infected￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- distributed￨L￨VBN￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- governing￨L￨VBG￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- written￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- coupled￨L￨VBN￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- alternate￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- also￨L￨RB￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A derivatives￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- governing￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- boundary￨L￨NN￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- a￨L￨DT￨O￨- non-exponential￨L￨JJ￨O￨- but￨L￨CC￨O￨- algebraic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- stage￨L￨NN￨O￨- on￨L￨IN￨O￨- strongly￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- hub￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- so￨L￨RB￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- global￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- strongly￨L￨RB￨O￨- fluctuates￨L￨VBZ￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- hub￨L￨NN￨O￨- node￨L￨NN￨O￨- was￨L￨VBD￨O￨- first￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- broad￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cluster￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- intermediate-time￨L￨JJ￨O￨- regime￨L￨NN￨O￨- exhibits￨L￨VBZ￨O￨- too￨L￨RB￨O￨- large￨L￨JJ￨O￨- fluctuation￨L￨NN￨O￨- in￨L￨IN￨O￨- size￨L￨NN￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- its￨L￨PRP$￨O￨- mean￨L￨NN￨O￨- size￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- representative￨L￨JJ￨TITLE￨- value￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- main￨L￨JJ￨O￨- finding￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- I￨U￨PRP￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- quite￨L￨RB￨O￨- different￨L￨JJ￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- runs￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- intermediate-time￨L￨JJ￨O￨- regime￨L￨NN￨O￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- contrary￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- taken￨L￨VBN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- concentrated￨L￨VBN￨O￨- at￨L￨IN￨O￨- its￨L￨PRP$￨O￨- mean￨L￨NN￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A time￨L￨NN￨O￨A to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- measure￨L￨NN￨O￨- .￨L￨.￨O￨- +Between￨U￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- thresholds￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- stage￨L￨NN￨O￨- but￨L￨CC￨O￨- then￨L￨RB￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- asymptotically￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- alertness￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- add￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨A spread￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- studied￨L￨VBN￨O￨- using￨L￨VBG￨O￨- results￨L￨NNS￨O￨- from￨L￨IN￨O￨- algebraic￨L￨JJ￨O￨A graph￨L￨NN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- center￨L￨NN￨O￨- manifold￨L￨NN￨O￨- theorem￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analytically￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A spread￨L￨NN￨O￨A .￨L￨.￨O￨- +An￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨A describes￨L￨VBZ￨O￨A how￨L￨WRB￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- spread￨L￨VBP￨O￨- throughout￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- talk￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- agent-network￨L￨JJ￨O￨- coevolution￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- where￨L￨WRB￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- spreading￨L￨VBG￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- non-infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨A are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- avoiding￨L￨VBG￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- infected￨L￨JJ￨O￨- partners￨L￨NNS￨O￨- –￨L￨:￨O￨- perhaps￨L￨RB￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- risk￨L￨VB￨O￨- perception￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Susceptible￨U￨JJ￨O￨- agents￨L￨NNS￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- become￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- contagion￨L￨NN￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- ρ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- nI￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- recall￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- process￨L￨NN￨O￨- each￨L￨DT￨O￨- infected￨L￨JJ￨O￨- agent￨L￨NN￨O￨- recovers￨L￨VBZ￨O￨- and￨L￨CC￨O￨- becomes￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- say￨L￨VBP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- γ￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨A time￨L￨NN￨O￨A .￨L￨.￨O￨- +Susceptible￨U￨JJ￨O￨- agents￨L￨NNS￨O￨A are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- opportunity￨L￨NN￨O￨- of￨L￨IN￨O￨- breaking￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- links￨L￨NNS￨O￨- with￨L￨IN￨O￨- infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reconnecting￨L￨VBG￨O￨- those￨L￨DT￨O￨- links￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemiological￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +IN￨U￨IN￨O￨- TRODUC￨U￨NN￨LOCATION￨- T￨U￨NN￨O￨- ION￨U￨NN￨O￨- The￨U￨DT￨O￨- statistics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- interference-limited￨L￨JJ￨O￨- wireless￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- useful￨L￨JJ￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- us￨L￨PRP￨O￨- comprehend￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- performance￨L￨NN￨O￨- metrics￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- outage￨L￨NN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- throughput￨L￨NN￨O￨- ,￨L￨,￨O￨- vary￨L￨VBP￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- random￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- channel￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- power￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- gain￨L￨NN￨O￨- ,￨L￨,￨O￨- power￨L￨NN￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- spacial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- interfering￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- power￨L￨NN￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- opportunistic￨L￨JJ￨O￨- scheduling￨L￨NN￨O￨- that￨L￨WDT￨O￨- capture￨L￨VBP￨O￨- the￨L￨DT￨O￨- randomness￨L￨NN￨O￨- of￨L￨IN￨O￨- channel￨L￨NN￨O￨A gain￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- distance￨L￨NN￨O￨- can￨L￨MD￨O￨- significantly￨L￨RB￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- enhance￨L￨VB￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- SIR￨U￨NN￨O￨- but￨L￨CC￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- outage￨L￨NN￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- letter￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- SIR￨U￨NN￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- closed-form￨L￨NN￨O￨- for￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- random￨L￨JJ￨O￨- channel￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- power￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- gain￨L￨NN￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- distance￨L￨NN￨O￨- and￨L￨CC￨O￨- power￨L￨NN￨O￨- control￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conversely￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- large￨L￨JJ￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- specific￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- practical￨L￨JJ￨O￨- interest￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- Erd˝os￨U￨NNS￨O￨- -￨L￨:￨O￨- R´enyi￨U￨NN￨O￨- and￨L￨CC￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- random￨L￨JJ￨O￨A graphs￨L￨NNS￨O￨A .￨L￨.￨O￨- +Conversely￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- this￨L￨DT￨O￨- ratio￨L￨NN￨O￨- is￨L￨VBZ￨O￨- smaller￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- graph￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- practical￨L￨JJ￨O￨- interest￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- random￨L￨JJ￨O￨A graphs￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- Section￨U￨NN￨O￨- we￨L￨PRP￨O￨- took￨L￨VBD￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- giant￨L￨JJ￨O￨- component￨L￨NN￨O￨- for￨L￨IN￨O￨- various￨L￨JJ￨O￨- families￨L￨NNS￨O￨- of￨L￨IN￨O￨- graphs￨L￨NNS￨O￨A to￨L￨TO￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ultimately￨L￨RB￨O￨- removed￨L￨VBD￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Model￨U￨NNP￨TITLE￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- neighbourhood￨L￨NN￨O￨- structure￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- undirected￨L￨JJ￨O￨- ,￨L￨,￨O￨- labelled￨L￨JJ￨O￨- graph￨L￨NN￨O￨A G￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- node￨L￨NN￨O￨- set￨L￨NN￨O￨- V￨U￨NN￨O￨- and￨L￨CC￨O￨- edge￨L￨NN￨O￨- set￨L￨VBD￨O￨- E￨U￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨A node￨L￨NN￨O￨A u￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- slot￨L￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- Qv￨U￨NNP￨O￨- ∼￨L￨CD￨NUMBER￨- u￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- βXv￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- write￨L￨VBP￨O￨- v￨L￨LS￨O￨- ∼￨L￨SYM￨O￨- u￨L￨FW￨O￨- to￨L￨TO￨O￨- mean￨L￨VB￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- u￨L￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- E￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- mutational￨L￨JJ￨O￨- meltdown￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- extinct￨L￨JJ￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- falls￨L￨VBZ￨O￨- below￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- error￨L￨NN￨O￨A threshold￨L￨NN￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- classical￨L￨JJ￨O￨- quasispecies￨L￨NNS￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- physical￨L￨JJ￨O￨- space￨L￨NN￨O￨A limits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- advantage￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- can￨L￨MD￨O￨- obtain￨L￨VB￨O￨- from￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- offspring￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- clearance￨L￨NN￨O￨- may￨L￨MD￨O￨- result￨L￨VB￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- defenses￨L￨NNS￨O￨- beyond￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- quasispecies￨L￨NNS￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- cell-to-cell￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- or￨L￨CC￨O￨- local￨L￨JJ￨O￨- transport￨L￨NN￨O￨- of￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- unavoidably￨L￨RB￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- error￨L￨NN￨O￨A threshold￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- random￨L￨JJ￨O￨A graph￨L￨NN￨O￨A PAt￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- parameterised￨L￨VBN￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- constants￨L￨NNS￨O￨- :￨L￨:￨O￨- m￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- δ￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- >￨L￨JJR￨O￨- −￨L￨CD￨NUMBER￨- m.￨L￨NN￨NUMBER￨- gives￨L￨VBZ￨O￨- rise￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- sequence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- sequence￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- member￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- It￨U￨PRP￨O￨- ∞￨L￨VBD￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- PAt￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theme￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- bootstrap￨L￨NN￨O￨- percolation￨L￨NN￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- preferential￨L￨JJ￨O￨- attachment￨L￨NN￨O￨- random￨L￨JJ￨O￨A graph￨L￨NN￨O￨A on￨L￨IN￨O￨- t￨L￨NN￨O￨- vertices￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- denote￨L￨VBP￨O￨- by￨L￨IN￨O￨- PAt￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- tth￨L￨NN￨O￨- term￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sequence￨L￨NN￨O￨- ,￨L￨,￨O￨- PAt￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨A with￨L￨IN￨O￨- t￨L￨NN￨O￨- vertices￨L￨NNS￨O￨- and￨L￨CC￨O￨- mt￨L￨NN￨O￨- edges￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨A PAt￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- first￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- use￨L￨VB￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- define￨L￨VB￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- model￨L￨NN￨TITLE￨- PAt￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- Barab￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- asi-Albert￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- δ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Mean￨U￨NN￨O￨- field￨L￨NN￨O￨- approximation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- valued￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- evolution￨L￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨- a￨L￨DT￨O￨- generative￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- diffusion￨L￨NN￨O￨A .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- the￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A thresholds￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- generative￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 6￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- This￨U￨DT￨O￨- paper￨L￨NN￨O￨- deals￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- signal￨L￨NN￨O￨- processing￨L￨NN￨O￨- over￨L￨IN￨O￨- graphs￨L￨NNS￨O￨- for￨L￨IN￨O￨- tracking￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- diffusion￨L￨NN￨O￨A in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- infected￨L￨JJ￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- follow￨L￨VB￨O￨- polynomial￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- exact￨L￨JJ￨O￨- non-linear￨L￨JJ￨O￨- Bayesian￨U￨JJ￨MISC￨- filter￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- below-threshold￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- initiated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- approximation￨L￨NN￨O￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨A works￨L￨VBZ￨O￨- well￨L￨RB￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- above-threshold￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- initiated￨L￨VBN￨O￨- at￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- methods￨L￨NNS￨O￨- from￨L￨IN￨O￨- Hamiltonian￨U￨JJ￨IDEOLOGY￨- statistical￨L￨JJ￨O￨- mechanics￨L￨NNS￨O￨- yield￨L￨VBP￨O￨- correct￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- as￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- widely-used￨L￨JJ￨O￨- Ornstein-Uhlenbeck￨U￨NNP￨MISC￨- diffusion￨L￨NN￨MISC￨- approximation￨L￨NN￨O￨- gives￨L￨VBZ￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- poor￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- may￨L￨MD￨O￨- retain￨L￨VB￨O￨- some￨L￨DT￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨- comparisons￨L￨NNS￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- detailed￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- approximation￨L￨NN￨O￨- can￨L￨MD￨O￨- give￨L￨VB￨O￨- good￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- provide￨L￨VB￨O￨- correct￨L￨JJ￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- asymptotic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- relied￨L￨VBN￨O￨- upon￨L￨IN￨O￨- without￨L￨IN￨O￨- some￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- external￨L￨JJ￨O￨- validation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- eg￨L￨FW￨O￨- simulation￨L￨NN￨O￨- studies￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- theory￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- tells￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infectives￨L￨NNS￨O￨- process￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- consequently￨L￨RB￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- persistence￨L￨NN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- those￨L￨DT￨O￨- contained￨L￨VBN￨O￨- in￨L￨IN￨O￨- section￨L￨NN￨O￨- 11.3￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- justify￨L￨VB￨O￨- 2￨L￨CD￨NUMBER￨- Event￨U￨NN￨O￨- State￨U￨NN￨O￨- transition￨L￨NN￨O￨- Transition￨U￨NN￨O￨- rate￨L￨NN￨O￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- Recovery￨U￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- I￨U￨PRP￨O￨- →￨L￨VBP￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- →￨L￨VBP￨O￨- I￨U￨PRP￨O￨- −￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- β/N￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- Transition￨U￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨A SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨A SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- appear￨L￨VBP￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- extension￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- period￨L￨NN￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Approximating￨U￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- received￨L￨VBN￨O￨- state￨L￨NN￨O￨- generally￨L￨RB￨O￨- will￨L￨MD￨O￨- not￨L￨RB￨O￨- lose￨L￨VB￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- de￨L￨FW￨O￨- -￨L￨:￨O￨- ∗￨L￨CD￨NUMBER￨- Electronic￨U￨JJ￨O￨- address￨L￨NN￨O￨A :￨L￨:￨O￨- †￨L￨CD￨NUMBER￨- Electronic￨U￨JJ￨O￨- address￨L￨NN￨O￨- :￨L￨:￨O￨- scribing￨L￨VBG￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- contracting￨L￨NN￨O￨- Typhoid￨U￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- New￨U￨NNP￨O￨- Yorker￨U￨NNP￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- era￨L￨NN￨O￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- had￨L￨VBN￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- three￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- personal￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- make￨L￨VB￨O￨- her￨L￨PRP$￨O￨- more￨L￨JJR￨O￨- or￨L￨CC￨O￨- less￨L￨RBR￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- she￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- come￨L￨VBN￨O￨- into￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- apparent￨L￨JJ￨O￨A healthy￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- predicting￨L￨VBG￨O￨A if￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- will￨L￨MD￨O￨- adopt￨L￨VB￨O￨- a￨L￨DT￨O￨- contagion￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- modes￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- exposure/susceptibility￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨- neighbor￨L￨NN￨O￨- influence￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- her￨L￨PRP$￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- contagion￨L￨NN￨O￨A through￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- experiments￨L￨NNS￨O￨- on￨L￨IN￨O￨- synthetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- measure￨L￨VBP￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- latent￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨A network￨L￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- avoidance￨L￨NN￨O￨- behavior￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- avoidance￨L￨NN￨O￨- frequently￨L￨RB￨O￨- implemented￨L￨VBD￨O￨- via￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- rewiring￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- links￨L￨NNS￨O￨- away￨L￨RB￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- and￨L￨CC￨O￨- towards￨L￨IN￨O￨- other￨L￨JJ￨O￨- non-infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- considered￨L￨VBD￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨A scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- move￨L￨VB￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨A susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨A network￨L￨NN￨O￨- with￨L￨IN￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +ects￨L￨NNS￨O￨- of￨L￨IN￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨A network￨L￨NN￨O￨- Ilker￨U￨NNP￨PERSON￨- Tunc￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Leah￨U￨NNP￨PERSON￨- B￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Bass-SIR￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- new￨L￨JJ￨O￨- products￨L￨NNS￨O￨- Gadi￨U￨NNP￨PERSON￨- Fibich1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- ∗￨L￨CD￨NUMBER￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Applied￨U￨NNP￨O￨- Mathematics￨U￨NNP￨O￨- ,￨L￨,￨O￨- Tel￨U￨NNP￨ORGANIZATION￨- Aviv￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Tel￨U￨NNP￨CITY￨- Aviv￨U￨NNP￨CITY￨- 69978￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Israel￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- September￨U￨NNP￨DATE￨- 22￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- products￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- consumers￨L￨NNS￨O￨- who￨L￨WP￨O￨- adopt￨L￨VBP￨O￨- product￨L￨NN￨O￨- can￨L￨MD￨O￨- later￨L￨RB￨O￨- “￨L￨``￨O￨- recover￨L￨VB￨O￨- ”￨L￨''￨O￨- and￨L￨CC￨O￨- stop￨L￨VB￨O￨- influencing￨L￨VBG￨O￨- others￨L￨NNS￨O￨- to￨L￨TO￨O￨- adopt￨L￨VB￨O￨- the￨L￨DT￨O￨- product￨L￨NN￨O￨- .￨L￨.￨O￨- +Rather￨U￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- nonSIR￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- adopter￨L￨NN￨O￨- who￨L￨WP￨O￨- was￨L￨VBD￨O￨- j￨L￨NN￨O￨- recovers￨L￨VBZ￨O￨- in￨L￨IN￨O￨- contagious￨L￨JJ￨O￨A at￨L￨IN￨O￨- contagious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- “￨L￨``￨O￨- recover￨L￨VB￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- ∆￨L￨NN￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- Prob￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- ∆￨L￨NN￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- r￨L￨NN￨O￨- ∆￨L￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- o￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ∆￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- ∆￨L￨NN￨O￨- t￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- unlike￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- small-worlds￨L￨JJ￨O￨- structure￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- negligible￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- diffusion￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- Bass-SIR￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- only￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- consumers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Hc￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- A￨U￨DT￨O￨- ma￨L￨NN￨O￨- jority￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨O￨- to￨L￨TO￨O￨- Ebola￨U￨NNP￨MISC￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- viewed￨L￨VBN￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨A of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- dyadic￨L￨JJ￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- contact￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- duration￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- temporality￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- lessens￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- persist￨L￨VBP￨O￨- more￨L￨JJR￨O￨- easily￨L￨RB￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A than￨L￨IN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- static￨L￨JJ￨O￨- counterparts￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Lie￨U￨NN￨MISC￨- commutator￨L￨NN￨O￨- bracket￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrices￨L￨NNS￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- times￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- PACS￨U￨NNS￨O￨- numbers￨L￨NNS￨O￨- :￨L￨:￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- 89.75￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- pointedly￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- permissive￨L￨JJ￨O￨- cell￨L￨NN￨O￨A becomes￨L￨VBZ￨O￨- 2￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- whenever￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- cell￨L￨NN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighborhood￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- a￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- cell￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- dead￨L￨JJ￨O￨- neighboring￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- or￨L￨CC￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- integer￨L￨NN￨O￨- parameter￨L￨NN￨O￨- R￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- that￨L￨WDT￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cell￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- a￨L￨DT￨O￨- permissive￨L￨JJ￨O￨- cell￨L￨NN￨O￨A becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- cell￨L￨NN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighborhood￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- cell￨L￨NN￨O￨- needs￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- surrounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- R￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- dead￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- alternative￨L￨JJ￨O￨- explanation￨L￨NN￨O￨- put￨L￨VBD￨O￨- forward￨L￨RB￨O￨- by￨L￨IN￨O￨- Landini￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ulcer￨L￨NN￨CAUSE_OF_DEATH￨- shape￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contiguous￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨- modulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- cell￨L￨NN￨O￨A susceptibilities￨L￨NNS￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- tree￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- estimator￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨A node￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- path￨L￨NN￨O￨- that￨L￨WDT￨O￨- yields￨L￨VBZ￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- Jordan￨U￨NNP￨CITY￨- center￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- with￨L￨IN￨O￨- minimum￨L￨JJ￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Finding￨U￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- challenging￨L￨JJ￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- knowing￨L￨VBG￨O￨- just￨L￨RB￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- Susceptible-Infected￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- not￨L￨RB￨O￨- all￨L￨DT￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A ,￨L￨,￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- realization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- can￨L￨MD￨O￨- think￨L￨VB￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- or￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- “￨L￨``￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ”￨L￨''￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- spreadi￨L￨JJ￨O￨- ng￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- our￨L￨PRP$￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨A wit￨L￨NN￨O￨- h￨L￨NN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- set￨L￨VBD￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- positive￨L￨JJ￨O￨- unless￨L￨IN￨O￨- otherwise￨L￨RB￨O￨- specified￨L￨VBN￨O￨- :￨L￨:￨O￨- b￨L￨NN￨O￨- =￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨A birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- =￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- ε1￨L￨NN￨O￨- =￨L￨JJ￨O￨- excess￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- ,￨L￨,￨O￨- ε2￨L￨NN￨O￨- =￨L￨JJ￨O￨- excess￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- removeds￨L￨NNS￨O￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- =￨L￨JJ￨O￨- effective￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- =￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- removal￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- removeds￨L￨NNS￨O￨- .￨L￨.￨O￨- +Sub￨U￨NN￨O￨- ject￨L￨SYM￨O￨- Classification￨U￨NNP￨O￨- :￨L￨:￨O￨- 92D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- social￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- populations￨L￨NNS￨O￨- play￨L￨VBP￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- Model￨U￨NNP￨TITLE￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- as￨L￨IN￨O￨- nonconstant￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- infectives￨L￨NNS￨O￨A and￨L￨CC￨O￨- removeds￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- class￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- environment￨L￨NN￨O￨- we￨L￨PRP￨O￨- mean￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- population￨L￨NN￨O￨- has￨L￨VBZ￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- outside￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- we￨L￨PRP￨O￨- set￨L￨VBD￨O￨A P￨U￨NN￨O￨- =￨L￨JJ￨O￨- s￨L￨NNS￨O￨- +￨L￨CC￨O￨- i￨L￨FW￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- then￨L￨RB￨O￨- P￨U￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- P￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ε1￨L￨NN￨O￨- i￨L￨FW￨O￨- −￨L￨FW￨O￨- ε2r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- achieved￨L￨VBN￨O￨- a￨L￨DT￨O￨- big￨L￨JJ￨O￨- success￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- style￨L￨NN￨O￨- might￨L￨MD￨O￨- contain￨L￨VB￨O￨- some￨L￨DT￨O￨- unexpected￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- while￨L￨IN￨O￨- being￨L￨VBG￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SF￨U￨NN￨O￨- networks￨L￨NNS￨O￨- directly￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- potential￨L￨JJ￨O￨- infection-activity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- infectivity￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- its￨L￨PRP$￨O￨- possibly￨L￨RB￨O￨- maximal￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- process￨L￨NN￨O￨- within￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- strictly￨L￨RB￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- degree￨L￨NN￨O￨- .￨L￨.￨O￨- +R.￨U￨NNP￨O￨- China￨U￨NNP￨COUNTRY￨- 2Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Fribourg￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- CH-1700￨U￨NNP￨O￨- Fribourg￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- July￨U￨NNP￨DATE￨- 18￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- identical￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assigned￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- A￨U￨DT￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SF￨U￨NN￨O￨- networks￨L￨NNS￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- named￨L￨VBN￨O￨- hubs￨L￨NNS￨O￨- ,￨L￨,￨O￨- will￨L￨MD￨O￨- take￨L￨VB￨O￨- the￨L￨DT￨O￨- greater￨L￨JJR￨O￨- possession￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectivity￨L￨NN￨O￨A ,￨L￨,￨O￨- so-called￨L￨JJ￨O￨- super-spreader￨L￨JJ￨O￨- .￨L￨.￨O￨- +THE￨U￨DT￨O￨- MODEL￨U￨NN￨TITLE￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- node￨L￨NN￨O￨A presents￨L￨VBZ￨O￨- individual￨L￨JJ￨O￨- and￨L￨CC￨O￨- link￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- along￨L￨IN￨O￨- which￨L￨WDT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- techniques￨L￨NNS￨O￨- from￨L￨IN￨O￨- large-deviation￨L￨JJ￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- measurement￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- and￨L￨CC￨O￨- analyze￨L￨VB￨O￨- large￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- in￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Enhancement￨U￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- in￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Jason￨U￨NNP￨PERSON￨- Hindes￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ira￨U￨NNP￨ORGANIZATION￨- B.￨U￨NNP￨ORGANIZATION￨- Shaw￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mathematics￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Col￨U￨NNP￨O￨- lege￨L￨NN￨O￨- of￨L￨IN￨O￨- Wil￨U￨NNP￨PERSON￨- liam￨L￨NN￨PERSON￨- and￨L￨CC￨O￨- Mary￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Wil￨U￨NNP￨PERSON￨- liamsburg￨L￨NN￨PERSON￨- ,￨L￨,￨O￨- VA￨U￨NNP￨STATE_OR_PROVINCE￨- 23187￨L￨CD￨NUMBER￨- During￨U￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- may￨L￨MD￨O￨- adapt￨L￨VB￨O￨- their￨L￨PRP$￨O￨- connections￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- enhancement￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A with￨L￨IN￨O￨- increased￨L￨VBN￨O￨- rewiring￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- holding￨L￨VBG￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- constant￨L￨JJ￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- adaptivity￨L￨NN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- fluctuations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Nature￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- Marian￨U￨NNP￨PERSON￨- Bogu˜n￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- a￨L￨DT￨O￨- ,1￨L￨NN￨O￨- Claudio￨U￨NNP￨PERSON￨- Castellano￨U￨NNP￨PERSON￨- ,2￨L￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Romualdo￨U￨NNP￨PERSON￨- Pastor-Satorras4￨U￨NN￨O￨- 1Departament￨L￨NN￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- Fonamental￨U￨NNP￨O￨- ,￨L￨,￨O￨- Universitat￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Barcelona￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Mart￨U￨NNP￨ORGANIZATION￨- ´￨L￨POS￨O￨- ı￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Istituto￨U￨NNP￨ORGANIZATION￨- dei￨L￨FW￨ORGANIZATION￨- Sistemi￨U￨NNP￨ORGANIZATION￨- Complessi￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- ISC-CNR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- dei￨L￨FW￨O￨- Taurini￨U￨FW￨DATE￨- 19￨L￨CD￨DATE￨- ,￨L￨,￨O￨- I-00185￨U￨NN￨O￨- Roma￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 3Dipartimento￨L￨NNP￨O￨- di￨L￨NNP￨O￨- Fisica￨U￨NNP￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- Sapienza￨U￨NNP￨PERSON￨- ”￨L￨''￨O￨- Universit￨U￨NNP￨O￨- `￨L￨``￨O￨- a￨L￨DT￨O￨- di￨L￨FW￨O￨- Roma￨U￨FW￨ORGANIZATION￨- ,￨L￨,￨O￨- P.le￨U￨NNP￨O￨- A.￨U￨NNP￨O￨- Moro￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- I-00185￨U￨NN￨O￨- Roma￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- 4Departament￨L￨NNP￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- i￨L￨FW￨O￨- Enginyeria￨U￨NNP￨ORGANIZATION￨- Nuclear￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Universitat￨U￨NNP￨O￨- Polit￨U￨NNP￨O￨- `￨L￨``￨O￨- ecnica￨L￨FW￨O￨- de￨L￨FW￨O￨- Catalunya￨U￨FW￨O￨- ,￨L￨,￨O￨- Campus￨U￨NNP￨O￨- Nord￨U￨NNP￨O￨- B4￨U￨NN￨O￨- ,￨L￨,￨O￨- 08034￨L￨CD￨NUMBER￨- Barcelona￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- i￨L￨FW￨O￨- Franqu`es￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 08028￨L￨CD￨NUMBER￨- Barcelona￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- Italy￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 29￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- unravel￨L￨VB￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- origin￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- particularly￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- highly￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- vanishing￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨A limit￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- pointed￨L￨VBN￨O￨- out￨L￨RP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- small-world￨L￨JJ￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- decaying￨L￨VBG￨O￨- slower￨L￨JJR￨O￨- than￨L￨IN￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- vanishing￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨A limit￨L￨NN￨O￨A .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Observe￨U￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- K￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- containing￨L￨VBG￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- direct￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mouse￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- allowed￨L￨VBN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- accommodate￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- habitats￨L￨NNS￨O￨A and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- .￨L￨.￨O￨- +C.￨U￨NNP￨PERSON￨- de￨L￨NNP￨PERSON￨- Bariloche￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Argentina￨U￨NNP￨COUNTRY￨- 3Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Biology￨U￨NNP￨O￨- and￨L￨CC￨O￨- Museum￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Southwestern￨U￨NNP￨ORGANIZATION￨- Biology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- New￨U￨NNP￨ORGANIZATION￨- Mexico￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Albuquerque￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- Mexico￨U￨NNP￨STATE_OR_PROVINCE￨- 87131￨L￨CD￨NUMBER￨- 4Sevil￨L￨NN￨O￨- leta￨L￨NN￨O￨- Long-term￨U￨JJ￨O￨- Ecological￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- Program￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Biology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- New￨U￨NNP￨ORGANIZATION￨- Mexico￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Albuquerque￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- Mexico￨U￨NNP￨STATE_OR_PROVINCE￨- 87131￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Dated￨U￨VBN￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 27￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Traveling￨U￨VBG￨O￨- waves￨L￨NNS￨O￨- are￨L￨VBP￨O￨- analyzed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Hantavirus￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- deer￨L￨NNS￨O￨- mice￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- ,￨L￨,￨O￨- fronts￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- mice￨L￨NNS￨O￨A travel￨L￨VBP￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- speed￨L￨NN￨O￨- ,￨L￨,￨O￨- separated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- delay￨L￨NN￨O￨- .￨L￨.￨O￨- +s￨L￨NNS￨O￨- c￨L￨NN￨O￨- i￨L￨FW￨O￨- s￨L￨VBZ￨O￨- y￨L￨NN￨O￨- h￨L￨NN￨O￨- p￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- 8￨L￨CD￨NUMBER￨- 8￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- s￨L￨NNS￨O￨- c￨L￨NN￨O￨- i￨L￨FW￨O￨- s￨L￨VBZ￨O￨- y￨L￨NN￨O￨- h￨L￨NN￨O￨- p￨L￨NN￨O￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equations￨L￨NNS￨O￨A :￨L￨:￨O￨- ∂￨L￨CD￨NUMBER￨- MS￨U￨NN￨STATE_OR_PROVINCE￨- ∂￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- bM￨L￨NN￨O￨- −￨L￨NN￨O￨- cMS￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- MSM￨U￨NN￨O￨- K￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- aMSMI￨L￨NN￨O￨- +￨L￨CC￨O￨- D￨U￨NN￨O￨- ∇￨L￨CD￨NUMBER￨- 2MS￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ∂￨L￨SYM￨O￨- MI￨U￨FW￨O￨- ∂￨L￨FW￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- cMI￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- MI￨U￨NNP￨STATE_OR_PROVINCE￨- M￨U￨NN￨O￨- K￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- aMSMI￨L￨NN￨O￨- +￨L￨CC￨O￨- D￨U￨NN￨O￨- ∇￨L￨CD￨NUMBER￨- 2MS￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- equations￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- reduces￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- :￨L￨:￨O￨- ∂￨L￨CD￨NUMBER￨- M￨U￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- M￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- K￨U￨NN￨O￨- +￨L￨CC￨O￨- D￨U￨NN￨O￨- ∇￨L￨CD￨NUMBER￨- 2M￨L￨NN￨O￨- .￨L￨.￨O￨- +Red￨U￨NNP￨O￨- circles￨L￨NNS￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- subgraph￨L￨NN￨O￨- plus￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- connecting￨L￨VBG￨O￨- any￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- k￨L￨NN￨O￨- >￨L￨JJR￨O￨- ln￨L￨NN￨O￨A N￨U￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- path￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- degrees￨L￨NNS￨O￨- above￨L￨IN￨O￨- ln￨L￨NN￨O￨A N￨U￨NN￨O￨- plus￨L￨CC￨O￨- nodes￨L￨NNS￨O￨- connecting￨L￨VBG￨O￨- them￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- macroscopic￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨DATE￨- 1￨L￨CD￨DATE￨- a.￨L￨NN￨O￨- +They￨U￨PRP￨O￨- are￨L￨VBP￨O￨- right￨L￨JJ￨O￨- in￨L￨IN￨O￨- pointing￨L￨VBG￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- equation￨L￨NN￨O￨- predicts￨L￨VBZ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- activity￨L￨NN￨O￨- only￨L￨RB￨O￨- for￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- degrees￨L￨NNS￨O￨- above￨L￨IN￨O￨- ln￨L￨NN￨O￨A N￨U￨NN￨O￨- .￨L￨.￨O￨- +Blue￨U￨NNP￨O￨- squares￨L￨NNS￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- subgraph￨L￨NN￨O￨- made￨L￨VBN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- k￨L￨NN￨O￨- >￨L￨JJR￨O￨- ln￨L￨NN￨O￨A N￨U￨NN￨O￨- plus￨L￨CC￨O￨- their￨L￨PRP$￨O￨- direct￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- translated￨L￨VBN￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- nodes￨L￨NNS￨O￨A does￨L￨VBZ￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- truly￨L￨RB￨O￨- endemic￨L￨JJ￨O￨- activity￨L￨NN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- λ￨L￨NN￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- this￨L￨DT￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- dealing￨L￨VBG￨O￨- exclusively￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- perhaps￨L￨RB￨O￨- most￨L￨JJS￨O￨- biologically￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- again￨L￨RB￨O￨- deriving￨L￨VBG￨O￨- an￨L￨DT￨O￨- exact￨L￨JJ￨O￨- formula￨L￨NN￨O￨A and￨L￨CC￨O￨- then￨L￨RB￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- N￨U￨NN￨O￨- asymptotics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- crossover￨L￨NN￨O￨- regime￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- to￨L￨TO￨O￨- distinguish￨L￨VB￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- comparable￨L￨JJ￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- much￨L￨RB￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- N￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- shall￨L￨MD￨O￨- derive￨L￨VB￨O￨- an￨L￨DT￨O￨- exact￨L￨JJ￨O￨- formula￨L￨NN￨O￨A for￨L￨IN￨O￨- this￨L￨DT￨O￨- quantity￨L￨NN￨O￨- for￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- examine￨L￨VB￨O￨- its￨L￨PRP$￨O￨- large￨L￨JJ￨O￨- N￨U￨NN￨O￨- asymptotics￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- already￨L￨RB￨O￨- noted￨L￨VBN￨O￨- by￨L￨IN￨O￨- Nasell￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- infectivities￨L￨NNS￨O￨- of￨L￨IN￨O￨- width￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- N￨U￨NN￨O￨- around￨L￨IN￨O￨- threshold￨L￨NN￨O￨A ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crossover￨L￨NN￨O￨- region￨L￨NN￨O￨- that￨L￨WDT￨O￨- interpolates￨L￨VBZ￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- and￨L￨CC￨O￨- below￨L￨IN￨O￨- threshold￨L￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- Threshold￨U￨NN￨O￨- of￨L￨IN￨O￨- Susceptible-Infected-Susceptible￨U￨NNP￨O￨- Model￨U￨NNP￨TITLE￨- on￨L￨IN￨O￨- Complex￨U￨NN￨O￨- Networks￨U￨NNP￨O￨- Hyun￨U￨NNP￨PERSON￨- Keun￨U￨NNP￨PERSON￨- Lee￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Pyoung-Seop￨U￨NNP￨PERSON￨- Shim￨U￨NNP￨PERSON￨- ,1￨L￨NN￨O￨- and￨L￨CC￨O￨- Jae￨U￨NNP￨PERSON￨- Dong￨U￨NNP￨PERSON￨- Noh1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Seoul￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Seoul￨U￨NNP￨CITY￨- 130-743￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Korea￨U￨NNP￨COUNTRY￨- 2￨L￨CD￨NUMBER￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Korea￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Advanced￨U￨NNP￨ORGANIZATION￨- Study￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Seoul￨U￨NNP￨CITY￨- 130-722￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Korea￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- September￨U￨NNP￨DATE￨- 19￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨A networks￨L￨NNS￨O￨A can￨L￨MD￨O￨- have￨L￨VB￨O￨- an￨L￨DT￨O￨- inactive￨L￨JJ￨O￨- Griffiths￨U￨NNP￨O￨- phase￨L￨NN￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- slow￨L￨JJ￨O￨- relaxation￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨A networks￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- zero￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- resolved￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- occupied￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- degree-descending￨L￨JJ￨O￨- order￨L￨NN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- it￨L￨PRP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- phase￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- λc￨L￨NN￨O￨- =￨L￨JJ￨O￨- hki/hk2￨L￨NN￨O￨- i￨L￨FW￨O￨- with￨L￨IN￨O￨- hkn￨L￨NN￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- dkknP￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨A networks￨L￨NNS￨O￨A whose￨L￨WP$￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denoting￨L￨VBG￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- broad￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- contrasts￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- field￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- prediction￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨A networks￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- active￨L￨JJ￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- nonzero￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- assumptions￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- for￨L￨IN￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- dS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- dE￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- dR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A +￨L￨CC￨O￨- γR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- µI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- µI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- γR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- Kr￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Kr￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- µ￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- becomes￨L￨VBZ￨O￨- recovered￨L￨VBN￨O￨- ,￨L￨,￨O￨- γ￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VB￨O￨- again￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- Kr￨U￨NN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- latency￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- SEIRS￨U￨NN￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becames￨L￨VBZ￨O￨- stochastic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- way￨L￨NN￨O￨- dS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- dE￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- dR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- −￨L￨SYM￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A −￨L￨CD￨NUMBER￨- εS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dWt￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- +￨L￨CC￨O￨- εS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dWt￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- µI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- γR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- Kr￨U￨NN￨O￨- Kr￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- scarce￨L￨JJ￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIRS￨U￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- latency￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- expressed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- SEIRS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- delay￨L￨NN￨O￨A .￨L￨.￨O￨- +Bai￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- considers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- SEIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- varying￨L￨VBG￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- expressed￨L￨VBN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- fluid￨L￨NN￨O￨- and￨L￨CC￨O￨- diffusion￨L￨NN￨O￨- limits￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- ∞￨L￨VB￨O￨- and￨L￨CC￨O￨- deduce￨L￨VB￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- push￨L￨NN￨O￨- algorithm￨L￨NN￨O￨A :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- newly￨L￨RB￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- push￨L￨NN￨O￨- round￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- selections￨L￨NNS￨O￨- needed￨L￨VBN￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- percent￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- both￨L￨DT￨O￨- asymptotically￨L￨RB￨O￨- normal￨L￨JJ￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- large￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- nonzero￨L￨NN￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- pull￨L￨NN￨O￨- round￨L￨NN￨O￨- infects￨L￨VBZ￨O￨- slightly￨L￨RB￨O￨- more￨L￨RBR￨O￨- nodes￨L￨NNS￨O￨- on￨L￨IN￨O￨- average￨L￨JJ￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- rounds￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- until￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- proportion￨L￨NN￨O￨- λ￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- converges￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- for￨L￨IN￨O￨- almost￨L￨RB￨O￨- all￨L￨DT￨O￨- λ￨L￨NN￨O￨- ∈￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- formula￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- rounds￨L￨NNS￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- continue￨L￨VBP￨O￨- a￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- push￨L￨NN￨O￨- algorithm￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- pull￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- randomly￨L￨RB￨O￨- choose￨L￨VB￨O￨- peers￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- initiated￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- earlier￨L￨JJR￨O￨- work￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- peer￨L￨VB￨O￨- to￨L￨TO￨O￨- peer￨L￨VB￨O￨- ;￨L￨:￨O￨- pull￨L￨NN￨O￨- ;￨L￨:￨O￨- push￨L￨NN￨O￨- ;￨L￨:￨O￨- epidemics￨L￨NNS￨O￨- ;￨L￨:￨O￨- epidemic￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨A ;￨L￨:￨O￨- diffusion￨L￨NN￨O￨- ;￨L￨:￨O￨- fluid￨L￨NN￨O￨- ;￨L￨:￨O￨- approximation￨L￨NN￨O￨- ;￨L￨:￨O￨- asymptotic￨L￨JJ￨O￨- ;￨L￨:￨O￨- analysis￨L￨NN￨O￨- ;￨L￨:￨O￨- data￨L￨NNS￨O￨- dissemination￨L￨NN￨O￨- ;￨L￨:￨O￨- fully￨L￨RB￨O￨- connected￨L￨VBN￨O￨- ;￨L￨:￨O￨- network￨L￨NN￨O￨- ;￨L￨:￨O￨- graph￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Epidemic￨U￨JJ￨O￨- algorithms￨L￨NNS￨O￨- mimic￨L￨VBP￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- disseminate￨L￨VB￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- write￨L￨VBP￨O￨- this￨L￨DT￨O￨- round￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- whose￨L￨WP$￨O￨- each￨L￨DT￨O￨- step￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- transmits￨L￨VBZ￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- pushes￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A ;￨L￨:￨O￨- this￨L￨DT￨O￨- gives￨L￨VBZ￨O￨- recursive￨L￨JJ￨O￨- formulas￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- moments￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- newly￨L￨RB￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- push￨L￨NN￨O￨- round￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- push-type￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨A :￨L￨:￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- push￨L￨NN￨O￨- round￨L￨NN￨O￨- ,￨L￨,￨O￨- every￨L￨DT￨O￨- node￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- every￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- randomly￨L￨RB￨O￨- chooses￨L￨VBZ￨O￨- c￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- +￨L￨CC￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- quickly￨L￨RB￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- infecting￨L￨VBG￨O￨- few￨L￨JJ￨O￨- ;￨L￨:￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- takes￨L￨VBZ￨O￨- off￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- grows￨L￨VBZ￨O￨A exponentially￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- negligible￨L￨JJ￨O￨- ;￨L￨:￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- takes￨L￨VBZ￨O￨- off￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- grows￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- quicker￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- fatalities￨L￨NNS￨O￨- diminish￨L￨VBP￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- remains￨L￨VBZ￨O￨- super￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- go￨L￨VBP￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ;￨L￨:￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- takes￨L￨VBZ￨O￨- off￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- grows￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- quicker￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- fatalities￨L￨NNS￨O￨- turn￨L￨VBP￨O￨- the￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- decay￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- SE￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- infected￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨A ;￨L￨:￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- he/she￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- he/she￨L￨NN￨O￨- recovers￨L￨VBZ￨O￨- ∗￨L￨RB￨O￨- Corresponding￨U￨VBG￨O￨- author￨L￨NN￨TITLE￨- Email￨U￨VB￨O￨- addresses￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- Tom￨U￨NNP￨PERSON￨- Britton￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- Désiré￨U￨NNP￨PERSON￨- Ouédraogo￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- Preprint￨U￨NNP￨ORGANIZATION￨- submitted￨L￨VBD￨O￨- to￨L￨TO￨O￨- Elsevier￨U￨NNP￨O￨- September￨U￨NNP￨DATE￨- 27￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- life-long￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- other￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨- often￨L￨RB￨O￨- used￨L￨VBN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- compartment￨L￨NN￨O￨- E￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- or￨L￨CC￨O￨- latent￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- already￨L￨RB￨O￨- infected￨L￨JJ￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- compartment￨L￨NN￨O￨- R￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- or￨L￨CC￨O￨- removed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- healed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- permanent￨L￨JJ￨O￨A or￨L￨CC￨O￨- non-permanent￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- derived￨L￨VBD￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Malthusian￨U￨JJ￨MISC￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- stated￨L￨VBN￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨A phase￨L￨NN￨O￨A and￨L￨CC￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- proportions￨L￨NNS￨O￨- process￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- correlated￨L￨VBN￨O￨A heterogeneous￨L￨JJ￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- CSIS￨U￨NNS￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- βij￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- =￨L￨JJ￨O￨- βj￨L￨NN￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- j￨L￨FW￨O￨- is￨L￨VBZ￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- end￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- :￨L￨:￨O￨- βij￨L￨NN￨O￨- =￨L￨JJ￨O￨- c￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- didj￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- α￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- nodal￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- selected￨L￨VBN￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- correlated￨L￨VBN￨O￨A heterogeneous￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- CSIS￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- homogeneous￨L￨JJ￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- βij￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- =￨L￨JJ￨O￨- βj￨L￨NN￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- j￨L￨FW￨O￨- is￨L￨VBZ￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- degrees￨L￨NNS￨O￨- di￨L￨FW￨O￨- and￨L￨CC￨O￨- dj￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- :￨L￨:￨O￨- βij￨L￨NN￨O￨- =￨L￨JJ￨O￨- c￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- didj￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- α￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- α￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- and￨L￨CC￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- uncorrected￨L￨JJ￨O￨- but￨L￨CC￨O￨- still￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- scenario￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- reference￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- correlated￨L￨VBD￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- CSIS￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- shuffled￨L￨VBN￨O￨- and￨L￨CC￨O￨- reallocated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- such￨L￨JJ￨O￨- correlated￨L￨VBD￨O￨A heterogeneous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- influence￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- network￨L￨NN￨O￨- topologies￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- e.g.￨L￨FW￨O￨- their￨L￨PRP$￨O￨- interaction￨L￨NN￨O￨- frequency￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- correlated￨L￨VBD￨O￨A with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- nodal￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- partial￨L￨JJ￨O￨A immunity￨L￨NN￨O￨- q￨L￨NN￨O￨- ,￨L￨,￨O￨- leaky￨L￨JJ￨O￨- partial￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- each￨L￨DT￨O￨- immunized￨L￨VBN￨O￨- individual￨L￨JJ￨O￨- reduces￨L￨VBZ￨O￨- their￨L￨PRP$￨O￨- chances￨L￨NNS￨O￨- of￨L￨IN￨O￨- getting￨L￨VBG￨O￨- reinfected￨L￨VBN￨O￨- and￨L￨CC￨O￨- infecting￨L￨VBG￨O￨- others￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- proportion￨L￨NN￨O￨- q￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- perfect￨L￨JJ￨O￨- partial￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- q￨L￨NN￨O￨- of￨L￨IN￨O￨- immunized￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- enjoy￨L￨VBP￨O￨- full￨L￨JJ￨O￨- protection￨L￨NN￨O￨- from￨L￨IN￨O￨- reinfection￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- proportion￨L￨NN￨O￨- are￨L￨VBP￨O￨- completely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- dominated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- which￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- enjoy￨L￨VBP￨O￨- complete￨L￨JJ￨O￨- immunity￨L￨NN￨O￨A following￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Partial￨U￨JJ￨O￨- immunity￨L￨NN￨O￨- can￨L￨MD￨O￨- limit￨L￨VB￨O￨- transmissibility￨L￨NN￨O￨- either￨L￨CC￨O￨- by￨L￨IN￨O￨- lowering￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- reinfection￨L￨NN￨O￨A or￨L￨CC￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- sheds￨L￨NNS￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- standard￨L￨JJ￨O￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- assumes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- naive￨L￨JJ￨O￨- population￨L￨NN￨O￨- without￨L￨IN￨O￨- immunity￨L￨NN￨O￨A from￨L￨IN￨O￨- prior￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- G1￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V1￨U￨NN￨O￨- ,￨L￨,￨O￨- E1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- G2￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V2￨U￨NN￨O￨- ,￨L￨,￨O￨- E2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- independent￨L￨JJ￨RELIGION￨- instances￨L￨NNS￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Erd￨U￨NNP￨MISC￨- ¨￨L￨SYM￨MISC￨- os-R￨L￨NN￨MISC￨- ´￨L￨''￨O￨- enyi￨L￨FW￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- ensemble￨L￨NN￨O￨- with￨L￨IN￨O￨- n￨L￨NN￨O￨- vertices￨L￨NNS￨O￨A and￨L￨CC￨O￨- edge￨L￨NN￨O￨- probability￨L￨NN￨O￨- p.￨L￨NN￨O￨- time￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- ξt￨L￨NN￨O￨- ⊂￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- ξt￨L￨NN￨O￨- If￨U￨IN￨O￨- λ￨L￨NN￨O￨- =￨L￨JJ￨O￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- The￨U￨DT￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- G￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- denotes￨L￨VBZ￨O￨- time￨L￨NN￨O￨- t.￨L￨NN￨O￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- on￨L￨IN￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- very￨L￨RB￨O￨- close￨L￨RB￨O￨- to￨L￨TO￨O￨- uniformly￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- vertices￨L￨NNS￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- proof￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Lemmas￨U￨NNP￨O￨- 2.5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 4.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- communities￨L￨NNS￨O￨- as￨L￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- Erd￨U￨NNP￨O￨- ¨￨L￨SYM￨O￨- os-R￨L￨NN￨O￨- ´￨L￨''￨O￨- enyi￨L￨FW￨O￨- random￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- with￨L￨IN￨O￨- n￨L￨NN￨O￨- vertices￨L￨NNS￨O￨A and￨L￨CC￨O￨- edge￨L￨NN￨O￨- probability￨L￨NN￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- na￨L￨TO￨O￨- −￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- a￨L￨DT￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- add￨L￨VB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- bridge￨L￨NN￨O￨- edges￨L￨NNS￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A starts￨L￨VBZ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- ,￨L￨,￨O￨- ξ0￨L￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- v0￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ⊂￨L￨SYM￨O￨- G1￨U￨NN￨O￨- ,￨L￨,￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- log￨L￨NN￨O￨- log￨L￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- survival￨L￨NN￨O￨- probability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- 1/b￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- b￨L￨NN￨O￨- =￨L￨JJ￨O￨- npλ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Lemmas￨U￨JJ￨O￨- 3.1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 3.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- malicious￨L￨JJ￨O￨- software￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- devices￨L￨NNS￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- moving￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- city￨L￨NN￨O￨- area￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- establish￨L￨VB￨O￨- time￨L￨NN￨O￨- bounds￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- counter-measure￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- cleaner￨L￨JJR￨TITLE￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- pandemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- precisely￨L￨RB￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- mobile￨L￨JJ￨TITLE￨- devices￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨- upper￨L￨JJ￨O￨- bounds￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- needed￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- counter-measure￨L￨NN￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- effect￨L￨NN￨O￨- after￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- response-time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- susceptible￨L￨JJ￨O￨- devices￨L￨NNS￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- Contribution￨U￨NN￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- response-time￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- counter-measure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- cleaner￨L￨JJR￨TITLE￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- malware￨L￨NN￨O￨- in￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- devices￨L￨NNS￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- purpose￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨VBP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- malware￨L￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- device￨L￨NN￨O￨- mobility￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- simulator￨L￨NN￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- malware￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- formed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- devices￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨VBP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- malware￨L￨NN￨O￨- propagation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A along￨L￨IN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- device￨L￨NN￨O￨- mobility￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- ,￨L￨,￨O￨- utilizing￨L￨VBG￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- simulator￨L￨NN￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- malware￨L￨NN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- th￨L￨DT￨O￨- is￨L￨VBZ￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- asymptotics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- wireless￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- ad￨L￨NN￨O￨- hoc￨L￨FW￨O￨- and￨L￨CC￨O￨- cellular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- simple￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-simple￨L￨JJ￨O￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- singular￨L￨JJ￨O￨- and￨L￨CC￨O￨- bounded￨L￨VBD￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- analytical￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- di￨L￨FW￨O￨- stribution￨L￨FW￨O￨- seems￨L￨VBZ￨O￨- hopeless￨L￨JJ￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- scenario￨L￨NN￨O￨- but￨L￨CC￨O￨- comprehensively￨L￨RB￨O￨- covers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- both￨L￨DT￨O￨- ad￨L￨NN￨O￨- hoc￨L￨FW￨O￨- and￨L￨CC￨O￨- cellular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- both￨L￨DT￨O￨- singular￨L￨JJ￨O￨- and￨L￨CC￨O￨- bounded￨L￨VBD￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- laws￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- general￨L￨JJ￨TITLE￨- stationary￨L￨JJ￨O￨- point￨L￨NN￨O￨- processes1￨L￨NN￨O￨- and￨L￨CC￨O￨- general￨L￨JJ￨TITLE￨- fading￨L￨JJ￨O￨- —￨L￨:￨O￨- unless￨L￨IN￨O￨- otherwise￨L￨RB￨O￨- speci￨L￨NN￨O￨- fied￨L￨VBD￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- cellular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A with￨L￨IN￨O￨- Nakagami-m￨U￨NN￨MISC￨- fading￨L￨JJ￨O￨- and￨L￨CC￨O￨- both￨L￨DT￨O￨- singular￨L￨JJ￨O￨- and￨L￨CC￨O￨- bounded￨L￨VBD￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- defin￨L￨NN￨O￨- ed￨L￨VBD￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- complementary￨L￨JJ￨O￨- cumulative￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- function￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CCDF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- horizontally￨L￨RB￨O￨- shifted￨L￨VBN￨O￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- dB￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- high-reliability￨L￨JJ￨O￨- regime￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- tails￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- distributions￨L￨NNS￨O￨- decay￨L￨NN￨O￨- polynomially￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- solely￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- exponent￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- fading￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- upper￨L￨JJ￨O￨- tails￨L￨NNS￨O￨- decay￨L￨NN￨O￨- exponentially￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- exception￨L￨NN￨O￨- of￨L￨IN￨O￨- cellular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A with￨L￨IN￨O￨- singular￨L￨JJ￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nearest￨L￨JJS￨O￨- interferer￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- crisp￨L￨JJ￨O￨- conjectures￨L￨NNS￨O￨- that￨L￨WDT￨O￨- —￨L￨:￨O￨- if￨L￨IN￨O￨- true￨L￨JJ￨O￨- —￨L￨:￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨A properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- desired￨L￨JJ￨O￨- signal￨L￨NN￨O￨- and/or￨L￨CC￨O￨- nearest￨L￨JJS￨O￨- interferer￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- perturbation￨L￨NN￨O￨A theory￨L￨NN￨O￨- ,￨L￨,￨O￨- approximations￨L￨NNS￨O￨- and￨L￨CC￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- many-body￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- squared￨L￨VBN￨O￨- norm￨L￨NN￨O￨- of￨L￨IN￨O￨- probability￨L￨NN￨O￨- vector￨L￨NN￨O￨- |￨L￨SYM￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- asymmetric￨L￨JJ￨O￨- time￨L￨NN￨O￨- generators￨L￨NNS￨O￨- are￨L￨VBP￨O￨- replaced￨L￨VBN￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- symmetric￨L￨JJ￨O￨- counterparts￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- employed￨L￨VBN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Namely￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- agents￨L￨NNS￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- momentarily￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- island￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- multipartite￨L￨JJ￨O￨- network￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- weakly￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- III￨U￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨- the￨L￨DT￨O￨- meanfield￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- virus￨L￨NN￨O￨- spread￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- bipartite￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- Y￨U￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- Y￨U￨NN￨O￨- N￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Y￨U￨NN￨O￨- N￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- collecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- island￨L￨NN￨O￨A converges￨L￨VBZ￨O￨- weakly￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- .￨L￨.￨O￨- +,￨L￨,￨O￨- XN￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- macroscopic￨L￨JJ￨O￨- state￨L￨NN￨O￨- variable￨L￨JJ￨O￨- YN￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- Y￨U￨NN￨O￨- N￨U￨NN￨O￨- reference￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- considers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- multiclass￨L￨JJ￨O￨- flow￨L￨NN￨O￨- of￨L￨IN￨O￨- packets￨L￨NNS￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- network￨L￨NN￨O￨- It￨U￨PRP￨O￨- defines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- YN￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- converges￨L￨VBZ￨O￨- weakly￨L￨RB￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- Y￨U￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- i￨L￨FW￨O￨- of￨L￨IN￨O￨- packets￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- superneighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- island￨L￨NN￨O￨A 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- Given￨U￨VBD￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- G￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- induced￨L￨VBN￨O￨- multipartite￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- GN￨U￨NN￨O￨- =￨L￨JJ￨O￨- EN￨U￨NN￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- ,￨L￨,￨O￨- d1￨L￨NN￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +,￨L￨,￨O￨- NM￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- RM￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- M￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- islands￨L￨NNS￨O￨- ,￨L￨,￨O￨- Ni￨U￨NN￨MISC￨- is￨L￨VBZ￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- ith￨L￨NN￨O￨- island￨L￨NN￨O￨A of￨L￨IN￨O￨- GN￨U￨NNP￨O￨- and￨L￨CC￨O￨- V￨U￨NNP￨O￨- N￨U￨NNP￨O￨- i￨L￨FW￨O￨- ∼￨L￨FW￨O￨- V￨U￨NN￨O￨- N￨U￨NN￨O￨- j￨L￨NN￨O￨- ⇔￨L￨CD￨NUMBER￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- V￨U￨NN￨O￨- N￨U￨NN￨O￨- i￨L￨FW￨O￨- ∼￨L￨FW￨O￨- j￨L￨FW￨O￨- ∈￨L￨FW￨O￨- V￨U￨NN￨O￨- N￨U￨NN￨O￨- j￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- V￨U￨NN￨O￨- N￨U￨NN￨O￨- i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ith￨L￨NN￨O￨- island￨L￨NN￨O￨- of￨L￨IN￨O￨- GN￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- depicted￨L￨VBN￨O￨- in￨L￨IN￨O￨- figure￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- analogy￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- “￨L￨``￨O￨- coupon￨L￨NN￨O￨- collector￨L￨NN￨TITLE￨- ”￨L￨''￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- probability￨L￨NN￨O￨- theory￨L￨NN￨O￨- reveals￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- takeover￨L￨NN￨O￨- time￨L￨NN￨O￨- T￨U￨NN￨O￨- is￨L￨VBZ￨O￨- dominated￨L￨VBN￨O￨- by￨L￨IN￨O￨- extremal￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- near￨L￨IN￨O￨A the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- near￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- .￨L￨.￨O￨- +How￨U￨WRB￨O￨- many￨L￨JJ￨O￨- time￨L￨NN￨O￨- steps￨L￨NNS￨O￨- T￨U￨NN￨O￨- does￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- take￨L￨VB￨O￨- to￨L￨TO￨O￨- completely￨L￨RB￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- nodes￨L￨NNS￨O￨A ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- ?￨L￨.￨O￨- +Takeover￨U￨NN￨O￨- times￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A of￨L￨IN￨O￨- network￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- Bertrand￨U￨NNP￨O￨- Ottino-L￨U￨NNP￨O￨- ¨￨L￨NN￨O￨- offler￨L￨NN￨O￨- ,1￨L￨CD￨NUMBER￨- Jacob￨U￨NNP￨PERSON￨- G￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨- and￨L￨CC￨O￨- specificity￨L￨NN￨O￨- values￨L￨VBZ￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- permitting￨L￨VBG￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- originally￨L￨RB￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- testing￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- find￨L￨VBD￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- sensitivity￨L￨NN￨O￨- and￨L￨CC￨O￨- specificity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- testing￨L￨NN￨O￨A rate￨L￨NN￨O￨- for￨L￨IN￨O￨- reaching￨L￨VBG￨O￨- R0￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- testing￨L￨NN￨O￨A .￨L￨.￨O￨- +An￨U￨DT￨O￨- imperfect￨L￨JJ￨O￨A test￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- might￨L￨MD￨O￨- incorrectly￨L￨RB￨O￨- consider￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- false￨L￨JJ￨O￨- positives￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Infected￨U￨JJ￨O￨- individuals￨L￨NNS￨O￨- go￨L￨VBP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- state￨L￨NN￨O￨- “￨L￨``￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- tested￨L￨VBN￨O￨A positive￨L￨JJ￨O￨- ”￨L￨''￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- α￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- process￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- extended￨L￨JJ￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A on￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- ,￨L￨,￨O￨- finite-size￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibri￨L￨JJ￨O￨- um￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- scaled￨L￨VBN￨O￨- SIS￨U￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- derived￨L￨VBD￨O￨- in￨L￨IN￨O￨- closed-form￨L￨NN￨O￨- in￨L￨IN￨O￨- prior￨L￨JJ￨O￨- work￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- con￨L￨VBP￨O￨- firm￨L￨NN￨O￨- this￨L￨DT￨O￨- result￨L￨NN￨O￨- with￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- extended￨L￨JJ￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A with￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- scaled￨L￨VBN￨O￨- SIS￨U￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- this￨L￨DT￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- decide￨L￨VB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- polynomial-time￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- agents￨L￨NNS￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- substructures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- extended￨L￨JJ￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A with￨L￨IN￨O￨- nonzero￨L￨NN￨O￨- exogenous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- ǫ-SIS￨L￨NN￨O￨- ,￨L￨,￨O￨- ǫ￨L￨NN￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- model￨L￨JJ￨TITLE￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Extensive￨U￨JJ￨O￨- numerical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- method￨L￨NN￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- most￨L￨RBS￨O￨- popular￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- reduction￨L￨NN￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- sliced￨L￨VBN￨O￨- average￨L￨JJ￨O￨- variance￨L￨NN￨O￨- estimation￨L￨NN￨O￨- ,￨L￨,￨O￨- principal￨L￨JJ￨TITLE￨- Hessian￨U￨JJ￨MISC￨- direction￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- directional￨L￨JJ￨O￨- regression￨L￨NN￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- new￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- reduction￨L￨NN￨O￨- method￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Gaussian￨U￨JJ￨MISC￨- finite￨L￨NN￨O￨- mixtures￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- to￨L￨TO￨O￨- sliced￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- regression￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +MSIR￨U￨NN￨O￨- appears￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- flexible￨L￨JJ￨O￨- to￨L￨TO￨O￨- accommodate￨L￨VB￨O￨- various￨L￨JJ￨O￨- regression￨L￨NN￨O￨A functions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- performance￨L￨NN￨O￨- is￨L￨VBZ￨O￨- comparable￨L￨JJ￨O￨- with￨L￨IN￨O￨- or￨L￨CC￨O￨- better￨L￨JJR￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- as￨L￨IN￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- grows￨L￨VBZ￨O￨- ,￨L￨,￨O￨- than￨L￨IN￨O￨- other￨L￨JJ￨O￨- available￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model-based￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- MSIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- limitation￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- overcome￨L￨VBN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- failure￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- regression￨L￨NN￨O￨A symmetric￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- impose￨L￨VB￨O￨- further￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- dimension￨L￨NN￨O￨- reduction￨L￨NN￨O￨- ,￨L￨,￨O￨- sliced￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- regression￨L￨NN￨O￨A ,￨L￨,￨O￨- mixture￨L￨NN￨O￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- summary￨L￨NN￨O￨- plots￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- following￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- dS￨L￨NN￨O￨- dt￨L￨NN￨O￨A =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- dI￨L￨NNP￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- uI￨L￨NN￨O￨- ,￨L￨,￨O￨- dR￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- uI￨L￨NN￨O￨- Here￨U￨RB￨O￨- u￨L￨SYM￨O￨- -￨L￨:￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- ”￨L￨''￨O￨- treatment￨L￨NN￨O￨- ”￨L￨''￨O￨- Infected￨U￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- β￨L￨SYM￨O￨- -￨L￨:￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- for￨L￨IN￨O￨- Infected￨U￨JJ￨O￨- to￨L￨TO￨O￨- Susceptible￨U￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨A spreading￨L￨NN￨O￨- are￨L￨VBP￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- lots￨L￨NNS￨O￨- of￨L￨IN￨O￨- results￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- only￨L￨RB￨O￨- numerically￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Optimal￨U￨JJ￨O￨- control￨L￨NN￨O￨- for￨L￨IN￨O￨- virus￨L￨NN￨O￨A spreading￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- O.D.￨U￨NNP￨O￨- Klimenkova1￨U￨NNP￨O￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Applied￨U￨NNP￨O￨- Mathematics￨U￨NNP￨O￨- ,￨L￨,￨O￨- National￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Higher￨U￨JJR￨ORGANIZATION￨- School￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Economics￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 101000￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Moscow￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Russia￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A problem￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- ”￨L￨''￨O￨- vaccination￨L￨NN￨O￨- ”￨L￨''￨O￨- and￨L￨CC￨O￨- ”￨L￨''￨O￨- treatment￨L￨NN￨O￨- ”￨L￨''￨O￨- as￨L￨IN￨O￨- controls￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- section￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- investigated￨L￨VBN￨O￨- and￨L￨CC￨O￨- formulate￨L￨VB￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A problem￨L￨NN￨O￨- for￨L￨IN￨O￨- that￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- appendix￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A network￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- time-homogeneous￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- prove￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- identical￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- out-component￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- probability￨L￨NN￨O￨- space￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- percolation￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A networks￨L￨NNS￨O￨- accurately￨L￨RB￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- outline￨L￨VBP￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- undirected￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A networks￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- purely￨L￨RB￨O￨- directed￨L￨VBN￨O￨- because￨L￨IN￨O￨- undirected￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- disappear￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- analyzed￨L￨VBN￨O￨- by￨L￨IN￨O￨- mapping￨L￨VBG￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- onto￨L￨IN￨O￨- a￨L￨DT￨O￨- semi-directed￨L￨JJ￨O￨- network￨L￨NN￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- call￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SIR￨U￨NN￨O￨- filter￨L￨NN￨O￨- may￨L￨MD￨O￨- suffer￨L￨VB￨O￨- from￨L￨IN￨O￨- sample￨L￨NN￨O￨- impoverishment￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- resampling￨L￨NN￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- will￨L￨MD￨O￨- benefit￨L￨VB￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- sampling￨L￨NN￨O￨- proposal￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- heavier￨L￨JJR￨O￨- tail￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- transition￨L￨NN￨O￨- noise￨L￨NN￨O￨A simulated￨L￨JJ￨O￨- for￨L￨IN￨O￨- particle￨L￨NN￨O￨- preparation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- bigger￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- noise￨L￨NN￨O￨- involved￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- Note￨U￨NN￨O￨- concerns￨L￨NNS￨O￨- with￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- transition￨L￨NN￨O￨- noise￨L￨NN￨O￨A by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨- importance￨L￨NN￨O￨- resampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- filter￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- particle￨L￨NN￨O￨- filters￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- filter￨L￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- yield￨L￨VB￨O￨- a￨L￨DT￨O￨- biased￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- bigger-than-the-truth￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- noise￨L￨NN￨O￨A if￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- unknown￨L￨JJ￨O￨- and￨L￨CC￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- forward-only￨L￨JJ￨O￨- filtering￨L￨VBG￨O￨- estimation￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- Note￨U￨NN￨O￨- investigates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- bias￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨- importance￨L￨NN￨O￨- resampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- filter￨L￨NN￨O￨- in￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- transition￨L￨NN￨O￨- noise￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Keywords￨U￨NNP￨O￨- Particle￨U￨NNP￨O￨- filters￨L￨NNS￨O￨- ,￨L￨,￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- ,￨L￨,￨O￨- Markov￨U￨NNP￨PERSON￨- transition￨L￨NN￨O￨- noise￨L￨NN￨O￨A T￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨A population￨L￨NN￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- λI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- δR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- λI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- λI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- δR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- call￨L￨VBP￨O￨- ν￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ·￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- measure￨L￨NN￨O￨A and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- L´evy￨U￨NN￨O￨- measure￨L￨NN￨O￨- ,￨L￨,￨O￨- hence￨L￨RB￨O￨- ,￨L￨,￨O￨- tν￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- E￨U￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- If￨U￨IN￨O￨- β￨L￨JJ￨O￨- >￨L￨JJR￨O￨- λ￨L￨NN￨O￨- β￨L￨NN￨O￨- λ￨L￨NN￨O￨- β￨L￨NN￨O￨- λ￨L￨NN￨O￨- Nω￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Borel￨U￨NNP￨O￨- Measure￨U￨NN￨O￨- with￨L￨IN￨O￨- R￨U￨NN￨O￨- \￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- x￨L￨CC￨O￨- |￨L￨SYM￨O￨- 2￨L￨CD￨NUMBER￨- ∧￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ν￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dx￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- <￨L￨JJR￨O￨- ∞￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Lastly￨U￨RB￨O￨- ,￨L￨,￨O￨- take￨L￨VB￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- affect￨L￨NN￨O￨A of￨L￨IN￨O￨- random￨L￨JJ￨O￨- jumps￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- −￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- every￨L￨DT￨O￨- y￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- continuously￨L￨RB￨O￨- differentiable￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- B￨U￨NN￨O￨- ∈￨L￨NN￨O￨- B￨U￨NN￨O￨- Rd￨U￨NN￨O￨- \￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- show￨L￨VB￨O￨- ˜Nω￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- martingale￨L￨NN￨O￨- and￨L￨CC￨O￨- E￨U￨NN￨O￨- or￨L￨CC￨O￨- Applebaum￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- We￨U￨PRP￨O￨- are￨L￨VBP￨O￨- ready￨L￨JJ￨O￨- to￨L￨TO￨O￨- stochastically￨L￨RB￨O￨A perturb￨L￨VB￨O￨- the￨L￨DT￨O￨- systems￨L￨NNS￨O￨- above￨L￨IN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- partial￨L￨JJ￨O￨- sliced￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- regression￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PSIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- merit￨L￨NN￨O￨- of￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- predictors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- responses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Quality-relevant￨U￨JJ￨O￨- multivariate￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- process￨L￨NN￨O￨- monitoring￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- active￨L￨JJ￨O￨- research￨L￨NN￨O￨- topics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- interdisciplinary￨L￨JJ￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- and￨L￨CC￨O￨- engineering￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- two￨L￨CD￨DURATION￨- decades￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- introduces￨L￨VBZ￨O￨- a￨L￨DT￨O￨- popular￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- reduction￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- sliced￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- regression￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- into￨L￨IN￨O￨- multivariate￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- process￨L￨NN￨O￨- monitoring￨L￨NN￨O￨A .￨L￨.￨O￨- +Dunia￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Qin￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Qin￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- gave￨L￨VBD￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- for￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- space￨L￨NN￨O￨- decomposition￨L￨NN￨O￨- via￨L￨IN￨O￨- PCA￨U￨NNP￨ORGANIZATION￨- to￨L￨TO￨O￨- perform￨L￨VB￨O￨- the￨L￨DT￨O￨- fault￨L￨NN￨O￨- detection￨L￨NN￨O￨- in￨L￨IN￨O￨- process￨L￨NN￨O￨- monitoring￨L￨NN￨O￨A .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latest￨L￨JJS￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- analysis￨L￨NN￨O￨- multivariate￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨A process￨L￨NN￨O￨- are￨L￨VBP￨O￨- principal￨L￨JJ￨TITLE￨- component￨L￨NN￨O￨- analysis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PCA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- partial￨L￨JJ￨O￨- least￨L￨JJS￨O￨- square￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PLS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Multiple￨U￨JJ￨O￨- transitions￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- Ang￨U￨VBG￨PERSON￨- ´￨L￨''￨O￨- elica￨L￨FW￨O￨- S.￨U￨FW￨O￨- Ferreira1￨U￨NN￨O￨- 1Departamento￨L￨NN￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- ,￨L￨,￨O￨- Universidade￨U￨NNP￨ORGANIZATION￨- Federal￨U￨NNP￨ORGANIZATION￨- de￨L￨NNP￨ORGANIZATION￨- Vi￨U￨NNP￨ORGANIZATION￨- ¸￨L￨NNP￨O￨- cosa￨L￨NN￨O￨- ,￨L￨,￨O￨- 36570-000￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Vi￨U￨NNP￨O￨- ¸￨L￨NNP￨O￨- cosa￨L￨NN￨O￨- ,￨L￨,￨O￨- MG￨U￨NN￨O￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- having￨L￨VBG￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- with￨L￨IN￨O￨- exponent￨L￨NN￨O￨- γ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 3￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- different￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- predict￨L￨VBP￨O￨- different￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- observed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- transitions￨L￨NNS￨O￨A involving￨L￨VBG￨O￨- thresholds￨L￨NNS￨O￨- which￨L￨WDT￨O￨- vanishes￨L￨VBZ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨- limit￨L￨NN￨O￨- involve￨L￨VBP￨O￨- localized￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- vanishing￨L￨VBG￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- effectively￨L￨RB￨O￨- contribute￨L￨VBP￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- activity￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- ,￨L￨,￨O￨- occurs￨L￨VBZ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- observed￨L￨VBD￨O￨- concomitant￨L￨JJ￨O￨- multiple￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨A in￨L￨IN￨O￨- individual￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- presenting￨L￨VBG￨O￨- large￨L￨JJ￨O￨- gaps￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- obtained￨L￨VBN￨O￨- multiple￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- theories￨L￨NNS￨O￨- .￨L￨.￨O￨- +INTRODUCTION￨U￨NNP￨O￨- Phase￨U￨NN￨O￨- transitions￨L￨NNS￨O￨A involving￨L￨VBG￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- non-equilibrium￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- begun￨L￨VBN￨O￨- drawing￨L￨VBG￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- interest￨L￨NN￨O￨- soon￨L￨RB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- boom￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- science￨L￨NN￨O￨- at￨L￨IN￨O￨- late￨L￨JJ￨O￨- 90￨L￨CD￨NUMBER￨- ’s￨L￨POS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- prove￨L￨VBP￨O￨A that￨L￨IN￨O￨- R0￨U￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- sign￨L￨NN￨O￨- as￨L￨IN￨O￨- µp￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- sup￨L￨NN￨O￨- ϕ￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- L2￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Ω￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ϕ￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- dI￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- RΩ￨U￨NN￨O￨- RΩ￨U￨NN￨O￨- J￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- ϕ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- ϕ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- dydx￨L￨NN￨O￨- +￨L￨CC￨O￨- RΩ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ϕ2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dx￨L￨NN￨O￨- RΩ￨U￨NN￨O￨- ϕ2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dx￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- by￨L￨IN￨O￨- itself￨L￨PRP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- squared￨L￨VBN￨O￨- norm￨L￨NN￨O￨- of￨L￨IN￨O￨- probability￨L￨NN￨O￨- vector￨L￨NN￨O￨A ,￨L￨,￨O￨- |￨L￨SYM￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- an￨L￨DT￨O￨- algebraic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- stationary￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- independent￨L￨JJ￨RELIGION￨- Markov￨U￨NNP￨PERSON￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Analytical￨U￨NNP￨O￨- methods￨L￨NNS￨O￨- using￨L￨VBG￨O￨- operatorial￨L￨JJ￨O￨- content￨L￨NN￨O￨- are￨L￨VBP￨O￨- sub￨L￨JJ￨O￨- jected￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- asymmetric￨L￨JJ￨O￨- eigenvalue￨L￨NN￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- restraining￨L￨VBG￨O￨- the￨L￨DT￨O￨- usability￨L￨NN￨O￨- of￨L￨IN￨O￨- standard￨L￨JJ￨O￨- perturbative￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- small￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨A space￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- exponentially￨L￨RB￨O￨- with￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- equation￨L￨NN￨O￨A requires￨L￨VBZ￨O￨- eigenvalues￨L￨NNS￨O￨- of￨L￨IN￨O￨- symmetrized￨L￨JJ￨O￨- time￨L￨NN￨O￨- generators￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- take￨L￨VBP￨O￨- full￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- symmetries￨L￨NNS￨O￨- ,￨L￨,￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- sparse￨L￨JJ￨O￨- matrix￨L￨NN￨O￨- diagonalization￨L￨NN￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- models￨L￨NNS￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A evolution￨L￨NN￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- vertices￨L￨NNS￨O￨- are￨L￨VBP￨O￨- either￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- agents￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- internal￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- super￨L￨JJ￨O￨- node￨L￨NN￨O￨- induce￨L￨VBP￨O￨- localized￨L￨JJ￨O￨A state￨L￨NN￨O￨- with￨L￨IN￨O￨- limited￨L￨JJ￨O￨- lifetime￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- neighboring￨L￨VBG￨O￨- super￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- path￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- hops￨L￨VBZ￨O￨- enable￨L￨VB￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- trapping￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absorbing￨L￨VBG￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- marking￨L￨VBG￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +Localized-endemic￨U￨JJ￨MISC￨- state￨L￨NN￨O￨- transition￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- Zong-Wen￨U￨NNP￨O￨- Wei￨U￨NNP￨O￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ∗￨L￨CD￨NUMBER￨- Hao￨U￨NNP￨PERSON￨- Liao￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Hai-Feng￨U￨NNP￨PERSON￨- Zhang￨U￨NNP￨PERSON￨- ,3￨L￨CD￨NUMBER￨- Jia-Rong￨U￨NNP￨PERSON￨- Xie￨U￨NNP￨PERSON￨- ,2￨L￨CD￨NUMBER￨- Bing-Hong￨U￨NNP￨O￨- Wang￨U￨NNP￨O￨- ,2￨L￨NN￨O￨- ,￨L￨,￨O￨- †￨L￨NN￨O￨- and￨L￨CC￨O￨- Guo-Liang￨U￨JJ￨O￨- Chen1￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Guangdong￨U￨NNP￨ORGANIZATION￨- Province￨U￨NNP￨ORGANIZATION￨- Key￨U￨NNP￨ORGANIZATION￨- Laboratory￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Popular￨U￨NNP￨ORGANIZATION￨- High￨U￨NNP￨ORGANIZATION￨- Performance￨U￨NNP￨ORGANIZATION￨- Computers￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- College￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Computer￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Software￨U￨NNP￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Shenzhen￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Shenzhen￨U￨NNP￨CITY￨- 518060￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 2￨L￨CD￨NUMBER￨- Department￨U￨NNP￨O￨- of￨L￨IN￨O￨- Modern￨U￨NNP￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hefei￨U￨NNP￨CITY￨- 230027￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 3￨L￨CD￨NUMBER￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mathematical￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Anhui￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hefei￨U￨NNP￨CITY￨- 230601￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 13￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- longstanding￨L￨JJ￨O￨- debate￨L￨NN￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- localized￨L￨JJ￨O￨A state￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- hybrid￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- render￨L￨VBP￨O￨- highly￨L￨RB￨O￨A connected￨L￨VBN￨O￨A nodes￨L￨NNS￨O￨- exponentially￨L￨RB￨O￨- increasing￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- truly￨L￨RB￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- null￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +That￨U￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- diffusing￨L￨VBG￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- integer￨L￨NN￨O￨- when￨L￨WRB￨O￨- one￨L￨CD￨NUMBER￨- uses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Busy￨U￨NNP￨O￨- Beaver￨U￨NNP￨O￨- game￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- toy￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- may￨L￨MD￨O￨- trigger￨L￨VB￨O￨- an￨L￨DT￨O￨- unlimited￨L￨JJ￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- expected￨L￨VBN￨O￨- emergent￨L￨JJ￨O￨A algorithmic￨L￨JJ￨O￨- information￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- randomly￨L￨RB￨O￨- generated￨L￨VBN￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- computable￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- grows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- now￨L￨RB￨DATE￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- former￨L￨JJ￨O￨- comes￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- stationEmergent￨L￨JJ￨O￨- Open-Endedness￨U￨NN￨O￨- from￨L￨IN￨O￨- Contagion￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Fittest￨U￨NNP￨O￨- 5￨L￨CD￨NUMBER￨- First￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- remember￨L￨VBP￨O￨- that￨L￨IN￨O￨- algorithmic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- G￨U￨NN￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- defined3￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- upon￨L￨IN￨O￨- theoretical￨L￨JJ￨O￨- machines￨L￨NNS￨O￨- P￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- generalized4￨L￨NN￨O￨- graph￨L￨NN￨O￨- G￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- function￨L￨NN￨O￨- b￨L￨NN￨O￨- that￨L￨WDT￨O￨- makes￨L￨VBZ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- to￨L￨TO￨O￨- correspond￨L￨VB￨O￨- to￨L￨TO￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- P￨U￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- G￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- mapped￨L￨VBN￨O￨A one-to-one￨L￨JJ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- element￨L￨NN￨O￨- of￨L￨IN￨O￨- P.￨U￨NNP￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- emergent￨L￨JJ￨O￨A irreducible￨L￨JJ￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- randomly￨L￨RB￨O￨- generated￨L￨VBN￨O￨- computable￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- networked￨L￨JJ￨O￨- and￨L￨CC￨O￨- 8￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- u￨L￨NN￨O￨- J￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- this￨L￨DT￨O￨- networked￨L￨JJ￨O￨A population￨L￨NN￨O￨- of￨L￨IN￨O￨- randomly￨L￨RB￨O￨- generated￨L￨VBN￨O￨- Turing￨U￨JJ￨O￨- machines￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- general￨L￨JJ￨TITLE￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- networked￨L￨JJ￨O￨- computable￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- called￨L￨VBN￨O￨- as￨L￨RB￨O￨- algorithmic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +6￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 8￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Emergent￨U￨JJ￨O￨- Open-Endedness￨U￨NN￨O￨- from￨L￨IN￨O￨- Contagion￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Fittest￨U￨NNP￨ORGANIZATION￨- 2￨L￨CD￨NUMBER￨- algorithmic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- bring￨L￨VB￨O￨- these￨L￨DT￨O￨- topics￨L￨NNS￨O￨A into￨L￨IN￨O￨- an￨L￨DT￨O￨- abstract￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- counts￨L￨NNS￨O￨A and￨L￨CC￨O￨- present￨L￨VB￨DATE￨- a￨L￨DT￨O￨- functional￨L￨JJ￨O￨- central￨L￨JJ￨O￨- limit￨L￨NN￨O￨- theorem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FCLT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- grows￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- be￨L￨VB￨O￨- precise￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- counts￨L￨NNS￨O￨A ,￨L￨,￨O￨- when￨L￨WRB￨O￨- appropriately￨L￨RB￨O￨- scaled￨L￨VBN￨O￨- ,￨L￨,￨O￨- converge￨L￨VBP￨O￨- weakly￨L￨RB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- Gaussian￨U￨JJ￨MISC￨- vector￨L￨NN￨O￨- martingale￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- space￨L￨NN￨O￨- of￨L￨IN￨O￨- vector-valued￨L￨JJ￨O￨- càdlàg￨L￨NN￨O￨- functions￨L￨VBZ￨O￨- endowed￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- Skorohod￨U￨NNP￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +Functional￨U￨JJ￨O￨- Central￨U￨NNP￨O￨- Limit￨U￨NNP￨O￨- Theorem￨U￨NNP￨O￨- for￨L￨IN￨O￨- Susceptible-Infected￨U￨NNP￨O￨- Process￨U￨VB￨O￨- on￨L￨IN￨O￨- Configuration￨U￨NNP￨O￨- Model￨U￨NNP￨TITLE￨- Graphs￨U￨NNP￨O￨- Wasiur￨U￨NNP￨O￨- R.￨U￨NNP￨O￨- Rempała￨U￨NNP￨O￨- ‡￨L￨NNP￨O￨- Heinz￨U￨NNP￨O￨- Koeppl￨U￨NNP￨O￨- §￨L￨NNP￨O￨- September￨U￨NNP￨DATE￨- 26￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- configuration￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- a￨L￨DT￨O￨- Central￨U￨NNP￨O￨- Limit￨U￨NNP￨O￨- Theorem￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨A time￨L￨NN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- simple￨L￨JJ￨O￨- random￨L￨JJ￨O￨- walks￨L￨VBZ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- graph￨L￨NN￨O￨- with￨L￨IN￨O￨- n￨L￨NN￨O￨- vertices￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- chain￨L￨NN￨O￨- starts￨L￨VBZ￨O￨- from￨L￨IN￨O￨- A0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- D0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- V0￨U￨NN￨O￨- =￨L￨JJ￨O￨- n￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- comes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- end￨L￨NN￨O￨- as￨L￨RB￨O￨- soon￨L￨RB￨O￨- some￨L￨DT￨O￨- discrete￨L￨JJ￨O￨A time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- At￨U￨IN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Note￨U￨VB￨O￨- that￨L￨DT￨O￨- from￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- −￨L￨FW￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- w.p.￨L￨NN￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- w.p.￨L￨NN￨O￨- n￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- as￨L￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- discrete￨L￨JJ￨O￨A values￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- ∈￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +Пусть￨U￨NNP￨O￨- xt￨L￨NNP￨O￨- –￨L￨:￨O￨- численность￨L￨NN￨O￨- индивидуумов￨L￨NN￨O￨- из￨L￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- yt￨L￨NN￨O￨- –￨L￨:￨O￨- численность￨L￨NN￨O￨- индивидуумов￨L￨NN￨O￨- из￨L￨NN￨O￨- L￨U￨NN￨O￨- ,￨L￨,￨O￨- zt￨L￨NN￨O￨- –￨L￨:￨O￨- численность￨L￨NN￨O￨- индивидуумов￨L￨NN￨O￨- из￨L￨NN￨O￨- T￨U￨NN￨O￨- ,￨L￨,￨O￨- rt￨L￨NN￨O￨A –￨L￨:￨O￨- численность￨L￨NN￨O￨- индивидуумов￨L￨NN￨O￨- из￨L￨NN￨O￨- R￨U￨NN￨O￨- в￨L￨NN￨O￨- моменты￨L￨NN￨O￨- времени￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- random￨L￨JJ￨O￨A graph￨L￨NN￨O￨A representation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- characterise￨L￨VB￨O￨- the￨L￨DT￨O￨- fractions￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- among￨L￨IN￨O￨- all￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- limit￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- identify￨L￨VBP￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two-type￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- type￨L￨NN￨O￨A infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- type￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- maximised￨L￨VBN￨O￨- among￨L￨IN￨O￨- all￨L￨DT￨O￨- two-type￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- branching￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- mean￨L￨NN￨O￨- offspring￨L￨VBG￨O￨- matrix￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- susceptibility￨L￨NN￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vertex￨L￨NN￨O￨- v￨L￨LS￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- vertices￨L￨NNS￨O￨- u￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vertex￨L￨NN￨O￨- set￨L￨VBN￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- path￨L￨NN￨O￨- from￨L￨IN￨O￨- u￨L￨FW￨O￨- to￨L￨TO￨O￨- v￨L￨LS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- restricted￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- random￨L￨JJ￨O￨A graph￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- random￨L￨JJ￨O￨A graph￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- coupled￨L￨VBN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- that￨L￨IN￨O￨- u￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- v￨L￨LS￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- v￨L￨LS￨O￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- conditioned￨L￨VBN￨O￨- on￨L￨IN￨O￨- u￨L￨NN￨O￨- being￨L￨VBG￨O￨- initially￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- couple￨L￨VBP￨O￨- a￨L￨DT￨O￨- multi-type￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- directed￨L￨VBN￨O￨- random￨L￨JJ￨O￨A graph￨L￨NN￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- edges￨L￨NNS￨O￨- have￨L￨VBP￨O￨- random￨L￨JJ￨O￨- lengths￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- easy￨L￨JJ￨O￨- to￨L￨TO￨O￨- find￨L￨JJ￨O￨- numerous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- of￨L￨IN￨O￨- ad-hoc￨L￨JJ￨O￨- fractional￨L￨JJ￨O￨- order￨L￨NN￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- derivatives￨L￨NNS￨O￨A are￨L￨VBP￨O￨- simply￨L￨RB￨O￨- replaced￨L￨VBN￨O￨- with￨L￨IN￨O￨- nonlocal￨L￨JJ￨O￨- Caputo￨U￨NNP￨PERSON￨- fractional￨L￨JJ￨O￨- derivatives￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- fractional￨L￨JJ￨O￨- order￨L￨NN￨O￨- time￨L￨NN￨O￨- derivatives￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- governing￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- physical￨L￨JJ￨O￨- underlying￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨A from￨L￨IN￨O￨- a￨L￨DT￨O￨- directed￨L￨VBN￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- compartments￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- drawn￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- waiting￨L￨VBG￨O￨- time￨L￨NN￨O￨- probability￨L￨NN￨O￨- density￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- derivation￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨A process￨L￨NN￨O￨A is￨L￨VBZ￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- stable￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- recovery￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- transmitters￨L￨NNS￨O￨A are￨L￨VBP￨O￨- initially￨L￨RB￨O￨- deployed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PPP￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- based￨L￨VBN￨O￨- scheduling￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- PPP￨U￨NNP￨ORGANIZATION￨- no￨L￨RB￨O￨- longer￨L￨RB￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- locations￨L￨NNS￨O￨- of￨L￨IN￨O￨- retained￨L￨VBN￨O￨- transmitters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- probing￨L￨VBG￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- transmission￨L￨NN￨O￨- phases￨L￨NNS￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- interference￨L￨NN￨O￨- induced￨L￨VBD￨O￨- coupling￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- decisions￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- very￨L￨RB￨O￨- complicated￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨VBD￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- single-stage￨L￨JJ￨O￨- probing￨L￨VBG￨O￨- and￨L￨CC￨O￨- find￨L￨NN￨O￨- t￨L￨NN￨O￨- hat￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- set￨L￨VBN￨O￨- sufficiently￨L￨RB￨O￨- small￨L￨JJ￨O￨- to￨L￨TO￨O￨- assure￨L￨VB￨O￨- an￨L￨DT￨O￨- acceptable￨L￨JJ￨O￨- interference￨L￨NN￨O￨- level￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- scheme￨L￨NN￨O￨A can￨L￨MD￨O￨- greatly￨L￨RB￨O￨- outperform￨L￨VB￨O￨- the￨L￨DT￨O￨- non-scheduling￨L￨JJ￨O￨- reference￨L￨NN￨O￨- scheme￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- only￨L￨RB￨O￨- local￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- information￨L￨NN￨O￨- is￨L￨VBZ￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- making￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- decision￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- scheme￨L￨NN￨O￨A is￨L￨VBZ￨O￨- appropriate￨L￨JJ￨O￨- for￨L￨IN￨O￨- distributed￨L￨VBN￨O￨- implementation￨L￨NN￨O￨- in￨L￨IN￨O￨- practical￨L￨JJ￨O￨- wireless￨L￨JJ￨O￨- ad￨L￨NN￨O￨- hoc￨L￨FW￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- signal-to-interference-ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- threshold￨L￨NN￨O￨- based￨L￨VBN￨O￨- scheduling￨L￨NN￨O￨- scheme￨L￨NN￨O￨A :￨L￨:￨O￨- by￨L￨IN￨O￨- starting￨L￨VBG￨O￨- with￨L￨IN￨O￨- initial￨L￨JJ￨O￨- probing￨L￨VBG￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- transmitter￨L￨NN￨O￨- iteratively￨L￨RB￨O￨- decides￨L￨VBZ￨O￨- to￨L￨TO￨O￨- further￨L￨JJ￨O￨- probe￨L￨NN￨O￨- or￨L￨CC￨O￨- stay￨L￨VB￨O￨- idle￨L￨JJ￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- proceeding￨L￨NN￨O￨- probing￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- larger￨L￨JJR￨O￨- or￨L￨CC￨O￨- smaller￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- prede￨L￨NN￨O￨- fined￨L￨VBD￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- studies￨L￨NNS￨O￨- spatial￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- wireless￨L￨JJ￨O￨- ad￨L￨NN￨O￨A hoc￨L￨FW￨O￨A network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- multi-stage￨L￨JJ￨O￨- probing￨L￨VBG￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- sequentially￨L￨RB￨O￨- performed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Usually￨U￨RB￨O￨- ,￨L￨,￨O￨- interference￨L￨NN￨O￨A in￨L￨IN￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- network￨L￨NN￨O￨- significantly￨L￨RB￨O￨- dominates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- performance￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- effectively￨L￨RB￨O￨- evaluated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- metric￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- signal-to-interference￨L￨NN￨O￨- power￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- RXs￨U￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- aid￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- derived￨L￨VBN￨O￨- Shannon￨U￨NNP￨PERSON￨- transform￨L￨VB￨O￨- identity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ergodic￨L￨JJ￨O￨- link￨L￨NN￨O￨- capacities￨L￨NNS￨O￨- of￨L￨IN￨O￨- K￨U￨NN￨O￨- -￨L￨:￨O￨- type￨L￨NN￨O￨- RXs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- complexity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- transmitting￨L￨VBG￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- multi-antenna￨L￨JJ￨O￨- communication￨L￨NN￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- power￨L￨NN￨O￨A control￨L￨NN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- throughput￨L￨NN￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- network￨L￨NN￨O￨- defined￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- derived￨L￨VBN￨O￨A K￨U￨NN￨O￨- success￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- and￨L￨CC￨O￨- ergodic￨L￨JJ￨O￨- link￨L￨NN￨O￨- capacities￨L￨NNS￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- maximum￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- ignore￨L￨VBP￨O￨- the￨L￨DT￨O￨- synergistic￨L￨JJ￨O￨- effect￨L￨NN￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- infected-susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨A ,￨L￨,￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- previous￨L￨JJ￨O￨- efforts￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- synergy￨L￨NN￨O￨- on￨L￨IN￨O￨- irreversible￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- interplay￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- concrete￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- existed￨L￨VBD￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- biological￨L￨JJ￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- infected-susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- would￨L￨MD￨O￨- enhance￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- [￨L￨-LRB-￨O￨- 26￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- fungal￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- soil-borne￨L￨JJ￨O￨- plant￨L￨NN￨O￨- pathogens￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- its￨L￨PRP$￨O￨- susceptible￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- striking￨L￨JJ￨O￨- finding￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- synergy￨L￨NN￨O￨- reinforcement￨L￨NN￨O￨- effect￨L￨NN￨O￨- is￨L￨VBZ￨O￨- above￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A versus￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- exhibits￨L￨VBZ￨O￨- an￨L￨DT￨O￨- explosively￨L￨RB￨O￨- increasing￨L￨VBG￨O￨- behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- hysteresis￨L￨NN￨O￨- loop￨L￨NN￨O￨- emerges￨L￨VBZ￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- fill￨L￨VB￨O￨- this￨L￨DT￨O￨- knowledge￨L￨NN￨O￨- gap￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- articulate￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- local￨L￨JJ￨O￨- synergistic￨L￨JJ￨O￨- effect￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- infected￨L￨VBN￨O￨- through￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- neighbor￨L￨NN￨O￨- is￨L￨VBZ￨O￨- enhanced￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- neighborhood￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- contains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A .￨L￨.￨O￨- +Another￨U￨DT￨O￨- result￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- irreversible￨L￨JJ￨O￨- and￨L￨CC￨O￨- reversible￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- continuously￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expected￨L￨VBN￨O￨- intuitively￨L￨RB￨O￨- .￨L￨.￨O￨- +Pattern￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- contagions￨L￨NNS￨O￨- Li￨U￨NNP￨ORGANIZATION￨- Chen￨U￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Information￨U￨NNP￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Shaanxi￨U￨NNP￨STATE_OR_PROVINCE￨- Normal￨U￨JJ￨O￨- University￨U￨NNP￨O￨- ,￨L￨,￨O￨- Xi’an￨U￨NNP￨LOCATION￨- 710062￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨ORGANIZATION￨- Beijing￨U￨NNP￨ORGANIZATION￨- Computational￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- Center￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 100193￨L￨CD￨NUMBER￨- Beijing￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- 13353￨L￨CD￨NUMBER￨- Berlin￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Germany￨U￨NNP￨COUNTRY￨- ∗￨L￨NNP￨O￨- Robert￨U￨NNP￨PERSON￨- Koch-Institute￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Nordufer￨U￨NNP￨PERSON￨- 20￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- May￨U￨NNP￨DATE￨- 17￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- rumors￨L￨NNS￨O￨- ,￨L￨,￨O￨- fashions￨L￨NNS￨O￨- ,￨L￨,￨O￨- innovations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- complex￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- embedded￨L￨JJ￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- networked￨L￨JJ￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- contexts￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contagion￨L￨NN￨O￨A process￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- follows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- kinetics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- interaction￨L￨NN￨O￨- introduces￨L￨VBZ￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- propensity￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +Interestingly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- exhibits￨L￨VBZ￨O￨- pattern￨L￨NN￨O￨A hysteresis￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- that￨L￨WDT￨O￨- quite￨L￨RB￨O￨- different￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- regions￨L￨NNS￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- patterns￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- eradication￨L￨NN￨O￨- by￨L￨IN￨O￨- its￨L￨PRP$￨O￨- reduction￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- two￨L￨CD￨NUMBER￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- say￨L￨VBP￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- interact￨L￨VBP￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- and￨L￨CC￨O￨- diffuse￨L￨NN￨O￨- simultaneously￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- space￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- increases￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- exhibits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- absorbing￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- disease-free￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- phase￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dies￨L￨VBZ￨O￨- exponentially￨L￨RB￨O￨- fast￨L￨JJ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- endemic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- phase￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- becomes￨L￨VBZ￨O￨- persistent￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- that￨L￨DT￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- connecting￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- j￨L￨FW￨O￨- is￨L￨VBZ￨O￨- endowed￨L￨JJ￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- βij￨L￨NN￨O￨- =￨L￨JJ￨O￨- λwij￨L￨NN￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨A of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- contact￨L￨NN￨O￨- wij￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- wij￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- face-to-face￨L￨JJ￨O￨- experiments￨L￨NNS￨O￨- analyzed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Cattuto￨U￨NNP￨LOCATION￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- introduces￨L￨VBZ￨O￨- an￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- absorbing￨L￨VBG￨O￨A region￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dies￨L￨VBZ￨O￨- very￨L￨RB￨O￨- slowly￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- stretched￨L￨VBN￨O￨- exponential￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- Erdős-Rényi￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- ER￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- across￨L￨IN￨O￨- links￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨A of￨L￨IN￨O￨- encounters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- width￨L￨NN￨O￨- a￨L￨DT￨O￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- large￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- a￨L￨DT￨O￨- −￨L￨NN￨O￨- λ￨L￨NN￨O￨- space￨L￨NN￨O￨- with￨L￨IN￨O￨- anomalous￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- reminiscent￨L￨JJ￨O￨- of￨L￨IN￨O￨- rare￨L￨JJ￨O￨- region￨L￨NN￨O￨A effects￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Griffiths￨U￨NNS￨O￨- phases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- quenched￨L￨VBN￨O￨- disorder￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- address￨L￨VBP￨O￨- this￨L￨DT￨O￨- question￨L￨NN￨O￨- by￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- cells￨L￨NNS￨O￨A infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨- syncytial￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RSV-A￨U￨NN￨O￨- and￨L￨CC￨O￨- RSV-B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- in￨L￨FW￨O￨- vitro￨L￨FW￨O￨- experiment￨L￨NN￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- point￨L￨NN￨O￨A process￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- cells￨L￨NNS￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- point￨L￨NN￨O￨A process￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- this￨L￨DT￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨VBP￨O￨- prove￨L￨VB￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- previously￨L￨RB￨DATE￨- derived￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- holds￨L￨VBZ￨O￨- true￨L￨JJ￨O￨- for￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- limit￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- reaction-diffusion￨L￨JJ￨O￨- equation￨L￨NN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- as￨L￨IN￨O￨- ∂￨L￨NN￨O￨- tρS￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- µρI￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- −￨L￨FW￨O￨- βi￨L￨FW￨O￨- ρi￨L￨FW￨O￨- ∂￨L￨FW￨O￨- tρI￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- µρI￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- +￨L￨CC￨O￨- βi￨L￨FW￨O￨- ρS￨L￨FW￨O￨- ,￨L￨,￨O￨- iρI￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- −￨L￨FW￨O￨- DS￨U￨NN￨O￨- Xj￨U￨NN￨O￨- ρS￨L￨NN￨O￨- ,￨L￨,￨O￨- iρI￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- −￨L￨FW￨O￨- DI￨U￨FW￨MISC￨- Xj￨U￨NN￨MISC￨- ρi￨L￨NN￨MISC￨- Lij￨U￨NN￨MISC￨- ρS￨L￨NN￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- Lij￨U￨NN￨O￨- ρI￨L￨NN￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- ρS￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- ρI￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- particles￨L￨NNS￨O￨A at￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- derive￨L￨VBP￨O￨- an￨L￨DT￨O￨- improved￨L￨JJ￨O￨- condition￨L￨NN￨O￨A showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- rich-club￨L￨JJ￨O￨- property￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- high￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- prone￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SIS￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- exhibits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- βc￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- β￨L￨NN￨O￨- >￨L￨JJR￨O￨- βc￨L￨NN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- emerges￨L￨VBZ￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- particles￨L￨NNS￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- state￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- node￨L￨NN￨O￨A i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- set￨L￨VBN￨O￨- to￨L￨TO￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- ρi￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- power-law￨L￨NN￨O￨- scaling￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- βi￨L￨NN￨O￨- ≡￨L￨NN￨O￨- β￨L￨NN￨O￨- ργ￨L￨NN￨O￨- i￨L￨FW￨O￨- with￨L￨IN￨O￨- γ￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- pattern￨L￨NN￨O￨- is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- inconsistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- target￨L￨NN￨O￨- cell￨L￨NN￨O￨- depletion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- principal￨L￨JJ￨TITLE￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- controlling￨L￨VBG￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- argue￨L￨VBP￨O￨- that￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- pattern￨L￨NN￨O￨- constitutes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- criterion￨L￨NN￨O￨- for￨L￨IN￨O￨- rejecting￨L￨VBG￨O￨- many￨L￨JJ￨O￨- resource￨L￨NN￨O￨- depletion￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- target￨L￨NN￨O￨- cell￨L￨NN￨O￨- depletion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- minor￨L￨JJ￨O￨- factor￨L￨NN￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨A natural￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- antibodies￨L￨NNS￨O￨- and￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- control￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +How￨U￨WRB￨O￨- important￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- resource￨L￨NN￨O￨- depletion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- depletion￨L￨NN￨O￨- of￨L￨IN￨O￨- target￨L￨NN￨O￨- cells￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ?￨L￨.￨O￨- +A￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- innate￨L￨JJ￨O￨- interferon￨L￨NN￨O￨- response￨L￨NN￨O￨- that￨L￨WDT￨O￨- renders￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A resistant￨L￨JJ￨O￨- fits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- reasonably￨L￨RB￨O￨- well￨L￨RB￨O￨- .￨L￨.￨O￨- +Next￨U￨RB￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- expectations￨L￨NNS￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- conditioning￨L￨NN￨O￨- random￨L￨JJ￨O￨- variable￨L￨JJ￨O￨- τ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- E￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ≤￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- exp￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- τ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- exp￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- −￨L￨CD￨NUMBER￨- βE￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- exp￨L￨NN￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- t￨L￨NN￨O￨- Xv￨U￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- π2￨L￨NN￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- inequality￨L￨NN￨O￨- follows￨L￨VBZ￨O￨- from￨L￨IN￨O￨- Jensen￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- inequality￨L￨NN￨O￨- .￨L￨.￨O￨- +Lemma￨U￨NNP￨PERSON￨- 1￨L￨CD￨NUMBER￨- also￨L￨RB￨O￨- gives￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- an￨L￨DT￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- ≤￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- exp￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- t/n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Sudden￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- seed￨L￨NN￨O￨A fraction￨L￨NN￨O￨- Takehisa￨U￨NNP￨PERSON￨- Hasegawa1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- ∗￨L￨NN￨O￨- and￨L￨CC￨O￨- Ko￨U￨NNP￨PERSON￨- ji￨L￨NN￨O￨- Nemoto2￨U￨NN￨O￨- ,￨L￨,￨O￨- †￨L￨SYM￨O￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Mathematics￨U￨NNS￨O￨- and￨L￨CC￨O￨- Informatics￨U￨NNS￨O￨- ,￨L￨,￨O￨- Ibaraki￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 2-1-1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Bunkyo￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Mito￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 310-8512￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- 2Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- Hokkaido￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Kita￨U￨NNP￨PERSON￨- 10￨L￨CD￨NUMBER￨- Nishi￨U￨NNP￨ORGANIZATION￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kita-ku￨U￨NN￨O￨- ,￨L￨,￨O￨- Sapporo￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Hokkaido￨U￨NNP￨O￨- ,￨L￨,￨O￨- 060-0810￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-weakened-infected-removed￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- regular￨L￨JJ￨O￨- random￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- situation￨L￨NN￨O￨- where￨L￨WRB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- starts￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- seeds￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Extensive￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- on￨L￨IN￨O￨- simple￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- accurate￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- described￨L￨VBN￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- discovered￨L￨VBN￨O￨- new￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- localization￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- stretching￨L￨VBG￨O￨- of￨L￨IN￨O￨- criticality￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Performing￨U￨VBG￨O￨- Monte￨U￨NNP￨O￨- Carlo￨U￨NNP￨O￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- evaluating￨L￨VBG￨O￨- approximate￨L￨JJ￨O￨- master￨L￨NN￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- critical￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- seed￨L￨NN￨O￨A fraction￨L￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- seed￨L￨NN￨O￨A ,￨L￨,￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- discontinuous￨L￨JJ￨O￨- transition￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Genetic￨U￨JJ￨O￨- Algorithm￨U￨NN￨O￨- for￨L￨IN￨O￨- Epidemic￨U￨JJ￨O￨- Mitigation￨U￨NN￨O￨- by￨L￨IN￨O￨- Removing￨U￨VBG￨O￨- Relationships￨U￨NNPS￨O￨- Fernando￨U￨NNP￨PERSON￨- Concatto￨U￨NNP￨PERSON￨- Universidade￨U￨NNP￨PERSON￨- do￨L￨VBP￨O￨- Vale￨U￨NNP￨O￨- do￨L￨VBP￨O￨- Itaja￨U￨NNP￨O￨- ´￨L￨POS￨O￨- ı￨L￨NN￨O￨- Itaja￨U￨NN￨O￨- ´￨L￨''￨O￨- ı￨L￨NN￨O￨- ,￨L￨,￨O￨- SC￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- 88302-901￨L￨CD￨NUMBER￨- Wellington￨U￨NNP￨ORGANIZATION￨- Zunino￨U￨NNP￨ORGANIZATION￨- Universidade￨U￨NNP￨ORGANIZATION￨- do￨L￨VBP￨ORGANIZATION￨- Vale￨U￨NNP￨ORGANIZATION￨- do￨L￨VBP￨O￨- Itaja￨U￨NNP￨O￨- ´￨L￨POS￨O￨- ı￨L￨NN￨O￨- Itaja￨U￨NN￨O￨- ´￨L￨''￨O￨- ı￨L￨NN￨O￨- ,￨L￨,￨O￨- SC￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- 88302-901￨L￨CD￨NUMBER￨- Luigi￨U￨NNP￨ORGANIZATION￨- A.￨U￨NN￨ORGANIZATION￨- Lamb￨U￨NNP￨ORGANIZATION￨- Federal￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Rio￨U￨NNP￨ORGANIZATION￨- Grande￨U￨NNP￨ORGANIZATION￨- do￨L￨VBP￨O￨- Sul￨U￨NNP￨O￨- Porto￨U￨NNP￨O￨- Alegre￨U￨NNP￨O￨- ,￨L￨,￨O￨- RS￨U￨NN￨O￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- 91501-970￨L￨CD￨NUMBER￨- ABSTRACT￨U￨NN￨O￨- Min-SEIS-Cluster￨U￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨A which￨L￨WDT￨O￨- aims￨L￨VBZ￨O￨- at￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- genetic￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨A surpassed￨L￨VBD￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- heuristic￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- significantly￨L￨RB￨O￨- ,￨L￨,￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- therefore￨L￨RB￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- new￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- state-of-the-art￨L￨JJ￨O￨- heuristic￨L￨NN￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨A that￨L￨WDT￨O￨- solves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Min-SEIS-Cluster￨U￨NNP￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- under￨L￨IN￨O￨- perfect￨L￨JJ￨O￨- and￨L￨CC￨O￨- instantaneous￨L￨JJ￨O￨- information￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- are/are￨L￨VBP￨O￨- not￨L￨RB￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- budget￨L￨NN￨O￨A required￨L￨VBN￨O￨- for￨L￨IN￨O￨- curing￨L￨VBG￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- precisely￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- combinatorial￨L￨JJ￨O￨- property￨L￨NN￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- CutWidth￨U￨NNP￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- curing￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SI￨U￨NNP￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- known￨L￨JJ￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- budget￨L￨NN￨O￨A to￨L￨TO￨O￨- use￨L￨VB￨O￨- to￨L￨TO￨O￨- transition￨L￨NN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- cure￨L￨VB￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- setting￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- optimize￨L￨VB￨O￨- the￨L￨DT￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- curing￨L￨VBG￨O￨- budget￨L￨NN￨O￨A across￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- every￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- those￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- contiguous￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- it￨L￨PRP￨O￨- will￨L￨MD￨O￨- take￨L￨VB￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- graph￨L￨NN￨O￨A .￨L￨.￨O￨- +If￨U￨IN￨O￨- every￨L￨DT￨O￨- other￨L￨JJ￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- will￨L￨MD￨O￨- take￨L￨VB￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- time￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- modi￨L￨NN￨O￨- fied￨L￨VBD￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- geographical￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- inversely￨L￨RB￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Euclidean￨U￨JJ￨MISC￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- In￨U￨IN￨O￨- an￨L￨DT￨O￨- SF￨U￨NN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- exponent￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- γ￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- second-order￨L￨JJ￨O￨- moment￨L￨NN￨O￨- hk2￨L￨NN￨O￨- i￨L￨FW￨O￨- will￨L￨MD￨O￨- approach￨L￨VB￨O￨- to￨L￨TO￨O￨- infinite￨L￨VB￨O￨A as￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- an￨L￨DT￨O￨- infinite￨L￨NN￨O￨- velocity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Immunization￨U￨NN￨O￨- of￨L￨IN￨O￨- Susceptible-Infected￨U￨NNP￨O￨- Model￨U￨NNP￨TITLE￨- on￨L￨IN￨O￨- Scale-Free￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- Department￨U￨NNP￨O￨- of￨L￨IN￨O￨- Modern￨U￨NNP￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hefei￨U￨NNP￨CITY￨- 230026￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- PR￨U￨NN￨STATE_OR_PROVINCE￨- China￨U￨NNP￨COUNTRY￨- Wen-Jie￨U￨NNP￨PERSON￨- Bai￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Tao￨U￨NNP￨PERSON￨- Zhou￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- ∗￨L￨NN￨O￨- and￨L￨CC￨O￨- Bing-Hong￨U￨NNP￨PERSON￨- Wang￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- August￨U￨NNP￨DATE￨- 29￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- ma￨L￨NN￨O￨- jor￨L￨NN￨O￨- immunization￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- random￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- and￨L￨CC￨O￨- targeted￨L￨VBN￨O￨- immunization￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Model￨U￨NNP￨TITLE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Barab￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- asi-Albert￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- BA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- separately￨L￨RB￨O￨- but￨L￨CC￨O￨- almost￨L￨RB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- immunization￨L￨NN￨O￨A is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- less￨L￨JJR￨O￨- effectivity￨L￨NN￨O￨- for￨L￨IN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- SF￨U￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- plots￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- BA￨U￨NN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- fixed￨L￨VBN￨O￨A as￨L￨IN￨O￨- hki￨L￨NN￨O￨- =￨L￨JJ￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- plots￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- fixed￨L￨VBN￨O￨- as￨L￨IN￨O￨- λ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.001￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +lattice￨L￨NN￨O￨- Zd￨U￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- initially￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- site￨L￨NN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- For￨U￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- d-dimensional￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- λc￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- parameter￨L￨NN￨O￨- λ￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- λ￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- λc￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- λ￨L￨NN￨O￨- >￨L￨JJR￨O￨- λc￨L￨NN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- survives￨L￨VBZ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- linearly￨L￨RB￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- converging￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- non-trivial￨L￨JJ￨O￨- invariant￨L￨JJ￨O￨- measure￨L￨NN￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- survives￨L￨VBZ￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- convergence￨L￨NN￨O￨- see￨L￨VBP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Part￨U￨NNP￨O￨- I￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- linear￨L￨JJ￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- d￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- linear￨L￨JJ￨O￨- spread￨L￨NN￨O￨- with￨L￨IN￨O￨- convergence￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- limiting￨L￨VBG￨O￨- shape￨L￨NN￨O￨- in￨L￨IN￨O￨- d￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- see￨L￨VBP￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- particle￨L￨NN￨O￨- system￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- spatial￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- upper￨L￨JJ￨O￨- and￨L￨CC￨O￨- lower￨L￨JJR￨O￨- bounds￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- prove￨L￨VBP￨O￨- convergence￨L￨NN￨O￨A of￨L￨IN￨O￨- critical￨L￨JJ￨O￨- values￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- small￨L￨JJ￨O￨- and￨L￨CC￨O￨- large￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- identify￨L￨VB￨O￨- a￨L￨DT￨O￨- limiting￨L￨VBG￨O￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- SEIS￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- converges￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +the￨L￨DT￨O￨- process￨L￨NN￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- According￨U￨VBG￨O￨- to￨L￨TO￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- in￨L￨IN￨O￨- d￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SEIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- behaves￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- way￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- that￨L￨WDT￨O￨- varies￨L￨VBZ￨O￨- slightly￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- latent￨L￨JJ￨O￨A time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- 1￨L￨CD￨NUMBER￨- linearly￨L￨RB￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- survives￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- or￨L￨CC￨O￨- countably￨L￨JJ￨O￨- infinite￨L￨NN￨O￨- connected￨L￨VBN￨O￨- undirected￨L￨JJ￨O￨- graph￨L￨NN￨O￨- G￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- bounded￨L￨VBN￨O￨- degree￨L￨NN￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- d￨L￨NN￨O￨- <￨L￨JJR￨O￨- ∞￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- |￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- :￨L￨:￨O￨- xy￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- ≤￨L￨SYM￨O￨- d￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- x￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SEIS￨U￨NNP￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- parameter￨L￨NN￨O￨- λ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- average￨L￨JJ￨O￨- latent￨L￨JJ￨O￨A time￨L￨NN￨O￨- τ￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Letting￨U￨VBG￨O￨- 0￨L￨CD￨NUMBER￨- denote￨L￨VBP￨O￨A susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- denote￨L￨VBP￨O￨- exposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- denote￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- site￨L￨NN￨O￨- x￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- later￨L￨RB￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- types￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- transitions￨L￨NNS￨O￨- •￨L￨SYM￨O￨- •￨L￨SYM￨O￨- •￨L￨SYM￨O￨- 0￨L￨CD￨NUMBER￨- →￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- λn2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- →￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- 1/τ￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- instantaneously￨L￨RB￨O￨- if￨L￨IN￨O￨- τ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- onset￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- →￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- recovery￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- n2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- cardinality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨VBN￨O￨- {￨L￨-LRB-￨O￨- xy￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- :￨L￨:￨O￨- y￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- state￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- transmissions￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- surrounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- ni￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A rates￨L￨NNS￨O￨A as￨L￨IN￨O￨- In￨U￨IN￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- which￨L￨WDT￨O￨- ignores￨L￨VBZ￨O￨- cooperative￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- Λni￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- δ￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- ni￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- λj￨L￨NN￨O￨- i￨L￨FW￨O￨- δ￨L￨FW￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +†￨L￨SYM￨O￨- The￨U￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- cooperative￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- synergy￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- analytically￨L￨RB￨O￨- and￨L￨CC￨O￨- numerically￨L￨RB￨O￨- for￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- rules￨L￨NNS￨O￨- of￨L￨IN￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- regular￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rate￨L￨NN￨O￨- equation￨L￨NN￨O￨- We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- synergistic￨L￨JJ￨O￨- SIS￨U￨NNP￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- nodes￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- connectivity￨L￨NN￨O￨- defines￨L￨VBZ￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- regular￨L￨JJ￨O￨- graph￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨A is￨L￨VBZ￨O￨- randomly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- k￨L￨NN￨O￨- different￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- neighbourhood￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- below￨L￨IN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- when￨L￨WRB￨O￨- individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A rates￨L￨NNS￨O￨A depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- neighbours￨L￨NNS￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- In￨U￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- synergistic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- do￨L￨VBP￨O￨- i.e.￨L￨FW￨O￨- λj￨L￨FW￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- λni￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- j￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- its￨L￨PRP$￨O￨- degree￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- these￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- rules￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- σi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ≡￨L￨CD￨NUMBER￨- pi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- δ￨L￨NN￨O￨- t￨L￨NN￨O￨- obeys￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- δpi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- δ￨L￨NN￨O￨- t￨L￨NN￨O￨- ≡￨L￨CD￨NUMBER￨- pi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- pi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- δ￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- pi￨L￨NN￨O￨- ,￨L￨,￨O￨- {￨L￨-LRB-￨O￨- σj￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- pi￨L￨NN￨O￨- ,￨L￨,￨O￨- {￨L￨-LRB-￨O￨- σj￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- µpi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- k￨L￨NN￨O￨- Xn￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- X￨U￨NN￨O￨- {￨L￨-LRB-￨O￨- σj￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ΛnP￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0i￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- {￨L￨-LRB-￨O￨- σj￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- δni￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- function￨L￨NN￨O￨- with￨L￨IN￨O￨- Λn￨U￨NN￨O￨- obeying￨L￨VBG￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- and￨L￨CC￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- variation￨L￨NN￨O￨A within￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- paradigms￨L￨NNS￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Agent￨U￨NNP￨MISC￨- Based￨U￨VBD￨MISC￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- at￨L￨IN￨O￨- capturing￨L￨VBG￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- variation￨L￨NN￨O￨- within￨L￨IN￨O￨- SIR￨U￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- equivalent￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- using￨L￨VBG￨O￨- System￨U￨NNP￨MISC￨- Dynamics￨U￨NNP￨MISC￨- with￨L￨IN￨O￨- Monte-Carlo￨U￨NNP￨O￨- simulation￨L￨NN￨O￨- .￨L￨.￨O￨- +Currently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- classical￨L￨JJ￨O￨- System￨U￨NNP￨O￨- Dynamics￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SD￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- aggregated￨L￨VBN￨O￨- to￨L￨TO￨O￨- fixed￨L￨VBN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- output￨L￨NN￨O￨- has￨L￨VBZ￨O￨- no￨L￨DT￨O￨- variation￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- Agent￨U￨NNP￨O￨- Based￨U￨VBD￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- uncertainty￨L￨NN￨O￨- or￨L￨CC￨O￨- variance￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- inherent￨L￨JJ￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- simulations￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- produce￨L￨VBP￨O￨- non-deterministic￨L￨JJ￨O￨- results￨L￨NNS￨O￨- directly￨L￨RB￨O￨- without￨L￨IN￨O￨- input￨L￨NN￨O￨- parameter￨L￨NN￨O￨- variation￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- approaches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- examined￨L￨VBN￨O￨- by￨L￨IN￨O￨- generating￨L￨VBG￨O￨- an￨L￨DT￨O￨- SD￨U￨NN￨STATE_OR_PROVINCE￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Monte-Carlo￨U￨NNP￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- ABM￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- output￨L￨NN￨O￨A values￨L￨NNS￨O￨- against￨L￨IN￨O￨- published￨L￨VBN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- defined￨L￨VBN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- demonstrate￨L￨VB￨O￨- this￨L￨DT￨O￨- effect￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- using￨L￨VBG￨O￨- both￨L￨DT￨O￨- System￨U￨NNP￨O￨- Dynamics￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- Monte-Carlo￨U￨NNP￨MISC￨- simulation￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Agent￨U￨NNP￨MISC￨- Based￨U￨VBD￨MISC￨- Modelling￨U￨VBG￨MISC￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- make￨L￨VBP￨O￨- a￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- model￨L￨NN￨TITLE￨A parameters￨L￨NNS￨O￨A that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- fitting￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Mexican￨U￨JJ￨NATIONALITY￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- generalize￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Mexican￨U￨JJ￨NATIONALITY￨- case￨L￨NN￨O￨A using￨L￨VBG￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Mexican￨U￨JJ￨NATIONALITY￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨A some￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Spatial￨U￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- Mexican￨U￨JJ￨NATIONALITY￨- epidemic￨L￨JJ￨O￨- Mario￨U￨NNP￨O￨- A￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- current￨L￨JJ￨DATE￨- approach￨L￨NN￨O￨- examines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- via￨L￨IN￨O￨- novel￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- integrated￨L￨VBN￨O￨- ,￨L￨,￨O￨- temporally￨L￨RB￨O￨A extended￨L￨VBD￨O￨- network￨L￨NN￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- interaction￨L￨NN￨O￨- data￨L￨NNS￨O￨- across￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- processes￨L￨NNS￨O￨- directly￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- methodology￨L￨NN￨O￨- presented￨L￨VBN￨O￨- here￨L￨RB￨O￨- captures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- and/or￨L￨CC￨O￨- structural￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- temporally￨L￨RB￨O￨A extended￨L￨JJ￨O￨- network￨L￨NN￨O￨- representation￨L￨NN￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- it￨L￨PRP￨O￨- encodes￨L￨VBZ￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- interactions￨L￨NNS￨O￨- as￨L￨IN￨O￨- network￨L￨NN￨O￨- connections￨L￨NNS￨O￨- ,￨L￨,￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- measures￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- “￨L￨``￨O￨- temporal￨L￨JJ￨O￨- web￨L￨NN￨O￨- ”￨L￨''￨O￨- to￨L￨TO￨O￨- reveal￨L￨VB￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- themselves￨L￨PRP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- technique￨L￨NN￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SEIS￨U￨NN￨O￨- epidemiological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- people￨L￨NNS￨O￨A go￨L￨VBP￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- stages￨L￨NNS￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- removed/recovered￨L￨VBN￨O￨- and￨L￨CC￨O￨- alternatively￨L￨RB￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- people￨L￨NNS￨O￨- become￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- again￨L￨RB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- state￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- or￨L￨CC￨O￨- adapted￨L￨VBN￨O￨- network￨L￨NN￨O￨- measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- structural￨L￨JJ￨O￨A properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- time￨L￨NN￨O￨- slices￨L￨NNS￨O￨- are￨L￨VBP￨O￨- calculated￨L￨VBN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- slices￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- solve￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨A and￨L￨CC￨O￨- differential￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- its￨L￨PRP$￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- topology-infection￨L￨JJ￨O￨- matrix￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Generalizations￨U￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨A have￨L￨VBP￨O￨- revealed￨L￨VBN￨O￨- an￨L￨DT￨O￨- intimate￨L￨JJ￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- matrix￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- failure￨L￨NN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- differential￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- over/under￨L￨NN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- fundamental￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- independent￨L￨JJ￨RELIGION￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- connected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- the￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- behaviors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- generalized￨L￨VBN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- topology￨L￨NN￨O￨- and￨L￨CC￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- networks￨L￨NNS￨O￨- become￨L￨VBP￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨- a￨L￨DT￨O￨- pocket￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- when￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- connect￨L￨VB￨O￨- with￨L￨IN￨O￨- others￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- segregated￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Weak￨U￨JJ￨O￨- endemic￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- spreads￨L￨VBZ￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- layers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- interconnected￨L￨VBN￨O￨A ,￨L￨,￨O￨- show￨L￨VBP￨O￨- a￨L￨DT￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- phase￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- rewiring￨L￨NN￨O￨- overcomes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- that￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +San￨U￨NNP￨O￨- Miguel4￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- IFLYSIB￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Instituto￨U￨NNP￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- de￨L￨IN￨O￨- L´ıquidos￨U￨NNP￨O￨- y￨L￨NNP￨O￨- Sistemas￨U￨NNP￨O￨- Biol￨U￨NNP￨O￨- ´￨L￨POS￨O￨- ogicos￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- UNLP-CONICET￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 1900￨L￨CD￨DATE￨- La￨U￨NNP￨CITY￨- Plata￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Argentina￨U￨NNP￨COUNTRY￨- ∗￨L￨SYM￨O￨- 2Departament￨L￨NN￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- Fonamental￨U￨NNP￨O￨- ,￨L￨,￨O￨- Universitat￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Barcelona￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Mart￨U￨NNP￨ORGANIZATION￨- ´￨L￨POS￨O￨- ı￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- Instituci´o￨U￨NNP￨ORGANIZATION￨- Catalana￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Recerca￨U￨NNP￨ORGANIZATION￨- i￨L￨FW￨O￨- Estudis￨U￨NNP￨O￨- Avan￨U￨NNP￨O￨- ¸￨L￨NNP￨O￨- cats￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ICREA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Barcelona￨U￨NNP￨ORGANIZATION￨- 08010￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- 4￨L￨CD￨NUMBER￨- IFISC￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Instituto￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- F´ısica￨U￨NNP￨ORGANIZATION￨- Interdisciplinar￨U￨NNP￨ORGANIZATION￨- y￨L￨NNP￨O￨- Sistemas￨U￨NNP￨ORGANIZATION￨- Complejos￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CSIC-UIB￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E-07122￨U￨NN￨O￨- Palma￨U￨NNP￨O￨- de￨L￨IN￨O￨- Mal￨U￨NNP￨O￨- lorca￨L￨NNP￨O￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- i￨L￨FW￨O￨- Franqu`es￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 08028￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Barcelona￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- August￨U￨NNP￨DATE￨- 29￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- layers￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- interconnected￨L￨VBN￨O￨A by￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- rewired￨L￨VBN￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- interlayer￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- strong￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- on￨L￨IN￨O￨- each￨L￨DT￨O￨- separate￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- layer￨L￨NN￨TITLE￨- decreases￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rewiring￨L￨NN￨O￨A ,￨L￨,￨O￨- arriving￨L￨VBG￨O￨- to￨L￨TO￨O￨- single￨L￨JJ￨O￨- network￨L￨NN￨O￨- values￨L￨NNS￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- infinitely￨L￨RB￨O￨- fast￨L￨JJ￨O￨- rewiring￨L￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SusceptibleInfected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- interconnected￨L￨JJ￨O￨A systems￨L￨NNS￨O￨- can￨L￨MD￨O￨- support￨L￨VB￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- each￨L￨DT￨O￨- isolated￨L￨VBN￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- so￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- inter-network￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- boost￨L￨VBP￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- two-network￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- systems￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- interconnected￨L￨JJ￨O￨A layers￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- network￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- connectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Assuming￨U￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- distributed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨ORGANIZATION￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PPP￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- percolation￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- formation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- unbounded￨L￨JJ￨O￨- connected￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- graph￨L￨NN￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- PPP￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- enough￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- interval￨L￨NN￨O￨- of￨L￨IN￨O￨- densities￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- percolation￨L￨NN￨O￨A happens￨L￨VBZ￨O￨- with￨L￨IN￨O￨- non-zero￨L￨JJ￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +Conversely￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- enough￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- interval￨L￨NN￨O￨- of￨L￨IN￨O￨- densities￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- percolation￨L￨NN￨O￨A is￨L￨VBZ￨O￨- zero￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- A￨U￨DT￨O￨- wireless￨L￨JJ￨O￨A communication￨L￨NN￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- where￨L￨WRB￨O￨- any￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +Connectivity￨U￨NN￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- graph￨L￨NN￨O￨A are￨L￨VBP￨O￨- also￨L￨RB￨O￨- studied￨L￨VBN￨O￨- by￨L￨IN￨O￨- restricting￨L￨VBG￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- lie￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- bounded￨L￨JJ￨O￨- area￨L￨NN￨O￨- .￨L￨.￨O￨- +Exploiting￨U￨VBG￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- expectation￨L￨NN￨O￨- operator￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- indicator￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- Bernoulli￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- random￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨A governing￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- are￨L￨VBP￨O￨- basic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- deductions￨L￨NNS￨O￨- from￨L￨IN￨O￨- their￨L￨PRP$￨O￨- exact￨L￨JJ￨O￨A stochastic￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- without￨L￨IN￨O￨- making￨L￨VBG￨O￨- approximations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- scarce￨L￨JJ￨O￨- .￨L￨.￨O￨- +Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- maximum￨L￨JJ￨O￨- average￨L￨NN￨O￨- fraction￨L￨NN￨O￨- yI￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- written￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- quadratic￨L￨JJ￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨A ’s￨L￨POS￨O￨- Laplacian￨U￨NN￨MISC￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- our￨L￨PRP$￨O￨- new￨L￨JJ￨O￨- Laplacian￨U￨NN￨MISC￨- expression￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- deduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- graph￨L￨NN￨O￨A .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Although￨U￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Removed￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- basic￨L￨JJ￨O￨A corner-stones￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- +Droplet￨U￨NNP￨O￨- diffusion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- inefficient￨L￨JJ￨O￨- mode￨L￨NN￨O￨- of￨L￨IN￨O￨- droplet￨L￨NN￨O￨- transport￨L￨NN￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- minimal￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨A spread￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- ambient￨L￨JJ￨O￨- airflow￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- incorporated￨L￨VBN￨O￨- leading￨L￨VBG￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- delay￨L￨NN￨O￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- droplet￨L￨NN￨O￨- density￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- density￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- larger￨L￨JJR￨O￨- droplets￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ∼￨L￨CD￨NUMBER￨- 4￨L￨CD￨NUMBER￨- µm￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- wave￨L￨NN￨O￨- propagating￨L￨VBG￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨A population￨L￨NN￨O￨A or￨L￨CC￨O￨- a￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- localised￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- temporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- documented￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨A spread￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- driving￨L￨VBG￨O￨- it￨L￨PRP￨O￨- are￨L￨VBP￨O￨- less￨L￨RBR￨O￨- well￨L￨RB￨O￨- understood￨L￨VBN￨O￨- .￨L￨.￨O￨- +Respirable￨U￨JJ￨O￨- pathogen-carrying￨L￨JJ￨O￨- droplets￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨A spread￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- droplet￨L￨NN￨O￨- transport￨L￨NN￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- diffusive￨L￨JJ￨O￨- and￨L￨CC￨O￨- convective￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- marginal￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- upper￨L￨JJ￨O￨- bounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- n-dimensional￨L￨JJ￨O￨- linear￨L￨JJ￨O￨- time-invariant￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- is￨L￨VBZ￨O￨- “￨L￨``￨O￨- fast-mixing￨L￨JJ￨O￨- ”￨L￨''￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- LTI￨U￨NN￨ORGANIZATION￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- when￨L￨WRB￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- per￨L￨IN￨O￨- link￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- eigenvalue￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- best￨L￨JJS￨O￨- known￨L￨VBN￨O￨- lower-bound￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- 1/λmax￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- inverse￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- leading￨L￨VBG￨O￨- eigenvalue￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- marginal￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Improved￨U￨VBN￨O￨- Bounds￨U￨NNPS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Epidemic￨U￨JJ￨O￨- Threshold￨U￨NN￨O￨- of￨L￨IN￨O￨- Exact￨U￨JJ￨O￨- SIS￨U￨NN￨O￨- Models￨U￨NNS￨O￨- on￨L￨IN￨O￨- Complex￨U￨NN￨O￨- Networks￨U￨NNP￨O￨- Navid￨U￨NNP￨PERSON￨- Azizan￨U￨NNP￨PERSON￨- Ruhi￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Christos￨U￨NNP￨PERSON￨- Thrampoulidis￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Babak￨U￨NNP￨PERSON￨- Hassibi￨U￨NNP￨PERSON￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- The￨U￨NNP￨O￨- SIS￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- making￨L￨VBG￨O￨- approximations￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- 2n￨L￨NN￨O￨- -￨L￨:￨O￨- state￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- absorbing￨L￨VBG￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- all-healthy￨L￨JJ￨O￨- state￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- behavior￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- once￨L￨RB￨DATE￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A τ￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- approaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- τc￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- appears￨L￨VBZ￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- die￨L￨VB￨O￨- out￨L￨RP￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- improved￨L￨VBN￨O￨- bound￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- tighter￨L￨JJR￨O￨- eigenvalue￨L￨NN￨O￨A conditions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- guarantee￨L￨VBP￨O￨- fast￨L￨RB￨O￨- mixing￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- logarithmic￨L￨JJ￨O￨- mixing￨L￨JJ￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- chain￨L￨NN￨O￨- .￨L￨.￨O￨- +Formulating￨U￨VBG￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- entropy￨L￨NN￨O￨A problem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- an￨L￨DT￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dispersion￨L￨NN￨O￨- entropy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- metastable￨L￨JJ￨O￨- state￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- dispersion￨L￨NN￨O￨- entropy￨L￨NN￨O￨A measure￨L￨NN￨O￨- that￨L￨WDT￨O￨- quantifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- localization￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- contact￨L￨NN￨O￨- graph￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨A sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- any￨L￨DT￨O￨- initial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- either￨L￨CC￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- or￨L￨CC￨O￨- reaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- localized￨L￨JJ￨O￨- metastable￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +5￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 6￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨JJ￨O￨- —￨L￨:￨O￨- The￨U￨DT￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨A process￨L￨NN￨O￨A on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- show￨L￨VB￨O￨- metastability￨L￨NN￨O￨- ,￨L￨,￨O￨- resembling￨L￨VBG￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- quenched￨L￨VBN￨O￨- mean￨L￨NN￨O￨- -￨L￨:￨O￨- field￨L￨NN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- HMF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- suppressed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- greatest￨L￨JJS￨O￨- extent￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- curing￨L￨VBG￨O￨A rate￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- directly￨L￨RB￨O￨- proportional￨L￨JJ￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- λopt￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- hki￨L￨NN￨O￨- where￨L￨WRB￨O￨- hki￨L￨NN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- weak￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- region￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- &￨L￨CC￨O￨- λopt￨L￨NN￨O￨- is￨L￨VBZ￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- combine￨L￨VBP￨O￨- a￨L￨DT￨O￨- c￨L￨NN￨O￨- perturbation￨L￨NN￨O￨- theory￨L￨NN￨O￨- with￨L￨IN￨O￨- Lagrange￨U￨NNP￨LOCATION￨- multiplier￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LMM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- the￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- curing￨L￨VBG￨O￨A rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- minimized￨L￨VBN￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- solve￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- as￨L￨IN￨O￨- how￨L￨WRB￨O￨- best￨L￨JJS￨O￨- to￨L￨TO￨O￨- allocate￨L￨VB￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- curing￨L￨VBG￨O￨A rate￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- positively￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- medical￨L￨JJ￨O￨- resource￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- region￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- >￨L￨JJR￨O￨- λopt￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- high-dimensional￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- converted￨L￨VBN￨O￨- into￨L￨IN￨O￨- numerically￨L￨RB￨O￨- c￨L￨NN￨O￨- solving￨L￨VBG￨O￨- low-dimensional￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- HMF￨U￨NN￨O￨- theory￨L￨NN￨O￨A and￨L￨CC￨O￨- LMM￨U￨NN￨O￨- .￨L￨.￨O￨- +Sparse￨U￨JJ￨MISC￨- Sliced￨U￨NNP￨MISC￨- Inverse￨U￨NNP￨MISC￨- Regression￨U￨NN￨MISC￨- Via￨U￨NNP￨MISC￨- Lasso￨U￨NNP￨PERSON￨- Qian￨U￨NNP￨PERSON￨- Lin￨U￨NNP￨PERSON￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Zhigen￨U￨NNP￨PERSON￨- Zhao￨U￨NNP￨PERSON￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Jun￨U￨NN￨PERSON￨- S.￨U￨NNP￨PERSON￨- Liuc￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- Center￨U￨NNP￨O￨- of￨L￨IN￨O￨- Statistical￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- Tsinghua￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Statistical￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Temple￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Statistics￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Harvard￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Abstract￨U￨NNP￨ORGANIZATION￨- :￨L￨:￨O￨- For￨U￨IN￨O￨- multiple￨L￨JJ￨O￨- index￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- sliced￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- regression￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- reduction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SDR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- space￨L￨NN￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- ρ￨L￨NN￨O￨- =￨L￨JJ￨O￨- lim￨L￨NN￨O￨- p￨L￨NN￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- p￨L￨NN￨O￨- is￨L￨VBZ￨O￨- same￨L￨JJ￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- order￨L￨NN￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- additional￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- resulting￨L￨VBG￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- Lasso-SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- consistent￨L￨JJ￨O￨A and￨L￨CC￨O￨- achieve￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- convergence￨L￨NN￨O￨- rate￨L￨NN￨O￨- under￨L￨IN￨O￨- certain￨L￨JJ￨O￨- sparsity￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- when￨L￨WRB￨O￨- p￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- o￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n2λ2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- signal-to-noise￨L￨NN￨O￨- ratio￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- constructing￨L￨VBG￨O￨- artificial￨L￨JJ￨O￨- response￨L￨NN￨O￨- variables￨L￨NNS￨O￨- made￨L￨VBD￨O￨- up￨L￨RP￨O￨- from￨L￨IN￨O￨- top￨L￨JJ￨O￨- eigenvectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- conditional￨L￨JJ￨O￨- covariance￨L￨NN￨O￨- matrix￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- Lasso￨U￨NNP￨O￨- regression￨L￨NN￨O￨A method￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SDR￨U￨NNP￨O￨- space￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- p￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dimension￨L￨NN￨O￨A and￨L￨CC￨O￨- n￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- the￨L￨DT￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- sparsity￨L￨NN￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- imposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- consistency￨L￨NN￨O￨- for￨L￨IN￨O￨- SIR￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- captures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- phases￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HIV-1￨U￨NN￨MISC￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- cohort￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- naive￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- accurately￨L￨RB￨O￨- predicts￨L￨VBZ￨O￨A the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Short￨U￨JJ￨MISC￨- Pulse￨U￨NN￨MISC￨- Anti-Retroviral￨U￨JJ￨MISC￨- Therapy￨U￨NN￨MISC￨- at￨L￨IN￨MISC￨- Seroconversion￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- SPARTAC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- trial￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- hybrid￨L￨NN￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- seed￨L￨NN￨O￨- and￨L￨CC￨O￨- establish￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- cell-to-cell￨L￨JJ￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- increased￨L￨VBD￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cell￨L￨NN￨O￨A activation￨L￨NN￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- HIV-1￨U￨NN￨MISC￨- progression￨L￨NN￨O￨- .￨L￨.￨O￨- +HIV-1￨U￨NN￨O￨- can￨L￨MD￨O￨- disseminate￨L￨VB￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- mechanisms￨L￨NNS￨O￨- :￨L￨:￨O￨- cell-free￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- following￨L￨VBG￨O￨- fluid-phase￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- virions￨L￨NNS￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- highly-efficient￨L￨JJ￨O￨- direct￨L￨JJ￨O￨- cell-to-cell￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- at￨L￨IN￨O￨- immune￨L￨JJ￨O￨- cell￨L￨NN￨O￨A contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Can￨U￨MD￨O￨- we￨L￨PRP￨O￨- predict￨L￨VB￨O￨- what￨L￨WP￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- will￨L￨MD￨O￨- actually￨L￨RB￨O￨- get￨L￨VB￨O￨- ”￨L￨''￨O￨- infected￨L￨VBN￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- spread￨L￨VBD￨O￨- the￨L￨DT￨O￨- idea￨L￨NN￨O￨- or￨L￨CC￨O￨- buy￨L￨VB￨O￨- the￨L￨DT￨O￨- competing￨L￨VBG￨O￨- product￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- appear￨L￨VBP￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- different￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- profile￨L￨NN￨O￨- ?￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- profiles￨L￨NNS￨O￨- can￨L￨MD￨O￨- infect￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- under￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- apart￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- weak￨L￨JJ￨O￨- profile￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- great￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- stronger￨L￨JJR￨O￨- profile￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- low￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- will￨L￨MD￨O￨- get￨L￨VB￨O￨- infected￨L￨VBN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- profiles￨L￨NNS￨O￨- A￨U￨DT￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- profile￨L￨NN￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- profile￨L￨NN￨O￨- B￨U￨NN￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- spreading￨L￨VBG￨O￨- virus￨L￨NN￨O￨- with￨L￨IN￨O￨- probabilities￨L￨NNS￨O￨- βA￨L￨NN￨O￨- and￨L￨CC￨O￨- βB￨L￨NN￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- what￨L￨WDT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- profiles￨L￨NNS￨O￨- will￨L￨MD￨O￨- actually￨L￨RB￨O￨A get￨L￨VB￨O￨- infected￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- ?￨L￨.￨O￨- +Virus￨U￨NN￨O￨- Propagation￨U￨NN￨O￨- in￨L￨IN￨O￨- Multiple￨U￨JJ￨ORGANIZATION￨- Profile￨U￨NNP￨ORGANIZATION￨- Networks￨U￨NNP￨ORGANIZATION￨- A.￨U￨NNP￨ORGANIZATION￨- Tzimas￨U￨NNP￨ORGANIZATION￨- Technological￨U￨NNP￨ORGANIZATION￨- Educational￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Western￨U￨NNP￨ORGANIZATION￨- Greece￨U￨NNP￨ORGANIZATION￨- Nafpaktos￨U￨NNP￨ORGANIZATION￨- Greece￨U￨NNP￨ORGANIZATION￨- ABSTRACT￨U￨NN￨O￨- Suppose￨U￨VB￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- or￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- competing￨L￨VBG￨O￨A idea/product￨L￨NN￨O￨- that￨L￨WDT￨O￨- propagates￨L￨VBZ￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- multiple￨L￨JJ￨O￨- profile￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- part￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- display￨L￨VB￨O￨- the￨L￨DT￨O￨- blow-up￨L￨NN￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- point￨L￨NN￨O￨- encounters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- fortuitously￨L￨RB￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- occur￨L￨VB￨O￨- for￨L￨IN￨O￨- 1-dimensional￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- over-all￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- motion￨L￨NN￨O￨A but￨L￨CC￨O￨- does￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- plane￨L￨NN￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- show￨L￨VBP￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- by￨L￨IN￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- reaction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- passing￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- walker￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- extended￨L￨JJ￨O￨- region￨L￨NN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +Confined￨U￨NNP￨ORGANIZATION￨- Random￨U￨NNP￨ORGANIZATION￨- Walkers￨U￨NNPS￨ORGANIZATION￨- in￨L￨IN￨O￨- Dimensions￨U￨NNPS￨MISC￨- Higher￨U￨JJR￨MISC￨- Than￨U￨IN￨MISC￨- One￨U￨CD￨NUMBER￨- and￨L￨CC￨O￨- Analysis￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Transmission￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Infection￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- Epidemics￨U￨NNP￨O￨- S.￨U￨NNP￨O￨- M.￨U￨NNP￨O￨- Kenkre1￨U￨NNP￨O￨- ,￨L￨,￨O￨- †￨L￨CD￨NUMBER￨- 1Consortium￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- for￨L￨IN￨O￨- Interdisciplinary￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Astronomy￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- New￨U￨NNP￨ORGANIZATION￨- Mexico￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Albuquerque￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- Mexico￨U￨NNP￨STATE_OR_PROVINCE￨- 87131￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Dated￨U￨VBN￨O￨- :￨L￨:￨O￨- September￨U￨NNP￨DATE￨- 23￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- walkers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- motion￨L￨NN￨O￨A of￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- dimensions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- confined￨L￨VBN￨O￨- spatially￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- action￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- quadratic￨L￨JJ￨O￨- potential￨L￨JJ￨O￨- centered￨L￨VBN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- walks￨L￨VBZ￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- analyzed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- reaction-diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- continuum￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dimensionality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- reaction￨L￨NN￨O￨- event￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- instances￨L￨NNS￨O￨- trapping￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- present￨L￨JJ￨DATE￨- case￨L￨NN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- via￨L￨IN￨O￨- contact￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- smaller￨L￨JJR￨O￨- than￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- over-all￨L￨JJ￨O￨- motion￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- walker￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- occurs￨L￨VBZ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- walkers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- animals￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- rodents￨L￨NNS￨O￨- in￨L￨IN￨O￨- considerations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Hantavirus￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- reaction￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- confining￨L￨VBG￨O￨- potential￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- tendency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- animals￨L￨NNS￨O￨- to￨L￨TO￨O￨- stay￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- neighborhood￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- home￨L￨NN￨O￨- range￨L￨NN￨O￨- centers￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- a￨L￨DT￨O￨- message-passing￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- network￨L￨NN￨O￨- immunization￨L￨NN￨O￨A that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- immunized￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- find￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- nearly￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- optimal￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- sets￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- choice￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- costs￨L￨NNS￨O￨- .￨L￨.￨O￨- +Zecchina1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Applied￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Politecnico￨U￨NNP￨ORGANIZATION￨- di￨L￨NNP￨ORGANIZATION￨- Torino￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Corso￨U￨NNP￨PERSON￨- Duca￨U￨NNP￨PERSON￨- degli￨L￨NNP￨O￨- Abruzzi￨U￨NNP￨ORGANIZATION￨- 24￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10129￨L￨CD￨NUMBER￨- Torino￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- 2Col￨L￨NN￨O￨- legio￨L￨NN￨O￨- Carlo￨U￨NNP￨PERSON￨- Alberto￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Via￨U￨NNP￨O￨- Real￨U￨NNP￨O￨- Col￨U￨NNP￨O￨- legio￨L￨NN￨O￨- 30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10024￨L￨CD￨NUMBER￨- Moncalieri￨U￨NNP￨O￨- ,￨L￨,￨O￨- 3Human￨L￨NNP￨O￨- Genetics￨U￨NNP￨ORGANIZATION￨- Foundation￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Via￨U￨NNP￨O￨- Nizza￨U￨NNP￨PERSON￨- 52￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10126￨L￨CD￨NUMBER￨- Torino￨U￨NNP￨O￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- Italy￨U￨NNP￨COUNTRY￨- The￨U￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- network￨L￨NN￨O￨- immunization￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- immunize￨L￨VB￨O￨- or￨L￨CC￨O￨- vaccinate￨L￨VB￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- a￨L￨DT￨O￨- tradeoff￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- stationary￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- expected￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- computational￨L￨JJ￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- recalculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- metric￨L￨JJ￨O￨- after￨L￨IN￨O￨- each￨L￨DT￨O￨- immunization￨L￨NN￨O￨A step￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- after￨L￨IN￨O￨- removing￨L￨VBG￨O￨- the￨L￨DT￨O￨- immunized￨L￨VBN￨O￨- node￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- usually￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- much￨L￨RB￨O￨- better￨L￨JJR￨O￨- results￨L￨NNS￨O￨- than￨L￨IN￨O￨- computing￨L￨VBG￨O￨- it￨L￨PRP￨O￨- only￨L￨RB￨O￨- once￨L￨RB￨DATE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simple￨L￨JJ￨O￨- random￨L￨JJ￨O￨- immunization￨L￨NN￨O￨A strategy￨L￨NN￨O￨- can￨L￨MD￨O￨- consist￨L￨VB￨O￨- in￨L￨IN￨O￨- fixing￨L￨VBG￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- immunized￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- averaging￨L￨VBG￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- over￨L￨IN￨O￨- all￨L￨DT￨O￨- possible￨L￨JJ￨O￨- realizations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immunization￨L￨NN￨O￨- set￨L￨NN￨O￨- .￨L￨.￨O￨- +Further￨U￨JJ￨O￨- improvements￨L￨NNS￨O￨- were￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- more￨L￨JJR￨O￨- complex￨L￨NN￨O￨- immunization￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- graph￨L￨NN￨O￨- partitioning￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- size￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- simulation￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- indirect￨L￨JJ￨O￨A links￨L￨NNS￨O￨- play￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- of￨L￨IN￨O￨- direct￨L￨JJ￨O￨- links￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- hidden￨L￨JJ￨O￨- spreader￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- large￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SPDT￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- causes￨L￨VBZ￨O￨- no￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- direct￨L￨JJ￨O￨- link￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- called￨L￨VBN￨O￨- same￨L￨JJ￨O￨- place￨L￨NN￨O￨- different￨L￨JJ￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SPDT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- indirect￨L￨JJ￨O￨A transmissions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- happen￨L￨VBP￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- leaves￨L￨NNS￨O￨- before￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- arrival￨L￨NN￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- direct￨L￨JJ￨O￨- transmissions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- indirect￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- links￨L￨NNS￨O￨- significantly￨L￨RB￨O￨- enhance￨L￨VBP￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- simulating￨L￨VBG￨O￨- airborne￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- synthetic￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Current￨U￨JJ￨DATE￨- network-based￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨A models￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- transmit￨L￨VBP￨O￨- through￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- where￨L￨WRB￨O￨- both￨L￨DT￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- co-located￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Behavior￨U￨NN￨O￨- of￨L￨IN￨O￨- Epidemics￨U￨NNS￨O￨- under￨L￨IN￨O￨- Bounded￨U￨NNP￨O￨- Susceptibility￨U￨NN￨O￨- Subhashini￨U￨NNP￨PERSON￨- Krishnasamy￨U￨NNP￨PERSON￨- Depar￨U￨NNP￨PERSON￨- tment￨L￨NN￨O￨- of￨L￨IN￨O￨- ECE￨U￨NNP￨ORGANIZATION￨- UT￨U￨NNP￨ORGANIZATION￨- Austin￨U￨NNP￨ORGANIZATION￨- Siddhar￨U￨NNP￨ORGANIZATION￨- tha￨L￨NN￨O￨- Banerjee￨U￨NNP￨O￨- Depar￨U￨NNP￨O￨- tment￨L￨NN￨O￨- of￨L￨IN￨O￨- MS&E￨U￨NNP￨O￨- Stanford￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Sanjay￨U￨NNP￨PERSON￨- Shakkottai￨U￨NNP￨PERSON￨- Depar￨U￨NNP￨PERSON￨- tment￨L￨NN￨O￨- of￨L￨IN￨O￨- ECE￨U￨NNP￨ORGANIZATION￨- UT￨U￨NNP￨ORGANIZATION￨- Austin￨U￨NNP￨ORGANIZATION￨- ABSTRACT￨U￨NN￨O￨- We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- bounded￨L￨VBN￨O￨A susceptibility￨L￨NN￨O￨- constraint￨L￨NN￨O￨- –￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- regular￨L￨JJ￨O￨- SI/SIS￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- sub￨L￨NN￨O￨- ject￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- cap￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- clique-like￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- unaffected￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- star-like￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- sharp￨L￨JJ￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- extinction￨L￨NN￨O￨- times￨L￨NNS￨O￨- under￨L￨IN￨O￨- bounded￨L￨VBN￨O￨A susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- SI￨U￨NNP￨ORGANIZATION￨- dynamics￨L￨NNS￨ORGANIZATION￨- ,￨L￨,￨O￨- bounded￨L￨VBD￨O￨A susceptibility￨L￨NN￨O￨- has￨L￨VBZ￨O￨- no￨L￨DT￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- star-like￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- dramatically￨L￨RB￨O￨- alters￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- clique-like￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Interestingly￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- bipolar￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- transmit￨L￨VBP￨O￨- probability￨L￨NN￨O￨- p￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- while￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- density￨L￨NN￨O￨- λ￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- concurrent￨L￨JJ￨O￨- transmitters￨L￨NNS￨O￨- λp￨L￨NN￨O￨- stays￨L￨VBZ￨O￨- constant￨L￨JJ￨O￨- as￨L￨IN￨O￨- p￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ps￨U￨NN￨O￨- degenerates￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- links￨L￨NNS￨O￨- have￨L￨VBP￨O￨- exactly￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- success￨L￨NN￨O￨A probability￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- link￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- introduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- notion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- meta￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- success￨L￨NN￨O￨A probability￨L￨NN￨O￨A Ps￨U￨NNS￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- provides￨L￨VBZ￨O￨- bounds￨L￨NNS￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- exact￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- expression￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- for￨L￨IN￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- ”￨L￨''￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- quantity￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- interference-limited￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨A probability￨L￨NN￨O￨A ps￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- θ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- >￨L￨JJR￨O￨- θ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- link￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- complementary￨L￨JJ￨O￨- cumulative￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ccdf￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- the￨L￨DT￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- meta￨L￨NN￨O￨- distribution￨L￨NN￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- refined￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- performance￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- HCNs￨U￨NNS￨O￨- ,￨L￨,￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- K￨U￨NN￨O￨- -￨L￨:￨O￨- tier￨L￨NN￨TITLE￨A heterogeneous￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- independent￨L￨JJ￨RELIGION￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HIP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- range￨L￨NN￨O￨- expansion￨L￨NN￨O￨- bias￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- offloading￨L￨NN￨O￨- bias￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- tier￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- biases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- detrimental￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- mean￨L￨NN￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- b-th￨L￨JJ￨O￨- moment￨L￨NN￨O￨- curve￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- versus￨L￨CC￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- threshold￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- tier￨L￨NN￨TITLE￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- excellently￨L￨RB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- horizontal￨L￨JJ￨O￨- shifted￨L￨VBN￨O￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- moment￨L￨NN￨O￨- curve￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- single-tier￨L￨JJ￨O￨- PPP￨U￨NNP￨ORGANIZATION￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Expressions￨U￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- b-th￨L￨JJ￨O￨- moment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- each￨L￨DT￨O￨- tier￨L￨NN￨TITLE￨A are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- meta￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- beta￨L￨NN￨O￨- approximations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- .￨L￨.￨O￨- +Key￨U￨NN￨O￨- performance￨L￨NN￨O￨- metrics￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- local￨L￨JJ￨O￨- delay￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- gains￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- tier￨L￨NN￨TITLE￨A are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- .￨L￨.￨O￨- +–￨L￨:￨O￨- We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- quenched￨L￨VBN￨O￨- mean-field￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- QMF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- dynamical￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- connected￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- are￨L￨VBP￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨A approximation￨L￨NN￨O￨- .￨L￨.￨O￨- +the￨L￨DT￨O￨- core￨L￨NN￨O￨- issue￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- recent￨L￨JJ￨O￨- works￨L￨NNS￨O￨- about￨L￨IN￨O￨- The￨U￨DT￨O￨- former￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- relied￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- neglecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- highly￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨A structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- inherent￨L￨JJ￨O￨- to￨L￨TO￨O￨- real￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- mean-field￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HMF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- theory￨L￨NN￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- benchmark￨L￨NN￨O￨- for￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- running￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- HMF￨U￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- dynamical￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- depend￨L￨VBP￨O￨- only￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vertex￨L￨NN￨O￨A degree￨L￨NN￨O￨- and￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- specific￨L￨NN￨O￨- location￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Novozhilov￨U￨NNP￨PERSON￨- provided￨L￨VBD￨O￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- proof￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- that￨L￨WDT￨O￨- for￨L￨IN￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- inversely￨L￨RB￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨VBG￨O￨- speed￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- spreading￨L￨VBG￨O￨- speed￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- derived￨L￨VBD￨O￨- a￨L￨DT￨O￨- formula￨L￨NN￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨A size￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- case￨L￨NN￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- closed￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- contacting￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- moving￨L￨VBG￨O￨- homogeneously￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨A are￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- and￨L￨CC￨O￨- constant￨L￨JJ￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- dS￨L￨NN￨O￨- dt￨L￨NN￨O￨- dI￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- βS￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- more￨L￨JJR￨O￨- heterogeneity￨L￨NN￨O￨A in￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- less￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- progression￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contrary￨L￨NN￨O￨- ,￨L￨,￨O￨- more￨L￨JJR￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- —￨L￨:￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- either￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- or￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- stays￨L￨VBZ￨O￨- fixed￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- obtained￨L￨VBD￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨A size￨L￨NN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- transferred￨L￨VBN￨O￨- between￨L￨IN￨O￨- network￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- possesses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Pareto￨U￨NNP￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- implying￨L￨VBG￨O￨- scale-free￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨A describing￨L￨VBG￨O￨A data￨L￨NNS￨O￨- dissemination￨L￨NN￨O￨- in￨L￨IN￨O￨- opportunistic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- setting￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- thresholds￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- Silvio￨U￨NNP￨PERSON￨- C.￨U￨NNP￨PERSON￨- Taking￨U￨VBG￨PERSON￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨A matrix￨L￨NN￨O￨A ,￨L￨,￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- predicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- given￨L￨VBN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- inverse￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- λQMF￨L￨NN￨O￨- c￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ΛN￨U￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- in￨L￨IN￨O￨- HMF￨U￨NN￨O￨- theory￨L￨NN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- replaced￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- annealed￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- QMF￨U￨NN￨O￨- theory￨L￨NN￨O￨- fully￨L￨RB￨O￨- preserves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- quenched￨L￨VBN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- as￨L￨IN￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨A matrix￨L￨NN￨O￨A .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- λCL￨L￨NN￨O￨- c￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- c1￨L￨NN￨O￨- /￨L￨:￨O￨- √￨L￨SYM￨O￨- kmax￨L￨FW￨O￨- √￨L￨FW￨O￨- kmax￨L￨FW￨O￨- >￨L￨JJR￨O￨- hk2￨L￨NN￨O￨- i￨L￨FW￨O￨- hki￨L￨FW￨O￨A ln2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- hki￨L￨NN￨O￨- >￨L￨JJR￨O￨- √￨L￨CD￨NUMBER￨- kmax￨L￨NN￨O￨- ln￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- c2￨L￨NN￨O￨- /￨L￨:￨O￨- hk2￨L￨NN￨O￨- i￨L￨FW￨O￨- hki￨L￨FW￨O￨- hk2￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- kmax￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- degree￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- c1￨L￨NN￨O￨- and￨L￨CC￨O￨- c2￨L￨NN￨O￨- are￨L￨VBP￨O￨- numerical￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨A vanishes￨L￨VBZ￨O￨- for￨L￨IN￨O￨- large￨L￨JJ￨O￨- N￨U￨NN￨O￨- as￨L￨RB￨O￨- soon￨L￨RB￨O￨- as￨L￨IN￨O￨- kmax￨L￨NN￨O￨- diverges￨L￨VBZ￨O￨- with￨L￨IN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- much￨L￨JJ￨O￨- attention￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- control￨L￨NN￨O￨- via￨L￨IN￨O￨- social￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- adjustment￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- seems￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- strategies￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- similar￨L￨JJ￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- shortening￨L￨VBG￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- somehow￨L￨RB￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- chances￨L￨NNS￨O￨- for￨L￨IN￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A .￨L￨.￨O￨- +Intuitively￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- done￨L￨VBN￨O￨- either￨L￨CC￨O￨- by￨L￨IN￨O￨- shortening￨L￨VBG￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- or￨L￨CC￨O￨- by￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- opportunities￨L￨NNS￨O￨- for￨L￨IN￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- deepen￨L￨VB￨O￨- the￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- shed￨L￨VBD￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨A of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- conveniently￨L￨RB￨O￨- split￨L￨VBN￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- contributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- λd-r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- max￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- +￨L￨CC￨O￨- βd-r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- α￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- elementary￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- isolated￨L￨VBN￨O￨A d-r￨L￨NN￨O￨- pair￨L￨NN￨O￨- exhibiting￨L￨VBG￨O￨- no￨L￨DT￨O￨- synergistic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- d-synergy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- βd-r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- βnd￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- nd￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- neighbours￨L￨NNS￨O￨A connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- donor￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- λd-r￨L￨NN￨O￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- isolated￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nd￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- r-synergy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- βd-r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- nr￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbours￨L￨NNS￨O￨A challenging￨L￨VBG￨O￨- where￨L￨WRB￨O￨- nr￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- recipient￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- particular￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- denoted￨L￨VBN￨O￨A as￨L￨IN￨O￨- r-synergy￨L￨NN￨O￨- and￨L￨CC￨O￨- d-synergy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- between￨L￨IN￨O￨- any￨L￨DT￨O￨- donor-recipient￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- d-r￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- pair￨L￨NN￨O￨A of￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- r-synergy￨L￨NN￨O￨- r￨L￨NN￨O￨- b￨L￨NN￨O￨- d-synergy￨L￨NN￨O￨- d￨L￨NN￨O￨- FIG￨U￨NNP￨O￨- .￨L￨.￨O￨- +XX.XX.XX￨U￨NNP￨O￨- No￨U￨NNP￨O￨- PACS￨U￨NNS￨O￨- code￨L￨VBP￨O￨- given￨L￨VBN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- pk￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- WWW￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Internet￨U￨NN￨MISC￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- biological￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- robustness￨L￨NN￨O￨A against￨L￨IN￨O￨- failures￨L￨NNS￨O￨- or￨L￨CC￨O￨- intentional￨L￨JJ￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +numerically￨L￨RB￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- robustness￨L￨NN￨O￨A of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- against￨L￨IN￨O￨- random￨L￨JJ￨O￨- failure￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- sequentially￨L￨RB￨O￨- removed￨L￨VBN￨O￨- with￨L￨IN￨O￨- equal￨L￨JJ￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- intentional￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- hubs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- having￨L￨VBG￨O￨- γ￨L￨NN￨O￨- ≤￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- robust￨L￨JJ￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- failure￨L￨NN￨O￨- :￨L￨:￨O￨- you￨L￨PRP￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- remove￨L￨VB￨O￨- almost￨L￨RB￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- disintegrate￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- result￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- correlated￨L￨VBD￨O￨A networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- robust￨L￨JJ￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- uncorrelated￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- whether￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- assortative￨L￨JJ￨O￨- or￨L￨CC￨O￨- disassortative￨L￨JJ￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- too￨L￨RB￨O￨- large￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- robustness￨L￨NN￨O￨A of￨L￨IN￨O￨- correlated￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- against￨L￨IN￨O￨- propagating￨L￨VBG￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +3￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Robustness￨U￨NN￨O￨- of￨L￨IN￨O￨- correlated￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- against￨L￨IN￨O￨- propagating￨L￨VBG￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨A Takehisa￨U￨NNP￨PERSON￨- Hasegawa1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Keita￨U￨NNP￨PERSON￨- Konno2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Ko￨U￨NNP￨PERSON￨- ji￨L￨NN￨O￨- Nemoto2￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Graduate￨U￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Information￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Tohoku￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 6-3-09￨L￨CD￨DATE￨- ,￨L￨,￨O￨- Aramaki-Aza-Aoba￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Sendai￨U￨NN￨CITY￨- ,￨L￨,￨O￨- 980-8579￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- JAPAN￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Key￨U￨NN￨O￨- words￨L￨NNS￨O￨- :￨L￨:￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A ,￨L￨,￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Epidemic￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- successful￨L￨JJ￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- studied￨L￨VBN￨O￨- applications￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- several￨L￨JJ￨O￨- modular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- formed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- and￨L￨CC￨O￨- scale-free￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- global￨L￨JJ￨O￨- ,￨L￨,￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- community-level￨L￨JJ￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- several￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨A is￨L￨VBZ￨O￨- faster￨L￨RBR￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- random￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- average￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- degree￨L￨NN￨O￨- .￨L￨.￨O￨- +000￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 000￨L￨CD￨NUMBER￨- issn￨L￨NN￨O￨- 0364-765X￨L￨NN￨O￨- |￨L￨SYM￨O￨- eissn￨L￨FW￨O￨- 1526-5471￨L￨CD￨DURATION￨- |￨L￨SYM￨O￨- 00￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- 0000￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- 0001￨L￨CD￨DATE￨- INFORMS￨U￨NNP￨O￨- doi￨L￨FW￨O￨- 10.1287￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- xxxx￨L￨NN￨O￨- .0000.0000￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- 0000￨L￨CD￨DATE￨- INFORMS￨U￨VBZ￨O￨- The￨U￨DT￨O￨- Cost￨U￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- Epidemic￨U￨JJ￨MISC￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- Complex￨U￨NN￨O￨- Network￨U￨NNP￨O￨- :￨L￨:￨O￨- A￨U￨NNP￨O￨- Random￨U￨NNP￨O￨- Matrix￨U￨NNP￨O￨- Approach￨U￨NNP￨O￨- *￨L￨SYM￨O￨- Dept.￨U￨NNP￨O￨- We￨U￨PRP￨O￨- also￨L￨RB￨O￨- give￨L￨VBP￨O￨- an￨L￨DT￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- cost￨L￨NN￨O￨- for￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- finite￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- and￨L￨CC￨O￨- illustrate￨L￨VBP￨O￨- both￨L￨CC￨O￨- calculated￨L￨VBN￨O￨- costs￨L￨NNS￨O￨- using￨L￨VBG￨O￨- extensive￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨A and￨L￨CC￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- work￨L￨NN￨O￨- applies￨L￨VBZ￨O￨- techniques￨L￨NNS￨O￨- from￨L￨IN￨O￨- percolation￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- attempting￨L￨VBG￨O￨- to￨L￨TO￨O￨- answer￨L￨VB￨O￨- whether￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- start￨L￨VB￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨A node￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- giant￨L￨JJ￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Moore￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Newman￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Newman￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Kenah￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Robins￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨A network￨L￨NN￨O￨A that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- variant￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- Erd￨U￨NNP￨O￨- ¨￨L￨SYM￨O￨- os-R￨L￨NN￨O￨- ´￨L￨''￨O￨- enyi￨L￨FW￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- Chung￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Lu￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Newman￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- define￨L￨VB￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨PDT￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨A network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- entirely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- evolves￨L￨VBZ￨O￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- linear￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- migration￨L￨NN￨O￨A process￨L￨NN￨O￨- with￨L￨IN￨O￨- per-capita￨L￨JJ￨O￨- migration￨L￨NN￨O￨- rates￨L￨NNS￨O￨- R.￨U￨NNP￨O￨- Suppose￨U￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- minimise￨L￨VB￨O￨- some￨L￨DT￨O￨- quantity￨L￨NN￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- π￨L￨NN￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- calculated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Minimising￨U￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- Consider￨U￨VB￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- m￨L￨NN￨O￨- groups￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- group￨L￨NN￨O￨- i￨L￨FW￨O￨- contains￨L￨VBZ￨O￨- Xi￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- susceptibles￨L￨NNS￨O￨- and￨L￨CC￨O￨- Yi￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infectives￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- act￨L￨VB￨O￨- collectively￨L￨RB￨O￨- to￨L￨TO￨O￨- limit￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- specifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- that￨L￨WDT￨O￨- minimises￨L￨VBZ￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infectives￨L￨NNS￨O￨A are￨L￨VBP￨O￨- migrating￨L￨VBG￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- maximise￨L￨VB￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +,￨L￨,￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- transition￨L￨NN￨O￨A rate￨L￨NN￨O￨A matrix￨L￨NN￨O￨- R￨U￨NN￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- transition￨L￨NN￨O￨- rate￨L￨NN￨O￨- matrix￨L￨NN￨O￨- Q￨U￨NNP￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- node￨L￨NN￨O￨- and￨L￨CC￨O￨- edge￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- lower￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- over￨L￨IN￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- proportionality￨L￨NN￨O￨- constant￨L￨NN￨O￨- that￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- adaptation￨L￨NN￨O￨A rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- a￨L￨DT￨O￨- closed-form￨L￨JJ￨O￨- expression￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨A bound￨L￨VBN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ASIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- node￨L￨NN￨O￨- and￨L￨CC￨O￨- edge￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨A susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- ASIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- healthy￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- allowed￨L￨VBN￨O￨- to￨L￨TO￨O￨- temporarily￨L￨RB￨O￨- cut￨L￨VB￨O￨- edges￨L￨NNS￨O￨- connecting￨L￨VBG￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- to￨L￨TO￨O￨- optimally￨L￨RB￨O￨- tune￨L￨VB￨O￨- the￨L￨DT￨O￨- adaptation￨L￨NN￨O￨A rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- transient￨L￨JJ￨O￨A characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- recovery￨L￨NN￨O￨- policy￨L￨NN￨O￨- modeled￨L￨VBD￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- state-dependent￨L￨JJ￨O￨- retrial￨L￨NN￨O￨- queueing￨L￨VBG￨O￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- arriving￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- upon￨L￨IN￨O￨- finding￨L￨VBG￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- units￨L￨NNS￨O￨- busy￨L￨JJ￨O￨- ,￨L￨,￨O￨- join￨L￨VB￨O￨- a￨L￨DT￨O￨- virtual￨L￨JJ￨O￨- buffer￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- try￨L￨VB￨O￨- persistently￨L￨RB￨O￨- for￨L￨IN￨O￨- service￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- regain￨L￨VB￨O￨- susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- regard￨L￨NN￨O￨- to￨L￨TO￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- queueing￨L￨VBG￨O￨- theory￨L￨NN￨O￨- in￨L￨IN￨O￨- quantitative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- progression￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- showed￨L￨VBD￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- moment￨L￨NN￨O￨- of￨L￨IN￨O￨- first￨L￨NN￨O￨- detection￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- geometrically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- by￨L￨IN￨O￨- formulating￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- M￨U￨NN￨O￨- /￨L￨:￨O￨- G/1￨U￨NN￨O￨- queue￨L￨NN￨O￨- with￨L￨IN￨O￨- processor￨L￨NN￨TITLE￨- sharing￨L￨NN￨O￨- service￨L￨NN￨O￨A discipline￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SI￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- added￨L￨VBN￨O￨- retrial￨L￨NN￨O￨- phenomenon￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- continuous-time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CTMC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- derive￨L￨VB￨O￨- the￨L￨DT￨O￨- Laplace￨U￨NNP￨CITY￨- transforms￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- transient￨L￨JJ￨O￨A state￨L￨NN￨O￨- probability￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- corresponding￨L￨JJ￨O￨- moments￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +2N￨L￨SYM￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- transient￨L￨JJ￨O￨A distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- birth-death￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- detailed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- ∗￨L￨CD￨NUMBER￨- Radboud￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Nijmegen￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Faculty￨U￨NNP￨O￨- of￨L￨IN￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- P.O.￨U￨NNP￨O￨- Box￨U￨NNP￨O￨- 9010￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6500￨L￨CD￨NUMBER￨- GL￨U￨NNP￨O￨- Nijmegen￨U￨NNP￨O￨- ,￨L￨,￨O￨- The￨U￨DT￨O￨- Netherlands￨U￨NNPS￨COUNTRY￨- ;￨L￨:￨O￨- email￨L￨NN￨O￨A :￨L￨:￨O￨- †￨L￨CD￨NUMBER￨- Amsterdam￨U￨NNP￨ORGANIZATION￨- Free￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Faculty￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- De￨U￨NNP￨O￨- Boelelaan￨U￨NNP￨O￨- 1081￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 1081￨L￨CD￨DATE￨- HV￨U￨NNP￨O￨- Amsterdam￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- The￨U￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- email￨L￨NN￨O￨- :￨L￨:￨O￨- ‡￨L￨CD￨NUMBER￨- Delft￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Faculty￨U￨NNP￨O￨- of￨L￨IN￨O￨- EECS￨U￨NNP￨O￨- ,￨L￨,￨O￨- P.O.￨U￨NNP￨O￨- Box￨U￨NNP￨O￨- 5031￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2600￨L￨CD￨DATE￨- GA￨U￨NNP￨STATE_OR_PROVINCE￨- Delft￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- The￨U￨DT￨O￨- Netherlands￨U￨NNPS￨COUNTRY￨- ;￨L￨:￨O￨- email￨L￨NN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- G￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- specified￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- Bernoulli￨U￨NNP￨O￨- random￨L￨JJ￨O￨- variable￨L￨JJ￨O￨- Xi￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Xi￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- healthy￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- Xi￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- consider￨L￨VB￨O￨- non-Markovian￨L￨JJ￨MISC￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- characteristics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- all￨L￨DT￨O￨- curing￨L￨VBG￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- resilience￨L￨NN￨O￨A of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λ2￨L￨NN￨O￨- during￨L￨IN￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- perturbations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- control￨L￨NN￨O￨- state￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- λ1￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- even￨L￨RB￨O￨- for￨L￨IN￨O￨- λ2￨L￨NN￨O￨- <￨L￨JJR￨O￨- λc￨L￨CD￨NUMBER￨A ,￨L￨,￨O￨- epidemics￨L￨NNS￨O￨- eventually￨L￨RB￨O￨- could￨L￨MD￨O￨- bounce￨L￨VB￨O￨- back￨L￨RB￨O￨- if￨L￨IN￨O￨- control￨L￨NN￨O￨- duration￨L￨NN￨O￨- is￨L￨VBZ￨O￨- below￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- critical￨L￨JJ￨O￨- control￨L￨NN￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- resilience￨L￨NN￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- cdmax￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- diameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- relation￨L￨NN￨O￨- cdmax￨L￨NN￨O￨- ∼￨L￨CD￨NUMBER￨- dα￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- resilience￨L￨NN￨O￨A of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nonzero￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- λc￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- for￨L￨IN￨O￨- ER￨U￨NN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- goals￨L￨NNS￨O￨- of￨L￨IN￨O￨- household￨L￨NN￨O￨A studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨- secondary￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SAR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- direct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- A￨U￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- household￨L￨NN￨O￨- member￨L￨NN￨O￨- B￨U￨NN￨O￨- during￨L￨IN￨O￨- A￨U￨DT￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨A secondary￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SAR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- household￨L￨NN￨O￨- member￨L￨NN￨O￨- A￨U￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- member￨L￨NN￨O￨- B￨U￨NN￨O￨- during￨L￨IN￨O￨- A￨U￨DT￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SAR￨U￨NN￨ORGANIZATION￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- binomial￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- biased￨L￨VBN￨O￨- upward￨L￨RB￨O￨- and￨L￨CC￨O￨- produces￨L￨VBZ￨O￨- confidence￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- with￨L￨IN￨O￨- poor￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Accurate￨U￨JJ￨O￨- point￨L￨NN￨O￨- and￨L￨CC￨O￨- interval￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SAR￨U￨NN￨ORGANIZATION￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- using￨L￨VBG￨O￨- chain￨L￨NN￨O￨- binomial￨L￨JJ￨O￨A models￨L￨NNS￨O￨- or￨L￨CC￨O￨- pairwise￨L￨JJ￨O￨- survival￨L￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- household￨L￨NN￨O￨A with￨L￨IN￨O￨- m￨L￨NN￨O￨- susceptibles￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- treated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- binomial￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- random￨L￨JJ￨O￨- variable￨L￨JJ￨O￨- where￨L￨WRB￨O￨- p￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- SAR￨U￨NN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- researchers￨L￨NNS￨O￨- report￨L￨VBP￨O￨- risk￨L￨NN￨O￨- ratios￨L￨NNS￨O￨- in￨L￨IN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outcomes￨L￨NNS￨O￨- within￨L￨IN￨O￨- clusters￨L￨NNS￨O￨A or￨L￨CC￨O￨- single￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- Ti￨U￨NNP￨PERSON￨- be￨L￨VB￨O￨- Yij￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- binary￨L￨JJ￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- sub￨L￨NN￨O￨- ject￨L￨NN￨O￨- j￨L￨NN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- outcomes￨L￨NNS￨O￨- in￨L￨IN￨O￨- cluster￨L￨NN￨O￨A i￨L￨FW￨O￨- are￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- and￨L￨CC￨O￨- recorded￨L￨VBN￨O￨- by￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- structural￨L￨JJ￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- formalizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemiologic￨L￨JJ￨O￨- intuition￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- risk￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- both￨L￨DT￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- traits￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- risk￨L￨NN￨O￨- ratio￨L￨NN￨O￨- is￨L￨VBZ￨O￨- implicitly￨L￨RB￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨- time￨L￨NN￨O￨- Ti￨U￨NNP￨PERSON￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- cluster￨L￨NN￨O￨A i￨L￨FW￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- uncertainty￨L￨NN￨O￨- persists￨L￨VBZ￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- cefazolin￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- controversies￨L￨NNS￨O￨- over￨L￨IN￨O￨- its￨L￨PRP$￨O￨- efficacy￨L￨NN￨O￨A in￨L￨IN￨O￨- deep￨L￨JJ￨O￨- MSSA￨U￨NN￨ORGANIZATION￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- possible￨L￨JJ￨O￨- negative￨L￨JJ￨O￨- ecological￨L￨JJ￨O￨- impact￨L￨NN￨O￨- .￨L￨.￨O￨- +75018￨L￨CD￨NUMBER￨- Paris￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- France￨U￨NNP￨COUNTRY￨- Tel￨U￨NNP￨O￨- :￨L￨:￨O￨- +￨L￨CC￨O￨- 33￨L￨CD￨NUMBER￨A 1￨L￨CD￨DATE￨- 40￨L￨CD￨DATE￨- 25￨L￨CD￨DATE￨- 78￨L￨CD￨DATE￨- 03￨L￨CD￨DATE￨- Fax￨U￨NN￨O￨- :￨L￨:￨O￨- +￨L￨CC￨O￨- 33￨L￨CD￨NUMBER￨- 1￨L￨CD￨DATE￨- 40￨L￨CD￨DATE￨- 25￨L￨CD￨DATE￨- 88￨L￨CD￨DATE￨- 60￨L￨CD￨DATE￨- Electronic￨U￨JJ￨O￨- address￨L￨NN￨O￨- :￨L￨:￨O￨- Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Staphylococcus￨U￨FW￨O￨- aureus￨L￨FW￨O￨- ,￨L￨,￨O￨- cloxacillin￨L￨NN￨O￨- ,￨L￨,￨O￨- cefazolin￨L￨NN￨O￨- ,￨L￨,￨O￨- bacteremia￨L￨NN￨O￨- ,￨L￨,￨O￨- safety￨L￨NN￨O￨- ,￨L￨,￨O￨- efficacy￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- comparative￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- effectiveness￨L￨NN￨O￨- and￨L￨CC￨O￨- safety￨L￨NN￨O￨- profile￨L￨NN￨O￨- of￨L￨IN￨O￨- cefazolin￨L￨NN￨O￨- versus￨L￨CC￨O￨A ASPs￨U￨NNS￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- remain￨L￨VBP￨O￨- unclear￨L￨JJ￨O￨- .￨L￨.￨O￨- +Anti-staphylococcal￨U￨JJ￨O￨- penicillins￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ASPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- recommended￨L￨VBN￨O￨A as￨L￨IN￨O￨- first-line￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- in￨L￨IN￨O￨- methicillin-susceptible￨L￨JJ￨O￨- Staphylococcus￨U￨FW￨MISC￨- aureus￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- MSSA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- bacteremia￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- setting￨L￨NN￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- choose￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- curing￨L￨NN￨O￨A rates￨L￨NNS￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- degree-based￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- plus￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- selected￨L￨VBN￨O￨- curing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- per-unit￨L￨JJ￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- curing￨L￨VBG￨O￨A rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- high￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- true￨L￨JJ￨O￨- expectation￨L￨NN￨O￨- minimizers￨L￨NNS￨O￨- choose￨L￨VB￨O￨- the￨L￨DT￨O￨- curing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- zero￨L￨CD￨NUMBER￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- curing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- nonzero￨L￨NN￨O￨- under￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- probability￨L￨NN￨O￨- weighting￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- pairwise-type￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- weighted￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- solution￨L￨NN￨O￨- than￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- weighted￨L￨JJ￨O￨A susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- proximity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- associated￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- diffusive￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- weighted￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- shed￨L￨VBD￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- validity￨L￨NN￨O￨- of￨L￨IN￨O￨- mean-field￨L￨JJ￨O￨- theory￨L￨NN￨O￨- on￨L￨IN￨O￨- weighted￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Experimental￨U￨JJ￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A prevalence￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- largely￨L￨RB￨O￨- promoted￨L￨VBN￨O￨- when￨L￨WRB￨O￨- strong￨L￨JJ￨O￨- ties￨L￨NNS￨O￨- are￨L￨VBP￨O￨- favored￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Feedback￨U￨NN￨O￨- between￨L￨IN￨O￨- behavioral￨L￨JJ￨O￨- adaptation￨L￨NN￨O￨A and￨L￨CC￨O￨- prevalence￨L￨NN￨O￨- creates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- combined￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- damped￨L￨VBN￨O￨- and￨L￨CC￨O￨- sustained￨L￨VBN￨O￨- oscillations￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- bistability￨L￨NN￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨IN￨O￨- neglect￨L￨NN￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- or￨L￨CC￨O￨- only￨L￨RB￨O￨- consider￨L￨VB￨O￨- behavior￨L￨NN￨O￨- adaptation￨L￨NN￨O￨A by￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- yield￨L￨VB￨O￨- misleading￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- or￨L￨CC￨O￨- omit￨L￨VB￨O￨- significant￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- trajectory￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- extinction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- for￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- where￨L￨WRB￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- behavior￨L￨NN￨O￨- adaptation￨L￨NN￨O￨A driving￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- downward￨L￨JJ￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- conversely￨L￨RB￨O￨- endemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- for￨L￨IN￨O￨- arbitrarily￨L￨RB￨O￨- low￨L￨JJ￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- possible￨L￨JJ￨O￨- if￨L￨IN￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- sufficiently￨L￨RB￨O￨- high￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- STI￨U￨NNP￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- prophylactic￨L￨NN￨O￨A use￨L￨VBP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- links￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Susceptible-Infectious-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- evolutionary￨L￨JJ￨O￨- game￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- combined￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- protective￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- by￨L￨IN￨O￨- both￨L￨CC￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- closure￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨JJS￨O￨- basic￨L￨JJ￨O￨- or￨L￨CC￨O￨- fundamental￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- on￨L￨IN￨O￨- homogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- approximately￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- degree￨L￨NN￨O￨- n.￨L￨NN￨O￨- Hence￨U￨RB￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- for￨L￨IN￨O￨- graphs￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- bimodal￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- or￨L￨CC￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- super￨L￨JJ￨O￨- compact￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- closure￨L￨NN￨O￨- relation￨L￨NN￨O￨- that￨L￨WDT￨O￨- involves￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- and￨L￨CC￨ORDINAL￨- third￨L￨JJ￨ORDINAL￨- moments￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- the￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- super￨L￨JJ￨O￨- compact￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- 4￨L￨CD￨NUMBER￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- describing￨L￨VBG￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- heterogenous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- consist￨L￨VBP￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- N￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- N￨U￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +=￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ∂￨L￨CD￨NUMBER￨- U￨U￨NNP￨O￨- ∂￨L￨NNP￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ∞￨L￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Heston￨U￨NNP￨PERSON￨- conjectures￨L￨NNS￨O￨- a￨L￨DT￨O￨- solution￨L￨NN￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Black-Scholes￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- U￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- ,￨L￨,￨O￨- K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- ·￨L￨NN￨O￨- R1￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- K￨U￨NNP￨O￨- ·￨L￨NN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ·￨L￨SYM￨O￨- R2￨U￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- following￨L￨VBG￨O￨- semi-explicit￨L￨JJ￨O￨- formula￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- price￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- European￨U￨JJ￨NATIONALITY￨- Option￨U￨NN￨MISC￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- U￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- x￨L￨CC￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- ,￨L￨,￨O￨- ln￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- x￨L￨CC￨O￨- ·￨L￨SYM￨O￨- R1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- ;￨L￨:￨O￨- ln￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- ln￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ·￨L￨NN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ·￨L￨SYM￨O￨- R2￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- ;￨L￨:￨O￨- ln￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- x￨L￨NN￨O￨- =￨L￨JJ￨O￨- ln￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- =￨L￨JJ￨O￨- T￨U￨NN￨O￨- −￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- function￨L￨NN￨O￨- Rj￨U￨NN￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Rj￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- ;￨L￨:￨O￨- ln￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- π￨L￨NN￨O￨- Z￨U￨NN￨O￨- ∞￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Re￨U￨NNP￨O￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- iφ￨L￨NN￨O￨- ln￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- fj￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- ,￨L￨,￨O￨- φ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- iφ￨L￨NN￨O￨- dφ￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- fj￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- ;￨L￨:￨O￨- φ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- eC￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- ;￨L￨:￨O￨- φ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- D￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- ;￨L￨:￨O￨- φ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- iφx￨L￨NN￨O￨- ,￨L￨,￨O￨- C￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- ;￨L￨:￨O￨- φ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- r0φiτ￨L￨NN￨O￨- +￨L￨CC￨O￨- σ2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- bj￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ρσφi￨L￨NN￨O￨- +￨L￨CC￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- τ￨L￨NN￨O￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ln￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- gedτ￨L￨NN￨O￨- a￨L￨DT￨O￨- bj￨L￨NN￨O￨- −￨L￨NN￨O￨- ρσφi￨L￨NN￨O￨- +￨L￨CC￨O￨- d￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- gedτ￨L￨NN￨O￨- ,￨L￨,￨O￨- σ2￨L￨NN￨O￨- d￨L￨NN￨O￨- =￨L￨JJ￨O￨- q￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ρσφi￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- bj￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- σ2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2ζj￨L￨JJ￨O￨- φi￨L￨NN￨O￨- −￨L￨NN￨O￨- φ2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- =￨L￨JJ￨O￨- κθ￨L￨NN￨O￨- ,￨L￨,￨O￨- b1￨L￨NN￨O￨- =￨L￨JJ￨O￨- κ￨L￨NN￨O￨- +￨L￨CC￨O￨- λ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ρσ￨L￨NN￨O￨- ,￨L￨,￨O￨- b2￨L￨NN￨O￨- =￨L￨JJ￨O￨- κ￨L￨NN￨O￨- +￨L￨CC￨O￨- λ￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- no￨L￨DT￨O￨- arbitrage￨L￨NN￨O￨- arguments￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- claim￨L￨NN￨O￨- must￨L￨MD￨O￨- satisfy￨L￨VB￨O￨A :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- vS￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ∂￨L￨CD￨NUMBER￨- 2U￨L￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- ρσvS￨L￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- 2U￨L￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- σ2￨L￨NN￨O￨- v￨L￨LS￨O￨- ∂￨L￨SYM￨O￨- 2U￨L￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- v2￨L￨NN￨O￨- +￨L￨CC￨O￨- r0S￨L￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- U￨U￨NNP￨O￨- ∂￨L￨NNP￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- κ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- θ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ∂￨L￨CD￨NUMBER￨- U￨U￨NNP￨O￨- ∂￨L￨NNP￨O￨- v￨L￨LS￨O￨- −￨L￨SYM￨O￨- r0U￨L￨NN￨O￨- +￨L￨CC￨O￨- ∂￨L￨CD￨NUMBER￨- U￨U￨NNP￨O￨- ∂￨L￨NNP￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- ¯￨L￨SYM￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- ¯￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- v￨L￨LS￨O￨- and￨L￨CC￨O￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- price￨L￨NN￨O￨- of￨L￨IN￨O￨- volatility￨L￨NN￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Heston￨U￨NNP￨ORGANIZATION￨- SV￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- We￨U￨PRP￨O￨- recall￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- Heston￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- µ￨L￨NN￨O￨- ¯￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A +￨L￨CC￨O￨- p￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ¯￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- ¯￨L￨SYM￨O￨- z1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- κ￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- θ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ¯￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- +￨L￨CC￨O￨- σp￨L￨NN￨O￨- ¯￨L￨NN￨O￨- v￨L￨LS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- z2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- ¯￨L￨SYM￨O￨- z1￨L￨NN￨O￨- and￨L￨CC￨O￨- ¯￨L￨NN￨O￨- z2￨L￨NN￨O￨- are￨L￨VBP￨O￨- Wiener￨U￨NNP￨PERSON￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- without￨L￨IN￨O￨- demography￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨A population￨L￨NN￨O￨A remains￨L￨VBZ￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- we￨L￨PRP￨O￨- choose￨L￨VB￨O￨- N￨U￨NN￨O￨- as￨L￨IN￨O￨- this￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- components￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- Z￨U￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- proportions￨L￨NNS￨O￨- of￨L￨IN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- Z￨U￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨CC￨O￨- i￨L￨FW￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- each￨L￨DT￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- k/N￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- k￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- +￨L￨CC￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- Pd￨U￨NN￨O￨- if￨L￨IN￨O￨- Z￨U￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨CC￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- i￨L￨FW￨O￨- –￨L￨:￨O￨- th￨L￨DT￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- Z￨U￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- i￨L￨FW￨O￨- ≤￨L￨FW￨O￨- d￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Set-up￨U￨NN￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- A￨U￨NN￨O￨- ⊂￨L￨CD￨NUMBER￨- Rd￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- whose￨L￨WP$￨O￨- properties￨L￨NNS￨O￨- we￨L￨PRP￨O￨- specify￨L￨VBP￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- define￨L￨VB￨O￨A the￨L￨DT￨O￨- grids￨L￨NNS￨O￨- Zd￨U￨NN￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- x￨L￨CC￨O￨- ∈￨L￨SYM￨O￨- Rd￨U￨NNP￨O￨- |￨L￨SYM￨O￨- xi￨L￨NN￨O￨- =￨L￨JJ￨O￨- j￨L￨NN￨O￨- /￨L￨:￨O￨- N￨U￨NN￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- j￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- AN￨U￨DT￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- As￨U￨IN￨O￨- Vx￨U￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sometimes￨L￨RB￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- x￨L￨NN￨O￨- or￨L￨CC￨O￨- Vx￨U￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- =￨L￨JJ￨O￨- ∅￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- define￨L￨VBP￨O￨- for￨L￨IN￨O￨- y￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Rd￨U￨NN￨O￨- ,￨L￨,￨O￨- ˜Vy￨L￨NN￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- nµ￨L￨NN￨O￨- ∈￨L￨NN￨O￨- Rd￨U￨NN￨O￨- +￨L￨CC￨O￨- |￨L￨SYM￨O￨- y￨L￨NN￨O￨- =￨L￨JJ￨O￨- Xj￨U￨NN￨O￨- µj￨L￨NN￨O￨- hj￨L￨NN￨O￨- o￨L￨NN￨O￨- We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- cone￨L￨NN￨O￨- spanned￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- finite￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- vj￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- j￨L￨NN￨O￨- C￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- vj￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- nv￨L￨NN￨O￨- =￨L￨JJ￨O￨- Xj￨U￨NN￨O￨- αj￨L￨NN￨O￨- vj￨L￨NN￨O￨- |￨L￨SYM￨O￨- αj￨L￨FW￨O￨- ≥￨L￨FW￨O￨- 0o￨L￨FW￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- components￨L￨NNS￨O￨- of￨L￨IN￨O￨- Z￨U￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- can￨L￨MD￨O￨- still￨L￨RB￨O￨- continue￨L￨VB￨O￨- to￨L￨TO￨O￨- define￨L￨VB￨O￨A Z￨U￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨CC￨O￨- provided￨L￨VBN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- i￨L￨FW￨O￨- ≤￨L￨FW￨O￨- d￨L￨NN￨O￨- and￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- j￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- xi￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ⇒￨L￨CD￨NUMBER￨- βj￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- xi￨L￨VB￨O￨- ≤￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ⇒￨L￨NN￨O￨- βj￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- we￨L￨PRP￨O￨- shall￨L￨MD￨O￨A prove￨L￨VB￨O￨- below￨L￨RB￨O￨- ,￨L￨,￨O￨- Z￨U￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨CC￨O￨- →￨L￨CD￨NUMBER￨- Y￨U￨NN￨O￨- x￨L￨NN￨O￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Y￨U￨NN￨O￨- x￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ODE￨U￨NNP￨O￨- Y￨U￨NN￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- Y￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- Z￨U￨NN￨O￨- t￨L￨NN￨O￨- b￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Y￨U￨NN￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ds￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- t￨L￨NN￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- b￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- kXj￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- βj￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- hj￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Martin-L￨U￨NNP￨O￨- ¨￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- also￨L￨RB￨O￨- Aldous￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- S￨U￨NN￨O￨- =￨L￨JJ￨O￨- SN￨U￨NN￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- interesting￨L￨JJ￨O￨- and￨L￨CC￨O￨- nontrivial￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- :￨L￨:￨O￨- If￨U￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- X0￨U￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- bN￨L￨NN￨O￨- 1/3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- SN￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- defined￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- times￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- limit￨L￨NN￨O￨- distribution￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- SN￨U￨NNP￨O￨- /￨L￨:￨O￨- N￨U￨NN￨O￨- 2/3￨L￨CD￨NUMBER￨- D￨U￨NN￨O￨- −￨L￨SYM￨O￨- →￨L￨SYM￨O￨- T￨U￨NN￨O￨- ∗￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- where￨L￨WRB￨O￨- T￨U￨NN￨O￨- ∗￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- passage￨L￨NN￨O￨A time￨L￨NN￨O￨- of￨L￨IN￨O￨- W￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- t2/2￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- W￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Wiener￨U￨NNP￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- scaling￨L￨NN￨O￨- law￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- stochastic￨L￨JJ￨O￨- epiIf￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- √￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- when￨L￨WRB￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- number￨L￨NN￨O￨- currently￨L￨RB￨DATE￨- infected￨L￨VBN￨O￨- are￨L￨VBP￨O￨- both￨L￨DT￨O￨- scaled￨L￨VBN￨O￨- by￨L￨IN￨O￨- √￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- process￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A process￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Feller￨U￨NNP￨O￨- diffusion￨L￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- drift￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- either￨L￨CC￨O￨- sub-or￨L￨JJ￨O￨- supercritical￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- large-population￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨A is￨L￨VBZ￨O￨- reasonably￨L￨RB￨O￨- well-understood￨L￨JJ￨O￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- subcritical￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- stochastically￨L￨RB￨O￨- dominated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- subcritical￨L￨JJ￨O￨- Galton-Watson￨U￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- supercritical￨L￨JJ￨O￨- case￨L￨NN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- may￨L￨MD￨O￨- become￨L￨VB￨O￨- endemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Norden￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- Kryscio￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Lef￨U￨NNP￨O￨- `￨L￨``￨O￨- evre￨L￨FW￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- four￨L￨CD￨NUMBER￨- dimensional￨L￨JJ￨O￨- ecoepidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- prey￨L￨NN￨O￨A ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccinated￨L￨VBN￨O￨- prey￨L￨NN￨O￨- and￨L￨CC￨O￨- predator￨L￨NN￨O￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- .￨L￨.￨O￨- +Chattopadhyay￨U￨NNP￨O￨- and￨L￨CC￨O￨- Orino￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- proposed￨L￨VBD￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBD￨O￨- a￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- dimensional￨L￨JJ￨O￨- predator-prey￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- prey￨L￨NN￨O￨A population￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- ob￨L￨NN￨O￨- jective￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- spatial￨L￨JJ￨O￨A epidemics￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- formulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- partial￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- domains￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- ma￨L￨NN￨O￨- jor￨L￨NN￨O￨- difficulty￨L￨NN￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- spatial￨L￨JJ￨O￨A variability￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- in￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- contexts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Deterministic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨A spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- geographical￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨O￨A epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- Puerto￨U￨NNP￨LOCATION￨- Rico￨U￨NNP￨CRIMINAL_CHARGE￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨A ,￨L￨,￨O￨- deterministic￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- successful￨L￨JJ￨O￨- ly￨L￨RB￨O￨- obtained￨L￨VBN￨O￨- an￨L￨DT￨O￨- exact￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Mckendrick￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- coupled￨L￨VBN￨O￨- nonlinear￨L￨JJ￨O￨- differential￨L￨JJ￨O￨A equations￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- dilemma￨L￨NN￨O￨- with￨L￨IN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨A is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- sometimes￨L￨RB￨O￨- even￨L￨RB￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- with￨L￨IN￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- first-order￨L￨NN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- non-integrable￨L￨JJ￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨A has￨L￨VBZ￨O￨- grown￨L￨VBN￨O￨- rapidly￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- having￨L￨VBG￨O￨- been￨L￨VBN￨O￨- formulated￨L￨VBN￨O￨- and￨L￨CC￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- -￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- biology￨L￨NN￨O￨- named￨L￨VBN￨O￨- as￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- epidemiology￨L￨NN￨O￨A many￨L￨JJ￨O￨- researchers￨L￨NNS￨O￨- believe￨L￨VBP￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- hard￨L￨JJ￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- an￨L￨DT￨O￨- exact￨L￨JJ￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- verified￨L￨VBD￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- parameters￨L￨NNS￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- rubella￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- prevaccine￨L￨NN￨O￨- era￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- proposed￨L￨VBN￨O￨- DA￨U￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- performed￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- two￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- rubella￨L￨NN￨O￨A .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- a￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- spatial￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A having￨L￨VBG￨O￨- only￨L￨RB￨O￨- local￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- lattice￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- PA￨U￨NN￨STATE_OR_PROVINCE￨- scheme￨L￨NN￨O￨- to￨L￨TO￨O￨- approach￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- is￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- some￨L￨DT￨O￨- details￨L￨NNS￨O￨- are￨L￨VBP￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- section￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transfer￨L￨NN￨O￨- rates￨L￨NNS￨O￨- among￨L￨IN￨O￨- classes￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- make￨L￨VBP￨O￨- a￨L￨DT￨O￨- decomposition￨L￨NN￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- prG￨L￨NN￨O￨- +￨L￨CC￨O￨- qrL￨L￨NN￨O￨- being￨L￨VBG￨O￨- q￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- and￨L￨CC￨O￨- rG￨L￨NN￨O￨- ,￨L￨,￨O￨- rL￨L￨NN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- that￨L￨WDT￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- global￨L￨JJ￨O￨- an￨L￨DT￨O￨- local￨L￨JJ￨O￨- infective￨L￨JJ￨O￨A contacts￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- studied￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- agreement￨L￨NN￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- SM￨U￨NN￨O￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- DA￨U￨NN￨O￨- was￨L￨VBD￨O￨- very￨L￨RB￨O￨- good￨L￨JJ￨O￨- .￨L￨.￨O￨- +ir￨L￨NN￨O￨- 2Assistant￨L￨JJ￨O￨- Professor￨U￨NNP￨TITLE￨- of￨L￨IN￨O￨- Software￨U￨NNP￨O￨- Engineering￨U￨NNP￨O￨- Faculty￨U￨NNP￨O￨- of￨L￨IN￨O￨- Electrical￨U￨JJ￨O￨- and￨L￨CC￨O￨- Computer￨U￨NNP￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Tabriz￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Tabriz￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Iran￨U￨NNP￨COUNTRY￨- pashazadeh￨L￨NN￨O￨- @￨L￨SYM￨O￨- ir￨L￨FW￨O￨- ABSTRACT￨U￨NN￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- applied￨L￨VBD￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- manoeuvring￨L￨VBG￨O￨- targets￨L￨NNS￨O￨- in￨L￨IN￨O￨- SIR￨U￨NN￨O￨- particle￨L￨NN￨O￨A filter￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- improving￨L￨VBG￨O￨- tracking￨L￨NN￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- manoeuvring￨L￨NN￨O￨- targets￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- proposed￨L￨VBN￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- color￨L￨NN￨O￨- distribution￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- changes￨L￨NNS￨O￨- of￨L￨IN￨O￨- target￨L￨NN￨O￨A 's￨L￨POS￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- approach￨L￨NN￨O￨- was￨L￨VBD￨O￨- also￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- examined￨L￨VBN￨O￨- ,￨L￨,￨O￨- parameterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- contact￨L￨NN￨O￨- trials￨L￨NNS￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- range￨L￨VBP￨O￨- from￨L￨IN￨O￨- contact￨L￨NN￨O￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- contagion￨L￨NN￨O￨- expands￨L￨VBZ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- neighbor￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- reactive￨L￨JJ￨O￨A processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- effectively￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- all￨L￨PDT￨O￨- its￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- to￨L￨TO￨O￨- expand￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- help￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- frameworks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨A process￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- repeatedly￨L￨RB￨O￨- emphasized￨L￨VBN￨O￨- ,￨L￨,￨O￨- yielding￨L￨VBG￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- exponentially￨L￨RB￨O￨- bounded￨L￨VBN￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- vanishing￨L￨VBG￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- infinite￨L￨NN￨O￨- uncorrelated￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- power-law￨L￨NN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- answer￨L￨VB￨O￨- this￨L￨DT￨O￨- question￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- both￨L￨CC￨O￨- an￨L￨DT￨O￨- upper￨L￨JJ￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infective￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infective-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- :￨L￨:￨O￨- reactive￨L￨JJ￨O￨A and￨L￨CC￨O￨- contact￨L￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- such￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- inhomogeneous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probabilities￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- with￨L￨IN￨O￨- prescribed￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- where￨L￨WRB￨O￨- model￨L￨NN￨TITLE￨- ’s￨L￨POS￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- for￨L￨IN￨O￨- i.i.d.￨L￨NNP￨O￨- weights￨L￨NNS￨O￨A and￨L￨CC￨O￨- for￨L￨IN￨O￨- weights￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degrees￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- influence￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- on￨L￨IN￨O￨- microscopic￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- neighboring￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- non-social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- weights￨L￨NNS￨O￨- often￨L￨RB￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- functions￨L￨NNS￨O￨- performed￨L￨VBN￨O￨- by￨L￨IN￨O￨- edges￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- traffic￨L￨NN￨O￨- flowing￨L￨NN￨O￨- along￨L￨IN￨O￨- connections￨L￨NNS￨O￨- in￨L￨IN￨O￨- world-wide￨L￨JJ￨O￨- airport￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- joint￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- coauthors￨L￨NNS￨O￨- in￨L￨IN￨O￨- scientist￨L￨NN￨TITLE￨- collaboration￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- synapses￨L￨NNS￨O￨- and￨L￨CC￨O￨- gap￨L￨NN￨O￨- junctions￨L￨NNS￨O￨- in￨L￨IN￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- carbon￨L￨NN￨O￨- flow￨L￨NN￨O￨- between￨L￨IN￨O￨- species￨L￨NNS￨O￨- in￨L￨IN￨O￨- food￨L￨NN￨O￨- webs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- steady-state￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- density￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- speed￨L￨NN￨O￨A are￨L￨VBP￨O￨- respectively￨L￨RB￨O￨- optimized￨L￨VBN￨O￨- by￨L￨IN￨O￨- adjusting￨L￨VBG￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- edge￨L￨NN￨O￨- ’s￨L￨POS￨O￨- strength￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨NN￨O￨- ability￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- weighted￨L￨JJ￨O￨A scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- results￨L￨VBZ￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- homogeneous￨L￨JJ￨O￨- weight￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- quickly￨L￨RB￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- on￨L￨IN￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +Conclusions/Significance￨U￨NNP￨O￨- :￨L￨:￨O￨- Experimental￨U￨JJ￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- strong￨L￨JJ￨O￨- and￨L￨CC￨O￨- weak￨L￨JJ￨O￨- ties￨L￨NNS￨O￨A play￨L￨VBP￨O￨- distinguishable￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- former￨L￨JJ￨O￨- enlarge￨L￨VB￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- density￨L￨NN￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- fasten￨L￨NN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Experiments￨U￨NNS￨O￨- on￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- density￨L￨NN￨O￨- is￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- when￨L￨WRB￨O￨- strong￨L￨JJ￨O￨- ties￨L￨NNS￨O￨A are￨L￨VBP￨O￨- favored￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- is￨L￨VBZ￨O￨- enhanced￨L￨VBN￨O￨- when￨L￨WRB￨O￨- weak￨L￨JJ￨O￨- ties￨L￨NNS￨O￨- are￨L￨VBP￨O￨- favored￨L￨VBN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infectious-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- here￨L￨RB￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- propagator￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- realistic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- a￨L￨DT￨O￨- varying￨L￨VBG￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- per￨L￨IN￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- time￨L￨NN￨O￨- resolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A network￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- wide￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- regime￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- representing￨L￨VBG￨O￨- a￨L￨DT￨O￨- predictor￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- vulnerability￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- two￨L￨CD￨NUMBER￨- temporal￨L￨JJ￨O￨A network￨L￨NN￨O￨A models￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- dataset￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- threshold￨L￨NN￨O￨A depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- its￨L￨PRP$￨O￨- time￨L￨NN￨O￨- variation￨L￨NN￨O￨- .￨L￨.￨O￨- +Aggregating￨U￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A network￨L￨NN￨O￨A rapidly￨L￨RB￨O￨- deteriorates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- for￨L￨IN￨O￨- slow￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- once￨L￨IN￨DATE￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- preserved￨L￨VBN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- notions￨L￨NNS￨O￨- from￨L￨IN￨O￨- positive￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- novel￨L￨JJ￨O￨- proofs￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A asymptotic￨L￨JJ￨O￨A stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- cases￨L￨NNS￨O￨- over￨L￨IN￨O￨- strongly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- quantity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- threshold￨L￨NN￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- value￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- curing￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨A topology￨L￨NN￨O￨A ,￨L￨,￨O￨- determines￨L￨VBZ￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- will￨L￨MD￨O￨- converge￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨A properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- so-called￨L￨JJ￨O￨- the￨L￨DT￨O￨- n-intertwined￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- over￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- directed￨L￨JJ￨O￨- network￨L￨NN￨O￨- topologies￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- over￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨A and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parametric￨L￨JJ￨O￨- study￨L￨NN￨O￨- demonstrates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- upon￨L￨IN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- concurrent￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- made￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- per￨L￨IN￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- results￨L￨VBZ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- such￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- critical￨L￨JJ￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- minimum￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- made￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A below￨L￨IN￨O￨- which￨L￨WDT￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- method￨L￨NN￨O￨A based￨L￨VBN￨O￨A upon￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- edge￨L￨NN￨O￨A adaptation￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Hebbian￨U￨JJ￨MISC￨- rule￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- evolved￨L￨VBN￨O￨- in￨L￨IN￨O￨- accordance￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- leads￨L￨VBZ￨O￨- an￨L￨DT￨O￨- initially￨L￨RB￨O￨- unbalanced￨L￨JJ￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- structurally￨L￨RB￨O￨- balanced￨L￨JJ￨O￨- state￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Kertesz3￨U￨NN￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- Shahid￨U￨NNP￨ORGANIZATION￨- Beheshti￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- G.C.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2Physics￨L￨NNP￨O￨- Department￨U￨NNP￨O￨- ,￨L￨,￨O￨- 3Center￨L￨NNP￨O￨- for￨L￨IN￨O￨- Network￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- Central￨U￨NNP￨ORGANIZATION￨- European￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- H-1051￨U￨NN￨O￨- ,￨L￨,￨O￨- Budapest￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Hungary￨U￨NNP￨COUNTRY￨- 4￨L￨CD￨NUMBER￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Budapest￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Economics￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- H-1111￨U￨NN￨O￨- ,￨L￨,￨O￨- Budapest￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Hungary￨U￨NNP￨COUNTRY￨- in￨L￨IN￨O￨- Basic￨U￨NNP￨O￨- Sciences￨U￨NNPS￨O￨- ,￨L￨,￨O￨- 45195-1159￨L￨CD￨NUMBER￨- Zanjan￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Advanced￨U￨NNP￨ORGANIZATION￨- Studies￨U￨NNPS￨ORGANIZATION￨- Iran￨U￨NNP￨ORGANIZATION￨- Iran￨U￨NNP￨ORGANIZATION￨- Most￨U￨JJS￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- as￨L￨IN￨O￨- obtained￨L￨VBN￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- contagion￨L￨NN￨O￨- ,￨L￨,￨O￨- though￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- influences￨L￨NNS￨O￨A people￨L￨NNS￨O￨- ’s￨L￨POS￨O￨- willingnes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Dated￨U￨VBN￨O￨- :￨L￨:￨O￨- April￨U￨NNP￨DATE￨- 16￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 7￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- M￨U￨NN￨O￨- 9￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- h￨L￨NN￨O￨- p￨L￨NN￨O￨- -￨L￨:￨O￨- c￨L￨NN￨O￨- o￨L￨NN￨O￨- s￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- changes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- runs￨L￨VBZ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- signed￨L￨VBN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- edge￨L￨NN￨O￨A signs￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨A of￨L￨IN￨O￨- opinions￨L￨NNS￨O￨- over￨L￨IN￨O￨- signed￨L￨VBN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Spatial￨U￨JJ￨O￨- correlations￨L￨NNS￨O￨A in￨L￨IN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- HENRYK￨U￨NNP￨O￨- FUK￨U￨NNP￨O￨- ´S￨L￨POS￨O￨- †￨L￨SYM￨O￨- RYAN￨U￨NNP￨O￨- DUCHESNE￨U￨NNP￨O￨- †￨L￨SYM￨O￨- ANNA￨U￨NNP￨O￨- T.￨U￨NNP￨O￨- Key-Words￨U￨NNP￨O￨- :￨L￨:￨O￨- -￨L￨:￨O￨- Epidemic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- lattice￨L￨NN￨O￨- gas￨L￨NN￨O￨- automata￨L￨NN￨O￨- ,￨L￨,￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- main￨L￨JJ￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- influenza￨L￨NN￨O￨A pandemics￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- reveal￨L￨VB￨O￨- spatial￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- strong￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨O￨- times￨L￨NNS￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨O￨- is￨L￨VBZ￨O￨- statistically￨L￨RB￨O￨- uniform￨L￨JJ￨O￨- in￨L￨IN￨O￨- space￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- possible￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- for￨L￨IN￨O￨- destruction￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨A correlations￨L￨NNS￨O￨- ,￨L￨,￨O￨- trying￨L￨VBG￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- similar￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- as￨L￨IN￨O￨- those￨L￨DT￨O￨- reported￨L￨VBN￨O￨- by￨L￨IN￨O￨- Bonabeau￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- examined￨L￨VBD￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨A correlation￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infl￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- high-quality￨L￨JJ￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- practitioners￨L￨NNS￨O￨- in￨L￨IN￨O￨- France￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- will￨L￨MD￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- |￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- |￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- x￨L￨CC￨O￨- ∈￨L￨SYM￨O￨- Rn￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- problem￨L￨NN￨O￨- :￨L￨:￨O￨- St￨U￨NNP￨O￨- −￨L￨CD￨NUMBER￨- d1￨L￨NN￨O￨- ∆￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- =￨L￨JJ￨O￨- b￨L￨NN￨O￨- −￨L￨SYM￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µ1S￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- It￨U￨PRP￨O￨- −￨L￨VBD￨O￨- d2￨L￨NN￨O￨- ∆￨L￨NN￨O￨- I￨U￨NN￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- µ2￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- αI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Rt￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- d3￨L￨NN￨O￨- ∆￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- αI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µ3R￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Sr￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- Ir￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- Rr￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- h￨L￨NN￨O￨- ′￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- µIr￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- h0￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- I0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- R0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- r￨L￨NN￨O￨- <￨L￨JJR￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- r￨L￨NN￨O￨- <￨L￨JJR￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- △￨L￨SYM￨O￨- w￨L￨NN￨O￨- =￨L￨JJ￨O￨- wrr￨L￨NN￨O￨- +￨L￨CC￨O￨- n￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- wr￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- moving￨L￨VBG￨O￨- boundary￨L￨NN￨O￨A to￨L￨TO￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- ,￨L￨,￨O￨- h0￨L￨NN￨O￨- ,￨L￨,￨O￨- di￨L￨FW￨O￨- and￨L￨CC￨O￨- µ￨L￨FW￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- result￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- not￨L￨RB￨O￨- spread￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- area￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- radius￨L￨NN￨O￨A h0￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- small￨L￨JJ￨O￨- even￨L￨RB￨O￨- that￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- spread￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- area￨L￨NN￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- radius￨L￨NN￨O￨A h0￨L￨NN￨O￨- is￨L￨VBZ￨O￨- suitably￨L￨RB￨O￨- large￨L￨JJ￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- spread￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- area￨L￨NN￨O￨- if￨L￨IN￨O￨- h0￨L￨NN￨O￨- is￨L￨VBZ￨O￨- suitably￨L￨RB￨O￨- large￨L￨JJ￨O￨- ;￨L￨:￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- vanish￨L￨VB￨O￨- if￨L￨IN￨O￨- h0￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨A small￨L￨JJ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 1.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Ecologically￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- free￨L￨JJ￨O￨- boundary￨L￨NN￨O￨A r￨L￨NN￨O￨- =￨L￨JJ￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- primary￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- acts￨L￨VBZ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- slow￨L￨JJ￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- does￨L￨VBZ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- fast￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- a￨L￨DT￨O￨- dimension￨L￨NN￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- making￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- tractable￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- whose￨L￨WP$￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- demography￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- facilitates￨L￨VBZ￨O￨- individuals￨L￨NNS￨O￨- acquiring￨L￨VBG￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- secondary￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- opportunistic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨A parasite￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- falls￨L￨VBZ￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- syndemic￨L￨JJ￨O￨- :￨L￨:￨O￨- aggregation￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- some￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- that￨L￨WDT￨O￨- exacerbates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- negative￨L￨JJ￨O￨- health￨L￨NN￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- or￨L￨CC￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- situations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- either￨L￨CC￨O￨- acting￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- opportunistic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- or￨L￨CC￨O￨- recovery￨L￨NN￨O￨A rates￨L￨NNS￨O￨A or￨L￨CC￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- allow￨L￨VBP￨O￨- to￨L￨TO￨O￨- eradicate/promote￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- endemicity￨L￨NN￨O￨- .￨L￨.￨O￨- +0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 7￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- many￨L￨JJ￨O￨- incurable￨L￨JJ￨O￨- and￨L￨CC￨O￨- newly￨L￨RB￨O￨- emerging￨L￨VBG￨O￨- viral￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- HCV￨U￨NN￨O￨- ,￨L￨,￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨O￨- ,￨L￨,￨O￨- dengue￨L￨NN￨O￨- ,￨L￨,￨O￨- SARS￨U￨NNP￨O￨- or￨L￨CC￨O￨- Ebola￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- mention￨L￨VB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- knowing￨L￨VBG￨O￨- more￨L￨JJR￨O￨- about￨L￨IN￨O￨- possible￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- viruses￨L￨NNS￨O￨- can￨L￨MD￨O￨- exist￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨A population￨L￨NN￨O￨- .￨L￨.￨O￨- +Even￨U￨RB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- classification￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- being￨L￨VBG￨O￨- either￨L￨CC￨O￨- A￨U￨DT￨O￨- :￨L￨:￨O￨- medium￨L￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- :￨L￨:￨O￨- high￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- C￨U￨NN￨O￨- :￨L￨:￨O￨- low￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- host-contact￨L￨JJ￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- mode￨L￨NN￨O￨A are￨L￨VBP￨O￨- revealed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- .￨L￨.￨O￨- +Besides￨U￨IN￨O￨- structural￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host-contact￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- parameters/concepts￨L￨NNS￨O￨- appear￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- key￨L￨JJ￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infectiousness￨L￨NN￨O￨- during￨L￨IN￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- encode￨L￨VBP￨O￨- the￨L￨DT￨O￨- mode￨L￨NN￨O￨A of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- third￨L￨JJ￨ORDINAL￨- the￨L￨DT￨O￨- immunity￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- pair￨L￨NN￨O￨A occur￨L￨VBP￨O￨- at￨L￨IN￨O￨- specific￨L￨JJ￨O￨- time￨L￨NN￨O￨- stamps￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- time￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- could￨L￨MD￨O￨- possibly￨L￨RB￨O￨- propagate￨L￨VB￨O￨- only￨L￨RB￨O￨- through￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- links￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- backbone￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- pair￨L￨NN￨O￨A indicates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- likely￨L￨JJ￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- pair￨L￨NN￨O￨- appear￨L￨VBP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- trajectory￨L￨NN￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- backbone￨L￨NN￨O￨- GB￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- →￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- equals￨L￨VBZ￨O￨- the￨L￨DT￨O￨- integrated￨L￨VBN￨O￨- weighted￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- pair￨L￨NN￨O￨A counts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- in￨L￨IN￨O￨- between￨L￨IN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- construction￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- information￨L￨NN￨O￨A diffusion￨L￨NN￨O￨A backbone￨L￨NN￨O￨- GB￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- spreading￨L￨VBG￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- β￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- Hi￨U￨UH￨O￨- denote￨L￨VBP￨O￨- a￨L￨DT￨O￨- nonnegative￨L￨JJ￨O￨- random￨L￨JJ￨O￨- variable￨L￨JJ￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- fading￨L￨JJ￨O￨- and￨L￨CC￨O￨- shadowing￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- signal￨L￨NN￨O￨- from￨L￨IN￨O￨- BS￨U￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- user￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Hi￨U￨UH￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- mutually￨L￨RB￨O￨- independent￨L￨JJ￨RELIGION￨- and￨L￨CC￨O￨- identically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- i.i.d.￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨A process￨L￨NN￨O￨A Φ￨U￨NN￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- Φ￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- Xi￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- N￨U￨NN￨O￨- denote￨L￨VBP￨O￨- a￨L￨DT￨O￨- point￨L￨NN￨O￨A process￨L￨NN￨O￨A on￨L￨IN￨O￨- Rd￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- mostly￨L￨RB￨O￨- d￨L￨NN￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- supposed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- points￨L￨NNS￨O￨- are￨L￨VBP￨O￨- ordered￨L￨VBN￨O￨- ∗￨L￨NNP￨O￨- Research￨U￨NNP￨O￨- supported￨L￨VBN￨O￨- by￨L￨IN￨O￨- JSPS￨U￨NN￨O￨- Grant-in-Aid￨U￨NN￨O￨- for￨L￨IN￨O￨- Scientific￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- C￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- 16K00030￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- point￨L￨NN￨O￨A process￨L￨NN￨O￨A Φ￨U￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- simple￨L￨JJ￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- in￨L￨IN￨O￨- probability￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- P-a.s.￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- stationary￨L￨JJ￨O￨- in￨L￨IN￨O￨- P￨U￨NN￨O￨- with￨L￨IN￨O￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- finite￨L￨JJ￨O￨- intensity￨L￨NN￨O￨- λ￨L￨NN￨O￨- =￨L￨JJ￨O￨- EΦ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NN￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- explores￨L￨VBZ￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨A prey￨L￨NN￨O￨A analogy￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Internet￨U￨NN￨MISC￨- and￨L￨CC￨O￨- presents￨L￨VBZ￨O￨- findings￨L￨NNS￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- diversification￨L￨NN￨O￨- effects￨L￨NNS￨O￨- network￨L￨NN￨O￨- resilience￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- will￨L￨MD￨O￨- look￨L￨VB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- utilizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- under￨L￨IN￨O￨- pinning￨L￨VBG￨O￨- of￨L￨IN￨O￨- predator￨L￨NN￨O￨A prey￨L￨NN￨O￨A models￨L￨NNS￨O￨- from￨L￨IN￨O￨- biological￨L￨JJ￨O￨- science￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- recent￨L￨JJ￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- complexity￨L￨NN￨O￨- and￨L￨CC￨O￨- mechanics￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- examining￨L￨VBG￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- network￨L￨NN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- modeling￨L￨NN￨O￨- cyberspace￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- predator￨L￨NN￨O￨A prey￨L￨NN￨O￨A landscape￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- PREDATOR￨U￨NNP￨O￨- PREY￨U￨NNP￨O￨- APPROACH￨U￨NNP￨O￨- TO￨U￨TO￨O￨- D￨U￨NNP￨O￨- IVERSITY￨U￨NNP￨O￨- BASED￨U￨NN￨O￨- D￨U￨NN￨O￨- EFENSES￨U￨NNP￨O￨- IN￨U￨IN￨O￨- HETEROGENEOUS￨U￨NNP￨O￨- NETWORKS￨U￨NNP￨O￨- Sean￨U￨NNP￨PERSON￨- P.￨U￨NNP￨PERSON￨- Often￨U￨RB￨PERSON￨- times￨L￨NNS￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- networks￨L￨NNS￨O￨- only￨L￨RB￨O￨- subsets￨L￨NNS￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨A are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- SI￨U￨NNP￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- heterogeneous￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- power￨L￨NN￨O￨A law￨L￨NN￨O￨A ,￨L￨,￨O￨- separable￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- AMS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- MOS￨U￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- sub￨L￨NN￨O￨- ject￨L￨NN￨O￨- classification￨L￨NN￨O￨- :￨L￨:￨O￨- 34C20￨L￨NN￨O￨- ,￨L￨,￨O￨- 34G20￨L￨NN￨O￨- ,￨L￨,￨O￨- 92D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- customary￨L￨JJ￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- transmission￨L￨NN￨O￨- function￨L￨NN￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- time￨L￨NN￨O￨- unit￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- main￨L￨JJ￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- note￨L￨NN￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨A law￨L￨NN￨O￨A transmission￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- heterogeneous￨L￨JJ￨O￨- susceptibles￨L￨NNS￨O￨- –￨L￨:￨O￨- infectives￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- assumption￨L￨NN￨O￨- .￨L￨.￨O￨- +Comparison￨U￨NN￨O￨- with￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- this￨L￨DT￨O￨- transmission￨L￨NN￨O￨- function￨L￨NN￨O￨A accurately￨L￨RB￨O￨- approximate￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- highly￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- constantly￨L￨RB￨O￨- argued￨L￨VBN￨O￨- that￨L￨IN￨O￨- such￨L￨JJ￨O￨- form￨L￨NN￨O￨- reflects￨L￨NNS￨O￨- population￨L￨NN￨O￨- heterogeneities￨L￨NNS￨O￨- including￨L￨VBG￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨- pattern￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- patchiness￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- function￨L￨NN￨O￨A itself￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- phenomenological￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- function￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- power￨L￨NN￨O￨A law￨L￨NN￨O￨A relationship￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- power-law￨L￨NN￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A ,￨L￨,￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- contact￨L￨NN￨O￨- pattern￨L￨NN￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- essential￨L￨JJ￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- five￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- but￨L￨CC￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- simulated￨L￨JJ￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- acute￨L￨JJ￨O￨- and￨L￨CC￨O￨- chronic￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A on￨L￨IN￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- SI￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨NNP￨O￨- –￨L￨:￨O￨- Infected￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- –￨L￨:￨O￨- Infected￨U￨JJ￨O￨- –￨L￨:￨O￨- Susceptible￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- ob￨L￨NN￨O￨- jective￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- observe￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨A structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A may￨L￨MD￨O￨- be￨L￨VB￨O￨- considerably￨L￨RB￨O￨- different￨L￨JJ￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- metapopulations￨L￨NNS￨O￨- D.￨U￨NNP￨O￨- G￨U￨NNP￨O￨- ´￨L￨POS￨O￨- omez-Garde￨L￨JJ￨O￨- ˜nes1￨L￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- †￨L￨CD￨NUMBER￨- 1Departamento￨L￨NN￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- de￨L￨FW￨O￨- la￨L￨FW￨O￨- Materia￨U￨FW￨ORGANIZATION￨- Condensada￨U￨FW￨ORGANIZATION￨- ,￨L￨,￨O￨- Universidad￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Zaragoza￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 50009￨L￨CD￨NUMBER￨- Zaragoza￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- 2GOTHAM￨L￨NNP￨O￨- Lab￨U￨NNP￨O￨- ,￨L￨,￨O￨- Instituto￨U￨NNP￨PERSON￨- de￨L￨IN￨PERSON￨- Biocomputaci￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- on￨L￨IN￨O￨- y￨L￨NN￨O￨- F´ısica￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Sistemas￨U￨NNP￨ORGANIZATION￨- Complejos￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- BIFI￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Universidad￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Zaragoza￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 50018￨L￨CD￨NUMBER￨- Zaragoza￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- 3Facultad￨L￨NNP￨O￨- de￨L￨IN￨O￨- Ingenier￨U￨NNP￨O￨- ´￨L￨POS￨O￨- ıa￨L￨NN￨O￨- Industrial￨U￨NNP￨O￨- ,￨L￨,￨O￨- Universidad￨U￨NNP￨PERSON￨- Pontificia￨U￨NNP￨PERSON￨- Bolivariana￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Medell￨U￨NNP￨ORGANIZATION￨- ´￨L￨POS￨O￨- ın￨L￨NN￨O￨- ,￨L￨,￨O￨- Colombia￨U￨NNP￨COUNTRY￨- 4Departament￨L￨NNP￨O￨- d’Enginyeria￨L￨NNP￨O￨- Inform￨U￨NNP￨O￨- `￨L￨``￨O￨- atica￨L￨FW￨O￨- i￨L￨FW￨O￨- Matem￨U￨FW￨O￨- `￨L￨``￨O￨- atiques￨L￨NNS￨O￨- ,￨L￨,￨O￨- Universitat￨U￨NNP￨PERSON￨- Rovira￨U￨NNP￨PERSON￨- i￨L￨FW￨O￨- Virgili￨U￨NNP￨O￨- ,￨L￨,￨O￨- 43007￨L￨CD￨NUMBER￨- Tarragona￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- February￨U￨NNP￨DATE￨- 13￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- structured￨L￨JJ￨O￨- metapopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- subjected￨L￨VBN￨O￨- to￨L￨TO￨O￨- recurrent￨L￨JJ￨O￨- mobility￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- composition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- metapopulations￨L￨NNS￨O￨- as￨L￨IN￨O￨- layers￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- would￨L￨MD￨O￨- correspond￨L￨VB￨O￨- to￨L￨TO￨O￨- geographical￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- and￨L￨CC￨O￨- layers￨L￨NNS￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A of￨L￨IN￨O￨- agents￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analyze￨L￨VBP￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Removed￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- framework￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- macroscopic￨L￨JJ￨O￨- and￨L￨CC￨O￨- microscopic￨L￨JJ￨O￨- indicators￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- extensive￨L￨JJ￨O￨- Monte￨U￨NNP￨O￨- Carlo￨U￨NNP￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- tackle￨L￨VB￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- has￨L￨VBZ￨O￨- relied￨L￨VBN￨O￨A on￨L￨IN￨O￨- reaction-diffusion￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- metapopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- first￨L￨VBP￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- ecology￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- periodically￨L￨RB￨O￨- forced￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- S￨U￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- µ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ′￨L￨VBP￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- µR￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ∗￨L￨SYM￨O￨- email￨L￨NN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- variants￨L￨NNS￨O￨- of￨L￨IN￨O￨- it￨L￨PRP￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- extensively￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- seasonally￨L￨RB￨O￨A recurrent￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- describe￨L￨VBP￨O￨- some￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- compute￨L￨VBP￨O￨- the￨L￨DT￨O￨- T￨U￨NN￨O￨- -￨L￨:￨O￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- T￨U￨NN￨O￨- -￨L￨:￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- subharmonic￨L￨JJ￨O￨- or￨L￨CC￨O￨- chaotic￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- Galerkin￨U￨NNP￨O￨- scheme￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- time-dependent￨L￨JJ￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- MC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- simulations￨L￨NNS￨O￨- at￨L￨IN￨O￨- criticality￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- block￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- two-dimensional￨L￨JJ￨O￨- lattices￨L￨NNS￨O￨- decreases￨L￨VBZ￨O￨- as￨L￨IN￨O￨- dilution￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- logarithmic￨L￨JJ￨O￨- dependence￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- finite￨L￨NN￨O￨- size￨L￨NN￨O￨- scaling￨L￨NN￨O￨- near￨L￨IN￨O￨- criticality￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- general￨L￨JJ￨TITLE￨- scaling￨L￨NN￨O￨- relation￨L￨NN￨O￨- :￨L￨:￨O￨- hi￨L￨UH￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- ∼￨L￨FW￨O￨- t￨L￨NN￨O￨- −￨L￨SYM￨O￨- β/νk￨L￨FW￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- ∆￨L￨CD￨NUMBER￨- t1/νk￨L￨NN￨O￨- ,￨L￨,￨O￨- L￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- td/z￨L￨NN￨O￨- ,￨L￨,￨O￨- d0￨L￨NN￨O￨- tβ/νk￨L￨NN￨O￨- +￨L￨CC￨O￨- θ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- Ld￨U￨NN￨O￨- PLd￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- j￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- σj￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- d￨L￨NN￨O￨- −￨L￨NN￨O￨- dimensional￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- h￨L￨NN￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- i￨L￨FW￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨NN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- evolutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +PACS￨U￨NNS￨O￨- numbers￨L￨NNS￨O￨- :￨L￨:￨O￨- 02.50.-r￨L￨NN￨O￨- ;￨L￨:￨O￨- 05.40.-a￨L￨NN￨O￨- ;￨L￨:￨O￨- 89.65.-s￨L￨NNS￨O￨- Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Refinement￨U￨NN￨O￨- of￨L￨IN￨O￨- critical￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- Models￨U￨NNS￨O￨- with￨L￨IN￨O￨- absorbent￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- Time-dependent￨U￨JJ￨O￨- Monte￨U￨NNP￨LOCATION￨- Carlo￨U￨NNP￨LOCATION￨- simulation￨L￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- paper￨L￨NN￨O￨- in￨L￨IN￨O￨- distributed￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- section￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- compute￨L￨VBP￨O￨- the￨L￨DT￨O￨- equilibria￨L￨NN￨O￨A points￨L￨NNS￨O￨- and￨L￨CC￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- existence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- real￨L￨JJ￨O￨- values￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- positivity￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- section￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibria￨L￨NNS￨O￨- points￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +Fraction￨U￨NN￨O￨- the￨L￨DT￨O￨- vertical￨L￨JJ￨O￨- m￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- newborns￨L￨NNS￨O￨- with￨L￨IN￨O￨- mothers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- classes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- vaccinated￨L￨VBN￨O￨- and￨L￨CC￨O￨- appeared￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- class￨L￨NN￨O￨A ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- fraction￨L￨NN￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- appears￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- function￨L￨NN￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- +￨L￨CC￨O￨- αI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- describing￨L￨VBG￨O￨- kI￨L￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nonnegative￨L￨JJ￨O￨- constant￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- extend￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- rate￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α2￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- β2￨L￨NN￨O￨- I￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- α2￨L￨NN￨O￨- ,￨L￨,￨O￨- β2￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- obtaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- dS￨L￨NN￨O￨- dt￨L￨NN￨O￨A dI￨L￨NN￨O￨- dt￨L￨NN￨O￨- dR￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- bm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- bS￨L￨NN￨O￨- +￨L￨CC￨O￨- pδI￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- αI￨L￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- qδ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- δ￨L￨NN￨O￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- αI￨L￨NN￨O￨- β2￨L￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α2￨L￨CD￨NUMBER￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- bR￨L￨NN￨O￨- +￨L￨CC￨O￨- bm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- β2￨L￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α2￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- 2-dimensional￨L￨JJ￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- −￨L￨CD￨NUMBER￨- bS￨L￨NN￨O￨- +￨L￨CC￨O￨- bm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- pδI￨L￨NN￨O￨- dS￨L￨NN￨O￨- dt￨L￨NN￨O￨A dI￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- αI￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- pδI￨L￨NN￨O￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- βS￨L￨NN￨O￨- I￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- αI￨L￨NN￨O￨- β2￨L￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α2￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- adding￨L￨VBG￨O￨- both￨L￨CC￨O￨- derivatives￨L￨NNS￨O￨- of￨L￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- get￨L￨VBP￨O￨- :￨L￨:￨O￨- d￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- bS￨L￨NN￨O￨- +￨L￨CC￨O￨- bm￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- bmI￨L￨NN￨O￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- β2￨L￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α2￨L￨CD￨NUMBER￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 4￨L￨CD￨NUMBER￨- Being￨U￨VBG￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ≥￨L￨VBP￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- I￨U￨PRP￨O￨- ≤￨L￨VBP￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +dS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- −￨L￨NN￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A +￨L￨CC￨O￨- σ1S￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dB1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- global￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- non-degenerate￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- ρ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- +￨L￨CC￨O￨- σ2I￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dB2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨JJ￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- +￨L￨CC￨O￨- σ3R￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dB3￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- B1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- B2￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- B3￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- mutually￨L￨RB￨O￨- independent￨L￨JJ￨RELIGION￨- Brownian￨U￨JJ￨MISC￨- motions￨L￨NNS￨O￨- ,￨L￨,￨O￨- σ1￨L￨NN￨O￨- ,￨L￨,￨O￨- σ2￨L￨NN￨O￨- ,￨L￨,￨O￨- σ3￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- intensities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- white￨L￨JJ￨O￨- noises￨L￨NNS￨O￨- .￨L￨.￨O￨- +dS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- −￨L￨NN￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A +￨L￨CC￨O￨- σ1S￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dB￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Brownian￨U￨JJ￨MISC￨- motions￨L￨NNS￨O￨- B1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- B2￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- B3￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- ρ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- +￨L￨CC￨O￨- σ2I￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dB￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨JJ￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- +￨L￨CC￨O￨- σ3R￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dB￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- standard￨L￨JJ￨O￨- arguments￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- positive￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- u￨L￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- R2￨U￨NN￨O￨- ,￨L￨,￨O￨- ◦￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- u￨L￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- u￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- exists￨L￨VBZ￨O￨- uniquely￨L￨RB￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- solution￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Su￨U￨FW￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Iu￨U￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- that￨L￨WDT￨O￨- remains￨L￨VBZ￨O￨- in￨L￨IN￨O￨- R2￨U￨NN￨O￨- ,￨L￨,￨O￨- ◦￨L￨NN￨O￨- +￨L￨CC￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- there￨L￨RB￨O￨- +￨L￨CC￨O￨- 4￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- follows￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- comparison￨L￨NN￨O￨- theorem￨L￨NN￨O￨A [￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Theorem￨U￨NNP￨O￨- 1.1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- p.￨L￨NN￨O￨- 437￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- Su￨U￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- stationary￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- with￨L￨IN￨O￨- density￨L￨NN￨O￨- By￨U￨IN￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- Fokker-Planck￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- f￨L￨FW￨O￨- ∗￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ba￨L￨NN￨O￨- Γ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- +1￨L￨NN￨NUMBER￨- )￨L￨-RRB-￨O￨- e￨L￨SYM￨O￨- −￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Γ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ·￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Gamma￨U￨NN￨MISC￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- LaSalle￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- invariance￨L￨NN￨O￨- principle￨L￨NN￨O￨- and￨L￨CC￨O￨- Lyapunov￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- direct￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- prove￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨A asymptotically￨L￨RB￨O￨A stable￨L￨JJ￨O￨A if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- some￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- imposed￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- function￨L￨NN￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- initially￨L￨RB￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- /￨L￨:￨O￨- ψ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- psychological￨L￨JJ￨O￨- effect￨L￨NN￨O￨- ”￨L￨''￨O￨- :￨L￨:￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨DATE￨- 1￨L￨LS￨DATE￨- 2￨L￨CD￨NUMBER￨- ´￨L￨''￨O￨- ANGEL￨U￨NNP￨O￨- G.￨U￨NNP￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- non-linear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A and￨L￨CC￨O￨- transfer￨L￨NN￨O￨- from￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- .￨L￨.￨O￨- +Ruan￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- non-linear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- β￨L￨NN￨O￨- I￨U￨PRP￨O￨- 2S￨L￨VBP￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- +￨L￨CC￨O￨- ρI￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 1c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Note￨U￨VBP￨O￨- that￨L￨IN￨O￨- S￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S1￨U￨NN￨O￨- ,￨L￨,￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ,￨L￨,￨O￨- Sn￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I1￨U￨NN￨O￨- ,￨L￨,￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ,￨L￨,￨O￨- In￨U￨IN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- R1￨U￨NN￨O￨- ,￨L￨,￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ,￨L￨,￨O￨- Rn￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- N1￨U￨NN￨O￨- ,￨L￨,￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ,￨L￨,￨O￨- Nn￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- subpopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- zonal￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibria￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Ni￨U￨NN￨MISC￨- =￨L￨JJ￨O￨- Si￨U￨NNP￨O￨- +￨L￨CC￨O￨- Ii￨U￨NN￨O￨- +￨L￨CC￨O￨- Ri￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- zones￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- current￨L￨JJ￨DATE￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- from￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- previously￨L￨RB￨DATE￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- separation￨L￨NN￨O￨- analysis￨L￨NN￨O￨A was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- exclude￨L￨VB￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ˙S￨L￨NN￨O￨- =￨L￨JJ￨O￨- µ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- diag￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- diag￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- diag￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ν￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- 1diag￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- κR￨L￨NN￨O￨- +￨L￨CC￨O￨- σ￨L￨NN￨O￨- ⊲￨L￨CD￨NUMBER￨- ΦS￨U￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1a￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ˙I￨L￨NN￨O￨- =￨L￨JJ￨O￨- diag￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- diag￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- diag￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ν￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- 1diag￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- pσ￨L￨NN￨O￨- ⊲￨L￨NN￨O￨- ΦI￨U￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ˙R￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- κ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- σ￨L￨NN￨O￨- ⊲￨L￨CD￨NUMBER￨- ΦR￨U￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- through￨L￨IN￨O￨- methods￨L￨NNS￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- first￨L￨JJ￨O￨- passage￨L￨NN￨O￨- percolation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- until￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- vertex￨L￨NN￨O￨A gets￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- use￨L￨VB￨O￨- subcritical￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- to￨L￨TO￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Volz￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- keeping￨L￨VBG￨O￨- track￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- vertex￨L￨NN￨O￨A of￨L￨IN￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨- avoids￨L￨VBZ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- epidemiological￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- terms￨L￨NNS￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- uniformly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- vertex￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- uniformly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- vertex￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- an￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- infinite￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- so-called￨L￨JJ￨O￨- Susceptible-Infectious-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- uniformly￨L￨RB￨O￨A mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- all￨L￨DT￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- contact￨L￨NN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- independently￨L￨RB￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Much￨U￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- already￨L￨RB￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- for￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- variants￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- by￨L￨IN￨O￨- calculating￨L￨VBG￨O￨A the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- infected￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- or￨L￨CC￨O￨- ma￨L￨NN￨O￨- jor￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- sparse￨L￨JJ￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sub-selection￨L￨NN￨O￨- of￨L￨IN￨O￨- candidate￨L￨NN￨TITLE￨- models￨L￨NNS￨O￨- near￨L￨IN￨O￨- the￨L￨DT￨O￨- Pareto￨U￨NNP￨O￨- frontier￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- tractable￨L￨JJ￨O￨- computation￨L￨NN￨O￨- of￨L￨IN￨O￨- AIC￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Akaike￨U￨NNP￨O￨- information￨L￨NN￨O￨- criteria￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- BIC￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Bayes￨U￨NNP￨PERSON￨- information￨L￨NN￨O￨- criteria￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- scores￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- candidate￨L￨NN￨TITLE￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- innovation￨L￨NN￨O￨- circumvents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- disadvantage￨L￨NN￨O￨- of￨L￨IN￨O￨- standard￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- which￨L￨WDT￨O￨- typically￨L￨RB￨O￨- limits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- candidate￨L￨NN￨TITLE￨- models￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- intractability￨L￨NN￨O￨- of￨L￨IN￨O￨- computing￨L￨VBG￨O￨- information￨L￨NN￨O￨- criteria￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- consideration￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- combinatorially￨L￨RB￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- candidate￨L￨NN￨TITLE￨A models￨L￨NNS￨O￨- governing￨L￨VBG￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- information￨L￨NN￨O￨- criteria￨L￨NNS￨O￨A hierarchically￨L￨RB￨O￨- ranks￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- informative￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- enabling￨L￨VBG￨O￨- the￨L￨DT￨O￨- automatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- principled￨L￨JJ￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- strongest￨L￨JJS￨O￨- support￨L￨NN￨O￨- in￨L￨IN￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mangan￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Kutz￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Brunton￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Proctor￨U￨NNP￨ORGANIZATION￨- Model￨U￨NNP￨ORGANIZATION￨- selection￨L￨NN￨O￨- for￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- via￨L￨IN￨O￨- sparse￨L￨JJ￨O￨- regression￨L￨NN￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- criteria￨L￨NNS￨O￨A Niall￨U￨NNP￨PERSON￨- M￨U￨NN￨PERSON￨- .￨L￨.￨O￨- +Beyond￨U￨IN￨O￨- this￨L￨DT￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- successive￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- between￨L￨IN￨O￨- states￨L￨NNS￨O￨- were￨L￨VBD￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- frameworks￨L￨NNS￨O￨- :￨L￨:￨O￨- ODE/PDE￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Diekmann￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Heesterbeek￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- difference￨L￨NN￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- continuous￨L￨JJ￨O￨- or￨L￨CC￨O￨- discrete-time￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Daley￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Gani￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Diekmann￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- renewal￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- branching￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- diffusion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +the￨L￨DT￨O￨- approximation￨L￨NN￨O￨- of￨L￨IN￨O￨- density-dependent￨L￨JJ￨O￨- SIR-like￨U￨JJ￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- diffusion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- with￨L￨IN￨O￨- First￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- previous￨L￨JJ￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- small￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- generalized￨L￨VBN￨O￨- to￨L￨TO￨O￨- non￨L￨JJ￨O￨- -￨L￨:￨O￨- 1￨L￨CD￨DATE￨- √￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- autonomous￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- start￨L￨VBP￨O￨- building￨L￨VBG￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- statistics￨L￨NNS￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- approximating￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- Z￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Multidimensional￨U￨JJ￨O￨- continuous-time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- jump￨L￨NN￨O￨- processes￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Z￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- Z￨U￨NN￨O￨- p￨L￨NN￨O￨- form￨L￨VBP￨O￨- a￨L￨DT￨O￨- usual￨L￨JJ￨O￨- set-up￨L￨NN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- SIR-like￨U￨JJ￨MISC￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- that￨L￨IN￨O￨- l￨L￨NN￨O￨- N￨U￨NN￨O￨- SI￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- gI￨L￨NN￨O￨- Z￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- initial￨L￨JJ￨O￨- state￨L￨NN￨O￨- Z￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S0￨U￨NN￨O￨- ,￨L￨,￨O￨- I0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∀￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- define￨L￨VB￨O￨- −￨L￨SYM￨O￨- →￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- →￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- l￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- transitions￨L￨NNS￨O￨A rate￨L￨NN￨O￨- and￨L￨CC￨O￨- g￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- inverse￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- duration￨L￨NN￨O￨- d￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- oscillation￨L￨NN￨O￨- diagrams￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- amplitude￨L￨NN￨O￨- and￨L￨CC￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- how￨L￨WRB￨O￨- oscillations￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- destabilized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- characteristic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- times￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨- destabilize￨L￨VBP￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- giving￨L￨VBG￨O￨- rise￨L￨NN￨O￨- to￨L￨TO￨O￨- stable￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨A for￨L￨IN￨O￨- certain￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- values￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- type￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- one￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- during￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- agent￨L￨NN￨O￨- stays￨L￨VBZ￨O￨A in￨L￨IN￨O￨- category￨L￨NN￨O￨- I￨U￨NN￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- immune￨L￨JJ￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- during￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- agent￨L￨NN￨O￨- stays￨L￨VBZ￨O￨- in￨L￨IN￨O￨- category￨L￨NN￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- re-infection￨L￨NN￨O￨- until￨L￨IN￨O￨- it￨L￨PRP￨O￨- returns￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Oscillations￨U￨NNS￨O￨- in￨L￨IN￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- distributed￨L￨VBN￨O￨- delays￨L￨NNS￨O￨A Sebasti´an￨U￨JJ￨O￨- Gon￨U￨NN￨O￨- ¸￨L￨NN￨O￨- calves1￨L￨NN￨O￨- ,￨L￨,￨O￨- G.￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 9￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Oscil￨U￨NN￨O￨- lations￨L￨NNS￨O￨- in￨L￨IN￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- distributed￨L￨VBN￨O￨- delays￨L￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- Abstract￨U￨JJ￨O￨- .￨L￨.￨O￨- +PRELIMINARY￨U￨JJ￨O￨- Let￨U￨VB￨O￨- us￨L￨PRP￨O￨- consider￨L￨VB￨O￨- a￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- ξt￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- space￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Ω￨U￨NN￨O￨- ,￨L￨,￨O￨- F￨U￨NN￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- values￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- elements￨L￨NNS￨O￨- ,￨L￨,￨O￨- say￨L￨VBP￨O￨A E￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- +￨L￨CC￨O￨- ,￨L￨,￨O￨- −￨L￨SYM￨O￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- simulation￨L￨NN￨O￨- results￨L￨VBZ￨O￨- illustrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- telegraph￨L￨NN￨O￨- noise￨L￨NN￨O￨A .￨L￨.￨O￨- +DYNAMICAL￨U￨JJ￨O￨- BEHAVIOR￨U￨NN￨O￨- OF￨U￨IN￨O￨- A￨U￨DT￨O￨- STOCHASTIC￨U￨JJ￨O￨- SIRS￨U￨NNP￨O￨- EPIDEMIC￨U￨NNP￨O￨- MODEL￨U￨NNP￨TITLE￨- N.￨U￨NNP￨PERSON￨- T.￨U￨NNP￨PERSON￨- HIEU￨U￨NNP￨PERSON￨- DYNAMICAL￨U￨NNP￨O￨- BEHAVIOR￨U￨NNP￨O￨- OF￨U￨IN￨O￨- A￨U￨DT￨O￨- STOCHASTIC￨U￨JJ￨O￨- SIRS￨U￨NNP￨O￨- EPIDEMIC￨U￨NNP￨O￨- MODEL￨U￨NNP￨TITLE￨- 3￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- paper￨L￨NN￨O￨- has￨L￨VBZ￨O￨- 5￨L￨CD￨NUMBER￨- sections￨L￨NNS￨O￨A .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- Kernack-MacKendrick￨U￨NNP￨LOCATION￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- telegraph￨L￨NN￨O￨- noise￨L￨NN￨O￨A ξt￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ˙S￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- ξt￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξt￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- −￨L￨NN￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ˙I￨L￨NN￨O￨- =￨L￨JJ￨O￨- a￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- ξt￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- b￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξt￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- g￨L￨NN￨O￨- :￨L￨:￨O￨- E￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- +￨L￨CC￨O￨- ,￨L￨,￨O￨- −￨L￨SYM￨O￨- }￨L￨-RRB-￨O￨- →￨L￨SYM￨O￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- for￨L￨IN￨O￨- g￨L￨NN￨O￨- =￨L￨JJ￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- c.￨L￨NN￨O￨- +(￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- I￨U￨NN￨O￨- =￨L￨JJ￨O￨- hx0￨L￨NN￨O￨- ℓ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Px￨U￨NN￨O￨- ∈￨L￨NN￨O￨- Φ￨U￨NN￨O￨- \￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- x0￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- hx￨L￨NN￨O￨- ℓ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Under￨U￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- threshold￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- reception￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- Φ￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨A process￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- PPP￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Rayleigh￨U￨NNP￨PERSON￨- fading￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ℓ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- kxk￨L￨NN￨O￨- −￨L￨NN￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- was￨L￨VBD￨O￨- determined￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- horizontal￨L￨JJ￨O￨- shift￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- gain￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- tractable￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨A process￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- PPP￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- gain￨L￨NN￨O￨A at￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- mean￨L￨NN￨O￨- interference-to-signal￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MISR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- PPP￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- consideration￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- gain￨L￨NN￨O￨- at￨L￨IN￨O￨- in￨L￨IN￨O￨- finity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- fading-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EFIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- Φ￨U￨NNP￨O￨- ⊂￨L￨SYM￨O￨- R2￨U￨NN￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- point￨L￨NN￨O￨A process￨L￨NN￨O￨A representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- locations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- BSs￨U￨NNS￨O￨- and￨L￨CC￨O￨- let￨L￨VB￨O￨- x0￨L￨NN￨O￨- ∈￨L￨NN￨O￨- Φ￨U￨NN￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- serving￨L￨VBG￨O￨- BS￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- user￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- de￨L￨FW￨O￨- fine￨L￨FW￨O￨- x0￨L￨NN￨O￨- ,￨L￨,￨O￨- arg￨L￨NN￨O￨- min￨L￨NN￨DURATION￨- {￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Φ￨U￨NN￨O￨- :￨L￨:￨O￨- kxk￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Gaussian￨U￨JJ￨MISC￨- hypergeometric￨L￨JJ￨O￨- function￨L￨NN￨O￨- 2F1￨L￨NN￨O￨- as￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- ccdf￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨A probability￨L￨NN￨O￨A i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- ps￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- θ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≡￨L￨SYM￨O￨- ¯￨L￨SYM￨O￨- FSIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- θ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- explicitly￨L￨RB￨O￨- how￨L￨WRB￨O￨- intervention￨L￨NN￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- mean￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- fraction￨L￨NN￨O￨- ,￨L￨,￨O￨- modulates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- extinction￨L￨NN￨O￨A times￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- go￨L￨VB￨O￨- extinct￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- random￨L￨JJ￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- new￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- prohibitively￨L￨RB￨O￨- long￨L￨RB￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- properly￨L￨RB￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- extinction￨L￨NN￨O￨A requires￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- along￨L￨IN￨O￨- these￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- simulated￨L￨JJ￨O￨- through￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨A defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- collected￨L￨VBN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- aggregated￨L￨JJ￨O￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- temporal￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- much￨L￨JJ￨O￨- larger￨L￨JJR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨A than￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- value￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2-5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- and￨L￨CC￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- well-identified￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 6-10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 11-13￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- important￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- want￨L￨VBP￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- data-driven￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- temporal￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- shaping￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +-￨L￨:￨O￨- 2￨L￨LS￨DATE￨- -￨L￨:￨O￨- Background￨U￨NN￨O￨- The￨U￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨A among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- determinant￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Background￨U￨NN￨O￨- The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- crucially￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨A among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- start￨L￨VBP￨O￨- by￨L￨IN￨O￨- looking￨L￨VBG￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- actual￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- news￨L￨NN￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- network￨L￨NN￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- ideas￨L￨NNS￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- topic￨L￨NN￨O￨- Modeling￨U￨NN￨O￨- ,￨L￨,￨O￨- connecting￨L￨VBG￨O￨- similar￨L￨JJ￨O￨- articles￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- bounds￨L￨NNS￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- window￨L￨NN￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨A .￨L￨.￨O￨- +News￨U￨NNP￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- internet￨L￨NN￨O￨- media￨L￨NNS￨O￨- outlets￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- process￨L￨NN￨O￨- generating￨L￨VBG￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨A between￨L￨IN￨O￨- published￨L￨VBN￨O￨- articles￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- methodology￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- language￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- articles￨L￨NNS￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨A network￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- specific￨L￨NN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- news￨L￨NN￨O￨- articles￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- factors￨L￨NNS￨O￨- influence￨L￨VBP￨O￨A their￨L￨PRP$￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- postulate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- approximates￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- it￨L￨PRP￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Network￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Starting￨U￨VBG￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- {￨L￨-LRB-￨O￨- wi￨L￨NN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- two￨L￨CD￨NUMBER￨- steps￨L￨NNS￨O￨- consist￨L￨VBP￨O￨- in￨L￨IN￨O￨- sampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S.￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- particles￨L￨NNS￨O￨A ˜xi￨L￨VBP￨O￨- from￨L￨IN￨O￨- importance￨L￨NN￨O￨- densities￨L￨NNS￨O￨- qi￨L￨NN￨O￨- and￨L￨CC￨O￨- weighting￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- W.￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- them￨L￨PRP￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- discrepancy￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- and￨L￨CC￨O￨- importance￨L￨NN￨O￨- densities￨L￨NNS￨O￨- ;￨L￨:￨O￨- then￨L￨RB￨O￨- Θt￨U￨NN￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- as￨L￨IN￨O￨- bΘSIS￨L￨NN￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- superscript￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- justified￨L￨VBN￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Semi-independent￨U￨JJ￨O￨- resampling￨L￨VBG￨O￨- for￨L￨IN￨O￨- particle￨L￨NN￨O￨A filtering￨L￨VBG￨O￨- Roland￨U￨NNP￨PERSON￨- Lamberti￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Yohan￨U￨NNP￨PERSON￨- Petetin￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- François￨U￨NNP￨PERSON￨- Desbouvries￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Senior￨U￨NNP￨O￨- Member￨U￨NNP￨O￨- ,￨L￨,￨O￨- IEEE￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- François￨U￨NNP￨O￨- Septier￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- Among￨U￨IN￨O￨- Sequential￨U￨JJ￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- SMC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- Sampling￨U￨VBG￨O￨- Importance￨U￨NN￨O￨- Resampling￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- algorithms￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Importance￨U￨NN￨O￨- Sampling￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- IS￨U￨VBZ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- some￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- resampling-based￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- rejuvenation￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- which￨L￨WDT￨O￨- aims￨L￨VBZ￨O￨- at￨L￨IN￨O￨- fighting￨L￨VBG￨O￨- against￨L￨IN￨O￨- weight￨L￨NN￨O￨- degeneracy￨L￨NN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- a￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- (￨L￨-LRB-￨O￨- optional￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- step￨L￨NN￨O￨- consists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- re-sampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R.￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- particles￨L￨NNS￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- in￨L￨IN￨O￨- re-drawing￨L￨JJ￨O￨- each￨L￨DT￨O￨- particle￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- weight￨L￨NN￨O￨- and￨L￨CC￨O￨- assigning￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- resampled￨L￨JJ￨O￨- particles￨L￨NNS￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- weight￨L￨NN￨O￨- N￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- performed￨L￨VBN￨O￨- whatever￨L￨WDT￨O￨- t￨L￨NN￨O￨- or￨L￨CC￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- some￨L￨DT￨O￨- criterion￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- particles￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- t￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- xi￨L￨NN￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- N￨U￨NNP￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- PN￨U￨NN￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ˜wi￨L￨NN￨O￨- t￨L￨NN￨O￨- ϕ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ˜xi￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- R.￨U￨NNP￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- ways￨L￨NNS￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- F1￨U￨NN￨O￨- and￨L￨CC￨O￨- F2￨U￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- macro￨L￨NN￨O￨- cell￨L￨NN￨O￨- tier￨L￨NN￨TITLE￨A uses￨L￨VBZ￨O￨- F1￨U￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- micro￨L￨JJ￨O￨- cell￨L￨NN￨O￨- tier￨L￨NN￨TITLE￨- uses￨L￨VBZ￨O￨- F2￨U￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- macro￨L￨NN￨O￨- cell￨L￨NN￨O￨- tier￨L￨NN￨TITLE￨- uses￨L￨VBZ￨O￨- only￨L￨RB￨O￨- F1￨U￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- micro￨L￨JJ￨O￨- cell￨L￨NN￨O￨- tier￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- use￨L￨VB￨O￨- both￨L￨DT￨O￨- F1￨U￨NN￨O￨- and￨L￨CC￨O￨- F2￨U￨NN￨O￨- :￨L￨:￨O￨- F2￨U￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- micro￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- for￨L￨IN￨O￨- biased￨L￨VBN￨O￨- User￨U￨NN￨O￨- Equipments￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- UEs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- only￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- those￨L￨DT￨O￨- UEs￨U￨NNS￨O￨- ,￨L￨,￨O￨- originally￨L￨RB￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- macro￨L￨NN￨O￨- cell￨L￨NN￨O￨- tier￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- forced￨L￨VBN￨O￨- to￨L￨TO￨O￨- associate￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- micro￨L￨JJ￨O￨- cell￨L￨NN￨O￨- tier￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- traffic￨L￨NN￨O￨- offloading￨L￨NN￨O￨- scheme￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +ACCEPTED￨U￨VBN￨O￨- TO￨U￨TO￨O￨- BE￨U￨VB￨O￨- PUBLISHED￨U￨VBN￨O￨- ON￨U￨IN￨O￨- THE￨U￨DT￨O￨- JOURNAL￨U￨NN￨O￨- OF￨U￨IN￨O￨- COMMUNICATIONS￨U￨NNPS￨O￨- AND￨U￨CC￨O￨- NETWORKS￨U￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- LTE-A￨U￨NN￨O￨- Heterogeneous￨U￨JJ￨O￨- Networks￨U￨NNP￨O￨- with￨L￨IN￨O￨- SIR-based￨U￨JJ￨O￨- Cell￨U￨NN￨O￨- Association￨U￨NN￨O￨- and￨L￨CC￨O￨- Stochastic￨U￨NNP￨O￨- Geometry￨U￨NNP￨O￨- Giovanni￨U￨NNP￨PERSON￨- Giambene￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Van￨U￨NNP￨PERSON￨- Anh￨U￨NNP￨PERSON￨- Le￨U￨NNP￨PERSON￨- Abstract￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- This￨U￨DT￨O￨- paper￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- Heterogeneous￨U￨JJ￨MISC￨- Networks￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- HetNets￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- positions￨L￨NNS￨O￨- of￨L￨IN￨O￨- base￨L￨NN￨O￨- stations￨L￨NNS￨O￨- and￨L￨CC￨O￨- users￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- Poisson￨U￨NNP￨O￨- Point￨U￨NN￨O￨- Processes￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- stochastic￨L￨JJ￨O￨A geometry￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- highlight￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- adopted￨L￨VBN￨O￨- cell￨L￨NN￨O￨- association￨L￨NN￨O￨- technique￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- very￨L￨RB￨O￨- low￨L￨JJ￨O￨- outage￨L￨NN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- fulfillment￨L￨NN￨O￨- of￨L￨IN￨O￨- certain￨L￨JJ￨O￨- bit-rate￨L￨JJ￨O￨- requirements￨L￨NNS￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- adequate￨L￨JJ￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- reuse￨L￨NN￨O￨- factor￨L￨NN￨O￨- and￨L￨CC￨O￨- micro￨L￨JJ￨O￨A cell￨L￨NN￨O￨- density￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- forcing￨L￨VBG￨O￨- UEs￨U￨NNS￨O￨- to￨L￨TO￨O￨- associate￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- cell￨L￨NN￨O￨A providing￨L￨VBG￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- maximum-biased￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- received￨L￨VBD￨O￨- power￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- mean￨L￨VB￨O￨- having￨L￨VBG￨O￨- Signal-to-Interference￨U￨NN￨O￨- plus￨L￨CC￨O￨- Noise￨U￨NN￨O￨- Ratio￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SINR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- SINR￨U￨NN￨O￨- threshold￨L￨NN￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- UEs￨U￨NNS￨O￨- may￨L￨MD￨O￨- experience￨L￨VB￨O￨- outage￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- formally￨L￨RB￨O￨- derive￨L￨VB￨O￨- outage￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- rate￨L￨NN￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- mean￨L￨VB￨O￨- user￨L￨NN￨O￨- bit-rate￨L￨NN￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- frequency￨L￨NN￨O￨- reuse￨L￨NN￨O￨- of￨L￨IN￨O￨- K￨U￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- prioritized￨L￨VBN￨O￨- SIR-based￨U￨JJ￨MISC￨- cell￨L￨NN￨O￨A association￨L￨NN￨O￨- scheme￨L￨NN￨O￨- are￨L￨VBP￨O￨- applied￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- and￨L￨CC￨O￨- prevent￨L￨VBP￨O￨- unbounded￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- function￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- The￨U￨DT￨O￨- precise￨L￨JJ￨O￨- interpretations￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Λ￨U￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- µ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- δ￨L￨NN￨O￨- stands￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- inducing￨L￨VBG￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- γ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- signifies￨L￨NNS￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- lose￨L￨VB￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- return￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- ;￨L￨:￨O￨- ν￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- stipulates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A ;￨L￨:￨O￨- SG￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ·￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- G￨U￨NN￨O￨- :￨L￨:￨O￨- R￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- )￨L￨-RRB-￨O￨- manifests￨L￨VBZ￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- per￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- pioneer￨L￨NN￨O￨- work￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- Kermack-McKendrick￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- 1￨L￨CD￨NUMBER￨- dSt￨L￨NNP￨O￨- dt￨L￨NNP￨O￨A dIt￨L￨NNP￨O￨- dt￨L￨NNP￨O￨- dRt￨L￨NNP￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- Λ￨U￨NN￨O￨- −￨L￨NN￨O￨- µSt￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- StG￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- It￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γRt￨L￨NN￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- StG￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- It￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- ν￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- It￨U￨PRP￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ν￨L￨NN￨O￨- It￨U￨PRP￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Rt￨U￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- SIR￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- Configuration￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Clustering￨U￨NN￨O￨- ,￨L￨,￨O￨- Branching￨U￨VBG￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- Vaccination￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- fate￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨- approximations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- expressions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- ma￨L￨FW￨O￨- jor￨L￨FW￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- vertices￨L￨NNS￨O￨- represent￨L￨VBP￨O￨A individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- →￨L￨NN￨O￨- Infectious￨U￨JJ￨O￨- →￨L￨NN￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- with￨L￨IN￨O￨- clustering￨L￨NN￨O￨A .￨L￨.￨O￨- +It￨U￨PRP￨O￨- was￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- Bollob￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1980￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- degenerate￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- every￨L￨DT￨O￨- node￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- degree￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- more￨L￨JJR￨O￨- general￨L￨JJ￨TITLE￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- by￨L￨IN￨O￨- Molloy￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Reed￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1995￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 1998￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Schwartz￨U￨NNP￨ORGANIZATION￨- Naval￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- Laboratory￨U￨NNP￨ORGANIZATION￨- Code￨U￨NNP￨O￨- 6792￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 5￨L￨CD￨NUMBER￨- Telephone￨U￨NNP￨O￨- :￨L￨:￨O￨- 202.404.8359￨L￨CD￨NUMBER￨- Fax￨U￨NN￨O￨- :￨L￨:￨O￨- 202.767.0631￨L￨CD￨NUMBER￨- page￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨A in￨L￨IN￨O￨- those￨L￨DT￨O￨- categories￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- deal￨L￨VBP￨O￨- only￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- :￨L￨:￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- µN￨L￨NN￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- IS￨U￨VBZ￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- dI￨L￨NN￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- IS￨U￨VBZ￨O￨- -￨L￨:￨O￨- gI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- µ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birthrate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- new￨L￨JJ￨O￨- susceptibles￨L￨NNS￨O￨- are￨L￨VBP￨O￨- added￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨A ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b/N￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- g￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- recover￨L￨VBP￨O￨- .￨L￨.￨O￨- +Classical￨U￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- term￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- people￨L￨NNS￨O￨A in￨L￨IN￨O￨- separate￨L￨JJ￨O￨- patches￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- patches￨L￨NNS￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨A .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- scale￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- patch￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- traveling￨L￨VBG￨O￨- wave￨L￨NN￨O￨A solutions￨L￨NNS￨O￨- connecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- trivial￨L￨JJ￨O￨- disease-free￨L￨JJ￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- ξ￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- ∞￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- ahead￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- front￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- non-trivial￨L￨JJ￨O￨- states￨L￨NNS￨O￨- as￨L￨IN￨O￨- ξ￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- a￨L￨DT￨O￨- traveling￨L￨VBG￨O￨- wave￨L￨NN￨O￨A solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- bounded￨L￨JJ￨O￨- solution￨L￨NN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨- by￨L￨IN￨O￨- sn￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- φ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- ct￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ψ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- ct￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- n￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- and￨L￨CC￨O￨- t￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- nonnegative￨L￨JJ￨O￨- bounded￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- φ￨L￨VBP￨O￨- ,￨L￨,￨O￨- ψ￨L￨VBP￨O￨- on￨L￨IN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- wave￨L￨NN￨O￨- profiles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- constant￨L￨JJ￨O￨- c￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- wave￨L￨NN￨O￨- speed￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- any￨L￨DT￨O￨- c￨L￨NN￨O￨- ≥￨L￨NN￨O￨- c￨L￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- bounded￨L￨JJ￨O￨- classical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- φ￨L￨NN￨O￨- ,￨L￨,￨O￨- ψ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 1.6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- φ￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- ψ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- R￨U￨NN￨O￨- lim￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- φ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ψ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ξ￨L￨NN￨O￨- →￨L￨SYM￨O￨- −￨L￨SYM￨O￨- ∞￨L￨SYM￨O￨- TRAVELING￨U￨VBG￨O￨- WAVE￨U￨NNP￨O￨- FOR￨U￨IN￨O￨- A￨U￨DT￨O￨- LATTICE￨U￨NNP￨O￨- DYNAMICAL￨U￨NNP￨O￨- SYSTEM￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- lim￨L￨CD￨NUMBER￨- inf￨L￨NN￨O￨- ξ￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- φ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- ∗￨L￨SYM￨O￨- ≤￨L￨SYM￨O￨- lim￨L￨FW￨O￨- sup￨L￨FW￨O￨- ξ￨L￨FW￨O￨- →￨L￨FW￨O￨- +￨L￨CC￨O￨- ∞￨L￨FW￨O￨- φ￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- lim￨L￨CD￨NUMBER￨- inf￨L￨NN￨O￨- ξ￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- ψ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- ∗￨L￨SYM￨O￨- ≤￨L￨SYM￨O￨- lim￨L￨FW￨O￨- sup￨L￨FW￨O￨- ξ￨L￨FW￨O￨- →￨L￨FW￨O￨- +￨L￨CC￨O￨- ∞￨L￨FW￨O￨- ψ￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- <￨L￨JJR￨O￨- +￨L￨CC￨O￨- ∞￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- e￨L￨SYM￨O￨- ∗￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- dsn￨L￨NN￨O￨- dt￨L￨NN￨O￨A din￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- sn￨L￨JJ￨O￨- +1￨L￨NN￨NUMBER￨- +￨L￨CC￨O￨- sn￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- 2sn￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- −￨L￨NN￨O￨- µ￨L￨NN￨O￨- sn￨L￨NN￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- sn￨L￨NN￨O￨- in￨L￨IN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- d￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- +1￨L￨NN￨NUMBER￨- +￨L￨CC￨O￨- in￨L￨IN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- 2in￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µ￨L￨NN￨O￨- in￨L￨IN￨O￨- +￨L￨CC￨O￨- β￨L￨NN￨O￨- sn￨L￨NN￨O￨- in￨L￨IN￨O￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- in￨L￨IN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- sn￨L￨NN￨O￨- =￨L￨JJ￨O￨- sn￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- =￨L￨JJ￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- µ￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- setting￨L￨VBG￨O￨A ξ￨L￨NN￨O￨- =￨L￨JJ￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- ct￨L￨NN￨O￨- and￨L￨CC￨O￨- substituting￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- sn￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- φ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ψ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- −￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- φ￨L￨NN￨O￨- ′￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- D￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- φ￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- φ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- β￨L￨FW￨O￨- φ￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ψ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- ψ￨L￨NN￨O￨- ′￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- d￨L￨NN￨O￨- D￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- ψ￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ψ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- β￨L￨NN￨O￨- φ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ψ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- ξ￨L￨JJ￨O￨- ∈￨L￨NN￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- D￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- f￨L￨FW￨O￨- ]￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨JJ￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- 2f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- yet￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- PDE￨U￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- well-defined￨L￨JJ￨O￨- Vlasov￨U￨NNP￨PERSON￨- scaling￨L￨VBG￨O￨- limits￨L￨NNS￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨- system￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- agent-to-agent-interaction￨L￨NN￨O￨- ,￨L￨,￨O￨- hence￨L￨RB￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨A level￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨A agent-to-agent￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- already￨L￨RB￨O￨- done￨L￨VBN￨O￨- e.g.￨L￨FW￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- host-vector￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- configuration￨L￨NN￨O￨- space￨L￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Microscopic￨U￨JJ￨O￨- Model￨U￨NNP￨TITLE￨- In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- host-vector￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- via￨L￨IN￨O￨- marked￨L￨JJ￨O￨- configuration￨L￨NN￨O￨A spaces￨L￨NNS￨O￨- .￨L￨.￨O￨- +Virus￨U￨NN￨O￨- circulation￨L￨NN￨O￨- ,￨L￨,￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- present￨L￨VBP￨DATE￨- little￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- statistics￨L￨NNS￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨A period￨L￨NN￨O￨- provided￨L￨VBD￨O￨- the￨L￨DT￨O￨- median￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- coincidence￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- research￨L￨NN￨O￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- producing￨L￨VBG￨O￨- dengue￨L￨JJ￨O￨A models￨L￨NNS￨O￨- for￨L￨IN￨O￨- public￨L￨JJ￨O￨- policy￨L￨NN￨O￨- use￨L￨NN￨O￨- began￨L￨VBD￨O￨- with￨L￨IN￨O￨- Newton￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Reiter￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- who￨L￨WP￨O￨- introduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- dengue￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- Ordinary￨U￨NNP￨O￨- Differential￨U￨NNP￨O￨- Equations￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- ODE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- disaggregated￨L￨VBN￨O￨- in￨L￨IN￨O￨- Susceptible￨U￨NNP￨O￨- ,￨L￨,￨O￨- Exposed￨U￨VBN￨O￨- ,￨L￨,￨O￨- Infected￨U￨JJ￨O￨- and￨L￨CC￨O￨- Recovered￨U￨VBN￨O￨- compartments￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- basis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IBM￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨A population￨L￨NN￨O￨A ,￨L￨,￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- independent￨L￨JJ￨RELIGION￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- treated￨L￨VBN￨O￨- by￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SEI￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Exponential￨U￨NNP￨O￨- ,￨L￨,￨O￨- deterministic￨L￨JJ￨O￨- and￨L￨CC￨O￨- experimental￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- human￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- exposed￨L￨VBN￨O￨- period￨L￨NN￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- weather￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- temperate￨L￨VB￨O￨- climate￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- to￨L￨TO￨O￨- tropical￨L￨JJ￨O￨- climate￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mosquito￨L￨NN￨O￨A population￨L￨NN￨O￨A was￨L￨VBD￨O￨- not￨L￨RB￨O￨- modeled￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- early￨L￨JJ￨O￨- work￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- that￨L￨DT￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨A an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- 17￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 30￨L￨CD￨NUMBER￨- coupled￨L￨VBN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- later￨L￨RB￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- eigenvalues￨L￨NNS￨O￨- by￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- Jacobian￨U￨JJ￨MISC￨- matrix￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- begin￨L￨VB￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- two￨L￨CD￨NUMBER￨- preliminary￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- consist￨L￨VBP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- SEI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨A ,￨L￨,￨O￨- Chikungunya￨U￨NNP￨LOCATION￨- or￨L￨CC￨O￨- Zika￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- any￨L￨DT￨O￨- possible￨L￨JJ￨O￨- coinfection￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Aedes￨U￨NNS￨O￨- aegypti￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- known￨L￨JJ￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- Dengue￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Chikungunya￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Zika￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- propose￨L￨VB￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Up￨U￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A that￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- Dengue￨U￨NNP￨O￨- ,￨L￨,￨O￨- Chikungunya￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Zika￨U￨NNP￨PERSON￨- have￨L￨VBP￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- triple￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNP￨O￨- Epidemic￨U￨NNP￨O￨- ,￨L￨,￨O￨- Differential￨U￨JJ￨O￨- Equation￨U￨NN￨O￨- ,￨L￨,￨O￨- Dengue￨U￨NNP￨O￨- ,￨L￨,￨O￨- Chikungunya￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Zika￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨A 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- computational￨L￨JJ￨O￨- scientist￨L￨NN￨TITLE￨- hoping￨L￨VBG￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- SDR￨U￨NNP￨O￨- for￨L￨IN￨O￨- parameter￨L￨NN￨O￨A space￨L￨NN￨O￨A dimension￨L￨NN￨O￨- reduction￨L￨NN￨O￨- encounters￨L￨VBZ￨O￨- a￨L￨DT￨O￨- problem￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨- prediction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- best￨L￨JJS￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- inputs￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- data￨L￨NNS￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- simulation￨L￨NN￨O￨- queries￨L￨NNS￨O￨- fail￨L￨VBP￨O￨- to￨L￨TO￨O￨- satisfy￨L￨VB￨O￨- the￨L￨DT￨O￨- SDR￨U￨NN￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- address￨L￨VB￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- interpret￨L￨VBP￨O￨- SDR￨U￨NN￨O￨- methods￨L￨NNS￨O￨- sliced￨L￨VBD￨O￨- inverse￨L￨JJ￨O￨- regression￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- sliced￨L￨VBN￨O￨- average￨L￨JJ￨O￨- variance￨L￨NN￨O￨- estimation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SAVE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- directions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- ridge￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- composition￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- low-dimensional￨L￨JJ￨O￨- linear￨L￨JJ￨O￨- transformation￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- this￨L￨DT￨O￨- interpretation￨L￨NN￨O￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SAVE￨U￨VB￨O￨- estimate￨L￨NN￨O￨- matrices￨L￨NNS￨O￨- of￨L￨IN￨O￨- integrals￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- column￨L￨NN￨O￨- spaces￨L￨NNS￨O￨A are￨L￨VBP￨O￨- contained￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ridge￨L￨NN￨O￨- directions￨L￨NNS￨O￨- ’￨L￨POS￨O￨- span￨L￨NN￨O￨- ;￨L￨:￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- and￨L￨CC￨O￨- numerically￨L￨RB￨O￨- verify￨L￨VB￨O￨- convergence￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- column￨L￨NN￨O￨- spaces￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- samples￨L￨NNS￨O￨- increases￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- regression￨L￨NN￨O￨A modeling￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- given￨L￨VBN￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- predictor/response￨L￨JJ￨O￨- pairs￨L￨NNS￨O￨- {￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- xi￨L￨NN￨O￨- ,￨L￨,￨O￨- yi￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- independent￨L￨JJ￨RELIGION￨- realizations￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- vector￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- joint￨L￨JJ￨O￨- predictor/response￨L￨NN￨O￨- probability￨L￨NN￨O￨- density￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- help￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- degrees-of-freedom￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- BS￨U￨NN￨O￨- height￨L￨NN￨O￨- for￨L￨IN￨O￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- first￨L￨NN￨O￨- order￨L￨NN￨O￨- statistics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- coverage￨L￨NN￨O￨A probability￨L￨NN￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- optimal￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network-wide￨L￨JJ￨O￨- sense￨L￨NN￨O￨- .￨L￨.￨O￨- +Optimal￨U￨JJ￨O￨- Coverage￨U￨NNP￨O￨- and￨L￨CC￨O￨- Rate￨U￨NNP￨O￨- in￨L￨IN￨O￨- Downlink￨U￨NNP￨MISC￨- Cellular￨U￨NNP￨MISC￨- Networks￨U￨NNP￨MISC￨- :￨L￨:￨O￨- A￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- Meta-Distribution￨U￨NNP￨O￨- Based￨U￨VBD￨O￨- Approach￨U￨NNP￨O￨- A.￨U￨NNP￨O￨- Ghogho￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- spectral￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- downlink￨L￨NN￨O￨A cellular￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- interest￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- early￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨A and￨L￨CC￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨DATE￨- future￨L￨JJ￨DATE￨- transition￨L￨NN￨O￨- by￨L￨IN￨O￨- extending￨L￨VBG￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- cycle￨L￨NN￨O￨- .￨L￨.￨O￨- +Without￨U￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- tendency￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- result￨L￨VBP￨O￨- wi￨L￨NN￨O￨- th￨L￨DT￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- record￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- find￨L￨VB￨O￨- important￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- which￨L￨WDT￨O￨- influenced￨L￨VBD￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- considers￨L￨VBZ￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- SEIR-based￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- local￨L￨JJ￨O￨A areas￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- global￨L￨JJ￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- countries￨L￨NNS￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- international￨L￨JJ￨O￨- travelers￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- considering￨L￨VBG￨O￨A the￨L￨DT￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- ’s￨L￨POS￨O￨- condition￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- simulation￨L￨NN￨O￨- results￨L￨VBZ￨O￨- show￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- was￨L￨VBD￨O￨- much￨L￨JJ￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- international￨L￨JJ￨O￨A relationships￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- run￨L￨VBP￨O￨- another￨L￨DT￨O￨- experiment￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- war￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- ;￨L￨:￨O￨- simulation￨L￨NN￨O￨- considering￨L￨VBG￨O￨- international￨L￨JJ￨O￨A relationships￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- 19￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨A traffic￨L￨NN￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- comparing￨L￨VBG￨O￨- this￨L￨DT￨O￨- simulation￨L￨NN￨O￨- result￨L￨VBP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- see￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- Cold￨U￨NNP￨MISC￨- War￨U￨NNP￨CAUSE_OF_DEATH￨- influenced￨L￨VBD￨O￨A the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +NLP-SIR￨U￨NNP￨O￨- :￨L￨:￨O￨- A￨U￨NNP￨O￨- Natural￨U￨NNP￨ORGANIZATION￨- Language￨U￨NNP￨ORGANIZATION￨- Approach￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Spreadsheet￨U￨NNP￨ORGANIZATION￨- Information￨U￨NNP￨ORGANIZATION￨- Retrieval￨U￨NNP￨ORGANIZATION￨- Derek￨U￨NNP￨ORGANIZATION￨- Flood￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Kevin￨U￨NNP￨PERSON￨- Mc￨U￨NN￨PERSON￨- Daid￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Fergal￨U￨NNP￨ORGANIZATION￨- Mc￨U￨NN￨ORGANIZATION￨- Caffery￨U￨NNP￨ORGANIZATION￨- Dundalk￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ABSTRACT￨U￨NN￨O￨- Spreadsheets￨U￨NNS￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- ubiquitous￨L￨JJ￨O￨- software￨L￨NN￨O￨- tool￨L￨NN￨O￨- ,￨L￨,￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- tasks￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- financial￨L￨JJ￨O￨A modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- statistical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- inventory￨L￨NN￨O￨- management￨L￨NN￨O￨- .￨L￨.￨O￨- +Extracting￨U￨VBG￨O￨- meaningful￨L￨JJ￨O￨- information￨L￨NN￨O￨A from￨L￨IN￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- difficult￨L￨JJ￨O￨- task￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- for￨L￨IN￨O￨- novice￨L￨NN￨O￨- users￨L￨NNS￨O￨- unfamiliar￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- advanced￨L￨JJ￨O￨- data￨L￨NN￨O￨- processing￨L￨NN￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- spreadsheet￨L￨NN￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- introduces￨L￨VBZ￨O￨- NLP-SIR￨U￨NN￨MISC￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Natural￨U￨JJ￨MISC￨- language￨L￨NN￨O￨A interface￨L￨NN￨O￨- for￨L￨IN￨O￨- spreadsheet￨L￨NN￨O￨- information￨L￨NN￨O￨- retrieval￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- evaluation￨L￨NN￨O￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- NLP-SIR￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- spreadsheet￨L￨NN￨O￨- information￨L￨NN￨O￨A retrieval￨L￨NN￨O￨- .￨L￨.￨O￨- +NLP-SIR￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- NLI￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨O￨- spreadsheet￨L￨NN￨O￨- information￨L￨NN￨O￨A retrieval￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- gPC￨L￨NN￨O￨- and￨L￨CC￨O￨- PCE￨U￨NN￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- quantity￨L￨NN￨O￨A of￨L￨IN￨O￨- interest￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- QoI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- u￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g￨L￨NN￨O￨- ,￨L￨,￨O￨- velocity￨L￨NN￨O￨- ,￨L￨,￨O￨- temperature￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- <￨L￨JJR￨O￨- ∞￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ξd￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- T￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- stochastic￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- and￨L￨CC￨O￨- boundary￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- d-dimensional￨L￨JJ￨O￨- random￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- ξ￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- ξ1￨L￨NN￨O￨- ,￨L￨,￨O￨- ξ2￨L￨NN￨O￨- ,￨L￨,￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- unknown￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- approximated￨L￨VBN￨O￨- as￨L￨IN￨O￨- u￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- Xn￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- cnψn￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ∗￨L￨SYM￨O￨- †￨L￨SYM￨O￨- ‡￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- ε￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- truncation￨L￨NN￨O￨- error￨L￨NN￨O￨- ;￨L￨:￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- integer￨L￨NN￨O￨- ;￨L￨:￨O￨- cn￨L￨NN￨O￨- are￨L￨VBP￨O￨- coefficients￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- ψn￨L￨NN￨O￨- are￨L￨VBP￨O￨- multivariate￨L￨JJ￨O￨- orthonormal￨L￨JJ￨O￨- polynomials￨L￨NNS￨O￨- satisfying￨L￨VBG￨O￨- E￨U￨NN￨O￨- {￨L￨-LRB-￨O￨- ψi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ψj￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ZRd￨U￨NN￨O￨- ψi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ψj￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ρξ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dx￨L￨NN￨O￨- =￨L￨JJ￨O￨- δi￨L￨NN￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Kronecker￨U￨NNP￨O￨- delta￨L￨NN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- density￨L￨NN￨O￨- function￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PDF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- ξ￨L￨NN￨O￨- where￨L￨WRB￨O￨- ρξ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- δij￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- spectral-method-based￨L￨JJ￨O￨- surrogate￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- polynomial￨L￨JJ￨O￨- chaos￨L￨NN￨O￨- expansion￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- PCE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- generalized￨L￨VBN￨O￨- polynomial￨L￨JJ￨O￨- chaos￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- gPC￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- UQ￨U￨NNP￨O￨- in￨L￨IN￨O￨- engineering￨L￨NN￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- sciences￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- sliced￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- regression￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- guess￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- alternating￨L￨VBG￨O￨- direction￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- enhance￨L￨VB￨O￨- sparsity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Hermite￨U￨NNP￨O￨- polynomial￨L￨JJ￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- quantity￨L￨NN￨O￨A of￨L￨IN￨O￨- interest￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- {￨L￨-LRB-￨O￨- ξi￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- and￨L￨CC￨O￨- identically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- i.i.d.￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Gaussian￨U￨JJ￨MISC￨- random￨L￨JJ￨O￨- variables￨L￨NNS￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- ξ￨L￨FW￨O￨- ∼￨L￨FW￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Gaussian￨U￨JJ￨MISC￨- measure￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ψn￨L￨NN￨O￨- are￨L￨VBP￨O￨- normalized￨L￨VBN￨O￨- multi-variate￨L￨JJ￨O￨- Hermite￨U￨NNP￨O￨- polynomials￨L￨NNS￨O￨- .￨L￨.￨O￨- +Neighboring￨U￨JJ￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- network￨L￨NN￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- interact￨L￨VB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- epidemiological￨L￨JJ￨O￨- states￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨A ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- thus￨L￨RB￨O￨- change￨L￨VB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- avoiding￨L￨VBG￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- infective￨L￨JJ￨O￨A acquaintances￨L￨NNS￨O￨- amounts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- breaking￨L￨VBG￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infective￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- agent￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨A agent￨L￨NN￨O￨- may￨L￨MD￨O￨- lead￨L￨VB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- former￨L￨JJ￨O￨- .￨L￨.￨O￨- +Connections￨U￨NNP￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infective￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- broken￨L￨VBN￨O￨- by￨L￨IN￨O￨- either￨L￨CC￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- reconnected￨L￨VBD￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- member￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- reconnection￨L￨NN￨O￨- can￨L￨MD￨O￨- completely￨L￨RB￨O￨- suppress￨L￨VB￨O￨A the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- by￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- and￨L￨CC￨O￨- discontinuous￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infection-free￨L￨JJ￨O￨- states￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- scheme￨L￨NN￨O￨- of￨L￨IN￨O￨- SIS￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- S-nodes￨U￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- rate￨L￨NN￨O￨- p￨L￨NN￨O￨- along￨L￨IN￨O￨- links￨L￨NNS￨O￨- connecting￨L￨VBG￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- I-nodes￨U￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- fraction￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- ]￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- recover￨L￨VB￨O￨- with￨L￨IN￨O￨- rate￨L￨NN￨O￨- r.￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- incorporated￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- awareness￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- a￨L￨DT￨O￨- topology-changing￨L￨JJ￨O￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- link-number￨L￨JJ￨O￨- preserving￨L￨NN￨O￨- ,￨L￨,￨O￨- rewiring￨L￨VBG￨O￨A mechanism￨L￨NN￨O￨- :￨L￨:￨O￨- S-nodes￨U￨NNS￨O￨- try￨L￨VBP￨O￨- to￨L￨TO￨O￨- evade￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- retracting￨L￨VBG￨O￨- links￨L￨NNS￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- with￨L￨IN￨O￨- rate￨L￨NN￨O￨- w￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- rewiring￨L￨VBG￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- randomly￨L￨RB￨O￨- selected￨L￨VBN￨O￨- S-nodes￨U￨NNS￨O￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- show￨L￨VBP￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- phase￨L￨NN￨O￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- density￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- link￨L￨NN￨O￨- rewiring￨L￨NN￨O￨A prompts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- convergence￨L￨NN￨O￨- towards￨L￨IN￨O￨- a￨L￨DT￨O￨- well￨L￨RB￨O￨- defi￨L￨JJ￨O￨- ned￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- irrespective￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- paper￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- steady-state￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- from￨L￨IN￨O￨- individual-based￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- very￨L￨RB￨O￨- well￨L￨RB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨- integration￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- status￨L￨NN￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨A .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- active￨L￨JJ￨O￨- phase￨L￨NN￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- coevolving￨L￨VBG￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- and￨L￨CC￨O￨- maintain￨L￨VB￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- well￨L￨RB￨O￨- de￨L￨IN￨O￨- fined￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- s￨L￨VBZ￨O￨- not￨L￨RB￨O￨- A￨U￨DT￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- p-1￨L￨NN￨O￨- –￨L￨:￨O￨- Wieland￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- growing￨L￨VBG￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- may￨L￨MD￨O￨- adaptively￨L￨RB￨O￨- break￨L￨VB￨O￨- the￨L￨DT￨O￨- connections￨L￨NNS￨O￨- with￨L￨IN￨O￨- infected￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- yet￨L￨RB￨O￨- avoid￨L￨VBP￨O￨- getting￨L￨VBG￨O￨- isolated￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- reveal￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- phenomenon￨L￨NN￨O￨- -￨L￨:￨O￨- epidemic￨L￨JJ￨O￨- reemergence￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- incubated￨L￨VBN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- level￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- bursts￨L￨NNS￨O￨- up￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- linearly￨L￨RB￨O￨- growing￨L￨VBG￨O￨A network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- oscillatory￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- adopted￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- linearly￨L￨RB￨O￨- growing￨L￨VBG￨O￨A networks￨L￨NNS￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- may￨L￨MD￨O￨- break￨L￨VB￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +MODEL￨U￨NN￨TITLE￨- Consider￨U￨VB￨O￨- a￨L￨DT￨O￨- Barabasi-Albert￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- BA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- N￨U￨NN￨O￨- nodes￨L￨NNS￨O￨A as￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- nodal￨L￨JJ￨O￨- degree￨L￨NN￨O￨- hki￨L￨NN￨O￨- =￨L￨JJ￨O￨- 2m￨L￨NN￨O￨- and￨L￨CC￨O￨- m￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- attached￨L￨VBN￨O￨- by￨L￨IN￨O￨- each￨L￨DT￨O￨- newly￨L￨RB￨O￨- added￨L￨VBN￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +Interestingly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- reemergence￨L￨NN￨O￨- phenomenon￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A may￨L￨MD￨O￨- stay￨L￨VB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- level￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- bursts￨L￨NNS￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +emit￨L￨VB￨O￨- signals￨L￨NNS￨O￨- upon￨L￨IN￨O￨- making￨L￨VBG￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨A from￨L￨IN￨O￨- state￨L￨NN￨O￨- T￨U￨NN￨O￨- to￨L￨TO￨O￨- state￨L￨NN￨O￨- D￨U￨NN￨O￨- ;￨L￨:￨O￨- we￨L￨PRP￨O￨- adopt￨L￨VBP￨O￨- concentration￨L￨NN￨O￨- Individuals￨U￨NNS￨O￨- units￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- each￨L￨DT￨O￨- such￨L￨JJ￨O￨- event￨L￨NN￨O￨- produces￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- unit￨L￨NN￨O￨- of￨L￨IN￨O￨- signal￨L￨NN￨O￨- molecules￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- An￨U￨DT￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- state￨L￨NN￨O￨- D￨U￨NN￨O￨- has￨L￨VBZ￨O￨- transition￨L￨NN￨O￨A rates￨L￨NNS￨O￨- wDS￨L￨NN￨O￨- and￨L￨CC￨O￨- wDR￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- states￨L￨NNS￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +dCij￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- D￨U￨NN￨O￨- ∆￨L￨CD￨NUMBER￨- Cij￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- λCij￨L￨NN￨O￨- +￨L￨CC￨O￨- nij￨L￨NN￨O￨- X￨U￨NN￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- δ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- tk￨L￨NN￨O￨- ;￨L￨:￨O￨- ij￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- ∆￨L￨SYM￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- Laplacian￨U￨NN￨MISC￨- ,￨L￨,￨O￨- D￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- decay￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- nij￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- times￨L￨NNS￨O￨- site￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- made￨L￨VBN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨A from￨L￨IN￨O￨- T￨U￨NN￨O￨- to￨L￨TO￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- tk￨L￨NN￨O￨- ;￨L￨:￨O￨- ij￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- times￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- An￨U￨DT￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- state￨L￨NN￨O￨- T￨U￨NN￨O￨- has￨L￨VBZ￨O￨- transition￨L￨NN￨O￨A rates￨L￨NNS￨O￨- wT￨L￨VBP￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- wT￨L￨NN￨O￨- D￨U￨NN￨O￨- and￨L￨CC￨O￨- wT￨L￨NN￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- states￨L￨NNS￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- D￨U￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +age￨L￨NN￨O￨- since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ·￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ·￨L￨NN￨O￨- quarantine￨L￨NN￨O￨A ·￨L￨CD￨NUMBER￨- SARS￨U￨NNP￨O￨- ·￨L￨NN￨O￨- Keywords￨U￨NNS￨O￨- smallpox￨L￨VBP￨O￨- Mathematics￨U￨NNP￨O￨- Sub￨U￨NN￨O￨- ject￨L￨NN￨O￨- Classification￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 92B05￨L￨NN￨O￨- ·￨L￨NN￨O￨- 35Q92￨L￨NN￨O￨- ·￨L￨NN￨O￨- 37N25￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Our￨U￨PRP$￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- identifying￨L￨VBG￨O￨- and￨L￨CC￨O￨- isolating￨L￨VBG￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- tracing￨L￨VBG￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- quarantine￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- basic￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- identifying￨L￨VBG￨O￨- and￨L￨CC￨O￨- isolating￨L￨VBG￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- tracing￨L￨VBG￨O￨- and￨L￨CC￨O￨- quarantine￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- identified￨L￨JJ￨O￨- infectives￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- partial￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- variable￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- age￨L￨NN￨O￨- since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A infectives￨L￨NNS￨O￨- and￨L￨CC￨O￨- quarantining￨L￨VBG￨O￨- susceptibles￨L￨NNS￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- two￨L￨CD￨NUMBER￨- practical￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- guidelines￨L￨NNS￨O￨- about￨L￨IN￨O￨- emergency￨L￨NN￨O￨- preparedness￨L￨NN￨O￨- and￨L￨CC￨O￨- response￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨- bioterrorist￨L￨NN￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- SARS￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Taiwan￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- avoided￨L￨VBN￨O￨- by￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A .￨L￨.￨O￨- +Isolation￨U￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- important￨L￨JJ￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- quarantine￨L￨NN￨O￨A of￨L￨IN￨O￨- traced￨L￨VBN￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- known￨L￨JJ￨O￨- infectives￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contact￨L￨NN￨O￨- interval￨L￨NN￨O￨- from￨L￨IN￨O￨- person￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- person￨L￨NN￨O￨- j￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- in￨L￨IN￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨A contact￨L￨NN￨O￨A from￨L￨IN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- de￨L￨FW￨O￨- fine￨L￨FW￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- suf￨L￨NN￨O￨- ficient￨L￨NN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- suscep￨L￨JJ￨O￨- tible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- nonparametric￨L￨JJ￨O￨- MLE￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- interval￨L￨NN￨O￨A cumulative￨L￨JJ￨O￨- hazard￨L￨NN￨O￨- function￨L￨NN￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- call￨L￨VBP￨O￨- the￨L￨DT￨O￨- marginal￨L￨JJ￨O￨- Nelson-Aalen￨U￨JJ￨MISC￨- estimate￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- prey￨L￨NN￨O￨A ,￨L￨,￨O￨- σ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- q￨L￨VB￨O￨- the￨L￨DT￨O￨- predation￨L￨NN￨O￨- rate￨L￨NN￨O￨- on￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- w￨L￨VB￨O￨- the￨L￨DT￨O￨- predation￨L￨NN￨O￨- rate￨L￨NN￨O￨- on￨L￨IN￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- µ￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- plus￨L￨CC￨O￨- disease-related￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- predators￨L￨NNS￨O￨- ,￨L￨,￨O￨- e￨L￨SYM￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- uptake￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- predation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- predators￨L￨NNS￨O￨- ,￨L￨,￨O￨- K￨U￨NNP￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- ’s￨L￨POS￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- .￨L￨.￨O￨- +T￨U￨NN￨O￨- −￨L￨SYM￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- 2K￨L￨NN￨O￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- w￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- P￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- introduces￨L￨VBZ￨O￨- another￨L￨DT￨O￨- new￨L￨JJ￨O￨- variable￨L￨NN￨O￨- ,￨L￨,￨O￨- A￨U￨NN￨O￨- =￨L￨JJ￨O￨- V￨U￨NN￨O￨- T￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- replacing￨L￨VBG￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- reformulate￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- dA￨L￨NN￨O￨- dt￨L￨NN￨O￨A dT￨L￨NN￨O￨- dt￨L￨NN￨O￨- dP￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- r￨L￨NN￨O￨- K￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- σ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- A2￨U￨NN￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- A2T￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- q￨L￨JJ￨O￨- −￨L￨NN￨O￨- w￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- P￨U￨NN￨O￨- A￨U￨NN￨O￨- −￨L￨NN￨O￨- K￨U￨NN￨O￨- r￨L￨NN￨O￨- AT￨U￨IN￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- w￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- T￨U￨NN￨O￨- µ￨L￨NN￨O￨- T￨U￨NN￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- µ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- AT￨U￨IN￨O￨- +￨L￨CC￨O￨- w￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- mP￨L￨NN￨O￨- +￨L￨CC￨O￨- f￨L￨FW￨O￨- P￨U￨NN￨O￨- T￨U￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- g￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- P￨U￨NN￨O￨- AT￨U￨IN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- thus￨L￨RB￨O￨- obtain￨L￨VB￨O￨- dS￨L￨NN￨O￨- dt￨L￨NN￨O￨A dT￨L￨NN￨O￨- dt￨L￨NN￨O￨- dP￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- r￨L￨NN￨O￨- σ￨L￨NN￨O￨- P￨U￨NN￨O￨- S￨U￨NN￨O￨- S￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- T￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- µ￨L￨NN￨O￨- T￨U￨NN￨O￨- r￨L￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- K￨U￨NNP￨O￨- S￨U￨NN￨O￨- T￨U￨NN￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- µ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- T￨U￨NN￨O￨- P￨U￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- mP￨L￨NN￨O￨- +￨L￨CC￨O￨- f￨L￨FW￨O￨- P￨U￨NN￨O￨- T￨U￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- g￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +AT￨U￨IN￨O￨- 3￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- 2K￨L￨NN￨O￨- −￨L￨NN￨O￨- +￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- P￨U￨NN￨O￨- A2￨U￨NN￨O￨- T￨U￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- −￨L￨NN￨O￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- A￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- P￨U￨NN￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- q￨L￨NN￨O￨- w￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- unsatisfactory￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- variable￨L￨JJ￨O￨A T￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- denominator￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- dV￨L￨NN￨O￨- dt￨L￨NN￨O￨A dT￨L￨NN￨O￨- dt￨L￨NN￨O￨- dP￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- r￨L￨NN￨O￨- r￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- 2T￨L￨NN￨O￨- +￨L￨CC￨O￨- σ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- 2K￨L￨NN￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- σ￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- µ￨L￨NN￨O￨- r￨L￨NN￨O￨- µ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- q￨L￨VB￨O￨- w￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- P￨U￨NN￨O￨- V￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- T￨U￨NN￨O￨- T￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- V￨U￨NN￨O￨- T￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- w￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- P￨U￨NN￨O￨- V￨U￨NN￨O￨- K￨U￨NN￨O￨- T￨U￨NN￨O￨- V￨U￨NN￨O￨- T￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- µ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- +￨L￨CC￨O￨- w￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- P￨U￨NN￨O￨- V￨U￨NN￨O￨- q￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- mP￨L￨NN￨O￨- +￨L￨CC￨O￨- f￨L￨FW￨O￨- P￨U￨NN￨O￨- T￨U￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- g￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- P￨U￨NN￨O￨- V￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- shortest￨L￨JJS￨O￨A path￨L￨NN￨O￨- lengths￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- shortest￨L￨JJS￨O￨- path￨L￨NN￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- characterize￨L￨VBP￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- shortest￨L￨JJS￨O￨- path￨L￨NN￨O￨- lengths￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- centre￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- six￨L￨CD￨NUMBER￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- separation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- small-world￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Gleeson1￨U￨NN￨O￨- 1MACSI￨L￨NN￨O￨- ,￨L￨,￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mathematics￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Statistics￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Limerick￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Ireland￨U￨NNP￨COUNTRY￨- We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- calculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- shortest￨L￨JJS￨O￨A paths￨L￨NNS￨O￨- lengths￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- called￨L￨VBN￨O￨- intervertex￨L￨NN￨O￨- distances￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- geodesic￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- unweighted￨L￨JJ￨O￨- undirected￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- method￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- shortest￨L￨JJS￨O￨A path￨L￨NN￨O￨- lengths￨L￨NNS￨O￨- on￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- joint￨L￨JJ￨O￨- degree-degree￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- analytical￨L￨JJ￨O￨A results￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- analogy￨L￨NN￨O￨- between￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- reaching￨L￨VBG￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- n￨L￨NN￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- steps￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- node￨L￨NN￨O￨- being￨L￨VBG￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- distance￨L￨NN￨O￨- n￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- obtain￨L￨VBP￨O￨- very￨L￨RB￨O￨- accurate￨L￨JJ￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- synthetic￨L￨JJ￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- specified￨L￨JJ￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- networks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- worthwhile￨L￨JJ￨O￨- and￨L￨CC￨O￨- Sr￨U￨NNP￨O￨- to￨L￨TO￨O￨- point￨L￨VB￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- exhibiting￨L￨VBG￨O￨- hysteresis￨L￨NN￨O￨- of￨L￨IN￨O￨- Sl￨U￨NN￨O￨- or￨L￨CC￨O￨- Sr￨U￨NNP￨O￨- types￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- must￨L￨MD￨O￨- exist￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- stable￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- fixed￨L￨JJ￨O￨- points￨L￨NNS￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨A rates￨L￨NNS￨O￨A as￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨O￨- most￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- stable￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- fixed￨L￨JJ￨O￨- point￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- of￨L￨IN￨O￨- C￨U￨NN￨O￨- type￨L￨NN￨O￨- .￨L￨.￨O￨- +Three￨U￨CD￨NUMBER￨- positive￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- called￨L￨VBD￨O￨A the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- inPSfrag￨L￨NN￨O￨- replacements￨L￨NNS￨O￨- fection￨L￨JJ￨O￨- factor￨L￨NN￨O￨- ,￨L￨,￨O￨- PSfrag￨U￨NN￨O￨- replacements￨L￨NNS￨O￨- relative￨L￨JJ￨O￨- coinfection￨L￨NN￨O￨- factors￨L￨NNS￨O￨- class￨L￨NN￨O￨- and￨L￨CC￨O￨- singly￨L￨RB￨O￨- infected￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- to￨L￨TO￨O￨- C￨U￨NN￨O￨- be￨L￨VB￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- uniformity￨L￨NN￨O￨- of￨L￨IN￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NNP￨O￨- 1a￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- case￨L￨NN￨O￨- that￨L￨WDT￨O￨- min￨L￨NN￨DURATION￨- {￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- resp.￨L￨NN￨O￨- ,￨L￨,￨O￨- max￨L￨NN￨O￨A {￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- cooperative￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- resp.￨L￨JJ￨O￨- ,￨L￨,￨O￨- AB￨U￨NNP￨STATE_OR_PROVINCE￨- competitive￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- coinfection￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- min￨L￨NN￨DURATION￨- {￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- max￨L￨NN￨O￨A {￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- In￨U￨IN￨O￨- Ref￨U￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- C￨U￨NN￨O￨- =￨L￨JJ￨O￨- a￨L￨DT￨O￨- =￨L￨JJ￨O￨- b￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Sr￨U￨NNP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- uniform￨L￨JJ￨O￨- and￨L￨CC￨O￨- corresponds￨L￨VBZ￨O￨A to￨L￨TO￨O￨- noninteracting￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- said￨L￨VBD￨O￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- illustrated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨- yellow￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- resurgence￨L￨NN￨O￨- in￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A infested￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- procedures￨L￨NNS￨O￨- apply￨L￨VBP￨O￨- for￨L￨IN￨O￨- other￨L￨JJ￨O￨- aedestransmitted￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- chikungunya￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- consists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- function￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- straightforwardly￨L￨RB￨O￨- .￨L￨.￨O￨- +keywords￨L￨NNS￨O￨- :￨L￨:￨O￨- Aedes￨U￨NNS￨O￨- aegypti￨L￨NNS￨O￨- ,￨L￨,￨O￨- mosquitoes￨L￨NNS￨O￨A '￨L￨POS￨O￨- densities￨L￨NNS￨O￨- ,￨L￨,￨O￨- dengue￨L￨NN￨O￨- ,￨L￨,￨O￨- zika￨L￨NN￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- yellow￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- aedes￨L￨NNS￨O￨- mosquitoes￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- dengue￨L￨NN￨O￨- .￨L￨.￨O￨- +Empirical￨U￨JJ￨O￨- efforts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquitoes￨L￨NNS￨O￨A populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- affected￨L￨VBN￨O￨- areas￨L￨NNS￨O￨- are￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- in￨L￨IN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- very￨L￨RB￨O￨- laboriously￨L￨RB￨O￨- done￨L￨VBN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Model￨U￨NNP￨TITLE￨- Formulation￨U￨NNP￨O￨- The￨U￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- sub-populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A C￨U￨NN￨CAUSE_OF_DEATH￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- acute￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- undergoing￨L￨VBG￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- chronic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Ch￨U￨NN￨COUNTRY￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- Ch￨U￨NN￨COUNTRY￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- usual￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨A for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- includes￨L￨VBZ￨O￨- compartments￨L￨NNS￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- under￨L￨IN￨O￨- treatment￨L￨NN￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- had￨L￨VBN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- HCV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- coefficients￨L￨NNS￨O￨- of￨L￨IN￨O￨- HCV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- acute￨L￨JJ￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A C￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- chronic￨L￨JJ￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨- C￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Ch￨U￨NN￨COUNTRY￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- undergoing￨L￨VBG￨O￨- treatment￨L￨NN￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- cured￨L￨VBN￨O￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- β1￨L￨NN￨O￨- ,￨L￨,￨O￨- β2￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- β3￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HCV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dS￨L￨NN￨O￨- dt￨L￨NN￨O￨A dE￨L￨NN￨O￨- dt￨L￨NN￨O￨- dI￨L￨NNP￨O￨- dt￨L￨NNP￨O￨- dT￨L￨NNP￨O￨- dt￨L￨VBD￨O￨- dCh￨L￨NNP￨O￨- dt￨L￨NNP￨O￨- dV￨L￨NNP￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Λ￨U￨NN￨O￨- +￨L￨CC￨O￨- ρT￨L￨NN￨O￨- +￨L￨CC￨O￨- αV￨L￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β1￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- β2Ch￨L￨NN￨O￨- +￨L￨CC￨O￨- β3T￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- σCh￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- µS￨L￨NN￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- β1￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- β2Ch￨L￨NN￨O￨- +￨L￨CC￨O￨- β3T￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- ψ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- β1￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- β2Ch￨L￨NN￨O￨- +￨L￨CC￨O￨- β3T￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- V￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ǫ￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- ǫE￨L￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- κ￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- π1κI￨L￨NN￨O￨- +￨L￨CC￨O￨- π2Ch￨L￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ρ￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- T￨U￨NN￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- π1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- κI￨L￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- π2￨L￨NN￨O￨- +￨L￨CC￨O￨- σ￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Ch￨U￨NN￨COUNTRY￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- bΛ￨L￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- V￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- ψ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- β1￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- β2Ch￨L￨NN￨O￨- +￨L￨CC￨O￨- β3T￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- V￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- considers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A C￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HCV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proved￨L￨VBD￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- balancedness￨L￨NN￨O￨- center￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- uniform￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- preferential￨L￨JJ￨O￨- attachment￨L￨NN￨O￨- tree￨L￨NN￨O￨A growth￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- growing￨L￨VBG￨O￨- tree￨L￨NN￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- popular￨L￨JJ￨O￨- Susceptible-Infected￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- regular￨L￨JJ￨O￨- tree￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- Independent￨U￨NNP￨ORGANIZATION￨- Cascade￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- IC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- Susceptible￨U￨NNP￨O￨- Infected￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- subgraph￨L￨NN￨O￨- grows￨L￨VBZ￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Jordan￨U￨NNP￨CITY￨- center￨L￨NN￨O￨A persists￨L￨VBZ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- timesteps￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- regular￨L￨JJ￨O￨- tree￨L￨NN￨O￨A on￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- starts￨L￨VBZ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- root￨L￨NN￨O￨- node￨L￨NN￨O￨- and￨L￨CC￨O￨- spreads￨L￨NNS￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- various￨L￨JJ￨O￨- random￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- bound￨L￨VBD￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- Jordan￨U￨NNP￨CITY￨- center￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- root￨L￨NN￨O￨- node￨L￨NN￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- adopted￨L￨VBD￨O￨- the￨L￨DT￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- mechanism￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- called￨L￨VBN￨O￨- density-dependent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- mechanism￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptibleinfected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- incidence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- encounters￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- mathematically￨L￨RB￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- bilinear￨L￨JJ￨O￨- function￨L￨NN￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- performing￨L￨VBG￨O￨- qualitative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- uniform￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- property￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- in￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- profile￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨A equilibria￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- when￨L￨WRB￨O￨- exist￨L￨VBP￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- environment￨L￨NN￨O￨- as￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- .￨L￨.￨O￨- +SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- reaction-diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- mechanism￨L￨NN￨O￨A ,￨L￨,￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- endemic￨L￨JJ￨O￨- equilibria￨L￨NNS￨O￨- ,￨L￨,￨O￨- small￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- asymptotic￨L￨JJ￨O￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- persistence/extinction￨L￨NN￨O￨- .￨L￨.￨O￨- +Employing￨U￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- mechanism￨L￨NN￨O￨A and￨L￨CC￨O￨- instead￨L￨RB￨O￨- considering￨L￨VBG￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptibleinfectedsusceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- ODE￨U￨NN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- S￨U￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- βS￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ′￨L￨VBP￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- γ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- initial￨L￨JJ￨O￨- data￨L￨NNS￨O￨- fulfilling￨L￨VBG￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Defining￨U￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- β￨L￨NN￨O￨- /￨L￨:￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DFE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨A if￨L￨IN￨O￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- /￨L￨:￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- /￨L￨:￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- travelers￨L￨NNS￨O￨- network￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- simulate￨L￨VB￨O￨- 65￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- see￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A spread￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- from￨L￨IN￨O￨- different￨L￨JJ￨O￨- 14￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- as￨L￨IN￨O￨- origins￨L￨NNS￨O￨- of￨L￨IN￨O￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- pandemic￨L￨NN￨O￨A in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- origins￨L￨NNS￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- considering￨L￨VBG￨O￨- local￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- pandemic￨L￨JJ￨O￨A originates￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- ,￨L￨,￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- China￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- results￨L￨VBZ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- war￨L￨NN￨CAUSE_OF_DEATH￨- varies￨L￨VBZ￨O￨- in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- which￨L￨WDT￨O￨- were￨L￨VBD￨O￨- deeply￨L￨RB￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- war￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- much￨L￨JJ￨O￨- influenced￨L￨VBN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- war￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- which￨L￨WDT￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- much￨L￨JJ￨O￨- engaged￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- war￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- war￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- another￨L￨DT￨O￨- scenario￨L￨NN￨O￨- :￨L￨:￨O￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- no￨L￨DT￨O￨- military￨L￨JJ￨O￨- traffic￨L￨NN￨O￨A during￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenced￨L￨VBN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- war￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- 12￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨- traffic￨L￨NN￨O￨A in￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- -1917￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- dotted-line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- solid-line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- We￨U￨PRP￨O￨- hypothesize￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- traffic￨L￨NN￨O￨A pattern￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- Keywords-Simulation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Pandemic￨U￨NNP￨O￨- ,￨L￨,￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- SEIR￨U￨NNP￨O￨- ,￨L￨,￨O￨- Social￨U￨NNP￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨- traffic￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- both￨L￨DT￨O￨- the￨L￨DT￨O￨- civil￨L￨JJ￨O￨- traffic￨L￨NN￨O￨- and￨L￨CC￨O￨- Network￨U￨NNP￨O￨- ,￨L￨,￨O￨- Spanish￨U￨NNP￨CAUSE_OF_DEATH￨- Flu￨U￨NNP￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- International￨U￨NNP￨ORGANIZATION￨- Traffic￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨CAUSE_OF_DEATH￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- the￨L￨DT￨O￨- military￨L￨JJ￨O￨- traffic￨L￨NN￨O￨- since￨L￨IN￨O￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- First￨U￨NNP￨ORDINAL￨- World￨U￨NNP￨MISC￨- War￨U￨NNP￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 1914-I￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- tra￨L￨NN￨O￨- jectories￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- methodology￨L￨NN￨O￨- is￨L￨VBZ￨O￨- applied￨L￨VBN￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- evidence￨L￨NN￨O￨- in￨L￨IN￨O￨- related￨L￨JJ￨O￨- public￨L￨JJ￨O￨A health￨L￨NN￨O￨A decisions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Epidemics￨U￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- modelled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- non-linear￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- through￨L￨IN￨O￨- partial￨L￨JJ￨O￨- and￨L￨CC￨O￨- noisy￨L￨JJ￨O￨A data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Much￨U￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A has￨L￨VBZ￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- proposed￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- approach￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- addressing￨L￨VBG￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A problem￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- conventional￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- yield￨L￨VB￨O￨- more￨L￨JJR￨O￨- effective￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- suppression￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- graph-based￨L￨JJ￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- tested￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A methods￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- Method￨U￨NN￨O￨- for￨L￨IN￨O￨- Reducing￨U￨VBG￨O￨- the￨L￨DT￨O￨- Severity￨U￨NN￨O￨- of￨L￨IN￨O￨- Epidemics￨U￨NNS￨O￨- by￨L￨IN￨O￨- Allocating￨U￨VBG￨O￨- Vaccines￨U￨NNS￨O￨- According￨U￨VBG￨O￨- to￨L￨TO￨O￨- Centrality￨U￨NNP￨O￨- Krzysztof￨U￨NNP￨PERSON￨- Drewniak￨U￨NNP￨PERSON￨- Joseph￨U￨NNP￨PERSON￨- Helsing￨U￨NNP￨PERSON￨- Armin￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- Mikler￨U￨NNP￨PERSON￨- ABSTRACT￨U￨NN￨O￨- One￨U￨CD￨NUMBER￨- long-standing￨L￨JJ￨O￨- question￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- research￨L￨NN￨O￨- is￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- best￨L￨JJS￨O￨- to￨L￨TO￨O￨- allocate￨L￨VB￨O￨- limited￨L￨JJ￨O￨- amounts￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨A or￨L￨CC￨O￨- similar￨L￨JJ￨O￨- preventative￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- physical￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- Infected￨U￨JJ￨O￨- Susceptible￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- process￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- UAU￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Unaware￨U￨JJ￨O￨- Aware￨U￨JJ￨O￨- Unaware￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- process￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- virtual￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- mediated￨L￨VBN￨O￨- awareness￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Further￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- awareness￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨A significantly￨L￨RB￨O￨- lowers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Similarly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- information￨L￨NN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- awareness￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨A depends￨L￨VBZ￨O￨- upon￨L￨IN￨O￨- its￨L￨PRP$￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨A depends￨L￨VBZ￨O￨- upon￨L￨IN￨O￨- its￨L￨PRP$￨O￨- awareness￨L￨NN￨O￨- probability￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- awareness￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- work￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- lattice￨L￨NN￨O￨- with￨L￨IN￨O￨- random￨L￨JJ￨O￨- bond￨L￨NN￨O￨- strengths￨L￨NNS￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- with￨L￨IN￨O￨- strong￨L￨JJ￨O￨- disorder￨L￨NN￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- patchiness￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- likely￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- criterion￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- strongly￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disorder￨L￨NN￨O￨- .￨L￨.￨O￨- +Firewalls￨U￨NNS￨O￨- ,￨L￨,￨O￨- Disorder￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Percolation￨U￨NN￨O￨- in￨L￨IN￨O￨- Epidemics￨U￨NNP￨O￨- C.￨U￨NNP￨O￨- M.￨U￨NNP￨O￨- Sokolov2￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Michigan￨U￨NNP￨STATE_OR_PROVINCE￨- Center￨U￨NNP￨O￨- for￨L￨IN￨O￨- Theoretical￨U￨NNP￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Michigan￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Ann￨U￨NNP￨CITY￨- Arbor￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- MI￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- 48109-1120￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- USA￨U￨NNP￨ORGANIZATION￨- 2￨L￨CD￨NUMBER￨- Theoretische￨U￨NNP￨ORGANIZATION￨- Polymerphysik￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Unversit￨U￨NNP￨O￨- ¨￨L￨CD￨NUMBER￨- at￨L￨IN￨O￨- Freiburg￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Freiburg￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Germany￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- October￨U￨NNP￨DATE￨- 23￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- (￨L￨-LRB-￨O￨- site￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- percolation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- lattice￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- where￨L￨WRB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- site￨L￨NN￨O￨- is￨L￨VBZ￨O￨- occupied￨L￨VBN￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- susceptible￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- where￨L￨WRB￨O￨- some￨L￨DT￨O￨- agents￨L￨NNS￨O￨- travel￨L￨VBP￨O￨- long￨L￨JJ￨O￨- distances￨L￨NNS￨O￨- ,￨L￨,￨O￨- ‘￨L￨``￨O￨- small-world￨L￨JJ￨O￨- ’￨L￨''￨O￨- theory￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- extends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- weighted￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- connecting￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- higher-degree￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- gives￨L￨VBZ￨O￨- an￨L￨DT￨O￨- edge-based￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- weight￨L￨NN￨O￨A distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- quantitatively￨L￨RB￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- results￨L￨VBZ￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- weighted￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- weight￨L￨NN￨O￨A distribution￨L￨NN￨O￨- will￨L￨MD￨O￨- slow￨L￨VB￨O￨- down￨L￨RP￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- Spreading￨U￨NN￨O￨- in￨L￨IN￨O￨- Weighted￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- :￨L￨:￨O￨- An￨U￨DT￨O￨- Edge-Based￨U￨JJ￨MISC￨- Mean-Field￨U￨NNP￨MISC￨- Solution￨U￨NN￨MISC￨- Zimo￨U￨NNP￨PERSON￨- Yang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Tao￨U￨NNP￨O￨- Zhou￨U￨NNP￨O￨- ∗￨L￨NNP￨O￨- Web￨U￨NN￨O￨- Sciences￨U￨NNP￨O￨- Center￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electronic￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Chengdu￨U￨NNP￨CITY￨- 610054￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- People￨U￨NNPS￨LOCATION￨- ’s￨L￨POS￨LOCATION￨- Republic￨U￨NN￨COUNTRY￨- of￨L￨IN￨COUNTRY￨- China￨U￨NNP￨COUNTRY￨- Weight￨U￨NNP￨O￨- distribution￨L￨NN￨O￨- largely￨L￨RB￨O￨- impacts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A taking￨L￨VBG￨O￨- place￨L￨NN￨O￨- on￨L￨IN￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- studies￨L￨NNS￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- regular￨L￨JJ￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- weight￨L￨NN￨O￨A distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Kermack￨U￨NNP￨O￨- –￨L￨:￨O￨- McKendrick￨U￨NNP￨PERSON￨- threshold￨L￨NN￨O￨- theorem￨L￨NN￨O￨A is￨L￨VBZ￨O￨- replaced￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- takes￨L￨VBZ￨O￨- place￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- started￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- K0￨U￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- initially￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- 2￨L￨CD￨NUMBER￨- thus￨L￨RB￨O￨- being￨L￨VBG￨O￨- positive￨L￨JJ￨O￨- exactly￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- offspring￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- approximately￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- exceeds￨L￨VBZ￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ∞￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- branching￨L￨VBG￨O￨A approximation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- approximates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- potentially￨L￨RB￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- individual￨L￨JJ￨O￨- K￨U￨NN￨O￨- —￨L￨:￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Diekmann￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Heesterbeek￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- .￨L￨.￨O￨- +Letting￨U￨VBG￨O￨- t￨L￨NN￨O￨- →￨L￨SYM￨O￨- ∞￨L￨SYM￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- gives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A size￨L￨NN￨O￨A equation￨L￨NN￨O￨- if￨L￨IN￨O￨- ,￨L￨,￨O￨- −￨L￨IN￨O￨- log￨L￨NN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ∞￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- R0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ∞￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- ∞￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- dv￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- made￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- unit￨L￨NN￨O￨- density￨L￨NN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- proportion￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ∞￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- this￨L￨DT￨O￨- backward￨L￨RB￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- contains￨L￨VBZ￨O￨- few￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- when￨L￨WRB￨O￨- its￨L￨PRP$￨O￨- branching￨L￨VBG￨O￨A approximation￨L￨NN￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- K￨U￨NN￨O￨- is￨L￨VBZ￨O￨- unlikely￨L￨JJ￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- contains￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- branching￨L￨VBG￨O￨- approximation￨L￨NN￨O￨- never￨L￨RB￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- ,￨L￨,￨O￨- K￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- certain￨L￨JJ￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- well￨L￨RB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- or￨L￨CC￨O￨- less￨L￨RBR￨O￨- deterministic￨L￨JJ￨O￨- course￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- Dated￨U￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- Binary-state￨U￨JJ￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- Glauber￨U￨NNP￨PERSON￨- spin￨L￨VB￨O￨- dynamics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- accurately￨L￨RB￨O￨- approximated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- master￨L￨NN￨O￨A equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- strongly￨L￨RB￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- determine￨L￨VB￨O￨- critical￨L￨JJ￨O￨A values￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Ising￨U￨NN￨O￨- spin￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- disease-spread￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- master￨L￨NN￨O￨A equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- critical￨L￨JJ￨O￨- points￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- noise￨L￨NN￨O￨- level￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ma￨L￨NN￨O￨- jority-vote￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Six￨U￨CD￨NUMBER￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- Models￨U￨NNS￨O￨- on￨L￨IN￨O￨- Scale-free￨U￨JJ￨O￨- Networks￨U￨NNP￨O￨- Satoru￨U￨NNP￨PERSON￨- Morita￨U￨NNP￨PERSON￨- ∗￨L￨NNP￨O￨- Department￨U￨NNP￨O￨- of￨L￨IN￨O￨- Mathematical￨U￨NNP￨O￨- and￨L￨CC￨O￨- Systems￨U￨NNP￨O￨- Engineering￨U￨NNP￨O￨- ,￨L￨,￨O￨- Shizuoka￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hamamatsu￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- 432-8561￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- August￨U￨NNP￨DATE￨- 10￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Spreading￨U￨VBG￨O￨- phenomena￨L￨NNS￨O￨- are￨L￨VBP￨O￨- ubiquitous￨L￨JJ￨O￨A in￨L￨IN￨O￨- nature￨L￨NN￨O￨- and￨L￨CC￨O￨- society￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨A spread￨L￨VBN￨O￨A over￨L￨IN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- N￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- categorize￨L￨VB￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- compartments￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- only￨L￨RB￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨A individual￨L￨NN￨O￨A is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +–￨L￨:￨O￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- rare￨L￨JJ￨O￨- events￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- both￨L￨DT￨O￨- internal￨L￨JJ￨O￨A and￨L￨CC￨O￨- external￨L￨JJ￨O￨- noise￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- formalism￨L￨NN￨O￨- for￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- rare￨L￨JJ￨O￨- events￨L￨NNS￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- pair-quenched￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- and￨L￨CC￨O￨- large-deviation￨L￨JJ￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +Though￨U￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- metastable￨L￨JJ￨O￨- above￨L￨IN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- continually￨L￨RB￨O￨- fluctuates￨L￨VBZ￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- random￨L￨JJ￨O￨- perturbations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- nodal￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- call￨L￨VBP￨O￨- external￨L￨JJ￨O￨- and￨L￨CC￨O￨- internal￨L￨JJ￨O￨A noise￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- probability￨L￨NN￨O￨- versus￨L￨CC￨O￨A the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- connecting￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- φ￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- 6-regular￨L￨JJ￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- 500￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- β0￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.262￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- probability￨L￨NN￨O￨- versus￨L￨CC￨O￨A the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- xL￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- node￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- star￨L￨NN￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- 1001￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- β0￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.160￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- sensitivity￨L￨NN￨O￨- and￨L￨CC￨O￨- cost-effectiveness￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- done￨L￨VBN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- and￨L￨CC￨O￨- solved￨L￨VBN￨O￨- with￨L￨IN￨O￨- treatment￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- variable￨L￨NN￨O￨- .￨L￨.￨O￨- +140￨L￨CD￨NUMBER￨- PARAMETER￨U￨NN￨O￨- ESTIMATION￨U￨NN￨O￨- ,￨L￨,￨O￨- SENSITIVITY￨U￨NN￨O￨- ANALYSIS￨U￨NNS￨O￨- AND￨U￨CC￨O￨- OPTIMAL￨U￨JJ￨O￨- CONTROL￨U￨NNP￨O￨- OF￨U￨IN￨O￨- A￨U￨DT￨O￨- PERIODIC￨U￨JJ￨O￨- EPIDEMIC￨U￨NNP￨O￨- MODEL￨U￨NNP￨TITLE￨- interact￨L￨VBP￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- upon￨L￨IN￨O￨- phenomenological￨L￨JJ￨O￨A assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- built￨L￨VBN￨O￨- up￨L￨RP￨O￨- from￨L￨IN￨O￨- there￨L￨EX￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- research￨L￨NN￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- addresses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- fitting￨L￨VBG￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Florida￨U￨NNP￨STATE_OR_PROVINCE￨- HRSV￨U￨NN￨O￨- surveillance￨L￨NN￨O￨- system￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨A SEIRS￨U￨NNP￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- ,￨L￨,￨O￨- 60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- infants￨L￨NNS￨O￨A are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- during￨L￨IN￨O￨- their￨L￨PRP$￨O￨- first￨L￨JJ￨O￨- HRSV￨U￨NN￨O￨- season￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- nearly￨L￨RB￨O￨- all￨L￨DT￨O￨- children￨L￨NNS￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- three￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- is￨L￨VBZ￨O￨- shared￨L￨VBN￨O￨- by￨L￨IN￨O￨- m￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- p￨L￨NN￨O￨- arthropod￨L￨NN￨O￨- vector￨L￨NN￨O￨A species￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- each￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- is￨L￨VBZ￨O￨- structured￨L￨VBN￨O￨- into￨L￨IN￨O￨- n￨L￨NN￨O￨- stages￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- parameter￨L￨NN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- vector￨L￨NN￨O￨A species￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R2￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- investigate￨L￨VB￨O￨- less￨L￨JJR￨O￨- or￨L￨CC￨O￨- greater￨L￨JJR￨O￨A than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- push￨L￨VB￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- further￨L￨JJ￨O￨- realism￨L￨NN￨O￨- and￨L￨CC￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- past￨L￨NN￨DATE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- and￨L￨CC￨O￨- future￨L￨JJ￨DATE￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- characterized￨L￨VBN￨O￨- mathematically￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- help￨L￨NN￨O￨- of￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- investigations￨L￨NNS￨O￨- in￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- Ebola￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- tuberculosis￨L￨NNP￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- HIV/AIDS￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- ,￨L￨,￨O￨- 60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- infants￨L￨NNS￨O￨A are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- during￨L￨IN￨O￨- their￨L￨PRP$￨O￨- first￨L￨JJ￨O￨- HRSV￨U￨NN￨O￨- season￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- nearly￨L￨RB￨O￨- all￨L￨DT￨O￨- children￨L￨NNS￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- three￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Human￨U￨JJ￨O￨- respiratory￨L￨JJ￨O￨- syncytial￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HRSV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- compartmental￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- fractional￨L￨JJ￨O￨A optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- fractional￨L￨JJ￨O￨A optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- formulated￨L￨VBN￨O￨- and￨L￨CC￨O￨- solved￨L￨VBN￨O￨- ,￨L￨,￨O￨- having￨L￨VBG￨O￨- treatment￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- non-local￨L￨JJ￨O￨- fractional￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- non-integer￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- order￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Finite￨U￨JJ￨O￨- size￨L￨NN￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- QMF￨U￨NN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- disappearance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- λc￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨A limit￨L￨NN￨O￨A and￨L￨CC￨O￨- an￨L￨DT￨O￨- inverse￨L￨JJ￨O￨- participation￨L￨NN￨O￨- ratio￨L￨NN￨O￨- ∼￨L￨CD￨NUMBER￨- 0.25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- localization￨L￨NN￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- disassortative￨L￨JJ￨O￨- weight￨L￨NN￨O￨- scheme￨L￨NN￨O￨- .￨L￨.￨O￨- +Numerical￨U￨JJ￨O￨- simulations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- mean-field￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HMF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- theory￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- show￨L￨VBP￨O￨- strong￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- CP￨U￨NN￨O￨- defined￨L￨VBN￨O￨A on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- ubiquitous￨L￨JJ￨O￨- scale-free￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- exhibiting￨L￨VBG￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∼￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- singular￨L￨JJ￨O￨- behavior￨L￨NN￨O￨A is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- a￨L￨DT￨O￨- debated￨L￨VBN￨O￨- issue￨L￨NN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- CP￨U￨NNP￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- other￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- quenched￨L￨VBN￨O￨- disorder￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- relevant￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- defined￨L￨VBN￨O￨A on￨L￨IN￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- null￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infinite￨L￨NN￨O￨- size￨L￨NN￨O￨- limit￨L￨NN￨O￨- for￨L￨IN￨O￨- random￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A with￨L￨IN￨O￨- PL￨U￨NN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∼￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- irrespective￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- exponent￨L￨NN￨O￨- γ￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- degree-centrality￨L￨JJ￨O￨- ranks￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨JJS￨O￨- basic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- statistically￨L￨RB￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨- selected￨L￨VBN￨O￨- vertex￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- k￨L￨NN￨O￨- connections￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- prompt￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- and￨L￨CC￨O￨- predict￨L￨VB￨O￨- its￨L￨PRP$￨O￨- evolution￨L￨NN￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨A time￨L￨NN￨O￨A as￨L￨IN￨O￨- data￨L￨NNS￨O￨- accumulate￨L￨VBP￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- These￨U￨DT￨O￨- models￨L￨NNS￨O￨- rely￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- direct￨L￨JJ￨O￨- data￨L￨NNS￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- calls￨L￨VBZ￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- complex￨L￨NN￨O￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- requiring￨L￨VBG￨O￨- the￨L￨DT￨O￨- synthesis￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨A time￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- position￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- units￨L￨NNS￨O￨A does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- change￨L￨VB￨O￨- significantly￨L￨RB￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- cells￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- tissue￨L￨NN￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- viral￨L￨JJ￨O￨- or￨L￨CC￨O￨- bacterial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- trees￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- forest￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- organisms￨L￨NNS￨O￨- carrying￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- moving￨L￨VBG￨O￨- around￨L￨RB￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- are￨L￨VBP￨O￨- acquiring￨L￨VBG￨O￨- new￨L￨JJ￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- connections￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- perhaps￨L￨RB￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- common￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- involving￨L￨VBG￨O￨- long￨L￨JJ￨O￨- distance￨L￨NN￨O￨- flights￨L￨NNS￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- observations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- resulted￨L￨VBN￨O￨- in￨L￨IN￨O￨- major￨L￨JJ￨O￨- discoveries￨L￨NNS￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- highly￨L￨RB￨O￨- mobile￨L￨JJ￨TITLE￨- susceptible￨L￨JJ￨O￨- units￨L￨NNS￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- virtually￨L￨RB￨O￨- no￨L￨DT￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- about￨L￨IN￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- immobile￨L￨JJ￨O￨- units￨L￨NNS￨O￨- .￨L￨.￨O￨- +Statistical￨U￨JJ￨O￨- physics￨L￨NN￨O￨- inspired￨L￨VBD￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- fractal￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- clusters￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- their￨L￨PRP$￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- seem￨L￨VBP￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- percolation￨L￨NN￨O￨- theory￨L￨NN￨O￨- based￨L￨VBN￨O￨- interpretation￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- was￨L￨VBD￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- both￨L￨DT￨O￨- making￨L￨VBG￨O￨A video￨L￨NN￨O￨- recordings￨L￨NNS￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- photos￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- tracking￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- both￨L￨CC￨O￨- GFP￨U￨NN￨O￨- expression￨L￨NN￨O￨- and￨L￨CC￨O￨- making￨L￨VBG￨O￨- preparations￨L￨NNS￨O￨- with￨L￨IN￨O￨- various￨L￨JJ￨O￨- selective￨L￨JJ￨O￨- ,￨L￨,￨O￨- immuno-histochemistry￨L￨JJ￨O￨- based￨L￨VBN￨O￨- stainings￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- in￨L￨FW￨O￨- vitro￨L￨FW￨O￨- spreading￨L￨NN￨O￨A of￨L￨IN￨O￨- Listeria￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- Shigella￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- in￨L￨IN￨O￨- 2D￨L￨NN￨O￨- cell￨L￨NN￨O￨- cultures￨L￨NNS￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- circular￨L￨JJ￨O￨- or￨L￨CC￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- plaques￨L￨NNS￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- typically￨L￨RB￨O￨- take￨L￨VBP￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- variability￨L￨NN￨O￨A ,￨L￨,￨O￨- age￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- seasonal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- multi-scale￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- account￨L￨NN￨O￨- for￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- more￨L￨JJR￨O￨- homogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- decreased￨L￨VBN￨O￨- for￨L￨IN￨O￨- low￨L￨JJ￨O￨- concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- caretakers￨L￨NNS￨O￨- whereas￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- emerges￨L￨VBZ￨O￨A if￨L￨IN￨O￨- caretaker￨L￨NN￨TITLE￨- concentration￨L￨NN￨O￨- passes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- well￨L￨RB￨O￨- defined￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- pure￨L￨JJ￨O￨- avoidance￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- few￨L￨JJ￨O￨- caretaker￨L￨NN￨TITLE￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- curtailing￨L￨VBG￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- possess￨L￨VBP￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- topological￨L￨JJ￨O￨- variability￨L￨NN￨O￨A .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- awareness￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- typically￨L￨RB￨O￨A yields￨L￨VBZ￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- evolves￨L￨VBZ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- caretaker￨L￨NN￨TITLE￨- links￨L￨NNS￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- react￨L￨VBP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- or￨L￨CC￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- they￨L￨PRP￨O￨- make￨L￨VBP￨O￨- with￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- authors￨L￨NNS￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- mean￨L￨NN￨O￨- –￨L￨:￨O￨- field￨L￨JJ￨O￨- level￨L￨NN￨O￨- and￨L￨CC￨O￨- observed￨L￨VBN￨O￨- that￨L￨IN￨O￨- cooperative￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- strength￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- a￨L￨DT￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- transition￨L￨NN￨O￨A from￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- to￨L￨TO￨O￨- discontinuous￨L￨JJ￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- CGCG￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- mutual￨L￨JJ￨O￨- cooperative￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- co￨L￨NN￨O￨- –￨L￨:￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- Two￨U￨CD￨NUMBER￨- different￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- simultaneously￨L￨RB￨O￨- spread￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- :￨L￨:￨O￨- having￨L￨VBG￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- gives￨L￨VBZ￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- probability￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- large￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- strong￨L￨JJ￨O￨- finite￨L￨NN￨O￨- size￨L￨NN￨O￨- effects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- present￨L￨JJ￨DATE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- discontinuous￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨A is￨L￨VBZ￨O￨- manifest￨L￨JJ￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨A is￨L￨VBZ￨O￨- strictly￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- continuous￨L￨JJ￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- large￨L￨JJ￨O￨- cooperativity￨L￨NN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- transition￨L￨NN￨O￨A is￨L￨VBZ￨O￨- always￨L￨RB￨O￨- abrupt￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- discontinuity￨L￨NN￨O￨- decreasing￨L￨VBG￨O￨- as￨L￨IN￨O￨- clustering￨L￨NN￨O￨- is￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- .￨L￨.￨O￨- +Murray￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- co-workers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- studied￨L￨VBD￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A among￨L￨IN￨O￨- foxes￨L￨NNS￨O￨- formulated￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- partial￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Numerical￨U￨JJ￨O￨- simulations￨L￨NNS￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epizootic￨L￨JJ￨O￨- front￨L￨NN￨O￨- depend￨L￨VBP￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- and￨L￨CC￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- rabid￨L￨JJ￨O￨- foxes￨L￨NNS￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- territory￨L￨NN￨O￨- .￨L￨.￨O￨- +Lattice￨U￨NN￨O￨- models￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A among￨L￨IN￨O￨- foxes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- models￨L￨NNS￨O￨- take￨L￨VBP￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- short-range￨L￨JJ￨O￨- character￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A process￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- diffusive￨L￨JJ￨O￨- motion￨L￨NN￨O￨- of￨L￨IN￨O￨- rabid￨L￨JJ￨O￨- foxes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fox￨L￨NN￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨A into￨L￨IN￨O￨- three-species￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- incubating￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- or￨L￨CC￨O￨- rabid￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Markov￨U￨NNP￨PERSON￨- Chain￨U￨NNP￨O￨- ;￨L￨:￨O￨- epidemic￨L￨JJ￨O￨- ;￨L￨:￨O￨- pairwise￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- pairwise￨L￨JJ￨O￨- closure￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- :￨L￨:￨O￨- exact￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- graphs￨L￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- Section￨U￨NN￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- two￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- that￨L￨WDT￨O￨- motivate￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- investigations￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- possible￨L￨JJ￨O￨- extension￨L￨NN￨O￨- where￨L￨WRB￨O￨- progress￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- following￨L￨VBG￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- methods￨L￨NNS￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- includes￨L￨VBZ￨O￨- revisiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- classic￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨A models￨L￨NNS￨O￨- with￨L￨IN￨O￨- closures￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- triples￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- effective-degree-type￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- generating￨L￨VBG￨O￨- function￨L￨NN￨O￨- formalism￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- significant￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- closure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Kolmogorov￨U￨NNP￨MISC￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨- defined￨L￨VBN￨O￨- approximate￨L￨JJ￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- 1/N￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- KE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- first￨L￨NN￨O￨- motivation￨L￨NN￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- comes￨L￨VBZ￨O￨- from￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- paradigm￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- -￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- connected￨L￨VBN￨O￨A graph￨L￨NN￨O￨- with￨L￨IN￨O￨- N￨U￨NN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1/N￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- difference￨L￨NN￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- system￨L￨NN￨O￨- obtained￨L￨VBN￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- triple￨L￨JJ￨O￨- closure￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- network￨L￨NN￨O￨- evolves￨L￨VBZ￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- q￨L￨NN￨O￨- that￨L￨WDT￨O￨- aims￨L￨VBZ￨O￨- at￨L￨IN￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- quarantine￨L￨NN￨O￨- or￨L￨CC￨O￨- isolation￨L￨NN￨O￨A process￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- with￨L￨IN￨O￨- acquaintances￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- disrupted￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- standard￨L￨JJ￨O￨- policies￨L￨NNS￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- inspect￨L￨VBP￨O￨- the￨L￨DT￨O￨- reliability￨L￨NN￨O￨- of￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- and￨L￨CC￨O￨- quelling￨L￨VBG￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- mimicked￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- and￨L￨CC￨O￨- implementable￨L￨JJ￨O￨- quarantine￨L￨NN￨O￨- and￨L￨CC￨O￨- isolation￨L￨NN￨O￨A policies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Time￨U￨NNP￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- Infected￨U￨JJ￨O￨- individuals￨L￨NNS￨O￨- for￨L￨IN￨O￨- d￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- q￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.3￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- left￨L￨JJ￨O￨- side￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- q￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.8￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- right￨L￨JJ￨O￨- side￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- typical￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- λ￨L￨NN￨O￨- for￨L￨IN￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- 104￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- hki￨L￨NN￨O￨A =￨L￨JJ￨O￨- 5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Karsai￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- colleagues￨L￨NNS￨O￨- simulated￨L￨JJ￨O￨- the￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- bursty￨L￨JJ￨O￨A activity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- slow￨L￨VB￨O￨- down￨L￨RP￨O￨- contagions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Bursty￨U￨JJ￨O￨- activity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- long-tailed￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interevent￨L￨JJ￨O￨- intervals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IEIs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- simulate￨L￨VB￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- read￨L￨VBD￨O￨- the￨L￨DT￨O￨- events￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- event￨L￨NN￨O￨- sequence￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- chronological￨L￨JJ￨O￨- order￨L￨NN￨O￨- and￨L￨CC￨O￨- possibly￨L￨RB￨O￨- update￨L￨VB￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- traditional￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- them￨L￨PRP￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- aggregated￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- are￨L￨VBP￨O￨- drawn￨L￨VBN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- communicate￨L￨VBP￨O￨- in￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- event￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- investigate￨L￨VBP￨O￨- structural￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- aggregated￨L￨JJ￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- carry￨L￨VBP￨O￨- out￨L￨RP￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- real￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- network￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- that￨L￨IN￨O￨- bursty￨L￨JJ￨O￨A activity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- facilitate￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- and￨L￨CC￨O￨- richer￨L￨JJR￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- them￨L￨PRP￨O￨- as￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- only￨L￨RB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- event￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- and￨L￨CC￨O￨- predefined￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- activity￨L￨NN￨O￨- restriction￨L￨NN￨O￨A on￨L￨IN￨O￨- global￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- suppression￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- shortcuts￨L￨NNS￨O￨- existing￨L￨VBG￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- geographically￨L￨RB￨O￨- far￨L￨RB￨O￨- away￨L￨RB￨O￨- are￨L￨VBP￨O￨- worth￨L￨JJ￨O￨- extra￨L￨JJ￨O￨- attention￨L￨NN￨O￨- .￨L￨.￨O￨- +Inspired￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- territorial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- networked￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- refs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- incorporate￨L￨VBP￨O￨- a￨L￨DT￨O￨- multi-layer￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- regular￨L￨JJ￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- segregated￨L￨VBN￨O￨- spatial￨L￨JJ￨O￨- domains￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- representing￨L￨VBG￨O￨- individual-based￨L￨JJ￨O￨- linkage￨L￨NN￨O￨- ,￨L￨,￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- incorporating￨L￨VBG￨O￨- segregated￨L￨VBN￨O￨- spatial￨L￨JJ￨O￨- domain￨L￨NN￨O￨- and￨L￨CC￨O￨- individual-based￨L￨JJ￨O￨- linkage￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- change￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- territorial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- networked￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨A structures￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- Z.H.￨U￨NNP￨PERSON￨- Liu￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- 0.5￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- τ￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- linkage￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- depicting￨L￨VBG￨O￨- preventive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- transmitting￨L￨VBG￨O￨- probability￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- particular￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- immune￨L￨JJ￨O￨- or￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- previous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- information￨L￨NN￨O￨A diffusion￨L￨NN￨O￨A indeed￨L￨RB￨O￨- inhibits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- significantly￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- enhance￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- results￨L￨NNS￨O￨- and￨L￨CC￨O￨- numerical￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- approach￨L￨NN￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- information-driven￨L￨JJ￨O￨- adaptive￨L￨JJ￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- slow￨L￨VB￨O￨- down￨L￨RP￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- diminish￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- state￨L￨NN￨O￨- significa￨L￨NN￨O￨- ntly￨L￨RB￨O￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- spreading￨L￨NN￨O￨- dynamic￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- issues￨L￨NNS￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- science￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- related￨L￨JJ￨O￨- research￨L￨NN￨O￨- processes￨L￨NNS￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨A diffusion￨L￨NN￨O￨A in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- information-driven￨L￨JJ￨O￨- adaptive￨L￨JJ￨O￨A process￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- abilities￨L￨NNS￨O￨- to￨L￨TO￨O￨- recognize￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- would￨L￨MD￨O￨- break￨L￨VB￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- neighbors￨L￨NNS￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- from￨L￨IN￨O￨- further￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Nowadays￨U￨RB￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- information￨L￨NN￨O￨A diffusion￨L￨NN￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- theoretically￨L￨RB￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- concurrency￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- has￨L￨VBZ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- network￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- can￨L￨MD￨O￨- suppress￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- yield￨L￨VB￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- concurrency￨L￨NN￨O￨- is￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- enhance￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- concurrency￨L￨NN￨O￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- .￨L￨.￨O￨- +is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- node￨L￨NN￨O￨A Activity￨U￨NN￨O￨- potential￨L￨JJ￨O￨- ai￨L￨VBP￨O￨- i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- activated￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- window￨L￨NN￨O￨- of￨L￨IN￨O￨- constant￨L￨JJ￨O￨- duration￨L￨NN￨O￨- τ￨L￨NN￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- i￨L￨FW￨O￨- ≤￨L￨FW￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- drawn￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- density￨L￨NN￨O￨- F￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- assigned￨L￨VBN￨O￨- an￨L￨DT￨O￨- activity￨L￨NN￨O￨A potential￨L￨JJ￨O￨- ai￨L￨VBP￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- a￨L￨DT￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- most￨L￨JJS￨O￨- prior￨L￨JJ￨O￨- works￨L￨NNS￨O￨- which￨L￨WDT￨O￨- consider￨L￨VBP￨O￨- mean￨L￨JJ￨O￨- field￨L￨NN￨O￨- ,￨L￨,￨O￨- open-loop￨L￨JJ￨O￨- control￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- develops￨L￨VBZ￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨A of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- which￨L￨WDT￨O￨- leverages￨L￨VBZ￨O￨- incomplete￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conclude￨L￨VBP￨O￨- by￨L￨IN￨O￨- formulating￨L￨VBG￨O￨- a￨L￨DT￨O￨- one-step￨L￨JJ￨O￨- lookahead￨L￨JJ￨O￨- controller￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨A process￨L￨NN￨O￨A which￨L￨WDT￨O￨- leverages￨L￨VBZ￨O￨- the￨L￨DT￨O￨- developed￨L￨JJ￨O￨- Bayesian￨U￨JJ￨MISC￨- inference￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- causes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- die￨L￨VB￨O￨- out￨L￨RP￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- chosen￨L￨VBN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- leverage￨L￨NN￨O￨- the￨L￨DT￨O￨- attained￨L￨VBN￨O￨- conditional￨L￨JJ￨O￨- independence￨L￨NN￨O￨- property￨L￨NN￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- tractable￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- inference￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- avoiding￨L￨VBG￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- mean￨L￨JJ￨O￨A field￨L￨JJ￨O￨A approximations￨L￨NNS￨O￨- or￨L￨CC￨O￨- combinatorial￨L￨JJ￨O￨- representations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- observation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A process￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- well￨L￨RB￨O￨- structured￨L￨VBN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- which￨L￨WDT￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- ’￨L￨''￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- conditionally￨L￨RB￨O￨- independent￨L￨JJ￨RELIGION￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- observations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Pappas￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨A method￨L￨NN￨O￨- for￨L￨IN￨O￨- net-worked￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- game￨L￨NN￨O￨A framework￨L￨NN￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- choose￨L￨VB￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- themselves￨L￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- risk￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- degree-based￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- decide￨L￨VBP￨O￨- whether￨L￨IN￨O￨- to￨L￨TO￨O￨- purchase￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- or￨L￨CC￨O￨- risk￨L￨NN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨A state￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- N-Intertwined￨U￨NNP￨MISC￨- Mean￨U￨NN￨MISC￨- Field￨U￨NN￨MISC￨- Approximation￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- NIMFA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approach￨L￨NN￨O￨- above￨L￨IN￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- myriad￨L￨JJ￨O￨- of￨L￨IN￨O￨- mean-field￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptibleinfected-susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- certain￨L￨JJ￨O￨- network￨L￨NN￨O￨- types￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- tree￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- networks￨L￨NNS￨O￨- build￨L￨VBP￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- dimensionality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- scales￨L￨NNS￨O￨- as￨L￨IN￨O￨- mN￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- m￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- states￨L￨NNS￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- mean-field￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- exact￨L￨JJ￨O￨A master￨L￨JJ￨O￨- equation￨L￨NN￨O￨- AMS￨U￨NNP￨O￨- classification￨L￨NN￨O￨- :￨L￨:￨O￨- 34C12￨L￨NN￨O￨- ,￨L￨,￨O￨- 34C23￨L￨NN￨O￨- ,￨L￨,￨O￨- 37G10￨L￨NN￨O￨- ,￨L￨,￨O￨- 60J28￨L￨NN￨O￨- ,￨L￨,￨O￨- 90B10￨L￨NN￨O￨- ,￨L￨,￨O￨- 92D30￨L￨NN￨O￨- ∗￨L￨CD￨NUMBER￨- corresponding￨L￨JJ￨O￨- author￨L￨NN￨TITLE￨- email￨L￨NN￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- p￨L￨NN￨O￨- A￨U￨NN￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- C￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- comparison￨L￨NN￨O￨- theorems￨L￨NNS￨O￨- from￨L￨IN￨O￨- classical￨L￨JJ￨O￨- ODE￨U￨NN￨O￨- theory￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- rigorously￨L￨RB￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- N-Intertwined￨U￨JJ￨MISC￨- Mean-Field￨U￨NNP￨MISC￨- Approximation￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- NIMFA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- upper￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨A stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +4￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 7￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Modelling￨U￨NN￨O￨- transmission￨L￨NN￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- rumours￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨A to￨L￨TO￨O￨- many￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- this￨L￨DT￨O￨- computational￨L￨JJ￨O￨- difficulty￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- common￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- lower-bound￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- decay￨L￨NN￨O￨A rate￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- first-order￨L￨NN￨O￨- mean-field￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- existing￨L￨VBG￨O￨- lower-bounds￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- decay￨L￨NN￨O￨A rate￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- first-order￨L￨NN￨O￨- mean-field￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- accompanied￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- error￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- inefficient￨L￨JJ￨O￨- containment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Even￨U￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- decay￨L￨NN￨O￨A rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvalues￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- matrix￨L￨NN￨O￨- whose￨L￨WP$￨O￨- size￨L￨NN￨O￨- grows￨L￨VBZ￨O￨- exponential￨L￨JJ￨O￨- ly￨L￨RB￨O￨- fast￨L￨RB￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- various￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- decay￨L￨NN￨O￨A rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- fundamental￨L￨JJ￨O￨- importance￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- specifically￨L￨RB￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- lower-bound￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- decay￨L￨NN￨O￨A rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- stochastic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- network￨L￨NN￨O￨- measures￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- clear￨L￨JJ￨O￨- maxima￨L￨NNS￨O￨- or￨L￨CC￨O￨- minima￨L￨FW￨O￨- close￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- potentially￨L￨RB￨O￨- serve￨L￨VB￨O￨- as￨L￨IN￨O￨- early-warning￨L￨JJ￨O￨- signs￨L￨NNS￨O￨A .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- network￨L￨NN￨O￨- quantities￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- branching￨L￨VBG￨O￨- ratio￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- harmonic￨L￨JJ￨O￨- mean￨L￨NN￨O￨- distance￨L￨NN￨O￨- ,￨L￨,￨O￨- show￨L￨VBP￨O￨- scaling￨L￨VBG￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- singularity￨L￨NN￨O￨- at￨L￨IN￨O￨- λ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- at￨L￨IN￨O￨- λc￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- incapable￨L￨JJ￨O￨- of￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- clarify￨L￨VBP￨O￨- to￨L￨TO￨O￨- what￨L￨WP￨O￨- extent￨L￨NN￨O￨- these￨L￨DT￨O￨- changes￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- early-warning￨L￨JJ￨O￨- signs￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λc￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- collapses￨L￨VBZ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- disintegrates￨L￨VBZ￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- measures￨L￨NNS￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- link￨L￨VBP￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- triplet￨L￨NN￨O￨- densities￨L￨NNS￨O￨A ,￨L￨,￨O￨- clustering￨L￨NN￨O￨- ,￨L￨,￨O￨- assortativity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- eigenvalue￨L￨NN￨O￨- gap￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- link￨L￨VBP￨O￨- density￨L￨NN￨O￨- and￨L￨CC￨O￨- triplet￨L￨NN￨O￨- densities￨L￨NNS￨O￨A the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- originate￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- co-existence￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- power￨L￨NN￨O￨- laws￨L￨NNS￨O￨- .￨L￨.￨O￨- +Correlated￨U￨VBN￨O￨- bursts￨L￨NNS￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A slow￨L￨VB￨O￨- down￨L￨RP￨O￨- spreading￨L￨VBG￨O￨- Takayuki￨U￨NNP￨PERSON￨- Hiraoka1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- ∗￨L￨NN￨O￨- and￨L￨CC￨O￨- Hang-Hyun￨U￨JJ￨O￨- Jo1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- †￨L￨CD￨NUMBER￨- 1Asia￨L￨NN￨O￨- Pacific￨U￨NNP￨O￨- Center￨U￨NNP￨O￨- for￨L￨IN￨O￨- Theoretical￨U￨NNP￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- Pohang￨U￨NNP￨O￨- 37673￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Republic￨U￨NNP￨COUNTRY￨- of￨L￨IN￨COUNTRY￨- Korea￨U￨NNP￨COUNTRY￨- 2Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- Pohang￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Pohang￨U￨NNP￨O￨- 37673￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Republic￨U￨NNP￨COUNTRY￨- of￨L￨IN￨COUNTRY￨- Korea￨U￨NNP￨COUNTRY￨- 3Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Computer￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- Aalto￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Espoo￨U￨NNP￨ORGANIZATION￨- FI-00076￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Finland￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- July￨U￨NNP￨DATE￨- 10￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Spreading￨U￨VBG￨O￨- dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- place￨L￨NN￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- temporal￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- show￨L￨VBP￨O￨- non-Poissonian￨L￨JJ￨MISC￨- bursty￨L￨JJ￨O￨- nature￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- those￨L￨DT￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- two-step￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- probabilistic￨L￨JJ￨O￨- SI￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- inhomogeneous￨L￨JJ￨O￨A and￨L￨CC￨O￨- correlated￨L￨VBD￨O￨- IETs￨U￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- correlated￨L￨VBD￨O￨- bursts￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- IET￨U￨NNP￨ORGANIZATION￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- little￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- correlations￨L￨NNS￨O￨A between￨L￨IN￨O￨- IETs￨U￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- for￨L￨IN￨O￨- few￨L￨JJ￨O￨- recent￨L￨JJ￨O￨- works￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +fully￨L￨RB￨O￨- understood￨L￨VBN￨O￨- both￨L￨CC￨O￨- by￨L￨IN￨O￨- inhomogeneous￨L￨JJ￨O￨A interevent￨L￨JJ￨O￨- times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IETs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- IETs￨U￨NNS￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +Index￨U￨NNP￨O￨- Terms￨U￨NNS￨O￨- —￨L￨:￨O￨- Complex￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- Localization￨U￨NN￨O￨- ,￨L￨,￨O￨- Epidemic￨U￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ✦￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- INTRODUCT￨U￨NNP￨O￨- ION￨U￨NN￨O￨- T￨U￨NN￨O￨- H￨U￨NN￨O￨- E￨U￨NN￨O￨- near-threshold￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- many￨L￨JJ￨O￨- real￨L￨JJ￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- may￨L￨MD￨O￨- operate￨L￨VB￨O￨- near￨L￨IN￨O￨A the￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- point￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Network￨U￨NNP￨O￨- localization￨L￨NN￨O￨A is￨L￨VBZ￨O￨- unalterable￨L￨JJ￨O￨- by￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- bursts￨L￨NNS￨O￨- Qiang￨U￨NNP￨PERSON￨- Liu￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Piet￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Mieghem￨U￨NNP￨PERSON￨- Abstract￨U￨NNP￨PERSON￨- —￨L￨:￨O￨- We￨U￨PRP￨O￨- argue￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- localization￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- no￨L￨DT￨O￨- spreading￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- can￨L￨MD￨O￨- transform￨L￨VB￨O￨- a￨L￨DT￨O￨- localized￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- delocalized￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- extensively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- dynamical￨L￨JJ￨O￨A processes￨L￨NNS￨O￨A in￨L￨IN￨O￨- network￨L￨NN￨O￨- science￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- integrate￨L￨VB￨O￨- the￨L￨DT￨O￨- information-epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- process￨L￨NN￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- game￨L￨NN￨O￨- in￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- influences￨L￨NNS￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- density￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- unveil￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- two-layer￨L￨JJ￨O￨- coupled￨L￨VBN￨O￨- susceptible-alert-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SAIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- tendency￨L￨NN￨O￨- and￨L￨CC￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- cost￨L￨NN￨O￨- is￨L￨VBZ￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- range￨L￨NN￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A even￨L￨RB￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- decline￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Impact￨U￨NN￨O￨- of￨L￨IN￨O￨- Information￨U￨NN￨O￨- Dissemination￨U￨NN￨O￨- on￨L￨IN￨O￨- Vaccinating￨U￨VBG￨O￨- Epidemics￨U￨NNS￨O￨- in￨L￨IN￨O￨- Multiplex￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- Xiao-Jie￨U￨NNP￨PERSON￨- Li￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Cong￨U￨NNP￨PERSON￨- Li￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Xiang￨U￨NNP￨PERSON￨- Li￨U￨NNP￨PERSON￨- *￨L￨SYM￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- The￨U￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- control￨L￨NN￨O￨- essentially￨L￨RB￨O￨- affects￨L￨VBZ￨O￨- individual￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- smaller￨L￨JJR￨O￨- quotient￨L￨NN￨O￨- graph￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- only￨L￨RB￨O￨- captures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- macroscopic￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- all￨L￨DT￨O￨- we￨L￨PRP￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- know￨L￨VB￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- decide￨L￨VB￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- healthy-state￨L￨NN￨O￨- defines￨L￨VBZ￨O￨- a￨L￨DT￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- or￨L￨CC￨O￨- an￨L￨DT￨O￨- unstable￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- are￨L￨VBP￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- naturally￨L￨RB￨O￨- partitioned￨L￨VBN￨O￨- into￨L￨IN￨O￨- n￨L￨NN￨O￨- communities￨L￨NNS￨O￨- :￨L￨:￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A set￨L￨VBN￨O￨- partition￨L￨NN￨O￨- π￨L￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- V1￨U￨NN￨O￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- Vn￨U￨NNP￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- disjoint￨L￨NN￨O￨- nonempty￨L￨JJ￨O￨- subsets￨L￨NNS￨O￨- of￨L￨IN￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- union￨L￨NN￨O￨- is￨L￨VBZ￨O￨- V￨U￨NN￨O￨- .￨L￨.￨O￨- +susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- hierarchical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- graph￨L￨NN￨O￨A spectra￨L￨NNS￨O￨- ,￨L￨,￨O￨- equitable￨L￨JJ￨O￨- and￨L￨CC￨O￨- almost￨L￨RB￨O￨- equitable￨L￨JJ￨O￨- partitions￨L￨NNS￨O￨- AMS￨U￨NNP￨O￨- sub￨L￨NN￨O￨- ject￨L￨NN￨O￨- classifications￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- over￨L￨IN￨O￨- an￨L￨DT￨O￨- undirected￨L￨JJ￨O￨- graph￨L￨NN￨O￨A G￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- edge￨L￨NN￨O￨- set￨L￨NN￨O￨- E￨U￨NN￨O￨- and￨L￨CC￨O￨- node￨L￨NN￨O￨- set￨L￨NN￨O￨- V￨U￨NN￨O￨- .￨L￨.￨O￨- +Every￨U￨DT￨O￨- node￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- either￨L￨RB￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- pi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Xi￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- healthy￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- but￨L￨CC￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- pi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Xi￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- undirected￨L￨JJ￨O￨- TRGs￨U￨NNS￨O￨- displays￨L￨VBZ￨O￨- very￨L￨RB￨O￨- similar￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- to￨L￨TO￨O￨- TRGs￨U￨NNS￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- directed￨L￨VBN￨O￨A )￨L￨-RRB-￨O￨- feed-back-loops￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- using￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- directed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- feed-forward-loops￨L￨NNS￨O￨- as￨L￨IN￨O￨- network-entities￨L￨NNS￨O￨- significantly￨L￨RB￨O￨- slows￨L￨VBZ￨O￨- down￨L￨RP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- lowers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +SIS￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- Triadic￨U￨NNP￨MISC￨- Random￨U￨NNP￨MISC￨- Graphs￨U￨NNP￨MISC￨- Ilja￨U￨NNP￨PERSON￨- Rausch￨U￨NNP￨PERSON￨- ∗￨L￨NNP￨O￨- Universit￨U￨NNP￨O￨- ¨￨L￨NN￨O￨- at￨L￨IN￨O￨- W￨U￨NNP￨O￨- ¨￨L￨SYM￨O￨- urzburg￨L￨NN￨O￨- ,￨L￨,￨O￨- Fakult￨U￨NN￨O￨- ¨￨L￨NN￨O￨- at￨L￨IN￨O￨- f￨L￨FW￨O￨- ¨￨L￨FW￨O￨- ur￨L￨NN￨O￨- Physik￨U￨NN￨O￨- und￨L￨NN￨O￨- Astronomie￨U￨NN￨O￨- ,￨L￨,￨O￨- Am￨U￨VBP￨O￨- Hubland￨U￨NN￨O￨- ,￨L￨,￨O￨- 97074￨L￨CD￨NUMBER￨- W￨U￨NN￨O￨- ¨￨L￨CD￨NUMBER￨- urzburg￨L￨NN￨O￨- ,￨L￨,￨O￨- Germany￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 9￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨A exhibit￨L￨VBP￨O￨A community￨L￨NN￨O￨- structures￨L￨NNS￨O￨- and￨L￨CC￨O￨- non-trivial￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- which￨L￨WDT￨O￨- comes￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- notable￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- triangular￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- their￨L￨PRP$￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- Triadic￨U￨NNP￨MISC￨- Random￨U￨NNP￨MISC￨- Graph￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- TRG￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- small￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- 49￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- ,￨L￨,￨O￨- closed￨L￨VBD￨O￨- ,￨L￨,￨O￨- directed￨L￨VBD￨O￨A triadic￨L￨JJ￨O￨- subpatterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- go￨L￨VBP￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- for￨L￨IN￨O￨- standard￨L￨JJ￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- happens￨L￨VBZ￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A rule￨L￨NN￨O￨- and￨L￨CC￨O￨- degree￨L￨NN￨O￨- exponent￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- non-monotonic￨L￨JJ￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- on￨L￨IN￨O￨- D￨U￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- optimum￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨A rate￨L￨NN￨O￨- D￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- efficient￨L￨JJ￨O￨- ,￨L￨,￨O￨- diffusion￨L￨NN￨O￨- while￨L￨IN￨O￨- monotonic￨L￨JJ￨O￨- decays￨L￨NNS￨O￨- are￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- biased￨L￨VBN￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- diffusive￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- with￨L￨IN￨O￨- diffusion￨L￨NN￨O￨A rate￨L￨NN￨O￨- D￨U￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +Analyses￨U￨NNS￨O￨- on￨L￨IN￨O￨- star￨L￨NN￨O￨- and￨L￨CC￨O￨- max￨L￨NN￨O￨A k-core￨L￨NN￨O￨- subgraphs￨L￨NNS￨O￨- explain￨L￨VBP￨O￨- several￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusive￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Imposing￨U￨VBG￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SF￨U￨NN￨O￨- reveals￨L￨VBZ￨O￨- interesting￨L￨JJ￨O￨- and￨L￨CC￨O￨- surprising￨L￨JJ￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- natural￨L￨JJ￨O￨- limits￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- incremental￨L￨JJ￨O￨- detours￨L￨NNS￨O￨- permissible￨L￨JJ￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- exact￨L￨JJ￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- SIR-feasible￨U￨JJ￨O￨- ”￨L￨''￨O￨- routes￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- boast￨L￨VBP￨O￨- sublinear￨L￨JJ￨O￨- upper￨L￨JJ￨O￨- and￨L￨CC￨O￨- lower￨L￨JJR￨O￨- bounds￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- fractional￨L￨JJ￨O￨- detours￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- exact￨L￨JJ￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- sequentially￨L￨RB￨O￨- fair￨L￨JJ￨O￨- cost￨L￨NN￨O￨- sharing￨L￨VBG￨O￨A schemes￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- requirement￨L￨NN￨O￨- that￨L￨WDT￨O￨- passengers￨L￨NNS￨O￨- must￨L￨MD￨O￨- compensate￨L￨VB￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- detour￨L￨NN￨O￨- inconveniences￨L￨NNS￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- cause￨L￨VBP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- new￨L￨JJ￨O￨- algorithmic￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- and￨L￨CC￨O￨- motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- SIR￨U￨NN￨O￨- .￨L￨.￨O￨- +Next￨U￨RB￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- that￨L￨IN￨O￨- cost￨L￨NN￨O￨- sharing￨L￨NN￨O￨A can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- viewed￨L￨VBN￨O￨- as￨L￨IN￨O￨- benefit￨L￨NN￨O￨- sharing￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- inspires￨L￨VBZ￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- sequential￨L￨JJ￨O￨- fairness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- incremental￨L￨JJ￨O￨- benefit￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- customer￨L￨NN￨O￨- is￨L￨VBZ￨O￨- shared￨L￨VBN￨O￨- among￨L￨IN￨O￨- existing￨L￨VBG￨O￨- customers￨L￨NNS￨O￨- in￨L￨IN￨O￨- proportion￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- incremental￨L￨JJ￨O￨- inconvenience￨L￨NN￨O￨- suffered￨L￨VBN￨O￨- .￨L￨.￨O￨- +Key￨U￨NN￨O￨- words￨L￨NNS￨O￨- :￨L￨:￨O￨- shared￨L￨JJ￨O￨- service￨L￨NN￨O￨- system￨L￨NN￨O￨- ;￨L￨:￨O￨- ridesharing￨L￨VBG￨O￨- ;￨L￨:￨O￨- cost￨L￨NN￨O￨- sharing￨L￨NN￨O￨A ;￨L￨:￨O￨- sequential￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- rationality￨L￨NN￨O￨- ;￨L￨:￨O￨- sequential￨L￨JJ￨O￨- fairness￨L￨NN￨O￨- ;￨L￨:￨O￨- algorithmic￨L￨JJ￨O￨- mechanism￨L￨NN￨O￨- design￨L￨NN￨O￨- ;￨L￨:￨O￨- graph￨L￨NN￨O￨- algorithms￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- Gopalakrishnan￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Mukherjee￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Tulabandhula￨U￨NNP￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- Costs￨U￨NNS￨O￨- and￨L￨CC￨O￨- Benefits￨U￨NNS￨O￨- of￨L￨IN￨O￨- Sharing￨U￨VBG￨O￨- Article￨U￨NNP￨O￨- submitted￨L￨VBD￨O￨- to￨L￨TO￨O￨- Management￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- ;￨L￨:￨O￨- manuscript￨L￨NN￨O￨- no￨L￨DT￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Costs￨U￨NNS￨O￨- and￨L￨CC￨O￨- Benefits￨U￨NNS￨O￨- of￨L￨IN￨O￨- Sharing￨U￨VBG￨O￨- :￨L￨:￨O￨- Sequential￨U￨JJ￨O￨- Individual￨U￨JJ￨O￨- Rationality￨U￨NN￨O￨- and￨L￨CC￨O￨- Fairness￨U￨NNP￨O￨- Ragavendran￨U￨NNP￨O￨- Gopalakrishnan￨U￨NNP￨O￨- Conduent￨U￨NNP￨O￨- Labs￨U￨NNPS￨O￨- India￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- formerly￨L￨RB￨O￨- Xerox￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- Centre￨U￨NNP￨ORGANIZATION￨- India￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Koyel￨U￨NNP￨PERSON￨- Mukherjee￨U￨NNP￨PERSON￨- IBM￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- India￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Theja￨U￨NNP￨ORGANIZATION￨- Tulabandhula￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Illinois￨U￨NNP￨ORGANIZATION￨- Chicago￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- In￨U￨IN￨O￨- designing￨L￨VBG￨O￨- dynamic￨L￨JJ￨O￨- shared￨L￨JJ￨O￨- service￨L￨NN￨O￨A systems￨L￨NNS￨O￨- that￨L￨WDT￨O￨- incentivize￨L￨VBP￨O￨- customers￨L￨NNS￨O￨- to￨L￨TO￨O￨- opt￨L￨VB￨O￨- for￨L￨IN￨O￨- shared￨L￨JJ￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- exclusive￨L￨JJ￨O￨- service￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- notion￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- rationality￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- insufficient￨L￨JJ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- customer￨L￨NN￨O￨- ’s￨L￨POS￨O￨- estimated￨L￨VBN￨O￨- utility￨L￨NN￨O￨- could￨L￨MD￨O￨- fluctuate￨L￨VB￨O￨- arbitrarily￨L￨RB￨O￨- during￨L￨IN￨O￨- their￨L￨PRP$￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- shared￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- their￨L￨PRP$￨O￨- realized￨L￨VBN￨O￨- utility￨L￨NN￨O￨- at￨L￨IN￨O￨- service￨L￨NN￨O￨- completion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- worse￨L￨JJR￨O￨- than￨L￨IN￨O￨- that￨L￨DT￨O￨- for￨L￨IN￨O￨- exclusive￨L￨JJ￨O￨- service￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- pointwise￨L￨JJ￨O￨- convergence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- function￨L￨NN￨O￨- towards￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- function￨L￨NN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- Dini￨U￨NNP￨PERSON￨- theorem￨L￨NN￨O￨- to￨L￨TO￨O￨- conclude￨L￨VB￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- convergence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- uniform￨L￨JJ￨O￨- on￨L￨IN￨O￨- any￨L￨DT￨O￨- compact￨L￨JJ￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- hence￨L￨RB￨O￨- for￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- <￨L￨JJR￨O￨- ∞￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- j￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- k￨L￨NN￨O￨- lim￨L￨NN￨O￨A N￨U￨NN￨O￨- →￨L￨SYM￨O￨- ∞￨L￨SYM￨O￨- sup￨L￨FW￨O￨- u￨L￨FW￨O￨- ≤￨L￨FW￨O￨- v￨L￨LS￨O￨- |￨L￨SYM￨O￨- fM￨L￨NN￨O￨- N￨U￨NN￨O￨- j￨L￨NN￨O￨- it￨L￨PRP￨O￨- follows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- u￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- |￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- a.s.￨L￨IN￨O￨- lim￨L￨NN￨O￨- N￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- sup￨L￨NN￨O￨- t￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- T￨U￨NN￨O￨- ξN￨L￨NN￨O￨- j￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- a.s￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- other￨L￨JJ￨O￨- words￨L￨NNS￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- G￨U￨NN￨O￨- open￨L￨JJ￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- DT￨U￨NNP￨O￨- ,￨L￨,￨O￨- A￨U￨NNP￨O￨- and￨L￨CC￨O￨- F￨U￨NN￨O￨- closed￨L￨VBD￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- DT￨U￨NNP￨O￨- ,￨L￨,￨O￨- A￨U￨DT￨O￨- we￨L￨PRP￨O￨- want￨L￨VBP￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- inequalities￨L￨NNS￨O￨- :￨L￨:￨O￨- −￨L￨CD￨NUMBER￨- inf￨L￨NN￨O￨- φ￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- G￨U￨NN￨O￨- IT￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- φ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨CD￨NUMBER￨- lim￨L￨NN￨O￨A inf￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- →￨L￨SYM￨O￨- ∞￨L￨SYM￨O￨- lim￨L￨FW￨O￨- sup￨L￨FW￨O￨- N￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- log￨L￨NN￨O￨- Pz￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Z￨U￨NN￨O￨- N￨U￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- G￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- log￨L￨NN￨O￨- Pz￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Z￨U￨NN￨O￨- N￨U￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- F￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨SYM￨O￨- −￨L￨SYM￨O￨- inf￨L￨FW￨O￨- φ￨L￨FW￨O￨- ∈￨L￨FW￨O￨- F￨U￨NN￨O￨- IT￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- φ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Robustness￨U￨NNP￨O￨- and￨L￨CC￨O￨- fragility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- Wesley￨U￨NNP￨PERSON￨- Cota￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Ang￨U￨NNP￨O￨- ´￨L￨POS￨O￨- elica￨L￨NN￨O￨- S.￨U￨NNP￨O￨- All￨U￨NNP￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- in￨L￨IN￨O￨- mean-field￨L￨JJ￨O￨- theories￨L￨NNS￨O￨- but￨L￨CC￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- simulations￨L￨NNS￨O￨- yield￨L￨VBP￨O￨- a￨L￨DT￨O￨- dual￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- modified￨L￨JJ￨O￨A SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- either￨L￨CC￨O￨- dramatically￨L￨RB￨O￨- altered￨L￨JJ￨O￨- or￨L￨CC￨O￨- remain￨L￨VBP￨O￨- unchanged￨L￨JJ￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- uncorrelated￨L￨JJ￨O￨- synthetic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- having￨L￨VBG￨O￨- a￨L￨DT￨O￨- power-law￨L￨NN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- with￨L￨IN￨O￨- exponent￨L￨NN￨O￨- γ￨L￨NN￨O￨- <￨L￨JJR￨O￨- 5/2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- robust￨L￨JJ￨O￨- exhibiting￨L￨VBG￨O￨- essentially￨L￨RB￨O￨A the￨L￨DT￨O￨- same￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- investigated￨L￨VBN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- γ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- activation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- modified￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- collective￨L￨JJ￨O￨- involving￨L￨VBG￨O￨- essentially￨L￨RB￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- while￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- triggered￨L￨VBN￨O￨- by￨L￨IN￨O￨- hubs￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- verify￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- modified￨L￨JJ￨O￨A SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- triggered￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- innermost￨L￨NN￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- k-core￨L￨NN￨O￨- decomposition￨L￨NN￨O￨- for￨L￨IN￨O￨- γ￨L￨NN￨O￨- <￨L￨JJR￨O￨- 3￨L￨CD￨NUMBER￨- while￨L￨IN￨O￨- it￨L￨PRP￨O￨- happens￨L￨VBZ￨O￨- only￨L￨RB￨O￨- for￨L￨IN￨O￨- γ￨L￨NN￨O￨- <￨L￨JJR￨O￨- 5/2￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- birth-death￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- transition￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨A 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Birth-death￨U￨NN￨MISC￨- processes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- including￨L￨VBG￨O￨- evolutionary￨L￨JJ￨O￨- biology￨L￨NN￨O￨- ,￨L￨,￨O￨- ecology￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- queuing￨L￨VBG￨O￨- theory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- fast￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- approximating￨L￨VBG￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨A under￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- simplification￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- continued￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- representation￨L￨NN￨O￨- method￨L￨NN￨O￨- with￨L￨IN￨O￨- application￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨DATE￨- 17th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- plague￨L￨VB￨O￨- in￨L￨IN￨O￨- Eyam￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +Notably￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ubiquitous￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- susceptible-infectious-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- falls￨L￨VBZ￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- emphasize￨L￨VBP￨O￨- that￨L￨IN￨O￨- computable￨L￨JJ￨O￨- transition￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨A newly￨L￨RB￨O￨- enable￨L￨VBP￨O￨- direct￨L￨JJ￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- efficient￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- finite-time￨L￨JJ￨O￨- transition￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨A of￨L￨IN￨O￨- bivariate￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- restricted￨L￨VBN￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- recent￨L￨JJ￨O￨- works￨L￨NNS￨O￨- on￨L￨IN￨O￨- metapopulation￨L￨NN￨O￨- propagation￨L￨NN￨O￨A ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- finding￨L￨NN￨O￨- specific￨L￨JJ￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- physical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- approximate￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- generality￨L￨NN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- different￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- guaranteed￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨A system￨L￨NN￨O￨- by￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- construction￨L￨NN￨O￨- ,￨L￨,￨O￨- conditional￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- ma￨L￨FW￨O￨- jor￨L￨FW￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- techniques￨L￨NNS￨O￨- from￨L￨IN￨O￨- Ethier￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Kurtz￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fractions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- satisfy￨L￨VB￨O￨- a￨L￨DT￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- LLN￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- over￨L￨IN￨O￨- any￨L￨DT￨O￨- finite￨L￨JJ￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- more￨L￨JJR￨O￨- specifically￨L￨RB￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- converge￨L￨VBP￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- limiting￨L￨VBG￨O￨A deterministic￨L￨JJ￨O￨- process￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- associated￨L￨VBN￨O￨- functional￨L￨JJ￨O￨- central￨L￨JJ￨O￨- limit￨L￨NN￨O￨- theorem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CLT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- fluctuations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- limiting￨L￨VBG￨O￨- deterministic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- limiting￨L￨VBG￨O￨A deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- dropping￨L￨VBG￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- as￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- without￨L￨IN￨O￨- dropping￨L￨VBG￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- but￨L￨CC￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- though￨L￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- ma￨L￨FW￨O￨- jor￨L￨FW￨O￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- greater￨L￨JJR￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- dropping￨L￨VBG￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- Bollob￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- as￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- see￨L￨VBP￨O￨- Bollob￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- as￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- for￨L￨IN￨O￨- further￨L￨JJ￨O￨- references￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- comes￨L￨VBZ￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- versions￨L￨NNS￨O￨- :￨L￨:￨O￨- either￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- degrees￨L￨NNS￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- sequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- degrees￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Molloy￨U￨NNP￨PERSON￨- –￨L￨:￨O￨- Reed￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- MR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- independent￨L￨JJ￨RELIGION￨- and￨L￨CC￨O￨- identically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Newman￨U￨NNP￨PERSON￨- –￨L￨:￨O￨- Strogatz￨U￨NNP￨PERSON￨- –￨L￨:￨O￨- Watts￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- NSW￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- specialised￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- without￨L￨IN￨O￨- dropping￨L￨VBG￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨A to￨L￨TO￨O￨- yield￨L￨VB￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- central￨L￨JJ￨O￨- limit￨L￨NN￨O￨- theorems￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- Markovian￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- configuration-model￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- giant￨L￨JJ￨O￨- components￨L￨NNS￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- effective￨L￨JJ￨O￨- degree￨L￨NN￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- conjunction￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- density￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- population￨L￨NN￨O￨- processes￨L￨NNS￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- limit￨L￨NN￨O￨A theorem￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- proposes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- network￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- game￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- self-interests￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- react￨L￨VBP￨O￨- to￨L￨TO￨O￨- current￨L￨JJ￨DATE￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- reactions￨L￨NNS￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- stochastically￨L￨RB￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- above￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- averse￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- eradicate￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- preemptive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sick￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Sick￨U￨JJ￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- healthy￨L￨JJ￨O￨A contacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- adopt￨L￨VB￨O￨- preemptive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- surge￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A models￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- concern￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- empathy￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- sick￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- eradicated￨L￨VBN￨O￨- fast￨L￨RB￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- directed￨L￨VBN￨O￨A networks￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- WWW￨U￨NNP￨O￨- ,￨L￨,￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- metabolic￨L￨JJ￨O￨- reactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- phone￨L￨NN￨O￨- calls￨L￨NNS￨O￨- have￨L￨VBP￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∝￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- and￨L￨CC￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- ℓ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∝￨L￨SYM￨O￨- ℓ￨L￨SYM￨O￨- −￨L￨SYM￨O￨- γ￨L￨SYM￨O￨- ′￨L￨SYM￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- large￨L￨JJ￨O￨- indegrees￨L￨NNS￨O￨- k￨L￨NN￨O￨- and￨L￨CC￨O￨- outdegrees￨L￨NN￨O￨- ℓ￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- inevitably￨L￨RB￨O￨- have￨L￨VBP￨O￨- finite￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- ℓ￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- directed￨L￨JJ￨O￨A network￨L￨NN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- models￨L￨NNS￨O￨- approaches￨L￨VBZ￨O￨- zero￨L￨CD￨NUMBER￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- nodal￨L￨JJ￨O￨- indegrees￨L￨NNS￨O￨- and￨L￨CC￨O￨- outdegrees￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ob￨L￨NN￨O￨- jective￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- directed￨L￨VBN￨O￨A networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- below￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- directed￨L￨VBN￨O￨A network￨L￨NN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- passes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- through￨L￨IN￨O￨- outgoing￨L￨JJ￨O￨- links￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- incoming￨L￨JJ￨O￨- links￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- continue￨L￨VBP￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- pitfalls￨L￨NNS￨O￨- in￨L￨IN￨O￨- modeling￨L￨NN￨O￨- this￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- explain￨L￨VBP￨O￨A that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- properly￨L￨RB￨O￨- used￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Ross-Macdonald￨U￨NNP￨LOCATION￨- model￨L￨NN￨TITLE￨- works￨L￨VBZ￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- extents￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- some￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Usually￨U￨RB￨O￨- towns￨L￨NNS￨O￨- or￨L￨CC￨O￨- cities￨L￨NNS￨O￨- report￨L￨VBP￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- recur￨L￨VBP￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- environmental￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- explain￨L￨VB￨O￨A the￨L￨DT￨O￨- disappearance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in-between￨L￨JJ￨O￨- the￨L￨DT￨O￨- peaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- measured￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- estimated￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- predicts￨L￨VBZ￨O￨- a￨L￨DT￨O￨- much￨L￨RB￨O￨- greater￨L￨JJR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- than￨L￨IN￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨A observed￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- exemplified￨L￨VBN￨O￨- by￨L￨IN￨O￨- actual￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A outbreaks￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- recurrence￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- from￨L￨IN￨O￨- some￨L￨DT￨O￨- Brazilian￨U￨JJ￨NATIONALITY￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rightmost￨L￨NN￨O￨- particle￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- nth￨L￨NN￨O￨- generation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- branching￨L￨VBG￨O￨- random￨L￨JJ￨O￨A walk￨L￨NN￨O￨A are￨L￨VBP￨O￨- reviewed￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- of￨L￨IN￨O￨- anomalous￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- speeds￨L￨NNS￨O￨- ,￨L￨,￨O￨- noticed￨L￨VBD￨O￨- recently￨L￨RB￨DATE￨- in￨L￨IN￨O￨- related￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- Hammersley￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- contribution￨L￨NN￨O￨- was￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- postulates￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- cover￨L￨VB￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- birth￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- nth￨L￨NN￨O￨- generation￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- Bellman￨U￨NNP￨LOCATION￨- –￨L￨:￨O￨- Harris￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- .1￨L￨CD￨NUMBER￨- Hammersley￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 1974￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- showed￨L￨VBD￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- other￨L￨JJ￨O￨- things￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- a￨L￨DT￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Probability￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Statistics￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Hicks￨U￨NNP￨ORGANIZATION￨- Building￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Sheffield￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Sheffield￨U￨NNP￨O￨- S3￨U￨NN￨O￨- 7RH￨L￨NN￨O￨- ;￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Subsequently￨U￨NNP￨O￨- ,￨L￨,￨O￨- Liggett￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- 1985￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- established￨L￨VBD￨O￨- the￨L￨DT￨O￨- theorem￨L￨NN￨O￨- under￨L￨IN￨O￨- weaker￨L￨JJR￨O￨- postulates￨L￨VBZ￨O￨- .￨L￨.￨O￨- +D.￨U￨NNP￨PERSON￨- Biggins￨U￨NNP￨PERSON￨- 2￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- The￨U￨DT￨O￨- branching￨L￨VBG￨O￨- random￨L￨JJ￨O￨A walk￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- BRW￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- starts￨L￨VBZ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- particle￨L￨NN￨O￨- located￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨- .￨L￨.￨O￨- +I￨U￨PRP￨O￨- will￨L￨MD￨O￨- also￨L￨RB￨O￨- go￨L￨VB￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- my￨L￨PRP$￨O￨- beginnings￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- outlining￨L￨VBG￨O￨- something￨L￨NN￨O￨- new￨L￨JJ￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- multitype￨L￨JJ￨O￨- version￨L￨NN￨O￨- that￨L￨WDT￨O￨- concerns￨L￨VBZ￨O￨- the￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨A of￨L￨IN￨O￨- ‘￨L￨``￨O￨- anomalous￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- speeds￨L￨NNS￨O￨- ’￨L￨POS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- noted￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- related￨L￨JJ￨O￨- context￨L￨NN￨O￨- in￨L￨IN￨O￨- Weinberger￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- P￨U￨NN￨O￨- and￨L￨CC￨O￨- E￨U￨NN￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- expectation￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- let￨L￨VB￨O￨A Z￨U￨NN￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- generic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- points￨L￨NNS￨O￨- in￨L￨IN￨O￨- R.￨U￨NNP￨O￨- +1.1￨L￨CD￨NUMBER￨- Let￨U￨VB￨O￨- G￨U￨NN￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- locally￨L￨RB￨O￨- connected￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- d-dimensional￨L￨JJ￨O￨- compact￨L￨JJ￨O￨- Lie￨U￨NN￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- let￨L￨VB￨O￨- EG￨U￨NN￨O￨- be￨L￨VB￨O￨- multiplicative￨L￨JJ￨O￨- cohomology￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- admits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- interpretation￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- G-equivariant￨U￨JJ￨O￨- cobordism￨L￨NN￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- manifolds￨L￨NNS￨O￨- with￨L￨IN￨O￨- ‘￨L￨``￨O￨- E￨U￨NN￨O￨- -￨L￨:￨O￨- structure￨L￨NN￨O￨- ’￨L￨''￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- sort￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- non-equivariant￨L￨JJ￨O￨- theory￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sphere￨L￨NN￨O￨- spectrum￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- noncommutative￨L￨JJ￨O￨- spectrum￨L￨NN￨O￨- M￨U￨NN￨O￨- ξ￨L￨NN￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- M￨U￨NNP￨O￨- U￨U￨NNP￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- O￨U￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- hard￨L￨JJ￨O￨- we￨L￨PRP￨O￨- ’re￨L￨VBP￨O￨- willing￨L￨JJ￨O￨- to￨L￨TO￨O￨- work￨L￨VB￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- H￨U￨NN￨O￨- Z.￨U￨NNP￨O￨- Two￨U￨CD￨NUMBER￨- such￨L￨JJ￨O￨- man-in￨L￨JJ￨O￨- other￨L￨JJ￨O￨- ifolds￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- said￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- cobordant￨L￨JJ￨O￨- if￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- manifold￨L￨NN￨O￨- W￨U￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- transversal￨L￨JJ￨O￨- partition￨L￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- W￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Z￨U￨NN￨O￨- +￨L￨CC￨O￨- ⊔￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- op￨L￨NN￨O￨- −￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∪￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- with￨L￨IN￨O￨- G-action￨U￨JJ￨MISC￨- free￨L￨JJ￨O￨- on￨L￨IN￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- V￨U￨NNP￨O￨- GEOMETRIC￨U￨NNP￨MISC￨- TATE-SWAN￨U￨NNP￨MISC￨- COHOMOLOGY￨U￨NNP￨O￨- OF￨U￨IN￨O￨- EQUIVARIANT￨U￨NNP￨O￨- SPECTRA￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- by￨L￨IN￨O￨- multiplication￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- unit￨L￨NN￨O￨- quaternions￨L￨NNS￨O￨- ,￨L￨,￨O￨- defines￨L￨VBZ￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- ℘￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ∈￨L￨CD￨NUMBER￨- tSU￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 4￨L￨CD￨NUMBER￨- M￨U￨NN￨O￨- Sp￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- sketch￨L￨NN￨O￨- a￨L￨DT￨O￨- quick￨L￨JJ￨O￨- and￨L￨CC￨O￨- dirty￨L￨JJ￨O￨- geometric￨L￨JJ￨O￨A approach￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Tate-Swan￨U￨JJ￨MISC￨- cohomology￨L￨NN￨O￨- of￨L￨IN￨O￨- equivariant￨L￨JJ￨O￨- spectra￨L￨NNS￨O￨- ,￨L￨,￨O￨- illustrating￨L￨VBG￨O￨- it￨L￨PRP￨O￨- with￨L￨IN￨O￨- conjectural￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- Atiyah-Segal￨U￨JJ￨O￨- K￨U￨NN￨O￨- -￨L￨:￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- circle￨L￨NN￨O￨- actions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- possible￨L￨JJ￨O￨- geometric￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- cyclic￨L￨JJ￨O￨- homology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sphere￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- .￨L￨.￨O￨- +Similarly￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- action￨L￨NN￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- on￨L￨IN￨O￨- Z￨U￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- fact￨L￨NN￨O￨- free￨L￨JJ￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- geometric￨L￨JJ￨O￨A quotient￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- Z/G￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- BG￨U￨NN￨O￨- +￨L￨CC￨O￨- ]￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- En￨U￨IN￨O￨- −￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BG￨U￨NN￨O￨- +￨L￨CC￨O￨- )￨L￨-RRB-￨O￨- identifies￨L￨NNS￨O￨- Z￨U￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- principal￨L￨JJ￨TITLE￨- G-bundle￨U￨NN￨O￨- .￨L￨.￨O￨- +Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- Ensemble￨U￨NN￨O￨- mode￨L￨NN￨O￨- peak￨L￨NN￨O￨- week￨L￨NN￨DURATION￨A predictions￨L￨NNS￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- Week￨U￨NN￨DURATION￨- 49￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- 12￨L￨CD￨NUMBER￨- cities￨L￨NNS￨O￨- plotted￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- probability/confidence￨L￨NN￨O￨- calibrated￨L￨VBN￨O￨- from￨L￨IN￨O￨- historical￨L￨JJ￨O￨- city￨L￨NN￨O￨- ,￨L￨,￨O￨- regional￨L￨JJ￨O￨- and￨L￨CC￨O￨- national￨L￨JJ￨O￨- prediction￨L￨NN￨O￨- accuracy￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- semi-infected￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fully-infected￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- immediately￨L￨RB￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- equivalently￨L￨RB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- state￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- reduces￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- critical￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- high-dimensional￨L￨JJ￨O￨- two-stage￨L￨JJ￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A Xiaofeng￨U￨NNP￨PERSON￨- Xue￨U￨NNP￨PERSON￨- ∗￨L￨NNP￨O￨- Beijing￨U￨NNP￨ORGANIZATION￨- Jiaotong￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Abstract￨U￨NNP￨ORGANIZATION￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- two-stage￨L￨JJ￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- lattice￨L￨NN￨O￨- Zd￨U￨NN￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- any￨L￨DT￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- C￨U￨NN￨O￨- A￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- moment￨L￨NN￨O￨- probability￨L￨NN￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two-stage￨L￨JJ￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A {￨L￨-LRB-￨O￨- ηt￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- parameter￨L￨NN￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- ∅￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- is￨L￨VBZ￨O￨- obviously￨L￨RB￨O￨- that￨L￨IN￨O￨- P￨U￨NN￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- increasing￨L￨VBG￨O￨- with￨L￨IN￨O￨- λ￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two-stage￨L￨JJ￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A {￨L￨-LRB-￨O￨- ηt￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- on￨L￨IN￨O￨- Zd￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- X1￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Zd￨U￨NNP￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- if￨L￨IN￨O￨- ηt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- if￨L￨IN￨O￨- ηt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- Py￨U￨NN￨O￨- :￨L￨:￨O￨- y￨L￨VB￨O￨- ∼￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- ηt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- otherwise￨L￨RB￨O￨- ηt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- →￨L￨SYM￨O￨- i￨L￨FW￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- if￨L￨IN￨O￨- ηt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- ηt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- x￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- d￨L￨NN￨O￨- and￨L￨CC￨O￨- t￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- and￨L￨CC￨O￨- 1A￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- indicator￨L￨NN￨O￨A function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- A￨U￨NN￨O￨- .￨L￨.￨O￨- +Plasmodium￨U￨NN￨O￨- knowlesi￨L￨NNS￨O￨- H￨U￨NN￨O￨- strain￨L￨NN￨O￨- pregnancy￨L￨NN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A immune￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- Report￨U￨NNP￨O￨- Regular￨U￨JJ￨O￨- A￨U￨NN￨O￨- journal￨L￨NN￨O￨- for￨L￨IN￨O￨- biology￨L￨NN￨O￨- beyond￨L￨IN￨O￨- borders￨L￨NNS￨O￨- International￨U￨NNP￨ORGANIZATION￨- Journal￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Integrative￨U￨NNP￨ORGANIZATION￨- Biology￨U￨NNP￨ORGANIZATION￨- IJIB￨U￨NNP￨ORGANIZATION￨- ISSN￨U￨NNP￨ORGANIZATION￨- 0973-8363￨L￨CD￨DURATION￨- Plasmodium￨U￨NN￨O￨- knowlesi￨L￨NN￨O￨- H￨U￨NN￨O￨- strain￨L￨NN￨O￨- pregnancy￨L￨NN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- immune￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- in￨L￨IN￨O￨- olive￨L￨JJ￨O￨- baboons￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Papio￨U￨NN￨O￨- anubis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Barasa￨U￨NN￨O￨- Mustafa1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- Mwangi￨U￨NNP￨PERSON￨- Irungu￨U￨NNP￨PERSON￨- Michael1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mutiso￨U￨NNP￨PERSON￨- Muli￨U￨NNP￨PERSON￨- Joshua1￨U￨NN￨PERSON￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kagasi￨U￨NNP￨O￨- Ambogo￨U￨NNP￨O￨- Esther2￨U￨NN￨O￨- ,￨L￨,￨O￨- Ozwara￨U￨NNP￨PERSON￨- Suba￨U￨NNP￨PERSON￨- Hastings2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Gicheru￨U￨NNP￨ORGANIZATION￨- Muita￨U￨NNP￨ORGANIZATION￨- Michael1￨U￨NN￨ORGANIZATION￨- 1Zoological￨L￨NNP￨ORGANIZATION￨- Sciences￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- School￨U￨NNP￨O￨- of￨L￨IN￨O￨- Pure￨U￨NNP￨O￨- and￨L￨CC￨O￨- Applied￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Kenyatta￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Nairobi￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Tropical￨U￨JJ￨ORGANIZATION￨- and￨L￨CC￨O￨- Infectious￨U￨JJ￨O￨- Diseases￨U￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Primate￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Nairobi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Kenya￨U￨NNP￨COUNTRY￨- Submitted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨DATE￨- Apr.￨U￨NN￨DATE￨- 2010￨L￨CD￨DATE￨- ;￨L￨:￨O￨- Accepted￨U￨JJ￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨DATE￨- Jun.￨U￨NN￨DATE￨- 2010￨L￨CD￨DATE￨- ABSTRACT￨U￨NN￨O￨- Approximately￨U￨RB￨O￨- 24￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- pregnant￨L￨JJ￨O￨- women￨L￨NNS￨O￨- in￨L￨IN￨O￨- Sub-Saharan￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- are￨L￨VBP￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- suffering￨L￨VBG￨O￨- from￨L￨IN￨O￨- pregnancy￨L￨NN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Baboons￨U￨NNS￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- Plasmodium￨U￨NN￨O￨- knowlesi￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- reproductive￨L￨JJ￨O￨- physiology￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- pathogen￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- them￨L￨PRP￨O￨- attractive￨L￨JJ￨O￨- for￨L￨IN￨O￨- development￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- mechanisms￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- pregnancy￨L￨NN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- exploited￨L￨VBD￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- baboons￨L￨NNS￨O￨- to￨L￨TO￨O￨- Plasmodium￨U￨NN￨LOCATION￨- knowlesi￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- cytokine￨L￨NN￨O￨- and￨L￨CC￨O￨- peripheral￨L￨JJ￨O￨- blood￨L￨NN￨O￨- mononuclear￨L￨JJ￨O￨- cell￨L￨NN￨O￨- recall￨L￨NN￨O￨- proliferation￨L￨NN￨O￨- responses￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- the￨L￨DT￨O￨- pathogenesis￨L￨NN￨O￨- of￨L￨IN￨O￨- pregnancy￨L￨NN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- baboons￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Plasmodium￨U￨NN￨O￨- knowlesi￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- aimed￨L￨VBN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- immunological￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- cytokine￨L￨NN￨O￨- and￨L￨CC￨O￨- recall￨L￨NN￨O￨- proliferation￨L￨NN￨O￨- responses￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- underlying￨L￨JJ￨O￨- pregnancy￨L￨NN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- baboon-P￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨DATE￨- 150th￨L￨JJ￨DATE￨- day￨L￨NN￨DATE￨- of￨L￨IN￨O￨- gestation￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- pregnant￨L￨JJ￨O￨- baboons￨L￨NNS￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- non￨L￨JJ￨O￨- pregnant￨L￨JJ￨O￨- controls￨L￨NNS￨O￨- were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Plasmodium￨U￨NN￨O￨- knowlesi￨L￨NN￨O￨- H￨U￨NN￨O￨- strain￨L￨NN￨O￨A parasites￨L￨NNS￨O￨- .￨L￨.￨O￨- +Infectious￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ·￨L￨VBP￨O￨- Dynamic￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- ·￨L￨VBP￨O￨- Random￨U￨JJ￨O￨- vaccination￨L￨NN￨O￨A ·￨L￨NN￨O￨- Contact￨U￨NN￨O￨- Keywords￨U￨NNS￨O￨- rewiring￨L￨VBG￨O￨- Mathematics￨U￨NNP￨O￨- Subject￨U￨NNP￨O￨- Classification￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 92D30￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- epidemiology￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ·￨L￨SYM￨O￨- 05C82￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- small￨L￨JJ￨O￨- world￨L￨NN￨O￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ·￨L￨SYM￨O￨- 34C60￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- qualitative￨L￨JJ￨O￨- investigation￨L￨NN￨O￨- and￨L￨CC￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ·￨L￨SYM￨O￨- 90B15￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Since￨U￨IN￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- mathematical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- —￨L￨:￨O￨- in￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modelled￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- stand￨L￨VBP￨O￨- for￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- among￨L￨IN￨O￨- them￨L￨PRP￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- public￨L￨JJ￨O￨- policies￨L￨NNS￨O￨- for￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- wealth￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- various￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- powerful￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- inhibition￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- some￨L￨DT￨O￨- vaccines￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- reach￨L￨VBP￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- imperfect￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨A on￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- macroscopic￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- random￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- protection￨L￨NN￨O￨- is￨L￨VBZ￨O￨- characterised￨L￨VBN￨O￨- by￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- rewiring￨L￨VBG￨O￨- contacts￨L￨NNS￨O￨- from￨L￨IN￨O￨- infective￨L￨JJ￨O￨- neighbours￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- targeted￨L￨VBN￨O￨- vaccination￨L￨NN￨O￨A towards￨L￨IN￨O￨- high-degree￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- widely￨L￨RB￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- effectiveness￨L￨NN￨O￨- than￨L￨IN￨O￨- random￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- —￨L￨:￨O￨- either￨L￨RB￨O￨- in￨L￨IN￨O￨- SF￨U￨NN￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- in￨L￨IN￨O￨- small-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- additional￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- temporal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨A ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- or￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- MERS￨U￨NN￨O￨- coronavirus￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- West￨U￨JJ￨MISC￨- African￨U￨JJ￨NATIONALITY￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Zaire￨U￨NNP￨COUNTRY￨- strain￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- challenged￨L￨VBN￨O￨- epidemiologists￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨A history￨L￨NN￨O￨A ,￨L￨,￨O￨- modes￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and/or￨L￨CC￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- well￨L￨RB￨O￨- understood￨L￨VBN￨O￨- during￨L￨IN￨O￨- initial￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- emergence￨L￨NN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- recent￨L￨JJ￨O￨- innovations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- description￨L￨NN￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- in￨L￨IN￨O￨- use￨L￨NN￨O￨- for￨L￨IN￨O￨- pro￨L￨JJ￨O￨A jection￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- tra￨L￨NN￨O￨- jectories￨L￨NNS￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- a￨L￨DT￨DURATION￨- century￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- novel￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- emerge￨L￨VBP￨O￨- or￨L￨CC￨O￨- familiar￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- resurge￨L￨VBP￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- serve￨L￨VB￨O￨- as￨L￨IN￨O￨- useful￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- synthesis￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- pro￨L￨JJ￨O￨A jection￨L￨NN￨O￨- of￨L￨IN￨O￨- likely￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- tra￨L￨NN￨O￨- jectories￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- plenty￨L￨NN￨O￨- of￨L￨IN￨O￨- DTN￨U￨NNP￨ORGANIZATION￨- routing￨L￨VBG￨O￨- schemes￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- of￨L￨IN￨O￨- relay￨L￨NN￨O￨- selection￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- many￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- message￨L￨NN￨O￨A forwarding￨L￨NN￨O￨- in￨L￨IN￨O￨- DTN￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- as￨L￨RB￨O￨- CISER￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- message￨L￨NN￨O￨A propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- DTN￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- amoebiasis￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨A CISER￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- additional￨L￨JJ￨O￨- states￨L￨NNS￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- resource￨L￨NN￨O￨- constrained￨L￨VBD￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- DTN￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- CISER￨U￨NN￨O￨- :￨L￨:￨O￨- An￨U￨DT￨O￨- Amoebiasis￨U￨NN￨O￨- inspired￨L￨VBD￨O￨A Model￨U￨NNP￨TITLE￨- for￨L￨IN￨O￨- Epidemic￨U￨NNP￨O￨- Message￨U￨NNP￨O￨- Propagation￨U￨NN￨O￨- in￨L￨IN￨O￨- DTN￨U￨NNP￨ORGANIZATION￨- Sobin￨U￨NNP￨ORGANIZATION￨- CC￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Student￨U￨NN￨TITLE￨- Member￨U￨NNP￨O￨- ,￨L￨,￨O￨- IEEE￨U￨NNP￨O￨- Snehanshu￨U￨NNP￨O￨- Saha￨U￨NNP￨O￨- ,￨L￨,￨O￨- Senior￨U￨NNP￨O￨- Member￨U￨NNP￨O￨- ,￨L￨,￨O￨- IEEE￨U￨NNP￨O￨- Vaskar￨U￨NNP￨O￨- Raychoudhury￨U￨NNP￨O￨- ,￨L￨,￨O￨- Senior￨U￨NNP￨O￨- Member￨U￨NNP￨O￨- ,￨L￨,￨O￨- IEEE￨U￨NNP￨O￨- Hategekimana￨U￨NNP￨PERSON￨- Fidele￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Sumana￨U￨NNP￨PERSON￨- Sinha￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Member￨U￨NNP￨O￨- ,￨L￨,￨O￨- IEEE￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- Delay￨U￨NNP￨O￨- Tolerant￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- DTNs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- sparse￨L￨JJ￨O￨- mobile￨L￨JJ￨TITLE￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- experiences￨L￨VBZ￨O￨- frequent￨L￨JJ￨O￨- disruptions￨L￨NNS￨O￨- in￨L￨IN￨O￨- connectivity￨L￨NN￨O￨- among￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Inspired￨U￨VBN￨O￨- from￨L￨IN￨O￨- such￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- that￨L￨IN￨O￨- amoebiasis￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modeling￨L￨NN￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- in￨L￨IN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- message￨L￨NN￨O￨A forwarding￨L￨NN￨O￨- in￨L￨IN￨O￨- Delay￨U￨NNP￨O￨- Tolerant￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- DTNs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- classical￨L￨JJ￨O￨- SIR-SI￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- arboviruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- directions￨L￨NNS￨O￨- :￨L￨:￨O￨- we￨L￨PRP￨O￨- begin￨L￨VBP￨O￨- by￨L￨IN￨O￨- describing￨L￨VBG￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- proof￨L￨NN￨O￨A of￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- known￨L￨VBN￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- results￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- Lyapunov￨U￨NNP￨MISC￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- these￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- asymptotic￨L￨JJ￨O￨- regimes￨L￨NNS￨O￨- naturally￨L￨RB￨O￨- appear￨L￨VBP￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- fast￨L￨JJ￨O￨A host￨L￨NN￨TITLE￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- fast￨L￨JJ￨O￨- vector￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨A disappears￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- directly￨L￨RB￨O￨- contagious￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- conserve￨L￨VB￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- parallel￨L￨JJ￨O￨- detailed￨L￨JJ￨O￨- study￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- white￨L￨JJ￨O￨A noise￨L￨NN￨O￨A processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- critical￨L￨JJ￨O￨- examination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- intensities￨L￨NNS￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- eradication￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- system￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- elsewhere￨L￨RB￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- white￨L￨JJ￨O￨A noise￨L￨NN￨O￨A process￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- may￨L￨MD￨O￨- destabilize￨L￨VB￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- population￨L￨NN￨O￨- by￨L￨IN￨O￨- exhibiting￨L￨VBG￨O￨- high￨L￨JJ￨O￨- intensity￨L￨NN￨O￨- values￨L￨NNS￨O￨- or￨L￨CC￨O￨- high￨L￨JJ￨O￨- standard￨L￨JJ￨O￨- deviation￨L￨NN￨O￨- values￨L￨NNS￨O￨- which￨L￨WDT￨O￨- generally￨L￨RB￨O￨- displace￨L￨VBP￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- vector-borne￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- white￨L￨JJ￨O￨A noise￨L￨NN￨O￨A processes￨L￨NNS￨O￨- originating￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- fails￨L￨VBZ￨O￨- to￨L￨TO￨O￨- exist￨L￨VB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- white￨L￨JJ￨O￨A noise￨L￨NN￨O￨A process￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- positive￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- interference-limited￨L￨JJ￨O￨- regime￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- reveal￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- MRC￨U￨NNP￨ORGANIZATION￨- receivers￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- super-linear￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- polynomial￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- scaling￨L￨VBG￨O￨- law￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- base￨L￨NN￨O￨A station￨L￨NN￨O￨A antennas￨L￨NNS￨O￨- and￨L￨CC￨O￨- scheduled￨L￨VBN￨O￨- users￨L￨NNS￨O￨- per￨L￨IN￨O￨- cell￨L￨NN￨O￨- preserves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- uplink￨L￨NN￨O￨- SIR￨U￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- applies￨L￨VBZ￨O￨- to￨L￨TO￨O￨- ZF￨U￨NN￨O￨- receivers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- expressions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- for￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- average￨L￨JJ￨O￨- SINR￨U￨NN￨O￨- distributions￨L￨NNS￨O￨- over￨L￨IN￨O￨- user￨L￨NN￨O￨- and￨L￨CC￨O￨- base￨L￨NN￨O￨A station￨L￨NN￨O￨A distributions￨L￨NNS￨O￨- with￨L￨IN￨O￨- maximum￨L￨NN￨O￨- ratio￨L￨NN￨O￨- combining￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- MRC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- zero-forcing￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- receivers￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- uplink￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- massive￨L￨JJ￨O￨- MIMO￨U￨NNP￨ORGANIZATION￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- maximum￨L￨NN￨O￨- ratio￨L￨NN￨O￨- combining￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- MRC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- zero-forcing￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- receivers￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- base￨L￨NN￨O￨A station￨L￨NN￨O￨A topology￨L￨NN￨O￨- .￨L￨.￨O￨- +ZF￨U￨NN￨O￨- receivers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- outperform￨L￨VB￨O￨- MRC￨U￨NNP￨ORGANIZATION￨- receivers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- gap￨L￨NN￨O￨- is￨L￨VBZ￨O￨- quantified￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- th￨L￨DT￨O￨- e￨L￨SYM￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- antennas￨L￨NNS￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- distribution￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- cache-enabled￨L￨JJ￨O￨- D2D￨U￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- FD￨U￨NN￨O￨- radios￨L￨NNS￨O￨- can￨L￨MD￨O￨- promise￨L￨VB￨O￨- more￨L￨RBR￨O￨- advantages￨L￨NNS￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- its￨L￨PRP$￨O￨- HD￨U￨NN￨O￨- counterpart￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- providing￨L￨VBG￨O￨- more￨L￨RBR￨O￨- content￨L￨JJ￨O￨A delivery￨L￨NN￨O￨- opportunities￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- improving￨L￨VBG￨O￨- spectral￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- and￨L￨CC￨O￨- reducing￨L￨VBG￨O￨- end-to-end￨L￨JJ￨O￨- delay￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- characterize￨L￨VBP￨O￨- network￨L￨NN￨O￨- performance￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- content￨L￨JJ￨O￨A availability￨L￨NN￨O￨- ,￨L￨,￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- operating￨L￨NN￨O￨- mode￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- D2D￨U￨NN￨O￨- receiver￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- D2D￨U￨NN￨O￨- network￨L￨NN￨O￨- formation￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- content￨L￨NN￨O￨A cached￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- user￨L￨NN￨O￨- devices￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- their￨L￨PRP$￨O￨- demands￨L￨NNS￨O￨- .￨L￨.￨O￨- +determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- transmitting￨L￨VBG￨O￨- users￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- user￨L￨NN￨O￨A operating￨L￨NN￨O￨- modes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- HD/FD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- receiver￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- which￨L￨WDT￨O￨- directly￨L￨RB￨O￨- impacts￨L￨VBZ￨O￨- SIR￨U￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- bioinformatic￨L￨JJ￨O￨- tool￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- alternates￨L￨VBZ￨O￨- between￨L￨IN￨O￨- clustering￨L￨NN￨O￨- and￨L￨CC￨O￨- standard￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- performed￨L￨VBD￨O￨- a￨L￨DT￨O￨- "￨L￨``￨O￨- double￨L￨JJ￨O￨- blind￨L￨JJ￨O￨- "￨L￨''￨O￨- search￨L￨NN￨O￨- of￨L￨IN￨O￨- published￨L￨VBN￨O￨- gene￨L￨NN￨O￨A expression￨L￨NN￨O￨A data￨L￨NNS￨O￨- of￨L￨IN￨O￨- subjects￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- childhood￨L￨NN￨O￨- ALL￨U￨NN￨O￨- subtypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- looking￨L￨VBG￨O￨- for￨L￨IN￨O￨- unanticipated￨L￨JJ￨O￨- partitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- ,￨L￨,￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- unexpected￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨- with￨L￨IN￨O￨- correlated￨L￨VBN￨O￨- expression￨L￨NN￨O￨- .￨L￨.￨O￨- +Uri￨U￨NNP￨PERSON￨- Einav1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Yuval￨U￨NNP￨PERSON￨- Tabach1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Gad￨U￨NNP￨PERSON￨- Getz1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Assif￨U￨NNP￨PERSON￨- Yitzhaky1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Ugur￨U￨NNP￨O￨- Ozbek3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Ninette￨U￨NNP￨O￨- Amariglio2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Shai￨U￨NNP￨PERSON￨- Izraeli2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Gideon￨U￨NNP￨PERSON￨- Rechavi2￨U￨NNP￨O￨- ,4￨L￨NN￨O￨- and￨L￨CC￨O￨- Eytan￨U￨NNP￨O￨- Domany￨U￨NNP￨O￨- 1,4￨L￨CD￨NUMBER￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- of￨L￨IN￨O￨- Complex￨U￨JJ￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Weizmann￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Rehovot￨U￨NNP￨LOCATION￨- 76100￨L￨CD￨NUMBER￨- Israel￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- 2Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Pediatric￨U￨NNP￨ORGANIZATION￨- Hematology-Oncology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Safra￨U￨NNP￨ORGANIZATION￨- Children￨U￨NNP￨ORGANIZATION￨- 's￨L￨POS￨ORGANIZATION￨- Hospital￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Sheba￨U￨NNP￨ORGANIZATION￨- Medical￨U￨NNP￨ORGANIZATION￨- Center￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- Sackler￨U￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Medicine￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Tel￨U￨NNP￨ORGANIZATION￨- Aviv￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Tel￨U￨NNP￨CITY￨- Aviv￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Israel￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- 3Genetics￨L￨NNP￨O￨- Department￨U￨NNP￨O￨- ,￨L￨,￨O￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Experimental￨U￨JJ￨ORGANIZATION￨- Medical￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- DETAE￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Istanbul￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Turkey￨U￨NNP￨COUNTRY￨- Running￨U￨VBG￨O￨- title￨L￨NN￨O￨- :￨L￨:￨O￨- interferon￨L￨NN￨O￨- induced￨L￨VBD￨O￨- pathway￨L￨NN￨O￨A in￨L￨IN￨O￨- human￨L￨JJ￨O￨- cancers￨L￨NNS￨O￨- Key￨U￨NN￨O￨- words￨L￨NNS￨O￨- :￨L￨:￨O￨- gene￨L￨NN￨O￨- expression￨L￨NN￨O￨- ,￨L￨,￨O￨- ALL￨U￨NN￨O￨- ,￨L￨,￨O￨- class￨L￨NN￨O￨- discovery￨L￨NN￨O￨- ,￨L￨,￨O￨- interferon￨L￨NN￨O￨- pathway￨L￨NN￨O￨- ,￨L￨,￨O￨- viral￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +email￨L￨NN￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- phone￨L￨NN￨O￨- :￨L￨:￨O￨- +972￨L￨SYM￨NUMBER￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 8-9343964￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- abbreviations￨L￨NNS￨O￨- used￨L￨VBN￨O￨- are￨L￨VBP￨O￨- :￨L￨:￨O￨- ALL￨U￨NN￨O￨- ,￨L￨,￨O￨- acute￨L￨JJ￨O￨- ltmphoblastic￨L￨JJ￨O￨- leukemia￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- IIG￨U￨NNP￨O￨- ,￨L￨,￨O￨- interferon￨L￨NN￨O￨- inducible￨L￨JJ￨O￨- genes￨L￨NNS￨O￨A ;￨L￨:￨O￨- CTWC￨U￨NNP￨O￨- ,￨L￨,￨O￨- Coupled￨U￨JJ￨O￨- Two-Way￨U￨NNP￨O￨- Clustering￨U￨NN￨O￨- ;￨L￨:￨O￨- ATL￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Adult￨U￨JJ￨O￨- T-cell￨U￨NN￨O￨- leukaemia￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- HTLV￨U￨NN￨O￨- ,￨L￨,￨O￨- Human￨U￨JJ￨O￨- T-cell￨U￨NN￨O￨- Lymphotropic￨U￨JJ￨O￨- Viruses￨U￨NNS￨O￨- ;￨L￨:￨O￨- TNoM￨U￨NN￨O￨- ,￨L￨,￨O￨- Threshold￨U￨NNP￨O￨- Number￨U￨NN￨O￨- of￨L￨IN￨O￨- Misclassifications￨U￨NNPS￨O￨- ;￨L￨:￨O￨- EBV￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Epstein-Barr￨U￨JJ￨MISC￨- virus￨L￨NN￨O￨- ;￨L￨:￨O￨- SPC￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Superparamagnetic￨U￨NNP￨O￨- Clustering￨U￨NNP￨O￨- ;￨L￨:￨O￨- FDR￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- false￨L￨JJ￨O￨- discovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- MMTV￨U￨NN￨O￨- ,￨L￨,￨O￨- mouse￨L￨NN￨O￨- mammary￨L￨JJ￨O￨- tumor￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- discovered￨L￨VBD￨O￨- a￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- about￨L￨IN￨O￨- thirty￨L￨CD￨NUMBER￨- genes￨L￨NNS￨O￨- ,￨L￨,￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- interferon￨L￨NN￨O￨- response￨L￨NN￨O￨- pathway￨L￨NN￨O￨A ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- expression￨L￨NN￨O￨- levels￨L￨NNS￨O￨- divide￨L￨VBP￨O￨- the￨L￨DT￨O￨- ALL￨U￨NN￨O￨- samples￨L￨NNS￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- subgroups￨L￨NNS￨O￨- ;￨L￨:￨O￨- high￨L￨JJ￨O￨- in￨L￨IN￨O￨- 50￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- low￨L￨JJ￨O￨- in￨L￨IN￨O￨- 285￨L￨CD￨NUMBER￨- patients￨L￨NNS￨O￨- .￨L￨.￨O￨- +Oncogene￨U￨NN￨ORGANIZATION￨- 24￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6367￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2005￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Gene￨U￨NN￨O￨- expression￨L￨NN￨O￨- analysis￨L￨NN￨O￨- reveals￨L￨VBZ￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- signature￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- interferon￨L￨NN￨O￨- induced￨L￨VBD￨O￨- pathway￨L￨NN￨O￨A in￨L￨IN￨O￨- childhood￨L￨NN￨O￨- lymphoblastic￨L￨JJ￨O￨- leukemia￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- breast￨L￨NN￨O￨- and￨L￨CC￨O￨- ovarian￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- informed￨L￨VBN￨O￨- by￨L￨IN￨O￨- other￨L￨JJ￨O￨- aware￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- in￨L￨IN￨O￨- information￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- self-awareness￨L￨NN￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- local￨L￨JJ￨O￨- information￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- mass￨L￨NN￨O￨- media￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- global￨L￨JJ￨O￨- information￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +studied￨L￨VBN￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- several￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- of￨L￨IN￨O￨- self-initiated￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨A changes￨L￨NNS￨O￨A into￨L￨IN￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- such￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- may￨L￨MD￨O￨- produce￨L￨VB￨O￨- a￨L￨DT￨O￨- negative￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- In￨U￨IN￨O￨- Refs￨U￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- network￨L￨NN￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- paths￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- information￨L￨NN￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨- will￨L￨MD￨O￨- cause￨L￨VB￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- social￨L￨JJ￨O￨- distances￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- approach￨L￨NN￨O￨- and￨L￨CC￨O￨- numerical￨L￨JJ￨O￨- computations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- structures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- awareness￨L￨NN￨O￨A .￨L￨.￨O￨- +Local￨U￨JJ￨O￨- structure￨L￨NN￨O￨- entropy￨L￨NN￨O￨A of￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- Qi￨U￨NNP￨PERSON￨- Zhang￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Meizhu￨U￨NNP￨PERSON￨- Li￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Yuxian￨U￨NNP￨MISC￨- Du￨U￨NNP￨MISC￨- ,1￨L￨NN￨O￨- and￨L￨CC￨O￨- Yong￨U￨NNP￨PERSON￨- Deng1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ∗￨L￨CD￨NUMBER￨- 1School￨L￨NN￨O￨- of￨L￨IN￨O￨- Computer￨U￨NN￨O￨- and￨L￨CC￨O￨- Information￨U￨NN￨O￨- Science￨U￨NN￨O￨- ,￨L￨,￨O￨- Southwest￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Chongqing￨U￨NNP￨CITY￨- 400715￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 2School￨L￨NN￨O￨- of￨L￨IN￨O￨- Automation￨U￨NN￨O￨- ,￨L￨,￨O￨- Northwestern￨U￨NNP￨ORGANIZATION￨- Polytechnical￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Xian￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Shaanxi￨U￨NNP￨STATE_OR_PROVINCE￨- 710072￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- August￨U￨NNP￨DATE￨- 16￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Identifying￨U￨VBG￨O￨- influential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- theoretical￨L￨JJ￨O￨- and￨L￨CC￨O￨- practical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- structure￨L￨NN￨O￨- entropy￨L￨NN￨O￨A which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- centrality￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- mechanics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- influential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +PACS￨U￨NNS￨O￨- numbers￨L￨NNS￨O￨- :￨L￨:￨O￨- 89.20.-a￨L￨NN￨O￨- ,￨L￨,￨O￨- 05.10.-a￨L￨NN￨O￨- ,￨L￨,￨O￨- 02.50.-r￨L￨NN￨O￨- ,￨L￨,￨O￨- 02.10.-v￨L￨JJ￨O￨- Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Complex￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- Structure￨U￨NN￨O￨- entropy￨L￨NN￨O￨A ,￨L￨,￨O￨- Local￨U￨JJ￨O￨- structure￨L￨NN￨O￨- entropy￨L￨NN￨O￨- ,￨L￨,￨O￨- Influential￨U￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- SI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- I.￨U￨NN￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- idea￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- structure￨L￨NN￨O￨- entropy￨L￨NN￨O￨A is￨L￨VBZ￨O￨- try￨L￨VB￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- replace￨L￨VB￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- influential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- structure￨L￨NN￨O￨- entropy￨L￨NN￨O￨A are￨L￨VBP￨O￨- the￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- exist￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- golden￨L￨JJ￨O￨- times￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two-step￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- scale￨L￨VBP￨O￨- as￨L￨IN￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- 1/3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- ζ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- on￨L￨IN￨O￨- Erd˝os￨U￨NNS￨O￨- -￨L￨:￨O￨- R´enyi￨U￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- measured￨L￨VBN￨O￨A ζ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- slightly￨L￨RB￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- 1/4￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- exponent￨L￨NN￨O￨- 1/3￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- N￨U￨NN￨O￨- -￨L￨:￨O￨- dependence￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- golden￨L￨JJ￨O￨- time￨L￨NN￨O￨- is￨L￨VBZ￨O￨- universal￨L￨JJ￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- models￨L￨NNS￨O￨- showing￨L￨VBG￨O￨- discontinuous￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- cascading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- measured￨L￨VBN￨O￨- ζ￨L￨NN￨O￨- exponents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- 1/4￨L￨CD￨NUMBER￨- but￨L￨CC￨O￨- show￨L￨VBP￨O￨- model-dependence￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- reference￨L￨NN￨O￨- ,￨L￨,￨O￨- similar￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- done￨L￨VBN￨O￨- on￨L￨IN￨O￨- some￨L￨DT￨O￨- elementary￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- integer￨L￨NN￨O￨- lattices￨L￨NNS￨O￨A in￨L￨IN￨O￨- different￨L￨JJ￨O￨- dimensions￨L￨NNS￨O￨- and￨L￨CC￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- tested￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- exponential￨L￨JJ￨O￨A growth￨L￨NN￨O￨A characterizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- restricted￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- low-dimensional￨L￨JJ￨O￨- spacial￨L￨JJ￨O￨- constraint￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- two-dimensional￨L￨JJ￨O￨- square￨L￨NN￨O￨- lattice￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- finite￨L￨JJ￨O￨- integer￨L￨NN￨O￨- lattices￨L￨NNS￨O￨- of￨L￨IN￨O￨- sufficiently￨L￨RB￨O￨- high￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- shows￨L￨VBZ￨O￨- exponential￨L￨JJ￨O￨A growth￨L￨NN￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expected￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- primary￨L￨JJ￨O￨A case￨L￨NN￨O￨A infects￨L￨VBZ￨O￨- during￨L￨IN￨O￨- its￨L￨PRP$￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- mostly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- initial￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- analyzed￨L￨VBN￨O￨- by￨L￨IN￨O￨- fitting￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- generalised￨L￨VBN￨O￨- growth￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- confront￨L￨VBP￨O￨- this￨L￨DT￨O￨- challenge￨L￨NN￨O￨- and￨L￨CC￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- discrete-time￨L￨JJ￨O￨- governing￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- closed￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- ,￨L￨,￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- to￨L￨TO￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +Efficient￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- containment￨L￨NN￨O￨A using￨L￨VBG￨O￨- link￨L￨NN￨O￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Joan￨U￨NNP￨PERSON￨- T.￨U￨NNP￨PERSON￨- Matamalas￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- ∗￨L￨CD￨NUMBER￨- Alex￨U￨NNP￨PERSON￨- Arenas￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Sergio￨U￨NNP￨PERSON￨- G´omez￨U￨NNP￨O￨- Departament￨U￨NNP￨O￨- d’Enginyeria￨L￨NNP￨O￨- Inform￨U￨NNP￨O￨- `￨L￨``￨O￨- atica￨L￨FW￨O￨- i￨L￨FW￨O￨- Matem￨U￨FW￨O￨- `￨L￨``￨O￨- atiques￨L￨NNS￨O￨- ,￨L￨,￨O￨- Universitat￨U￨NNP￨PERSON￨- Rovira￨U￨NNP￨PERSON￨- i￨L￨FW￨O￨- Virgili￨U￨NNP￨O￨- ,￨L￨,￨O￨- 43007￨L￨CD￨NUMBER￨- Tarragona￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- March￨U￨NNP￨DATE￨- 26￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Epidemic￨U￨JJ￨O￨- containment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- ma￨L￨NN￨O￨- jor￨L￨NN￨O￨- concern￨L￨NN￨O￨- when￨L￨WRB￨O￨- confronting￨L￨VBG￨O￨- large-scale￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- validated￨L￨VBN￨O￨- in￨L￨IN￨O￨- synthetic￨L￨JJ￨O￨- and￨L￨CC￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- obtaining￨L￨VBG￨O￨- an￨L￨DT￨O￨- accurate￨L￨JJ￨O￨- determination￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- links￨L￨NNS￨O￨- inform￨L￨VBP￨O￨A about￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- carrying￨L￨VBG￨O￨- the￨L￨DT￨O￨- contagion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- far￨L￨RB￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- work￨L￨NN￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- controlling￨L￨VBG￨O￨- behavioral￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- pinning￨L￨VBG￨O￨- feedback￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- quenched￨L￨VBN￨O￨- mean￨L￨NN￨O￨- field￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- control￨L￨NN￨O￨- synchronization￨L￨NN￨O￨A models￨L￨NNS￨O￨- with￨L￨IN￨O￨- inhibition￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- constructed￨L￨VBN￨O￨- ,￨L￨,￨O￨- combining￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- network￨L￨NN￨O￨- carrying￨L￨VBG￨O￨- extra￨L￨JJ￨O￨- controllers￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- investigates￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- control￨L￨NN￨O￨- behavioral￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- via￨L￨IN￨O￨- pinning￨L￨VBG￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infected￨L￨JJ￨O￨- situation￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- depended￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ’￨L￨POS￨O￨- information￨L￨NN￨O￨- are￨L￨VBP￨O￨- designed￨L￨VBN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- only￨L￨RB￨O￨- adds￨L￨VBZ￨O￨- controllers￨L￨NNS￨O￨- to￨L￨TO￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- adds￨L￨VBZ￨O￨- controllers￨L￨NNS￨O￨- both￨L￨CC￨O￨- to￨L￨TO￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- hopeful￨L￨JJ￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- more￨L￨RBR￨O￨- deeper￨L￨JJR￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- essence￨L￨NN￨O￨- between￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ’s￨L￨POS￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- collective￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- controlling￨L￨VBG￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- adopt￨L￨VBP￨O￨- a￨L￨DT￨O￨- step-by-step￨L￨JJ￨O￨- approach￨L￨NN￨O￨- whereby￨L￨IN￨O￨- we￨L￨PRP￨O￨- first￨L￨VBP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- rewiring￨L￨VBG￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- with￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- assigned￨L￨VBN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- but￨L￨CC￨O￨- without￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- finally￨L￨RB￨O￨- ,￨L￨,￨O￨- running￨L￨VBG￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- simultaneously￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- present￨L￨VBP￨DATE￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- rewiring￨L￨VBG￨O￨A on￨L￨IN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- cluster-ing￨L￨NN￨O￨- when￨L￨WRB￨O￨- rewiring￨L￨VBG￨O￨- operates￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Sections￨U￨NNS￨O￨- II￨U￨CD￨NUMBER￨- A-II￨U￨NN￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- labelled￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Section￨U￨NN￨O￨- II￨U￨CD￨NUMBER￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +6￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 4￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- spatial￨L￨JJ￨O￨- component￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- rewiring￨L￨NN￨O￨A strategy￨L￨NN￨O￨- was￨L￨VBD￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- link￨L￨VBP￨O￨- is￨L￨VBZ￨O￨- cut￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- individual￨L￨NN￨O￨- will￨L￨MD￨O￨- reconnect￨L￨VB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- probability￨L￨NN￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- random￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- irrespective￨L￨RB￨O￨- of￨L￨IN￨O￨- distance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- close-by￨L￨JJ￨O￨- or￨L￨CC￨O￨- neighbouring￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- p￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- constrained￨L￨VBN￨O￨- rewiring￨L￨NN￨O￨A on￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- node￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +Large￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- emerge￨L￨VBP￨O￨- in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- Hui￨U￨NNP￨O￨- Yang￨U￨NNP￨O￨- ∗￨L￨SYM￨O￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Ming￨U￨NNP￨O￨- Tang￨U￨NNP￨O￨- †￨L￨SYM￨O￨- ,1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Thilo￨U￨NNP￨O￨- Gross2￨U￨NNP￨O￨- 1Web￨L￨NNP￨O￨- Sciences￨U￨NNP￨O￨- Center￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electronic￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Chengdu￨U￨NNP￨CITY￨- 610054￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 2Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Engineering￨U￨NNP￨O￨- Mathematics￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Bristol￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Bristol￨U￨NNP￨CITY￨- BS8￨U￨NN￨O￨- 1UB￨L￨NN￨O￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- May￨U￨NNP￨DATE￨- 15￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- famous￨L￨JJ￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- science￨L￨NN￨O￨- states￨L￨NNS￨O￨- that￨L￨WDT￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- than￨L￨IN￨O￨- their￨L￨PRP$￨O￨- more￨L￨JJR￨O￨- homogeneous￨L￨JJ￨O￨- counterparts￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- identical￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- network￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- lower￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- epidemics￨L￨NNS￨O￨- can￨L￨MD￨O￨- invade￨L￨VB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Heterogeneity￨U￨NN￨O￨- in￨L￨IN￨O￨- structure￨L￨NN￨O￨- can￨L￨MD￨O￨- enhance￨L￨VB￨O￨- or￨L￨CC￨O￨- diminish￨L￨VB￨O￨- the￨L￨DT￨O￨- resilience￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- and￨L￨CC￨O￨- intrinsic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- pointed￨L￨VBN￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- intrinsically￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- very￨L￨RB￨O￨- resilient￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Network￨U￨NNP￨O￨- heterogeneity￨L￨NN￨O￨A can￨L￨MD￨O￨- thus￨L￨RB￨O￨- allow￨L￨VB￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- lower￨L￨JJR￨O￨- transmission￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- and￨L￨CC￨O￨- spread￨L￨VB￨O￨- .￨L￨.￨O￨- +Optimal￨U￨JJ￨O￨- Vaccine￨U￨NN￨O￨- Allocation￨U￨NN￨O￨- to￨L￨TO￨O￨- Control￨U￨VB￨ORGANIZATION￨- Epidemic￨U￨JJ￨ORGANIZATION￨- Outbreaks￨U￨NNS￨ORGANIZATION￨- in￨L￨IN￨ORGANIZATION￨- Arbitrary￨U￨NNP￨ORGANIZATION￨- Networks￨U￨NNP￨ORGANIZATION￨- Victor￨U￨NNP￨ORGANIZATION￨- M.￨U￨NNP￨ORGANIZATION￨- 3￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 3￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- by￨L￨IN￨O￨- distributing￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- resources￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- written￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- condition￨L￨NN￨O￨- involving￨L￨VBG￨O￨- the￨L￨DT￨O￨- eigenvalues￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- matrix￨L￨NN￨O￨- that￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- are￨L￨VBP￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- under￨L￨IN￨O￨- what￨L￨WP￨O￨- circumstances￨L￨NNS￨O￨- a￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- response￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- awareness￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- control￨L￨NN￨O￨- measure￨L￨NN￨O￨- :￨L￨:￨O￨- whether￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- would￨L￨MD￨O￨- predict￨L￨VB￨O￨- an￨L￨DT￨O￨- elevated￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- would￨L￨MD￨O￨- prevent￨L￨VB￨O￨- future￨L￨JJ￨DATE￨- flare-ups￨L￨NNS￨O￨- from￨L￨IN￨O￨- low￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- approaches￨L￨NNS￨O￨- cast￨L￨VBD￨O￨- preventive￨L￨JJ￨O￨- actions￨L￨NNS￨O￨- into￨L￨IN￨O￨- classic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- dividing￨L￨VBG￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible/infectious/removed￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- between￨L￨IN￨O￨- responsive￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-responsive￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- by￨L￨IN￨O￨- explicitly￨L￨RB￨O￨- considering￨L￨VBG￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- both￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- aware￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- lowered￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- unaware￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- consider￨L￨VB￨O￨- awareness￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- will￨L￨MD￨O￨- both￨L￨CC￨O￨- induce￨L￨VBP￨O￨- a￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- response￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- given￨L￨VBN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- willing￨L￨JJ￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- this￨L￨DT￨O￨- assumption￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- awareness￨L￨NN￨O￨A may￨L￨MD￨O￨- drive￨L￨VB￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- to￨L￨TO￨O￨- very￨L￨RB￨O￨- low￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- eliminate￨L￨VB￨O￨- it￨L￨PRP￨O￨- or￨L￨CC￨O￨- change￨L￨VB￨O￨- its￨L￨PRP$￨O￨- stability￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- non-reactive￨L￨JJ￨O￨- SAIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- without￨L￨IN￨O￨- decay￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨A ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨- causes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- elevation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- respect￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- authors￨L￨NNS￨O￨- de￨L￨IN￨O￨- fined￨L￨VBN￨O￨- an￨L￨DT￨O￨- e￨L￨SYM￨O￨- ffective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- rate￨L￨NN￨O￨- R￨U￨NN￨O￨- ∗￨L￨CD￨NUMBER￨- Preprint￨U￨NNP￨O￨- submitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- Journal￨U￨NNP￨O￨- of￨L￨IN￨O￨- Theoretical￨U￨NNP￨O￨- Biology￨U￨NNP￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- level￨L￨NN￨O￨- and￨L￨CC￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- its￨L￨PRP$￨O￨- expression￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- case￨L￨NN￨O￨- with￨L￨IN￨O￨- R0￨U￨NN￨O￨- →￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- travel￨L￨NN￨O￨- rate￨L￨NN￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- mean￨L￨NN￨O￨- -￨L￨:￨O￨- field￨L￨NN￨O￨- approximation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- R￨U￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- hk2￨L￨NN￨O￨- i￨L￨FW￨O￨- −￨L￨FW￨O￨- hki￨L￨FW￨O￨- hki2￨L￨NN￨O￨- pNα￨L￨NN￨O￨- µ￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- brackets￨L￨NNS￨O￨- h￨L￨NN￨O￨- ·￨L￨NN￨O￨- i￨L￨FW￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- average￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- con￨L￨NN￨O￨- -￨L￨:￨O￨- figurations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- α￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- city￨L￨NN￨O￨A during￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- 1/µ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- time￨L￨NN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- stays￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- city￨L￨NN￨O￨- .￨L￨.￨O￨- +Equation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- assumptions￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- uncorrelated￨L￨JJ￨O￨- and￨L￨CC￨O￨- tree-like￨L￨JJ￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- importantly￨L￨RB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- going￨L￨VBG￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- city￨L￨NN￨O￨A to￨L￨TO￨O￨- another￨L￨DT￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- d￨L￨NN￨O￨- =￨L￨JJ￨O￨- pNα/µ￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- level￨L￨NN￨O￨A of￨L￨IN￨O￨- description￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- analytically￨L￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- problems￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- authors￨L￨NNS￨O￨A studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- isolated￨L￨VBN￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- rate￨L￨NN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- invade￨L￨VB￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- mapping￨L￨NN￨O￨- enables￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- lower￨L￨JJR￨O￨A bound￨L￨VBN￨O￨A )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- case￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- possible￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ma￨L￨NN￨O￨- jor￨L￨NN￨O￨- novelty￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- promote￨L￨VBP￨O￨- lies￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- taking￨L￨VBG￨O￨- place￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- specified￨L￨VBN￨O￨- in￨L￨IN￨O￨- advance￨L￨NN￨O￨- but￨L￨CC￨O￨- evolves￨L￨VBZ￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Without￨U￨IN￨O￨- assuming￨L￨VBG￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- underlying￨L￨JJ￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨A process￨L￨NN￨O￨A introduced￨L￨VBN￨O￨- describes￨L￨VBZ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- flexible￨L￨JJ￨O￨- and￨L￨CC￨O￨- realistic￨L￨JJ￨O￨- manner￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- non-uniformly￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- possibly￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- to￨L￨TO￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- graph-valued￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- communicable￨L￨JJ￨O￨A infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +AN￨U￨DT￨O￨- SIR￨U￨NN￨O￨- GRAPH￨U￨NN￨O￨- GROWTH￨U￨NN￨O￨- MODEL￨U￨NN￨TITLE￨- FOR￨U￨IN￨O￨- THE￨U￨DT￨O￨- EPIDEMICS￨U￨NNS￨O￨- OF￨U￨IN￨O￨- COMMUNICABLE￨U￨JJ￨O￨- DISEASES￨U￨NNS￨CAUSE_OF_DEATH￨- CHARANPAL￨U￨JJ￨O￨- DHANJAL￨U￨NNPS￨O￨- AND￨U￨CC￨O￨- ST￨U￨JJ￨O￨- ´￨L￨''￨O￨- EPHAN￨U￨NNP￨O￨- CL￨U￨NN￨O￨- ´EM￨L￨NN￨O￨- ENC￨U￨NN￨O￨- ¸￨L￨CD￨NUMBER￨- ON￨U￨IN￨O￨- T´el￨U￨NN￨O￨- ´￨L￨''￨O￨- ecom￨L￨FW￨O￨- ParisTech￨U￨NNP￨O￨- ,￨L￨,￨O￨- 46￨L￨CD￨NUMBER￨A rue￨L￨NN￨LOCATION￨- Barrault￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- 75634￨L￨CD￨NUMBER￨- Paris￨U￨NNP￨ORGANIZATION￨- Cedex￨U￨NNP￨ORGANIZATION￨- 13￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- France￨U￨NNP￨COUNTRY￨- Abstract￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- distributed￨L￨VBN￨O￨- and￨L￨CC￨O￨- adaptive￨L￨JJ￨O￨- CSMA￨U￨NNP￨O￨- algorithm￨L￨NN￨O￨A under￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- interference￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- channels￨L￨NNS￨O￨- .￨L￨.￨O￨- +Related￨U￨JJ￨O￨- Work￨U￨NN￨O￨- A￨U￨DT￨O￨- large￨L￨JJ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- literature￨L￨NN￨O￨- on￨L￨IN￨O￨- scheduling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- weight￨L￨NN￨O￨- scheduling￨L￨NN￨O￨- algorithm￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- throughput￨L￨JJ￨O￨- optimal￨L￨JJ￨O￨- under￨L￨IN￨O￨- fairly￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨NN￨O￨- among￨L￨IN￨O￨- them￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- achievable￨L￨JJ￨O￨- throughput￨L￨NN￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- scheduling￨L￨NN￨O￨- algorithm￨L￨NN￨O￨A is￨L￨VBZ￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- arrival￨L￨NN￨O￨- rates￨L￨NNS￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- can￨L￨MD￨O￨- stabilize￨L￨VB￨O￨- the￨L￨DT￨O￨- queues￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- distributed￨L￨VBN￨O￨- algorithm￨L￨NN￨O￨A was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- adaptively￨L￨RB￨O￨- choose￨L￨VB￨O￨- the￨L￨DT￨O￨- CSMA￨U￨NNP￨O￨- parameters￨L￨NNS￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- throughput￨L￨NN￨O￨- optimality￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pSEIRS￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- takes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- probabilities￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- realistic￨L￨JJ￨O￨- scale￨L￨NN￨O￨- free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- problem￨L￨NN￨O￨- with￨L￨IN￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- existing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- tailored￨L￨VBN￨O￨- to￨L￨TO￨O￨- random￨L￨JJ￨O￨- or￨L￨CC￨O￨- Erdos￨U￨NNP￨O￨- type￨L￨NN￨O￨- networks￨L￨NNS￨O￨- since￨L￨IN￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- varying￨L￨VBG￨O￨- probabilities￨L￨NNS￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- immunity￨L￨NN￨O￨- per￨L￨IN￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- pSEIRS￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨A rate￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- excess￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- are￨L￨VBP￨O￨- constant￨L￨JJ￨O￨- for￨L￨IN￨O￨- infective￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +KEYWORDS￨U￨NNS￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- SEIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- Delay￨U￨NNP￨O￨- differential￨L￨JJ￨O￨A equations￨L￨NNS￨O￨A ;￨L￨:￨O￨- Epidemic￨U￨JJ￨O￨- threshold￨L￨NN￨O￨- ;￨L￨:￨O￨- Scale￨U￨NNP￨O￨- free￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +KEYWORDS￨U￨NNS￨O￨- :￨L￨:￨O￨- Delay￨U￨VB￨O￨- equations￨L￨NNS￨O￨- ;￨L￨:￨O￨- distributed￨L￨VBN￨O￨- delay￨L￨NN￨O￨A ;￨L￨:￨O￨- stability￨L￨NN￨O￨- ;￨L￨:￨O￨- number￨L￨NN￨O￨- ;￨L￨:￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ;￨L￨:￨O￨- bifurcation￨L￨NN￨O￨- ;￨L￨:￨O￨- persistence￨L￨NN￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- AMS￨U￨NNP￨O￨- Classification￨U￨NNP￨O￨- :￨L￨:￨O￨- 34K08￨L￨NN￨O￨- ;￨L￨:￨O￨- 34K18￨L￨NN￨O￨- ;￨L￨:￨O￨- 34K20￨L￨NN￨O￨- ;￨L￨:￨O￨- 92D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Motivation￨U￨NN￨O￨- and￨L￨CC￨O￨- background￨L￨NN￨O￨- Classical￨U￨JJ￨O￨- approaches￨L￨NNS￨O￨- in￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- present￨L￨VB￨DATE￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infectives￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- consider￨L￨VB￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- transitions￨L￨NNS￨O￨- among￨L￨IN￨O￨- these￨L￨DT￨O￨- compartments￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- usual￨L￨JJ￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- or￨L￨CC￨O￨- equal￨L￨JJ￨O￨- than￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- for￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- persists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- side￨L￨NN￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- hosts￨L￨NNS￨O￨- who￨L￨WP￨O￨- recovered￨L￨VBD￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- and￨L￨CC￨O￨- since￨L￨IN￨O￨- then￨L￨RB￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- receive￨L￨VB￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- boosting￨L￨VBG￨O￨- nor￨L￨CC￨O￨- die￨L￨VB￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- exp￨L￨NN￨O￨A I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- u￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- du￨L￨NNP￨O￨- .￨L￨.￨O￨- +Z￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- τ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- dτ￨L￨NN￨O￨- −￨L￨NN￨O￨- ν￨L￨NN￨O￨- β￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- side￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- hosts￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- was￨L￨VBD￨O￨- boosted￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- and￨L￨CC￨O￨- [￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- die￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- interval￨L￨JJ￨O￨- ν￨L￨NN￨O￨- β￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- exp￨L￨NN￨O￨A −￨L￨CD￨NUMBER￨- dτ￨L￨NN￨O￨- −￨L￨NN￨O￨- ν￨L￨NN￨O￨- β￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- u￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- du￨L￨NNP￨O￨- .￨L￨.￨O￨- +Z￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- τ￨L￨NN￨O￨- All￨U￨DT￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- S￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- d￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- β￨L￨SYM￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- ν￨L￨NN￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- Z￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- τ￨L￨SYM￨O￨- ×￨L￨SYM￨O￨- exp￨L￨FW￨O￨A −￨L￨FW￨O￨- dτ￨L￨FW￨O￨- −￨L￨FW￨O￨- ν￨L￨FW￨O￨- β￨L￨FW￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- u￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- du￨L￨NNP￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- φI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- φS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- −￨L￨NN￨O￨- τ￨L￨NN￨O￨- ≤￨L￨NN￨O￨- t￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- ≤￨L￨NN￨O￨- t￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- given￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- φS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- φI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- φS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- φI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- t￨L￨NN￨O￨- ∈￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-infectious-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- well-documented￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- outbreaks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- epidemic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- well-documented￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- outbreaks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- via￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-infectious-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- smooth￨L￨JJ￨O￨- transition￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- after￨L￨IN￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A are￨L￨VBP￨O￨- put￨L￨VBN￨O￨- in￨L￨IN￨O￨- place￨L￨NN￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Ebola￨U￨NN￨O￨- hemorrhagic￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- lethal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- named￨L￨VBN￨O￨A after￨L￨IN￨O￨- a￨L￨DT￨O￨- river￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Democratic￨U￨JJ￨COUNTRY￨- Republic￨U￨NN￨COUNTRY￨- of￨L￨IN￨COUNTRY￨- the￨L￨DT￨COUNTRY￨- Congo￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- formerly￨L￨RB￨O￨- Zaire￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- first￨L￨JJ￨O￨- identifi￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Twelve￨U￨CD￨NUMBER￨- outbreaks￨L￨NNS￨O￨A of￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- Congo￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Sudan￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Gabon￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Uganda￨U￨NNP￨COUNTRY￨- as￨L￨IN￨O￨- of￨L￨IN￨O￨- September￨U￨NNP￨DATE￨- 14￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2003￨L￨CD￨DATE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- propose￨L￨VB￨O￨- a￨L￨DT￨O￨- formula￨L￨NN￨O￨- for￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- serology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- also￨L￨RB￨O￨- extensively￨L￨RB￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- its￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- below￨L￨IN￨O￨- and￨L￨CC￨O￨- above￨L￨IN￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨A threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- more￨L￨RBR￨O￨- recent￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SW￨U￨NN￨MISC￨- N￨U￨NN￨MISC￨- was￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Newman￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Watts￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- k￨L￨NN￨O￨- of￨L￨IN￨O￨- Nearest￨U￨NNP￨O￨- Neighbors￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NNP￨O￨- N￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- conserved￨L￨VBN￨O￨- but￨L￨CC￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- rewiring￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- added￨L￨VBD￨O￨- an￨L￨DT￨O￨- average￨L￨JJ￨O￨- density￨L￨NN￨O￨- φ￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- bonds￨L￨NNS￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- site￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- except￨L￨IN￨O￨- its￨L￨PRP$￨O￨- nearest￨L￨JJS￨O￨A neighbors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- expected￨L￨VBN￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- excludes￨L￨VBZ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disorder￨L￨NN￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- a￨L￨DT￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- any￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- steps￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- excludes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- regular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- nearest￨L￨JJS￨O￨A neighbor￨L￨NN￨O￨- connections￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨A threshold￨L￨NN￨O￨- was￨L￨VBD￨O￨- extensively￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- dependence￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- N￨U￨NN￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- SC￨U￨NN￨ORGANIZATION￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- satisfy￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- equation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- φ￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- pc￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- k/2￨L￨NN￨O￨- pc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- This￨U￨DT￨O￨- threshold￨L￨NN￨O￨- corresponds￨L￨VBZ￨O￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- smallest￨L￨JJS￨O￨- concentration￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- site￨L￨NN￨O￨- percolation￨L￨NN￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- SW￨U￨NN￨O￨- N￨U￨NN￨O￨- with￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- and￨L￨CC￨O￨- φ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- representing￨L￨VBG￨O￨- a￨L￨DT￨O￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- age￨L￨NN￨O￨- children￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fluctuations￨L￨NNS￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- SC￨U￨NN￨ORGANIZATION￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- an￨L￨DT￨O￨- alternative￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- small￨L￨JJ￨O￨- world￨L￨NN￨O￨A network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- structure￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- reliably￨L￨RB￨O￨- produce￨L￨VB￨O￨- simulations￨L￨NNS￨O￨- quantitative￨L￨JJ￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Surrogate￨U￨NN￨O￨- data￨L￨NNS￨O￨- methods￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- simple￨L￨JJ￨O￨- random￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- insufficient￨L￨JJ￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- fully￨L￨RB￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- variability￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Various￨U￨JJ￨O￨- human￨L￨JJ￨O￨- activity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- tele-communications￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- E-mail￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- surface￨L￨NN￨O￨- mail￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- web￨L￨NN￨O￨- browsing￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- instant￨L￨JJ￨O￨- messaging￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨- calls￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- physical￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- probed￨L￨VBN￨O￨- by￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- devices￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- sexual￨L￨JJ￨O￨- contact￨L￨NN￨O￨- survey￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- revealed￨L￨VBN￨O￨- high￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- power-law￨L￨NN￨O￨- waiting￨L￨VBG￨O￨- time￨L￨NN￨O￨A distribution￨L￨NN￨O￨A P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∼￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- −￨L￨NN￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- consecutive￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- departure￨L￨NN￨O￨- from￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- assumption￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- decays￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨A law￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- limit￨L￨NN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∼￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- extremely￨L￨RB￨O￨- slow￨L￨VB￨O￨- prevalence￨L￨NN￨O￨- decay￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- exponent￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- waiting￨L￨VBG￨O￨- time￨L￨NN￨O￨A distribution￨L￨NN￨O￨A ,￨L￨,￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- agents￨L￨NNS￨O￨- but￨L￨CC￨O￨- is￨L￨VBZ￨O￨- insensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- strategy￨L￨NN￨O￨- believed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- efficient￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- immunization￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- immunizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- betweenness￨L￨NN￨O￨A centrality￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- links￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- adaptive￨L￨JJ￨O￨- betweenness￨L￨NN￨O￨A centrality￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- shortest￨L￨JJS￨O￨- paths￨L￨NNS￨O￨- passing￨L￨VBG￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- ,￨L￨,￨O￨- recalculated￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- non￨L￨JJ￨O￨- immunized￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- step￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immunization￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Targeted￨U￨VBN￨O￨- immunization￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- links￨L￨NNS￨O￨- playing￨L￨VBG￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- architecture￨L￨NN￨O￨- are￨L￨VBP￨O￨- immunized￨L￨VBN￨O￨- first￨L￨NN￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- proven￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- very￨L￨RB￨O￨- effective￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- immunize￨L￨VB￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- links￨L￨NNS￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- [￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Sanders2￨U￨NN￨O￨- ,￨L￨,￨O￨- ‡￨L￨CD￨NUMBER￨- 1Bristol￨L￨NN￨O￨- Centre￨U￨NNP￨O￨- for￨L￨IN￨O￨- Complexity￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- Mathematics￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Biological￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Bristol￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- BS8￨U￨NN￨O￨- 1TR￨L￨NN￨O￨- ,￨L￨,￨O￨- Bristol￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- 2Departamento￨L￨NNP￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- ,￨L￨,￨O￨- Facultad￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Ciencias￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Centro￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Ciencias￨U￨NNP￨ORGANIZATION￨- de￨L￨FW￨ORGANIZATION￨- la￨L￨FW￨ORGANIZATION￨- Complejidad￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- C3￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Universidad￨U￨NNP￨ORGANIZATION￨- Nacional￨U￨NNP￨ORGANIZATION￨- Aut￨U￨NNP￨ORGANIZATION￨- ´￨L￨POS￨O￨- onoma￨L￨NN￨O￨- de￨L￨IN￨O￨- M￨U￨NN￨O￨- ´￨L￨''￨O￨- exico￨L￨NN￨O￨- ,￨L￨,￨O￨- Ciudad￨U￨NNP￨ORGANIZATION￨- Universitaria￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- M￨U￨NNP￨O￨- ´￨L￨POS￨O￨- exico￨L￨JJ￨O￨- D.F.￨U￨NNP￨O￨- 04510￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mexico￨U￨NNP￨COUNTRY￨- We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- encounter￨L￨NN￨O￨A times￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- random￨L￨JJ￨O￨- walkers￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- dimension￨L￨NN￨O￨- when￨L￨WRB￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- segregated￨L￨VBN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- domain￨L￨NN￨O￨- and￨L￨CC￨O￨- shares￨L￨NNS￨O￨- with￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighbor￨L￨NN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- very￨L￨RB￨O￨- good￨L￨JJ￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- numerically-exact￨L￨JJ￨O￨- calculations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- encounter￨L￨NN￨O￨A times￨L￨NNS￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- analytically￨L￨RB￨O￨- the￨L￨DT￨O￨- macroscopic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- confining￨L￨VBG￨O￨- geometry￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- animal￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- cause￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- non-trivial￨L￨JJ￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reaction￨L￨NN￨O￨A rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- local￨L￨JJ￨O￨- parameKeywords￨L￨NNS￨O￨- Epidemic￨U￨JJ￨O￨- spreading￨L￨VBG￨O￨- ⋅￨L￨SYM￨O￨- Diffusion￨U￨NNP￨O￨- ⋅￨L￨NNP￨O￨- Complex￨U￨NN￨O￨- networks￨L￨NNS￨O￨- ⋅￨L￨VBP￨O￨- Heterogenous￨U￨JJ￨O￨- ters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- topology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- global￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cross-over￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- that￨L￨WDT￨O￨- separates￨L￨VBZ￨O￨- “￨L￨``￨O￨- village￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ”￨L￨''￨O￨- from￨L￨IN￨O￨- “￨L￨``￨O￨- city￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ”￨L￨''￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- analytic￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- we￨L￨PRP￨O￨- calculate￨L￨VBP￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- metaopoluation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- limit￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- characterising￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A that￨L￨WDT￨O￨- separates￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- non-epidemic￨L￨JJ￨O￨- phase￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- metapopulation￨L￨NN￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- grouped￨L￨VBN￨O￨- in￨L￨IN￨O￨- subpopulations￨L￨NNS￨O￨A symbolising￨L￨VBG￨O￨- cities￨L￨NNS￨O￨- and￨L￨CC￨O￨- villages￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- coupled￨L￨VBN￨O￨- by￨L￨IN￨O￨- human￨L￨JJ￨O￨- travel￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- transportation￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨- that￨L￨IN￨O￨- large￨L￨JJ￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- subpopulations￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- cities￨L￨NNS￨O￨- or￨L￨CC￨O￨- villages￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- architecture￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- new￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- co-operative￨L￨JJ￨O￨- and￨L￨CC￨O￨- supportive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- involves￨L￨VBZ￨O￨- a￨L￨DT￨O￨- preprocessing￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- input￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- renders￨L￨VBZ￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Regarding￨U￨VBG￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- phenomenon￨L￨NN￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- neural￨L￨JJ￨O￨A network￨L￨NN￨O￨- architecture￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- vital￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Dynamical￨U￨JJ￨O￨- systems￨L￨NNS￨O￨- ;￨L￨:￨O￨- Mutual￨U￨JJ￨O￨- interference￨L￨NN￨O￨- ;￨L￨:￨O￨- Polynomial￨U￨NNP￨O￨- regression￨L￨NN￨O￨- ;￨L￨:￨O￨- Epidemics￨U￨NNS￨O￨- ;￨L￨:￨O￨- K-means￨U￨NNS￨MISC￨- clustering￨L￨NN￨O￨- ;￨L￨:￨O￨- Cooperative￨U￨NNP￨O￨- and￨L￨CC￨O￨- supportive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +So￨U￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- desirable￨L￨JJ￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- realistic￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨A interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- Simple￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- predators￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- also￨L￨RB￨O￨- other￨L￨JJ￨O￨- food￨L￨NN￨O￨- sources￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- reproduce￨L￨VBP￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- clearly￨L￨RB￨O￨- get￨L￨VB￨O￨- a￨L￨DT￨O￨- benefit￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- prey￨L￨NN￨O￨- expressed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- e￨L￨SYM￨O￨- <￨L￨JJR￨O￨- c.￨L￨NN￨O￨- with￨L￨IN￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease-safety￨L￨JJ￨O￨- niche￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibles￨L￨NNS￨O￨- reads￨L￨VBZ￨O￨- In￨U￨IN￨O￨- summary￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ecoepidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- dR￨L￨NN￨O￨- dt￨L￨NN￨O￨- dU￨L￨NN￨O￨- dt￨L￨NN￨O￨- dF￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- −￨L￨NN￨O￨- bR￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- cF￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ωU￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- λ￨L￨NN￨O￨- max￨L￨NN￨O￨A {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- U￨U￨NNP￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- λ￨L￨NN￨O￨- max￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- U￨U￨NNP￨O￨- −￨L￨NNP￨O￨- U￨U￨NNP￨O￨- [￨L￨-LRB-￨O￨- kF￨L￨NNP￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- µU￨L￨NN￨O￨- ,￨L￨,￨O￨- =￨L￨JJ￨O￨- F￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- eR￨L￨NN￨O￨- −￨L￨NN￨O￨- f￨L￨FW￨O￨- F￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- hU￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Its￨U￨PRP$￨O￨- population￨L￨NN￨O￨- values￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- solving￨L￨VBG￨O￨- for￨L￨IN￨O￨- F￨U￨NN￨O￨- and￨L￨CC￨O￨- U￨U￨NNP￨O￨- respectively￨L￨RB￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- and￨L￨CC￨ORDINAL￨- third￨L￨JJ￨ORDINAL￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- obviously￨L￨RB￨O￨A R6￨U￨NN￨O￨- >￨L￨JJR￨O￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- giving￨L￨VBG￨O￨- F6￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R6￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- ω￨L￨SYM￨O￨- −￨L￨SYM￨O￨- µ￨L￨SYM￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- U6￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- eR6￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- f￨L￨LS￨O￨- F6￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +P3￨U￨NN￨O￨- =￨L￨JJ￨O￨- ab￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P4￨U￨NN￨O￨- =￨L￨JJ￨O￨- af￨L￨FW￨O￨- −￨L￨FW￨O￨- cd￨L￨NN￨O￨- bf￨L￨NN￨O￨- +￨L￨CC￨O￨- ce￨L￨NN￨O￨- P5￨U￨NN￨O￨- =￨L￨JJ￨O￨- λs￨L￨NN￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- λ￨L￨NN￨O￨- bf￨L￨NN￨O￨- +￨L￨CC￨O￨- ce￨L￨NN￨O￨- ,￨L￨,￨O￨- ae￨L￨NN￨O￨- +￨L￨CC￨O￨- bd￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- −￨L￨NN￨O￨- bR5￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R5￨U￨NN￨O￨- µ￨L￨NN￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- The￨U￨DT￨O￨- first￨L￨NN￨O￨- three￨L￨CD￨NUMBER￨- points￨L￨NNS￨O￨- are￨L￨VBP￨O￨- always￨L￨RB￨O￨- feasible￨L￨JJ￨O￨A ,￨L￨,￨O￨- P4￨U￨NN￨O￨- is￨L￨VBZ￨O￨- feasible￨L￨JJ￨O￨- for￨L￨IN￨O￨- and￨L￨CC￨O￨- P5￨U￨NN￨O￨- is￨L￨VBZ￨O￨- whenever￨L￨WRB￨O￨- a￨L￨DT￨O￨- ≥￨L￨NN￨O￨- bR5￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- for￨L￨IN￨O￨- af￨L￨FW￨O￨- ≥￨L￨FW￨O￨- cd￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- λs￨L￨NN￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨CD￨NUMBER￨- aλ￨L￨NN￨O￨- .￨L￨.￨O￨- +Observe￨U￨VB￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- reinfections￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- rate￨L￨NN￨O￨- as￨L￨IN￨O￨- initial￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- λ￨L￨FW￨O￨- =￨L￨JJ￨O￨- µ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- reinfections￨L￨NNS￨O￨- are￨L￨VBP￨O￨- disallowed￨L￨VBN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- µ￨L￨FW￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- reduces￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- extensively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Transition￨U￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- ζt￨L￨NN￨O￨- are￨L￨VBP￨O￨- specified￨L￨VBN￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- flip￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- ζt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- u￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- −￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- →￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- →￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- →￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- |￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- −￨L￨SYM￨O￨- →￨L￨SYM￨O￨- vu￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- :￨L￨:￨O￨- ζt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- µ￨L￨NN￨O￨- |￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- −￨L￨SYM￨O￨- →￨L￨SYM￨O￨- vu￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- :￨L￨:￨O￨- ζt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- where￨L￨WRB￨O￨- |￨L￨SYM￨O￨- A￨U￨DT￨O￨- |￨L￨SYM￨O￨- denotes￨L￨VBZ￨O￨- cardinality￨L￨NN￨O￨- of￨L￨IN￨O￨- set￨L￨VBN￨O￨- A.￨U￨NN￨MISC￨- Initial￨U￨JJ￨MISC￨- configuration￨L￨NN￨O￨A η￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- incorporated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- notation￨L￨NN￨O￨- below￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- fashion￨L￨NN￨O￨- :￨L￨:￨O￨- ζ￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- η￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NNP￨O￨- ,￨L￨,￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- and￨L￨CC￨O￨- results￨L￨VBZ￨O￨- The￨U￨DT￨O￨- three￨L￨CD￨NUMBER￨- state￨L￨NN￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- µ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- digraph￨L￨NN￨O￨- G￨U￨NN￨O￨- ≡￨L￨CD￨NUMBER￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- ζt￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- configuration￨L￨NN￨O￨- space￨L￨NN￨O￨- X￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- −￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- V￨U￨NNP￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- functions￨L￨NNS￨O￨- from￨L￨IN￨O￨- V￨U￨NN￨O￨- to￨L￨TO￨O￨- {￨L￨-LRB-￨O￨- −￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨A process￨L￨NN￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- which￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- time￨L￨NN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- The￨U￨NNP￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- modulat￨L￨NN￨O￨- ion￨L￨NN￨O￨A o￨L￨NN￨O￨- f￨L￨FW￨O￨- surface￨L￨NN￨O￨- properties￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- protein￨L￨NN￨O￨- adsorption￨L￨NN￨O￨- can￨L￨MD￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- architecture￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bio￨L￨NN￨O￨- film￨L￨NN￨O￨- that￨L￨WDT￨O￨- forms￨L￨VBZ￨O￨- on￨L￨IN￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- in-depth￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- o￨L￨NN￨O￨- f￨L￨FW￨O￨- the￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- of￨L￨IN￨O￨- protein￨L￨NN￨O￨- adsorption￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- biomaterial￨L￨JJ￨O￨- surface￨L￨NN￨O￨- is￨L￨VBZ￨O￨- crit￨L￨JJ￨O￨- ical￨L￨JJ￨O￨- for￨L￨IN￨O￨- developing￨L￨VBG￨O￨- and￨L￨CC￨O￨- designing￨L￨VBG￨O￨- suitable￨L￨JJ￨O￨- biomaterial￨L￨JJ￨O￨- surfaces￨L￨NNS￨O￨- to￨L￨TO￨O￨- deter￨L￨VB￨O￨- the￨L￨DT￨O￨- bio￨L￨NN￨O￨- film￨L￨NN￨O￨- format￨L￨NN￨O￨- ion￨L￨NN￨O￨A o￨L￨NN￨O￨- f￨L￨FW￨O￨- bacteria￨L￨NNS￨O￨- .￨L￨.￨O￨- +Knowledge￨U￨NN￨O￨- o￨L￨NN￨O￨- f￨L￨FW￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- protein￨L￨NN￨O￨- adsorption￨L￨NN￨O￨- on￨L￨IN￨O￨- implant￨L￨VB￨O￨- infect￨L￨VB￨O￨- ion￨L￨NN￨O￨A will￨L￨MD￨O￨- be￨L￨VB￨O￨- very￨L￨RB￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- chemistry￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- biomaterial￨L￨JJ￨O￨- surfaces￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- deter￨L￨VB￨O￨- the￨L￨DT￨O￨- format￨L￨NN￨O￨- ion￨L￨NN￨O￨- of￨L￨IN￨O￨- bio￨L￨NN￨O￨- films￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- considers￨L￨VBZ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A contact￨L￨NN￨O￨- network￨L￨NN￨O￨- —￨L￨:￨O￨- where￨L￨WRB￨O￨- one￨L￨CD￨NUMBER￨- knows￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- contacts￨L￨NNS￨O￨- happen￨L￨VB￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- between￨L￨IN￨O￨- whom￨L￨WP￨O￨- —￨L￨:￨O￨- then￨L￨RB￨O￨- larger￨L￨JJR￨O￨- R￨U￨NN￨O￨- ₀￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- imply￨L￨VB￨O￨- larger￨L￨JJR￨O￨- Ω￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- numerically￨L￨RB￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨A between￨L￨IN￨O￨- R￨U￨NN￨O￨- ₀￨L￨NN￨O￨- and￨L￨CC￨O￨- Ω￨U￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- descriptors￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- and￨L￨CC￨O￨- topological￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨A between￨L￨IN￨O￨- R￨U￨NN￨O￨- ₀￨L￨NN￨O￨- and￨L￨CC￨O￨- Ω￨U￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- traditional￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- common￨L￨JJ￨O￨- formulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- relationship￨L￨NN￨O￨A between￨L￨IN￨O￨- R￨U￨NN￨O￨- ₀￨L￨NN￨O￨- and￨L￨CC￨O￨- Ω￨U￨NN￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- 31￨L￨CD￨NUMBER￨- explanatory￨L￨JJ￨O￨- descriptors￨L￨NNS￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- those￨L￨DT￨O￨- that￨L￨WDT￨O￨- make￨L￨VBP￨O￨- R￨U￨NN￨O￨- ₀￨L￨CD￨NUMBER￨- an￨L￨DT￨O￨- imperfect￨L￨JJ￨O￨- predictor￨L￨NN￨O￨- of￨L￨IN￨O￨- Ω￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- genes￨L￨NNS￨O￨A responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- host-pathogen￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- paying￨L￨VBG￨O￨- particular￨L￨JJ￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- genes￨L￨NNS￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- sialylated￨L￨VBN￨O￨- glycans￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- endothelial￨L￨JJ￨O￨- membrane￨L￨NN￨O￨- ,￨L￨,￨O￨- mucus￨L￨NN￨O￨- ,￨L￨,￨O￨- genes￨L￨NNS￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- viral￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- escape￨L￨NN￨CRIMINAL_CHARGE￨- mechanisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- genes￨L￨NNS￨O￨- particularly￨L￨RB￨O￨- expressed￨L￨VBN￨O￨- after￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- outcome￨L￨NN￨O￨- .￨L￨.￨O￨- +Genomic￨U￨JJ￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- largely￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- remains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- sparsely￨L￨RB￨O￨- documented￨L￨VBN￨O￨- topic￨L￨NN￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- its￨L￨PRP$￨O￨- crucial￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Immunity￨U￨NN￨O￨- to￨L￨TO￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- research￨L￨NN￨O￨- topic￨L￨NN￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- 70￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- impact￨L￨NN￨O￨- the￨L￨DT￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- on￨L￨IN￨O￨- global￨L￨JJ￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- .￨L￨.￨O￨- +Genes￨U￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- virus￨L￨NN￨O￨- entry￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- cell￨L￨NN￨O￨- are￨L￨VBP￨O￨- responsible￨L￨JJ￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- production￨L￨NN￨O￨- and￨L￨CC￨O￨- assembly￨L￨NN￨O￨- of￨L￨IN￨O￨- Neu5Ac-α2￨U￨NN￨O￨- ,6-Galβ1￨L￨NN￨O￨- ,4-GlcNAc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- human￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Neu5ac-α2￨U￨NN￨O￨- ,3-Galβ1￨L￨NN￨O￨- ,4-GlcNAc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- avian￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- receptors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- membrane￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- liposome￨L￨NN￨O￨- encapsulated￨L￨VBD￨O￨- vancomycin￨L￨NN￨O￨- on￨L￨IN￨O￨- MRSA￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- evaluated￨L￨VBD￨O￨- the￨L￨DT￨O￨- antibacterial￨L￨JJ￨O￨- activity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- liposome-entrapped￨L￨JJ￨O￨- drug￨L￨NN￨O￨A in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- free￨L￨JJ￨O￨- drug￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- inhibitory￨L￨JJ￨O￨- concentration￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MIC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- drug￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- growth￨L￨NN￨O￨- response￨L￨NN￨O￨- of￨L￨IN￨O￨- MRSA￨U￨NNP￨ORGANIZATION￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- liposomal￨L￨JJ￨O￨- vancomycin￨L￨NN￨O￨- induced￨L￨VBD￨O￨- the￨L￨DT￨O￨- culture￨L￨NN￨O￨A to￨L￨TO￨O￨- go￨L￨VB￨O￨- into￨L￨IN￨O￨- bacteriostatic￨L￨JJ￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- phagocytic￨L￨JJ￨O￨- killing￨L￨NN￨O￨- was￨L￨VBD￨O￨- enhanced￨L￨VBN￨O￨- .￨L￨.￨O￨- +Emergence￨U￨NN￨O￨- of￨L￨IN￨O￨- Methicillin￨U￨NNP￨O￨- Resistant￨U￨JJ￨O￨- Staphylococcus￨U￨FW￨O￨- aureus￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- MRSA￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- necessitated￨L￨VBD￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- vancomycin￨L￨NN￨O￨- “￨L￨``￨O￨- the￨L￨DT￨O￨- drug￨L￨NN￨O￨A of￨L￨IN￨O￨- last￨L￨JJ￨O￨- resort￨L￨NN￨O￨- ”￨L￨''￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- these￨L￨DT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- MIC￨U￨NN￨O￨- for￨L￨IN￨O￨- liposomal￨L￨JJ￨O￨- vancomycin￨L￨NN￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- about￨L￨IN￨O￨- half￨L￨NN￨O￨A of￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- free￨L￨JJ￨O￨- vancomycin￨L￨NN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- minor￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- occurs￨L￨VBZ￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- different￨L￨JJ￨O￨- interpretation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨A approach￨L￨NN￨O￨- ,￨L￨,￨O￨- ma￨L￨FW￨O￨- jor￨L￨FW￨O￨- epidemic￨L￨JJ￨O￨- occurs￨L￨VBZ￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- predicts￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- settle￨L￨VB￨O￨- down￨L￨RP￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +Stochastic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- identify￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- minor￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- can￨L￨MD￨O￨- possibly￨L￨RB￨O￨- occur￨L￨VB￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- deterministic￨L￨JJ￨O￨A and￨L￨CC￨O￨- stochastiic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +IN￨U￨IN￨O￨- TRODUC￨U￨NN￨O￨- T￨U￨NN￨O￨- ION￨U￨NN￨O￨- in￨L￨IN￨O￨- process￨L￨NN￨O￨- sources￨L￨NNS￨O￨- external￨L￨JJ￨O￨A processes￨L￨NNS￨O￨- transition￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- SIS/SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- large￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- external￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- -￨L￨:￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- settings￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- information/infection￨L￨NN￨O￨- spreads￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- via￨L￨IN￨O￨- an￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- aided￨L￨VBN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- spread￨L￨VBN￨O￨- by￨L￨IN￨O￨- unconstrained￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS/SIR￨U￨NN￨MISC￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- is￨L￨VBZ￨O￨- aided￨L￨VBN￨O￨- by￨L￨IN￨O￨- external￨L￨JJ￨O￨A agents￨L￨NNS￨O￨- -￨L￨:￨O￨- sources￨L￨NNS￨O￨- unconstrained￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- possessing￨L￨VBG￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- or￨L￨CC￨O￨- virulence￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- any￨L￨DT￨O￨- external￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- strategy￨L￨NN￨O￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- virulence￨L￨NN￨O￨- either￨L￨CC￨O￨- fails￨L￨VBZ￨O￨- to￨L￨TO￨O￨- significantly￨L￨RB￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- lifetime￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- at￨L￨IN￨O￨- best￨L￨JJS￨O￨- ,￨L￨,￨O￨- sustains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- lifetime￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- polynomial￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- 1￨L￨CD￨DATE￨- 3￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- external￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- sources￨L￨NNS￨O￨- on￨L￨IN￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- fundamental￨L￨JJ￨O￨- standard￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- generalized￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- exactly￨L￨RB￨O￨- solvable￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- social￨L￨JJ￨O￨- or￨L￨CC￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- people￨L￨NNS￨O￨- are￨L￨VBP￨O￨- distinguished￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- play￨L￨VBP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- solutions￨L￨NNS￨O￨A provide￨L￨VBP￨O￨- exact￨L￨JJ￨O￨- criteria￨L￨NNS￨O￨- for￨L￨IN￨O￨- deciding￨L￨VBG￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- will￨L￨MD￨O￨- occur￨L￨VB￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- people￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- modi￨L￨JJ￨O￨- fied￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- simulation￨L￨NN￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- approximate￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- treatments￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- can￨L￨MD￨O￨- play￨L￨VB￨O￨A a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- defining￨L￨VBG￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- di￨L￨FW￨O￨- sease￨L￨FW￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Solutions￨U￨NNPS￨O￨- are￨L￨VBP￨O￨- possible￨L￨JJ￨O￨- for￨L￨IN￨O￨- cases￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- or￨L￨CC￨O￨- correlated￨L￨VBD￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- cases￨L￨NNS￨O￨- incorporating￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- complex￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- abandon￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- other￨L￨JJ￨O￨- unrealistic￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- usual￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- equal￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- catch￨L￨VBP￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- remain￨L￨VBP￨O￨- infective￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- such￨L￨JJ￨O￨- topologies￨L￨NNS￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- undergoes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- single￨L￨JJ￨O￨- contact￨L￨NN￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- exceed￨L￨VB￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- typically￨L￨RB￨O￨- show￨L￨VBP￨O￨- a￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- high￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- average￨L￨JJ￨O￨- pathlength￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Susceptible-Infected￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- geographical￨L￨JJ￨O￨A structure￨L￨NN￨O￨- has￨L￨VBZ￨O￨- great￨L￨JJ￨O￨- influences￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- network￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- geographically￨L￨RB￨O￨- constrained￨L￨VBN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- smoothly￨L￨RB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- clearly￨L￨RB￨O￨- hierarchical￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pervades￨L￨VBZ￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- progressive￨L￨JJ￨IDEOLOGY￨- cascade￨L￨NN￨O￨- across￨L￨IN￨O￨- smaller-degree￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- in￨L￨IN￨O￨- Barab￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- asi-Albert￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Key￨U￨NN￨O￨- words￨L￨NNS￨O￨- :￨L￨:￨O￨- Epidemic￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- ;￨L￨:￨O￨- geographical￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ;￨L￨:￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- classical￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- either￨L￨CC￨O￨- ignores￨L￨VBZ￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- or￨L￨CC￨O￨- treats￨L￨VBZ￨O￨- populations￨L￨NNS￨O￨- as￨L￨IN￨O￨- distributed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- regular￨L￨JJ￨O￨- medium￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- wide￨L￨JJ￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- nature￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨A of￨L￨IN￨O￨- topological￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- geographical￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- lattice-embedded￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Preprint￨U￨NNP￨O￨- submitted￨L￨VBD￨O￨- to￨L￨TO￨O￨- Elsevier￨U￨NNP￨ORGANIZATION￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- nodes￨L￨NNS￨O￨- represent￨L￨VBP￨O￨A individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- them￨L￨PRP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Size￨U￨NN￨O￨- of￨L￨IN￨O￨- Outbreaks￨U￨NNP￨O￨- Near￨U￨IN￨O￨- the￨L￨DT￨O￨- Epidemic￨U￨JJ￨O￨- Threshold￨U￨NNP￨O￨- E.￨U￨NNP￨O￨- Scaling￨U￨NNP￨O￨- laws￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- originating￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- main￨L￨JJ￨O￨- result￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- near￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- n￨L￨NN￨O￨- ∗￨L￨NN￨O￨- grows￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- power-law￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- ∗￨L￨CD￨NUMBER￨- ∼￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- 2/3￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- scaling￨L￨NN￨O￨- law￨L￨NN￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨A size￨L￨NN￨O￨A hni￨L￨NN￨O￨- scales￨L￨NNS￨O￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- 1/3￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- maximal￨L￨JJ￨O￨A size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- n￨L￨NN￨O￨- ∗￨L￨VBG￨O￨- scales￨L￨NNS￨O￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- 2/3￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- N￨U￨NN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- numerically￨L￨RB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- extra-mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- periodicities￨L￨NNS￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- age-structure￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- variable￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- multigroup￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- emphasised￨L￨VBN￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨A equilibria￨L￨NNS￨O￨A are￨L￨VBP￨O￨- possible￨L￨JJ￨O￨- .￨L￨.￨O￨- +Concerning￨U￨VBG￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨A equilibria￨L￨NNS￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- without￨L￨IN￨O￨- age￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- see￨L￨VBP￨O￨- also￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- bibliography￨L￨NN￨O￨- therein￨L￨RB￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- β￨L￨NN￨O￨- normalised￨L￨VBD￨O￨- to￨L￨TO￨O￨- ∂￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- ∂￨L￨NN￨O￨- N￨U￨NN￨O￨- ∂￨L￨VBD￨O￨- a￨L￨DT￨O￨- +￨L￨CC￨O￨- µ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0Φ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- Z￨U￨NN￨O￨- a￨L￨DT￨O￨- †￨L￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- Rd￨U￨NN￨O￨- In￨U￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- µ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- vital￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- satisfy￨L￨VBP￨O￨- where￨L￨WRB￨O￨- Z￨U￨NN￨O￨- a￨L￨DT￨O￨- †￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- π￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dσ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- π￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- R￨U￨NN￨O￨- a￨L￨DT￨O￨- 0￨L￨CD￨NUMBER￨- µ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dσ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- survival￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- Rd￨U￨NN￨O￨- is￨L￨VBZ￨O￨- 0￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- at￨L￨IN￨O￨- birth￨L￨NN￨O￨- of￨L￨IN￨O￨- surviving￨L￨VBG￨O￨- to￨L￨TO￨O￨- age￨L￨NN￨O￨A a￨L￨DT￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- point￨L￨VBP￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- made￨L￨VBN￨O￨- ,￨L￨,￨O￨- equation￨L￨NN￨O￨- Rd￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Φ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Qd￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- solution￨L￨NN￨O￨- Q￨U￨NNP￨O￨- ∗￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- non￨L￨JJ￨O￨- trivial￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- ∗￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- Q￨U￨NNP￨O￨- ∗￨L￨CD￨NUMBER￨- dπ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- π￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dσ￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- a￨L￨DT￨O￨- †￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Measuring￨U￨VBG￨O￨- node￨L￨NN￨O￨- spreading￨L￨NN￨O￨- power￨L￨NN￨O￨- by￨L￨IN￨O￨- expected￨L￨VBN￨O￨- cluster￨L￨NN￨O￨- degree￨L￨NN￨O￨- Glenn￨U￨NNP￨PERSON￨- Lawyer￨U￨NNP￨TITLE￨- ∗￨L￨NNP￨O￨- Max￨U￨NNP￨ORGANIZATION￨- Planck￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Informatics￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- November￨U￨NNP￨DATE￨- 7￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Traditional￨U￨JJ￨O￨- metrics￨L￨NNS￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- influence￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- degree￨L￨NN￨O￨- or￨L￨CC￨O￨- betweenness￨L￨NN￨O￨- identify￨L￨VBP￨O￨- highly￨L￨RB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- are￨L￨VBP￨O￨- rarely￨L￨RB￨O￨- usefully￨L￨RB￨O￨- accurate￨L￨JJ￨O￨- in￨L￨IN￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- current￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- proposes￨L￨VBZ￨O￨- instead￨L￨RB￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected-susceptible￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- measure￨L￨NN￨O￨- predicts￨L￨VBZ￨O￨- spreading￨L￨VBG￨O￨- power￨L￨NN￨O￨A in￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- competitive￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- simulated￨L￨JJ￨O￨- on￨L￨IN￨O￨- large￨L￨JJ￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Early￨U￨RB￨O￨- metrics￨L￨NNS￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- influence￨L￨NN￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- highly￨L￨RB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- macroscopic￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- degree￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- k-shell￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- centrality￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Worryingly￨U￨RB￨O￨- ,￨L￨,￨O￨- structural￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- centrality￨L￨NN￨O￨- may￨L￨MD￨O￨- considerably￨L￨RB￨O￨- underestimate￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- power￨L￨NN￨O￨A of￨L￨IN￨O￨- non-hub￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- rank￨L￨VB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- without￨L￨IN￨O￨- quantifying￨L￨VBG￨O￨A the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- 1￨L￨CD￨DATE￨- 2￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- More￨U￨RBR￨O￨- recently￨L￨RB￨DATE￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- realism￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- contact￨L￨VB￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- were￨L￨VBD￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- exhibit￨L￨VB￨O￨- several￨L￨JJ￨O￨- interesting￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- strong￨L￨JJ￨O￨- constructive￨L￨JJ￨O￨- synergy￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- local￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- bond￨L￨NN￨O￨- rewiring￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- negative￨L￨JJ￨O￨- role￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- it￨L￨PRP￨O￨- reduces￨L￨VBZ￨O￨- invasion￨L￨NN￨O￨- probability￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- destructive￨L￨JJ￨O￨- or￨L￨CC￨O￨- weak￨L￨JJ￨O￨- constructive￨L￨JJ￨O￨- synergy￨L￨NN￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- local￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- rewiring￨L￨VBG￨O￨- helps￨L￨VBZ￨O￨- epidemics￨L￨NNS￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- finally￨L￨RB￨O￨- ,￨L￨,￨O￨- rewiring￨L￨VBG￨O￨- always￨L￨RB￨O￨- enhances￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- synergy￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- connectivity￨L￨NN￨O￨A effects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- by￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- with￨L￨IN￨O￨- lattices￨L￨NNS￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- local￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- with￨L￨IN￨O￨- networks￨L￨NNS￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- both￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- random￨L￨JJ￨O￨- bond-rewiring￨L￨NN￨O￨- to￨L￨TO￨O￨- nodes￨L￨NNS￨O￨- within￨L￨IN￨O￨- certain￨L￨JJ￨O￨- distance￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- particular￨L￨JJ￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- cooperative￨L￨JJ￨O￨- effects￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- called￨L￨VBN￨O￨- synergy￨L￨NN￨O￨- effects￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- neighbours￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- life-time￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- can￨L￨MD￨O￨- depend￨L￨VB￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- donor-recipient￨L￨JJ￨O￨- pair￨L￨NN￨O￨A but￨L￨CC￨O￨- also￨L￨RB￨O￨- on￨L￨IN￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Taraskin￨U￨NNP￨O￨- Epidemics￨U￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- cooperation￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- connectivity￨L￨NN￨O￨A between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- ID￨U￨NNP￨STATE_OR_PROVINCE￨- 136263:9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2014￨L￨CD￨DATE￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- prevention￨L￨NN￨O￨A of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Pastor-Satorras￨U￨NNP￨O￨- :￨L￨:￨O￨- Numerical￨U￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- percolation￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- critical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- position￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A point￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- infinite￨L￨JJ￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- limit￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- associated￨L￨VBN￨O￨- critical￨L￨JJ￨O￨- exponents￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- finite-size￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FSS￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- theory￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- computational￨L￨JJ￨O￨- efforts￨L￨NNS￨O￨- devoted￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- position￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A point￨L￨NN￨O￨A in￨L￨IN￨O￨- either￨L￨CC￨O￨- SIR￨U￨NN￨O￨- or￨L￨CC￨O￨- percolation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- rely￨L￨VBP￨O￨- on￨L￨IN￨O￨- some￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- “￨L￨``￨O￨- susceptibility￨L￨NN￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- moments￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cluster￨L￨NN￨O￨- or￨L￨CC￨O￨- outbreak￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- approaches￨L￨NNS￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- degree￨L￨NN￨O￨- un-is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- k￨L￨NN￨O￨- and￨L￨CC￨O￨- correlated￨L￨VBD￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- important￨L￨JJ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- percolation￨L￨NN￨O￨A and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- omission￨L￨NN￨O￨- of￨L￨IN￨O￨- topological￨L￨JJ￨O￨- and￨L￨CC￨O￨- dynamical￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- numerically￨L￨RB￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A point￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- associated￨L￨VBN￨O￨- critical￨L￨JJ￨O￨- exponents￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- usually￨L￨RB￨O￨- studies￨L￨NNS￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- mean￨L￨NN￨O￨- cluster￨L￨NN￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- χ￨L￨NN￨O￨- =￨L￨JJ￨O￨- s￨L￨NNS￨O￨- s￨L￨NNS￨O￨- sns￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- s￨L￨VBZ￨O￨- s￨L￨NNS￨O￨- ns￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Sec.￨U￨NNP￨DATE￨- 3￨L￨CD￨DATE￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- different￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- detectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- criticality￨L￨NN￨O￨- for￨L￨IN￨O￨- percolation￨L￨NN￨O￨A processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- determine￨L￨VBP￨O￨- analytically￨L￨RB￨O￨- and￨L￨CC￨O￨- verify￨L￨VB￨O￨- numerically￨L￨RB￨O￨- which￨L￨WDT￨O￨- one￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- suitable￨L￨JJ￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- configurations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- entirely￨L￨RB￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- occupation￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- calls￨L￨VBZ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- representation￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- second-quantized￨L￨JJ￨O￨- bosonic￨L￨JJ￨O￨- operators￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- introduce￨L￨VB￨O￨- creation￨L￨NN￨O￨- and￨L￨CC￨O￨- annihilation￨L￨NN￨O￨- operators￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- normal￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- h￨L￨NN￨O￨- †￨L￨NN￨O￨- and￨L￨CC￨O￨- h￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- relations￨L￨NNS￨O￨- c￨L￨NN￨O￨- †￨L￨NN￨O￨- and￨L￨CC￨O￨- c.￨L￨NN￨O￨- Transition￨U￨NN￨O￨- Description￨U￨NN￨O￨- Contribution￨U￨NN￨O￨- to￨L￨TO￨O￨- H￨U￨NN￨O￨- N￨U￨NN￨O￨- bh￨L￨VBP￨O￨- −￨L￨SYM￨O￨- →￨L￨SYM￨O￨- N￨U￨NN￨O￨- +￨L￨CC￨O￨- N￨U￨NN￨O￨- birth￨L￨NN￨O￨- of￨L￨IN￨O￨- normal￨L￨JJ￨O￨- cell￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- bh￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- C￨U￨NN￨O￨- bc￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- →￨L￨NN￨O￨- C￨U￨NN￨O￨- +￨L￨CC￨O￨- C￨U￨NN￨O￨- N￨U￨NN￨O￨- dh￨L￨VBP￨O￨- −￨L￨SYM￨O￨- →￨L￨SYM￨O￨- ∅￨L￨SYM￨O￨- C￨U￨$￨O￨- dc￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- →￨L￨SYM￨O￨- ∅￨L￨SYM￨O￨- N￨U￨NN￨O￨- λ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- →￨L￨NN￨O￨- C￨U￨NN￨O￨- birth￨L￨NN￨O￨- of￨L￨IN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- cell￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- bc￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- bh￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- bh￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- †￨L￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- bc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- −￨L￨NN￨O￨- c￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- †￨L￨NN￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- bc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- †￨L￨NN￨O￨- m￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dh￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- dh￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- −￨L￨NN￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- dc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- death￨L￨NN￨O￨- of￨L￨IN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- cell￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- dc￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- change￨L￨NN￨O￨- normal￨L￨JJ￨O￨- →￨L￨NN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- −￨L￨NN￨O￨- c￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- death￨L￨NN￨O￨- of￨L￨IN￨O￨- normal￨L￨JJ￨O￨- cell￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- dh￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- As￨U￨IN￨O￨- usual￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- quantization￨L￨NN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- say￨L￨VBP￨O￨- that￨L￨IN￨O￨- h￨L￨NN￨O￨- †￨L￨NN￨O￨- and￨L￨CC￨O￨- c￨L￨NN￨O￨- †￨L￨CD￨NUMBER￨- “￨L￨``￨O￨- create￨L￨VB￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- build￨L￨VB￨O￨- our￨L￨PRP$￨O￨- space￨L￨NN￨O￨- from￨L￨IN￨O￨- basis￨L￨NN￨O￨- vectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- |￨L￨NN￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- =￨L￨JJ￨O￨- h￨L￨NN￨O￨- †￨L￨NN￨O￨- n￨L￨NN￨O￨- c￨L￨NN￨O￨- †￨L￨NN￨O￨- m￨L￨NN￨O￨- |￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- employ￨L￨VBP￨O￨- the￨L￨DT￨O￨- very￨L￨RB￨O￨- same￨L￨JJ￨O￨- methodology￨L￨NN￨O￨- established￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- field-theory￨L￨JJ￨O￨- inspired￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- tumour￨L￨NN￨O￨- growth￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- analogy￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- SI￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- would￨L￨MD￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A cells￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- interacting￨L￨VBG￨O￨- populations￨L￨NNS￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- normal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- healthy￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A cells￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Leslie-Gower￨U￨NNP￨PERSON￨- Holling￨U￨NNP￨PERSON￨- type￨L￨NN￨O￨- III￨U￨CD￨NUMBER￨- predator-prey￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- predator￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- biological￨L￨JJ￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- LG￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Holling￨U￨JJ￨PERSON￨- type￨L￨NN￨O￨- II￨U￨CD￨NUMBER￨- response￨L￨NN￨O￨- function￨L￨NN￨O￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- predator￨L￨NN￨O￨A is￨L￨VBZ￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- get￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- non￨L￨JJ￨O￨- negative￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- dx￨L￨VBP￨O￨- dt￨L￨NN￨O￨A =￨L￨JJ￨O￨- a1x￨L￨NN￨O￨- −￨L￨NN￨O￨- b1x2￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- c1x2￨L￨NN￨O￨- y￨L￨NN￨O￨- k1￨L￨NN￨O￨- +￨L￨CC￨O￨- x2￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- pc1x2￨L￨NN￨O￨- z￨L￨SYM￨O￨- k1￨L￨NN￨O￨- +￨L￨CC￨O￨- x2￨L￨NN￨O￨- =￨L￨JJ￨O￨- f1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- dy￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- a2y￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- c2y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- +￨L￨CC￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- k2￨L￨NN￨O￨- +￨L￨CC￨O￨- x￨L￨CC￨O￨- −￨L￨SYM￨O￨- θyz￨L￨NN￨O￨- =￨L￨JJ￨O￨- f2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dz￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- θyz￨L￨NN￨O￨- +￨L￨CC￨O￨- a3￨L￨NN￨O￨- z￨L￨SYM￨O￨- −￨L￨SYM￨O￨- c3￨L￨NN￨O￨- z￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- +￨L￨CC￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- k2￨L￨NN￨O￨- +￨L￨CC￨O￨- x￨L￨NN￨O￨- =￨L￨JJ￨O￨- f3￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- z￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a2￨L￨NN￨O￨- ,￨L￨,￨O￨- a3￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a2￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- a3￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- the￨L￨DT￨O￨- Jacobian￨U￨JJ￨MISC￨- matrix￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- J￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- mij￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- R3￨U￨NN￨O￨- ×￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- entries￨L￨NNS￨O￨- m11￨L￨NN￨O￨- =￨L￨JJ￨O￨- a1￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- 2b1x￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- 2c1￨L￨NN￨O￨- xy￨L￨NN￨O￨- m21￨L￨NN￨O￨- =￨L￨JJ￨O￨- c2￨L￨NN￨O￨- y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- +￨L￨CC￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- x2￨L￨NN￨O￨- +￨L￨CC￨O￨- k1￨L￨NN￨O￨- +￨L￨CC￨O￨- 2c1￨L￨NN￨O￨- x3￨L￨NN￨O￨- y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x2￨L￨NN￨O￨- +￨L￨CC￨O￨- k1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- 2pc1￨L￨NN￨O￨- xz￨L￨NN￨O￨- x2￨L￨NN￨O￨- +￨L￨CC￨O￨- k1￨L￨NN￨O￨- +￨L￨CC￨O￨- 2pc1￨L￨NN￨O￨- x3￨L￨NN￨O￨- z￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- x2￨L￨NN￨O￨- +￨L￨CC￨O￨- k1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- m12￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- c1￨L￨NN￨O￨- x2￨L￨NN￨O￨- m22￨L￨NN￨O￨- =￨L￨JJ￨O￨- a2￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- c2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2y￨L￨NN￨O￨- +￨L￨CC￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- m23￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- c2￨L￨NN￨O￨- y￨L￨NN￨O￨- m33￨L￨NN￨O￨- =￨L￨JJ￨O￨- θy￨L￨NN￨O￨- +￨L￨CC￨O￨- a3￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- c3￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- +2￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- x2￨L￨NN￨O￨- +￨L￨CC￨O￨- k1￨L￨NN￨O￨- ,￨L￨,￨O￨- m13￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- pc1￨L￨NN￨O￨- x2￨L￨NN￨O￨- x2￨L￨NN￨O￨- +￨L￨CC￨O￨- k1￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- k2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- x￨L￨CC￨O￨- +￨L￨CC￨O￨- k2￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- θz￨L￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- k2￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- θy￨L￨NN￨O￨- ,￨L￨,￨O￨- m31￨L￨NN￨O￨- =￨L￨JJ￨O￨- c3￨L￨NN￨O￨- z￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- +￨L￨CC￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- k2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- m32￨L￨NN￨O￨- =￨L￨JJ￨O￨- θz￨L￨NN￨O￨- −￨L￨NN￨O￨- c3￨L￨NN￨O￨- z￨L￨SYM￨O￨- x￨L￨CC￨O￨- +￨L￨CC￨O￨- k2￨L￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- k2￨L￨NN￨O￨- .￨L￨.￨O￨- +Unlike￨U￨IN￨O￨- existing￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- proposed￨L￨VBN￨O￨- algorithm￨L￨NN￨O￨- identifies￨L￨NNS￨O￨- as￨L￨IN￨O￨- sources￨L￨NNS￨O￨A those￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- when￨L￨WRB￨O￨- set￨L￨VBN￨O￨- as￨L￨IN￨O￨- sources￨L￨NNS￨O￨- ,￨L￨,￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- smallest￨L￨JJS￨O￨- dominant￨L￨JJ￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- reduced￨L￨VBN￨O￨- non-backtracking￨L￨JJ￨O￨- matrix￨L￨NN￨O￨- deduced￨L￨VBN￨O￨- from￨L￨IN￨O￨- message￨L￨NN￨O￨- passing￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Index￨U￨NNP￨O￨- Terms￨U￨NNS￨O￨- —￨L￨:￨O￨- Dominant￨U￨JJ￨O￨- eigenvalue￨L￨NN￨O￨- ,￨L￨,￨O￨- message￨L￨NN￨O￨- passing￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- multiple￨L￨JJ￨O￨- rumor￨L￨NN￨O￨A sources￨L￨NNS￨O￨- ,￨L￨,￨O￨- nonbacktracking￨L￨JJ￨O￨- matrix￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptible-infected￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- works￨L￨NNS￨O￨- have￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- rumor￨L￨NN￨O￨A sources￨L￨NNS￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- snapshot￨L￨NN￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 8￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- ABSTRACT￨U￨NN￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- rumor￨L￨NN￨O￨A sources￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- obeys￨L￨VBZ￨O￨- a￨L￨DT￨O￨- time-slotted￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Key￨U￨NN￨O￨- words￨L￨NNS￨O￨- :￨L￨:￨O￨- Epidemic￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- Basic￨U￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ;￨L￨:￨O￨- Pulse￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- ;￨L￨:￨O￨- Uniform￨U￨NNP￨O￨- Persistence￨U￨NNP￨O￨- ;￨L￨:￨O￨- Globally￨U￨RB￨O￨- stability￨L￨NN￨O￨- ;￨L￨:￨O￨- Infection-free￨U￨JJ￨O￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨A ;￨L￨:￨O￨- Positive￨U￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- .￨L￨.￨O￨- +Pulse￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- periodic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- Zhen￨U￨NNP￨PERSON￨- Jin￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ∗￨L￨CD￨NUMBER￨- Mainul￨U￨NNP￨O￨- Haque￨U￨NNP￨O￨- ,2￨L￨NN￨O￨- ,￨L￨,￨O￨- †￨L￨NN￨O￨- and￨L￨CC￨O￨- Quanxing￨U￨VBG￨O￨- Liu1￨U￨NN￨O￨- ,￨L￨,￨O￨- ‡￨L￨SYM￨O￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematics￨L￨NNS￨O￨- ,￨L￨,￨O￨- North￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Taiyuan￨U￨NNP￨CITY￨- 030051￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P.￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- September￨U￨NNP￨DATE￨- 26￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- pulse￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection-free￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨A is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- provided￨L￨VBN￨O￨- R0￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Standard￨U￨NNP￨O￨- bifurcation￨L￨NN￨O￨- theory￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- →￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- Epidemic￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨A in￨L￨IN￨O￨- weighted￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- 4￨L￨CD￨NUMBER￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- healthy￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- immunized￨L￨VBN￨O￨- or￨L￨CC￨O￨- dead￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +And￨U￨CC￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- sensitive￨L￨JJ￨O￨- than￨L￨IN￨O￨- β￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transformation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- factor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- infectivity￨L￨NN￨O￨- exponent￨L￨NN￨O￨A α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- take￨L￨VBP￨O￨- more￨L￨JJR￨O￨- responsibility￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- extrinsic￨L￨JJ￨O￨- factor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨- exponent￨L￨NN￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- the￨L￨DT￨O￨- modified￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- infectivity￨L￨NN￨O￨- exponent￨L￨NN￨O￨A α￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨- exponent￨L￨NN￨O￨- β￨L￨NN￨O￨- are￨L￨VBP￨O￨- added￨L￨VBN￨O￨- ;￨L￨:￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- modified￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- for￨L￨IN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- weighted￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- analytical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- weighted￨L￨VBN￨O￨- .￨L￨.￨O￨- +Concretely￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- infectivity￨L￨NN￨O￨- exponent￨L￨NN￨O￨A α￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨- exponent￨L￨NN￨O￨- β￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- combination￨L￨NN￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- α￨L￨NN￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- and￨L￨CC￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theorem￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- VPM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- all￨L￨DT￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- standard￨L￨JJ￨O￨- literature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- say￨L￨VB￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- contact￨L￨NN￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- answer￨L￨NN￨O￨- always￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- matrix￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- we￨L￨PRP￨O￨- cover￨L￨VBP￨O￨- all￨L￨DT￨O￨- models￨L￨NNS￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- survey￨L￨NN￨O￨- by￨L￨IN￨O￨- Hethcote￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- models￨L￨NNS￨O￨- like￨L￨IN￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- no￨L￨DT￨O￨- immunity￨L￨NN￨O￨A ,￨L￨,￨O￨- like￨L￨IN￨O￨- flu￨L￨SYM￨O￨- -￨L￨:￨O￨- ‘￨L￨``￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ’￨L￨''￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- life-time￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- :￨L￨:￨O￨- ‘￨L￨``￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- ’￨L￨''￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- irrespective￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- topology￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- captured￨L￨VBN￨O￨- by￨L￨IN￨O￨- just￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- parameter￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- eigenvalue￨L￨NN￨O￨- λ1￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- A￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- include￨L￨VBP￨O￨- numerous￨L￨JJ￨O￨- other￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- like￨L￨IN￨O￨- SIRS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- temporary￨L￨JJ￨O￨A immunity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- useful￨L￨JJ￨O￨- generalizations￨L￨NNS￨O￨- SIV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- vigilance/vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- SEIV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- vigilance/vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- virus￨L￨NN￨O￨- incubation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- many￨L￨JJ￨O￨- more￨L￨JJR￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- question￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- ;￨L￨:￨O￨- intuitively￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- answer￨L￨NN￨O￨- should￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- connectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- VPM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Feedback￨U￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- bifurcation￨L￨NN￨O￨- analysis￨L￨NN￨O￨A of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- of￨L￨IN￨O￨- stochasticity￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinearity￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- has￨L￨VBZ￨O￨- provided￨L￨VBN￨O￨- substantial￨L￨JJ￨O￨- insight￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- conduct￨L￨VB￨O￨- inference￨L￨NN￨O￨- with￨L￨IN￨O￨- models￨L￨NNS￨O￨- defined￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- these￨L￨DT￨O￨- results￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- classical￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨A study￨L￨NN￨O￨A .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- analysis￨L￨NN￨O￨A perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- varying￨L￨VBG￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- formality￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- attempted￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- variants￨L￨NNS￨O￨- are￨L￨VBP￨O￨- ubiquitous￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- plants￨L￨NNS￨O￨A and￨L￨CC￨O￨- animals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨A study￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- give￨L￨VBP￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- tail￨L￨NN￨O￨- approximation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- subcritical￨L￨JJ￨O￨- multitype￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- with￨L￨IN￨O￨- given￨L￨VBN￨O￨- degrees￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨A corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- vertex￨L￨NN￨O￨- degree￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- new￨L￨JJ￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- type￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- spores￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- J￨U￨NN￨O￨- say￨L￨VBP￨O￨- ,￨L￨,￨O￨- chosen￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- given￨L￨VBN￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- pj￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∞￨L￨CD￨NUMBER￨- j￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- immunization￨L￨NN￨O￨A strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- that￨L￨IN￨O￨- uses￨L￨VBZ￨O￨- only￨L￨RB￨O￨- local￨L￨JJ￨O￨- information￨L￨NN￨O￨- available￨L￨JJ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- viz.￨L￨NN￨O￨- Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- find￨L￨VB￨O￨- out￨L￨RP￨O￨- most￨L￨RBS￨O￨- central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- immunize￨L￨VB￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- controlled￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- degree￨L￨NN￨O￨- centrality￨L￨NN￨O￨- based￨L￨VBN￨O￨- immunization￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- highest￨L￨JJS￨O￨- degree￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- immunized￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- controlled￨L￨VBN￨O￨A by￨L￨IN￨O￨- removing￨L￨VBG￨O￨- central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Immunization￨U￨NN￨O￨- of￨L￨IN￨O￨- central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨A may￨L￨MD￨O￨- keep￨L￨VB￨O￨- more￨L￨RBR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- away￨L￨RB￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- downlink￨L￨NN￨O￨- cellular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- base￨L￨NN￨O￨- stations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- BSs￨U￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- deployed￨L￨VBN￨O￨A according￨L￨VBG￨O￨- to￨L￨TO￨O￨- spatial￨L￨JJ￨O￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Euclidian￨U￨NNP￨MISC￨- plane￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- single-tier￨L￨JJ￨O￨- downlink￨L￨NN￨O￨- cellular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- base￨L￨NN￨O￨- stations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- deployed￨L￨VBN￨O￨A according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- stationary￨L￨JJ￨O￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Euclidean￨U￨JJ￨MISC￨- plane￨L￨NN￨O￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- i.i.d.￨L￨NN￨O￨- propagation￨L￨NN￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- tail￨L￨NN￨O￨- asymptotics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- single-tier￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- BSs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- deployed￨L￨VBN￨O￨A according￨L￨VBG￨O￨- to￨L￨TO￨O￨- general￨L￨JJ￨TITLE￨- stationary￨L￨JJ￨O￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- propagation￨L￨NN￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- S￨U￨NN￨O￨- IR￨U￨NN￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- cellular￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- provided￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- closed-form￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- numerically￨L￨RB￨O￨- computable￨L￨JJ￨O￨- form￨L￨NN￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- restricted￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- BSs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- deployed￨L￨VBN￨O￨A according￨L￨VBG￨O￨- to￨L￨TO￨O￨- homogeneous￨L￨JJ￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- or￨L￨CC￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- determinantal￨L￨JJ￨O￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- with￨L￨IN￨O￨- specific￨L￨NN￨O￨- propagation￨L￨NN￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- fad￨L￨NN￨O￨- ing￨L￨NN￨O￨- and￨L￨CC￨O￨- shadowing￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- BS￨U￨NN￨O￨- deployments￨L￨NNS￨O￨- and￨L￨CC￨O￨- propagation￨L￨NN￨O￨- effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- approximation￨L￨NN￨O￨- and/or￨L￨CC￨O￨- asymptotic￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- cope￨L￨VB￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- general￨L￨JJ￨TITLE￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- common￨L￨JJ￨O￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- enough￨L￨JJ￨O￨- measured￨L￨VBN￨O￨- variables￨L￨NNS￨O￨A ,￨L￨,￨O￨- so￨L￨IN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- f￨L￨FW￨O￨- itting￨L￨FW￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spreaders￨L￨NNS￨O￨- curve￨L￨NN￨O￨- by￨L￨IN￨O￨- selecting￨L￨VBG￨O￨- estimated￨L￨VBN￨O￨- variables￨L￨NNS￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +proposed￨L￨VBN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- concluded￨L￨VBN￨O￨- that￨L￨IN￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- users￨L￨NNS￨O￨- use￨L￨VBP￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- only￨L￨RB￨O￨- those￨L￨DT￨O￨- rumors￨L￨NNS￨O￨A which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- favorite￨L￨JJ￨O￨- category￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- science￨L￨NN￨O￨- or￨L￨CC￨O￨- conspiracy￨L￨NN￨CRIMINAL_CHARGE￨- theories￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- functionally￨L￨RB￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- RBF￨U￨NN￨ORGANIZATION￨- network￨L￨NN￨O￨- under￨L￨IN￨O￨- certain￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- unlike￨L￨IN￨O￨A the￨L￨DT￨O￨- RBF￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- ANFIS￨U￨NNP￨ORGANIZATION￨- allows￨L￨VBZ￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- qualitative￨L￨JJ￨O￨- research￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- close￨L￨JJ￨O￨- relations￨L￨NNS￨O￨- to￨L￨TO￨O￨- fuzzy￨L￨JJ￨O￨- logic￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- fuzzy￨L￨JJ￨O￨- logic￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Takagi-Sugeno￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- arises￨L￨VBZ￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- effort￨L￨NN￨O￨- for￨L￨IN￨O￨- systematically￨L￨RB￨O￨A generating￨L￨VBG￨O￨- linguistic￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- input-output￨L￨JJ￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Fuzzy￨U￨JJ￨O￨- logic￨L￨NN￨O￨- ;￨L￨:￨O￨- ANFIS￨U￨NNP￨O￨- ;￨L￨:￨O￨- Rumor￨U￨NN￨O￨- propagation￨L￨NN￨O￨- ;￨L￨:￨O￨- Epidemiology￨U￨NNP￨O￨- ;￨L￨:￨O￨- Deterministic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- Trend-ing￨U￨JJ￨O￨- topics￨L￨NNS￨O￨A .￨L￨.￨O￨- +Three￨U￨CD￨NUMBER￨- dynamical￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- are￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- for￨L￨IN￨O￨- small￨L￨JJ￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A ,￨L￨,￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- oscillatory￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- duration￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- a￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- synchronization￨L￨NN￨O￨- that￨L￨WDT￨O￨- invariably￨L￨RB￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- dynamical￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- numerical￨L￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- synchronization￨L￨NN￨O￨A and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- done￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- and￨L￨CC￨O￨- refractory￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- regime￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- one-and￨L￨JJ￨O￨- two-dimensional￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- probability￨L￨NN￨O￨- decays￨L￨VBZ￨O￨- as￨L￨IN￨O￨- r￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- α￨L￨NN￨O￨- with￨L￨IN￨O￨- distance￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- different￨L￨JJ￨O￨- mechanism￨L￨NN￨O￨- for￨L￨IN￨O￨- activity￨L￨NN￨O￨- extinction￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- through￨L￨IN￨O￨- extreme￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- display￨L￨VBP￨O￨- such￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +Dynamical￨U￨JJ￨O￨- extinction￨L￨NN￨O￨A is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- still￨L￨RB￨O￨- preceded￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- third￨L￨JJ￨ORDINAL￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- rapidly￨L￨RB￨O￨- intensifying￨L￨VBG￨O￨- synchronized￨L￨VBN￨O￨- oscillations￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- large￨L￨JJ￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- stage￨L￨NN￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- synchronized￨L￨VBN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- is￨L￨VBZ￨O￨- instead￨L￨RB￨O￨- a￨L￨DT￨O￨- long-lasting￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- incoherent￨L￨JJ￨O￨- activity￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmissibility￨L￨NN￨O￨A Tuv￨U￨NN￨PERSON￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- u￨L￨NN￨O￨- would￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- direct￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- neighbor￨L￨NN￨O￨- v￨L￨LS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- theoretically￨L￨RB￨O￨- analyze￨L￨VBP￨O￨- these￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- timescales￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- dependence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- community￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- inter-community￨L￨JJ￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- good￨L￨JJ￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- overlaps￨L￨VBZ￨O￨- between￨L￨IN￨O￨- successive￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- too￨L￨RB￨O￨- large￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- RB￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- RA￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- RNet￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- hereinafter￨L￨NN￨O￨- ,￨L￨,￨O￨- RNet￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- and￨L￨CC￨O￨- persist￨L￨VB￨O￨- within￨L￨IN￨O￨- community￨L￨NN￨O￨A B￨U￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- in￨L￨IN￨O￨- community￨L￨NN￨O￨- A￨U￨NN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- might￨L￨MD￨O￨- experience￨L￨VB￨O￨- alternately￨L￨RB￨O￨- Temporal￨U￨JJ￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- community￨L￨NN￨O￨- networks￨L￨NNS￨O￨- 6￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 20000￨L￨CD￨NUMBER￨- 40000￨L￨CD￨NUMBER￨- 60000￨L￨CD￨NUMBER￨- 80000￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 100000￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 4￨L￨CD￨DATE￨- 8￨L￨CD￨DATE￨- 12￨L￨CD￨DATE￨- 16￨L￨CD￨DATE￨- 20￨L￨CD￨DATE￨- t￨L￨NN￨O￨- in￨L￨IN￨O￨- community￨L￨NN￨O￨- A￨U￨NN￨O￨- in￨L￨IN￨O￨- community￨L￨NN￨O￨- B￨U￨NN￨O￨- N￨U￨NN￨O￨- u￨L￨NN￨O￨- m￨L￨NN￨O￨- e￨L￨SYM￨O￨- b￨L￨NN￨O￨- r￨L￨NN￨O￨- o￨L￨NN￨O￨- f￨L￨FW￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- f￨L￨FW￨O￨- e￨L￨SYM￨O￨- c￨L￨NN￨O￨- t￨L￨NN￨O￨- d￨L￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- 20￨L￨CD￨NUMBER￨- 40￨L￨CD￨NUMBER￨- 60￨L￨CD￨NUMBER￨- 80￨L￨CD￨NUMBER￨- 100￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- u￨L￨NN￨O￨- m￨L￨NN￨O￨- b￨L￨NN￨O￨- e￨L￨SYM￨O￨- r￨L￨NN￨O￨- o￨L￨NN￨O￨- f￨L￨FW￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- f￨L￨FW￨O￨- e￨L￨SYM￨O￨- c￨L￨NN￨O￨- t￨L￨NN￨O￨- e￨L￨SYM￨O￨- d￨L￨FW￨O￨- s￨L￨VBZ￨O￨- Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Note￨U￨VB￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- easier￨L￨JJR￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- denser￨L￨JJR￨O￨- community￨L￨NN￨O￨A B￨U￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- sparser￨L￨JJR￨O￨- community￨L￨NN￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- B￨U￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- larger￨L￨JJR￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- than￨L￨IN￨O￨- A￨U￨DT￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- RB￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- λ￨L￨NN￨O￨- γ￨L￨NN￨O￨- hkB￨L￨NN￨O￨- i￨L￨FW￨O￨- >￨L￨JJR￨O￨- λ￨L￨NN￨O￨- γ￨L￨NN￨O￨- hkAi￨L￨NN￨O￨- =￨L￨JJ￨O￨- RA￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Temporal￨U￨JJ￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- community￨L￨NN￨O￨- networks￨L￨NNS￨O￨- 5￨L￨CD￨NUMBER￨- 1￨L￨CD￨DATE￨- 2￨L￨CD￨DATE￨- 3￨L￨CD￨DATE￨- 4￨L￨CD￨DATE￨- 5￨L￨CD￨DATE￨- 6￨L￨CD￨DATE￨- 7￨L￨CD￨DATE￨- 8￨L￨CD￨DATE￨- 9￨L￨CD￨DATE￨- 10￨L￨CD￨DATE￨- 11￨L￨CD￨DATE￨- 12￨L￨CD￨DATE￨- 13￨L￨CD￨DATE￨- 14￨L￨CD￨DATE￨- 15￨L￨CD￨DATE￨- 16￨L￨CD￨DATE￨- 17￨L￨CD￨DATE￨- 18￨L￨CD￨DATE￨- 19￨L￨CD￨DATE￨- 20￨L￨CD￨DATE￨- 21￨L￨CD￨DATE￨- 22￨L￨CD￨DATE￨- 23￨L￨CD￨DATE￨- 24￨L￨CD￨DATE￨- 25￨L￨CD￨DATE￨- 26￨L￨CD￨DATE￨- 27￨L￨CD￨DATE￨- 28￨L￨CD￨DATE￨- 29￨L￨CD￨DATE￨- 30￨L￨CD￨DATE￨- 31￨L￨CD￨DATE￨- 32￨L￨CD￨DATE￨- 33￨L￨CD￨DATE￨- 34￨L￨CD￨DATE￨- 35￨L￨CD￨DATE￨- 36￨L￨CD￨DATE￨- 37￨L￨CD￨DATE￨- 38￨L￨CD￨DATE￨- 39￨L￨CD￨DATE￨- 40￨L￨CD￨DATE￨- 41￨L￨CD￨DATE￨- 42￨L￨CD￨DATE￨- 43￨L￨CD￨DATE￨- 44￨L￨CD￨DATE￨- 45￨L￨CD￨DATE￨- 46￨L￨CD￨DATE￨- 47￨L￨CD￨DATE￨- 48￨L￨CD￨DATE￨- 49￨L￨CD￨DATE￨- 50￨L￨CD￨DATE￨- 51￨L￨CD￨DATE￨- 52￨L￨CD￨DATE￨- 53￨L￨CD￨DATE￨- 54￨L￨CD￨DATE￨- 55￨L￨CD￨DATE￨- 56￨L￨CD￨DATE￨- 57￨L￨CD￨DATE￨- 58￨L￨CD￨DATE￨- 59￨L￨CD￨DATE￨- 60￨L￨CD￨DATE￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- dependent￨L￨JJ￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- interconnected￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analytically￨L￨RB￨O￨- derive￨L￨VBP￨O￨- λ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- +￨L￨CC￨O￨- αB￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- using￨L￨VBG￨O￨- perturbation￨L￨NN￨O￨- approximation￨L￨NN￨O￨- for￨L￨IN￨O￨- small￨L￨JJ￨O￨- and￨L￨CC￨O￨- large￨L￨JJ￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- and￨L￨CC￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- α￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- individual￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- interconnections￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- largest￨L￨JJS￨O￨- eigenvalues/eigenvectors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- an￨L￨DT￨O￨- N-intertwined￨U￨JJ￨MISC￨- mean-field￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- determine￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- susceptable-infected-susceptable￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- interconnected￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- 1/λ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- +￨L￨CC￨O￨- αB￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- β￨L￨NN￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- individual￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- αβ￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- interconnected￨L￨JJ￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- λ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- +￨L￨CC￨O￨- αB￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- matrix￨L￨NN￨O￨- A￨U￨NN￨O￨- +￨L￨CC￨O￨- αB￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- note￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- two￨L￨CD￨NUMBER￨- isolated￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- G1￨U￨NN￨O￨- and￨L￨CC￨O￨- G2￨U￨NN￨O￨- with￨L￨IN￨O￨- principle￨L￨NN￨O￨- eigenvectors￨L￨NNS￨O￨- x￨L￨CC￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- λ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- +￨L￨CC￨O￨- αB￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- higher￨L￨JJR￨O￨- when￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- j￨L￨FW￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- eigenvector￨L￨NN￨O￨- component￨L￨NN￨O￨- product￨L￨NN￨O￨- xiyj￨L￨NN￨O￨- are￨L￨VBP￨O￨- interconnected￨L￨VBN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨VBP￨O￨- show￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- β/δ￨L￨NN￨O￨- in￨L￨IN￨O￨- interconnected￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- via￨L￨IN￨O￨- NIMFA￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- τc￨L￨NN￨O￨- =￨L￨JJ￨O￨- λ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- +￨L￨CC￨O￨- αB￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- λ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- +￨L￨CC￨O￨- αB￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- matrix￨L￨NN￨O￨- A￨U￨NN￨O￨- +￨L￨CC￨O￨- αB￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- express￨L￨VBP￨O￨- λ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- +￨L￨CC￨O￨- αB￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- network￨L￨NN￨O￨- component￨L￨NN￨O￨A A1￨U￨NN￨O￨- ,￨L￨,￨O￨- A2￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- eigenvalues/eigenvectors￨L￨NNS￨O￨- to￨L￨TO￨O￨- reveal￨L￨VB￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- component￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Built￨U￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- strong￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- studies￨L￨NNS￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- strategic￨L￨JJ￨O￨A agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- decide￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- to￨L￨TO￨O￨- form￨L￨VB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- careful￨L￨JJ￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- current￨L￨JJ￨DATE￨- obtainable￨L￨JJ￨O￨- bene￨L￨NN￨O￨- fit￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- future￨L￨JJ￨DATE￨- cost￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- forming￨L￨VBG￨O￨- links￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- key￨L￨JJ￨O￨- result￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- whereas￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- eventually￨L￨RB￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- low￨L￨JJ￨O￨- in￨L￨IN￨O￨- exogenously￨L￨RB￨O￨- given￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- never￨L￨RB￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- when￨L￨WRB￨O￨- agents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- strategic￨L￨JJ￨O￨A regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- much￨L￨RB￨O￨- less￨L￨JJR￨O￨- knowledge￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- for￨L￨IN￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- endogenously￨L￨RB￨O￨- formed￨L￨VBN￨O￨- by￨L￨IN￨O￨- strategic￨L￨JJ￨O￨A agents￨L￨NNS￨O￨- who￨L￨WP￨O￨- can￨L￨MD￨O￨- decide￨L￨VB￨O￨- their￨L￨PRP$￨O￨- connections￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- interests￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- such￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- agents￨L￨NNS￨O￨- ’￨L￨POS￨O￨- strategic￨L￨JJ￨O￨A decisions￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- become￨L￨VBP￨O￨- complexly￨L￨RB￨O￨- coupled￨L￨VBN￨O￨- and￨L￨CC￨O￨- co-evolve￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- accounted￨L￨VBN￨O￨- for￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- every￨L￨DT￨O￨- 25￨L￨CD￨NUMBER￨- childhood￨L￨NN￨O￨- deaths￨L￨NNS￨O￨A ,￨L￨,￨O￨- significantly￨L￨RB￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- deaths￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- numerical￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- dimension￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- current-voltage￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- array￨L￨NN￨O￨A have￨L￨VBP￨O￨- self-induced￨L￨JJ￨O￨- resonant￨L￨JJ￨O￨- steps￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- disorder￨L￨NN￨O￨- and￨L￨CC￨O￨- coupling￨L￨NN￨O￨- strength￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- array￨L￨NN￨O￨- locks￨L￨VBZ￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- coherent￨L￨JJ￨O￨- ,￨L￨,￨O￨- periodic￨L￨JJ￨O￨- state￨L￨NN￨O￨- above￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- Josephson￨U￨NNP￨PERSON￨- junctions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- Na￨U￨NN￨MISC￨- active￨L￨JJ￨O￨- junctions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- synchronized￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- energy￨L￨NN￨O￨- emitted￨L￨VBD￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- resonant￨L￨JJ￨O￨- cavity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- quadratic￨L￨JJ￨O￨- with￨L￨IN￨O￨- Na￨U￨NN￨O￨- .￨L￨.￨O￨- +Resonant-Cavity-Induced￨U￨JJ￨O￨- Phase￨U￨NN￨O￨- Locking￨U￨NN￨O￨- and￨L￨CC￨O￨- Voltage￨U￨NNP￨ORGANIZATION￨- Steps￨U￨VBZ￨ORGANIZATION￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Josephson￨U￨NNP￨ORGANIZATION￨- Array￨U￨NNP￨ORGANIZATION￨- E.￨U￨NNP￨ORGANIZATION￨- Stroud￨U￨NNP￨ORGANIZATION￨- †￨L￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- The￨U￨DT￨O￨- Ohio￨U￨NNP￨ORGANIZATION￨- State￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Columbus￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Ohio￨U￨NNP￨STATE_OR_PROVINCE￨- 43210￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- October￨U￨NNP￨DATE￨- 31￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- underdamped￨L￨JJ￨O￨- Josephson￨U￨NNP￨PERSON￨- junction￨L￨NN￨O￨- array￨L￨NN￨O￨A coupled￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- resonant￨L￨JJ￨O￨- cavity￨L￨NN￨O￨- .￨L￨.￨O￨- +Adopting￨U￨VBG￨O￨- methodologies￨L￨NNS￨O￨- like￨L￨IN￨O￨- cellular￨L￨JJ￨O￨- automata￨L￨NN￨O￨A ,￨L￨,￨O￨- coupled￨L￨VBN￨O￨- map￨L￨NN￨O￨- lattices￨L￨NNS￨O￨- ,￨L￨,￨O￨- lattice￨L￨NN￨O￨- gas￨L￨NN￨O￨- cellular￨L￨JJ￨O￨- automata￨L￨NN￨O￨- or￨L￨CC￨O￨- agent￨L￨NN￨O￨- based￨L￨VBN￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- new￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- studied￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- with￨L￨IN￨O￨- various￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- abstraction￨L￨NN￨O￨- and￨L￨CC￨O￨- details￨L￨NNS￨O￨- :￨L￨:￨O￨- direct￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- types￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- removed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- movement￨L￨NN￨O￨- ;￨L￨:￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- on￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +INTRODUCTION￨U￨NN￨O￨- Studies￨U￨NNS￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Black￨U￨JJ￨O￨- Death￨U￨NN￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- from￨L￨IN￨O￨- 1347￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1350￨L￨CD￨DATE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- influenza￨L￨NN￨O￨- pandemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- fox￨L￨NN￨O￨- rabies￨L￨NNP￨O￨A in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨- among￨L￨IN￨O￨- raccoons￨L￨NNS￨O￨- in￨L￨IN￨O￨- eastern￨L￨JJ￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- and￨L￨CC￨O￨- Canada￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- infective￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- populations￨L￨NNS￨O￨- should￨L￨MD￨O￨- play￨L￨VB￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Until￨U￨IN￨O￨- recently￨L￨RB￨DATE￨- most￨L￨RBS￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- described￨L￨VBN￨O￨- interactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- aggregate￨L￨JJ￨O￨- form￨L￨NN￨O￨- and￨L￨CC￨O￨- often￨L￨RB￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- neglected￨L￨VBN￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨A distribution￨L￨NN￨O￨A of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- addressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- incorporates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- discreteness￨L￨NN￨O￨- and￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- population.We￨L￨NN￨O￨- find￨L￨NN￨O￨- that￨L￨WDT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- long-range￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- destroys￨L￨VBZ￨O￨- spatial￨L￨JJ￨O￨A correlations￨L￨NNS￨O￨- very￨L￨RB￨O￨- easily￨L￨RB￨O￨- if￨L￨IN￨O￨- neighbourhood￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- homogeneous￨L￨JJ￨O￨- .￨L￨.￨O￨- +22￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- No.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 541￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 575￨L￨CD￨NUMBER￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.1214￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 11-AAP773￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- LARGE￨U￨NNP￨O￨- GRAPH￨U￨NNP￨O￨- LIMIT￨U￨NNP￨O￨- FOR￨U￨IN￨O￨- AN￨U￨DT￨O￨- SIR￨U￨NN￨O￨- PROCESS￨U￨NN￨O￨- IN￨U￨IN￨O￨- RANDOM￨U￨NNP￨O￨- NETWORK￨U￨NNP￨O￨- WITH￨U￨IN￨O￨- HETEROGENEOUS￨U￨JJ￨O￨- CONNECTIVITY￨U￨NN￨O￨- By￨U￨IN￨O￨- Laurent￨U￨NNP￨PERSON￨- Decreusefond￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jean-St￨U￨NN￨O￨- ´￨L￨''￨O￨- ephane￨L￨NN￨O￨- Dhersin1￨U￨NN￨O￨- ,￨L￨,￨O￨- Pascal￨U￨NNP￨PERSON￨- Moyal￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Viet￨U￨NNP￨ORGANIZATION￨- Chi￨U￨NNP￨ORGANIZATION￨- Tran1￨U￨NNP￨ORGANIZATION￨- Telecom￨U￨NNP￨ORGANIZATION￨- Paristech￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Universit￨U￨NNP￨ORGANIZATION￨- ´￨L￨POS￨O￨- e￨L￨SYM￨O￨- Paris￨U￨NNP￨ORGANIZATION￨- 13￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Universit￨U￨NNP￨ORGANIZATION￨- ´￨L￨POS￨O￨- e￨L￨SYM￨O￨- de￨L￨FW￨O￨- Technologie￨U￨FW￨ORGANIZATION￨- de￨L￨FW￨O￨- Compi`egne￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Universit￨U￨NNP￨O￨- ´￨L￨POS￨O￨- e￨L￨SYM￨O￨- des￨L￨FW￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- et￨L￨FW￨ORGANIZATION￨- Technologies￨U￨NNPS￨ORGANIZATION￨- Lil￨U￨NNP￨ORGANIZATION￨- le￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Ecole￨U￨NNP￨ORGANIZATION￨- Polytechnique￨U￨NNP￨ORGANIZATION￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- propagating￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vertices￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- and￨L￨CC￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨A are￨L￨VBP￨O￨- randomly￨L￨RB￨O￨- matched￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- summed￨L￨VBN￨O￨- up￨L￨RP￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- measure-valued￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨A from￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- or￨L￨CC￨O￨- removed￨L￨VBN￨O￨- individual￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- .￨L￨.￨O￨- +for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- edge￨L￨NN￨O￨- ,￨L￨,￨O￨- alter￨L￨VBP￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- size-biased￨L￨JJ￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A :￨L￨:￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- The￨U￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- partitioned￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- convergence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- deterministic￨L￨JJ￨O￨- limit￨L￨NN￨O￨A for￨L￨IN￨O￨- large￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- was￨L￨VBD￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- proved￨L￨VBN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- static￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- a￨L￨DT￨O￨- kernel￨L￨NN￨O￨- smoother￨L￨JJR￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- particles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- filter￨L￨NN￨O￨- for￨L￨IN￨O￨- non-linear￨L￨JJ￨O￨- state￨L￨NN￨O￨A space￨L￨NN￨O￨A models￨L￨NNS￨O￨- with￨L￨IN￨O￨- additive￨L￨JJ￨O￨- Gaussian￨U￨JJ￨MISC￨- observation￨L￨NN￨O￨- noise￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- linear￨L￨JJ￨O￨- and￨L￨CC￨O￨- Gaussian￨U￨JJ￨MISC￨- state￨L￨NN￨O￨A space￨L￨NN￨O￨A models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Kalman￨U￨NNP￨MISC￨- Filter￨U￨NNP￨MISC￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- sequentially￨L￨RB￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- mean￨L￨NN￨O￨- and￨L￨CC￨O￨- covariance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- state￨L￨NN￨O￨- vector￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- adaptive￨L￨JJ￨O￨- bandwidth￨L￨NN￨O￨- selection￨L￨NN￨O￨- ;￨L￨:￨O￨- filter￨L￨NN￨O￨- ;￨L￨:￨O￨- state￨L￨NN￨O￨A space￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- variance￨L￨NN￨O￨- inflation￨L￨NN￨O￨- kernel￨L￨NN￨O￨- smoothing￨L￨NN￨O￨- ;￨L￨:￨O￨- likelihood￨L￨NN￨O￨- estimation￨L￨NN￨O￨- ;￨L￨:￨O￨- particle￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- State￨U￨NN￨O￨- space￨L￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- scientific￨L￨NN￨O￨- fields￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- particle￨L￨NN￨O￨- filter￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- prospect￨L￨NN￨O￨- of￨L￨IN￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- sampling-based￨L￨JJ￨O￨- consistent￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨A distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- particles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- bring￨L￨VB￨O￨- the￨L￨DT￨O￨- MC￨U￨NNP￨O￨- error￨L￨NN￨O￨- within￨L￨IN￨O￨- tolerable￨L￨JJ￨O￨- bounds￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- prohibitively￨L￨RB￨O￨- large￨L￨JJ￨O￨- .￨L￨.￨O￨- +Gaussian￨U￨JJ￨O￨- mixture￨L￨NN￨O￨- filters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- attempts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- non-normality￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- posterior￨L￨NN￨O￨A ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- nonlinearity￨L￨NN￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- equation￨L￨NN￨O￨- or￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨- equation￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- generate￨L￨VBP￨O￨- and￨L￨CC￨O￨- deliver￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- packets￨L￨NNS￨O￨- causing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- block￨L￨VBP￨O￨- the￨L￨DT￨O￨- delivery￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- packets￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- inhibits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A .￨L￨.￨O￨- +Increasing￨U￨VBG￨O￨- either￨L￨CC￨O￨- average￨L￨JJ￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨- or￨L￨CC￨O￨- homogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- will￨L￨MD￨O￨- facilitate￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A .￨L￨.￨O￨- +When￨U￨WRB￨O￨- packet￨L￨NN￨O￨- generation￨L￨NN￨O￨- rate￨L￨NN￨O￨- ρ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- ρ￨L￨NN￨O￨- favors￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- packets￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- ρ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- enough￨L￨RB￨O￨- ,￨L￨,￨O￨- traffic￨L￨NN￨O￨- congestion￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- which￨L￨WDT￨O￨- inhibits￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨DATE￨- decade￨L￨NN￨DATE￨- ago￨L￨RB￨DATE￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- first￨L￨NN￨O￨- demonstrated￨L￨VBD￨O￨- that￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A can￨L￨MD￨O￨- fundamentally￨L￨RB￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- –￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- vanishes￨L￨VBZ￨O￨- on￨L￨IN￨O￨- scale￨L￨NN￨O￨- free￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- γ￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- epidemics￨L￨NNS￨O￨- always￨L￨RB￨O￨- infect￨L￨VBP￨O￨- a￨L￨DT￨O￨- nontrivial￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- infinite￨L￨NN￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- finite￨L￨NN￨O￨- size￨L￨NN￨O￨- corrections￨L￨NNS￨O￨- later￨L￨RB￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .1￨L￨CD￨NUMBER￨- Later￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- threshold￨L￨NN￨O￨- also￨L￨RB￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- extremely￨L￨RB￨O￨- small￨L￨JJ￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- faster￨L￨JJR￨O￨- than￨L￨IN￨O￨- linear￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- on￨L￨IN￨O￨- such￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- .￨L￨.￨O￨- +example￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- A￨U￨DT￨O￨- related￨L￨JJ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- Exact￨U￨JJ￨O￨- mean￨L￨NN￨O￨- field￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic-like￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A 3￨L￨CD￨NUMBER￨- than￨L￨IN￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- .￨L￨.￨O￨- +Exact￨U￨JJ￨O￨- mean￨L￨NN￨O￨- field￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic-like￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A Andrew￨U￨NNP￨PERSON￨- Lucas￨U￨NNP￨PERSON￨- Jefferson￨U￨NNP￨ORGANIZATION￨- Physical￨U￨NNP￨ORGANIZATION￨- Laboratory￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Harvard￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Stanford￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- field￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- exactly￨L￨RB￨O￨- solved￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- extend￨L￨VBP￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- mean￨L￨JJ￨O￨A field￨L￨JJ￨O￨A theory￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- framework￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- late￨L￨JJ￨O￨- time￨L￨NN￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- scale￨L￨NN￨O￨- free￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- introducing￨L￨VBG￨O￨- some￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- .￨L￨.￨O￨- +14￨L￨CD￨NUMBER￨- 4￨L￨CD￨NUMBER￨- Recommendation￨U￨NN￨O￨- Spreading￨U￨VBG￨O￨- 16￨L￨CD￨NUMBER￨- 5￨L￨CD￨NUMBER￨- Conclusion￨U￨NN￨O￨- 18￨L￨CD￨NUMBER￨- Acknowledgements￨U￨NNS￨O￨- 19￨L￨CD￨NUMBER￨- References￨U￨NNS￨O￨- 19￨L￨CD￨NUMBER￨- Exact￨U￨JJ￨O￨- mean￨L￨NN￨O￨- field￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic-like￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- proposed￨L￨VBD￨O￨- adaptive￨L￨JJ￨O￨- CoMP￨U￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- downlink￨L￨VB￨O￨A zero-forcing￨L￨JJ￨O￨- beamforming￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZFBF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- interference￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- coordinated￨L￨VBN￨O￨- cells￨L￨NNS￨O￨- with￨L￨IN￨O￨- delayed￨L￨VBN￨O￨- overhead￨L￨NN￨O￨- messages￨L￨NNS￨O￨- .￨L￨.￨O￨- +Numerical￨U￨JJ￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- adaptive￨L￨JJ￨O￨A CoMP￨U￨NN￨O￨- scheme￨L￨NN￨O￨- can￨L￨MD￨O￨- make￨L￨VB￨O￨- the￨L￨DT￨O￨- throughput￨L￨NN￨O￨- gain￨L￨NN￨O￨- very￨L￨RB￨O￨- robust￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- overhead￨L￨JJ￨O￨- delay￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- significantly￨L￨RB￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- throughput￨L￨NN￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- BSs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- perfectly￨L￨RB￨O￨- coordinated￨L￨VBN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- CoMP￨U￨NN￨O￨- has￨L￨VBZ￨O￨- imperfect￨L￨JJ￨O￨A inter-cell￨L￨JJ￨O￨- overhead￨L￨NN￨O￨- messaging￨L￨NN￨O￨- ,￨L￨,￨O￨- throughput￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- significantly￨L￨RB￨O￨- degraded￨L￨VBN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- not￨L￨RB￨O￨- addressed￨L￨VBD￨O￨- too￨L￨RB￨O￨- much￨L￨JJ￨O￨- until￨L￨IN￨O￨- now￨L￨RB￨DATE￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- prior￨L￨JJ￨O￨- CoMP￨U￨NN￨O￨- works￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- consider￨L￨VB￨O￨- inter-cell￨L￨JJ￨O￨- overhead￨L￨NN￨O￨- message￨L￨NN￨O￨- delays￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- seemingly￨L￨RB￨O￨- astonishing￨L￨JJ￨O￨- CoMP￨U￨NN￨O￨- throughput￨L￨NN￨O￨- gain￨L￨NN￨O￨A is￨L￨VBZ￨O￨- attained￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- interacting￨L￨VBG￨O￨- cities￨L￨NNS￨O￨A linked￨L￨VBN￨O￨- 2￨L￨CD￨NUMBER￨- via￨L￨IN￨O￨- implied￨L￨VBN￨O￨- transportation￨L￨NN￨O￨- routes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- coupling￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- contribute￨L￨VBP￨O￨- to￨L￨TO￨O￨- tradeoffs￨L￨NNS￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- determine￨L￨VBP￨O￨- optimal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- allocation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- available￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- are￨L￨VBP￨O￨- insufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- at-risk￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- logistics￨L￨NNS￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- delayed￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨- deployment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- cities￨L￨NNS￨O￨A facilitates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- cities￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- until￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- lead￨L￨NN￨O￨- to￨L￨TO￨O￨- tradeoffs￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- dictate￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- of￨L￨IN￨O￨- distributing￨L￨VBG￨O￨- limited￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +Limited￨U￨JJ￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- coupling￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- cities￨L￨NNS￨O￨A lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- tradeoffs￨L￨NNS￨O￨- that￨L￨WDT￨O￨- impact￨L￨VBP￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨- can￨L￨MD￨O￨- change￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategy￨L￨NN￨O￨- which￨L￨WDT￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- fewest￨L￨JJS￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- greatly￨L￨RB￨O￨- impacting￨L￨VBG￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Assuming￨U￨VBG￨O￨- continuous￨L￨JJ￨O￨- measurement￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infectives￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- interval￨L￨JJ￨O￨A observers￨L￨NNS￨O￨- with￨L￨IN￨O￨- estimate-dependent￨L￨JJ￨O￨- gain￨L￨NN￨O￨- is￨L￨VBZ￨O￨- constructed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- asymptotic￨L￨JJ￨O￨- error￨L￨NN￨O￨- bounds￨L￨NNS￨O￨- are￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- .￨L￨.￨O￨- +interval￨L￨NN￨O￨- observers￨L￨NNS￨O￨- We￨U￨PRP￨O￨- are￨L￨VBP￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- in￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- repartition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- ,￨L￨,￨O￨- uncertain￨L￨JJ￨O￨A ,￨L￨,￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- these￨L￨DT￨O￨- preceding￨L￨VBG￨O￨- works￨L￨NNS￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- properly￨L￨RB￨O￨- capture￨L￨VB￨O￨- propagation￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- accurate￨L￨JJ￨O￨- performance￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- at￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- downlink￨L￨NN￨O￨- mmWave￨L￨NN￨O￨- SIR￨U￨NN￨O￨- coverage￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- realistic￨L￨JJ￨O￨- measurement-based￨L￨JJ￨O￨- channel￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- while￨L￨IN￨O￨- still￨L￨RB￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- tractable￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- works￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- mmWave￨L￨NNP￨O￨- network￨L￨NN￨O￨- coverage￨L￨NN￨O￨A by￨L￨IN￨O￨- using￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- geometry￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- tool￨L￨NN￨O￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- random￨L￨JJ￨O￨- interference￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- way￨L￨NN￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- a￨L￨DT￨O￨- closed-form￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- in￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- mmWave￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +Channel￨U￨NNP￨O￨- parameters￨L￨NNS￨O￨- follow￨L￨VBP￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- measurement-based￨L￨JJ￨O￨- mmWave￨L￨NN￨O￨- channel￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- NYU￨U￨NNP￨ORGANIZATION￨- Wireless￨U￨NNP￨ORGANIZATION￨- Group￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- Greenhalgh￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Liang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Mao￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- Markovian￨U￨JJ￨MISC￨- switching￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- dS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- dt￨L￨NN￨O￨A =￨L￨JJ￨O￨- Λ￨U￨NN￨O￨- −￨L￨NN￨O￨- µS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- λR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- dR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- δI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- presented￨L￨VBN￨O￨- by￨L￨IN￨O￨- Anderson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- May￨U￨NNP￨DATE￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- or￨L￨CC￨O￨- bacteria￨L￨NNS￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- facts￨L￨NNS￨O￨- mentioned￨L￨VBN￨O￨- above￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- both￨L￨DT￨O￨- linear￨L￨JJ￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- inci￨L￨SYM￨O￨- -￨L￨:￨O￨- 2￨L￨CD￨DATE￨- dence￨L￨NN￨O￨- rate￨L￨NN￨O￨- :￨L￨:￨O￨- dS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- dt￨L￨NN￨O￨A =￨L￨JJ￨O￨- Λ￨U￨NN￨O￨- −￨L￨NN￨O￨- µS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- λR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- βr￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- βr￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- dR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- δI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ·￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- function￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- drived￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- continuous-time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- taking￨L￨VBG￨O￨- values￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- M￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +Throughout￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- further￨L￨RB￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- H1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ·￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- →￨L￨NN￨O￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- twice-differentiable￨L￨JJ￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨SYM￨O￨- I￨U￨PRP￨O￨- G￨U￨NN￨O￨- ′￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- holds￨L￨VBZ￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- I￨U￨PRP￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- Lipschitz￨U￨NNP￨PERSON￨- on￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Λ/µ￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨A a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- ϑ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- H2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- ≤￨L￨SYM￨O￨- ϑ￨L￨SYM￨O￨- |￨L￨SYM￨O￨- x1￨L￨FW￨O￨- −￨L￨FW￨O￨- x2￨L￨FW￨O￨- |￨L￨SYM￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- x1￨L￨NN￨O￨- ,￨L￨,￨O￨- x2￨L￨NN￨O￨- ∈￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Λ/µ￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- x.￨L￨NN￨O￨- For￨U￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- z0￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- R3￨U￨NN￨O￨- +￨L￨CC￨O￨- ×￨L￨CD￨NUMBER￨- M￨U￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- z0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- z0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- z0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- t￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- wil￨L￨NN￨O￨- l￨L￨NN￨O￨- always￨L￨RB￨O￨- remain￨L￨VBP￨O￨- in￨L￨IN￨O￨- for￨L￨IN￨O￨- every￨L￨DT￨O￨- ω￨L￨NN￨O￨- ∈￨L￨NN￨O￨- eΩ￨L￨NN￨O￨- ,￨L￨,￨O￨- Λ￨U￨NN￨O￨- <￨L￨JJR￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- ω￨L￨NN￨O￨- ,￨L￨,￨O￨- z0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- ω￨L￨NN￨O￨- ,￨L￨,￨O￨- z0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- ω￨L￨NN￨O￨- ,￨L￨,￨O￨- z0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- <￨L￨JJR￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- t￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- t0￨L￨NN￨O￨- .￨L￨.￨O￨- +the￨L￨DT￨O￨- solution￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- property￨L￨NN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨A t0￨L￨NN￨O￨- =￨L￨JJ￨O￨- t0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ω￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Λ￨U￨NN￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- µ￨L￨NN￨O￨- Let￨U￨VB￨O￨- X￨U￨NN￨O￨- =￨L￨JJ￨O￨- K￨U￨NN￨O￨- ×￨L￨CD￨NUMBER￨- M￨U￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- K￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- x￨L￨CC￨O￨- ∈￨L￨SYM￨O￨- R3￨U￨NN￨O￨- +￨L￨CC￨O￨- :￨L￨:￨O￨- Λ￨U￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- <￨L￨JJR￨O￨- x1￨L￨NN￨O￨- +￨L￨CC￨O￨- x2￨L￨NN￨O￨- +￨L￨CC￨O￨- x3￨L￨NN￨O￨- <￨L￨JJR￨O￨- Λ/µ￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- stereoscopic￨L￨JJ￨O￨- retargeted￨L￨VBN￨O￨- images￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- introduces￨L￨VBZ￨O￨- novel￨L￨JJ￨O￨- features￨L￨NNS￨O￨- like￨L￨IN￨O￨- disparity￨L￨NN￨O￨- range￨L￨NN￨O￨- ,￨L￨,￨O￨- boundary￨L￨NN￨O￨- disparity￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- disparity￨L￨NN￨O￨- intensity￨L￨NN￨O￨- distribution￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- assessment￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Visual￨U￨JJ￨O￨- Comfort￨U￨NN￨O￨- Assessment￨U￨NNP￨O￨- for￨L￨IN￨O￨- Stereoscopic￨U￨NNP￨O￨- Image￨U￨NN￨O￨- Retargeting￨U￨VBG￨O￨- Ya￨U￨NNP￨ORGANIZATION￨- Zhou￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- Hefei￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- Wei￨U￨NNP￨ORGANIZATION￨- Zhou￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- Hefei￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- Ping￨U￨VB￨ORGANIZATION￨- An￨U￨DT￨ORGANIZATION￨- Shanghai￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Shanghai￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- Zhibo￨U￨NNP￨ORGANIZATION￨- Chen￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- Hefei￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- visual￨L￨JJ￨O￨- comfort￨L￨NN￨O￨- assessment￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- VCA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- 3D/stereoscopic￨L￨JJ￨O￨- content￨L￨NN￨O￨- has￨L￨VBZ￨O￨- aroused￨L￨VBN￨O￨- extensive￨L￨JJ￨O￨- attention￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- subjective￨L￨JJ￨O￨- experiment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- conducted￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- four￨L￨CD￨NUMBER￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- visual￨L￨JJ￨O￨- distortion￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- visual￨L￨JJ￨O￨- comfort￨L￨NN￨O￨- ,￨L￨,￨O￨- image￨L￨NN￨O￨- quality￨L￨NN￨O￨A ,￨L￨,￨O￨- depth￨L￨NN￨O￨- quality￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- quality￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- —￨L￨:￨O￨- visual￨L￨JJ￨O￨- comfort￨L￨NN￨O￨- ,￨L￨,￨O￨- stereoscopic￨L￨JJ￨O￨- subjective￨L￨JJ￨O￨- assessment￨L￨NN￨O￨A database￨L￨NN￨O￨- ,￨L￨,￨O￨- VCA-SIR￨U￨NN￨O￨- image￨L￨NN￨O￨- retargeting￨L￨NN￨O￨- ,￨L￨,￨O￨- I.￨U￨NN￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- Visual￨U￨JJ￨O￨- Comfort￨U￨NN￨O￨- Assessment￨U￨NNP￨O￨- metric￨L￨JJ￨O￨A for￨L￨IN￨O￨- Stereoscopic￨U￨JJ￨O￨- Image￨U￨NN￨O￨- Retargeting￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- VCA-SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- suspect￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- form￨L￨VBP￨O￨- a￨L￨DT￨O￨- connected￨L￨JJ￨O￨- subgraph￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- significantly￨L￨RB￨O￨- the￨L￨DT￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨A probability￨L￨NN￨O￨- if￨L￨IN￨O￨- δ￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reliable￨L￨JJ￨O￨- detection￨L￨NN￨O￨- exceeds￨L￨VBZ￨O￨- is￨L￨VBZ￨O￨- achieved￨L￨VBN￨O￨- as￨L￨IN￨O￨- δ￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- large￨L￨JJ￨O￨- ;￨L￨:￨O￨- furthermore￨L￨RB￨O￨- ,￨L￨,￨O￨- Pc￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- monotonically￨L￨RB￨O￨- decreases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- n￨L￨NN￨O￨- and￨L￨CC￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- δ￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- regular￨L￨JJ￨O￨- tree-type￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨- δ￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- characterize￨L￨VBP￨O￨- Pc￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- correct￨L￨JJ￨O￨- detection￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- estimator￨L￨NN￨O￨A upon￨L￨IN￨O￨- observing￨L￨VBG￨O￨- n￨L￨NN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- finite￨L￨NN￨O￨- and￨L￨CC￨O￨- asymptotic￨L￨JJ￨O￨- regimes￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- suspect￨L￨JJ￨O￨- set￨L￨NN￨O￨- degenerates￨L￨VBZ￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- entirety￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- every￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- belongs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- suspect￨L￨JJ￨O￨- set￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- 0.25￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 0.307￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- increases￨L￨NNS￨O￨A from￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- first￨L￨NN￨O￨- established￨L￨VBN￨O￨- in￨L￨IN￨O￨- Shah￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Zaman￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2011￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- approach￨L￨NN￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- mathematical￨L￨JJ￨O￨- machinery￨L￨NN￨O￨- ;￨L￨:￨O￨- furthermore￨L￨RB￨O￨- ,￨L￨,￨O￨- Pc￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- monotonically￨L￨RB￨O￨- decreases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- n￨L￨NN￨O￨- and￨L￨CC￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- δ￨L￨NN￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- finite-n￨L￨JJ￨O￨- regime￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨A knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- suspect￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- snapshot￨L￨NN￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- construct￨L￨VBP￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- a￨L￨DT￨O￨- posteriori￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MAP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- estimator￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- source￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Third￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- two￨L￨CD￨NUMBER￨- suspect￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- 0.75￨L￨CD￨NUMBER￨- if￨L￨IN￨O￨- δ￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- Pc￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- increases￨L￨VBZ￨O￨A with￨L￨IN￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- suspects￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- acute￨L￨JJ￨O￨A and￨L￨CC￨O￨- early￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- prevention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- Lilongwe￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Malawi￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- modelling￨L￨NN￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +Amplified￨U￨VBN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV-1￨U￨NN￨O￨- :￨L￨:￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV-1￨U￨NN￨MISC￨- concentrations￨L￨NNS￨O￨- in￨L￨IN￨O￨- semen￨L￨NN￨O￨- and￨L￨CC￨O￨- blood￨L￨NN￨O￨- during￨L￨IN￨O￨- acute￨L￨JJ￨O￨A and￨L￨CC￨O￨- chronic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Beneficial￨U￨JJ￨MISC￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Model￨U￨NNP￨TITLE￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Model￨U￨NNP￨TITLE￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Model￨U￨NNP￨TITLE￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Mode￨U￨NNP￨O￨- of￨L￨IN￨O￨- Benefit￨U￨NNP￨ORGANIZATION￨- Population￨U￨NNP￨ORGANIZATION￨- Transmission￨U￨NNP￨ORGANIZATION￨- Network￨U￨NNP￨ORGANIZATION￨- rewiring￨L￨VBG￨O￨- fitness￨L￨NN￨O￨- well-mixed￨L￨JJ￨O￨- vertical￨L￨JJ￨O￨- and￨L￨CC￨O￨- horizontal￨L￨JJ￨O￨A none￨L￨NN￨O￨- implicit￨L￨JJ￨O￨- via￨L￨IN￨O￨- connectivity￨L￨NN￨O￨- social￨L￨JJ￨O￨- horizontal￨L￨JJ￨O￨- fixed￨L￨JJ￨O￨- targeting￨L￨VBG￨O￨- explicit￨L￨JJ￨O￨- utility￨L￨NN￨O￨- social￨L￨JJ￨O￨- horizontal￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- Comparison￨U￨NN￨O￨- of￨L￨IN￨O￨- bene￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- beneficial￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- beneficial￨L￨JJ￨O￨- elements￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- facilitated￨L￨VBN￨O￨- in￨L￨IN￨O￨- biological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- by￨L￨IN￨O￨- horizontal￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- by￨L￨IN￨O￨- active￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Third￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- preferences￨L￨NNS￨O￨- for￨L￨IN￨O￨- increased￨L￨VBN￨O￨- global￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- accelerate￨L￨VB￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- produce￨L￨VBP￨O￨- superexponential￨L￨JJ￨O￨- fixation￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- preferences￨L￨NNS￨O￨- for￨L￨IN￨O￨- local￨L￨JJ￨O￨- assortativity￨L￨NN￨O￨- halt￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- by￨L￨IN￨O￨- disconnecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- infected￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- behavioral￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- cause￨L￨VBP￨O￨- increased￨L￨VBN￨O￨- connectivity￨L￨NN￨O￨A lead￨L￨NN￨O￨- to￨L￨TO￨O￨- superexponential￨L￨JJ￨O￨- fixation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Model￨U￨NNP￨TITLE￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- H￨U￨NN￨O￨- represents￨L￨VBZ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- horizontal￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- from￨L￨IN￨O￨- vertical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Characterisation￨U￨NN￨O￨- of￨L￨IN￨O￨- placental￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- olive￨L￨JJ￨O￨- baboons￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Papio￨U￨NN￨O￨- anubis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- International￨U￨NNP￨ORGANIZATION￨- Journal￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Integrative￨U￨NNP￨ORGANIZATION￨- Biology￨U￨NNP￨ORGANIZATION￨- Regular￨U￨JJ￨ORGANIZATION￨- A￨U￨NN￨O￨- journal￨L￨NN￨O￨- for￨L￨IN￨O￨- biology￨L￨NN￨O￨- beyond￨L￨IN￨O￨- borders￨L￨NNS￨O￨- Characterisation￨U￨NN￨O￨- of￨L￨IN￨O￨- placental￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- olive￨L￨JJ￨O￨- baboons￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Papio￨U￨NN￨O￨- anubis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- with￨L￨IN￨O￨- Plasmodium￨U￨NN￨O￨- knowlesi￨L￨NN￨O￨- H￨U￨NN￨O￨- strain￨L￨NN￨O￨- Barasa￨U￨NNP￨O￨- Mustafa1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- *￨L￨SYM￨O￨- Gicheru￨U￨NNP￨O￨- Muita￨U￨NNP￨O￨- Michael1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Kagasi￨U￨NNP￨O￨- Ambogo￨U￨NNP￨O￨- Esther1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ozwara￨U￨NNP￨ORGANIZATION￨- Suba￨U￨NNP￨ORGANIZATION￨- Hastings2￨U￨NN￨ORGANIZATION￨- 1Zoological￨L￨NNP￨ORGANIZATION￨- Sciences￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- School￨U￨NNP￨O￨- of￨L￨IN￨O￨- Pure￨U￨NNP￨O￨- and￨L￨CC￨O￨- Applied￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Kenyatta￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Nairobi￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Tropical￨U￨JJ￨ORGANIZATION￨- and￨L￨CC￨O￨- Infectious￨U￨JJ￨O￨- Diseases￨U￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Primate￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Nairobi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Kenya￨U￨NNP￨COUNTRY￨- Submitted￨U￨NNP￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨DATE￨- Dec.￨U￨NNP￨DATE￨- 2009￨L￨CD￨DATE￨- ;￨L￨:￨O￨- Revised￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨DATE￨- Feb.￨U￨NNP￨DATE￨- 2010￨L￨CD￨DATE￨- ;￨L￨:￨O￨- Accepted￨U￨JJ￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨DATE￨- Feb.￨U￨NNP￨DATE￨- 2010￨L￨CD￨DATE￨- INTRODUCTION￨U￨NNP￨O￨- Many￨U￨JJ￨O￨- experiments￨L￨NNS￨O￨- have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- P.￨U￨NNP￨O￨- falciparum￨L￨NN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- pregnant￨L￨JJ￨O￨- women￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +knowlesi￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- human￨L￨JJ￨O￨- placental/pregnancy￨L￨NN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A now￨L￨RB￨DATE￨- offers￨L￨VBZ￨O￨- an￨L￨DT￨O￨- opportunity￨L￨NN￨O￨- for￨L￨IN￨O￨- circumventing￨L￨VBG￨O￨- the￨L￨DT￨O￨- obstacles￨L￨NNS￨O￨- experienced￨L￨VBN￨O￨- during￨L￨IN￨O￨- human￨L￨JJ￨O￨- studie￨L￨NN￨O￨- s￨L￨NNS￨O￨- like￨L￨IN￨O￨- having￨L￨VBG￨O￨- inadequate￨L￨JJ￨O￨- tissue￨L￨NN￨O￨- for￨L￨IN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- inaccurate￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- gestational￨L￨JJ￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- moral￨L￨JJ￨O￨- ,￨L￨,￨O￨- ethical￨L￨JJ￨O￨- and￨L￨CC￨O￨- financial￨L￨JJ￨O￨- limitations￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- established￨L￨VBD￨O￨- and￨L￨CC￨O￨- characterized￨L￨VBD￨O￨- a￨L￨DT￨O￨- baboon￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- placental￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- baboons￨L￨NNS￨O￨- experimentally￨L￨RB￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Plasmodium￨U￨NN￨O￨- knowlesi￨L￨NN￨O￨- H￨U￨NN￨O￨- strain￨L￨NN￨O￨- parasites￨L￨NNS￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨DATE￨- 150th￨L￨JJ￨DATE￨- day￨L￨NN￨DATE￨- of￨L￨IN￨O￨- gestation￨L￨NN￨O￨- the￨L￨DT￨O￨- pregnant￨L￨JJ￨O￨- baboons￨L￨NNS￨O￨- were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Plasmodium￨U￨NN￨O￨- knowlesi￨L￨NN￨O￨- H￨U￨NN￨O￨- strain￨L￨NN￨O￨A parasites￨L￨NNS￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- nulligravid￨L￨NN￨O￨- control￨L￨NN￨O￨- baboons￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- II￨U￨CD￨NUMBER￨- we￨L￨PRP￨O￨- first￨L￨FW￨O￨- de￨L￨FW￨O￨- fine￨L￨FW￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨A region￨L￨NN￨O￨- for￨L￨IN￨O￨- K￨U￨NNP￨O￨- users￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- power￨L￨NN￨O￨- settings￨L￨NNS￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- RK￨U￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- of￨L￨IN￨O￨- K￨U￨NNP￨O￨- users￨L￨NNS￨O￨- each￨L￨DT￨O￨- user￨L￨NN￨O￨- i￨L￨FW￨O￨- encounters￨L￨VBZ￨O￨- a￨L￨DT￨O￨- signal-to-noise￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- above￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- γi￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨A region￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- energy￨L￨NN￨O￨- minimal￨L￨JJ￨O￨- power￨L￨NN￨O￨- settings￨L￨NNS￨O￨- assuming￨L￨VBG￨O￨- known￨L￨JJ￨O￨- channel￨L￨NN￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- fixed￨L￨VBD￨O￨- signature￨L￨NN￨O￨- and￨L￨CC￨O￨- linear￨L￨JJ￨O￨- receiver￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- in￨L￨IN￨O￨- CDMA￨U￨NNP￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- utility￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- expended￨L￨VBD￨O￨- power￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- Nash￨U￨NNP￨PERSON￨- bargaining￨L￨NN￨O￨- solution￨L￨NN￨O￨- ,￨L￨,￨O￨- whi￨L￨NN￨O￨- ch￨L￨NN￨COUNTRY￨- sheds￨L￨VBZ￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- power￨L￨NN￨O￨- assignment￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- game￨L￨NN￨O￨- theoretic￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨A region￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- power￨L￨NN￨O￨- allocations￨L￨NNS￨O￨- for￨L￨IN￨O￨- K￨U￨NNP￨O￨- users￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- everybody￨L￨NN￨O￨- meets￨L￨VBZ￨O￨- a￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- signal-to-interference￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Otherwise￨U￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- balance￨L￨NN￨O￨- con￨L￨NN￨O￨- flicting￨L￨VBG￨O￨- interests￨L￨NNS￨O￨- ,￨L￨,￨O￨- w￨L￨NN￨O￨- e￨L￨SYM￨O￨- suggest￨L￨VBP￨O￨- the￨L￨DT￨O￨- projection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨A region￨L￨NN￨O￨- onto￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- viable￨L￨JJ￨O￨- power￨L￨NN￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Span￨U￨NN￨O￨- ´￨L￨''￨O￨- o￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- Wright￨U￨NNP￨PERSON￨- –￨L￨:￨O￨- Fisher￨U￨NNP￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- type￨L￨NN￨O￨- a￨L￨DT￨O￨- genes￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨- a￨L￨DT￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- and￨L￨CC￨O￨- A￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- transition￨L￨NN￨O￨- density￨L￨NN￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- eigenfunction￨L￨NN￨O￨- expansion￨L￨NN￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- ;￨L￨:￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- fα￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- ρθ￨L￨NN￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- eP￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- n￨L￨NN￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- eP￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∞￨L￨SYM￨O￨- Xn￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- θ￨L￨NN￨O￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- +￨L￨CC￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- n￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- expn￨L￨NN￨O￨- −￨L￨NN￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- θ￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- ρθ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- eP￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- +￨L￨CC￨O￨- are￨L￨VBP￨O￨- orthonormal￨L￨JJ￨O￨- Jacobi￨U￨NNP￨PERSON￨- polynomials￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Beta￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- scaled￨L￨VBN￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- Y￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- δmn￨L￨NN￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- Y￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- eP￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- stationary￨L￨JJ￨O￨A distribution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- {￨L￨-LRB-￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reversible￨L￨JJ￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- Beta￨U￨NN￨O￨- stationary￨L￨JJ￨O￨A density￨L￨NN￨O￨- fα￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- yα￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- β￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- y￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- generator￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨A is￨L￨VBZ￨O￨- 1￨L￨CD￨NUMBER￨- L￨U￨NN￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- αx￨L￨NN￨O￨- +￨L￨CC￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∂￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ∂￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- mutation￨L￨NN￨O￨- rate￨L￨NN￨O￨- A￨U￨DT￨O￨- →￨L￨SYM￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- 2￨L￨CD￨NUMBER￨- α￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- a￨L￨DT￨O￨- →￨L￨NN￨O￨- A￨U￨NN￨O￨- is￨L￨VBZ￨O￨- 2￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- classical￨L￨JJ￨O￨- Jacobi￨U￨NNP￨PERSON￨- polynomials￨L￨NNS￨O￨- ,￨L￨,￨O￨- orthogonal￨L￨JJ￨O￨- on￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- α￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- x￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨A as￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- n￨L￨NN￨O￨- !￨L￨.￨O￨- +Modeling￨U￨VBG￨O￨- cellular￨L￨JJ￨O￨- base￨L￨NN￨O￨- stations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- BSs￨U￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PPP￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- explicit￨L￨JJ￨O￨- finite-integral￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨A prob￨L￨NN￨O￨- ability￨L￨NN￨O￨- with￨L￨IN￨O￨- ICIC￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- ICD￨U￨NN￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- temporal/spectral￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- signal￨L￨NN￨O￨- and￨L￨CC￨O￨- interference￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- high-spectral￨L￨JJ￨O￨- ef￨L￨NN￨O￨- ficiency￨L￨NN￨O￨- regime￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- threshold￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- in￨L￨IN￨O￨- finity￨L￨NN￨O￨- ,￨L￨,￨O￨- th￨L￨DT￨O￨- e￨L￨SYM￨O￨- order￨L￨NN￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨A probability￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- exist￨L￨VB￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- difference￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- ICIC￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- scheme￨L￨NN￨O￨- than￨L￨IN￨O￨- ICD￨U￨NN￨O￨- for￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- exponents￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- high-reliability￨L￨JJ￨O￨- regime￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- user￨L￨NN￨O￨- outage￨L￨NN￨O￨- probability￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ICIC￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- ICD￨U￨NN￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- coverage￨L￨NN￨O￨A in￨L￨IN￨O￨- drastically￨L￨RB￨O￨- different￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- :￨L￨:￨O￨- ICD￨U￨NN￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- order￨L￨NN￨O￨- gain￨L￨NN￨O￨- while￨L￨IN￨O￨- ICIC￨U￨NN￨ORGANIZATION￨- only￨L￨RB￨O￨- offers￨L￨VBZ￨O￨- gain￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- PPP￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- predicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨A probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- user￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- signal-to-interference-plus-noise￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SINR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- set￨L￨VBN￨O￨- to￨L￨TO￨O￨- 0￨L￨CD￨NUMBER￨- dB￨L￨NN￨O￨- —￨L￨:￨O￨- eve￨L￨NN￨O￨- n￨L￨NN￨O￨- if￨L￨IN￨O￨- noise￨L￨NN￨O￨- is￨L￨VBZ￨O￨- neglected￨L￨VBN￨O￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- Inter-cell￨U￨NN￨O￨- interference￨L￨NN￨O￨- coordination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ICIC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- intra-cell￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ICD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- play￨L￨VBP￨O￨- important￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- improving￨L￨VBG￨O￨- cellular￨L￨JJ￨O￨- downlink￨L￨NN￨O￨- coverage￨L￨NN￨O￨A .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- evidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- dynamic￨L￨JJ￨O￨- clusters￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- user￨L￨NN￨O￨- locations￨L￨NNS￨O￨- and￨L￨CC￨O￨- channel￨L￨NN￨O￨- propagation￨L￨NN￨O￨- features￨L￨VBZ￨O￨- perform￨L￨VB￨O￨- far￨L￨RB￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- their￨L￨PRP$￨O￨- fixed￨L￨JJ￨O￨- counterparts￨L￨NNS￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- clear￨L￨JJ￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- extending￨L￨VBG￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- geometry￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- to￨L￨TO￨O￨- such￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- cooperation￨L￨NN￨O￨- structures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Analytical￨U￨NNP￨O￨- expressions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- complementary￨L￨JJ￨O￨- cumulative￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- function￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CCDF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- instantaneous￨L￨JJ￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- relevant￨L￨JJ￨O￨- system￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- chiefly￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- BSs￨U￨NNS￨O￨- forming￨L￨VBG￨O￨- the￨L￨DT￨O￨- coordination￨L￨NN￨O￨- clusters￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- antennas￨L￨NNS￨O￨- per￨L￨IN￨O￨- BS￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- pathloss￨L￨NN￨O￨- exponent￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- coordinated￨L￨VBN￨O￨- beamforming￨L￨NN￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- beneficial￨L￨JJ￨O￨- to￨L￨TO￨O￨- users￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- outer￨L￨JJ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- cells￨L￨NNS￨O￨- yet￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- inner￨L￨JJ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- coordination￨L￨NN￨O￨- cluster￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- cardinality￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- user￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- scales￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- fading￨L￨JJ￨O￨A coherence￨L￨NN￨O￨- .￨L￨.￨O￨- +Utilizing￨U￨VBG￨O￨- this￨L￨DT￨O￨- CCDF￨U￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- pilot￨L￨NN￨TITLE￨- overheads￨L￨NNS￨O￨- further￨L￨RBR￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- BS￨U￨NN￨O￨- coordination￨L￨NN￨O￨- clusters￨L￨NNS￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- fading￨L￨JJ￨O￨- coherence￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- algorithm￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- RRHs￨U￨NNS￨O￨- ’￨L￨POS￨O￨- and￨L￨CC￨O￨- users￨L￨NNS￨O￨- ’￨L￨POS￨O￨- locations￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- the￨L￨DT￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- complementary￨L￨JJ￨O￨- cumulative￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- function￨L￨NN￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- algorithm￨L￨NN￨O￨A consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- phases￨L￨NNS￨O￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- phase￨L￨NN￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- remote￨L￨JJ￨O￨- radio￨L￨NN￨O￨- head￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RRH￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- determines￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- candidate￨L￨NN￨TITLE￨- set￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- predefined￨L￨JJ￨O￨- selection￨L￨NN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- approximating￨L￨VBG￨O￨- the￨L￨DT￨O￨- derived￨L￨VBN￨O￨- expression￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- optimum￨L￨JJ￨O￨- selection￨L￨NN￨O￨A threshold￨L￨NN￨O￨- that￨L￨WDT￨O￨- maximizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- complexity￨L￨NN￨O￨- antenna￨L￨NN￨O￨- selection￨L￨NN￨O￨- algorithm￨L￨NN￨O￨A for￨L￨IN￨O￨- low￨L￨JJ￨O￨- target￨L￨NN￨O￨- rate￨L￨NN￨O￨- users￨L￨NNS￨O￨- in￨L￨IN￨O￨- cloud￨L￨NN￨O￨- radio￨L￨NN￨O￨- access￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- obtained￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- characterize￨L￨VBP￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- algorithm￨L￨NN￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- regime￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- RRH￨U￨NN￨O￨- density￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- in￨L￨IN￨O￨- finity￨L￨NN￨O￨- .￨L￨.￨O￨- +•￨L￨SYM￨O￨- The￨U￨DT￨O￨- nonlinear￨L￨JJ￨O￨- functional￨L￨JJ￨O￨A response￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- F￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- m2I￨L￨NN￨O￨- h￨L￨NN￨O￨- ·￨L￨NN￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- l￨L￨NN￨O￨- •￨L￨SYM￨O￨- The￨U￨DT￨O￨- Beddington-DeAngelis￨U￨NNP￨O￨- functional￨L￨JJ￨O￨- response￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- F￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- m1S￨L￨NN￨O￨- +￨L￨CC￨O￨- m2I￨L￨NN￨O￨- ·￨L￨NN￨O￨- For￨U￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- these￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- property￨L￨NN￨O￨- :￨L￨:￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stale￨L￨JJ￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- see￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- point￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- white￨L￨JJ￨O￨- noises￨L￨NNS￨O￨- ,￨L￨,￨O￨- µS￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- µS￨L￨NN￨O￨- +￨L￨CC￨O￨- σ1￨L￨NN￨O￨- ˙B1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- µI￨L￨NN￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- µI￨L￨NN￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- +￨L￨CC￨O￨- σ2￨L￨NN￨O￨- ˙B2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- Bi￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- Brownian￨U￨JJ￨MISC￨- motions￨L￨NNS￨O￨- dS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- a1￨L￨NN￨O￨- −￨L￨NN￨O￨- b1S￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A +￨L￨CC￨O￨- σ1S￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dB1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- b2I￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- +￨L￨CC￨O￨- σ2I￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dB2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- rewritten￨L￨VBN￨O￨- the￨L￨DT￨O￨- coefficients￨L￨NNS￨O￨- :￨L￨:￨O￨- b1￨L￨NN￨O￨- =￨L￨JJ￨O￨- µS￨L￨NN￨O￨- ,￨L￨,￨O￨- b2￨L￨NN￨O￨- =￨L￨JJ￨O￨- µI￨L￨NN￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- and￨L￨CC￨O￨- F￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- special￨L￨JJ￨O￨- other￨L￨JJ￨O￨- motivation￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- acts￨L￨VBZ￨O￨- on￨L￨IN￨O￨- some￨L￨DT￨O￨- i.e￨L￨FW￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- →￨L￨FW￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ˙B3￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- functional￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- ,￨L￨,￨O￨- dS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- a1￨L￨NN￨O￨- −￨L￨NN￨O￨- b1S￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A −￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dB3￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- equation￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- b2I￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dB3￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Precisely￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- equation￨L￨NN￨O￨- as￨L￨IN￨O￨- following￨L￨VBG￨O￨- dS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- a1￨L￨NN￨O￨- −￨L￨NN￨O￨- b1S￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A +￨L￨CC￨O￨- σ1S￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dB1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dB3￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- b2I￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- +￨L￨CC￨O￨- σ2I￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dB2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- dB3￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- any￨L￨DT￨O￨- initial￨L￨JJ￨O￨- point￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- u￨L￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- R2￨U￨NN￨O￨- ,￨L￨,￨O￨- ◦￨L￨VBP￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- global￨L￨JJ￨O￨- solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Su￨U￨FW￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Iu￨U￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- u￨L￨NN￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- using￨L￨VBG￨O￨- mathematics￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- church￨L￨NN￨O￨- growth￨L￨NN￨O￨A is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- ideas￨L￨NNS￨O￨- from￨L￨IN￨O￨- population￨L￨NN￨O￨- modeling￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- church￨L￨NN￨O￨- growth￨L￨NN￨O￨A situations￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- ma￨L￨FW￨O￨- jor￨L￨FW￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- growth￨L￨NN￨O￨A is￨L￨VBZ￨O￨- through￨L￨IN￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- religious￨L￨JJ￨O￨- enthusiasts￨L￨NNS￨O￨- and￨L￨CC￨O￨- unbelievers￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- enthusiasts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- enthusiastic￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- even￨L￨RB￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- like￨L￨IN￨O￨- this￨L￨DT￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- churches￨L￨NNS￨O￨- grow￨L￨VBP￨O￨A ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- religious￨L￨JJ￨O￨- revival￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- latter￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- best￨L￨JJS￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- or￨L￨CC￨O￨- graphs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- communities￨L￨NNS￨O￨- ,￨L￨,￨O￨- power￨L￨NN￨O￨- plants￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- computers￨L￨NNS￨O￨A are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- links￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- acquaintance￨L￨NN￨O￨- among￨L￨IN￨O￨- people￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- computers￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Susceptible-Infected-Refractory￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- recovered/removal￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Ref￨U￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- take￨L￨VBP￨O￨- place￨L￨NN￨O￨- through￨L￨IN￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- nodes￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- understandably￨L￨RB￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- determining￨L￨VBG￨O￨- role￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- nodes￨L￨NNS￨O￨- connected￨L￨VBN￨O￨A randomly￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- substantial￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- eventually￨L￨RB￨O￨- recovered￨L￨VBD￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- H￨U￨NN￨O￨- independent￨L￨JJ￨RELIGION￨- hierarchies￨L￨NNS￨O￨- or￨L￨CC￨O￨- dimensions￨L￨NNS￨O￨A ,￨L￨,￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- groupings￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- layers￨L￨NNS￨O￨- of￨L￨IN￨O￨- subgroups￨L￨NNS￨O￨- .￨L￨.￨O￨- +epl￨L￨NN￨O￨- draft￨L￨NN￨O￨- Robust￨U￨JJ￨O￨- oscillations￨L￨NNS￨O￨A in￨L￨IN￨O￨- SIS￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- :￨L￨:￨O￨- Coarse-graining￨U￨NN￨O￨- by￨L￨IN￨O￨- automated￨L￨JJ￨O￨- moment￨L￨NN￨O￨- closure￨L￨NN￨O￨- Thilo￨U￨NNP￨O￨- Gross1￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Ioannis￨U￨NNP￨PERSON￨- G.￨U￨NNP￨PERSON￨- -￨L￨:￨O￨- We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- investigations￨L￨NNS￨O￨- reveal￨L￨VBP￨O￨- that￨L￨IN￨O￨- global￨L￨JJ￨O￨- coupling￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- enters￨L￨VBZ￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- awareness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- robust￨L￨JJ￨O￨- large-amplitude￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- combines￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- rewiring￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- connections￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- topological￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- to￨L￨TO￨O￨- quantitatively￨L￨RB￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨A viruses￨L￨NNS￨O￨- we￨L￨PRP￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- simultaneously￨L￨RB￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 14-17￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- communication￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 18-21￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨- users￨L￨NNS￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- MMS￨U￨NNP￨O￨- virus￨L￨NN￨O￨- can￨L￨MD￨O￨- send￨L￨VB￨O￨- a￨L￨DT￨O￨- copy￨L￨NN￨O￨- of￨L￨IN￨O￨- itself￨L￨PRP￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨A phones￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- numbers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- phone￨L￨NN￨O￨- ’s￨L￨POS￨O￨- address￨L￨NN￨O￨- book￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- range￨L￨NN￨O￨- spreading￨L￨NN￨O￨- pattern￨L￨NN￨O￨- previously￨L￨RB￨DATE￨- exploited￨L￨VBN￨O￨- only￨L￨RB￨O￨- by￨L￨IN￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨- users￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- characterizing￨L￨VBG￨O￨- a￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- virus￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- while￨L￨IN￨O￨- Bluetooth￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- can￨L￨MD￨O￨- reach￨L￨VB￨O￨- all￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- handsets￨L￨NNS￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- spread￨L￨VBD￨O￨- slowly￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨A ,￨L￨,￨O￨- offering￨L￨VBG￨O￨- ample￨L￨JJ￨O￨- opportunities￨L￨NNS￨O￨- to￨L￨TO￨O￨- deploy￨L￨VB￨O￨- antiviral￨L￨JJ￨O￨- software￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- may￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- and￨L￨CC￨O￨- reliable￨L￨JJ￨O￨- CG￨U￨NN￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- studying￨L￨VBG￨O￨- size￨L￨NN￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- best￨L￨JJS￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- attempt￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- made￨L￨VBN￨O￨- for￨L￨IN￨O￨- developing￨L￨VBG￨O￨- CG￨U￨NNP￨O￨- simulation￨L￨NN￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- usually￨L￨RB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- degree-based￨L￨JJ￨O￨- CG￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- d-CG￨L￨NN￨O￨- for￨L￨IN￨O￨- short￨L￨JJ￨O￨- hereafter￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- statistically￨L￨RB￨O￨A consistent￨L￨JJ￨O￨- scheme￨L￨NN￨O￨- ,￨L￨,￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- annealed￨L￨JJ￨O￨- network￨L￨NN￨O￨- approximation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ANA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- CG￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- oscillators￨L￨NNS￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- gene￨L￨NN￨O￨- regulatory￨L￨JJ￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- adaptive￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨A network￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- d-CG￨L￨NN￨O￨- approach￨L￨NN￨O￨A that￨L￨WDT￨O￨- merges￨L￨VBZ￨O￨- together￨L￨RB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- similar￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- does￨L￨VBZ￨O￨- warrant￨L￨VB￨O￨- the￨L￨DT￨O￨- CSC￨U￨NNP￨ORGANIZATION￨- within￨L￨IN￨O￨- ANA￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- studies￨L￨VBZ￨O￨- a￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- including￨L￨VBG￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- receive￨L￨VB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transmit￨L￨VB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- qualitative￨L￨JJ￨O￨- conclusion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- R0￨U￨NN￨O￨- gets￨L￨VBZ￨O￨- larger￨L￨JJR￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- heterogeneous￨L￨JJ￨O￨- but￨L￨CC￨O￨- that￨L￨IN￨O￨- different￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- weight￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- sometimes￨L￨RB￨O￨- have￨L￨VB￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- homogenizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- making￨L￨VBG￨O￨- R0￨U￨NN￨O￨- smaller￨L￨JJR￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- precisely￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- want￨L￨VBP￨O￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- how￨L￨WRB￨O￨- individual￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨A affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- composed￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- weighted￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- social￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- sexual￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- configuration￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- where￨L￨WRB￨O￨- edges￨L￨NNS￨O￨- have￨L￨VBP￨O￨- weights￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- reflecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sex-contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- R0￨U￨NN￨O￨- obtained￨L￨VBN￨O￨- for￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨A for￨L￨IN￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- VX￨U￨NN￨O￨- =￨L￨JJ￨O￨- C￨U￨NN￨O￨- VY￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- analysed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- suppress￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- explosion￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- wherein￨L￨WRB￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨- with￨L￨IN￨O￨- any￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- assigned￨L￨VBN￨O￨- a￨L￨DT￨O￨- curing￨L￨VBG￨O￨A rate￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- kα￨L￨VB￨O￨- with￨L￨IN￨O￨- k￨L￨NN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- α￨L￨VB￨O￨- an￨L￨DT￨O￨- adjustable￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- work￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- efficiently￨L￨RB￨O￨- suppress￨L￨VB￨O￨A epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- subpopulations￨L￨NNS￨O￨- with￨L￨IN￨O￨- higher￨L￨JJR￨O￨- degrees￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- allocated￨L￨VBN￨O￨- more￨L￨RBR￨O￨- resources￨L￨NNS￨O￨- than￨L￨IN￨O￨- just￨L￨RB￨O￨- being￨L￨VBG￨O￨- linearly￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- addressed￨L￨VBN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- question￨L￨NN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- µk￨L￨NN￨O￨- ∼￨L￨NN￨O￨- kα￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- k￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨A degree￨L￨NN￨O￨A and￨L￨CC￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- adjustable￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- studies￨L￨NNS￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- have￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- the￨L￨DT￨O￨- curing￨L￨VBG￨O￨A rate￨L￨NN￨O￨- µ￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- homogenous￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- interesting￨L￨JJ￨O￨- to￨L￨TO￨O￨- ask￨L￨VB￨O￨- :￨L￨:￨O￨- how￨L￨WRB￨O￨- would￨L￨MD￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ρc￨L￨NN￨O￨- ,￨L￨,￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- k￨L￨NN￨O￨- -￨L￨:￨O￨- dependent￨L￨JJ￨O￨- curing￨L￨VBG￨O￨A strategy￨L￨NN￨O￨- ?￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- immunization￨L￨NN￨O￨- effectively￨L￨RB￨O￨- prevent￨L￨VBP￨O￨- computer￨L￨NN￨O￨A viruses￨L￨NNS￨O￨A propagation￨L￨NN￨O￨- on￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- should￨L￨MD￨O￨- install￨L￨VB￨O￨- antivirus￨L￨JJ￨O￨- programs￨L￨NNS￨O￨- in￨L￨IN￨O￨- every￨L￨DT￨O￨- computer￨L￨NN￨O￨- node￨L￨NN￨O￨- and￨L￨CC￨O￨- frequently￨L￨RB￨O￨- update￨L￨VBP￨O￨- those￨L￨DT￨O￨- programs￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- computer￨L￨NN￨O￨A recovers￨L￨VBZ￨O￨- and￨L￨CC￨O￨- returns￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨- node￨L￨NN￨O￨- Jinyu￨U￨NNP￨PERSON￨- Huang￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- Eradicating￨U￨NNP￨O￨- Computer￨U￨NNP￨O￨- Viruses￨U￨NNS￨O￨- on￨L￨IN￨O￨- Networks￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- rewire￨L￨NN￨O￨- probability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- similar￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- ER￨U￨NN￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- viewed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- dρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- λhkiρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- hki￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨A network￨L￨NN￨O￨- and￨L￨CC￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +7￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- Jinyu￨U￨NNP￨PERSON￨- Huang￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- Eradicating￨U￨NNP￨O￨- Computer￨U￨NNP￨O￨- Viruses￨U￨NNS￨O￨- on￨L￨IN￨O￨- Networks￨U￨NNP￨O￨- Relevant￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- immunization￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- efficient￨L￨JJ￨O￨- on￨L￨IN￨O￨- SF￨U￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- α￨L￨NN￨O￨- vertices￨L￨NNS￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- recover￨L￨VB￨O￨- after￨L￨IN￨O￨- they￨L￨PRP￨O￨- become￨L￨VBP￨O￨- infective￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- better￨L￨JJR￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- SI￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- susceptible/infective￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- behavior￨L￨NN￨O￨- among￨L￨IN￨O￨- those￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- α￨L￨NN￨O￨- vertices￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- infinite￨L￨JJ￨O￨- topological￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- Barab￨U￨NNP￨PERSON￨- ´￨L￨POS￨O￨- asi-Albert￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- BA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- graph￨L￨NN￨O￨- slow￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- tree￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- weighting￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- suppress￨L￨VBP￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- propagation￨L￨NN￨O￨- among￨L￨IN￨O￨- hubs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- dissortative￨L￨JJ￨O￨- weighing￨L￨VBG￨O￨- scheme￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- wij￨L￨VBP￨O￨- ∈￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- effectively￨L￨RB￨O￨- slow￨L￨VB￨O￨A down￨L￨RP￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- result￨L￨NN￨O￨- in￨L￨IN￨O￨- long￨L￨JJ￨O￨- living￨L￨NN￨O￨- rare￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- causing￨L￨VBG￨O￨- slow￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- information￨L￨NN￨O￨A spreading￨L￨NN￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- denoted￨L￨VBN￨O￨- almost￨L￨RB￨O￨- torus￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- lattice￨L￨NN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- torus￨L￨NN￨O￨- length￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- almost￨L￨RB￨O￨- torus￨L￨NN￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- one￨L￨CD￨NUMBER￨- node￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- removed￨L￨VBN￨O￨A and￨L￨CC￨O￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- 5￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- removed￨L￨VBN￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- removed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- torus￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Almost￨U￨RB￨O￨- torus￨L￨NN￨O￨- networks￨L￨NNS￨O￨- consist￨L￨VBP￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- torus￨L￨NN￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- where￨L￨WRB￨O￨- some￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- edges￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- removed￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- notice￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Laplacian￨U￨NN￨MISC￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- written￨L￨VBN￨O￨- as￨L￨IN￨O￨- L￨U￨NN￨O￨- =￨L￨JJ￨O￨- D￨U￨NN￨O￨- −￨L￨NN￨O￨- A￨U￨NN￨O￨- where￨L￨WRB￨O￨- D￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- diagonal￨L￨JJ￨O￨- matrix￨L￨NN￨O￨A whose￨L￨WP$￨O￨- diagonal￨L￨JJ￨O￨- entries￨L￨NNS￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- and￨L￨CC￨O￨- A￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- systems￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- runs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- non-stationary￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- hence￨L￨RB￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- ∆￨L￨NN￨O￨- should￨L￨MD￨O￨- increase￨L￨VB￨O￨- getting￨L￨VBG￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- ,￨L￨,￨O￨- still￨L￨RB￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ∆￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- finite￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- exhibits￨L￨VBZ￨O￨A a￨L￨DT￨O￨- power-law￨L￨NN￨O￨- tail￨L￨NN￨O￨- ,￨L￨,￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ∆￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∼￨L￨SYM￨O￨- ∆￨L￨SYM￨O￨- −￨L￨SYM￨O￨- x￨L￨CC￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- exponent￨L￨NN￨O￨- x￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1.85￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- least￨L￨JJS￨O￨- square￨L￨JJ￨O￨- fitting￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Activity￨U￨NN￨O￨- driven￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- possess￨L￨VBP￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- selected￨L￨VBN￨O￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- ,￨L￨,￨O￨- node-dependent￨L￨JJ￨O￨- activity￨L￨NN￨O￨A potential￨L￨JJ￨O￨- Vi￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- exhibits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- F￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ∝￨L￨CD￨NUMBER￨- V￨U￨NN￨O￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- .￨L￨.￨O￨- +Times￨U￨NNP￨O￨- between￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- communication￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- deviate￨L￨VB￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- an￨L￨DT￨O￨- intermittent￨L￨JJ￨O￨- switching￨L￨NN￨O￨- between￨L￨IN￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- low￨L￨JJ￨O￨- activity￨L￨NN￨O￨A and￨L￨CC￨O￨- high￨L￨JJ￨O￨- activity￨L￨NN￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- fat-tailed￨L￨JJ￨O￨- inter-communication￨L￨NN￨O￨- time￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- I￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- by￨L￨IN￨O￨- extensive￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- if￨L￨IN￨O￨- rare-region￨L￨NN￨O￨- effects￨L￨NNS￨O￨- and￨L￨CC￨O￨- bursty￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- CP￨U￨NN￨O￨- or￨L￨CC￨O￨- Annihilating￨U￨VBG￨O￨- Random￨U￨NNP￨O￨- Walk￨U￨VB￨O￨- (￨L￨-LRB-￨O￨- ARW￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- processes￨L￨VBZ￨O￨- running￨L￨VBG￨O￨- on￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +dependent￨L￨JJ￨O￨- runs￨L￨NNS￨O￨- these￨L￨DT￨O￨- timing￨L￨NN￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- analyzed￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨A distribution￨L￨NN￨O￨A P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ∆￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- calculated￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- an￨L￨DT￨O￨- analytically￨L￨RB￨O￨A and￨L￨CC￨O￨- computationally￨L￨RB￨O￨- tractable￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- Kolmogorovlike￨U￨JJ￨LOCATION￨- forward￨L￨RB￨O￨- equations￨L￨NNS￨O￨- utilising￨L￨VBG￨O￨- the￨L￨DT￨O￨- Caputo￨U￨NNP￨PERSON￨- derivative￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- having￨L￨VBG￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- solve￨L￨VB￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +Cost-Optimal￨U￨JJ￨O￨- Switching￨U￨NN￨O￨- Protection￨U￨NN￨O￨- Strategy￨U￨NN￨O￨- in￨L￨IN￨O￨- Adaptive￨U￨JJ￨O￨- Networks￨U￨NNP￨O￨- Masaki￨U￨NNP￨PERSON￨- Ogura￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Victor￨U￨NNP￨ORGANIZATION￨- M.￨U￨NNP￨ORGANIZATION￨- 3￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 5￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- adaptation￨L￨NN￨O￨A mechanism￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- over￨L￨IN￨O￨- switching￨L￨NN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- adaptive￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- cost￨L￨NN￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- switching￨L￨VBG￨O￨- edges￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimization￨L￨NN￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- cost-optimal￨L￨JJ￨O￨- network￨L￨NN￨O￨- adaptation￨L￨NN￨O￨A law￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- costoptimal￨L￨JJ￨O￨- edge￨L￨NN￨O￨- switching￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- joint￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- “￨L￨``￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ”￨L￨''￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- “￨L￨``￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- conditions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- adaptation￨L￨NN￨O￨A law￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- switching￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reasons￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨- induces￨L￨VBZ￨O￨- an￨L￨DT￨O￨- adaptation￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- that￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- accordance￨L￨NN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- exponents￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- networks￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- conjecture￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- HMF￨U￨NN￨O￨- theory￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- universal￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- absorbing￨L￨VBG￨O￨A state￨L￨NN￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- locality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- absorbing￨L￨VBG￨O￨- states￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- highly￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- element￨L￨NN￨O￨- or￨L￨CC￨O￨- vertex￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- k￨L￨NN￨O￨- vertices￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- showing￨L￨VBG￨O￨A a￨L￨DT￨O￨- heavy-tailed￨L￨JJ￨O￨- form￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- strong￨L￨JJ￨O￨- impact￨L￨NN￨O￨- in￨L￨IN￨O￨- processes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- percolation￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- synchronization￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Ferreira￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ∗￨L￨NN￨O￨- and￨L￨CC￨O￨- Romualdo￨U￨NNP￨PERSON￨- Pastor-Satorras2￨U￨NN￨O￨- 1Departamento￨L￨NN￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- ,￨L￨,￨O￨- Universidade￨U￨NNP￨ORGANIZATION￨- Federal￨U￨NNP￨ORGANIZATION￨- de￨L￨NNP￨ORGANIZATION￨- Vi￨U￨NNP￨ORGANIZATION￨- ¸￨L￨NNP￨O￨- cosa￨L￨NN￨O￨- ,￨L￨,￨O￨- 36571-000￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Vi￨U￨NNP￨O￨- ¸￨L￨NNP￨O￨- cosa￨L￨SYM￨O￨- -￨L￨:￨O￨- MG￨U￨NN￨O￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- 2Departament￨L￨NNP￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- i￨L￨FW￨O￨- Enginyeria￨U￨NNP￨ORGANIZATION￨- Nuclear￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Universitat￨U￨NNP￨O￨- Polit￨U￨NNP￨O￨- `￨L￨``￨O￨- ecnica￨L￨FW￨O￨- de￨L￨FW￨O￨- Catalunya￨U￨FW￨O￨- ,￨L￨,￨O￨- Campus￨U￨NNP￨O￨- Nord￨U￨NNP￨O￨- B4￨U￨NN￨O￨- ,￨L￨,￨O￨- 08034￨L￨CD￨NUMBER￨- Barcelona￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- We￨U￨PRP￨O￨- instigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TCP￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- showing￨L￨VBG￨O￨- an￨L￨DT￨O￨- absorbing-state￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- with￨L￨IN￨O￨- infinitely￨L￨RB￨O￨- many￨L￨JJ￨O￨- absorbing￨L￨VBG￨O￨A states￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- finite￨L￨NN￨O￨- size￨L￨NN￨O￨- scaling￨L￨VBG￨O￨- exponents￨L￨NNS￨O￨A characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- mean￨L￨NN￨O￨- field￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HMF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- approximation￨L￨NN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- extensive￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- played￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- processes￨L￨NNS￨O￨- with￨L￨IN￨O￨- absorbing￨L￨VBG￨O￨A states￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- that￨L￨IN￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- usually￨L￨RB￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- formulated￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and/or￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- or￨L￨CC￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- motif￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and/or￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- connections￨L￨NNS￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- has￨L￨VBZ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Unfortunately￨U￨RB￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- comes￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨A scales￨L￨NNS￨O￨- exponentially￨L￨RB￨O￨- as￨L￨IN￨O￨- aN￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- models￨L￨NNS￨O￨- range￨L￨VBP￨O￨- from￨L￨IN￨O￨- classic￨L￨JJ￨O￨- mean￨L￨NN￨O￨- field￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- pairwise￨L￨JJ￨O￨A NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- het￨L￨NN￨O￨- erogenous￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- effective￨L￨JJ￨O￨- degree￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- individual-level￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- name￨L￨VB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- Complex￨U￨NN￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- recently￨L￨RB￨DATE￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- active￨L￨JJ￨O￨- research￨L￨NN￨O￨- topics￨L￨NNS￨O￨- in￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- physics￨L￨NNS￨O￨- and￨L￨CC￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- disciplines￨L￨NNS￨O￨- .1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- topology￨L￨NN￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- multiscale￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- spanning￨L￨VBG￨O￨- from￨L￨IN￨O￨- microscopic￨L￨JJ￨O￨A via￨L￨IN￨O￨- mesoscopic￨L￨JJ￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- macroscopic￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- like￨L￨IN￨O￨- human￨L￨JJ￨O￨- multiscale￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,9￨L￨CD￨NUMBER￨- module￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,10￨L￨CD￨NUMBER￨- multilayer￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,11￨L￨CD￨NUMBER￨- interconnected￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,12￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,13￨L￨CD￨NUMBER￨- etc￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- general￨L￨JJ￨TITLE￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- networked￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- just￨L￨RB￨O￨- adopting￨L￨VBG￨O￨- appropriate￨L￨JJ￨O￨- microscopic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- coarse￨L￨JJ￨O￨A graining￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- HMCG￨U￨NN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- works￨L￨VBZ￨O￨- very￨L￨RB￨O￨- well￨L￨RB￨O￨- in￨L￨IN￨O￨- reproducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨A models￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- accelerates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- with￨L￨IN￨O￨- signi￨L￨NNS￨O￨- ficant￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- savings￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- microscopic￨L￨JJ￨O￨- MC￨U￨NNP￨O￨- simulations￨L￨NNS￨O￨- directly￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- hybrid￨L￨NN￨O￨- multiscale￨L￨JJ￨O￨- coarse-grained￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- HMCG￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- which￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fine￨L￨NN￨O￨- Monte￨U￨NNP￨O￨- Carlo￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- MC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- simulation￨L￨NN￨O￨- on￨L￨IN￨O￨- th￨L￨DT￨O￨- e￨L￨SYM￨O￨- par￨L￨IN￨O￨- t￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- coarse￨L￨JJ￨O￨A Langevin￨U￨NN￨PERSON￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- par￨L￨NN￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +Introducing￨U￨VBG￨O￨- a￨L￨DT￨O￨- coupling￨L￨NN￨O￨- parameter￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- smaller￨L￨JJR￨O￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- perform￨L￨VBP￨O￨- an￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- spectrum￨L￨NN￨O￨- of￨L￨IN￨O￨- eigenvalues￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hierarchical￨L￨JJ￨O￨- product￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- here￨L￨RB￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- ’s￨L￨POS￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- N￨U￨NN￨O￨- ×￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- matrix￨L￨NN￨O￨- A￨U￨NN￨O￨- whose￨L￨WP$￨O￨- entries￨L￨NNS￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- edges￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- Aij￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- if￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- i￨L￨LS￨O￨- and￨L￨CC￨O￨- j￨L￨NN￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- otherwise￨L￨RB￨O￨- Structurally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- eigenvalues￨L￨NNS￨O￨A of￨L￨IN￨O￨- A￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- community￨L￨NN￨O￨- structures￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- limit￨L￨NN￨O￨- points￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- eigenvalue￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- limits￨L￨NNS￨O￨- of￨L￨IN￨O￨- small￨L￨JJ￨O￨- and￨L￨CC￨O￨- large￨L￨JJ￨O￨- coupling￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- leading-order￨L￨NN￨O￨- relaxation￨L￨NN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- values￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvalues￨L￨NNS￨O￨A and￨L￨CC￨O￨- eigenvectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- smaller￨L￨JJR￨O￨- graphs￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- great￨L￨JJ￨O￨- deal￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- structural￨L￨JJ￨O￨- and￨L￨CC￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- graph￨L￨NN￨O￨- or￨L￨CC￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvalue￨L￨NN￨O￨A sprectrum￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- associated￨L￨VBN￨O￨- coupling￨L￨NN￨O￨- matrices￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- eigenvalue￨L￨JJ￨O￨- spectrum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨A matrix￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- hierarchical￨L￨JJ￨O￨- product￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- graphs￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- novel￨L￨JJ￨O￨- multiple-contagion￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨A network￨L￨NN￨O￨- could￨L￨MD￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- spreading￨L￨VBG￨O￨- phenomena￨L￨NNS￨O￨- including￨L￨VBG￨O￨- communicable￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- cultural￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- addictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- information￨L￨NN￨O￨- spread￨L￨NN￨O￨- through￨L￨IN￨O￨- e-mail￨L￨JJ￨O￨- messages￨L￨NNS￨O￨- ,￨L￨,￨O￨- web￨L￨NN￨O￨- blogs￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- computer￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- contagions￨L￨NNS￨O￨- on￨L￨IN￨O￨- multilayer￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- different￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- channels￨L￨NNS￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- mutations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- while￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨A again￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- γ￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- random￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A are￨L￨VBP￨O￨- the￨L￨DT￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- extinction￨L￨NN￨O￨- in￨L￨IN￨O￨- finite￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- extinction￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- happen￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- analyzed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vast￨L￨JJ￨O￨- ma￨L￨NN￨O￨- jority￨L￨NN￨O￨- of￨L￨IN￨O￨- works￨L￨NNS￨O￨- on￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- –￨L￨:￨O￨- where￨L￨WRB￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- well￨L￨RB￨O￨- above￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- or￨L￨CC￨O￨- bifurcation￨L￨NN￨O￨- point￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- Extinction￨U￨NN￨O￨- Paths￨U￨NNS￨O￨- in￨L￨IN￨O￨- Complex￨U￨NN￨O￨- Networks￨U￨NNP￨O￨- Jason￨U￨NNP￨PERSON￨- Hindes￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ira￨U￨NNP￨O￨- B.￨U￨NNP￨O￨- Applying￨U￨VBG￨O￨- analytical￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- probable￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- optimal￨L￨JJ￨O￨- path￨L￨NN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- state￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- configurations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- quantifies￨L￨NNS￨O￨- characteristic￨L￨JJ￨O￨- scaling￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- path￨L￨NN￨O￨- and￨L￨CC￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A ,￨L￨,￨O￨- both￨L￨DT￨O￨- near￨L￨JJ￨O￨- and￨L￨CC￨O￨- away￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- eigenvector￨L￨NN￨O￨- centrality￨L￨NN￨O￨- and￨L￨CC￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- and￨L￨CC￨O￨- possibly￨L￨RB￨O￨- achieve￨L￨VB￨O￨- extinction￨L￨NN￨O￨A ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- extinction￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- naturally￨L￨RB￨O￨- captured￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- fluctuating￨L￨VBG￨O￨- equilibrium￨L￨NN￨O￨- or￨L￨CC￨O￨- cycle￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- state￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- several￨L￨JJ￨O￨- different￨L￨JJ￨O￨- spread￨L￨NN￨O￨A models￨L￨NNS￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- their￨L￨PRP$￨O￨- relationships￨L￨NNS￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- and￨L￨CC￨O￨- sufficient￨L￨JJ￨O￨- for￨L￨IN￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- present￨L￨JJ￨DATE￨- necessary￨L￨JJ￨O￨- and￨L￨CC￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- learning￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- interest￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- on￨L￨IN￨O￨- SIS￨U￨NNP￨O￨- spread￨L￨VBD￨O￨A models￨L￨NNS￨O￨A over￨L￨IN￨O￨- non-trivial￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- for￨L￨IN￨O￨- discrete￨L￨JJ￨O￨A time￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- parameter￨L￨NN￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- healing￨L￨NN￨O￨- rate￨L￨NN￨O￨- δ￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- some￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- zika￨L￨NN￨O￨A virus￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- published￨L￨VBN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +SIR￨U￨NN￨O￨- type￨L￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- validated￨L￨VBN￨O￨A using￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- found￨L￨VBN￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- several￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- parsimonious￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- both￨L￨CC￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨A populations￨L￨NNS￨O￨A best￨L￨JJS￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Mathematical￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- zika￨L￨NN￨O￨A ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- endogenous￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨A in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- was￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- analytical￨L￨JJ￨O￨A approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- and￨L￨CC￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- systemic￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- who￨L￨WP￨O￨- proposed￨L￨VBD￨O￨- what￨L￨WP￨O￨- would￨L￨MD￨O￨- later￨L￨RB￨O￨- been￨L￨VBN￨O￨- modified￨L￨VBN￨O￨- and￨L￨CC￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- divided￨L￨VBD￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- compartments￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- recovered/removed￨L￨VBN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- devised￨L￨VBD￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- states￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +Analytical￨U￨NNP￨O￨- Modelling￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Spread￨U￨NNP￨O￨- of￨L￨IN￨O￨- Disease￨U￨NNP￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Confined￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Crowded￨U￨NNP￨O￨- Spaces￨U￨NNP￨O￨- Lara￨U￨NNP￨O￨- Gosc￨U￨NNP￨O￨- ´￨L￨POS￨O￨- e￨L￨SYM￨O￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- A.W.￨U￨NNP￨PERSON￨- Barton￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Anders￨U￨NNP￨PERSON￨- Johansson￨U￨NNP￨PERSON￨- ∗￨L￨NNP￨O￨- Faculty￨U￨NNP￨O￨- of￨L￨IN￨O￨- Engineering￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Bristol￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- November￨U￨NNP￨DATE￨- 2￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- until￨L￨IN￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨A describing￨L￨VBG￨O￨A the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- mostly￨L￨RB￨O￨- been￨L￨VBN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRcompartmental￨U￨JJ￨O￨- type￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- homogeneous￨L￨JJ￨O￨- and￨L￨CC￨O￨- well-mixed￨L￨JJ￨O￨- .￨L￨.￨O￨- +Analysing￨U￨VBG￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- that￨L￨WDT￨O￨- arise￨L￨VBP￨O￨- when￨L￨WRB￨O￨- taking￨L￨VBG￨O￨- crowd￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- explicitly￨L￨RB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- walking￨L￨VBG￨O￨- speed￨L￨NN￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- crowd￨L￨NN￨O￨- density￨L￨NN￨O￨A around￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- introducing￨L￨VBG￨O￨- also￨L￨RB￨O￨- an￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- exposed￨L￨VBN￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- becomes￨L￨VBZ￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- ˙S￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- λI￨L￨NN￨O￨- S/N￨U￨NN￨O￨- ˙E￨L￨NN￨O￨- =￨L￨JJ￨O￨- λI￨L￨NN￨O￨- S/N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- kE￨L￨NN￨O￨- ˙I￨L￨NN￨O￨- =￨L￨JJ￨O￨- kE￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- αI￨L￨NN￨O￨- ˙R￨L￨NN￨O￨- =￨L￨JJ￨O￨- αI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- E￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNPS￨O￨- Stochastic￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- ·￨L￨NN￨O￨- Kermack-McKendrick￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ·￨L￨NN￨O￨- NonMarkovian￨U￨JJ￨O￨- ·￨L￨NN￨O￨- Message￨U￨NN￨O￨- passing￨L￨VBG￨O￨A ·￨L￨NN￨O￨- Pairwise￨U￨JJ￨O￨- ·￨L￨NN￨O￨- Network￨U￨NNP￨O￨- Mathematics￨U￨NNP￨O￨- Sub￨U￨NN￨O￨- ject￨L￨NN￨O￨- Classification￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 92D30￨L￨NN￨O￨- ·￨L￨NN￨O￨- 91D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- earliest￨L￨JJS￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- comprehensively￨L￨RB￨O￨- analysed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Kermack￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1927￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- convergence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- monotone￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- follows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- here￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- Kermack-McKendrick￨U￨NNP￨LOCATION￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- contact￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- non-Markovian￨L￨JJ￨MISC￨- pair￨L￨NN￨O￨- approximation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- has￨L￨VBZ￨O￨- well-known￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨- models￨L￨NNS￨O￨- as￨L￨IN￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- it￨L￨PRP￨O￨- takes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- contact￨L￨VB￨O￨A each￨L￨DT￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighbours￨L￨NNS￨O￨- after￨L￨IN￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- correlated￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- write￨L￨VBP￨O￨- down￨L￨RP￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A system￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- prove￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- feasible￨L￨JJ￨O￨- solution￨L￨NN￨O￨- .￨L￨.￨O￨- +bimodal￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- Alen￨U￨VBP￨PERSON￨- Lanˇci￨U￨NN￨PERSON￨- ´￨L￨''￨O￨- ca￨L￨MD￨O￨- ,￨L￨,￨O￨- ∗￨L￨SYM￨O￨- Nino￨U￨NNP￨O￨- Antulov-Fantulinb￨U￨NNP￨O￨- ,￨L￨,￨O￨- †￨L￨NN￨O￨- and￨L￨CC￨O￨- Mile￨U￨NNP￨O￨- ˇSiki￨L￨NNP￨O￨- ´￨L￨POS￨O￨- cb￨L￨NN￨O￨- ‡￨L￨NN￨O￨- aFaculty￨L￨NN￨O￨- bFaculty￨L￨NN￨O￨- of￨L￨IN￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mathematics￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- Electrical￨U￨JJ￨O￨- Engineering￨U￨NNP￨O￨- and￨L￨CC￨O￨- Computing￨U￨NNP￨O￨- ,￨L￨,￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electronic￨U￨NNP￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Information￨U￨NNP￨ORGANIZATION￨- Processing￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Zagreb￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Zagreb￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Croatia￨U￨NNP￨COUNTRY￨- Hrvo￨U￨NNP￨O￨- je￨L￨NN￨O￨- ˇStefanˇci￨L￨NN￨O￨- ´￨L￨''￨O￨- c￨L￨NN￨O￨- §￨L￨CD￨NUMBER￨- Theoretical￨U￨JJ￨O￨- Physics￨U￨NN￨O￨- Division￨U￨NNP￨O￨- ,￨L￨,￨O￨- Rudjer￨U￨NNP￨ORGANIZATION￨- Boˇskovi￨U￨NNP￨ORGANIZATION￨- ´￨L￨POS￨ORGANIZATION￨- c￨L￨NN￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- P.O.B.￨U￨NNP￨O￨- 180￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- HR-10002￨U￨NN￨O￨- Zagreb￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Croatia￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 17￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spreading￨L￨NN￨O￨A on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- on￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- reveal￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- specific￨L￨JJ￨O￨- regimes￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spreading￨L￨NN￨O￨A :￨L￨:￨O￨- local￨L￨JJ￨O￨- containment￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- reproduces￨L￨VBZ￨O￨- qualitative￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- phase￨L￨NN￨O￨- diagrams￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spreading￨L￨NN￨O￨A observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Phase￨U￨NN￨O￨- diagrams￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spreading￨L￨NN￨O￨A for￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- theoretical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spreading￨L￨NN￨O￨A on￨L￨IN￨O￨- m-ary￨L￨JJ￨O￨- tree￨L￨NN￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- both￨L￨DT￨O￨- analytically￨L￨RB￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- β￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- adequate￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- person￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- multiplied￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- τ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- waiting￨L￨VBG￨O￨- time￨L￨NN￨O￨- until￨L￨IN￨O￨- full￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- reads￨L￨VBZ￨O￨- dS￨L￨NN￨O￨- dt￨L￨NN￨O￨A =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- dI￨L￨NNP￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- ,￨L￨,￨O￨- dR￨L￨NN￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- S0￨U￨NN￨O￨- ,￨L￨,￨O￨- I0￨U￨NN￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- popular￨L￨JJ￨O￨- but￨L￨CC￨O￨- rudimentary￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- movement￨L￨NN￨O￨A of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- into￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- assume￨L￨VB￨O￨- some￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- random￨L￨JJ￨O￨- movement￨L￨NN￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- reaction-diffusion￨L￨NN￨O￨- type￨L￨NN￨O￨- equations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- further￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dispersal￨L￨NN￨O￨- behavior￨L￨NN￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- residence-times￨L￨JJ￨O￨- matrix￨L￨NN￨O￨- P￨U￨NN￨O￨- has￨L￨VBZ￨O￨- profound￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- patch￨L￨NN￨O￨A level￨L￨NN￨O￨- with￨L￨IN￨O￨- consequences￨L￨NNS￨O￨- that￨L￨WDT￨O￨- proper￨L￨JJ￨O￨- dispersal￨L￨NN￨O￨- behavior￨L￨NN￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- risk￨L￨NN￨O￨- can￨L￨MD￨O￨- either￨L￨RB￨O￨- promote￨L￨VB￨O￨- or￨L￨CC￨O￨- eliminate￨L￨VB￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- patches￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- n-patch￨L￨NN￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- whose￨L￨WP$￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- computed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- patch￨L￨NN￨O￨A residence-times￨L￨JJ￨O￨- matrix￨L￨NN￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- driven￨L￨VBN￨O￨- decision￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- phenomenological￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- contrast￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- constant￨L￨JJ￨O￨- versus￨L￨CC￨O￨- state￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- P￨U￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨A .￨L￨.￨O￨- +More￨U￨RBR￨O￨- generally￨L￨RB￨O￨- ,￨L￨,￨O￨- approximate￨L￨JJ￨O￨- closures￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- hierarchy￨L￨NN￨O￨- of￨L￨IN￨O￨- moment￨L￨NN￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- and￨L￨CC￨O￨- second￨L￨JJ￨ORDINAL￨- order￨L￨NN￨O￨- yielding￨L￨VBG￨O￨- mean-field￨L￨JJ￨O￨- and￨L￨CC￨O￨- pairwise￨L￨JJ￨O￨- models￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- prove￨L￨VB￨O￨- a￨L￨DT￨O￨- theorem￨L￨NN￨O￨- for￨L￨IN￨O￨- generating￨L￨VBG￨O￨- exact￨L￨JJ￨O￨- closures￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- here￨L￨RB￨O￨- expressing￨L￨VBG￨O￨- joint￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- constituent￨L￨NN￨O￨- marginal￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- susceptible-infectious-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- networks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- Markovian￨U￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- exact￨L￨NN￨O￨A closed￨L￨VBD￨O￨- models￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- at￨L￨IN￨O￨- all￨L￨DT￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hierarchy￨L￨NN￨O￨- of￨L￨IN￨O￨- moment￨L￨NN￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +All￨U￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- converge￨L￨VBP￨O￨- to￨L￨TO￨O￨- exact￨L￨JJ￨O￨A representations￨L￨NNS￨O￨- at￨L￨IN￨O￨- truncation￨L￨NN￨O￨- orders￨L￨NNS￨O￨- which￨L￨WDT￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- have￨L￨VBP￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- pair-level￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- variant￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- lowest￨L￨JJS￨O￨- (￨L￨-LRB-￨O￨- zeroth￨L￨NN￨ORDINAL￨- )￨L￨-RRB-￨O￨- order￨L￨NN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- truncation￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- unambiguously￨L￨RB￨O￨- define￨L￨VBP￨O￨- hierarchies￨L￨NNS￨O￨- of￨L￨IN￨O￨- approximate￨L￨JJ￨O￨A closed￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- utilise￨L￨VB￨O￨- subsystem￨L￨NN￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- order￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- show￨L￨VB￨O￨- how￨L￨WRB￨O￨- well-known￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- hierarchies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- multivariate￨L￨JJ￨O￨- birth￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- transition￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- ,￨L￨,￨O￨- Ebola￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Compartmental￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- plague￨L￨VB￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Ebola￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- calculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- for￨L￨IN￨O￨- discretely￨L￨RB￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- even￨L￨RB￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- –￨L￨:￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- ubiquitous￨L￨JJ￨O￨- susceptible-infectious-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- –￨L￨:￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- computationally￨L￨RB￨O￨- intractable￨L￨JJ￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- its￨L￨PRP$￨O￨- formulation￨L￨NN￨O￨- almost￨L￨RB￨O￨- a￨L￨DT￨DATE￨- century￨L￨NN￨DATE￨A ago￨L￨RB￨DATE￨- .￨L￨.￨O￨- +Stochastic￨U￨JJ￨O￨- compartmental￨L￨JJ￨O￨A models￨L￨NNS￨O￨A are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- prospective￨L￨JJ￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- policies￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨DATE￨- 17th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- plague￨L￨VB￨O￨A in￨L￨IN￨O￨- Eyam￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- classic￨L￨JJ￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- our￨L￨PRP$￨O￨- recursion￨L￨NN￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- sequential￨L￨JJ￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- analyze￨L￨VBP￨O￨- using￨L￨VBG￨O￨- HMC￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- foundation￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- for￨L￨IN￨O￨- discretely￨L￨RB￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- moments￨L￨NNS￨O￨- of￨L￨IN￨O￨- CSP￨U￨NNP￨ORGANIZATION￨- translate￨L￨VB￨O￨- to￨L￨TO￨O￨- various￨L￨JJ￨O￨- network￨L￨NN￨O￨- performance￨L￨NN￨O￨- metrics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- success￨L￨NN￨O￨- or￨L￨CC￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- 1-st￨L￨JJ￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- local￨L￨JJ￨O￨- delay￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- −￨L￨NN￨O￨- 1-st￨L￨JJ￨O￨- moment￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- setting￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- meta￨L￨NN￨O￨- moment￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- distribution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- complementary￨L￨JJ￨O￨- cumulative￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- success￨L￨NN￨O￨A probability￨L￨NN￨O￨A and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- 1-st￨L￨JJ￨O￨- and￨L￨CC￨O￨- 2-nd￨L￨JJ￨O￨- moments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- the￨L￨DT￨O￨- meta￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- moments￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- success￨L￨NN￨O￨A probability￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- CSP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- realization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmitters￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- co-channel￨L￨NN￨O￨- uplink￨L￨NN￨O￨- and￨L￨CC￨O￨- downlink￨L￨NN￨O￨- non-orthogonal￨L￨JJ￨O￨- multiple￨L￨JJ￨O￨- access￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NOMA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- NOMA￨U￨NN￨ORGANIZATION￨- cluster￨L￨NN￨O￨- per￨L￨IN￨O￨- cell￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- downlink￨L￨VBG￨O￨- NOMA￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- closed-form￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- moments￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- CSP￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- success￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- coverage￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- average￨L￨JJ￨O￨- local￨L￨JJ￨O￨- delay￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- meta￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- users￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- an￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- developed￨L￨VBN￨O￨- analytical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- closed-form￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- to￨L￨TO￨O￨- optimize￨L￨VB￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨- allocations￨L￨NNS￨O￨- for￨L￨IN￨O￨- downlink￨L￨VBG￨O￨- NOMA￨U￨NNP￨ORGANIZATION￨- users￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨A probability￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- NOMA￨U￨NNP￨ORGANIZATION￨- user￨L￨NN￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- latency￨L￨NN￨O￨- constraints￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Bass-SIR￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- everyone￨L￨NN￨O￨- ultimately￨L￨RB￨O￨- adopt￨L￨VB￨O￨A the￨L￨DT￨O￨- product￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- internal￨L￨JJ￨O￨- influences￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- consumers￨L￨NNS￨O￨- eventually￨L￨RB￨O￨- adopt￨L￨VB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- external￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- we￨L￨PRP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- small-worlds￨L￨JJ￨O￨- structure￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- negligible￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- on￨L￨IN￨O￨- Cartesian￨U￨JJ￨MISC￨- grids￨L￨NNS￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- one-sided￨L￨JJ￨O￨- 1D￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- nonspatial￨L￨JJ￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- least-and￨L￨JJ￨O￨- most-connected￨L￨JJS￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- conjecture￨L￨NN￨O￨- that￨L￨WDT￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- other￨L￨JJ￨O￨- connected￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- diffusion￨L￨NN￨O￨A is￨L￨VBZ￨O￨- faster￨L￨RBR￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- one-sided￨L￨JJ￨O￨- 1D￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- slower￨L￨JJR￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- nonspatial￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Section￨U￨NN￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- pointed￨L￨VBN￨O￨- out￨L￨RP￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- inappropriate￨L￨JJ￨O￨- for￨L￨IN￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- new￨L￨JJ￨O￨- products￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- diffusion￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Bass-SIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- new￨L￨JJ￨O￨- products￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- Bass-SIR￨U￨NN￨MISC￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- 7￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- a￨L￨DT￨O￨- M￨U￨NN￨O￨- 9￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- h￨L￨NN￨O￨- p￨L￨NN￨O￨- -￨L￨:￨O￨- c￨L￨NN￨O￨- o￨L￨NN￨O￨- s￨L￨NNS￨O￨- .￨L￨.￨O￨- +Part￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- that￨L￨IN￨O￨- those￨L￨DT￨O￨- efforts￨L￨NNS￨O￨- have￨L￨VBP￨O￨- implemented￨L￨VBN￨O￨- different￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- unrelated￨L￨JJ￨O￨- antibiotics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- relied￨L￨VB￨O￨- on￨L￨IN￨O￨- removal￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨A by￨L￨IN￨O￨- random￨L￨JJ￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- genes￨L￨NNS￨O￨- from￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- drift￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- captured￨L￨VBD￨O￨- those￨L￨DT￨O￨- differences￨L￨NNS￨O￨- by￨L￨IN￨O￨- characterizing￨L￨VBG￨O￨- complete￨L￨JJ￨O￨- adaptive￨L￨JJ￨O￨- landscapes￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- resistance￨L￨NN￨O￨A alleles￨L￨NNS￨O￨- blaTEM-50￨L￨NN￨O￨- and￨L￨CC￨O￨- blaTEM-85￨L￨NN￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- differs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- its￨L￨PRP$￨O￨- ancestor￨L￨NN￨O￨- blaTEM-1￨L￨NN￨O￨- by￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- mutations￨L￨NNS￨O￨- .￨L￨.￨O￨- +So￨U￨RB￨O￨- far￨L￨RB￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- attempts￨L￨NNS￨O￨- to￨L￨TO￨O￨- restore￨L￨VB￨O￨- susceptibility￨L￨NN￨O￨- after￨L￨IN￨O￨- resistance￨L￨NN￨O￨A has￨L￨VBZ￨O￨- arisen￨L￨VBN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- unsuccessful￨L￨JJ￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- restrictions￨L￨NNS￨O￨- on￨L￨IN￨O￨- prescribing￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- antibiotic￨L￨JJ￨O￨- cycling￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- resistance￨L￨NN￨O￨A phenotypes￨L￨NNS￨O￨- conferred￨L￨VBD￨O￨- by￨L￨IN￨O￨- variant￨L￨JJ￨O￨- alleles￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- resistance￨L￨NN￨O￨- gene￨L￨NN￨O￨- encoding￨L￨VBG￨O￨- the￨L￨DT￨O￨- TEM￨U￨NNP￨O￨- β-lactamase￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- blaTEM￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- varied￨L￨VBD￨O￨- greatly￨L￨RB￨O￨- among￨L￨IN￨O￨- 15￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- β-lactam￨L￨NN￨O￨- antibiotics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Title￨U￨NN￨O￨- :￨L￨:￨O￨- Designing￨U￨NNP￨O￨- antibiotic￨L￨JJ￨O￨- cycling￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- by￨L￨IN￨O￨- determining￨L￨VBG￨O￨- and￨L￨CC￨O￨- understanding￨L￨VBG￨O￨- local￨L￨JJ￨O￨- adaptive￨L￨JJ￨O￨A landscapes￨L￨NNS￨O￨- Authors￨U￨NNS￨O￨- :￨L￨:￨O￨- Christiane￨U￨NN￨PERSON￨- P￨U￨NN￨PERSON￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- 3D￨L￨NN￨O￨- simulated￨L￨JJ￨O￨- cone-beam￨L￨JJ￨O￨- data￨L￨NNS￨O￨- set￨L￨VBN￨O￨- and￨L￨CC￨O￨- synthetic￨L￨JJ￨O￨- helical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- set￨L￨VBP￨O￨- generated￨L￨VBN￨O￨- from￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- MPG￨U￨NN￨O￨- method￨L￨NN￨O￨- reduces￨L￨VBZ￨O￨- noise￨L￨NN￨O￨- and￨L￨CC￨O￨- decreases￨L￨VBZ￨O￨- bias￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- reconstructed￨L￨JJ￨O￨A images￨L￨NNS￨O￨- ,￨L￨,￨O￨- comparing￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- filtered￨L￨VBN￨O￨- back￨L￨RB￨O￨- projection￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FBP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- penalized￨L￨VBN￨O￨- weighted￨L￨JJ￨O￨- least-square￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PWLS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- shift￨L￨NN￨O￨- Poisson￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- SP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- ultra-low￨L￨JJ￨O￨- dose￨L￨NN￨O￨- CT￨U￨NN￨STATE_OR_PROVINCE￨- (￨L￨-LRB-￨O￨- ULDCT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- imaging￨L￨NN￨O￨- .￨L￨.￨O￨- +Statistical￨U￨JJ￨MISC￨- Image￨U￨NN￨MISC￨- Reconstruction￨U￨NN￨MISC￨- Using￨U￨VBG￨MISC￨- Mixed￨U￨JJ￨MISC￨- Poisson-Gaussian￨U￨JJ￨MISC￨- Noise￨U￨NN￨MISC￨- Model￨U￨NNP￨TITLE￨- for￨L￨IN￨O￨- X-Ray￨U￨NNP￨O￨- CT￨U￨NNP￨STATE_OR_PROVINCE￨- Qiaoqiao￨U￨NNP￨PERSON￨- Ding￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Yong￨U￨NNP￨PERSON￨- Long￨U￨NNP￨PERSON￨- ∗￨L￨NN￨PERSON￨- ,￨L￨,￨O￨- Xiaoqun￨U￨NNP￨PERSON￨- Zhang￨U￨NNP￨PERSON￨- ∗￨L￨NNP￨O￨- and￨L￨CC￨O￨- Jeffrey￨U￨NNP￨PERSON￨- A.￨U￨NNP￨PERSON￨- Fessler￨U￨NNP￨PERSON￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- Statistical￨U￨JJ￨O￨- image￨L￨NN￨O￨- reconstruction￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- X-ray￨U￨NN￨O￨- CT￨U￨NN￨STATE_OR_PROVINCE￨- produce￨L￨VBP￨O￨- high-quality￨L￨JJ￨O￨- and￨L￨CC￨O￨- accurate￨L￨JJ￨O￨- images￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- greatly￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- patient￨L￨NN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- radiation￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- non-positive￨L￨JJ￨O￨- values￨L￨NNS￨O￨- pose￨L￨VBP￨O￨- challenges￨L￨NNS￨O￨- to￨L￨TO￨O￨- post-log￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- require￨L￨VBP￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- logarithm￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- raw￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- causes￨L￨VBZ￨O￨- artifacts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- reconstructed￨L￨JJ￨O￨A images￨L￨NNS￨O￨- if￨L￨IN￨O￨- simple￨L￨JJ￨O￨- correction￨L￨NN￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- process￨L￨VB￨O￨- these￨L￨DT￨O￨- non-positive￨L￨JJ￨O￨- raw￨L￨JJ￨O￨- measurements￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- further￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- X-ray￨U￨NN￨O￨- dose￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- ultra-low￨L￨JJ￨O￨- level￨L￨NN￨O￨- by￨L￨IN￨O￨- lowering￨L￨VBG￨O￨- the￨L￨DT￨O￨- tube￨L￨NN￨O￨- current￨L￨JJ￨DATE￨- ,￨L￨,￨O￨- photon￨L￨JJ￨O￨- starvation￨L￨NN￨CAUSE_OF_DEATH￨- happens￨L￨VBZ￨O￨- and￨L￨CC￨O￨- electronic￨L￨JJ￨O￨- noise￨L￨NN￨O￨- starts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- dominate￨L￨VB￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- introduces￨L￨VBZ￨O￨- negative￨L￨JJ￨O￨- or￨L￨CC￨O￨- zero￨L￨CD￨NUMBER￨- values￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- raw￨L￨JJ￨O￨- measurements￨L￨NNS￨O￨A .￨L￨.￨O￨- +Surprisingly￨U￨RB￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨- share￨L￨VBP￨O￨- some￨L￨DT￨O￨- important￨L￨JJ￨O￨- topological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- small-world￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SW￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- properties￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- scale-free￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- or￨L￨CC￨O￨- connectivity￨L￨NN￨O￨A k￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- linked￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- topological￨L￨JJ￨O￨A features￨L￨NNS￨O￨- of￨L￨IN￨O￨- SF￨U￨NN￨O￨- networks￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- perhaps￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- interesting￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- fluctuations￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- unbounded￨L￨JJ￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- strongly￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- unbounded￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∼￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- ≤￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- seem￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- blueprint￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- studied￨L￨VBN￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- inserted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- editor￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- Spreading￨U￨VBG￨O￨- in￨L￨IN￨O￨- Structured￨U￨VBN￨MISC￨- Scale-Free￨U￨NNP￨MISC￨- Networks￨U￨NNP￨MISC￨- Yamir￨U￨NNP￨MISC￨- Moreno1a￨U￨NN￨MISC￨- and￨L￨CC￨O￨- Alexei￨U￨NNP￨PERSON￨- V´azquez￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- Abdus￨U￨NNP￨O￨- Salam￨U￨NNP￨O￨- International￨U￨NNP￨O￨- Centre￨U￨NNP￨O￨- for￨L￨IN￨O￨- Theoretical￨U￨NNP￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- P.O.￨U￨NNP￨O￨- Box￨U￨NNP￨O￨- 586￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 34100￨L￨CD￨NUMBER￨- Trieste￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- 2￨L￨CD￨NUMBER￨- International￨U￨NNP￨O￨- School￨U￨NNP￨O￨- for￨L￨IN￨O￨- Advanced￨U￨NNP￨O￨- Studies￨U￨NNPS￨O￨- SISSA/ISAS￨U￨NNP￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- Beirut￨U￨NNP￨CITY￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 34014￨L￨CD￨NUMBER￨- Trieste￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 24￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- /￨L￨:￨O￨- Revised￨U￨VBN￨O￨- version￨L￨NN￨O￨A :￨L￨:￨O￨- Abstract￨U￨NNP￨O￨- .￨L￨.￨O￨- +Newman￨U￨NNP￨PERSON￨- We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- and￨L￨CC￨O￨- solve￨L￨VBP￨O￨- exactly￨L￨RB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- both￨L￨DT￨O￨- a￨L￨DT￨O￨- tunable￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- tunable￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A coefficient￨L￨NN￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- other￨L￨JJ￨O￨- things￨L￨NNS￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- increased￨L￨VBN￨O￨- clustering￨L￨NN￨O￨A leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- giant￨L￨JJ￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- four￨L￨CD￨NUMBER￨- fundamental￨L￨JJ￨O￨- generating￨L￨VBG￨O￨- functions￨L￨NNS￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- use￨L￨VB￨O￨- :￨L￨:￨O￨- f0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ∞￨L￨CD￨NUMBER￨- Xm￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- rm￨L￨NN￨O￨- zm￨L￨NN￨O￨- ,￨L￨,￨O￨- f1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- µ￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ∞￨L￨CD￨NUMBER￨- Xm￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- mrm￨L￨NN￨O￨- zm￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- g0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ∞￨L￨CD￨NUMBER￨- Xn￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- sn￨L￨NN￨O￨- z￨L￨SYM￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- g1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- ν￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ∞￨L￨CD￨NUMBER￨- Xn￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- nsn￨L￨NN￨O￨- z￨L￨SYM￨O￨- n￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- µ￨L￨NN￨O￨- =￨L￨JJ￨O￨- Pm￨U￨NN￨O￨- mrm￨L￨NN￨O￨- and￨L￨CC￨O￨- ν￨L￨NN￨O￨- =￨L￨JJ￨O￨- Pn￨U￨NN￨O￨- nsn￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- groups￨L￨NNS￨O￨- per￨L￨IN￨O￨- person￨L￨NN￨O￨- and￨L￨CC￨O￨- people￨L￨NNS￨O￨- per￨L￨IN￨O￨- group￨L￨NN￨O￨- re-are￨L￨VBP￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨A spectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- N￨U￨NN￨O￨- △￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- 6￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- p3f￨L￨NN￨O￨- ′￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- ′￨L￨SYM￨O￨- ′￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- N3￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- p2￨L￨NN￨O￨- f￨L￨FW￨O￨- ′￨L￨FW￨O￨- ′￨L￨FW￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- g￨L￨NN￨O￨- ′￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- f￨L￨FW￨O￨- ′￨L￨FW￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- ′￨L￨SYM￨O￨- ′￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨A coefficient￨L￨NN￨O￨- is￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- C￨U￨NN￨O￨- =￨L￨JJ￨O￨- 3N￨L￨NN￨O￨- △￨L￨NN￨O￨- N3￨U￨NN￨O￨- =￨L￨JJ￨O￨- p￨L￨NN￨O￨- f￨L￨FW￨O￨- ′￨L￨FW￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- ′￨L￨SYM￨O￨- ′￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- f￨L￨SYM￨O￨- ′￨L￨SYM￨O￨- ′￨L￨SYM￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- g￨L￨NN￨O￨- ′￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- f￨L￨FW￨O￨- ′￨L￨FW￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- ′￨L￨SYM￨O￨- ′￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- pCb￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Cb￨U￨NNP￨O￨- mode￨L￨NN￨O￨- pro￨L￨JJ￨O￨- jection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bipartite￨L￨JJ￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- Fig.￨U￨NN￨O￨- 1b￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mean￨L￨JJ￨O￨- degree￨L￨NN￨O￨- hki￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- hki￨L￨NN￨O￨- =￨L￨JJ￨O￨- ∂￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- f0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- g1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- pz￨L￨NN￨O￨- +￨L￨CC￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- z￨L￨SYM￨O￨- =￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- pµg￨L￨NN￨O￨- ′￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- semiparametric￨L￨JJ￨O￨- single￨L￨JJ￨O￨- index￨L￨NN￨O￨- regression￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- Y￨U￨NN￨O￨- =￨L￨JJ￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- X￨U￨NN￨O￨- ,￨L￨,￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- response￨L￨NN￨O￨- variable￨L￨JJ￨O￨- Y￨U￨NN￨O￨- is￨L￨VBZ￨O￨- linked￨L￨VBN￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- an￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- link￨L￨NN￨O￨- function￨L￨NN￨O￨- f￨L￨FW￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- d-dimensional￨L￨JJ￨O￨- random￨L￨JJ￨O￨- vector￨L￨NN￨O￨- X￨U￨NN￨O￨- only￨L￨RB￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- d-dimensional￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +Sliced￨U￨JJ￨O￨- inverse￨L￨JJ￨O￨- regression￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- Duan￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Li￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1991￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- principal￨L￨JJ￨TITLE￨- hessian￨L￨JJ￨MISC￨- directions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- sliced￨L￨VBN￨O￨- average￨L￨JJ￨O￨- variance￨L￨NN￨O￨- estimation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SAVE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- developed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Cook￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- classical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- and￨L￨CC￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- subspace￨L￨NN￨O￨- spanned￨L￨VBN￨O￨- by￨L￨IN￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- estimate￨L￨VB￨O￨- this￨L￨DT￨O￨- subspace￨L￨NN￨O￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- uses￨L￨VBZ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨A expectation￨L￨NN￨O￨- of￨L￨IN￨O￨- X￨U￨NN￨O￨- given￨L￨VBN￨O￨- Y￨U￨NN￨O￨- under￨L￨IN￨O￨- mild￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- X￨U￨NN￨O￨- while￨L￨IN￨O￨- SAVE￨U￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- X￨U￨NN￨O￨- given￨L￨VBN￨O￨- Y￨U￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNPS￨O￨- Optimal￨U￨JJ￨O￨- quantization￨L￨NN￨O￨- ,￨L￨,￨O￨- Semiparametric￨U￨JJ￨O￨- regression￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Sliced￨U￨JJ￨MISC￨- In-verse￨U￨JJ￨MISC￨- Regression￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Reduction￨U￨NN￨O￨- dimension￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- a￨L￨DT￨O￨- J￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- T￨U￨NN￨O￨- S￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- especially￨L￨RB￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- is￨L￨VBZ￨O￨- orders￨L￨NNS￨O￨- of￨L￨IN￨O￨- magnitude￨L￨NN￨O￨- smaller￨L￨JJR￨O￨A than￨L￨IN￨O￨- the￨L￨DT￨O￨- lifetime￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- so￨L￨RB￨O￨- large￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- can￨L￨MD￨O￨- become￨L￨VB￨O￨- small￨L￨JJ￨O￨- and￨L￨CC￨O￨- fade-out￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- probable￨L￨JJ￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- medium-size￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- calculate￨L￨VBP￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- and￨L￨CC￨O￨- pre-factor￨L￨JJ￨O￨- contributions￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- WKB￨U￨NN￨O￨- approximation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- highly￨L￨RB￨O￨- oscillatory￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Fixing￨U￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- distribution￨L￨NN￨O￨- changes￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨A .￨L￨.￨O￨- +0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Epidemic￨U￨JJ￨O￨- outbreak￨L￨NN￨O￨A distributions￨L￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Noting￨U￨VBG￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- could￨L￨MD￨O￨- drive￨L￨VB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- not￨L￨RB￨O￨- normally￨L￨RB￨O￨- occur￨L￨VB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBD￨O￨- how￨L￨WRB￨O￨- migration￨L￨NN￨O￨A between￨L￨IN￨O￨- populations￨L￨NNS￨O￨- could￨L￨MD￨O￨- change￨L￨VB￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- respective￨L￨JJ￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- levels￨L￨NNS￨O￨- in￨L￨IN￨O￨- metapopulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analyze￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- imported￨L￨VBN￨O￨- between￨L￨IN￨O￨- subpopulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- region￨L￨NN￨O￨- by￨L￨IN￨O￨- short-term￨L￨JJ￨O￨- and￨L￨CC￨O￨- long-term￨L￨JJ￨O￨- migration￨L￨NN￨O￨A with￨L￨IN￨O￨- limited￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- coupled￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- how￨L￨WRB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- eradication￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- explicitly￨L￨RB￨O￨- on￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- migration￨L￨NN￨O￨A connectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- migration￨L￨NN￨O￨A changes￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- vaccination￨L￨NN￨O￨- rates￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- chosen￨L￨VBN￨O￨- to￨L￨TO￨O￨- maintain￨L￨VB￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- migration￨L￨NN￨O￨A rates￨L￨NNS￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- inserted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- editor￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- Dynamical￨U￨JJ￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- flu￨L￨NN￨O￨- seasonality￨L￨NN￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- ambient￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- :￨L￨:￨O￨- influenza￨L￨NN￨O￨A vs.￨L￨CC￨O￨- This￨U￨DT￨O￨- work￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- comparative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- Influenzanet￨U￨NNP￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨O￨- itself￨L￨PRP￨O￨- and￨L￨CC￨O￨- common￨L￨JJ￨CAUSE_OF_DEATH￨- cold￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- during￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DURATION￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- modelling￨L￨NN￨O￨- by￨L￨IN￨O￨- linearised￨L￨VBN￨O￨- SIRS￨U￨NN￨O￨- equations￨L￨NNS￨O￨- parametrically￨L￨RB￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- ambient￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- .￨L￨.￨O￨- +87.10.-e￨L￨JJ￨O￨- General￨U￨NNP￨TITLE￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- –￨L￨:￨O￨- Viral￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Influenza-like￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨A kind￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- moderate￨L￨JJ￨O￨- climate￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- Europe￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- argued￨L￨VBN￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- forecast￨L￨NN￨O￨- of￨L￨IN￨O￨- common￨L￨JJ￨CAUSE_OF_DEATH￨- cold￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- strict￨L￨JJ￨O￨- sense￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨CAUSE_OF_DEATH￨A cold￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- more￨L￨JJR￨O￨- serious￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- pleurisy￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- sinusitis￨L￨NN￨O￨- ,￨L￨,￨O￨- ear￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- begin￨L￨VBP￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- might￨L￨MD￨O￨- behave￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- ,￨L￨,￨O￨- vector￨L￨NN￨O￨- borne￨L￨VBD￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- another￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨- random￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨A network￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- and￨L￨CC￨O￨- make￨L￨VB￨O￨- different￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- sexual￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- structured￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- changing￨L￨VBG￨O￨- partnerships￨L￨NNS￨O￨- or￨L￨CC￨O￨- preferential￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- low-dimensional￨L￨JJ￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- appropriate￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- assumptions￨L￨NNS￨O￨- for￨L￨IN￨O￨- how￨L￨WRB￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- spread￨L￨VB￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- sexual￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- sexual￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- or￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- begin￨L￨VBP￨O￨- by￨L￨IN￨O￨- revisiting￨L￨VBG￨O￨- established￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- explore￨L￨VB￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- sexual￨L￨JJ￨O￨A network￨L￨NN￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- mode￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- new￨L￨JJ￨O￨- transmissions￨L￨NNS￨O￨A at￨L￨IN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- Markov-chain￨U￨NN￨MISC￨- approach￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MMCA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- class￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- added￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- case￨L￨NN￨O￨- considers￨L￨VBZ￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- policy￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- case￨L￨NN￨O￨- only￨L￨RB￨O￨- considers￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- possible￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- hospitalization￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +I.￨U￨NN￨O￨- INTRODUCTION￨U￨NNP￨O￨- Modeling￨U￨NNP￨O￨- how￨L￨WRB￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- spread￨L￨VBP￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- was￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨A by￨L￨IN￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- they￨L￨PRP￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infectious-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- supposed￨L￨VBD￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- non-intersecting￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- healthy￨L￨JJ￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- contract￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- contracted￨L￨VBN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- transmit￨L￨VB￨O￨- it￨L￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- recovered￨L￨VBN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- contract￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- anymore￨L￨RB￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- goals￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨A the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- optimality￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- means￨L￨VBZ￨O￨- balancing￨L￨VBG￨O￨- some￨L￨DT￨O￨- control￨L￨NN￨O￨- costs￨L￨NNS￨O￨- against￨L￨IN￨O￨- performance￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- solution￨L￨NN￨O￨- could￨L￨MD￨O￨- provide￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- vaccination￨L￨NN￨O￨- or￨L￨CC￨O￨- hospitalization￨L￨NN￨O￨A strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- showed￨L￨VBD￨O￨- stability￨L￨NN￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ˙S￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- λ￨L￨NN￨O￨- −￨L￨NN￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- h￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- ˙I￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- h￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ds￨L￨JJ￨O￨A −￨L￨NN￨O￨- µS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ηR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ds￨L￨JJ￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ˙R￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- extended￨L￨VBD￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- h￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- µ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- δ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- additional￨L￨JJ￨O￨- death￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨A behavior￨L￨NN￨O￨A around￨L￨IN￨O￨- is￨L￨VBZ￨O￨- provided￨L￨VBN￨O￨- while￨L￨IN￨O￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- invariant￨L￨JJ￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E0￨U￨NN￨O￨- measure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unique￨L￨JJ￨O￨- and￨L￨CC￨O￨- ergodic￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- µ￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- variable￨L￨JJ￨O￨- ˜µ￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- ˜µdt￨L￨NN￨O￨- =￨L￨JJ￨O￨- µdt￨L￨NN￨O￨- −￨L￨NN￨O￨- σdW￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- dS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- λ￨L￨NN￨O￨- −￨L￨NN￨O￨- µS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- H￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- It￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ηR￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- +￨L￨CC￨O￨- σS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dW￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- σ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- noise￨L￨NN￨O￨- and￨L￨CC￨O￨- W￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- scalar￨L￨JJ￨O￨- Brownian￨U￨NNP￨MISC￨- motion￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A and￨L￨CC￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- finite￨L￨JJ￨O￨- mixture￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- statistical￨L￨JJ￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- sampling￨L￨NN￨O￨- importance￨L￨NN￨O￨- resampling￨L￨NN￨O￨- ,￨L￨,￨O￨- elastic￨L￨JJ￨O￨- distance￨L￨NN￨O￨- ,￨L￨,￨O￨- persistence￨L￨NN￨O￨- landscape￨L￨NN￨O￨A 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- considerable￨L￨JJ￨O￨- growth￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- witnessed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- generation￨L￨NN￨O￨- in￨L￨IN￨O￨- modern￨L￨JJ￨O￨- sciences￨L￨NNS￨O￨- and￨L￨CC￨O￨- engineering￨L￨NN￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- the￨L￨DT￨O￨- creation￨L￨NN￨O￨- of￨L￨IN￨O￨- persistence￨L￨NN￨O￨- landscape￨L￨NN￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- parametrized￨L￨JJ￨O￨- curve￨L￨NN￨O￨- and￨L￨CC￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- sampling￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- process￨L￨NN￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- mixture￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- persistence￨L￨NN￨O￨- landscape￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FMMPL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- description￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- dataset￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mapper￨L￨NN￨O￨- method￨L￨NN￨O￨- covers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- metric￨L￨JJ￨O￨A space￨L￨NN￨O￨- and￨L￨CC￨O￨- inverse￨L￨NN￨O￨- of￨L￨IN￨O￨- mapping￨L￨NN￨O￨- ,￨L￨,￨O￨- construct￨L￨NN￨O￨- the￨L￨DT￨O￨- simplicial￨L￨JJ￨O￨- complex￨L￨NN￨O￨- with￨L￨IN￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- resolution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- represent￨L￨VBP￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨- to￨L￨TO￨O￨- shape￨L￨VB￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- function￨L￨NN￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- DTM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- estimates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨A diagram￨L￨NN￨O￨- on￨L￨IN￨O￨- metric￨L￨JJ￨O￨- space￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- persistence￨L￨NN￨O￨A homology￨L￨NN￨O￨- is￨L￨VBZ￨O￨- adapted￨L￨VBN￨O￨- for￨L￨IN￨O￨- computing￨L￨VBG￨O￨- confidence￨L￨NN￨O￨- interval￨L￨NN￨O￨- and￨L￨CC￨O￨- hypothesis￨L￨NN￨O￨- testing￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- allows￨L￨VBZ￨O￨- to￨L￨TO￨O￨- perform￨L￨VB￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- synthetic￨L￨JJ￨O￨- structured￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- fixed￨L￨VBN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- classes￨L￨NNS￨O￨A ,￨L￨,￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- possibly￨L￨RB￨O￨- empirical￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- contact￨L￨NN￨O￨- matrix￨L￨NN￨O￨- elements￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 35￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 36￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 37￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- simulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- community￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- representations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +spanned￨L￨VBN￨O￨- by￨L￨IN￨O￨- κ￨L￨NN￨O￨- ,￨L￨,￨O￨- µ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ν￨L￨NN￨O￨- with￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- enlarged￨L￨JJ￨O￨- three-dimensional￨L￨JJ￨O￨- phase￨L￨NN￨O￨- space￨L￨NN￨O￨- surface￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- usual￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A transition￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- surface￨L￨NN￨O￨- of￨L￨IN￨O￨- first￨L￨NN￨O￨- order￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- jump￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- κ￨L￨NN￨O￨- ,￨L￨,￨O￨- µ￨L￨NN￨O￨- ,￨L￨,￨O￨- ν￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- calculate￨L￨VBP￨O￨- the￨L￨DT￨O￨- scaling￨L￨VBG￨O￨A exponents￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- ε-expansion￨L￨NN￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- upper￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- dc￨L￨NN￨O￨- =￨L￨JJ￨O￨- 5￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- various￨L￨JJ￨O￨- observables￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- tricritical￨L￨JJ￨O￨- percolation￨L￨NN￨O￨- clusters￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- spreading￨L￨NN￨O￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- g4￨L￨NN￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- φ6￨L￨NN￨O￨- higher￨L￨JJR￨O￨- order￨L￨NN￨O￨- terms￨L￨NNS￨O￨- term￨L￨NN￨O￨- are￨L￨VBP￨O￨- irrelevant￨L￨JJ￨O￨- energy￨L￨NN￨O￨- density￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- is￨L￨VBZ￨O￨- positive￨L￨JJ￨O￨- then￨L￨RB￨O￨- and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- in￨L￨IN￨O￨- mean￨L￨JJ￨O￨- field￨L￨JJ￨O￨A theory￨L￨NN￨O￨A a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- order￨L￨NN￨O￨- transition￨L￨NN￨O￨- when￨L￨WRB￨O￨- τ￨L￨NN￨O￨- passes￨L￨VBZ￨O￨- through￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- renormalized￨L￨VBN￨O￨- field￨L￨NN￨O￨- theory￨L￨NN￨O￨- we￨L￨PRP￨O￨- work￨L￨VBP￨O￨- out￨L￨RP￨O￨- a￨L￨DT￨O￨- scaling￨L￨VBG￨O￨A description￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- universality￨L￨NN￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- tricritical￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- isotropic￨L￨JJ￨O￨- percolation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TdIP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- tricritical￨L￨JJ￨O￨- GGEP￨U￨NN￨O￨- belongs￨L￨VBZ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- scaling￨L￨VBG￨O￨A exponents￨L￨NNS￨O￨- we￨L￨PRP￨O￨- calculate￨L￨VBP￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- our￨L￨PRP$￨O￨- static￨L￨JJ￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- observables￨L￨NNS￨O￨- logarithmic￨L￨JJ￨O￨- corrections￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- behavior￨L￨NN￨O￨- at￨L￨IN￨O￨- dc￨L￨NN￨O￨- =￨L￨JJ￨O￨- 5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- worm￨L￨NN￨O￨A interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- performance￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- mathematically￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- worm￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- major￨L￨JJ￨O￨- worm￨L￨NN￨O￨- interaction￨L￨NN￨O￨- factors￨L￨NNS￨O￨- including￨L￨VBG￨O￨- worm￨L￨NN￨O￨- interaction￨L￨NN￨O￨- types￨L￨NNS￨O￨- ,￨L￨,￨O￨- network￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- node￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- using￨L￨VBG￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- our￨L￨PRP$￨O￨- proposed￨L￨VBN￨O￨- metrics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- mathematically￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- worm￨L￨NN￨O￨A interactions￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- worm￨L￨NN￨O￨- interaction￨L￨NN￨O￨- factors￨L￨NNS￨O￨- including￨L￨VBG￨O￨- worm￨L￨NN￨O￨- interaction￨L￨NN￨O￨- types￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- network￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- and￨L￨CC￨O￨- node￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- routing￨L￨VBG￨O￨- studies￨L￨NNS￨O￨- in￨L￨IN￨O￨- encounter-based￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- usually￨L￨RB￨O￨- assume￨L￨VBP￨O￨- ideal￨L￨JJ￨O￨- node￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨A including￨L￨VBG￨O￨- full￨L￨JJ￨O￨- node￨L￨NN￨O￨- cooperation￨L￨NN￨O￨- and￨L￨CC￨O￨- always-on￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- shall￨L￨MD￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- are￨L￨VBP￨O￨- key￨L￨JJ￨O￨- node￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- for￨L￨IN￨O￨- worm￨L￨NN￨O￨A propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- encounter-based￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- worm￨L￨NN￨O￨A propagation￨L￨NN￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- works￨L￨NNS￨O￨- also￨L￨RB￨O￨- assume￨L￨VBP￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- immune￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- worm￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- address￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- non-parametric￨L￨JJ￨O￨- bootstrapping￨L￨NN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- variability￨L￨NN￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- multi-model￨L￨JJ￨O￨- inference￨L￨NN￨O￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A uncertainty￨L￨NN￨O￨- .￨L￨.￨O￨- +Alternatively￨U￨RB￨O￨- ,￨L￨,￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- transmitted￨L￨VBN￨O￨- predominantly￨L￨RB￨O￨- through￨L￨IN￨O￨- non-sexual￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- conversational￨L￨JJ￨O￨- contact￨L￨NN￨O￨A which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- survey￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- typically￨L￨RB￨O￨- various￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- imposed￨L￨VBN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- Who-Acquires-Infection-From-Whom￨U￨NNP￨O￨- matrix￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- WAIFW￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- neighborhood￨L￨NN￨O￨A weakly￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- infectivity￨L￨NN￨O￨- but￨L￨CC￨O￨- strongly￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- other￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- fills￨L￨VBZ￨O￨- the￨L￨DT￨O￨- gap￨L￨NN￨O￨- by￨L￨IN￨O￨- performing￨L￨VBG￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- infected￨L￨JJ￨O￨- neighborhood￨L￨NN￨O￨A size￨L￨NN￨O￨- ,￨L￨,￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- Local￨U￨JJ￨O￨- Strategy￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- required￨L￨VBN￨O￨- extend￨L￨VBP￨O￨- of￨L￨IN￨O￨- prevention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- neighborhood￨L￨NN￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- relationship￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- time￨L￨NN￨O￨- till￨L￨IN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- till￨L￨IN￨O￨- treatment￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- non-nonlinear￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- power￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- law￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- spread￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- regular￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- different￨L￨JJ￨O￨- control￨L￨NN￨O￨- options￨L￨NNS￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- treating￨L￨VBG￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- to￨L￨TO￨O￨- local￨L￨JJ￨O￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- well-de￨L￨JJ￨O￨- fined￨L￨JJ￨O￨- neighborhood￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- neighborhood￨L￨NN￨O￨A is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- for￨L￨IN￨O￨- inefficien￨L￨NN￨O￨- t￨L￨NN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- application￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- non-susceptible￨L￨JJ￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- intentionally￨L￨RB￨O￨- inserted￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- feedback￨L￨NN￨O￨A loop￨L￨NN￨O￨- to￨L￨TO￨O￨- stop￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- ,￨L￨,￨O￨- strictly￨L￨RB￨O￨- by￨L￨IN￨O￨- themselves￨L￨PRP￨O￨- ,￨L￨,￨O￨- guarantee￨L￨VB￨O￨- its￨L￨PRP$￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- though￨L￨IN￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- give￨L￨VB￨O￨- that￨L￨IN￨O￨- appearance￨L￨NN￨O￨- by￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- refractory￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ’s￨L￨POS￨O￨- oscillations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- European￨U￨NNP￨ORGANIZATION￨- Union￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- elsewhere￨L￨RB￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- governments￨L￨NNS￨O￨- enacted￨L￨VBN￨O￨- legislation￨L￨NN￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- limit￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- via￨L￨IN￨O￨- elimination￨L￨NN￨O￨- or￨L￨CC￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- one-species￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A loops￨L￨NNS￨O￨- in￨L￨IN￨O￨- agricultural￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Bovine￨U￨JJ￨O￨- spongiform￨L￨NN￨O￨- encephalopathy￨L￨NN￨O￨- ,￨L￨,￨O￨- otherwise￨L￨RB￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- mad￨L￨JJ￨O￨- cow￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- cow￨L￨NN￨O￨- consumes￨L￨VBZ￨O￨- feed￨L￨NN￨O￨- containing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- tissues￨L￨NNS￨O￨- of￨L￨IN￨O￨- another￨L￨DT￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- forming￨L￨VBG￨O￨- a￨L￨DT￨O￨- one-species￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A loop￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- ecological￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- examines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rˆole￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A loops￨L￨NNS￨O￨- may￨L￨MD￨O￨- play￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- BSE￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- related￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- mad￨L￨JJ￨O￨- cow￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- BSE￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- transmissible￨L￨JJ￨O￨- spongiform￨L￨NN￨O￨- encephalopathy￨L￨NN￨O￨- ,￨L￨,￨O￨- prion￨L￨NN￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A modeling￨L￨NN￨O￨A Introduction￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- noted￨L￨VBN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- while￨L￨IN￨O￨- these￨L￨DT￨O￨- latter￨L￨JJ￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- exist￨L￨VBP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- human￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨A produced￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- way￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 2￨L￨CD￨NUMBER￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- mosquito-borne￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- interest￨L￨NN￨O￨- of￨L￨IN￨O￨- simplicity￨L￨NN￨O￨- and￨L￨CC￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- fit￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- neglect￨L￨NN￨O￨- them￨L￨PRP￨O￨- in￨L￨IN￨O￨- formulating￨L￨VBG￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- human￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨A arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- human￨L￨JJ￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- range￨L￨NN￨O￨- between￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 6￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- El￨U￨NNP￨COUNTRY￨- Salvador￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Suriname￨U￨NNP￨COUNTRY￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- median￨L￨NN￨O￨- of￨L￨IN￨O￨- 4.3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 5.3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +discoideum￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- susceptible￨L￨JJ￨O￨- or￨L￨CC￨O￨- resistant￨L￨JJ￨O￨- to￨L￨TO￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- P.￨U￨NNP￨O￨- Wild-type￨U￨JJ￨O￨- strains￨L￨NNS￨O￨A of￨L￨IN￨O￨- D.￨U￨NNP￨MISC￨- discoideum￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- isolated￨L￨VBN￨O￨- from￨L￨IN￨O￨- Massard￨U￨NNP￨LOCATION￨- Prairie￨U￨NNP￨LOCATION￨- soil￨L￨NN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- axenic-type￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- cultured￨L￨VBN￨O￨- free￨L￨JJ￨O￨- from￨L￨IN￨O￨- association￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- microbiota￨L￨NN￨O￨- .￨L￨.￨O￨- +aeruginosa￨L￨FW￨O￨- .16￨L￨FW￨NUMBER￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- wild-type￨L￨JJ￨O￨- D.￨U￨NNP￨O￨- aeruginosa￨L￨FW￨O￨- ,￨L￨,￨O￨- unlike￨L￨IN￨O￨- axenic-type￨L￨JJ￨O￨- strains￨L￨NNS￨O￨A that￨L￨WDT￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- limited￨L￨VBN￨O￨- resistivity￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- nearly￨L￨RB￨O￨- universal￨L￨JJ￨O￨- characteristic￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- dependence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- generalized￨L￨VBN￨O￨- to￨L￨TO￨O￨- kxk￨L￨VB￨O￨- −￨L￨NN￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨A exponent￨L￨NN￨O￨- α￨L￨NN￨O￨- being￨L￨VBG￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- Manuscript￨U￨NNP￨O￨- date￨L￨NN￨O￨- March￨U￨NNP￨DATE￨- 17￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2015￨L￨CD￨DATE￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- ultra-densi￨L￨JJ￨O￨- fication￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- network￨L￨NN￨O￨- density￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- in￨L￨IN￨O￨- finity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- near￨L￨JJ￨O￨- -￨L￨:￨O￨- field￨L￨NN￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨A exponent￨L￨NN￨O￨- if￨L￨IN￨O￨- α0￨L￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- unbounded￨L￨JJ￨O￨- potential￨L￨JJ￨O￨- throughput￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- asymptotically￨L￨RB￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- α0￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ultra-densi￨L￨JJ￨O￨- fication￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- extreme￨L￨JJ￨O￨- case￨L￨NN￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- throughput￨L￨NN￨O￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- Existing￨U￨VBG￨O￨- cellular￨L￨JJ￨O￨- network￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- typically￨L￨RB￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- received￨L￨VBN￨O￨- power￨L￨NN￨O￨- decays￨L￨VBZ￨O￨- like￨L￨IN￨O￨- kxk￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- α￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- distance￨L￨NN￨O￨- kxk￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- standard￨L￨JJ￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- quite￨L￨RB￨O￨- idealized￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- scenarios￨L￨NNS￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- exponent￨L￨NN￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- itself￨L￨PRP￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- kxk￨L￨NN￨O￨- ,￨L￨,￨O￨- typically￨L￨RB￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- decibel￨L￨JJ￨O￨- terms￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- Pr￨U￨NN￨O￨- =￨L￨JJ￨O￨- Pt￨U￨NN￨O￨- +￨L￨CC￨O￨- K0￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- 10α￨L￨CD￨NUMBER￨- log10￨L￨NN￨O￨- kxk￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- K0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- catch-all￨L￨JJ￨O￨- constant￨L￨NN￨O￨- that￨L￨WDT￨O￨- gives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- dB￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- distance￨L￨NN￨O￨- kxk￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VB￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A properties￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- estimate￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- modeling￨L￨NN￨O￨- simulated￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- SI￨U￨NNP￨O￨- and￨L￨CC￨O￨- SIS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- co-evolving￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Combined￨U￨VBN￨O￨- with￨L￨IN￨O￨- birth￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A constraints￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- non-trivial￨L￨JJ￨O￨- way￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- particular￨L￨JJ￨O￨- contact￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A cause￨L￨VBP￨O￨- earlier￨L￨JJR￨O￨- and￨L￨CC￨O￨- larger￨L￨JJR￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- to￨L￨TO￨O￨- homogeneous￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- algorithms￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- covariance￨L￨NN￨O￨- screening￨L￨NN￨O￨- and￨L￨CC￨O￨- least￨L￨JJS￨O￨- squares￨L￨NNS￨O￨- with￨L￨IN￨O￨- L1￨U￨NN￨O￨- penalization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- LASSO￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- enjoy￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- scalar￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rescaled￨L￨VBD￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- support￨L￨NN￨O￨A recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- albeit￨L￨IN￨O￨- under￨L￨IN￨O￨- slightly￨L￨RB￨O￨- different￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- on￨L￨IN￨O￨- f￨L￨FW￨O￨- and￨L￨CC￨O￨- ε￨L￨FW￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- based￨L￨VBN￨O￨- algorithms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Single￨U￨JJ￨O￨- index￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- Sparsity￨U￨NNP￨O￨- ,￨L￨,￨O￨- Support￨U￨NN￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- High-dimensional￨U￨JJ￨O￨- statistics￨L￨NNS￨O￨- ,￨L￨,￨O￨- LASSO￨U￨NNP￨ORGANIZATION￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Modern￨U￨NNP￨O￨- data￨L￨NNS￨O￨- applications￨L￨NNS￨O￨- often￨L￨RB￨O￨- require￨L￨VBP￨O￨- scientists￨L￨NNS￨O￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- high-dimensional￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨A size￨L￨NN￨O￨A n￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- much￨L￨RB￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- dimensionality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- covariates￨L￨NNS￨O￨- p￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- single￨L￨JJ￨O￨- index￨L￨NN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- Y￨U￨NN￨O￨- =￨L￨JJ￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- X￨U￨NN￨O￨- p￨L￨NN￨O￨- ×￨L￨CD￨NUMBER￨- 1β0￨L￨NN￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- support￨L￨NN￨O￨A impossible￨L￨JJ￨O￨- when￨L￨WRB￨O￨- X￨U￨NN￨O￨- ∼￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ip￨U￨NNP￨O￨- ×￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- complexity￨L￨NN￨O￨- adjusted￨L￨VBN￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- below￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +Critical￨U￨JJ￨O￨- paths￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- H1N1￨U￨NN￨O￨- :￨L￨:￨O￨- Efficiently￨U￨RB￨O￨- delaying￨L￨VBG￨O￨- influenza￨L￨NN￨O￨A spreading￨L￨NN￨O￨- through￨L￨IN￨O￨- flight￨L￨NN￨O￨- cancellation￨L￨NN￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- human￨L￨JJ￨O￨- travel￨L￨NN￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- topic￨L￨NN￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- witnessed￨L￨VBN￨O￨- during￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- SARS￨U￨NN￨O￨- pandemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- employ￨L￨VBP￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- takes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- cities￨L￨NNS￨O￨A ,￨L￨,￨O￨- simulates￨L￨VBZ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- cities￨L￨NNS￨O￨- and￨L￨CC￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- top￨L￨JJ￨O￨- 500￨L￨CD￨NUMBER￨- airports￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- tests￨L￨NNS￨O￨- different￨L￨JJ￨O￨- flight￨L￨NN￨O￨- cancellation￨L￨NN￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- limiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- test￨L￨VBP￨O￨- alternative￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- using￨L￨VBG￨O￨- edge￨L￨NN￨O￨- removal￨L￨NN￨O￨- ,￨L￨,￨O￨- cancelling￨L￨VBG￨O￨- targeted￨L￨VBN￨O￨- flight￨L￨NN￨O￨- connections￨L￨NNS￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- restricting￨L￨VBG￨O￨- traffic￨L￨NN￨O￨- for￨L￨IN￨O￨- network￨L￨NN￨O￨- hubs￨L￨NNS￨O￨A ,￨L￨,￨O￨- for￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- spreading￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- airline￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- stop￨L￨VB￨O￨- spreading￨L￨VBG￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- airline￨L￨NN￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨- for￨L￨IN￨O￨- major￨L￨JJ￨O￨- airports￨L￨NNS￨O￨- or￨L￨CC￨O￨- network￨L￨NN￨O￨- hubs￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- passengers￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- airport￨L￨NN￨O￨- .￨L￨.￨O￨- +Simulated￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- network￨L￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- 37￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- less￨L￨JJR￨O￨- individuals￨L￨NNS￨O￨- after￨L￨IN￨O￨- cancelling￨L￨VBG￨O￨- a￨L￨DT￨DURATION￨- quarter￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- flight￨L￨NN￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- cities￨L￨NNS￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- selected￨L￨VBN￨O￨- by￨L￨IN￨O￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- missing￨L￨VBG￨O￨- observations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- calibrated￨L￨VBN￨O￨- with￨L￨IN￨O￨- Approximate￨U￨NNP￨O￨- Bayesian￨U￨NNP￨O￨- Computation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- alternative￨L￨NN￨O￨- to￨L￨TO￨O￨- MCMC￨U￨NNP￨O￨- ,￨L￨,￨O￨- originally￨L￨RB￨O￨A proposed￨L￨VBN￨O￨- for￨L￨IN￨O￨- making￨L￨VBG￨O￨- inference￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Suceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨O￨- and￨L￨CC￨O￨- Recovered￨U￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨A distributions￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- with￨L￨IN￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- MCMC￨U￨NNP￨ORGANIZATION￨- are￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- convenient￨L￨JJ￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- under￨L￨IN￨O￨- study￨L￨NN￨O￨- a￨L￨DT￨O￨- topology￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- attracted￨L￨VBN￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- attention￨L￨NN￨O￨- lately￨L￨RB￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- multilayer￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- stress￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- focus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- what￨L￨WP￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- and￨L￨CC￨O￨- topological￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- onto￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +MODELING￨U￨VBG￨O￨- FRAMEWORK￨U￨NNP￨O￨- Our￨U￨PRP$￨O￨- purpose￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- epidemiological￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨A in￨L￨IN￨O￨- which￨L￨WDT￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- simultaneously￨L￨RB￨O￨- spread￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- whose￨L￨WP$￨O￨- dynamical￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- infectiousnesses￨L￨FW￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- depend￨L￨VBP￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- single￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- agents￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- have￨L￨VBP￨O￨- caught￨L￨VBN￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- both￨L￨DT￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- characterize￨L￨VBP￨O￨- analytically￨L￨RB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- compute￨L￨VBP￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- unfolding￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explicitly￨L￨RB￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- characterize￨L￨VBP￨O￨A their￨L￨PRP$￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- different￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- results￨L￨VBZ￨O￨- directly￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- both￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- following￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- b0￨L￨NN￨O￨- :￨L￨:￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨A birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- b1￨L￨NN￨O￨- :￨L￨:￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- born￨L￨VBN￨O￨- uninfected￨L￨JJ￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- :￨L￨:￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- born￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- b2￨L￨NN￨O￨- :￨L￨:￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- removed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- :￨L￨:￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- ε1￨L￨NN￨O￨- :￨L￨:￨O￨- ε2￨L￨NN￨O￨- :￨L￨:￨O￨- excess￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- excess￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- removed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- :￨L￨:￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- removal￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- :￨L￨:￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- removed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- :￨L￨:￨O￨- effective￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- eliminate￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- variable￨L￨JJ￨O￨- to￨L￨TO￨O￨- arrive￨L￨VB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- quadratic￨L￨JJ￨O￨- planar￨L￨NN￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- ′￨L￨SYM￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- +￨L￨CC￨O￨- β1￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- b0￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ε1￨L￨NN￨O￨- −￨L￨NN￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b0￨L￨NN￨O￨- +￨L￨CC￨O￨- ε1￨L￨NN￨O￨- −￨L￨NN￨O￨- λ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- b1￨L￨NN￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i2￨L￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b0￨L￨NN￨O￨- +￨L￨CC￨O￨- ε2￨L￨NN￨O￨- −￨L￨NN￨O￨- λ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- b2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ir￨L￨NN￨O￨- r￨L￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- β2￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- −￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- b0￨L￨NN￨O￨- +￨L￨CC￨O￨- ε2￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- r￨L￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b0￨L￨NN￨O￨- +￨L￨CC￨O￨- ε1￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- b1￨L￨NN￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ir￨L￨NN￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b0￨L￨NN￨O￨- +￨L￨CC￨O￨- ε2￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- b2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- r2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 5￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ′￨L￨SYM￨O￨- −￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- ′￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- D￨U￨NN￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- planar￨L￨JJ￨O￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- positively￨L￨RB￨O￨- invariant￨L￨JJ￨O￨A region￨L￨NN￨O￨- D1￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- i￨L￨FW￨O￨- ≥￨L￨FW￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Sub￨U￨NN￨O￨- ject￨L￨SYM￨O￨- Classification￨U￨NNP￨O￨- :￨L￨:￨O￨- 92D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- global￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- varying￨L￨VBG￨O￨- size￨L￨NN￨O￨- was￨L￨VBD￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Busenberg￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- van￨L￨NNP￨O￨- den￨L￨NN￨O￨A Driessch￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- sides￨L￨NNS￨O￨- of￨L￨IN￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- :￨L￨:￨O￨- s￨L￨NNS￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ⇒￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- b1￨L￨NN￨O￨- i￨L￨FW￨O￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b2￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- r￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ⇒￨L￨NN￨O￨- i￨L￨FW￨O￨- ′￨L￨FW￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- hence￨L￨RB￨O￨- the￨L￨DT￨O￨- line￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- invariant￨L￨JJ￨O￨A ,￨L￨,￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ⇒￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- β2￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i.￨L￨VBP￨O￨- β2￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- b2￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- sr2￨L￨NN￨O￨- +￨L￨CC￨O￨- +￨L￨CC￨O￨- s2￨L￨NN￨O￨- r￨L￨NN￨O￨- s2￨L￨NN￨O￨- i￨L￨FW￨O￨- ◦￨L￨FW￨O￨- D￨U￨NN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- ω￨L￨NN￨O￨- -￨L￨:￨O￨- limit￨L￨NN￨O￨- set￨L￨NN￨O￨- must￨L￨MD￨O￨- have￨L￨VB￨O￨- some￨L￨DT￨O￨- regular￨L￨JJ￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- ◦￨L￨NN￨O￨- D￨U￨NN￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- rest￨L￨NN￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +Tsimring1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- October￨U￨NNP￨DATE￨- 24￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- generalization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- susceptible-infectious-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- sparse￨L￨JJ￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- which￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- random￨L￨JJ￨O￨- screening￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- control￨L￨VBP￨O￨- in￨L￨IN￨O￨- small-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- its￨L￨PRP$￨O￨- effectiveness￨L￨NN￨O￨- grows￨L￨VBZ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- rewiring￨L￨NN￨O￨- probability￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- pair￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- [￨L￨-LRB-￨O￨- iτ￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- through￨L￨IN￨O￨- random￨L￨JJ￨O￨- screening￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- node￨L￨NN￨O￨- q￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- [￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- ]￨L￨-RRB-￨O￨- pair￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- through￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A of￨L￨IN￨O￨- node￨L￨NN￨O￨- q￨L￨NN￨O￨- from￨L￨IN￨O￨- node￨L￨NN￨O￨- r￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- q￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- triple￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- iiτ￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Random￨U￨NNP￨O￨- checking￨L￨VBG￨O￨- means￨L￨NNS￨O￨- choosing￨L￨VBG￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- βr￨L￨NN￨O￨- ∆￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- n￨L￨NN￨O￨- is￨L￨VBZ￨O￨- done￨L￨VBN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- βt￨L￨NN￨O￨- kt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∆￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- where￨L￨WRB￨O￨- kt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- traced￨L￨VBN￨O￨- state￨L￨NN￨O￨- T￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- all￨L￨DT￨O￨- simulations￨L￨NNS￨O￨- we￨L￨PRP￨O￨- varied￨L￨VBD￨O￨- the￨L￨DT￨O￨- tracing￨L￨VBG￨O￨A parameters￨L￨NNS￨O￨- βr￨L￨NN￨O￨- and￨L￨CC￨O￨- βt￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- constant￨L￨NN￨O￨- was￨L￨VBD￨O￨- set￨L￨VBN￨O￨- at￨L￨IN￨O￨- α￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- T￨U￨NN￨O￨- to￨L￨TO￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- Tij￨U￨NN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transition￨L￨NN￨O￨A from￨L￨IN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- may￨L￨MD￨O￨- write￨L￨VB￨O￨- wi￨L￨NN￨O￨- →￨L￨NN￨O￨- j￨L￨NN￨O￨- =￨L￨JJ￨O￨- Tij￨U￨NN￨O￨- τ￨L￨NN￨O￨- i￨L￨FW￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- time￨L￨NN￨O￨- constant￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- lifetime￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- i.￨L￨NNP￨O￨- To￨U￨TO￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- adequate￨L￨JJ￨O￨- quantity￨L￨NN￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- balance￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- removal￨L￨NN￨O￨- events￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- revisit￨L￨VBP￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A rate￨L￨NN￨O￨- R0￨U￨NN￨O￨- definition￨L￨NN￨O￨- for￨L￨IN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic-non-epidemic￨L￨JJ￨O￨- phases￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Master￨U￨NNP￨MISC￨- Equation￨U￨NN￨MISC￨- formalism￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- probabilities￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- markovian￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- Master￨U￨NNP￨O￨- Equation￨U￨NNP￨O￨- :￨L￨:￨O￨- dPi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- X￨U￨NN￨O￨- wj￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- iPj￨L￨NN￨O￨- −￨L￨NN￨O￨- X￨U￨NN￨O￨- wi￨L￨NN￨O￨- →￨L￨NN￨O￨- j￨L￨NN￨O￨- Pi￨U￨NN￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- j￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Pi￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- i￨L￨FW￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- wi￨L￨NN￨O￨- →￨L￨NN￨O￨- j￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨A probability￨L￨NN￨O￨- per￨L￨IN￨O￨- unity￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +s￨L￨NNS￨O￨- c￨L￨NN￨O￨- i￨L￨FW￨O￨- s￨L￨VBZ￨O￨- y￨L￨NN￨O￨- h￨L￨NN￨O￨- p￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- 3￨L￨CD￨DATE￨- 4￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 2￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 3￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- /￨L￨:￨O￨- s￨L￨NNS￨O￨- c￨L￨NN￨O￨- i￨L￨FW￨O￨- s￨L￨VBZ￨O￨- y￨L￨NN￨O￨- h￨L￨NN￨O￨- p￨L￨NN￨O￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- -￨L￨:￨O￨- The￨U￨DT￨O￨- basic￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A rate￨L￨NN￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- fundamental￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- epidemiologists￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Examples￨U￨NNS￨O￨- are￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- reaction-diffusion￨L￨NN￨O￨- systems￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- phenomena￨L￨NNS￨O￨- in￨L￨IN￨O￨- chemistry￨L￨NN￨O￨- and￨L￨CC￨O￨- physics￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- metapopulation￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- where￨L￨WRB￨O￨- particles￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- people￨L￨NNS￨O￨- moving￨L￨VBG￨O￨- across￨L￨IN￨O￨- different￨L￨JJ￨O￨- sub-populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- city￨L￨NN￨O￨- or￨L￨CC￨O￨- urban￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- reaction￨L￨NN￨O￨A processes￨L￨VBZ￨O￨- account￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- features￨L￨NNS￨O￨- ,￨L￨,￨O￨- often￨L￨RB￨O￨- mathematically￨L￨RB￨O￨- encoded￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- heavy-tailed￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- node￨L￨NN￨O￨- has￨L￨VBZ￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- evolution￨L￨NN￨O￨- altering￨L￨VBG￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨A behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- associated￨L￨VBN￨O￨- dynamical￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨A are￨L￨VBP￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- highly￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Online￨U￨NNP￨O￨- data￨L￨NNS￨O￨- processing￨L￨NN￨O￨- ;￨L￨:￨O￨- Bayesian￨U￨JJ￨O￨- estimation￨L￨NN￨O￨- ;￨L￨:￨O￨- regularized￨L￨VBN￨O￨- particle￨L￨NN￨O￨A filters￨L￨NNS￨O￨- ;￨L￨:￨O￨- stochastic￨L￨JJ￨O￨- volatility￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- phenomena￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- evolve￨L￨VBP￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- problem￨L￨NN￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- like￨L￨IN￨O￨- engineering￨L￨NN￨O￨- ,￨L￨,￨O￨- physics￨L￨NN￨O￨- ,￨L￨,￨O￨- biology￨L￨NN￨O￨- ,￨L￨,￨O￨- statistics￨L￨NNS￨O￨- ,￨L￨,￨O￨- economics￨L￨NNS￨O￨- and￨L￨CC￨O￨- finance￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- regularized￨L￨VBN￨O￨- particle￨L￨NN￨O￨A filters￨L￨NNS￨O￨- -￨L￨:￨O￨- the￨L￨DT￨O￨- regularized￨L￨VBN￨O￨- Sequential￨U￨NNP￨O￨- Importance￨U￨NNP￨O￨- Sampling￨U￨VBG￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- regularized￨L￨VBN￨O￨- Sampling￨U￨NNP￨O￨- Importance￨U￨NNP￨O￨- Resampling￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- regularized￨L￨VBN￨O￨- Auxiliary￨U￨NNP￨O￨- Particle￨U￨NNP￨O￨- Filter￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- APF￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- unknown￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- :￨L￨:￨O￨- yt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- xt￨L￨NN￨O￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- x0￨L￨NN￨O￨- θ0￨L￨NN￨O￨- ∼￨L￨CD￨NUMBER￨- ∼￨L￨SYM￨O￨- ∼￨L￨SYM￨O￨- ∼￨L￨SYM￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- yt￨L￨NN￨O￨- |￨L￨NN￨O￨- xt￨L￨NN￨O￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- y1￨L￨NN￨O￨- :￨L￨:￨O￨- t￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- measurement￨L￨NN￨O￨- density￨L￨NN￨O￨A ,￨L￨,￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- xt￨L￨NN￨O￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- t￨L￨NN￨O￨- |￨L￨SYM￨O￨- x0￨L￨NN￨O￨- :￨L￨:￨O￨- t￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- t￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- y1￨L￨NN￨O￨- :￨L￨:￨O￨- t￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- transition￨L￨NN￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x0￨L￨NN￨O￨- |￨L￨CD￨NUMBER￨- θ0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- π￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- θ￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- initial￨L￨JJ￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- prior￨L￨RB￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- denote￨L￨VBP￨O￨- by￨L￨IN￨O￨- {￨L￨-LRB-￨O￨- xt￨L￨NN￨O￨- ;￨L￨:￨O￨- t￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- xt￨L￨NN￨O￨- ∈￨L￨NN￨O￨- X￨U￨NN￨O￨- ⊆￨L￨CD￨NUMBER￨- Rnx￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- hidden￨L￨JJ￨O￨A states￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- {￨L￨-LRB-￨O￨- yt￨L￨NN￨O￨- ;￨L￨:￨O￨- t￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- N0￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- yt￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Y￨U￨NN￨O￨- ⊆￨L￨CD￨NUMBER￨- Rny￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- observable￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- {￨L￨-LRB-￨O￨- θ￨L￨NN￨O￨- t￨L￨NN￨O￨- ;￨L￨:￨O￨- t￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- t￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Θ￨U￨NN￨O￨- ⊆￨L￨CD￨NUMBER￨- Rnθ￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- entire￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- immunized￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- immunization￨L￨NN￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- perfect￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- immunization￨L￨NN￨O￨- with￨L￨IN￨O￨- immunization￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- impossible￨L￨JJ￨O￨- to￨L￨TO￨O￨- perfectly￨L￨RB￨O￨- immunize￨L￨VB￨O￨- entire￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- ob￨L￨JJ￨O￨- jects￨L￨NNS￨O￨- or￨L￨CC￨O￨- target￨L￨NN￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- immunization￨L￨NN￨O￨A and￨L￨CC￨O￨- immunization￨L￨NN￨O￨- rates￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- types￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- thresholds￨L￨NNS￨O￨- ,￨L￨,￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- bipartite￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- below￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- immunization￨L￨NN￨O￨A and￨L￨CC￨O￨- illustrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- with￨L￨IN￨O￨- STDs￨U￨NNS￨MISC￨- on￨L￨IN￨O￨- heterosexual￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- immunization￨L￨NN￨O￨A targets￨L￨NNS￨O￨- and￨L￨CC￨O￨- rates￨L￨NNS￨O￨- on￨L￨IN￨O￨- bipartite￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- some￨L￨DT￨O￨- immunization￨L￨NN￨O￨A schemes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- undirected￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- NumericCitation￨U￨NN￨O￨- also￨L￨RB￨O￨- offers￨L￨VBZ￨O￨- other￨L￨JJ￨O￨- schemes￨L￨NNS￨O￨- for￨L￨IN￨O￨- immunization￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- NumericCitation￨U￨NNP￨O￨- provides￨L￨VBZ￨O￨- targeted￨L￨VBN￨O￨- immunization￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- thresholds￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- set￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- immunization￨L￨NN￨O￨A rate￨L￨NN￨O￨- α￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- indegree￨L￨NN￨O￨- and￨L￨CC￨O￨- outdegree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- directed￨L￨VBN￨O￨A network￨L￨NN￨O￨- follow￨L￨VB￨O￨- power￨L￨NN￨O￨- laws￨L￨NNS￨O￨- :￨L￨:￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∝￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- and￨L￨CC￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- ℓ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∝￨L￨SYM￨O￨- ℓ￨L￨SYM￨O￨- −￨L￨SYM￨O￨- γ￨L￨SYM￨O￨- ′￨L￨SYM￨O￨- for￨L￨IN￨O￨- indegrees￨L￨NNS￨O￨- k￨L￨NN￨O￨- and￨L￨CC￨O￨- outdegrees￨L￨NN￨O￨- ℓ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- exponents￨L￨NNS￨O￨- satisfy￨L￨VBP￨O￨- 2￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ′￨L￨SYM￨O￨- ≤￨L￨SYM￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- scale-free￨L￨JJ￨O￨- .￨L￨.￨O￨- +City￨U￨NNP￨ORGANIZATION￨- Los￨U￨NNP￨ORGANIZATION￨- Angeles￨U￨NNP￨ORGANIZATION￨- San￨U￨NNP￨ORGANIZATION￨- Francisco￨U￨NNP￨ORGANIZATION￨- Denver￨U￨NNP￨ORGANIZATION￨- Miami￨U￨NNP￨ORGANIZATION￨- Atlanta￨U￨NNP￨ORGANIZATION￨- Chicago￨U￨NNP￨ORGANIZATION￨- St.￨U￨NNP￨ORGANIZATION￨- Louis￨U￨NNP￨ORGANIZATION￨- New￨U￨NNP￨ORGANIZATION￨- York￨U￨NNP￨ORGANIZATION￨- City￨U￨NNP￨ORGANIZATION￨- Memphis￨U￨NNP￨ORGANIZATION￨- Dallas￨U￨NNP￨ORGANIZATION￨- Houston￨U￨NNP￨ORGANIZATION￨- Seattle￨U￨NNP￨ORGANIZATION￨- Week￨U￨NNP￨ORGANIZATION￨- 50￨L￨CD￨NUMBER￨- Prediction￨U￨NN￨O￨- 52￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 50-95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 52￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 35-85￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 52￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 20-60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51￨L￨CD￨NUMBER￨A (￨L￨-LRB-￨O￨- 40-60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 80-99￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49-50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 55-95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 85-99￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 52￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 25-99￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 20-80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 65-90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 75-90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 52-53￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 0-55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- Week￨U￨NN￨DURATION￨- 49￨L￨CD￨NUMBER￨- Prediction￨U￨NN￨O￨- 51-52￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 35-90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51-52￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 25-40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 52￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 20-55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 40-99￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 90-99￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 55-95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 50-51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 80-99￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 25-99￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 20-80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49-50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 65-85￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 50-60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 52-53￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 5-55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- Week￨U￨NN￨DURATION￨- 48￨L￨CD￨NUMBER￨- Prediction￨U￨NN￨O￨- 51-52￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 20-55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 30-85￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51-52￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 0-55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 50-51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 40-55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 80-95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 35-80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 85-99￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 52-53￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 25-60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 15-80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 50-75￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 50-60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51-52￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 5-55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- Week￨U￨NN￨DURATION￨- 47￨L￨CD￨NUMBER￨- Prediction￨U￨NN￨O￨- 51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 15-30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 50-51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 25-60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 10-30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 50-51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 0-45￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 80-95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 35-80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 30-90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 53-54￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 25-55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49-50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 15-55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 40-85￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 49￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 50-85￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- 51￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 5-35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- Prediction￨U￨NN￨O￨- confidences￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shifted￨L￨VBN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- bit￨L￨NN￨O￨- .￨L￨.￨O￨- +2.1￨L￨CD￨DURATION￨- Week￨U￨NN￨DURATION￨- 50￨L￨CD￨NUMBER￨- Forecast￨U￨NNP￨O￨- The￨U￨NNP￨DATE￨- Week￨U￨NNP￨DATE￨- 50￨L￨CD￨NUMBER￨- forecast￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- initiated￨L￨VBN￨O￨- December￨U￨NNP￨DATE￨- 16￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- predicts￨L￨VBZ￨O￨- peaks￨L￨NNS￨O￨- for￨L￨IN￨O￨- Atlanta￨U￨NNP￨ORGANIZATION￨- Week￨U￨NNP￨ORGANIZATION￨- 49￨L￨CD￨ORGANIZATION￨A ,￨L￨,￨O￨- 1￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +New￨U￨NNP￨CITY￨- York￨U￨NNP￨CITY￨- City￨U￨NNP￨CITY￨- is￨L￨VBZ￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- peak￨L￨VB￨O￨- during￨L￨IN￨O￨- Week￨U￨NN￨DURATION￨- 52￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- last￨L￨JJ￨DATE￨- week￨L￨NN￨DATE￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- Week￨U￨NN￨DURATION￨- 51￨L￨CD￨NUMBER￨A .￨L￨.￨O￨- +Miami￨U￨NNP￨CITY￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- peak￨L￨VB￨O￨- in￨L￨IN￨O￨- Week￨U￨NN￨DATE￨- 51￨L￨CD￨DATE￨A .￨L￨.￨O￨- +Denver￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- too￨L￨RB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- peak￨L￨VB￨O￨- Week￨U￨NN￨DURATION￨- 52￨L￨CD￨NUMBER￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- before￨L￨RB￨O￨- .￨L￨.￨O￨- +2.1￨L￨CD￨DURATION￨- Week￨U￨NN￨DURATION￨- 51￨L￨CD￨NUMBER￨- Forecast￨U￨NNP￨O￨- The￨U￨NNP￨DATE￨- Week￨U￨NNP￨DATE￨- 51￨L￨CD￨NUMBER￨- forecast￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- initiated￨L￨VBN￨O￨- December￨U￨NNP￨DATE￨- 23￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- predicts￨L￨VBZ￨O￨- peaks￨L￨NNS￨O￨- for￨L￨IN￨O￨- Atlanta￨U￨NNP￨ORGANIZATION￨- Week￨U￨NNP￨ORGANIZATION￨- 49-50￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1-2￨L￨CD￨NUMBER￨- week￨L￨NN￨DURATION￨A in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Basically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- Atlanta￨U￨NNP￨CITY￨- has￨L￨VBZ￨O￨- shifted￨L￨VBN￨O￨- slightly￨L￨RB￨O￨- from￨L￨IN￨O￨- consistently￨L￨RB￨O￨- favoring￨L￨VBG￨O￨- Week￨U￨NN￨DURATION￨- 49￨L￨CD￨NUMBER￨A (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- even￨L￨RB￨O￨- split￨L￨VBN￨O￨- between￨L￨IN￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- peak￨L￨NN￨O￨- during￨L￨IN￨O￨- Week￨U￨NN￨DURATION￨- 49￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Week￨U￨NN￨DURATION￨- 50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- slight￨L￨JJ￨O￨- shift￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨DATE￨- Week￨U￨NN￨DATE￨- 49-50￨L￨CD￨NUMBER￨- peak￨L￨NN￨O￨- prediction￨L￨NN￨O￨- made￨L￨VBN￨O￨- last￨L￨JJ￨DATE￨- week￨L￨NN￨DATE￨A (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- current￨L￨JJ￨DATE￨- forecast￨L￨NN￨O￨- for￨L￨IN￨O￨- Chicago￨U￨NNP￨CITY￨- is￨L￨VBZ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- peak￨L￨NN￨O￨- during￨L￨IN￨O￨- Week￨U￨NN￨DURATION￨- 50￨L￨CD￨NUMBER￨A (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- parameter￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- percolated￨L￨VBN￨O￨- phase￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- cluster￨L￨NN￨O￨- ,￨L￨,￨O￨- takes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- definite￨L￨JJ￨O￨- value￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨A limit￨L￨NN￨O￨A ;￨L￨:￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- uniquely￨L￨RB￨O￨- determined￨L￨VBN￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨- limit￨L￨NN￨O￨- .￨L￨.￨O￨- +Intrinsic￨U￨JJ￨O￨- Unpredictability￨U￨NN￨O￨- of￨L￨IN￨O￨- Epidemic￨U￨JJ￨O￨- Outbreaks￨U￨NNS￨O￨- on￨L￨IN￨O￨- Networks￨U￨NNP￨O￨- Junya￨U￨NNP￨PERSON￨- Iwai1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Shin-ichi￨U￨NN￨MISC￨- Sasa2￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Department￨U￨NNP￨O￨- of￨L￨IN￨O￨- Basic￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- The￨U￨NNP￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Tokyo￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Komaba￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Tokyo￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- 53-8902￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- 2Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- Kyoto￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Kyoto￨U￨NNP￨LOCATION￨- 606-8502￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- May￨U￨NNP￨DATE￨- 12￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A outbreaks￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- human-to-human￨L￨JJ￨O￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- edge￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- Ref￨U￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- exhibiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- parameter￨L￨NN￨O￨- characterizing￨L￨VBG￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨A population￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- ρ￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- remarkable￨L￨JJ￨O￨- phenomenon￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- λ￨L￨NN￨O￨- exceeds￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨A λc￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- macroscopic￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨NNS￨O￨- which￨L￨WDT￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- functional￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- interpolation￨L￨NN￨O￨- of￨L￨IN￨O￨- given￨L￨VBN￨O￨- data￨L￨NNS￨O￨- points￨L￨NNS￨O￨- and￨L￨CC￨O￨- associated￨L￨VBN￨O￨- normals￨L￨NNS￨O￨- with￨L￨IN￨O￨- surface￨L￨NN￨O￨- parametric￨L￨JJ￨O￨- patches￨L￨NNS￨O￨- with￨L￨IN￨O￨- rational￨L￨JJ￨O￨- normal￨L￨JJ￨O￨A fields￨L￨NNS￨O￨- .￨L￨.￨O￨- +Key￨U￨NN￨O￨- words￨L￨NNS￨O￨- :￨L￨:￨O￨- Hermite￨U￨JJ￨O￨- interpolation￨L￨NN￨O￨- ,￨L￨,￨O￨- surfaces￨L￨NNS￨O￨- with￨L￨IN￨O￨- Pythagorean￨U￨NN￨MISC￨- normal￨L￨JJ￨O￨A fields￨L￨NNS￨O￨- ,￨L￨,￨O￨- rational￨L￨JJ￨O￨- offsets￨L￨NNS￨O￨- ,￨L￨,￨O￨- isotropic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Coons￨U￨NNP￨PERSON￨- patches￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- give￨L￨VBP￨O￨- some￨L￨DT￨O￨- arguments￨L￨NNS￨O￨- why￨L￨WRB￨O￨- a￨L￨DT￨O￨- dual￨L￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- especially￨L￨RB￨O￨- convenient￨L￨JJ￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- surfaces￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- traditionally￨L￨RB￨O￨- called￨L￨VBN￨O￨- Pythagorean￨U￨NNP￨MISC￨- normal￨L￨JJ￨O￨A vector￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PN￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- surfaces￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- patch￨L￨NN￨O￨- construction￨L￨NN￨O￨A which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- completely￨L￨RB￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- produces￨L￨VBZ￨O￨- surfaces￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- G1￨U￨NN￨O￨- continuity￨L￨NN￨O￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- This￨U￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- devoted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Hermite￨U￨JJ￨O￨- interpolation￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- surfaces￨L￨NNS￨O￨- possessing￨L￨VBG￨O￨- Pythagorean￨U￨NNP￨MISC￨- normal￨L￨JJ￨O￨A vector￨L￨NN￨O￨- fields￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PN￨U￨NN￨O￨- surfaces￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- the￨L￨DT￨O￨- vertex￨L￨NN￨O￨- weights￨L￨NNS￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- Ct￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- on￨L￨IN￨O￨- +￨L￨CC￨O￨- with￨L￨IN￨O￨- vertex￨L￨NN￨O￨- weights￨L￨NNS￨O￨- {￨L￨-LRB-￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- ∈￨L￨SYM￨O￨- Zd￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- x￨L￨CC￨O￨- ∈￨L￨NN￨O￨- Zd￨U￨NN￨O￨- Zd￨U￨NN￨O￨- +￨L￨CC￨O￨- and￨L￨CC￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- function￨L￨VBP￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- X￨U￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨NN￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- ⊆￨L￨SYM￨O￨- Zd￨U￨NN￨O￨- +￨L￨CC￨O￨- Ct￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- Ct￨U￨NN￨O￨- \￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Ct￨U￨NN￨O￨- S￨U￨NN￨O￨- {￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- if￨L￨IN￨O￨- x￨L￨CC￨O￨- ∈￨L￨SYM￨O￨- Ct￨U￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Ct￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- x￨L￨CC￨O￨- 6￨L￨CD￨NUMBER￨- ∈￨L￨NN￨O￨- Ct￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- Py￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- y￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- called￨L￨VBN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- while￨L￨IN￨O￨- 1A￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- indicator￨L￨NN￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- A.￨U￨NN￨O￨- For￨U￨IN￨O￨- any￨L￨DT￨O￨- λ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ρ2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- θ￨L￨NN￨O￨- defined￨L￨VBD￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- Equation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- lim￨L￨FW￨O￨A d￨L￨FW￨O￨- →￨L￨FW￨O￨- +￨L￨CC￨O￨- ∞￨L￨FW￨O￨- Pλ￨U￨FW￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- C￨U￨NN￨O￨- O￨U￨NN￨O￨- t￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- ∅￨L￨NN￨O￨- ,￨L￨,￨O￨- ∀￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- E￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- λρθ￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theorem￨L￨NN￨O￨- only￨L￨RB￨O￨- deals￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- λ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ρ2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- because￨L￨IN￨O￨- lim￨L￨NN￨O￨A 6￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- ∅￨L￨NN￨O￨- ,￨L￨,￨O￨- ∀￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ρ2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- theorem￨L￨NN￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Pλ￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- C￨U￨NN￨O￨- O￨U￨NN￨O￨- t￨L￨NN￨O￨- d￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- λ￨L￨NN￨O￨- <￨L￨JJR￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- When￨U￨WRB￨O￨- ρ￨L￨NN￨O￨- ≡￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- direct￨L￨JJ￨O￨- corollary￨L￨NN￨O￨- .￨L￨.￨O￨- +,￨L￨,￨O￨- yd￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨NN￨O￨- For￨U￨IN￨O￨- later￨L￨JJ￨O￨- use￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨A a￨L￨DT￨O￨- order￨L￨NN￨O￨- ≺￨L￨NN￨O￨- on￨L￨IN￨O￨- Zd￨U￨NN￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨CC￨O￨- ≺￨L￨FW￨O￨- y￨L￨FW￨O￨- when￨L￨WRB￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- j￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- ρ￨L￨JJ￨O￨- ≡￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- λ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- lim￨L￨FW￨O￨A d￨L￨FW￨O￨- →￨L￨FW￨O￨- +￨L￨CC￨O￨- ∞￨L￨FW￨O￨- Pλ￨U￨FW￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- C￨U￨NN￨O￨- O￨U￨NN￨O￨- t￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- ∅￨L￨NN￨O￨- ,￨L￨,￨O￨- ∀￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- λ￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- λ￨L￨NN￨O￨- .￨L￨.￨O￨- +2012￨L￨CD￨DATE￨- ACM￨U￨NNP￨MISC￨- Subject￨U￨NNP￨O￨- Classification￨U￨NNP￨O￨- Theory￨U￨NNP￨O￨- of￨L￨IN￨O￨- computation￨L￨NN￨O￨A →￨L￨CD￨NUMBER￨- Pattern￨U￨NN￨O￨- matching￨L￨NN￨O￨- ,￨L￨,￨O￨- Theory￨U￨NNP￨O￨- of￨L￨IN￨O￨- computation￨L￨NN￨O￨- →￨L￨NNP￨O￨- Data￨U￨NNP￨O￨- compression￨L￨NN￨O￨- ,￨L￨,￨O￨- Applied￨U￨NNP￨O￨- computing￨L￨VBG￨O￨- →￨L￨CD￨NUMBER￨- Computational￨U￨JJ￨O￨- genomics￨L￨NNS￨O￨- Keywords￨U￨NNS￨O￨- and￨L￨CC￨O￨- phrases￨L￨NNS￨O￨- FM-indexes￨U￨NNS￨O￨- ,￨L￨,￨O￨- variation￨L￨NN￨O￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- haplotypes￨L￨NNS￨O￨- Supplement￨U￨NNP￨O￨- Material￨U￨NNP￨O￨- The￨U￨NNP￨O￨- implementation￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- at￨L￨IN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 94￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- National￨U￨NNP￨ORGANIZATION￨- Institutes￨U￨NNPS￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- 5U41HG007234￨L￨NNP￨O￨- ,￨L￨,￨O￨- 1U01HL137183-01￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- W.￨U￨NNP￨DATE￨- 5￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 8￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 4:2￨L￨CD￨NUMBER￨- Haplotype-aware￨U￨NN￨O￨- graph￨L￨NN￨O￨- indexes￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Sequence￨U￨NN￨O￨- analysis￨L￨NN￨O￨- pipelines￨L￨NNS￨O￨- often￨L￨RB￨O￨- start￨L￨VBP￨O￨- by￨L￨IN￨O￨- mapping￨L￨VBG￨O￨- the￨L￨DT￨O￨- sequence￨L￨NN￨O￨- reads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- reference￨L￨NN￨O￨- genome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- species￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- simplifying￨L￨VBG￨O￨- variation￨L￨NN￨O￨- graphs￨L￨NNS￨O￨A for￨L￨IN￨O￨- k-mer￨L￨JJ￨O￨- indexing￨L￨NN￨O￨- without￨L￨IN￨O￨- losing￨L￨VBG￨O￨- any￨L￨DT￨O￨- k-mers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- haplotypes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- scalability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- implementation￨L￨NN￨O￨A by￨L￨IN￨O￨- indexing￨L￨NN￨O￨- the￨L￨DT￨O￨- 1000￨L￨CD￨DATE￨- Genomes￨U￨NNP￨O￨- Project￨U￨NNP￨O￨- haplotypes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- path￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- haplotype￨L￨NN￨O￨- ,￨L￨,￨O￨- though￨L￨IN￨O￨- most￨L￨JJS￨O￨- paths￨L￨NNS￨O￨- are￨L￨VBP￨O￨- unlikely￨L￨JJ￨O￨- recombinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- true￨L￨JJ￨O￨- haplotypes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- both￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- Lyapunov￨U￨NNP￨PERSON￨- exponents￨L￨NNS￨O￨A associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- B￨U￨NN￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- D￨U￨NN￨O￨- i￨L￨FW￨O￨- are￨L￨VBP￨O￨- negative￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- q￨L￨VB￨O￨- ;￨L￨:￨O￨- while￨L￨IN￨O￨- if￨L￨IN￨O￨- all￨L￨DT￨O￨- the￨L￨DT￨O￨- Lyapunov￨U￨NNP￨PERSON￨- exponents￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- B￨U￨NN￨O￨- i￨L￨FW￨O￨- are￨L￨VBP￨O￨- 1￨L￨CD￨NUMBER￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- to￨L￨TO￨O￨- D￨U￨NNP￨O￨- i￨L￨FW￨O￨- are￨L￨VBP￨O￨- negative￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- admits￨L￨VBZ￨O￨- an￨L￨DT￨O￨- invariant￨L￨JJ￨O￨- probability￨L￨NN￨O￨- measure￨L￨NN￨O￨- that￨L￨WDT￨O￨- gives￨L￨VBZ￨O￨- no￨L￨DT￨O￨- mass￨L￨NN￨O￨- to￨L￨TO￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ×￨L￨SYM￨O￨- Rm￨U￨FW￨O￨- ⊂￨L￨FW￨O￨- Rd￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- no￨L￨DT￨O￨- mass￨L￨NN￨O￨- to￨L￨TO￨O￨- q￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Zt￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Xt￨U￨NN￨O￨- ,￨L￨,￨O￨- It￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ∈￨L￨CD￨NUMBER￨- M￨U￨NN￨O￨- ×￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- X￨U￨NN￨O￨- evolves￨L￨VBZ￨O￨- according￨L￨VBG￨O￨A to￨L￨TO￨O￨- dXt￨L￨NNP￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- F￨U￨NN￨O￨- It￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- Xt￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- jump￨L￨NN￨O￨- process￨L￨NN￨O￨- taking￨L￨VBG￨O￨- values￨L￨NNS￨O￨- in￨L￨IN￨O￨- E￨U￨NN￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- X￨U￨NN￨O￨- :￨L￨:￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- It￨U￨PRP￨O￨- +￨L￨CC￨O￨- s￨L￨VBZ￨O￨- =￨L￨JJ￨O￨- j￨L￨NN￨O￨- |￨L￨SYM￨O￨- Ft￨U￨NN￨O￨- ,￨L￨,￨O￨- It￨U￨PRP￨O￨- =￨L￨JJ￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- aij￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Xt￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- s￨L￨VBZ￨O￨- +￨L￨CC￨O￨- o￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- j￨L￨NN￨O￨- =￨L￨JJ￨O￨- i￨L￨FW￨O￨- on￨L￨IN￨O￨- {￨L￨-LRB-￨O￨- It￨U￨PRP￨O￨- =￨L￨JJ￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Ft￨U￨NN￨O￨- =￨L￨JJ￨O￨- σ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- Xs￨U￨NNS￨O￨- ,￨L￨,￨O￨- Is￨U￨VBZ￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- s￨L￨NNS￨O￨- ≤￨L￨VBP￨O￨- t￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- shown￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- BLBMZ15￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infinitesimal￨L￨JJ￨O￨- generator￨L￨NN￨O￨- of￨L￨IN￨O￨- Z￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- operator￨L￨NN￨TITLE￨- L￨U￨NN￨O￨- acting￨L￨VBG￨O￨- on￨L￨IN￨O￨- functions￨L￨NNS￨O￨- g￨L￨NN￨O￨- :￨L￨:￨O￨- M￨U￨NN￨O￨- ×￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- smooth￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- variable￨L￨NN￨O￨- ,￨L￨,￨O￨- according￨L￨VBG￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- formula￨L￨NN￨O￨- j￨L￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- Lg￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- F￨U￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ∇￨L￨CD￨NUMBER￨- g￨L￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- aij￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- g￨L￨NN￨O￨- j￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- g￨L￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- g￨L￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- stands￨L￨VBZ￨O￨- for￨L￨IN￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- origin￨L￨NN￨O￨- lies￨L￨VBZ￨O￨A in￨L￨IN￨O￨- M￨U￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- al￨L￨NNP￨O￨- l￨L￨NN￨O￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- F￨U￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- m￨L￨NN￨O￨- =￨L￨JJ￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- x￨L￨CC￨O￨- ∈￨L￨SYM￨O￨- Rd￨U￨NN￨O￨- =￨L￨JJ￨O￨- Rn￨U￨NN￨O￨- ×￨L￨CD￨NUMBER￨- Rm￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- set￨L￨VBD￨O￨A x￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- xn￨L￨NN￨O￨- ,￨L￨,￨O￨- xm￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- community￨L￨NN￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- stochasticity￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- cases￨L￨NNS￨O￨A in￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- why￨L￨WRB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- recently￨L￨RB￨DATE￨- increased￨L￨VBN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- cases￨L￨NNS￨O￨A in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- in￨L￨IN￨O￨- late￨L￨JJ￨DATE￨- August￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- fitting￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transient￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- more￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- worsening￨L￨VBG￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- discrete￨L￨JJ￨O￨- seeding￨L￨NN￨O￨- events￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- into￨L￨IN￨O￨- new￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Background￨U￨NN￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- early￨L￨JJ￨O￨- growth￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- West￨U￨JJ￨MISC￨- African￨U￨JJ￨NATIONALITY￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- qualitatively￨L￨RB￨O￨- different￨L￨JJ￨O￨- for￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Liberia￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- likely￨L￨JJ￨O￨- began￨L￨VBD￨O￨- much￨L￨RB￨O￨- earlier￨L￨RBR￨O￨- in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Liberia￨U￨NNP￨COUNTRY￨- had￨L￨VBD￨O￨- approximately￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨A in￨L￨IN￨O￨- early￨L￨JJ￨DATE￨- August￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- twice￨L￨RB￨O￨- as￨L￨RB￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨DATE￨- end￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- August￨U￨NNP￨DATE￨- and￨L￨CC￨O￨- nearly￨L￨RB￨O￨- three￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- as￨L￨IN￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- mid-September￨L￨NN￨DATE￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- suspected￨L￨VBN￨O￨- cases￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- had￨L￨VBD￨O￨- exceeded￨L￨VBN￨O￨- 9,000￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- likely￨L￨RB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- underestimate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- simultaneous￨L￨JJ￨O￨- estimation￨L￨NN￨O￨A is￨L￨VBZ￨O￨- performed￨L￨VBN￨O￨- by￨L￨IN￨O￨- filtering￨L￨VBG￨O￨- an￨L￨DT￨O￨- extended￨L￨JJ￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- parameters￨L￨NNS￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- sequential-importance-resampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- filter￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- kernel￨L￨NN￨O￨- density￨L￨NN￨O￨- estimation￨L￨NN￨O￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +7￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- While￨U￨IN￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- maximum￨L￨NN￨O￨- ratio￨L￨NN￨O￨- combining￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- MRC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- understood￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- isolated￨L￨VBN￨O￨- link￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- true￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- interference￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- across￨L￨IN￨O￨- antennas￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- of￨L￨IN￨O￨- interferers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Modeling￨U￨VBG￨O￨- the￨L￨DT￨O￨- interference￨L￨NN￨O￨A field￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨ORGANIZATION￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- receive￨L￨VBP￨O￨- antennas￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- upper￨L￨JJ￨O￨- and￨L￨CC￨O￨- lower￨L￨JJR￨O￨- bounds￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- tractability￨L￨NN￨O￨- ,￨L￨,￨O￨- prior￨L￨JJ￨O￨- work￨L￨NN￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- extreme￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- interference￨L￨NN￨O￨A power￨L￨NN￨O￨- across￨L￨IN￨O￨- antennas￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- either￨L￨CC￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- fully￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- or￨L￨CC￨O￨- fully￨L￨RB￨O￨- uncorrelated￨L￨JJ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Index￨U￨NN￨O￨- Terms￨U￨NNS￨O￨- —￨L￨:￨O￨- Maximum￨U￨NNP￨O￨- ratio￨L￨NN￨O￨- combining￨L￨VBG￨O￨- ,￨L￨,￨O￨- multi-antenna￨L￨JJ￨O￨- receiver￨L￨NN￨O￨- ,￨L￨,￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- interference￨L￨NN￨O￨A correlation￨L￨NN￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- geometry￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- address￨L￨VBP￨O￨- this￨L￨DT￨O￨- shortcoming￨L￨NN￨O￨- and￨L￨CC￨O￨- characterize￨L￨VBP￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- MRC￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- spatially-correlated￨L￨JJ￨O￨- interference￨L￨NN￨O￨A across￨L￨IN￨O￨- antennas￨L￨NNS￨O￨- .￨L￨.￨O￨- +Transport￨U￨NN￨O￨- equations￨L￨NNS￨O￨A are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- transform￨L￨VB￨O￨- an￨L￨DT￨O￨- infinite￨L￨JJ￨O￨- dimens￨L￨NNS￨O￨- ional￨L￨JJ￨O￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- open￨L￨JJ￨O￨- population￨L￨NN￨O￨- case￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨NN￨O￨- dimensional￨L￨JJ￨O￨- system￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- v￨L￨LS￨O￨- ery￨L￨FW￨O￨- least￨L￨JJS￨O￨- ,￨L￨,￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- numerically￨L￨RB￨O￨- studied￨L￨VBN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- direct￨L￨JJ￨O￨- inheritance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distributed￨L￨VBN￨O￨- parameter￨L￨NN￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- qualiBenjamin￨L￨JJ￨O￨- R.￨U￨NNP￨ORGANIZATION￨- Keywords￨U￨NNP￨ORGANIZATION￨- Papillomaviruses￨U￨NNP￨ORGANIZATION￨- ·￨L￨NNP￨ORGANIZATION￨- Transport￨U￨NNP￨ORGANIZATION￨- Equations￨U￨NNPS￨ORGANIZATION￨- ·￨L￨SYM￨O￨- Distributed￨U￨VBN￨O￨- Parameters￨U￨NNS￨O￨- ·￨L￨VBP￨O￨- Differential￨U￨JJ￨O￨- Equations￨U￨NNS￨O￨- Mathematics￨U￨NNP￨O￨- Subject￨U￨NNP￨O￨- Classi￨U￨NNP￨O￨- fication￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 92D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Epidemic￨U￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- typically￨L￨RB￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- broken￨L￨VBN￨O￨- up￨L￨RP￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- that￨L￨WDT￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- members￨L￨NNS￨O￨- .￨L￨.￨O￨- +Phenomenologically￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- response￨L￨NN￨O￨- has￨L￨VBZ￨O￨- had￨L￨VBN￨O￨- general￨L￨JJ￨TITLE￨- theory￨L￨NN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- it￨L￨PRP￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- transport￨L￨NN￨O￨A equations/variables￨L￨NNS￨O￨- for￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- ˙X￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- w￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- w￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- F￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- w￨L￨NN￨O￨- ;￨L￨:￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Y￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ;￨L￨:￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Transport￨U￨NN￨O￨- Equations￨U￨NNS￨O￨- and￨L￨CC￨O￨- Open￨U￨VB￨MISC￨- Populations￨U￨NNS￨MISC￨- ˙Y￨L￨NN￨MISC￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- w￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Y￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ;￨L￨:￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +R￨U￨NN￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- w￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dw￨L￨NN￨O￨- being￨L￨VBG￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- type-X￨L￨JJ￨O￨- population￨L￨NN￨O￨- possessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- value￨L￨NN￨O￨- w￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- probability￨L￨NN￨O￨- In￨U￨IN￨O￨- other￨L￨JJ￨O￨- words￨L￨NNS￨O￨- w￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨A variable￨L￨NN￨O￨A with￨L￨IN￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- w￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- distribution￨L￨NN￨O￨- if￨L￨IN￨O￨- you￨L￨PRP￨O￨- will￨L￨MD￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- users￨L￨NNS￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- AP￨U￨NN￨MISC￨- which￨L￨WDT￨O￨- provides￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨JJ￨O￨- average￨L￨JJ￨O￨- received￨L￨VBN￨O￨- signal￨L￨NN￨O￨A power￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- gains￨L￨NNS￨O￨- of￨L￨IN￨O￨- SIC￨U￨NNP￨O￨- diminish￨L￨VB￨O￨- quickly￨L￨RB￨O￨- with￨L￨IN￨O￨- n￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modest￨L￨JJ￨O￨- for￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explicitly￨L￨RB￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- consecutive￨L￨JJ￨O￨- events￨L￨NNS￨O￨- of￨L￨IN￨O￨- canceling￨L￨VBG￨O￨- interferers￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- to￨L￨TO￨O￨- cancel￨L￨VB￨O￨- the￨L￨DT￨O￨- n-th￨L￨JJ￨O￨- strongest￨L￨JJS￨O￨- signal￨L￨NN￨O￨A and￨L￨CC￨O￨- to￨L￨TO￨O￨- decode￨L￨VB￨O￨- the￨L￨DT￨O￨- signal￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- after￨L￨IN￨O￨- n￨L￨NN￨O￨- cancellations￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- computationally￨L￨RB￨O￨- gorithm￨L￨NN￨O￨- can￨L￨MD￨O￨- recover￨L￨VB￨O￨- inefficient￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- that￨L￨WDT￨O￨- succeeds￨L￨VBZ￨O￨- in￨L￨IN￨O￨- support￨L￨NN￨O￨A recovery￨L￨NN￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- probability￨L￨NN￨O￨- as￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- n￨L￨NN￨O￨- s￨L￨NNS￨O￨- log￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- support￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- principal￨L￨JJ￨TITLE￨- eigenvector￨L￨NN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- feasible￨L￨JJ￨O￨- procedures￨L￨NNS￨O￨- ,￨L￨,￨O￨- Amini￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Wainwright￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- semidefinite￨L￨JJ￨O￨- programming￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SDP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- estimator￨L￨NN￨O￨- originally￨L￨RB￨O￨- suggested￨L￨VBD￨O￨- in￨L￨IN￨O￨- d’Aspremont￨L￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- was￨L￨VBD￨O￨- later￨L￨RB￨O￨- analyzed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Amini￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Wainwright￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- support￨L￨NN￨O￨A recovery￨L￨NN￨O￨- is￨L￨VBZ￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- DT￨U￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sparse￨L￨JJ￨O￨- spiked￨L￨JJ￨O￨- covariance￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- provided￨L￨VBD￨O￨- that￨L￨IN￨O￨- n￨L￨NN￨O￨- s2￨L￨NN￨O￨- log￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- look￨L￨VBP￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- computationally￨L￨RB￨O￨- inexpensive￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨A :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- thresholding￨L￨VBG￨O￨- sliced￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- regression￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DT-SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- β￨L￨NN￨O￨- i￨L￨FW￨O￨- ∈￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- ±￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- √￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- diagonal￨L￨JJ￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- Lin￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- SDR￨U￨NN￨O￨- algorithms￨L￨NNS￨O￨A in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- sparsity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- dimensionality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- unclear￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- super￨L￨JJ￨O￨- high-dimensional￨L￨JJ￨O￨- setting￨L￨NN￨O￨- where￨L￨WRB￨O￨- p￨L￨NN￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨A ,￨L￨,￨O￨- hinging￨L￨VBG￨O￨- on￨L￨IN￨O￨- regularization￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- LASSO￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Dantzig￨U￨NNP￨PERSON￨- Selector￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Li￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Nachtsheim￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2006￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Yu￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- perfect￨L￨JJ￨O￨- monitoring￨L￨NN￨O￨- of￨L￨IN￨O￨- traced￨L￨VBN￨O￨A cases￨L￨NNS￨O￨- or￨L￨CC￨O￨- perfect￨L￨JJ￨O￨- reporting￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- simple￨L￨JJ￨O￨- formulae￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- traced￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- bring￨L￨VB￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Re￨U￨NNP￨O￨- below￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Also￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- either￨L￨CC￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- Re￨U￨NNP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨- completely￨L￨RB￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- observable￨L￨JJ￨O￨- reported￨L￨VBN￨O￨- case/tracing￨L￨VBG￨O￨- quantities￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- Re￨U￨NNP￨O￨- =￨L￨JJ￨O￨- k￨L￨NN￨O￨- q￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- traced￨L￨VBN￨O￨A infected￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- primary￨L￨JJ￨O￨- untraced￨L￨JJ￨O￨- reported￨L￨VBN￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- km￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- traced￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- primary￨L￨JJ￨O￨- traced￨L￨VBN￨O￨- reported￨L￨VBN￨O￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- q￨L￨NN￨O￨- is￨L￨VBZ￨O￨- +￨L￨CC￨O￨- km￨L￨NN￨O￨- where￨L￨WRB￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- the￨L￨DT￨O￨- odds￨L￨NNS￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- reported￨L￨VBN￨O￨- case￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- traced￨L￨VBN￨O￨- contact￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- a￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- type￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- characterize￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- Re￨U￨NNP￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- .￨L￨.￨O￨- +properties￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- determine￨L￨VBP￨O￨- how￨L￨WRB￨O￨- relevant￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- case￨L￨NN￨O￨- reporting￨L￨NN￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- varying￨L￨VBG￨O￨- monitoring￨L￨NN￨O￨- protocols￨L￨NNS￨O￨- ,￨L￨,￨O￨- affect￨L￨IN￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- Ebola￨U￨NNP￨LOCATION￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- utilized￨L￨VBN￨O￨- to￨L￨TO￨O￨- form￨L￨VB￨O￨- real-time￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- Re￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- inform￨L￨VB￨O￨- our￨L￨PRP$￨O￨- pro￨L￨JJ￨O￨- jections￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- tra￨L￨NN￨O￨- jectory￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- formula￨L￨NN￨O￨- tions￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- large￨L￨JJ￨O￨- optimality￨L￨NN￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- about￨L￨RB￨O￨- 200￨L￨CD￨NUMBER￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- allow￨L￨VB￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Erd￨U￨NN￨MISC￨- ˝os￨L￨SYM￨MISC￨- -￨L￨:￨O￨- R￨U￨NN￨O￨- ´￨L￨''￨O￨- enyi/scale-free￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- controls￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- pro￨L￨FW￨O￨- ve￨L￨FW￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- prove￨L￨VB￨O￨- some￨L￨DT￨O￨- structural￨L￨JJ￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- controls￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- controls￨L￨NNS￨O￨- are￨L￨VBP￨O￨- non-increasing￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- formulate￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- optimizing￨L￨VBG￨O￨- a￨L￨DT￨O￨- net￨L￨JJ￨O￨- reward￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reward￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- information￨L￨NN￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- cost￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- controls￨L￨NNS￨O￨A .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- reveal￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- campaigning￨L￨NN￨O￨- resources￨L￨NNS￨O￨A to￨L￨TO￨O￨- various￨L￨JJ￨O￨- degree￨L￨NN￨O￨- classes￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- on￨L￨IN￨O￨- system￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- cost/abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨A problem￨L￨NN￨O￨A of￨L￨IN￨O￨- allocating￨L￨VBG￨O￨- campaigning￨L￨NN￨O￨- resources￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- campaign￨L￨NN￨O￨- duration￨L￨NN￨O￨- and￨L￨CC￨O￨- degree￨L￨NN￨O￨- classes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- motivates￨L￨VBZ￨O￨- adaptively￨L￨RB￨O￨- switching￨L￨VBG￨O￨- between￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- single-cell￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- beamforming￨L￨VBG￨O￨- and￨L￨CC￨O￨- ICIC￨U￨NN￨ORGANIZATION￨- at￨L￨IN￨O￨- low￨L￨JJ￨O￨- signal-to-noise￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SNR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- ICIC￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- preferred￨L￨VBN￨O￨- only￨L￨RB￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- accurate￨L￨JJ￨O￨- channel￨L￨NN￨O￨- estimation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- ICIC￨U￨NN￨ORGANIZATION￨- with￨L￨IN￨O￨- optimized￨L￨VBN￨O￨- training￨L￨NN￨O￨- and￨L￨CC￨O￨- feedback￨L￨NN￨O￨A at￨L￨IN￨O￨- high￨L￨JJ￨O￨- SNR￨U￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- analog￨L￨NN￨O￨- feedback￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- training￨L￨NN￨O￨- power￨L￨NN￨O￨- optimization￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- significant￨L￨JJ￨O￨- performance￨L￨NN￨O￨- gain￨L￨NN￨O￨- than￨L￨IN￨O￨- feedback￨L￨NN￨O￨- optimization￨L￨NN￨O￨- ;￨L￨:￨O￨- w￨L￨NN￨O￨- hile￨L￨NN￨O￨- conversely￨L￨RB￨O￨- for￨L￨IN￨O￨- digital￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- ,￨L￨,￨O￨- performance￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- feedback￨L￨NN￨O￨- bit￨L￨NN￨O￨- allocation￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- training￨L￨NN￨O￨- power￨L￨NN￨O￨- optimization￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- even￨L￨RB￨O￨- with￨L￨IN￨O￨- low-rate￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A and￨L￨CC￨O￨- standard￨L￨JJ￨O￨- training￨L￨NN￨O￨- ,￨L￨,￨O￨- ICIC￨U￨NN￨ORGANIZATION￨- can￨L￨MD￨O￨- transform￨L￨VB￨O￨- an￨L￨DT￨O￨- interference-limited￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- network￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- noise-limited￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +pilot￨L￨NN￨TITLE￨- power￨L￨NN￨O￨- allocation￨L￨NN￨O￨- for￨L￨IN￨O￨- CSI￨U￨NNP￨O￨- training￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- to￨L￨TO￨O￨- feed￨L￨VB￨O￨- back￨L￨RB￨O￨- CSI￨U￨NNP￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- channels￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- intercell￨L￨NN￨O￨- interference￨L￨NN￨O￨- cancellation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ICIC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- practical￨L￨JJ￨O￨- downlink￨L￨NN￨O￨- training￨L￨NN￨O￨- and￨L￨CC￨O￨- uplink￨L￨NN￨O￨- channel￨L￨NN￨O￨- state￨L￨NN￨O￨- information￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CSI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- feedback￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +42￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- No.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 237￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 310￨L￨CD￨NUMBER￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.1214￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 13-AOP846￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- PHASE￨U￨NNP￨O￨- TRANSITION￨U￨NN￨O￨- FOR￨U￨IN￨O￨- MEASURE-VALUED￨U￨NN￨O￨- SIR￨U￨NN￨O￨- EPIDEMIC￨U￨NN￨O￨- PROCESSES￨U￨NNS￨O￨- By￨U￨IN￨O￨- Steven￨U￨NNP￨PERSON￨- P.￨U￨NNP￨PERSON￨- Perkins2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Xinghua￨U￨NNP￨ORGANIZATION￨- Zheng3￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Chicago￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- British￨U￨NNP￨ORGANIZATION￨- Columbia￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- Hong￨U￨NNP￨ORGANIZATION￨- Kong￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- measure-valued￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- X￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Xt￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- solve￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- martingale￨L￨NN￨O￨- problem￨L￨NN￨O￨- :￨L￨:￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- measure￨L￨NN￨O￨- X0￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- smooth￨L￨JJ￨O￨- ,￨L￨,￨O￨- compactly￨L￨RB￨O￨- supported￨L￨VBD￨O￨- test￨L￨NN￨O￨- functions￨L￨NNS￨O￨- ϕ￨L￨VBP￨O￨- ,￨L￨,￨O￨- Xt￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- ϕ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- X0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ϕ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- Z￨U￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- Xs￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- ∆￨L￨CD￨NUMBER￨- ϕ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ds￨L￨JJ￨O￨A +￨L￨CC￨O￨- θ￨L￨JJ￨O￨- Z￨U￨NN￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Xs￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- ϕ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ds￨L￨JJ￨O￨- −￨L￨NN￨O￨- Z￨U￨NN￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Xs￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- Lsϕ￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ds￨L￨JJ￨O￨- +￨L￨CC￨O￨- Mt￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ϕ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +show￨L￨NN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- exist￨L￨VBP￨O￨- critical￨L￨JJ￨O￨- values￨L￨NNS￨O￨- θc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ∞￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- dimensions￨L￨NNS￨O￨A d￨L￨NN￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- θ￨L￨NN￨O￨- >￨L￨JJR￨O￨- θc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- survives￨L￨VBZ￨O￨- forever￨L￨RB￨O￨- with￨L￨IN￨O￨- positive￨L￨JJ￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- if￨L￨IN￨O￨- θ￨L￨NN￨O￨- <￨L￨JJR￨O￨- θc￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- in￨L￨IN￨O￨- finite￨L￨JJ￨O￨- time￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- Ls￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- time￨L￨NN￨O￨- density￨L￨NN￨O￨- process￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- X￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Mt￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ϕ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- martingale￨L￨NN￨O￨- with￨L￨IN￨O￨- quadratic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- M￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ϕ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Such￨U￨JJ￨O￨- processes￨L￨NNS￨O￨A arise￨L￨VBP￨O￨- as￨L￨IN￨O￨- scaling￨L￨NN￨O￨- limits￨L￨NNS￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- dimensions￨L￨NNS￨O￨A d￨L￨NN￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- locally￨L￨RB￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- θ￨L￨NN￨O￨- ;￨L￨:￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- compact￨L￨JJ￨O￨- set￨L￨NN￨O￨- K￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- Xt￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- eventually￨L￨RB￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- side-information￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- super-graph￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- graph￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨RB￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cascade￨L￨NN￨O￨A samples￨L￨NNS￨O￨- required￨L￨VBN￨O￨- –￨L￨:￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- cases￨L￨NNS￨O￨- –￨L￨:￨O￨- becomes￨L￨VBZ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- n.￨L￨NN￨O￨- Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- cascade￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- graph￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- times￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- moralization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- graph￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- cascade￨L￨NN￨O￨A spreads￨L￨NNS￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- times￨L￨NNS￨O￨- when￨L￨WRB￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- gets￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- observation￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- graph￨L￨NN￨O￨A learning￨L￨NN￨O￨- problem￨L￨NN￨O￨- decouples￨L￨VBZ￨O￨- into￨L￨IN￨O￨- n￨L￨NN￨O￨- local￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- –￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- a￨L￨DT￨O￨- multi-tier￨L￨JJ￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- orthogonal￨L￨JJ￨O￨- spectrum￨L￨NN￨O￨- allocation￨L￨NN￨O￨- among￨L￨IN￨O￨- tiers￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- biased￨L￨VBN￨O￨- average￨L￨JJ￨O￨- received￨L￨VBN￨O￨- power￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- tier￨L￨NN￨TITLE￨A association￨L￨NN￨O￨- metric￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- coverage￨L￨NN￨O￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- user￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stationary￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- handoffs￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- occur￨L￨VB￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- handoffs￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- user￨L￨NN￨O￨- is￨L￨VBZ￨O￨- mobile￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- handoffs￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- user￨L￨NN￨O￨- is￨L￨VBZ￨O￨- mobile￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- handoffs￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- optimum￨L￨JJ￨O￨- tier￨L￨NN￨TITLE￨A association￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- coverage￨L￨NN￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- user￨L￨NN￨O￨- ’s￨L￨POS￨O￨- speed￨L￨NN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- speed-dependent￨L￨JJ￨O￨- bias￨L￨NN￨O￨- factor￨L￨NN￨O￨- can￨L￨MD￨O￨- then￨L￨RB￨O￨- adjust￨L￨VB￨O￨- the￨L￨DT￨O￨- tier￨L￨NN￨TITLE￨- association￨L￨NN￨O￨- to￨L￨TO￨O￨- effectively￨L￨RB￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- system￨L￨NN￨O￨- performance￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- fully-loaded￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Index￨U￨NNP￨O￨- Terms￨U￨NNS￨O￨- Heterogeneous￨U￨JJ￨O￨- cellular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- range￨L￨NN￨O￨- expansion￨L￨NN￨O￨- ,￨L￨,￨O￨- user￨L￨NN￨O￨A association￨L￨NN￨O￨- ,￨L￨,￨O￨- hand-off￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- downlink￨L￨NN￨O￨- coverage￨L￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- begin￨L￨VBP￨O￨- by￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- handoff￨L￨NN￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- user￨L￨NN￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- irregular￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- access￨L￨NN￨O￨- point￨L￨NN￨O￨- locations￨L￨NNS￨O￨- modeled￨L￨VBD￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +F.￨U￨NNP￨O￨- Melendy1￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Electrical￨U￨JJ￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Renewable￨U￨NNP￨ORGANIZATION￨- Energy￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- The￨U￨DT￨O￨- Oregon￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 97070￨L￨CD￨NUMBER￨- USA￨U￨NN￨COUNTRY￨- 2Formerly￨L￨NN￨O￨- of￨L￨IN￨O￨- The￨U￨DT￨O￨- School￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Computational￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Liberty￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 24515￨L￨CD￨NUMBER￨- USA￨U￨NN￨COUNTRY￨- In￨U￨IN￨O￨- a￨L￨DT￨O￨- succession￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- articles￨L￨NNS￨O￨- published￨L￨VBN￨O￨- over￨L￨IN￨O￨- 65￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- ago￨L￨RB￨DATE￨- ,￨L￨,￨O￨- Sir￨U￨NNP￨O￨- Alan￨U￨NNP￨PERSON￨- Lloyd￨U￨NNP￨PERSON￨- Hodgkin￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Sir￨U￨NNP￨O￨- Andrew￨U￨NNP￨PERSON￨- Fielding￨U￨NNP￨PERSON￨- Huxley￨U￨NNP￨PERSON￨- discovered￨L￨VBD￨O￨- what￨L￨WP￨O￨- now￨L￨RB￨DATE￨- forms￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- contemporary￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- excitat￨L￨NN￨O￨- ion￨L￨NN￨O￨A in￨L￨IN￨O￨- nerve￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- axons￨L￨NNS￨O￨- conduct￨L￨VBP￨O￨- the￨L￨DT￨O￨- action￨L￨NN￨O￨- potential￨L￨NN￨O￨- .￨L￨.￨O￨- +Notwithstanding￨U￨IN￨O￨- the￨L￨DT￨O￨- elegance￨L￨NN￨O￨- of￨L￨IN￨O￨- Hodgkin￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Huxley￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- incisive￨L￨JJ￨O￨- and￨L￨CC￨O￨- explicat￨L￨NN￨O￨- ive￨L￨JJ￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- discoveries￨L￨NNS￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- relat￨L￨NN￨O￨- ively￨L￨RB￨O￨- complex￨L￨JJ￨O￨- ,￨L￨,￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- no￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- stochast￨L￨NN￨O￨- ic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- no￨L￨DT￨O￨- analyt￨L￨NN￨O￨- ical￨L￨JJ￨O￨- so￨L￨RB￨O￨- lut￨L￨JJ￨O￨- ion￨L￨NN￨O￨A ;￨L￨:￨O￨- solving￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- membrane￨L￨NN￨O￨- action￨L￨NN￨O￨- potential￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ionic￨L￨JJ￨O￨- currents￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- integrations￨L￨NNS￨O￨- approximated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- numerical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- cSIR￨L￨NN￨O￨- we￨L￨PRP￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- overcome￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- identify￨L￨VB￨O￨- unexposed￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- as￨L￨IN￨O￨- similar￨L￨JJ￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- estimation￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- counterfactual￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- of￨L￨IN￨O￨- no￨L￨DT￨O￨- exposure￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- make￨L￨VB￨O￨- inference￨L￨NN￨O￨- on￨L￨IN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- unexposed￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- using￨L￨VBG￨O￨- publicly￨L￨RB￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- available￨L￨JJ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- aggregation￨L￨NN￨O￨- than￨L￨IN￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- desired￨L￨VBN￨O￨- .￨L￨.￨O￨- +Assuming￨U￨VBG￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- hazard￨L￨NN￨O￨- representing￨L￨VBG￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- is￨L￨VBZ￨O￨- identified￨L￨VBN￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- estimand￨L￨NN￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- causal￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- cSIR￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- cSIR￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- ratio￨L￨NN￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- population￨L￨NN￨O￨- divided￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- counterfactual￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- scenario￨L￨NN￨O￨- of￨L￨IN￨O￨- no￨L￨DT￨O￨- exposure￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- response￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- recommends￨L￨VBZ￨O￨- that￨L￨IN￨O￨- departments￨L￨NNS￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- perform￨L￨VBP￨O￨- a￨L￨DT￨O￨- standardized￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- causal￨L￨JJ￨O￨- inference￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A cluster￨L￨NN￨O￨- investigations￨L￨NNS￨O￨- ,￨L￨,￨O￨- rooted￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- class￨L￨NN￨O￨- closure￨L￨NN￨O￨A affords￨L￨NNS￨O￨- strong￨L￨JJ￨O￨- mitigation￨L￨NN￨O￨- effects￨L￨NNS￨O￨- :￨L￨:￨O￨- closing￨L￨VBG￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- –￨L￨:￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- –￨L￨:￨O￨- whenever￨L￨WRB￨O￨- two￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- class￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- by￨L￨IN￨O￨- almost￨L￨RB￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- significantly￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- severe￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Mitigation￨U￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- school￨L￨NN￨O￨- :￨L￨:￨O￨- targeted￨L￨VBN￨O￨- class￨L￨NN￨O￨- closure￨L￨NN￨O￨A vs￨L￨CC￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- V.￨U￨NNP￨O￨- Methods￨U￨NNS￨O￨- and￨L￨CC￨O￨- Findings￨U￨NNS￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- mitigation￨L￨NN￨O￨- measures￨L￨NNS￨O￨- that￨L￨WDT￨O￨- involve￨L￨VBP￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- closure￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- classes￨L￨NNS￨O￨- or￨L￨CC￨O￨- grades￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- readily￨L￨RB￨O￨- available￨L￨JJ￨O￨- information￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- children￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Targeted￨U￨VBN￨O￨- class￨L￨NN￨O￨- closure￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- readily￨L￨RB￨O￨- available￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- sub￨L￨NN￨O￨- jects￨L￨NNS￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- limited￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- grade￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- almost￨L￨RB￨O￨- as￨L￨IN￨O￨- effective￨L￨JJ￨O￨- as￨L￨IN￨O￨- whole-school￨L￨JJ￨O￨- closure￨L￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- much￨L￨RB￨O￨- lower￨L￨JJR￨O￨- cost￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- closure￨L￨NN￨O￨A of￨L￨IN￨O￨- all￨L￨DT￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- grade￨L￨NN￨O￨- mitigates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- almost￨L￨RB￨O￨- as￨L￨RB￨O￨- much￨L￨JJ￨O￨- as￨L￨IN￨O￨- closing￨L￨VBG￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- school￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- leveraging￨L￨VBG￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨- –￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- connection￨L￨NN￨O￨- across￨L￨IN￨O￨- randomized￨L￨VBN￨O￨A units￨L￨NNS￨O￨- –￨L￨:￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- connectivity-informed￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- trial￨L￨NN￨O￨- designs￨L￨VBZ￨O￨- that￨L￨IN￨O￨- aim￨L￨NN￨O￨- both￨L￨CC￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- impact￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- l￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- preserving￨L￨VBG￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- intervention￨L￨NN￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +Cluster￨U￨NN￨O￨- randomized￨L￨VBD￨O￨- trials￨L￨NNS￨O￨A are￨L￨VBP￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- research￨L￨NN￨O￨- by￨L￨IN￨O￨- virtue￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- both￨L￨DT￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- latter￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- heavily￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- across￨L￨IN￨O￨- clusters￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- designs￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- end￨L￨VB￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- power￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- vaccine￨L￨NN￨O￨- effect￨L￨NN￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- trials￨L￨NNS￨O￨A during￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR-type￨U￨JJ￨MISC￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- network-structured￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- connectivity-informed￨L￨JJ￨O￨- designs￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- lower￨L￨VB￨O￨- peak￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- than￨L￨IN￨O￨- comparable￨L￨JJ￨O￨- traditional￨L￨JJ￨O￨- study￨L￨NN￨O￨- designs￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- cumulative￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- have￨L￨VBP￨O￨- little￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- length￨L￨NN￨O￨- .￨L￨.￨O￨- +Title￨U￨NN￨O￨- :￨L￨:￨O￨- Leveraging￨U￨VBG￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨- of￨L￨IN￨O￨- cluster￨L￨NN￨O￨- randomized￨L￨VBD￨O￨- trials￨L￨NNS￨O￨A Running￨U￨VBG￨O￨- Head￨U￨NNP￨O￨- :￨L￨:￨O￨- Network￨U￨NNP￨O￨- structured￨L￨VBD￨O￨- designs￨L￨NNS￨O￨- for￨L￨IN￨O￨- cluster￨L￨NN￨O￨- trials￨L￨NNS￨O￨- Authors￨U￨NNPS￨O￨- :￨L￨:￨O￨- Guy￨U￨NNP￨PERSON￨- Harling￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Rui￨U￨NNP￨PERSON￨- Wang￨U￨NNP￨PERSON￨- ,2,3￨L￨CD￨NUMBER￨- Jukka-Pekka￨U￨NNP￨O￨- Onnela￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- Victor￨U￨NNP￨PERSON￨- De￨U￨NNP￨PERSON￨- Gruttola￨U￨NNP￨PERSON￨- .2￨L￨NN￨NUMBER￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- both￨L￨DT￨O￨- the￨L￨DT￨O￨- Contact￨U￨NN￨O￨- Process￨U￨VB￨O￨- (￨L￨-LRB-￨O￨- CP￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- via￨L￨IN￨O￨- nearest￨L￨JJS￨O￨A neighbour￨L￨NN￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- passed￨L￨VBN￨O￨- on￨L￨IN￨O￨- to￨L￨TO￨O￨- healthy￨L￨JJ￨O￨- nearest￨L￨JJS￨O￨- neighbours￨L￨NNS￨O￨- stochastically￨L￨RB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- specific￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- while￨L￨IN￨O￨- infected￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- spontaneously￨L￨RB￨O￨- recover￨L￨VB￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- ǫ￨L￨NN￨O￨- .￨L￨.￨O￨- +Predictions￨U￨NNS￨O￨- for￨L￨IN￨O￨- critical￨L￨JJ￨O￨- exponents￨L￨NNS￨O￨A obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- mean-field￨L￨JJ￨O￨- theory￨L￨NN￨O￨- are￨L￨VBP￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- agree￨L￨VB￨O￨- with￨L￨IN￨O￨- simulation￨L￨NN￨O￨- results￨L￨VBZ￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- p￨L￨NN￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.95￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- sharply￨L￨RB￨O￨- cross￨L￨VB￨O￨- over￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- one-dimensional￨L￨JJ￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- k-regular￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- No.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 710￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 730￨L￨CD￨NUMBER￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.1214￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 08-AOAS217￨L￨NN￨O￨- c￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- STATISTICAL￨U￨NNP￨O￨- METHODS￨U￨NNS￨O￨- FOR￨U￨IN￨O￨- AUTOMATED￨U￨JJ￨O￨- DRUG￨U￨NN￨O￨- SUSCEPTIBILITY￨U￨NN￨O￨- TESTING￨U￨NN￨O￨- :￨L￨:￨O￨- BAYESIAN￨U￨NNP￨O￨- MINIMUM￨U￨NNP￨O￨- INHIBITORY￨U￨JJ￨O￨- CONCENTRATION￨U￨NNP￨O￨- PREDICTION￨U￨NNP￨O￨- FROM￨U￨NNP￨O￨- GROWTH￨U￨NN￨O￨- CURVES￨U￨NNS￨O￨- By￨U￨IN￨O￨- Xi￨U￨NN￨O￨- Kathy￨U￨NNP￨PERSON￨- Zhou￨U￨NNP￨PERSON￨- ,1,2￨L￨CD￨NUMBER￨- Merlise￨U￨NNP￨PERSON￨- A.￨U￨NN￨PERSON￨- Turner￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Tim￨U￨NNP￨PERSON￨- Wiles￨U￨NNP￨PERSON￨- Cornel￨U￨NNP￨PERSON￨- l￨L￨NN￨O￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Duke￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Becton￨U￨NNP￨PERSON￨- –￨L￨:￨O￨- Dickinson￨U￨NNP￨ORGANIZATION￨- Diagnostic￨U￨NNP￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Morgan￨U￨NNP￨ORGANIZATION￨- Stanley￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Insightful￨U￨NNP￨ORGANIZATION￨- Corporation￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Johns￨U￨NNP￨ORGANIZATION￨- Hopkins￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Becton￨U￨NNP￨PERSON￨- –￨L￨:￨O￨- Dickinson￨U￨NNP￨ORGANIZATION￨- Diagnostic￨U￨NNP￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- and￨L￨CC￨O￨- Becton￨U￨NNP￨PERSON￨- –￨L￨:￨O￨- Dickinson￨U￨NNP￨O￨- Diagnostic￨U￨NNP￨O￨- Systems￨U￨NNPS￨O￨- Determination￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- inhibitory￨L￨JJ￨O￨- concentration￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MIC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- drug￨L￨NN￨O￨- that￨L￨WDT￨O￨- prevents￨L￨VBZ￨O￨- microbial￨L￨JJ￨O￨- growth￨L￨NN￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- step￨L￨NN￨O￨- for￨L￨IN￨O￨- managing￨L￨NN￨O￨- patients￨L￨NNS￨O￨- with￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- probabilistic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- accurately￨L￨RB￨O￨- estimates￨L￨VBZ￨O￨- MICs￨U￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- panel￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- curves￨L￨NNS￨O￨A reflecting￨L￨VBG￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- growth￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- determining￨L￨VBG￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- dilution￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- antimicrobial￨L￨JJ￨O￨- agent￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- MIC￨U￨NN￨O￨- given￨L￨VBN￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- curves￨L￨NNS￨O￨A over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- point￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- MICs￨U￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- posterior￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- that￨L￨WDT￨O￨- each￨L￨DT￨O￨- dilution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- MIC￨U￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- growth￨L￨NN￨O￨- curves￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨VBP￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- description￨L￨NN￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- heterogeneous￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- HMF￨U￨NN￨ORGANIZATION￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- extremely￨L￨RB￨O￨- useful￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- thought￨L￨VBN￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- information￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- but￨L￨CC￨O￨- of￨L￨IN￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- framework￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- proved￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- exact￨L￨JJ￨O￨- in￨L￨IN￨O￨- annealed￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- degrees￨L￨NNS￨O￨- are￨L￨VBP￨O￨- sampled￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨A degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- step￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- its￨L￨PRP$￨O￨- specific￨L￨NN￨O￨- connectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- fixed￨L￨VBN￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- average￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +HMF￨U￨NN￨O￨- coarse-grains￨L￨NNS￨O￨- vertices￨L￨NNS￨O￨- within￨L￨IN￨O￨- degree￨L￨NN￨O￨A classes￨L￨NNS￨O￨- and￨L￨CC￨O￨- hypothesizes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- class￨L￨NN￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- also￨L￨RB￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- neglected￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- obtain￨L￨VB￨O￨- more￨L￨JJR￨O￨- details￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- node￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- description￨L￨NN￨O￨A ,￨L￨,￨O￨- usually￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- to￨L￨TO￨O￨- rely￨L￨VB￨O￨- on￨L￨IN￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- MC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- validate￨L￨VB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- using￨L￨VBG￨O￨- HMF￨U￨NN￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- susceptible-infectious-recovered/removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- an￨L￨DT￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨- whereby￨L￨WRB￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- combined￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- make￨L￨VBP￨O￨- infection-causing￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- recover￨L￨VB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- infecteds￨L￨NNS￨O￨- will￨L￨MD￨O￨- either￨L￨CC￨O￨- cause￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- ’￨L￨''￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rapidly￨L￨RB￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infinite￨L￨JJ￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- neighbours￨L￨NNS￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- contact￨L￨NN￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- sometimes￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨A probability￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- fractional￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- utilising￨L￨VBG￨O￨- percolation￨L￨NN￨O￨- theory￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- -￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- ‘￨L￨``￨O￨- Compartmental￨U￨JJ￨O￨- ’￨L￨''￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- -￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- interacting￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- in￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- ,￨L￨,￨O￨- capture￨L￨VBP￨O￨A the￨L￨DT￨O￨- essence￨L￨NN￨O￨- of￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- host-to-host￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- undirected￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- invasion￨L￨NN￨O￨A from￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- probabilistic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- endemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- following￨L￨VBG￨O￨- successful￨L￨JJ￨O￨- invasion￨L￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- relationship￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- directed￨L￨VBN￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨A such￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- which￨L￨WDT￨O￨- defines￨L￨VBZ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- slightly￨L￨RB￨O￨- different￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- on￨L￨IN￨O￨- long-range￨L￨JJ￨O￨- connected￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- disorder￨L￨NN￨O￨- renormalization￨L￨NN￨O￨- group￨L￨NN￨O￨- method￨L￨NN￨O￨- and￨L￨CC￨O￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Infinite￨U￨JJ￨O￨- randomness￨L￨NN￨O￨- critical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- long-range￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- R´obert￨U￨NN￨O￨- Juh￨U￨NN￨O￨- ´￨L￨''￨O￨- asz￨L￨NNP￨O￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Solid￨U￨JJ￨ORGANIZATION￨- State￨U￨NN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Optics￨U￨NNS￨ORGANIZATION￨- ,￨L￨,￨O￨- Wigner￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- Centre￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- H-1525￨U￨NN￨O￨- Budapest￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- P.O.￨U￨NNP￨O￨- Box￨U￨NNP￨O￨- 49￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Hungary￨U￨NNP￨COUNTRY￨- E-mail￨U￨NN￨O￨- :￨L￨:￨O￨- Istv￨U￨NN￨O￨- ´￨L￨''￨O￨- an￨L￨DT￨O￨- A￨U￨NN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- additional￨L￨JJ￨O￨- disorder￨L￨NN￨O￨- of￨L￨IN￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- infinite￨L￨NN￨O￨A randomness￨L￨NN￨O￨- critical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- disordered￨L￨VBN￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- critical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infinite￨L￨NN￨O￨A randomness￨L￨NN￨O￨- fixed￨L￨VBD￨O￨- point￨L￨NN￨O￨- which￨L￨WDT￨O￨- manifests￨L￨VBZ￨O￨- itself￨L￨PRP￨O￨- in￨L￨IN￨O￨- logarithmic￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- 0￨L￨CD￨DATE￨- 3￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Infinite￨U￨JJ￨MISC￨- randomness￨L￨NN￨O￨- critical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A process￨L￨NN￨O￨A 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Chemical￨U￨NNP￨O￨- reactions￨L￨NNS￨O￨A and￨L￨CC￨O￨- biochemical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- living￨L￨NN￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- societies￨L￨NNS￨O￨- and￨L￨CC￨O￨- technological￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- systems￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- states￨L￨NNS￨O￨- change￨L￨VBP￨O￨- at￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- random￨L￨JJ￨O￨- intervals￨L￨NNS￨O￨- ,￨L￨,￨O￨- defining￨L￨VBG￨O￨- a￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- events￨L￨NNS￨O￨- that￨L￨WDT￨O￨- conform￨L￨VBP￨O￨- a￨L￨DT￨O￨- mixture￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- practical￨L￨JJ￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- alike￨L￨RB￨O￨- the￨L￨DT￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- Markovian￨U￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- that￨L￨WDT￨O￨- now￨L￨RB￨DATE￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- events￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- elapsed￨L￨VBD￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨A last￨L￨JJ￨O￨- took￨L￨VBD￨O￨- place￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- assess￨L￨VB￨O￨- our￨L￨PRP$￨O￨- generalized￨L￨VBN￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- biochemical￨L￨JJ￨O￨- reactions￨L￨NNS￨O￨A with￨L￨IN￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- bridge￨L￨VB￨O￨- this￨L￨DT￨O￨- gap￨L￨NN￨O￨- between￨L￨IN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- practice￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- methodology￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- spreading￨L￨VBG￨O￨A processes￨L￨NNS￨O￨A with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- times￨L￨NNS￨O￨- using￨L￨VBG￨O￨- phase-type￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- practice￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- times￨L￨NNS￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- real￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A processes￨L￨NNS￨O￨A ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- web￨L￨NN￨O￨- content￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- Internet￨U￨NN￨MISC￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- far￨L￨RB￨O￨- from￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- 0￨L￨CD￨DATE￨- 5￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- Most￨U￨JJS￨O￨- theoretical￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨A processes￨L￨NNS￨O￨A over￨L￨IN￨O￨- networks￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- exponentially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- times￨L￨NNS￨O￨- .￨L￨.￨O￨- +Bio-Inspired￨U￨NNP￨O￨- Framework￨U￨NNP￨O￨- for￨L￨IN￨O￨- Allocation￨U￨NNP￨O￨- of￨L￨IN￨O￨- Protection￨U￨NNP￨O￨- Resources￨U￨NNPS￨O￨- in￨L￨IN￨O￨- Cyber-Physical￨U￨NNP￨ORGANIZATION￨- Networks￨U￨NNP￨ORGANIZATION￨- Victor￨U￨NNP￨ORGANIZATION￨- M.￨U￨NNP￨ORGANIZATION￨- 3￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 5￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- Chapter￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Understanding￨U￨VBG￨O￨- spreading￨L￨VBG￨O￨A processes￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- designing￨L￨VBG￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨- them￨L￨PRP￨O￨- are￨L￨VBP￨O￨- relevant￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- different￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- security￨L￨NN￨O￨- of￨L￨IN￨O￨- cyberphysical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- works￨L￨NNS￨O￨- that￨L￨WDT￨O￨- analyze￨L￨VBP￨O￨- different￨L￨JJ￨O￨A variations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- extensions￨L￨NNS￨O￨- to￨L￨TO￨O￨- higher￨L￨JJR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- states￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- explicit￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- birth￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- popular￨L￨JJ￨O￨A dynamic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- fast-slow￨L￨JJ￨O￨- heterogeneous￨L￨JJ￨O￨- population￨L￨NN￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- various￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- have￨L￨VBP￨O￨- crucial￨L￨JJ￨O￨- influences￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- scaling￨L￨NN￨O￨- laws￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- early-warning￨L￨JJ￨O￨- signs￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- noise￨L￨NN￨O￨- terms￨L￨NNS￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- the￨L￨DT￨O￨- fluctuation￨L￨NN￨O￨- effects￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- import￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- analyse￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- warning￨L￨NN￨O￨- signs￨L￨NNS￨O￨A for￨L￨IN￨O￨- critical￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- tipping￨L￨VBG￨O￨- points￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Epidemics￨U￨NNS￨O￨- ,￨L￨,￨O￨- heterogeneous￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- transcritical￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨- ,￨L￨,￨O￨- SIS-model￨U￨NN￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨- ,￨L￨,￨O￨- warning￨L￨VBG￨O￨- signs￨L￨NNS￨O￨A ,￨L￨,￨O￨- tipping￨L￨VBG￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- critical￨L￨JJ￨O￨- transition￨L￨NN￨O￨- ,￨L￨,￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨A and￨L￨CC￨O￨- stochasticity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +&￨L￨CC￨O￨- Scaling￨U￨NNP￨O￨- Laws￨U￨VBZ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- explain￨L￨VB￨O￨A and￨L￨CC￨O￨- especially￨L￨RB￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- of￨L￨IN￨O￨- enormous￨L￨JJ￨O￨- importance￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- τc￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- lower￨L￨JJR￨O￨- bounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- 1/λ1￨L￨NN￨O￨- in￨L￨IN￨O￨- directed￨L￨VBN￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- λ1￨L￨NN￨O￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- generating￨L￨VBG￨O￨- function￨L￨NN￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- directed￨L￨VBN￨O￨A networks￨L￨NNS￨O￨A with￨L￨IN￨O￨- ξ￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- .￨L￨.￨O￨- +Garlaschelli￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Loffredo￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- reciprocity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- in￨L￨IN￨O￨- directed￨L￨VBN￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- reciprocity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- ξ￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- network￨L￨NN￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ξ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- directed￨L￨JJ￨O￨A network￨L￨NN￨O￨- without￨L￨IN￨O￨- any￨L￨DT￨O￨- bidirectional￨L￨JJ￨O￨- link￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- ξ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨A set￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- tractable￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- conic￨L￨JJ￨O￨- geometric￨L￨JJ￨O￨- programming￨L￨NN￨O￨- ,￨L￨,￨O￨- recently￨L￨RB￨DATE￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Chandrasekaran￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Shah￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- ef￨L￨NN￨O￨- ficiently￨L￨RB￨O￨- find￨L￨VBD￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- worst-case￨L￨JJ￨O￨- spread￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- take￨L￨VB￨O￨- place￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- conic￨L￨JJ￨O￨- geometric￨L￨JJ￨O￨A programming￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- taking￨L￨VBG￨O￨- place￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- directed￨L￨VBN￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- unknown￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- data-driven￨L￨JJ￨O￨- robust￨L￨JJ￨O￨- convex￨L￨NN￨O￨- optimization￨L￨NN￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- allocatio￨L￨NN￨O￨- n￨L￨NN￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨- resources￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- vaccines￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- antidotes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- spread￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- fastest￨L￨JJS￨O￨- possible￨L￨JJ￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- current￨L￨JJ￨DATE￨- network￨L￨NN￨O￨- identi￨L￨NN￨O￨- fication￨L￨NN￨O￨- heuristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- networ￨L￨NN￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- identi￨L￨JJ￨O￨- fied￨L￨VBN￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- available￨L￨JJ￨O￨- dat￨L￨NN￨O￨- a￨L￨DT￨O￨- to￨L￨TO￨O￨- define￨L￨VB￨O￨- an￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨A set￨L￨NN￨O￨- containing￨L￨VBG￨O￨- all￨L￨DT￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- coherent￨L￨JJ￨O￨- with￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- theorem￨L￨NN￨O￨- holds￨L￨VBZ￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- deterministic￨L￨JJ￨O￨- asymptotically￨L￨RB￨O￨A stable￨L￨JJ￨O￨A compartmental￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DFE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- term￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- profile￨L￨NN￨O￨- of￨L￨IN￨O￨- invariant￨L￨JJ￨O￨A density￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- a￨L￨DT￨O￨- persistence￨L￨NN￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- RP￨U￨NN￨O￨- the￨L￨DT￨O￨- Fokker-Planck￨U￨JJ￨MISC￨- equation￨L￨NN￨O￨- associthe￨L￨NN￨O￨- and￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- give￨L￨VBP￨O￨- a￨L￨DT￨O￨- persistence￨L￨NN￨O￨- threshold￨L￨NN￨O￨- theorem￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- probabil￨L￨NN￨O￨- -￨L￨:￨O￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- persists￨L￨VBZ￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- probability￨L￨NN￨O￨- if￨L￨IN￨O￨- RP￨U￨NN￨O￨- ity￨L￨NN￨O￨- if￨L￨IN￨O￨- RP￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- recurrent￨L￨JJ￨O￨- if￨L￨IN￨O￨- RS￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- invariant￨L￨JJ￨O￨A density￨L￨NN￨O￨- for￨L￨IN￨O￨- ated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- SDE￨U￨NNP￨ORGANIZATION￨- SIS￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- when￨L￨WRB￨O￨- RS￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- existence￨L￨NN￨O￨- ,￨L￨,￨O￨- uniqueness￨L￨NN￨O￨- ,￨L￨,￨O￨- boundedness￨L￨NN￨O￨- and￨L￨CC￨O￨- positiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- counterpart￨L￨NN￨O￨- of￨L￨IN￨O￨- βN￨L￨NN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- σ￨L￨NN￨O￨- 2N￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- µ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- =￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A in￨L￨IN￨O￨- SDE￨U￨NNP￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- σ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- or￨L￨CC￨O￨- σ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- reduces￨L￨VBZ￨O￨A to￨L￨TO￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- one-dimensional￨L￨JJ￨O￨- SDE￨U￨NNP￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- βN￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- µ￨L￨NN￨O￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- +￨L￨CC￨O￨- σ￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- dB￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Information￨U￨NN￨O￨- and￨L￨CC￨O￨- Inference￨U￨NN￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- Journal￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- IMA￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Page￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- 31￨L￨CD￨NUMBER￨- doi￨L￨FW￨O￨- :￨L￨:￨O￨- 10.1093￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- imaiai/drn000￨L￨CD￨NUMBER￨- Optimal￨U￨JJ￨O￨- curing￨L￨VBG￨O￨A policy￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- population￨L￨NN￨O￨- ST￨U￨JJ￨O￨- E￨U￨NN￨O￨- FAN￨U￨NN￨O￨- IA￨U￨NN￨STATE_OR_PROVINCE￨- OT￨U￨NNP￨O￨- TAV￨U￨NNP￨O￨- IANO￨U￨NNP￨O￨- Fondazione￨U￨NNP￨O￨- Bruno￨U￨NNP￨PERSON￨- Kessler￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Via￨U￨NNP￨O￨- alla￨L￨FW￨O￨- Cascata￨U￨FW￨O￨- 56/d￨L￨NN￨O￨- ,￨L￨,￨O￨- 38123￨L￨CD￨NUMBER￨- Povo￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Trento￨U￨NN￨CITY￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨ORGANIZATION￨- Mathematics￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Trento￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Via￨U￨NNP￨O￨- Sommarive￨U￨NNP￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 38123￨L￨CD￨NUMBER￨- Povo￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Trento￨U￨NN￨CITY￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- Fondazione￨U￨NNP￨PERSON￨- Bruno￨U￨NNP￨PERSON￨- Kessler￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Via￨U￨NNP￨O￨- alla￨L￨FW￨O￨- Cascata￨U￨FW￨O￨- 56/d￨L￨NN￨O￨- ,￨L￨,￨O￨- 38123￨L￨CD￨NUMBER￨- Povo￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Trento￨U￨NN￨CITY￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- FRANCE￨U￨NNP￨COUNTRY￨- SCO￨U￨NN￨O￨- D￨U￨NN￨O￨- E￨U￨NN￨O￨- PE￨U￨NN￨STATE_OR_PROVINCE￨- L￨U￨NN￨O￨- L￨U￨NN￨O￨- EGR￨U￨NN￨O￨- IN￨U￨IN￨O￨- I￨U￨PRP￨O￨- ST￨U￨JJ￨O￨- E￨U￨NN￨O￨- FANO￨U￨NN￨O￨- BONACCOR￨U￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- Mathematics￨U￨NNP￨O￨- Department￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Trento￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Via￨U￨NNP￨O￨- Sommarive￨U￨NNP￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 38123￨L￨CD￨NUMBER￨- Povo￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Trento￨U￨NN￨CITY￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- AND￨U￨CC￨O￨- P￨U￨NN￨O￨- IE￨U￨JJ￨O￨- T￨U￨NN￨O￨- VAN￨U￨NN￨O￨- M￨U￨NN￨O￨- IEGHEM￨U￨NN￨O￨- EEMCS￨U￨NN￨O￨- ,￨L￨,￨O￨- Delft￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Mekelweg￨U￨NNP￨ORGANIZATION￨- 4￨L￨CD￨NUMBER￨- 2628￨L￨CD￨DATE￨- CD￨U￨NNP￨O￨- Delft￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- [￨L￨-LRB-￨O￨- Received￨U￨VBN￨O￨- on￨L￨IN￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ]￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- design￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- curing￨L￨NN￨O￨- policy￨L￨NN￨O￨- ,￨L￨,￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- stem￨L￨VB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- affordable￨L￨JJ￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- supporting￨L￨VBG￨O￨- the￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Exploiting￨U￨VBG￨O￨- the￨L￨DT￨O￨- computation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- determine￨L￨VBP￨O￨- a￨L￨DT￨O￨- cost-optimal￨L￨JJ￨O￨- curing￨L￨NN￨O￨A policy￨L￨NN￨O￨- by￨L￨IN￨O￨- solving￨L￨VBG￨O￨- a￨L￨DT￨O￨- convex￨L￨NN￨O￨- minimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- possesses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- dimension￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Institute￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Warwick￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Coventry￨U￨NNP￨O￨- CV4￨U￨NN￨O￨- 7AL￨L￨NN￨O￨- ,￨L￨,￨O￨- Trophic￨U￨JJ￨O￨- coherence￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- directed￨L￨VBN￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- organised￨L￨VBN￨O￨- in￨L￨IN￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- structural￨L￨JJ￨O￨- and￨L￨CC￨O￨- dynamical￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- graph￨L￨NN￨O￨- eigenspectra￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- or￨L￨CC￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- feedback￨L￨NN￨O￨A cycles￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- linear￨L￨JJ￨O￨- stability￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- yet￨L￨CC￨O￨- apparently￨L￨RB￨O￨- quite￨L￨RB￨O￨- different￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- –￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- adapted￨L￨VBD￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- complex￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- an￨L￨DT￨O￨- Amari-Hopfield￨U￨JJ￨MISC￨- neural￨L￨JJ￨O￨- network￨L￨NN￨O￨- –￨L￨:￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- cases￨L￨NNS￨O￨- the￨L￨DT￨O￨- related￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A processes￨L￨NNS￨O￨A are￨L￨VBP￨O￨- modulated￨L￨VBN￨O￨- in￨L￨IN￨O￨- similar￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- trophic￨L￨JJ￨O￨- coherence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- trophic￨L￨JJ￨O￨- coherence￨L￨NN￨O￨- can￨L￨MD￨O￨- exert￨L￨VB￨O￨- a￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- determining￨L￨VBG￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- pulse￨L￨NN￨O￨- of￨L￨IN￨O￨- activity￨L￨NN￨O￨A will￨L￨MD￨O￨- percolate￨L￨VB￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- network￨L￨NN￨O￨- or￨L￨CC￨O￨- remain￨L￨VBP￨O￨- confined￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- such￨L￨JJ￨O￨- activity￨L￨NN￨O￨- will￨L￨MD￨O￨- quickly￨L￨RB￨O￨- die￨L￨VB￨O￨- out￨L￨RP￨O￨- or￨L￨CC￨O￨- endure￨L￨VB￨O￨- indefinitely￨L￨RB￨O￨- .￨L￨.￨O￨- +Right￨U￨RB￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- and￨L￨CC￨O￨- L￨U￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- left￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- less￨L￨JJR￨O￨- trophically￨L￨RB￨O￨- coherent￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- q￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.49￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +INTRODUCTION￨U￨NN￨O￨- Contagion￨U￨NN￨O￨- processes￨L￨NNS￨O￨- abound￨L￨VBP￨O￨- in￨L￨IN￨O￨- nature￨L￨NN￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨A populations￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- adaptation￨L￨NN￨O￨- of￨L￨IN￨O￨- technology￨L￨NN￨O￨- and￨L￨CC￨O￨- norms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- activation￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- neural￨L￨JJ￨O￨- tissue￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- escape￨L￨NN￨CRIMINAL_CHARGE￨- mechanisms￨L￨NNS￨O￨- from￨L￨IN￨O￨- predators￨L￨NNS￨O￨- in￨L￨IN￨O￨- schooling￨L￨NN￨O￨- fish￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- agent￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- employed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- starting￨L￨VBG￨O￨- point￨L￨NN￨O￨- for￨L￨IN￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- involving￨L￨VBG￨O￨- several￨L￨JJ￨O￨- interacting￨L￨VBG￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- particularly￨L￨RB￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- microbiological￨L￨JJ￨O￨- ecosystems￨L￨NNS￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- system￨L￨NN￨O￨- exhibits￨L￨VBZ￨O￨- discontinuous￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- not￨L￨RB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- single￨L￨JJ￨O￨- agent￨L￨NN￨O￨- contagion￨L￨NN￨O￨A ,￨L￨,￨O￨- multi-stability￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- separation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- into￨L￨IN￨O￨- different￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- for￨L￨IN￨O￨- inception￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- affected￨L￨VBN￨O￨A by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- transmissible￨L￨JJ￨O￨- agent￨L￨NN￨O￨- A￨U￨DT￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- baseline￨L￨NN￨O￨- propensity￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- agent￨L￨NN￨O￨- B￨U￨NN￨O￨- and￨L￨CC￨O￨- vice￨L￨NN￨O￨- versa￨L￨RB￨O￨- .￨L￨.￨O￨- +13￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Haus￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10115￨L￨CD￨NUMBER￨- Berlin￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Germany￨U￨NNP￨COUNTRY￨- We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- cooperativity￨L￨NN￨O￨- between￨L￨IN￨O￨- contagion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- spread￨L￨VBP￨O￨- and￨L￨CC￨O￨- persist￨L￨VBP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Complex￨U￨NN￨O￨- contagion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- discontinuous￨L￨JJ￨O￨- transition￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- adoption￨L￨NN￨O￨A phase￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- individual￨L￨JJ￨O￨- adoption￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- section￨L￨NN￨O￨- III￨U￨CD￨NUMBER￨- we￨L￨PRP￨O￨- in￨L￨IN￨O￨- -￨L￨:￨O￨- troduce￨L￨NN￨O￨- a￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- evolution￨L￨NN￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- adopters￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- layer￨L￨NN￨TITLE￨A and￨L￨CC￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- points￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- stability￨L￨NN￨O￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- diagram￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- uncoupled￨L￨VBN￨O￨- and￨L￨CC￨O￨- coupled￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- adoption￨L￨NN￨O￨A layer￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- adoption￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- interlayer￨L￨NN￨O￨- connectivity￨L￨NN￨O￨- whereas￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- isolated￨L￨VBN￨O￨- single￨L￨JJ￨O￨- network￨L￨NN￨O￨- it￨L￨PRP￨O￨- would￨L￨MD￨O￨- decrease￨L￨VB￨O￨- with￨L￨IN￨O￨- average￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +Besides￨U￨IN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- transition￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- as￨L￨IN￨O￨- as￨L￨IN￨O￨- sudden￨L￨JJ￨O￨- drop￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- adopters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- layer￨L￨NN￨TITLE￨A .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- related￨L￨JJ￨O￨- works￨L￨NNS￨O￨- on￨L￨IN￨O￨- information￨L￨NN￨O￨- propagation￨L￨NN￨O￨- directly￨L￨RB￨O￨- define￨L￨JJ￨O￨- interpersonal￨L￨JJ￨O￨- influence￨L￨NN￨O￨- between￨L￨IN￨O￨- each￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- independent￨L￨JJ￨RELIGION￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- influences￨L￨NNS￨O￨A come￨L￨VBP￨O￨- from￨L￨IN￨O￨- or￨L￨CC￨O￨- affect￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- user￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- seen￨L￨VBN￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- learning￨L￨VBG￨O￨- sentimental￨L￨JJ￨O￨- influences￨L￨NNS￨O￨A from￨L￨IN￨O￨- users￨L￨NNS￨O￨- ’￨L￨POS￨O￨- behaviors￨L￨NNS￨O￨- yet￨L￨RB￨O￨- .￨L￨.￨O￨- +And￨U￨CC￨O￨- influences￨L￨NNS￨O￨A are￨L￨VBP￨O￨- learned￨L￨VBN￨O￨- from￨L￨IN￨O￨- user￨L￨NN￨O￨- ’s￨L￨POS￨O￨- propagation￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- temporal￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- sentiments￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- how￨L￨WRB￨O￨- network￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- shapes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- an￨L￨DT￨O￨- initially￨L￨RB￨O￨- endemic￨L￨JJ￨O￨- strain￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- emerging￨L￨VBG￨O￨A one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- both￨L￨CC￨O￨- strains￨L￨NNS￨O￨- follow￨L￨VBP￨O￨- a￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- comparable￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- evolution￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- attention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- devoted￨L￨VBN￨O￨A to￨L￨TO￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- co-circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- networked￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- competitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- cooperative￨L￨JJ￨O￨- interference￨L￨NN￨O￨- among￨L￨IN￨O￨- them￨L￨PRP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- strong￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- activity￨L￨NN￨O￨- volume￨L￨NN￨O￨- cause￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- emerging￨L￨VBG￨O￨A strain￨L￨NN￨O￨- replaces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- highly￨L￨RB￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- emergence￨L￨NN￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A on￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- research￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- significantly￨L￨RB￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- exponential￨L￨JJ￨O￨- cutoff￨L￨NN￨O￨- is￨L￨VBZ￨O￨- best￨L￨RB￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- semi-log￨L￨NN￨O￨- plot￨L￨NN￨O￨- after￨L￨IN￨O￨- removing￨L￨VBG￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- decay￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1e￨L￨NN￨O￨- ,￨L￨,￨O￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- decay￨L￨NN￨O￨- time￨L￨NN￨O￨- τE￨L￨NN￨O￨- =￨L￨JJ￨O￨- 25￨L￨CD￨NUMBER￨- ±￨L￨NN￨O￨- 2￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- τE￨L￨NN￨O￨- =￨L￨JJ￨O￨- 9￨L￨CD￨NUMBER￨- ±￨L￨NN￨O￨- 1￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- approximately￨L￨RB￨O￨- 270￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- university￨L￨NN￨O￨- and￨L￨CC￨O￨- commercial￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NNP￨O￨- 1c-f￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- predictions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- time￨L￨NN￨O￨- resolved￨L￨VBN￨O￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- virus￨L￨NN￨O￨- bulletins￨L￨NNS￨O￨- ,￨L￨,￨O￨- show￨L￨VBP￨O￨- a￨L￨DT￨O￨- decay￨L￨NN￨O￨A time￨L￨NN￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨DURATION￨- year￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- one￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- decay￨L￨NN￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Poisson￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- based￨L￨VBN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- non-Poisson￨L￨JJ￨MISC￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- decay￨L￨NN￨O￨A times￨L￨NNS￨O￨- significantly￨L￨RB￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Poisson￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- based￨L￨VBN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- email￨L￨NN￨O￨- activity￨L￨NN￨O￨- pattern￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- renewal￨L￨NN￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- inter-event￨L￨JJ￨O￨- time￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- residual￨L￨JJ￨O￨- waiting￨L￨VBG￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨A density￨L￨NN￨O￨A function￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- hτ￨L￨NN￨O￨- i￨L￨FW￨O￨- Z￨U￨NN￨O￨- ∞￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- dxP￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- intuitive￨L￨JJ￨O￨- rewiring￨L￨NN￨O￨A rule￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- connections￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- profound￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- specific￨L￨NN￨O￨- network￨L￨NN￨O￨- properties￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- assortative￨L￨JJ￨O￨- degree￨L￨NN￨O￨- correlations￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- formation￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- loosely￨L￨RB￨O￨- connected￨L￨VBN￨O￨- sub-compartments￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- on￨L￨IN￨O￨- scale￨L￨NN￨O￨- free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- detrimental￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- assortative￨L￨JJ￨O￨A degree￨L￨NN￨O￨- correlations￨L￨NNS￨O￨- on￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- vaccination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- attention￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- revealing￨L￨VBG￨O￨- that￨L￨IN￨O￨- simple￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- preferential￨L￨JJ￨O￨- attachment￨L￨NN￨O￨- or￨L￨CC￨O￨- selective￨L￨JJ￨O￨- rewiring￨L￨NN￨O￨A ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- complex￨L￨NN￨O￨- topologies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- doing￨L￨VBG￨O￨- so￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- adapt￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨A topology￨L￨NN￨O￨A dynamically￨L￨RB￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- study￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- susceptibles￨L￨NNS￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- rewiring￨L￨VBG￨O￨A their￨L￨PRP$￨O￨- network￨L￨NN￨O￨- connections￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- bound￨L￨VBD￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨A probability￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reached￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- path￨L￨NN￨O￨- starting￨L￨VBG￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- vertex￨L￨NN￨O￨- from￨L￨IN￨O￨- above￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- for￨L￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- density￨L￨NN￨O￨- ;￨L￨:￨O￨- this￨L￨DT￨O￨- generalizes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- Kuulasmaa￨U￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- by￨L￨IN￨O￨- assigning￨L￨VBG￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- Wv￨U￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- Wv￨U￨NN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- vertex￨L￨NN￨ORGANIZATION￨A v￨L￨LS￨O￨- in￨L￨IN￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- vectors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Wv￨U￨NN￨O￨- ,￨L￨,￨O￨- ¯￨L￨CD￨NUMBER￨- Wv￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- i.i.d.￨L￨VBN￨O￨- and￨L￨CC￨O￨- distributed￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- W￨U￨NN￨O￨- ,￨L￨,￨O￨- ¯￨L￨CD￨NUMBER￨- W￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- values￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- convex￨L￨NN￨O￨- subset￨L￨NN￨O￨- S￨U￨NN￨O￨- ¯￨L￨CD￨NUMBER￨- Wv￨U￨NN￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Spatial￨U￨JJ￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- 3￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- note￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- κ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- factorisable￨L￨JJ￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- if￨L￨IN￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- functions￨L￨NNS￨O￨- κ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- κ2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- κ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- κ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- κ2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- without￨L￨IN￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- generality￨L￨NN￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- κ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- xy￨L￨NN￨O￨- and￨L￨CC￨O￨- S￨U￨NN￨O￨- =￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- ,￨L￨,￨O￨- background￨L￨NN￨O￨- and￨L￨CC￨O￨- main￨L￨JJ￨O￨- results￨L￨NNS￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- →￨L￨NN￨O￨- Infectious￨U￨JJ￨O￨- →￨L￨NN￨O￨- Removed￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- directed￨L￨VBN￨O￨- graph￨L￨NN￨O￨- G￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- assume￨L￨VB￨O￨A that￨L￨DT￨O￨- Wv￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- weights￨L￨NNS￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- u￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- uv￨L￨NN￨O￨- ∈￨L￨NN￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- v￨L￨LS￨O￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- already￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- κ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Wu￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- ¯￨L￨CD￨NUMBER￨- Wv￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- κ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- some￨L￨DT￨O￨- connection￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- specified￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- critical￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Robustness￨U￨NNP￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- against￨L￨IN￨O￨- propagating￨L￨VBG￨O￨A attacks￨L￨NNS￨CAUSE_OF_DEATH￨- under￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- 3￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- network￨L￨NN￨O￨- unvaccinated￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- unvaccinated￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- vaccinated￨L￨VBN￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- vaccinated￨L￨VBN￨O￨- and￨L￨CC￨O￨- removed￨L￨VBN￨O￨- residual￨L￨JJ￨O￨- network￨L￨NN￨O￨- residual￨L￨JJ￨O￨- network￨L￨NN￨O￨- seed￨L￨NN￨O￨- node￨L￨NN￨O￨- seed￨L￨NN￨O￨- node￨L￨NN￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- robustness￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- against￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨A :￨L￨:￨O￨- random￨L￨JJ￨O￨- failure￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- sequentially￨L￨RB￨O￨- removed￨L￨VBN￨O￨- with￨L￨IN￨O￨- equal￨L￨JJ￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- intentional￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- hubs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- preferentially￨L￨RB￨O￨- removed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- robustness￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- against￨L￨IN￨O￨- propagating￨L￨VBG￨O￨A attacks￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- obey￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +T￨U￨NN￨O￨- and￨L￨CC￨O￨- T￨U￨NN￨O￨- fv￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- probabilities￨L￨NNS￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- eventually￨L￨RB￨O￨- removed￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- node￨L￨NN￨O￨- infects￨L￨VBZ￨O￨- an￨L￨DT￨O￨- unvaccinated￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- neighbor￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- propagating￨L￨VBG￨O￨A attack￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- 0￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Robustness￨U￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- against￨L￨IN￨O￨- propagating￨L￨VBG￨O￨A attacks￨L￨NNS￨CAUSE_OF_DEATH￨- under￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Further￨U￨RB￨O￨- more￨L￨RBR￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- consisted￨L￨VBD￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- acting￨L￨VBG￨O￨- with￨L￨IN￨O￨- heavy-tailed￨L￨JJ￨O￨- inter-event￨L￨JJ￨O￨- time￨L￨NN￨O￨A distribution￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- heavy-tailed￨L￨JJ￨O￨- inter-event￨L￨JJ￨O￨- time￨L￨NN￨O￨A distribution￨L￨NN￨O￨A at￨L￨IN￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- accepted￨L￨VBN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- acts￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- way￨L￨NN￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- under￨L￨IN￨O￨- debate￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- aim￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SI￨U￨NNP￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- creation￨L￨NN￨O￨- of￨L￨IN￨O￨- subgraphs￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- trying￨L￨VBG￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨A the￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +MSC￨U￨NNP￨ORGANIZATION￨- classes￨L￨NNS￨O￨A :￨L￨:￨O￨- 62P10￨L￨NN￨O￨- 60J10￨L￨NN￨O￨- Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Graph￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- SI￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Coevolution￨U￨NNP￨O￨- ,￨L￨,￨O￨- Adaptative￨U￨NNP￨O￨- social￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- Extinction￨U￨NN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨- and￨L￨CC￨O￨- prey￨L￨NN￨O￨A populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- coexist￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- ultimately￨L￨RB￨O￨- both￨L￨DT￨O￨- undergo￨L￨VBP￨O￨- extinction￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- happens￨L￨VBZ￨O￨- via￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- routes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- predator￨L￨NN￨O￨- and￨L￨CC￨O￨- prey￨L￨NN￨O￨A populations￨L￨NNS￨O￨- may￨L￨MD￨O￨- coexist￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- but￨L￨CC￨O￨- ultimately￨L￨RB￨O￨- both￨L￨DT￨O￨- go￨L￨VBP￨O￨- extinct￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- account￨L￨VBP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- form￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- competition￨L￨NN￨O￨- of￨L￨IN￨O￨- rabbits￨L￨NNS￨O￨- over￨L￨IN￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- the￨L￨DT￨O￨- elementary￨L￨JJ￨O￨- process￨L￨NN￨O￨- 2R￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- that￨L￨WDT￨O￨- becomes￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- at￨L￨IN￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨A sizes￨L￨NNS￨O￨A .￨L￨.￨O￨- +MODEL￨U￨NN￨TITLE￨- AND￨U￨CC￨O￨- MEAN-FIELD￨U￨NN￨O￨- DYNAMICS￨U￨NNS￨O￨- We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- predators￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- F￨U￨NN￨O￨- -￨L￨:￨O￨- foxes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- prey￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- R￨U￨NN￨ORGANIZATION￨- -￨L￨:￨O￨- rabbits￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- mixed￨L￨VBN￨O￨- in￨L￨IN￨O￨- space￨L￨NN￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- freedom￨L￨NN￨O￨- are￨L￨VBP￨O￨- irrelevant￨L￨JJ￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- effective￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- linearly￨L￨RB￨O￨- decrease￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A prevalence￨L￨NN￨O￨A in￨L￨IN￨O￨- small-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- for￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- acts￨L￨VBZ￨O￨- exponentially￨L￨RB￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- interesting￨L￨JJ￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- rate￨L￨NN￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- eradicating￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- preventing￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- vaccination￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A prevalence￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Classical￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- showed￨L￨VBN￨O￨- that￨L￨IN￨O￨- rabbits￨L￨NNS￨O￨- have￨L￨VBP￨O￨- low￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- PrPSc￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Vorberg￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- 2003￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Khan￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- 2001￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Nisbet￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Wen￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2003￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Khan￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨A time￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- positive￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- study￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- response￨L￨NN￨O￨- times￨L￨NNS￨O￨- influence￨L￨NN￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- uncorrelated￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- procedure￨L￨NN￨O￨- of￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨A times￨L￨NNS￨O￨- and￨L￨CC￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- accelerate￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- and￨L￨CC￨O￨- middle￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- heterogeneous￨L￨JJ￨O￨- response￨L￨NN￨O￨A times￨L￨NNS￨O￨- on￨L￨IN￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- with￨L￨IN￨O￨- adjustable￨L￨JJ￨O￨- power-law￨L￨NN￨O￨- response￨L￨NN￨O￨- time￨L￨NN￨O￨- distribution￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- uncorrelated￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- late￨L￨JJ￨O￨- stage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- slightly￨L￨RB￨O￨- more￨L￨RBR￨O￨- complicated￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- time￨L￨NN￨O￨- changing￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- response￨L￨NN￨O￨A times￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- time-degree￨L￨NN￨O￨- correlation￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- s￨L￨NNS￨O￨- tronger￨L￨VBP￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- response￨L￨NN￨O￨A times￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- faster￨L￨RBR￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- and￨L￨CC￨O￨- middle￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- .￨L￨.￨O￨- +8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- No.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 430￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 447￨L￨CD￨NUMBER￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.1214￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 13-AOAS693￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- TIME-VARYING￨U￨NNP￨O￨- SHARED￨U￨NNP￨O￨- FRAILTY￨U￨NNP￨O￨- MODEL￨U￨NNP￨TITLE￨- WITH￨U￨IN￨O￨- APPLICATION￨U￨NNP￨O￨- TO￨U￨TO￨O￨- INFECTIOUS￨U￨JJ￨O￨- DISEASES1￨U￨NN￨O￨- By￨U￨IN￨O￨- Doyo￨U￨NNP￨PERSON￨- G.￨U￨NNP￨PERSON￨- Paddy￨U￨NNP￨PERSON￨- Farrington￨U￨NNP￨PERSON￨- Open￨U￨NNP￨O￨- University￨U￨NNP￨O￨- We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- parametric￨L￨JJ￨O￨- time-varying￨L￨JJ￨O￨- shared￨L￨JJ￨O￨A frailty￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- changes￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- use￨L￨NN￨O￨- with￨L￨IN￨O￨- bivariate￨L￨JJ￨O￨- current￨L￨JJ￨DATE￨- status￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- uses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- transformation￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- time-invariant￨L￨JJ￨O￨- frailty￨L￨NN￨O￨- U￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- particularly￨L￨RB￨O￨- convenient￨L￨JJ￨O￨- when￨L￨WRB￨O￨- U￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- member￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- gamma￨L￨NN￨O￨- family￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- some￨L￨DT￨O￨- key￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- frailty￨L￨NN￨O￨- variance￨L￨NN￨O￨A function￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- describe￨L￨VB￨O￨- quenched￨L￨JJ￨O￨A disorder￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- Quenched￨U￨NNP￨O￨- Mean-Field￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- QMF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- approximation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- heterogeneities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- are￨L￨VBP￨O￨- quantified￨L￨VBN￨O￨- by￨L￨IN￨O￨- calculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- Inverse￨U￨NNP￨O￨- Participation￨U￨NNP￨O￨- Ratio￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- IPR￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- principal￨L￨JJ￨TITLE￨- eigenvector￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- .￨L￨.￨O￨- +Very￨U￨RB￨O￨- recently￨L￨RB￨DATE￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- bursty￨L￨VBP￨O￨A dynamics￨L￨NNS￨O￨- can￨L￨MD￨O￨- arise￨L￨VB￨O￨- naturally￨L￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- power-law￨L￨NN￨O￨- decaying￨L￨VBG￨O￨- auto-correlations￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- col￨L￨NN￨O￨- lective￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- Markovian￨U￨JJ￨MISC￨- variables￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- generic￨L￨JJ￨O￨- slow￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- was￨L￨VBD￨O￨- suggested￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- non-Markovian￨L￨JJ￨MISC￨- ,￨L￨,￨O￨- bursty￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- agents￨L￨NNS￨O￨- in￨L￨IN￨O￨- small￨L￨JJ￨O￨- world￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- finite￨L￨JJ￨O￨- topological￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- ∝￨L￨CD￨NUMBER￨- rD￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- chemical￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- distance￨L￨NN￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- disorder￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- relevant￨L￨JJ￨O￨- .￨L￨.￨O￨- +Localization￨U￨NN￨O￨- transition￨L￨NN￨O￨- ,￨L￨,￨O￨- Lifschitz￨U￨NNP￨PERSON￨- tails￨L￨NNS￨O￨- and￨L￨CC￨O￨- rare-region￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨A models￨L￨NNS￨O￨A G´eza￨U￨NN￨O￨- ´￨L￨''￨O￨- Odor￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- Center￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Natural￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Hungarian￨U￨JJ￨ORGANIZATION￨- Academy￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- and￨L￨CC￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- distributed￨L￨VBN￨O￨A solution￨L￨NN￨O￨- that￨L￨WDT￨O￨- enables￨L￨VBZ￨O￨- local￨L￨JJ￨O￨- computation￨L￨NN￨O￨- of￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- investment￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- antidotes￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- respectively￨L￨RB￨O￨- reduce￨L￨VB￨O￨- its￨L￨PRP$￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- increase￨L￨VB￨O￨- its￨L￨PRP$￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- contain￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- linearized￨L￨VBN￨O￨- SusceptibleInfected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A in￨L￨IN￨O￨- which￨L￨WDT￨O￨- agents￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- allocate￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- resources￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- prevention￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- antidotes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- treatment￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- contagion￨L￨NN￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 5￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- distributed￨L￨VBN￨O￨A resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- networked￨L￨JJ￨O￨- population￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Distributed￨U￨VBN￨O￨- Alternating￨U￨VBG￨O￨- Direction￨U￨NNP￨O￨- Method￨U￨NNP￨O￨- of￨L￨IN￨O￨- Multipliers￨U￨NNPS￨O￨- (￨L￨-LRB-￨O￨- D-ADMM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- algorithm￨L￨NN￨O￨- .￨L￨.￨O￨- +Next￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- separate￨L￨VBP￨O￨- the￨L￨DT￨O￨- network-wide￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- into￨L￨IN￨O￨- subproblems￨L￨NNS￨O￨- optimally￨L￨RB￨O￨- solved￨L￨VBN￨O￨- by￨L￨IN￨O￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- distributed￨L￨VBN￨O￨A way￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- distributed￨L￨VBN￨O￨A solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- iterative￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- –￨L￨:￨O￨- a￨L￨DT￨O￨- Distributed￨U￨VBN￨O￨- Alternating￨U￨VBG￨O￨- Direction￨U￨NNP￨O￨- Method￨U￨NNP￨O￨- of￨L￨IN￨O￨- Multipliers￨U￨NNPS￨O￨- (￨L￨-LRB-￨O￨- D-ADMM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- algorithm￨L￨NN￨O￨- .￨L￨.￨O￨- +Though￨U￨IN￨O￨- persisting￨L￨VBG￨O￨- for￨L￨IN￨O￨- long￨L￨JJ￨O￨A time￨L￨NN￨O￨A after￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- clearance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- memory￨L￨NN￨O￨- cell￨L￨NN￨O￨- population￨L￨NN￨O￨- slowly￨L￨RB￨O￨- decays￨L￨VBZ￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- run￨L￨NN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- might￨L￨MD￨O￨- lose￨L￨VB￨O￨- his￨L￨PRP$￨O￨- pathogen-specific￨L￨NN￨O￨- immunity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen-specific￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- maintained￨L￨VBN￨O￨- for￨L￨IN￨O￨- long￨L￨JJ￨O￨A time￨L￨NN￨O￨A at￨L￨IN￨O￨- a￨L￨DT￨O￨- level￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- naive￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Vaccinees￨U￨NNS￨O￨- experience￨L￨VBP￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- boosting￨L￨VBG￨O￨- and￨L￨CC￨O￨- waning￨L￨VBG￨O￨- immunity￨L￨NN￨O￨A ,￨L￨,￨O￨- just￨L￨RB￨O￨- as￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- recovered￨L￨VBN￨O￨- from￨L￨IN￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- do￨L￨VBP￨O￨- .￨L￨.￨O￨- +Active￨U￨JJ￨O￨- immunization￨L￨NN￨O￨- is￨L￨VBZ￨O￨- either￨L￨CC￨O￨- induced￨L￨VBN￨O￨A by￨L￨IN￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- administration￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Induced￨U￨VBN￨O￨- immunity￨L￨NN￨O￨A decays￨L￨VBZ￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- years￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- recovery/vaccination￨L￨NN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- might￨L￨MD￨O￨- become￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- again￨L￨RB￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- computer-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- ,￨L￨,￨O￨- tracking￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- parasites￨L￨NNS￨O￨A and￨L￨CC￨O￨- parasite-genes￨L￨NNS￨O￨- ,￨L￨,￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- host-population￨L￨NN￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- totally￨L￨RB￨O￨- recessive￨L￨JJ￨O￨- autosomes￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- anthelmintic￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- can￨L￨MD￨O￨- follow￨L￨VB￨O￨- either￨L￨CC￨O￨- a￨L￨DT￨O￨- fast￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- regime￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- slow￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- regime￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨- treatment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- selection￨L￨NN￨O￨- pressure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasites￨L￨NNS￨O￨A ,￨L￨,￨O￨- vaccines￨L￨NNS￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- decrease￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- alleles￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- .￨L￨.￨O￨- +Vaccines￨U￨NNS￨O￨- targeting￨L￨VBG￨O￨- adult￨L￨JJ￨O￨- parasites￨L￨NNS￨O￨A ,￨L￨,￨O￨- by￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- helminth￨L￨JJ￨O￨- fecundity￨L￨NN￨O￨- or￨L￨CC￨O￨- lifespan￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- than￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- targeting￨L￨VBG￨O￨- parasite￨L￨NN￨O￨- larvae￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- .￨L￨.￨O￨- +Genetics￨U￨NNP￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasites￨L￨NNS￨O￨A play￨L￨VBP￨O￨- key￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- packets￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- larvae￨L￨NNS￨O￨- can￨L￨MD￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- fast￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- fully￨L￨RB￨O￨- recessive￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- levamisole￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sheep￨L￨NN￨O￨- nematode￨L￨NN￨O￨- Haemoncus￨U￨NN￨MISC￨- contortus￨L￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Molecular￨U￨JJ￨O￨- dynamics￨L￨NNS￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- NMR￨U￨NN￨O￨- structures￨L￨NNS￨O￨- of￨L￨IN￨O￨- rabbit￨L￨NN￨O￨- prion￨L￨NN￨O￨- protein￨L￨NN￨O￨A wild-type￨L￨JJ￨O￨- and￨L￨CC￨O￨- mutants￨L￨NNS￨O￨- :￨L￨:￨O￨- surface￨L￨NN￨O￨- electrostatic￨L￨JJ￨O￨- charge￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Version￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Jiapu￨U￨NNP￨O￨- Zhangab￨U￨NNP￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- Feng￨U￨NNP￨PERSON￨- Wanga￨U￨NNP￨PERSON￨- aMolecular￨L￨NNP￨O￨- Model￨U￨NNP￨TITLE￨- Discovery￨U￨NNP￨O￨- Laboratory￨U￨NNP￨O￨- ,￨L￨,￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Chemistry￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Biotechnology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Faculty￨U￨NNP￨O￨- of￨L￨IN￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- Engineering￨U￨NNP￨O￨- &￨L￨CC￨O￨- Technology￨U￨NNP￨O￨- ,￨L￨,￨O￨- Swinburne￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hawthorn￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Victoria￨U￨NNP￨CITY￨- 3122￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- bGraduate￨L￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Information￨U￨NNP￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Centre￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Informatics￨U￨NNPS￨ORGANIZATION￨- and￨L￨CC￨O￨- Applied￨U￨NNP￨O￨- Optimisation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Faculty￨U￨NNP￨O￨- of￨L￨IN￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- The￨U￨DT￨O￨- Federation￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Australia￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Mount￨U￨NNP￨ORGANIZATION￨- Helen￨U￨NNP￨ORGANIZATION￨- Campus￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Mount￨U￨NNP￨LOCATION￨- Helen￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Ballarat￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Victoria￨U￨NNP￨CITY￨- 3353￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- *￨L￨SYM￨O￨- Correspondence￨U￨NN￨O￨- address￨L￨NN￨O￨- :￨L￨:￨O￨- Tel￨U￨NNP￨O￨- :￨L￨:￨O￨- +61-3-9214￨L￨CD￨NUMBER￨- 5596￨L￨CD￨DATE￨- ,￨L￨,￨O￨- +61-3-5327￨L￨CD￨NUMBER￨- 6335￨L￨CD￨DATE￨- ,￨L￨,￨O￨- +61-423 487 360￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- E-mails￨U￨NNS￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- Abstract￨U￨NNP￨O￨- :￨L￨:￨O￨- Prion￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- misfolded￨L￨JJ￨O￨- protein￨L￨NN￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- mammals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- causes￨L￨VBZ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nervous￨L￨JJ￨O￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- animals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- prion￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- rabbit￨L￨NN￨O￨- prion￨L￨NN￨O￨- protein￨L￨NN￨O￨A wild-type￨L￨JJ￨O￨- and￨L￨CC￨O￨- mutants￨L￨NNS￨O￨- ;￨L￨:￨O￨- NMR￨U￨NN￨O￨- structures￨L￨NNS￨O￨- ;￨L￨:￨O￨- molecular￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- study￨L￨NN￨O￨- ;￨L￨:￨O￨- surface￨L￨NN￨O￨- electrostatic￨L￨JJ￨O￨- charge￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- Abbreviations￨U￨NNS￨O￨- :￨L￨:￨O￨- PrPC￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- soluble￨L￨JJ￨O￨- normal￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- prion￨L￨NN￨O￨- protein￨L￨NN￨O￨- ;￨L￨:￨O￨- PrPSc￨U￨NN￨O￨- ,￨L￨,￨O￨- insoluble￨L￨JJ￨O￨- abnormally￨L￨RB￨O￨- folded￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- prions￨L￨NNS￨O￨- ;￨L￨:￨O￨- BSE￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- bovine￨L￨JJ￨O￨- spongiform￨L￨NN￨O￨- encephalopathy￨L￨NN￨O￨- ;￨L￨:￨O￨- TSE￨U￨NNP￨O￨- ,￨L￨,￨O￨- Transmissible￨U￨JJ￨MISC￨- Spongiform￨U￨NNP￨MISC￨- Encephalopathy￨U￨NNP￨MISC￨- ;￨L￨:￨MISC￨- CJD￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Creutzfeldt-Jakob￨U￨NNP￨MISC￨- Disease￨U￨NNP￨CAUSE_OF_DEATH￨- ;￨L￨:￨MISC￨- vCJD￨L￨NN￨MISC￨- ,￨L￨,￨O￨- variant￨L￨JJ￨O￨- CreutzfeldtJakob￨U￨NNP￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- saPMCA￨L￨NN￨O￨- ,￨L￨,￨O￨- serial￨L￨NN￨O￨- automated￨L￨VBN￨O￨- Protein￨U￨NN￨O￨- Misfolding￨U￨VBG￨O￨- Cyclic￨U￨JJ￨O￨- Amplification￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- can￨L￨MD￨O￨- conclude￨L￨VB￨O￨- that￨L￨IN￨O￨- surface￨L￨NN￨O￨A electrostatic￨L￨JJ￨O￨- charge￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- indeed￨L￨RB￨O￨- contribute￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- wild-type￨L￨JJ￨O￨- RaPrPC￨U￨NN￨O￨- ;￨L￨:￨O￨- this￨L￨DT￨DATE￨- may￨L￨MD￨DATE￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- medicinal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- prion￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- will￨L￨MD￨O￨- base￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- NMR￨U￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- RaPrPC￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- I214V￨U￨NN￨O￨- and￨L￨CC￨O￨- S173N￨U￨NN￨O￨- mutants￨L￨NNS￨O￨- :￨L￨:￨O￨- NMR￨U￨NN￨O￨- structure￨L￨NN￨O￨- PDB￨U￨NN￨O￨- entries￨L￨NNS￨O￨- 2JOM￨L￨NN￨O￨- ,￨L￨,￨O￨- 2JOH￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- using￨L￨VBG￨O￨- molecular￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MD￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- simulation￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- specific￨L￨NN￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- most￨L￨RBS￨O￨- notably￨L￨RB￨O￨- the￨L￨DT￨O￨- empirically￨L￨RB￨O￨- observed￨L￨VBN￨O￨- burstiness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- apparent￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- broad￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- inter-contact￨L￨JJ￨O￨- du-rations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨A processes￨L￨NNS￨O￨A on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- durations￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- agents￨L￨NNS￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- j￨L￨FW￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- inter-contact￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- agent￨L￨NN￨O￨- i￨L￨FW￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- link￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ∆￨L￨CD￨NUMBER￨- τi￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ∆￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- link￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- also￨L￨RB￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Section￨U￨NN￨O￨- II￨U￨CD￨NUMBER￨- presents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- ;￨L￨:￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- first￨L￨VBD￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- memory￨L￨NN￨O￨A effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- investigates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- affect￨L￨JJ￨O￨- network￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- dt￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- active￨L￨JJ￨O￨- links￨L￨NNS￨O￨- and￨L￨CC￨O￨- all￨L￨DT￨O￨- agents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- updated￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Each￨U￨DT￨O￨- active￨L￨JJ￨O￨- link￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- inactivated￨L￨VBN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- dt￨L￨NN￨O￨- z￨L￨SYM￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- f￨L￨FW￨O￨- may￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- z￨L￨SYM￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- contacts￨L￨NNS￨O￨- end￨L￨VBP￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Each￨U￨DT￨O￨- agent￨L￨NN￨O￨- i￨L￨FW￨O￨- initiates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- another￨L￨DT￨O￨- agent￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- dt￨L￨NN￨O￨- b￨L￨NN￨O￨- fa￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ti￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- fa￨L￨NN￨O￨- may￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- ti￨L￨NNS￨O￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- controls￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- Πa￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- tj￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Π￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- creation￨L￨NN￨O￨- .￨L￨.￨O￨- +B.￨U￨NNP￨O￨- Relating￨U￨NNP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ’s￨L￨POS￨O￨- ingredients￨L￨NNS￨O￨- to￨L￨TO￨O￨- memory￨L￨NN￨O￨A effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- memory￨L￨NN￨O￨- kernels￨L￨NNS￨O￨- ”￨L￨''￨O￨- f￨L￨SYM￨O￨- and￨L￨CC￨O￨- Π￨U￨NN￨O￨- control￨L￨VBP￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- is￨L￨VBZ￨O￨- inactivated￨L￨VBN￨O￨- and￨L￨CC￨O￨- activated￨L￨VBN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- fa￨L￨NN￨O￨- and￨L￨CC￨O￨- Πa￨U￨NN￨O￨- control￨L￨VBP￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- agents￨L￨NNS￨O￨- enter￨L￨VBP￨O￨- new￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- create￨L￨VB￨O￨- or￨L￨CC￨O￨- receive￨L￨VB￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- incorporates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- principle￨L￨NN￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨A tracing￨L￨VBG￨O￨A ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- identified￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- traced￨L￨VBN￨O￨- contact￨L￨NN￨O￨- is￨L￨VBZ￨O￨- either￨L￨CC￨O￨- incubating￨L￨VBG￨O￨- or￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- process.The￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- first￨L￨JJ￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- current￨L￨JJ￨DATE￨- cumulative￨L￨JJ￨O￨- reported￨L￨VBN￨O￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- predictions￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- containment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- requires￨L￨VBZ￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- identification￨L￨NN￨O￨- and￨L￨CC￨O￨- isolation￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A tracing￨L￨VBG￨O￨A process￨L￨NN￨O￨- for￨L￨IN￨O￨- removing￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- simulate￨L￨VBP￨O￨- forward￨L￨RB￨O￨- pro￨L￨JJ￨O￨- jections￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- varied￨L￨JJ￨O￨- efficiencies￨L￨NNS￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- ,￨L￨,￨O￨- isolating￨L￨VBG￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨A tracing￨L￨VBG￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- data￨L￨NNS￨O￨- fitted￨L￨VBD￨O￨- simulations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- then￨L￨RB￨O￨- pro￨L￨JJ￨O￨- jected￨L￨VBD￨O￨- forward￨L￨RB￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- varying￨L￨VBG￨O￨- parameter￨L￨NN￨O￨- regimes￨L￨NNS￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- contact￨L￨VB￨O￨A tracing￨L￨VBG￨O￨A efficiencies￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- also￨L￨RB￨O￨- incorporates￨L￨VBZ￨O￨- contact￨L￨NN￨O￨A tracing￨L￨VBG￨O￨A of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- analyzes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- and￨L￨CC￨O￨- isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- Increasingly￨U￨RB￨O￨- ,￨L￨,￨O￨- network￨L￨NN￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- include￨L￨VBP￨O￨- information￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨A of￨L￨IN￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- entities￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- approach￨L￨NN￨O￨- extracts￨L￨NNS￨O￨- all￨L￨DT￨O￨- subgraphs￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- we￨L￨PRP￨O￨- require￨L￨VBP￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- performs￨L￨VBZ￨O￨- sub-graph￨L￨JJ￨O￨- isomorphism￨L￨NN￨O￨- testing￨L￨NN￨O￨- on￨L￨IN￨O￨- each￨L￨DT￨O￨- subgraph￨L￨NN￨O￨A .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- query￨L￨NN￨O￨- graphs￨L￨NNS￨O￨A include￨L￨VBP￨O￨- an￨L￨DT￨O￨- enumeration￨L￨NN￨O￨- of￨L￨IN￨O￨- small￨L￨JJ￨O￨- random￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- and￨L￨CC￨O￨- fan-out-fan-in￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- time-respecting￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- search￨L￨NN￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- more￨L￨JJR￨O￨- meaningful￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- formulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- time-respecting￨L￨JJ￨O￨- subgraph￨L￨NN￨O￨A isomorphism￨L￨NN￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- communication￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨A of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- can￨L￨MD￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- flow￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- piece￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- Spreading￨U￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- phenomena￨L￨NNS￨O￨A from￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- to￨L￨TO￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- innovations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Topological￨U￨JJ￨O￨- aspects￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- activity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- burstiness￨L￨NN￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- severly￨L￨RB￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- time￨L￨NN￨O￨- stamped￨L￨JJ￨O￨- communication￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- dataset￨L￨NN￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨- records￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ;￨L￨:￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ;￨L￨:￨O￨- spreading￨L￨VBG￨O￨- phenomena￨L￨NNS￨O￨- ;￨L￨:￨O￨- SI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- bursty￨L￨JJ￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- ;￨L￨:￨O￨- non-Markovian￨L￨JJ￨MISC￨- processes￨L￨NNS￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- MSC￨U￨NNP￨O￨- :￨L￨:￨O￨- 90B18￨L￨NN￨O￨- ;￨L￨:￨O￨- 60K35￨L￨NNP￨O￨- ;￨L￨:￨O￨- 82C99￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Three￨U￨CD￨NUMBER￨- faces￨L￨NNS￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- importance￨L￨NN￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- :￨L￨:￨O￨- Exact￨U￨JJ￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- small￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- Petter￨U￨NNP￨O￨- Holme1￨U￨NNP￨O￨- ,￨L￨,￨O￨- ∗￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Innovative￨U￨JJ￨ORGANIZATION￨- Research￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Tokyo￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Tokyo￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- Susceptible-Infectious-Removed￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- influence￨L￨NN￨O￨- maximization￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- seed￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- how￨L￨WRB￨O￨- much￨L￨JJ￨O￨- deleting￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- would￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- sentinel￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- how￨L￨WRB￨O￨- early￨L￨RB￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- detected￨L￨VBN￨O￨- with￨L￨IN￨O￨- sensors￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- :￨L￨:￨O￨- node￨L￨NN￨O￨- separation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- important￨L￨JJ￨O￨- than￨L￨IN￨O￨- centrality￨L￨NN￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- active￨L￨JJ￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- influence￨L￨NN￨O￨- maximization￨L￨NN￨O￨A are￨L￨VBP￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- different￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- importance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- aspects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- similar￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- maximization￨L￨NN￨O￨A problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- being￨L￨VBG￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- would￨L￨MD￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- Ω￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- once￨L￨RB￨DATE￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- ,￨L￨,￨O￨- deleted￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- would￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨A size￨L￨NN￨O￨A the￨L￨DT￨O￨- most￨L￨RBS￨O￨- NumericCitation￨U￨JJ￨O￨- .￨L￨.￨O￨- +Third￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sentinel￨L￨NN￨O￨A surveillance￨L￨NN￨O￨A problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- infected￨L￨JJ￨O￨- early￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- E.T.Sepp￨U￨NNP￨O￨- ¨￨L￨NNP￨O￨- al￨L￨NNP￨O￨- ¨￨L￨NNP￨O￨- aandM.J.Alava￨L￨NNP￨O￨- ,￨L￨,￨O￨- Phys.Rev.E63￨U￨NN￨O￨- ,066109￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2001￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- K.Chung￨U￨NNP￨O￨- ,￨L￨,￨O￨- Y.Baek￨U￨NNP￨O￨- ,￨L￨,￨O￨- M.Ha￨U￨NNP￨O￨- ,￨L￨,￨O￨- andH.Jeong￨L￨NNP￨O￨- ,￨L￨,￨O￨- Phys.Rev.E93￨U￨NN￨O￨- ,052304￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2016￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- K.Chung￨U￨NNP￨O￨- ,￨L￨,￨O￨- Y.Baek￨U￨NNP￨O￨- ,￨L￨,￨O￨- D.Kim￨U￨NNP￨O￨- ,￨L￨,￨O￨- M.Ha￨U￨NNP￨O￨- ,￨L￨,￨O￨- andH.Jeong￨L￨NNP￨O￨- ,￨L￨,￨O￨- Phys.Rev.E89￨U￨NN￨O￨- ,052811￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- N.J.ZhouandB.Zheng￨U￨NNP￨O￨- ,￨L￨,￨O￨- Phys.Rev.E82￨U￨NN￨O￨- ,031139￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- rational￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨- from￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A contacts￨L￨NNS￨O￨A ,￨L￨,￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- be￨L￨VB￨O￨- beneficial￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- whole￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A can￨L￨MD￨O￨- worsen￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outcome￨L￨NN￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- network￨L￨NN￨O￨A models￨L￨NNS￨O￨A to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- negative￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- evolves￨L￨VBZ￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- distance￨L￨VB￨O￨- themselves￨L￨PRP￨O￨- from￨L￨IN￨O￨- their￨L￨PRP$￨O￨- infectious￨L￨JJ￨O￨A contacts￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- take￨L￨VBP￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- through￨L￨IN￨O￨- several￨L￨JJ￨O￨- network￨L￨NN￨O￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- three￨L￨CD￨NUMBER￨- basic￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- states￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- compartments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- proposed￨L￨VBD￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A propagation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ignorants￨L￨NNS￨O￨- ,￨L￨,￨O￨- spreaders￨L￨NNS￨O￨- and￨L￨CC￨O￨- stiflers￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- map￨L￨NN￨O￨- onto￨L￨IN￨O￨- those￨L￨DT￨O￨- for￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- removed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- close￨L￨JJ￨O￨- analogy￨L￨NN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- considered￨L￨VBN￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- immediate-response￨L￨JJ￨O￨- ,￨L￨,￨O￨- skeptically-driven￨L￨JJ￨O￨- reaction￨L￨NN￨O￨- directed￨L￨VBD￨O￨- toward￨L￨IN￨O￨- the￨L￨DT￨O￨- spreader￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Otherwise￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- ,￨L￨,￨O￨- non￨L￨JJ￨O￨- contagious￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- latency￨L￨NN￨O￨- after￨L￨IN￨O￨- having￨L￨VBG￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- agent￨L￨NN￨O￨- hesitates￨L￨VBZ￨O￨- and￨L￨CC￨O￨- access￨L￨NN￨O￨- its￨L￨PRP$￨O￨- plausibility￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- E￨U￨NN￨O￨- state￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +–￨L￨:￨O￨- We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- skeptically￨L￨RB￨O￨- oriented￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- oppose￨L￨VB￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- .￨L￨.￨O￨- +Edges￨U￨NNS￨O￨- are￨L￨VBP￨O￨- created￨L￨VBN￨O￨- independently￨L￨RB￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- ∗￨L￨RB￨O￨- Center￨U￨NNP￨O￨- for￨L￨IN￨O￨- Communicable￨U￨NNP￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Dynamics￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Epidemiology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Harvard￨U￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- †￨L￨NNP￨ORGANIZATION￨- Fogarty￨U￨NNP￨ORGANIZATION￨- International￨U￨NNP￨ORGANIZATION￨- Center￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- NIH￨U￨NNP￨ORGANIZATION￨- ‡￨L￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Epidemiology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Michigan￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Ann￨U￨NNP￨ORGANIZATION￨- Arbor￨U￨NNP￨ORGANIZATION￨- 1￨L￨CD￨NUMBER￨- Model￨U￨NNP￨TITLE￨- Contact￨U￨NN￨O￨- Duration￨U￨NNP￨O￨- Heterogeneity￨U￨NN￨O￨- type￨L￨NN￨O￨- Configuration￨U￨NNP￨O￨- Model￨U￨NNP￨TITLE￨- (￨L￨-LRB-￨O￨- CM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Mixed￨U￨NNP￨O￨- Poisson￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- MP￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- Dynamic￨U￨NNP￨O￨- Variable-Degree￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- DVD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Dynamic￨U￨NNP￨O￨- Fixed-Degree￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- DFD￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- Mean￨U￨NN￨MISC￨- Field￨U￨NN￨MISC￨- Social￨U￨NNP￨MISC￨- Heterogeneity￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- MFSH￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Permanent￨U￨JJ￨O￨- Permanent￨U￨JJ￨O￨- Finite￨U￨NNP￨O￨- Finite￨U￨NNP￨O￨- Fleeting￨U￨NNP￨O￨- Actual￨U￨NNP￨O￨- degree￨L￨NN￨O￨A k￨L￨NN￨O￨- Expected￨U￨VBN￨O￨- degree￨L￨NN￨O￨- κ￨L￨NN￨O￨- Expected￨U￨JJ￨O￨- degree￨L￨NN￨O￨- κ￨L￨NN￨O￨- Actual￨U￨JJ￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- Contact￨U￨NN￨O￨- rate￨L￨NN￨O￨- k￨L￨NN￨O￨- or￨L￨CC￨O￨- κ￨L￨NN￨O￨- Dormant￨U￨JJ￨O￨- Contact￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- DC￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- Finite￨U￨JJ￨O￨- active￨L￨JJ￨O￨- and￨L￨CC￨O￨- dormant￨L￨JJ￨O￨- Maximum￨U￨NNP￨O￨- degree￨L￨NN￨O￨- km￨L￨NN￨O￨- Mass￨U￨JJ￨STATE_OR_PROVINCE￨- Action￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- MA￨U￨NNP￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- Fleeting￨U￨JJ￨O￨- None￨U￨NN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- underlying￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- actual￨L￨JJ￨O￨A degree￨L￨NN￨O￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- assign￨L￨VBP￨O￨- an￨L￨DT￨O￨- actual￨L￨JJ￨O￨- integer￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- though￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dormant￨L￨JJ￨O￨- contact￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- not￨L￨RB￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- active￨L￨JJ￨O￨- at￨L￨IN￨O￨- all￨L￨DT￨O￨- times￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- modeled￨L￨VBD￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- representing￨L￨VBG￨O￨A individuals￨L￨NNS￨O￨- joined￨L￨VBN￨O￨- by￨L￨IN￨O￨- edges￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- potentially￨L￨RB￨O￨- transmitting￨L￨VBG￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- earlier￨L￨JJR￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- edge-based￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- contact￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- one￨L￨CD￨NUMBER￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- expected￨L￨VBN￨O￨- degree￨L￨NN￨O￨A models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assign￨L￨VBP￨O￨- an￨L￨DT￨O￨- expected￨L￨VBN￨O￨- degree￨L￨NN￨O￨- κ￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨A models￨L￨NNS￨O￨A with￨L￨IN￨O￨- varying￨L￨VBG￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- complexity￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- Susceptible-Infectious-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- choice￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- closely￨L￨RB￨O￨- the￨L￨DT￨O￨- outcomes￨L￨NNS￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- network￨L￨NN￨O￨- match￨L￨VBP￨O￨- the￨L￨DT￨O￨- outcomes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- network￨L￨NN￨O￨- constructed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- sensor￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Effects￨U￨NNS￨MISC￨- of￨L￨IN￨MISC￨- Contact￨U￨NN￨MISC￨- Network￨U￨NNP￨MISC￨- Models￨U￨NNS￨MISC￨- on￨L￨IN￨MISC￨- Stochastic￨U￨NNP￨MISC￨- Epidemic￨U￨NNP￨MISC￨- Simulations￨U￨NNP￨MISC￨- Rehan￨U￨NNP￨PERSON￨- Ahmad￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Kevin￨U￨NNP￨PERSON￨- S.￨U￨NNP￨O￨- Typically￨U￨RB￨O￨- one￨L￨CD￨NUMBER￨- uses￨L￨VBZ￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- a￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨A contacts￨L￨NNS￨O￨- over￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- propagate￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- evaluate￨L￨VBP￨O￨- these￨L￨DT￨O￨- network￨L￨NN￨O￨A models￨L￨NNS￨O￨A on￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- datasets￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- people￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Multi-state￨U￨JJ￨O￨- Epidemic￨U￨JJ￨O￨- Processes￨U￨NNS￨O￨- on￨L￨IN￨O￨- Complex￨U￨NN￨O￨- Networks￨U￨NNP￨O￨- Naoki￨U￨NNP￨PERSON￨- Masuda1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Norio￨U￨NNP￨PERSON￨- Konno2￨U￨NNP￨O￨- 1Laboratory￨L￨NNP￨O￨- for￨L￨IN￨O￨- Mathematical￨U￨NNP￨O￨- Neuroscience￨U￨NNP￨O￨- ,￨L￨,￨O￨- RIKEN￨U￨NNP￨ORGANIZATION￨- Brain￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 2-1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Hirosawa￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Wako￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Saitama￨U￨NNP￨CITY￨- 351-0198￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- 2Faculty￨L￨NNP￨O￨- of￨L￨IN￨O￨- Engineering￨U￨NNP￨O￨- ,￨L￨,￨O￨- Yokohama￨U￨NNP￨ORGANIZATION￨- National￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 79-5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Tokiwadai￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hodogaya￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Yokohama￨U￨NNP￨LOCATION￨- 240-8501￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- Abstract￨U￨NNP￨O￨- :￨L￨:￨O￨- Infectious￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- practically￨L￨RB￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- complex￨L￨JJ￨O￨- transition￨L￨NN￨O￨- rules￨L￨NNS￨O￨A corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- birth￨L￨NN￨O￨- ,￨L￨,￨O￨- death￨L￨NN￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- quarantine￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- competing￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- mutation￨L￨NN￨O￨- ,￨L￨,￨O￨- coexistence￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- for￨L￨IN￨O￨- small￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- network-independent￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨A rates￨L￨NNS￨O￨A .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨- without￨L￨IN￨O￨- spontaneous￨L￨JJ￨O￨- neighbor-independent￨L￨JJ￨O￨- state￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- cyclically￨L￨RB￨O￨- competing￨L￨VBG￨O￨A species￨L￨NNS￨O￨- ,￨L￨,￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- show￨L￨VB￨O￨- heterogeneity￨L￨NN￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- simple￨L￨JJ￨O￨- transition￨L￨NN￨O￨- rules￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- heterogeneous￨L￨JJ￨O￨- contact￨L￨NN￨O￨A rates￨L￨NNS￨O￨A are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- decrease￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analyze￨L￨VBP￨O￨- steady￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- multi-state￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- contact￨L￨NN￨O￨A rates￨L￨NNS￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- addresses￨L￨NNS￨O￨- this￨L￨DT￨O￨- issue￨L￨NN￨O￨- by￨L￨IN￨O￨- presenting￨L￨VBG￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- predicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resistance￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- shares￨L￨VBZ￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- superior￨L￨JJ￨O￨- competitor￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- come￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- being￨L￨VBG￨O￨- selected￨L￨VBN￨O￨- for￨L￨IN￨O￨- resistance￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨A may￨L￨MD￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- tradeoff￨L￨NN￨O￨- between￨L￨IN￨O￨- direct￨L￨JJ￨O￨- damage￨L￨NN￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨- benefits￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- confers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Selection￨U￨NN￨O￨- favors￨L￨VBZ￨O￨- lower￨L￨JJR￨O￨- resistance￨L￨NN￨O￨A when￨L￨WRB￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- spatially￨L￨RB￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- damage￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- competitor￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- outweigh￨L￨VB￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- selection￨L￨NN￨O￨- for￨L￨IN￨O￨- resistance￨L￨NN￨O￨A in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- host￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- mediated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- municipalities￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- implicit￨L￨JJ￨O￨- vector￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- daily￨L￨JJ￨SET￨A case￨L￨NN￨O￨- reporting￨L￨VBG￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- Antioquia￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Colombia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- most￨L￨RBS￨O￨- affected￨L￨JJ￨O￨- country￨L￨NN￨O￨- after￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approximate￨L￨JJ￨O￨- solution￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- recovered￨L￨VBN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- unit￨L￨NN￨O￨- ,￨L￨,￨O￨- allowed￨L￨VBN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Ro￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- confidence￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- parameters￨L￨NNS￨O￨- were￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- via￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- reported￨L￨VBN￨O￨- cumulative￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- regional￨L￨JJ￨O￨A surveillance￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- reproductive￨L￨JJ￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- municipalities￨L￨NNS￨O￨- of￨L￨IN￨O￨- Antioquia￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Colombia￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- stratifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- Juan￨U￨NNP￨O￨- Ospina1￨U￨NN￨O￨- ,￨L￨,￨O￨- Doracelly￨U￨NNP￨O￨- Hincapie-Palacio2￨U￨NN￨O￨- ,￨L￨,￨O￨- Jesús￨U￨NNP￨O￨- Ochoa2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Adriana￨U￨NNP￨PERSON￨- Molina2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Guillermo￨U￨NNP￨PERSON￨- Rúa3￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Dubán￨U￨NNP￨O￨- Pájaro4￨U￨NN￨O￨- ,￨L￨,￨O￨- Marcela￨U￨NNP￨PERSON￨- Arrubla4￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Rita￨U￨NNP￨PERSON￨- Almanza5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marlio￨U￨NNP￨O￨- Paredes6￨U￨NNP￨O￨- ,￨L￨,￨O￨- Anuj￨U￨NNP￨PERSON￨- Mubayi6￨U￨NNP￨O￨- 1Eafit￨L￨NNP￨O￨- University￨U￨NNP￨O￨- ,￨L￨,￨O￨- Medellín￨U￨NNP￨O￨- ,￨L￨,￨O￨- Colombia￨U￨NNP￨ORGANIZATION￨- 2National￨L￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- „￨L￨``￨O￨- Héctor￨U￨NNP￨PERSON￨- Abad￨U￨NNP￨PERSON￨- Gómez￨U￨NNP￨PERSON￨- ‟￨L￨NN￨O￨- ,￨L￨,￨O￨- Epidemiology￨U￨NNP￨ORGANIZATION￨- Group￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Antioquia￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Medellín￨U￨NNP￨O￨- ,￨L￨,￨O￨- Colombia￨U￨NNP￨COUNTRY￨- 3Group￨L￨NNP￨O￨- of￨L￨IN￨O￨- Entomology￨U￨NNP￨O￨- ,￨L￨,￨O￨- Faculty￨U￨NNP￨O￨- of￨L￨IN￨O￨- Medicine￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Antioquia￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Medellín￨U￨NNP￨O￨- ,￨L￨,￨O￨- Colombia￨U￨NNP￨ORGANIZATION￨- 4￨L￨CD￨NUMBER￨- Secretary￨U￨NNP￨TITLE￨- Regional￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- and￨L￨CC￨O￨- Social￨U￨NNP￨O￨- Protection￨U￨NNP￨O￨- of￨L￨IN￨O￨- Antioquia￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- between￨L￨IN￨O￨- 17￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 347￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨A from￨L￨IN￨O￨- these￨L￨DT￨O￨- municipalities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Including￨U￨VBG￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- demography￨L￨NN￨O￨A adds￨L￨VBZ￨O￨- substantially￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- run￨L￨NN￨O￨- time￨L￨NN￨O￨- by￨L￨IN￨O￨- several￨L￨JJ￨O￨- orders￨L￨NNS￨O￨- of￨L￨IN￨O￨- magnitude￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- changes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fits￨L￨NNS￨O￨- and￨L￨CC￨O￨- projections￨L￨NNS￨O￨- only￨L￨RB￨O￨- slightly￨L￨RB￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- extent￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨- inherent￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- we￨L￨PRP￨O￨- include￨L￨VBP￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- demography￨L￨NN￨O￨A including￨L￨VBG￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- background￨L￨NN￨O￨- mortality￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- age-specific￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- for￨L￨IN￨O￨- those￨L￨DT￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- on￨L￨IN￨O￨- anti-retroviral￨L￨JJ￨O￨- therapy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ART￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- age-specific￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- Weibull￨U￨NNP￨PERSON￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- survival￨L￨NN￨O￨- function￨L￨NN￨O￨- for￨L￨IN￨O￨- people￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- makes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- difference￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- trends￨L￨NNS￨O￨A in￨L￨IN￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- projected￨L￨VBN￨O￨- trends￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- fit￨L￨VBP￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- Kenya￨U￨NNP￨COUNTRY￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- successively￨L￨RB￨O￨- add￨L￨VB￨O￨- structure￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- drawing￨L￨VBG￨O￨- on￨L￨IN￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- that￨L￨IN￨O￨- different￨L￨JJ￨O￨- structural￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- have￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- fits￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- projections￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- analyse￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A problems￨L￨NNS￨O￨- related￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- ,￨L￨,￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- constraints￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +Three￨U￨CD￨NUMBER￨- vaccination￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- :￨L￨:￨O￨- unlimited￨L￨JJ￨O￨- supply￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨A ;￨L￨:￨O￨- limited￨L￨JJ￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- limited￨L￨JJ￨O￨- supply￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- instant￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- is￨L￨VBZ￨O￨- limited￨L￨VBN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- a￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- for￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- ASI￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- aquatic￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- epidemiological￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A describing￨L￨VBG￨O￨- a￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- associated￨L￨VBN￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- sensitivity￨L￨NN￨O￨A analysis￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- performed￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- sensitivity￨L￨NN￨O￨A analysis￨L￨NN￨O￨A ;￨L￨:￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ;￨L￨:￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- dengue￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- includes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- mosquito￨L￨NN￨O￨A populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- interaction￨L￨NN￨O￨- .￨L￨.￨O￨- +Sensitivity￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +INTRODUCTION￨U￨NNP￨O￨- Systems￨U￨NNPS￨O￨- biology￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- complicated￨L￨JJ￨O￨- models￨L￨NNS￨O￨- —￨L￨:￨O￨- and￨L￨CC￨O￨- rightfully￨L￨RB￨O￨- so￨L￨RB￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- vast￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- data￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- clearly￨L￨RB￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- cellular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- complexity￨L￨NN￨O￨A that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- far￨L￨RB￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- normally￨L￨RB￨O￨- encountered￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- physical￨L￨JJ￨O￨- world￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- matches￨L￨VBZ￨O￨- the￨L￨DT￨O￨- known￨L￨JJ￨O￨- phase￨L￨NN￨O￨- space￨L￨NN￨O￨- structure￨L￨NN￨O￨- for￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- planetary￨L￨JJ￨O￨- motion￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- avoids￨L￨VBZ￨O￨- overfitting￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- signaling￨L￨NN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- produces￨L￨VBZ￨O￨- accurate￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- yeast￨L￨NN￨O￨- glycolysis￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- only￨L￨JJ￨O￨- tens￨L￨NNS￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- points￨L￨NNS￨O￨- and￨L￨CC￨O￨- over￨L￨IN￨O￨- half￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interacting￨L￨VBG￨O￨- species￨L￨NNS￨O￨- unobserved￨L￨JJ￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- adaptive￨L￨JJ￨O￨- models￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- accurate￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- microscopic￨L￨JJ￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- studied￨L￨VBN￨O￨- systems￨L￨NNS￨O￨- are￨L￨VBP￨O￨- unknown￨L￨JJ￨O￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- insufficient￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- limited￨L￨JJ￨O￨- experimental￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- unknown￨L￨JJ￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- models￨L￨NNS￨O￨- built￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- ,￨L￨,￨O￨- mechanistic￨L￨JJ￨O￨- viewpoint￨L￨NN￨O￨- overfit￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- predictive￨L￨JJ￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- instead￨L￨RB￨O￨- constructs￨L￨NNS￨O￨- phenomenological￨L￨JJ￨O￨- ,￨L￨,￨O￨- coarse-grained￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- automatically￨L￨RB￨O￨- adapt￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- complexity￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Infectious￨U￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- —￨L￨:￨O￨- SIR￨U￨NN￨O￨- —￨L￨:￨O￨- Networks￨U￨NNP￨O￨- —￨L￨:￨O￨- Syphilis￨U￨NNP￨CAUSE_OF_DEATH￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Most￨U￨JJS￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- incorporate￨L￨VB￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- assumption￨L￨NN￨O￨- ,￨L￨,￨O￨- sometimes￨L￨RB￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨A action￨L￨NN￨O￨A [￨L￨-LRB-￨O￨- Ross￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1910￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Anderson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- May￨U￨NNP￨DATE￨- (￨L￨-LRB-￨O￨- 1991￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Diekmann￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Heesterbeek￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- product￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- predicting￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- on￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- typical￨L￨JJ￨O￨- contact￨L￨NN￨O￨- number￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- identities￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- contacts￨L￨NNS￨O￨A change￨L￨VBP￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Current￨U￨JJ￨DATE￨- mathematical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- forecasting￨L￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- largely￨L￨RB￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- contacts￨L￨NNS￨O￨A between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- fixed￨L￨VBN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- make￨L￨VBP￨O￨- contact￨L￨NN￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- identical￨L￨JJ￨O￨A rate￨L￨NN￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- identical￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- sin￨L￨NN￨O￨- ce￨L￨NN￨O￨- no￨L￨RB￨O￨- two￨L￨CD￨NUMBER￨- macro￨L￨NN￨O￨A base￨L￨NN￨O￨- stations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- deployed￨L￨VBN￨O￨- arbitrarily￨L￨RB￨O￨- close￨L￨RB￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- PPP￨U￨NNP￨ORGANIZATION￨- assumption￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- BS￨U￨NN￨O￨- locations￨L￨NNS￨O￨- fails￨L￨VBZ￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- repulsion￨L￨NN￨O￨- among￨L￨IN￨O￨- macro￨L￨NN￨O￨- BSs￨U￨NNS￨O￨- and￨L￨CC￨O￨- generally￨L￨RB￨O￨- gives￨L￨VBZ￨O￨- a￨L￨DT￨O￨- pessimistic￨L￨JJ￨O￨- signal-to-interference-plus-noise￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SINR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- distribution￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- empty￨L￨JJ￨O￨- space￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- nearest￨L￨JJS￨O￨- neighbor￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- interference￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- distribution￨L￨NN￨O￨- have￨L￨VBP￨O￨- explicit￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- representations￨L￨NNS￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- numerically￨L￨RB￨O￨- evaluated￨L￨VBN￨O￨- for￨L￨IN￨O￨- cellular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A with￨L￨IN￨O￨- DPP￨U￨NN￨ORGANIZATION￨- con￨L￨NN￨O￨- figured￨L￨VBD￨O￨- BSs￨U￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PPP￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- base￨L￨NN￨O￨- station￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- locations￨L￨NNS￨O￨- in￨L￨IN￨O￨- cellular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- idealized￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- neglects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- among￨L￨IN￨O￨- BSs￨U￨NNS￨O￨- .￨L￨.￨O￨- +3￨L￨CD￨NUMBER￨- ShΛhαhIhβhShIv/NhαhρhRhγhIhαhωhSvΛvαvIvβvSvIh/Nhαvβvβh￨U￨NNP￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- State￨U￨NNP￨O￨- variables￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- Symbol￨U￨NN￨O￨- Description￨U￨NN￨O￨- Sh￨U￨NN￨O￨- Ih￨U￨NN￨O￨- Rh￨U￨NN￨O￨- Sv￨U￨NN￨O￨- Iv￨U￨NN￨O￨- The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨A population￨L￨NN￨O￨- The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- population￨L￨NN￨O￨- Table￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- Parameters￨U￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- Symbol￨U￨NN￨O￨- Description￨U￨NN￨O￨- Λh￨U￨NN￨O￨- αh￨L￨NN￨O￨- βh￨L￨NN￨O￨- γh￨L￨NN￨O￨- ρh￨L￨NN￨O￨- ωh￨L￨NN￨O￨- Λv￨U￨NN￨O￨- αv￨L￨NN￨O￨- βv￨L￨NN￨O￨- The￨U￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- The￨U￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- The￨U￨DT￨O￨- human￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- Per￨U￨IN￨O￨- capita￨L￨NN￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- humans￨L￨NNS￨O￨- Per￨U￨IN￨O￨- capita￨L￨NN￨O￨- disease-induced￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- humans￨L￨NNS￨O￨- The￨U￨DT￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- The￨U￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- The￨U￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- The￨U￨DT￨O￨- mosquito￨L￨NN￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- βh￨L￨NN￨O￨- Sh￨U￨NN￨O￨- Iv￨U￨NN￨O￨- Nh￨U￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- Sh￨U￨VBP￨O￨- get￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- infected￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- Iv￨U￨NN￨O￨- and￨L￨CC￨O￨- βv￨L￨NN￨O￨- Sv￨U￨NN￨O￨- Ih￨U￨NN￨O￨- Nh￨U￨NN￨O￨- refers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- Sv￨U￨NNP￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- human￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- Ih￨U￨VBP￨O￨- .￨L￨.￨O￨- +15￨L￨CD￨NUMBER￨- From￨U￨IN￨O￨- the￨L￨DT￨O￨- Ross￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- by￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- who￨L￨WP￨O￨- extended￨L￨VBD￨O￨- his￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- different￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨A and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- age-related￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- acquired￨L￨VBD￨O￨- immunity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- bringing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A )￨L￨-RRB-￨O￨- induced￨L￨VBD￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- below￨L￨IN￨O￨- some￨L￨DT￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficient￨L￨JJ￨O￨- enough￨L￨RB￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- backward￨L￨RB￨O￨- bifurcation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- unstable￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stable￨L￨JJ￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- recovering￨L￨VBG￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A infective￨L￨JJ￨O￨- and￨L￨CC￨O￨- symptomatic￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- are￨L￨VBP￨O￨- close￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- and￨L￨CC￨O￨- evaluated￨L￨VBN￨O￨- directly￨L￨RB￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- uniformly￨L￨RB￨O￨- persistent￨L￨JJ￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- threshold￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- section￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- give￨L￨VB￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- uniformly￨L￨RB￨O￨- persistent￨L￨JJ￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- SIRS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- succession￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- discontinuous￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- seasonal￨L￨JJ￨O￨- succession￨L￨NN￨O￨- ,￨L￨,￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- threshold￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- makes￨L￨VBZ￨O￨- accurate￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- worm￨L￨NN￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- functional￨L￨JJ￨O￨- logic￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- underlying￨L￨VBG￨O￨- the￨L￨DT￨O￨- escape￨L￨NN￨CRIMINAL_CHARGE￨A response￨L￨NN￨O￨- .￨L￨.￨O￨- +9￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 8￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- quantitative￨L￨JJ￨O￨- biology￨L￨NN￨O￨- revolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- recent￨L￨JJ￨DURATION￨- decades￨L￨NNS￨DURATION￨- has￨L￨VBZ￨O￨- resulted￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- unprecedented￨L￨JJ￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨A to￨L￨TO￨O￨- perturbations￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- previously￨L￨RB￨DATE￨- reserved￨L￨VBN￨O￨- for￨L￨IN￨O￨- inanimate￨L￨NN￨O￨- ,￨L￨,￨O￨- physical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Instead￨U￨RB￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- phenomenologically￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- Sir￨U￨NNP￨O￨- Isaac￨U￨NNP￨PERSON￨- dynamical￨L￨JJ￨O￨A inference￨L￨NN￨O￨- platform￨L￨NN￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- automated￨L￨VBN￨O￨- fashion￨L￨NN￨O￨- directly￨L￨RB￨O￨- from￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- escape￨L￨NN￨CRIMINAL_CHARGE￨A behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- roundworm￨L￨NN￨O￨- Caenorhabditis￨U￨NN￨PERSON￨- elegans￨L￨NNS￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- noxious￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- stimulus￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- measured￨L￨VBN￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- seconds￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- hundreds￨L￨NNS￨O￨- of￨L￨IN￨O￨- worms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- inferred￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- requires￨L￨VBZ￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨A variable￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- biologically￨L￨RB￨O￨- interpretable￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- finite￨L￨NN￨O￨- size￨L￨NN￨O￨- scaling￨L￨NN￨O￨- near￨L￨IN￨O￨- criticality￨L￨NN￨O￨A follows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- scaling￨L￨NN￨O￨- relation￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∼￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- −￨L￨SYM￨O￨- β/ν￨L￨FW￨O￨- f￨L￨FW￨O￨- ∆￨L￨FW￨O￨- t1/v￨L￨NN￨O￨- ,￨L￨,￨O￨- L￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- td/z￨L￨NN￨O￨- ,￨L￨,￨O￨- d0￨L￨NN￨O￨- tθ￨L￨NN￨O￨- +￨L￨CC￨O￨- β/v￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- als￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- d￨L￨NN￨O￨- −￨L￨NN￨O￨- dimensional￨L￨JJ￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individlinear￨L￨JJ￨O￨- size￨L￨NN￨O￨- L￨U￨NN￨O￨- ,￨L￨,￨O￨- ∆￨L￨NN￨O￨- =￨L￨JJ￨O￨- c￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- cc￨L￨NN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- point￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- critical￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- ·￨L￨NN￨O￨- means￨L￨VBZ￨O￨- measures￨L￨NNS￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- point￨L￨NN￨O￨- c￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- usual￨L￨JJ￨O￨- average￨L￨NN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- Ns￨U￨NNS￨O￨- samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- criticality￨L￨NN￨O￨A ∆￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- power-law￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- :￨L￨:￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- tθ￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- t￨L￨NN￨O￨- <￨L￨JJR￨O￨- t0￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- β/zν￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- t0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- regime￨L￨NN￨O￨- t￨L￨NN￨O￨- <￨L￨JJR￨O￨- t0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- considering￨L￨VBG￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- and￨L￨CC￨O￨- all￨L￨DT￨O￨- other￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- are￨L￨VBP￨O￨- occupied￨L￨VBN￨O￨- by￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- v￨L￨LS￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exist￨L￨VBP￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨A line￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- immunization￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- recovers￨L￨VBZ￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- becomes￨L￨VBZ￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- reinfection￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- may￨L￨MD￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- Keywords￨U￨NNPS￨O￨- :￨L￨:￨O￨- network￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- integro-differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- non-Markovian￨L￨JJ￨MISC￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- pairwise￨L￨JJ￨O￨A approximation￨L￨NN￨O￨- ,￨L￨,￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- and￨L￨CC￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- long￨L￨RB￨O￨- been￨L￨VBN￨O￨- acknowledged￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- pattern￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- factor￨L￨NN￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analytically￨L￨RB￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- generalised￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- rigorous￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- conjecture￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- functional￨L￨JJ￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- pairwise￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- an￨L￨DT￨O￨- illustration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- applicability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- recover￨L￨VBP￨O￨- known￨L￨VBN￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- exponentially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- and￨L￨CC￨O￨- fixed￨L￨VBN￨O￨- recovery￨L￨NN￨O￨- time￨L￨NN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- new￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨A models￨L￨NNS￨O￨- with￨L￨IN￨O￨- gamma￨L￨NN￨O￨- and￨L￨CC￨O￨- uniformly￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- the￨L￨DT￨O￨- generalised￨L￨VBN￨O￨- mean-field￨L￨NN￨O￨- and￨L￨CC￨O￨- pairwise￨L￨JJ￨O￨A models￨L￨NNS￨O￨- for￨L￨IN￨O￨- nonMarkovian￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- time￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- popular￨L￨JJ￨O￨- node-level￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- perhaps￨L￨RB￨O￨- the￨L￨DT￨O￨- degree-based￨L￨JJ￨O￨- or￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨A models￨L￨NNS￨O￨- offering￨L￨VBG￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- both￨L￨CC￨O￨- at￨L￨IN￨O￨- node￨L￨NN￨O￨- and￨L￨CC￨O￨- link￨L￨NN￨O￨- level￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Compared￨U￨VBN￨O￨- with￨L￨IN￨O￨- existing￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- on￨L￨IN￨O￨- QDA￨U￨NNP￨O￨- variable￨L￨JJ￨O￨A selections￨L￨NNS￨O￨- ,￨L￨,￨O￨- SODA￨U￨NNP￨O￨- can￨L￨MD￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- high-dimensional￨L￨JJ￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- predictors￨L￨NNS￨O￨- much￨L￨RB￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- require￨L￨VB￨O￨- the￨L￨DT￨O￨- joint￨L￨JJ￨O￨- normality￨L￨NN￨O￨- assumption￨L￨NN￨O￨- on￨L￨IN￨O￨- predictors￨L￨NNS￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- much￨L￨RB￨O￨- enhanced￨L￨VBN￨O￨- robustness￨L￨NN￨O￨- .￨L￨.￨O￨- +Compared￨U￨VBN￨O￨- with￨L￨IN￨O￨- existing￨L￨VBG￨O￨- variable￨L￨JJ￨O￨A selection￨L￨NN￨O￨- methods￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Sliced￨U￨NNP￨MISC￨- Inverse￨U￨NNP￨MISC￨- Regression￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- SODA￨U￨NN￨O￨- requires￨L￨VBZ￨O￨- neither￨L￨CC￨O￨- the￨L￨DT￨O￨- linearity￨L￨NN￨O￨- nor￨L￨CC￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- variance￨L￨NN￨O￨- condition￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- robust￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- Stepwise￨U￨JJ￨O￨- cOnditional￨L￨JJ￨O￨- likelihood￨L￨NN￨O￨- variable￨L￨JJ￨O￨A selection￨L￨NN￨O￨- for￨L￨IN￨O￨- Discriminant￨U￨NNP￨O￨- Analysis￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SODA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- both￨L￨CC￨O￨- main￨L￨JJ￨O￨- and￨L￨CC￨O￨- quadratic￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- logistic￨L￨JJ￨O￨- regression￨L￨NN￨O￨- and￨L￨CC￨O￨- quadratic￨L￨JJ￨O￨- discriminant￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- QDA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- forward￨L￨JJ￨O￨- stage￨L￨NN￨O￨A ,￨L￨,￨O￨- SODA￨U￨NNP￨ORGANIZATION￨- adds￨L￨VBZ￨O￨- in￨L￨IN￨O￨- important￨L￨JJ￨O￨- predictors￨L￨NNS￨O￨- evaluated￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- overall￨L￨JJ￨O￨- contributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- backward￨L￨RB￨O￨- stage￨L￨NN￨O￨- SODA￨U￨NNP￨ORGANIZATION￨- removes￨L￨VBZ￨O￨- unimportant￨L￨JJ￨O￨- terms￨L￨NNS￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- optimize￨L￨VB￨O￨- the￨L￨DT￨O￨- extended￨L￨JJ￨O￨- Bayesian￨U￨NNP￨O￨- Information￨U￨NNP￨O￨- Criterion￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- EBIC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- extend￨L￨VBP￨O￨- SODA￨U￨NNP￨O￨- to￨L￨TO￨O￨- conduct￨L￨VB￨O￨- variable￨L￨JJ￨O￨A selection￨L￨NN￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- fitting￨L￨NN￨O￨- for￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- index￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨VBD￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- smallest￨L￨JJS￨O￨- non-zero￨L￨JJ￨O￨- eigenvalue￨L￨NN￨O￨- λ￨L￨NN￨O￨- of￨L￨IN￨O￨- var￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- x￨L￨CC￨O￨- |￨L￨SYM￨O￨- y￨L￨SYM￨O￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- over￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- aggregated￨L￨JJ￨O￨- estimator￨L￨NN￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- procedure￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- d￨L￨NN￨O￨- ∧￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- sd￨L￨NN￨O￨- +￨L￨CC￨O￨- s￨L￨NNS￨O￨- log￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ep/s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- nλ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- precisely￨L￨RB￨O￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- postulates￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- index￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- subspace￨L￨NN￨O￨- S￨U￨NN￨O￨- =￨L￨JJ￨O￨- span￨L￨NN￨O￨- β1￨L￨NN￨O￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- βd￨L￨NN￨O￨- y￨L￨NN￨O￨- =￨L￨JJ￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- βτ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- βτ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- βτ￨L￨NN￨O￨- via￨L￨IN￨O￨- an￨L￨DT￨O￨- eigen-analysis￨L￨NN￨O￨- d￨L￨NN￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- estimates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- conditional￨L￨JJ￨O￨- covariance￨L￨NN￨O￨- matrix￨L￨NN￨O￨- var￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- |￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- the￨L￨DT￨O￨- space￨L￨NN￨O￨- of￨L￨IN￨O￨- We￨U￨PRP￨O￨- then￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- optimal￨L￨JJ￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- scenarios￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- index￨L￨NN￨O￨A models￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- multiple￨L￨JJ￨O￨- index￨L￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- central￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- d￨L￨NN￨O￨- and￨L￨CC￨O￨- fixed￨L￨VBD￨O￨- λ￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- recently￨L￨RB￨DATE￨- showed￨L￨VBD￨O￨- under￨L￨IN￨O￨- mild￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨A space￨L￨NN￨O￨- is￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- lim￨L￨NN￨O￨- p￨L￨NN￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +consider￨L￨VB￨O￨- the￨L￨DT￨O￨- minimax￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- multiple￨L￨JJ￨O￨- index￨L￨NN￨O￨A models￨L￨NNS￨O￨- y￨L￨NN￨O￨- =￨L￨JJ￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- βτ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- βτ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- βτ￨L￨NN￨O￨- d￨L￨NN￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- at￨L￨IN￨O￨- most￨L￨JJS￨O￨- s￨L￨NNS￨O￨- active￨L￨JJ￨O￨- predictors￨L￨NNS￨O￨- where￨L￨WRB￨O￨- x￨L￨CC￨O￨- ∼￨L￨SYM￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ip￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- average￨L￨JJ￨O￨- member￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- sufficient￨L￨JJ￨O￨- contact￨L￨NN￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A to￨L￨TO￨O￨- βn￨L￨NN￨O￨- others￨L￨NNS￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- law￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- those￨L￨DT￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- rumor￨L￨NN￨O￨- leave￨L￨VBP￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- class￨L￨NN￨O￨- at￨L￨IN￨O￨- αi￨L￨CD￨NUMBER￨- rate￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- is￨L￨VBZ￨O￨- much￨L￨JJ￨O￨- faster￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- births￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- ignored￨L￨VBN￨O￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- constant￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- s￨L￨NNS￨O￨- +￨L￨CC￨O￨- i￨L￨FW￨O￨- +￨L￨CC￨O￨- r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- start￨L￨VBP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- Kermack-McKendrick￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- KM￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ds￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A di￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- dr￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- αi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- αi￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denote￨L￨VBP￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- β￨L￨VBP￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- removal￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- draws￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- rumor￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- nature￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- first￨L￨NN￨O￨- glance￨L￨NN￨O￨- it￨L￨PRP￨O￨- seems￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- PR￨U￨NN￨STATE_OR_PROVINCE￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- logistical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨RB￨O￨- ,￨L￨,￨O￨- initially￨L￨RB￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- may￨L￨MD￨O￨- know￨L￨VB￨O￨- some￨L￨DT￨O￨- rumor￨L￨NN￨O￨A .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- rumor￨L￨NN￨O￨A through￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A only￨L￨RB￨O￨- situation￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- space￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- discussed￨L￨VBN￨O￨- integer-valued￨L￨JJ￨O￨- autoregressive￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- INAR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Prediction￨U￨NN￨O￨- of￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- counts￨L￨NNS￨O￨- will￨L￨MD￨O￨- clearly￨L￨RB￨O￨- be￨L￨VB￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- situations￨L￨NNS￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- purpose￨L￨NN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- built￨L￨VBN￨O￨- around￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- process￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- adequate￨L￨JJ￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- TSIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- originally￨L￨RB￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic/endemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- first￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simple￨L￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- each￨L￨DT￨O￨- area￨L￨NN￨O￨- separately￨L￨RB￨O￨A and￨L￨CC￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- newly￨L￨RB￨O￨- collected￨L￨VBN￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- historic￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨A on￨L￨IN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- time￨L￨NN￨O￨- is￨L￨VBZ￨O￨- discretized￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- under￨L￨IN￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +Epigenetic￨U￨JJ￨O￨- silencing￨L￨NN￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨- via￨L￨IN￨O￨- heritable￨L￨JJ￨O￨- chromatin￨L￨NN￨O￨- modifications￨L￨NNS￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- ma￨L￨NN￨O￨- jor￨L￨NN￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- cell￨L￨NN￨O￨- fate￨L￨NN￨O￨A specification￨L￨NN￨O￨- in￨L￨IN￨O￨- higher￨L￨JJR￨O￨- organisms￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- boundary￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- locally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- states￨L￨NNS￨O￨A of￨L￨IN￨O￨- chromatin￨L￨NN￨O￨- :￨L￨:￨O￨- silenced￨L￨VBN￨O￨- and￨L￨CC￨O￨- unsilenced￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- of￨L￨IN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- guiding￨L￨VBG￨O￨- the￨L￨DT￨O￨- discussion￨L￨NN￨O￨A on￨L￨IN￨O￨- chromatin￨L￨NN￨O￨- silencing￨L￨NN￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- file-sharing￨L￨JJ￨O￨- peer-to-peer￨L￨JJ￨O￨- network￨L￨NN￨O￨- which￨L￨WDT￨O￨- resembles￨L￨VBZ￨O￨- the￨L￨DT￨O￨- popular￨L￨JJ￨O￨- BitTorrent￨U￨NNP￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- large￨L￨JJ￨O￨- files￨L￨NNS￨O￨- are￨L￨VBP￨O￨- split￨L￨VBN￨O￨- into￨L￨IN￨O￨- chunks￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- peer￨L￨VBP￨O￨- can￨L￨MD￨O￨- download￨L￨VB￨O￨A or￨L￨CC￨O￨- swap￨L￨VB￨O￨- from￨L￨IN￨O￨- another￨L￨DT￨O￨- peer￨L￨VBP￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- chunk￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- specific￨L￨NN￨O￨- interaction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- ←￨L￨NN￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- ′￨L￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- turns￨L￨VBZ￨O￨- A￨U￨DT￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- set￨L￨NN￨O￨- A￨U￨DT￨O￨- ′￨L￨NN￨O￨- differing￨L￨NN￨O￨- from￨L￨IN￨O￨- A￨U￨DT￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- single￨L￨JJ￨O￨- chunk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- ⊏￨L￨NN￨O￨- A￨U￨NN￨O￨- ′￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- |￨L￨SYM￨O￨- B￨U￨NN￨O￨- −￨L￨NN￨O￨- A￨U￨DT￨O￨- |￨L￨SYM￨O￨- chunks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- A￨U￨DT￨O￨- can￨L￨MD￨O￨- download￨L￨VB￨O￨A from￨L￨IN￨O￨- B￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- that￨L￨WDT￨O￨- picking￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- |￨L￨SYM￨O￨- B￨U￨NN￨O￨- −￨L￨NN￨O￨- A￨U￨NN￨O￨- |￨L￨NN￨O￨- .￨L￨.￨O￨- +P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- F￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- Consider￨U￨VB￨O￨- first￨L￨JJ￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- download￨L￨NN￨O￨A A￨U￨NN￨O￨- ←￨L￨NN￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- x￨L￨CC￨O￨- ∈￨L￨SYM￨O￨- Z￨U￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- download￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- ←￨L￨NN￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- ′￨L￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- equals￨L￨VBZ￨O￨- βxA￨L￨NN￨O￨- as￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- A￨U￨DT￨O￨- ⊏￨L￨NN￨O￨- A￨U￨NN￨O￨- ′￨L￨CD￨NUMBER￨- ⊂￨L￨NN￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- xB￨L￨NN￨O￨- |￨L￨NN￨O￨- B￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- A￨U￨DT￨O￨- |￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- DR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Examples￨U￨NNS￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- lasso￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- Tibshirani￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1996￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- SCAD￨U￨NN￨ORGANIZATION￨- [￨L￨-LRB-￨O￨- Fan￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1997￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Fan￨U￨NN￨MISC￨- and￨L￨CC￨O￨- Li￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2001￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Dantzig￨U￨NNP￨PERSON￨- selector￨L￨NN￨TITLE￨- [￨L￨-LRB-￨O￨- Candes￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Tao￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- MCP￨U￨NN￨ORGANIZATION￨- [￨L￨-LRB-￨O￨- Zhang￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- pursuit￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- Chen￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Donoho￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Saunders￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1999￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- many￨L￨JJ￨O￨- other￨L￨JJ￨O￨- L1￨U￨NN￨O￨- methods￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- Candes￨U￨NNS￨O￨- and￨L￨CC￨O￨- Tao￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2005￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2006￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Cand￨U￨NN￨O￨- `￨L￨``￨O￨- es￨L￨NNS￨O￨- ,￨L￨,￨O￨- Wakin￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Boyd￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- sparse￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨- conditions￨L￨NNS￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- regularized￨L￨VBN￨O￨- least￨L￨JJS￨O￨- squares￨L￨NNS￨O￨- estimator￨L￨NN￨O￨- enjoys￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nonasymptotic￨L￨JJ￨O￨- property￨L￨NN￨O￨- ,￨L￨,￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- weak￨L￨JJ￨O￨- oracle￨L￨NN￨TITLE￨- property￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- dimensionality￨L￨NN￨O￨- can￨L￨MD￨O￨- grow￨L￨VB￨O￨- exponentially￨L￨RB￨O￨- with￨L￨IN￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- Heavy￨U￨JJ￨O￨- traffic￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- control￨L￨NN￨O￨- led￨L￨VBD￨O￨- motorway￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- Brownian￨U￨JJ￨MISC￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- both￨L￨DT￨O￨- generalizes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- arises￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- heavy￨L￨JJ￨O￨A traffic￨L￨NN￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Inspired￨U￨VBN￨O￨- by￨L￨IN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- rate￨L￨NN￨O￨- control￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- developed￨L￨VBD￨O￨- for￨L￨IN￨O￨- Internet￨U￨NNP￨MISC￨- congestion￨L￨NN￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- Brownian￨U￨JJ￨MISC￨- network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A as￨L￨IN￨O￨- an￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- controlled￨L￨JJ￨O￨- motorway￨L￨NN￨O￨- and￨L￨CC￨O￨- consider￨L￨VB￨O￨- it￨L￨PRP￨O￨- operating￨L￨VBG￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- proportionally￨L￨RB￨O￨- fair￨L￨JJ￨O￨- ramp￨L￨NN￨O￨- metering￨L￨NN￨O￨- policy￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Internet￨U￨NN￨MISC￨- congestion￨L￨NN￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- to￨L￨TO￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- simplifications￨L￨NNS￨O￨- and￨L￨CC￨O￨- insights￨L￨NNS￨O￨- heavy￨L￨JJ￨O￨A traffic￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Road￨U￨NNP￨O￨- traffic￨L￨NN￨O￨- was￨L￨VBD￨O￨- an￨L￨DT￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- to￨L￨TO￨O￨- early￨L￨JJ￨O￨- researchers￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- recently￨L￨RB￨DATE￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- Internet￨U￨NN￨MISC￨- .￨L￨.￨O￨- +J.￨U￨NNP￨PERSON￨- Wil￨U￨NNP￨PERSON￨- liams￨L￨VBZ￨O￨- erences￨L￨NNS￨O￨- and￨L￨CC￨O￨- overviews￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- very￨L￨RB￨O￨- extensive￨L￨JJ￨O￨- literature￨L￨NN￨O￨- on￨L￨IN￨O￨- heavy￨L￨JJ￨O￨A traffic￨L￨NN￨O￨- for￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- Williams￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Bramson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Dai￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Harrison￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- Whitt￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- are￨L￨VBP￨O￨- recommended￨L￨VBN￨O￨- .￨L￨.￨O￨- +Green￨U￨NNP￨O￨- be￨L￨VB￨O￨- rewarded￨L￨VBN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- encourage￨L￨VB￨O￨- probabilists￨L￨NNS￨O￨- to￨L￨TO￨O￨- think￨L￨VB￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- statistical￨L￨JJ￨O￨A modelling￨L￨NN￨O￨- problems￨L￨NNS￨O￨- worth￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- attention￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- point￨L￨VB￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- another￨L￨DT￨O￨- important￨L￨JJ￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- John￨U￨NNP￨PERSON￨- Kingman￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- modern￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- methodology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- approaches￨L￨VBZ￨O￨- to￨L￨TO￨O￨- statistical￨L￨JJ￨O￨- genomics￨L￨NNS￨O￨- being￨L￨VBG￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- example￨L￨NN￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- papers￨L￨NNS￨O￨- by￨L￨IN￨O￨- Donnelly￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ewens￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Griffiths￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- volume￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- to￨L￨TO￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- modest￨L￨JJ￨O￨- generalisation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Dirichlet￨U￨NNP￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNPS￨MISC￨- Bayesian￨U￨JJ￨MISC￨- nonparametrics￨L￨NNS￨MISC￨- ,￨L￨,￨O￨- gene￨L￨NN￨O￨- expression￨L￨NN￨O￨- profiles￨L￨NNS￨O￨- ,￨L￨,￨O￨- hierarchical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- loss￨L￨NN￨O￨- functions￨L￨NNS￨O￨- ,￨L￨,￨O￨- MCMC￨U￨NNP￨O￨- samplers￨L￨NNS￨O￨- ,￨L￨,￨O￨- optimal￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- ,￨L￨,￨O￨- partition￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- P´olya￨U￨NN￨O￨- urn￨L￨NN￨O￨- ,￨L￨,￨O￨- stick￨L￨NN￨O￨- breaking￨L￨VBG￨O￨- AMS￨U￨NNP￨O￨- subject￨L￨JJ￨O￨- classification￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- 60G09￨L￨NN￨O￨- ,￨L￨,￨O￨- 62F15￨L￨NN￨O￨- ,￨L￨,￨O￨- 62G99￨L￨NN￨O￨- ,￨L￨,￨O￨- 62H30￨L￨NN￨O￨- ,￨L￨,￨O￨- 62M99￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- note￨L￨NN￨O￨- is￨L￨VBZ￨O￨- four-fold￨L￨RB￨O￨- :￨L￨:￨O￨- to￨L￨TO￨O￨- remind￨L￨VB￨O￨- some￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- nonparametricians￨L￨NNS￨MISC￨- gently￨L￨RB￨O￨- that￨L￨IN￨O￨- closer￨L￨JJR￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨A literature￨L￨NN￨O￨- might￨L￨MD￨O￨- a￨L￨DT￨O￨- School￨U￨NNP￨O￨- of￨L￨IN￨O￨- Mathematics￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Bristol￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Bristol￨U￨NNP￨CITY￨- BS8￨U￨NN￨O￨- 1TW￨L￨NN￨O￨- ;￨L￨:￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- M￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- M￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- variant￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- familiar￨L￨JJ￨O￨- Dirichlet￨U￨NNP￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- much￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- modelling￨L￨NN￨O￨A and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- machinery￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- Dirichlet￨U￨NNP￨O￨- process￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- readily￨L￨RB￨O￨- adapted￨L￨VBN￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- generalisation￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- simple￨L￨JJ￨O￨- mixture￨L￨NN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- clusters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- ‘￨L￨``￨O￨- colours￨L￨NNS￨O￨- ’￨L￨POS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- statistical￨L￨JJ￨O￨A characteristics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- constant￨L￨JJ￨O￨- within￨L￨IN￨O￨- colours￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- different￨L￨JJ￨O￨- between￨L￨IN￨O￨- colours￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- begin￨L￨VBP￨O￨- by￨L￨IN￨O￨- reviewing￨L￨VBG￨O￨- some￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- results￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- Dirichlet￨U￨NNP￨MISC￨- Process￨U￨VB￨MISC￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- close￨L￨JJ￨O￨- relatives￨L￨NNS￨O￨- ,￨L￨,￨O￨- focussing￨L￨VBG￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- statistical￨L￨JJ￨O￨A modelling￨L￨NN￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +Inference￨U￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- using￨L￨VBG￨O￨- multilocus￨L￨NN￨O￨- genotype￨L￨NN￨O￨A data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Model￨U￨NNP￨TITLE￨- for￨L￨IN￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneities￨L￨NNS￨O￨A in￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- and/or￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- correlate￨L￨VB￨O￨- with￨L￨IN￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- Model￨U￨NNP￨TITLE￨- for￨L￨IN￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- heterogeneities￨L￨NNS￨O￨- in￨L￨IN￨O￨- 3.1￨L￨CD￨NUMBER￨- 3.2￨L￨CD￨NUMBER￨- 3.3￨L￨CD￨NUMBER￨- 3.4￨L￨CD￨NUMBER￨- 3.5￨L￨CD￨NUMBER￨- Assortative￨U￨JJ￨O￨- mixing￨L￨VBG￨O￨- by￨L￨IN￨O￨- type￨L￨NN￨O￨- infectiousness￨L￨NN￨O￨- and/or￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- where￨L￨WRB￨O￨- contacts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- group￨L￨NN￨O￨- .￨L￨.￨O￨- +Multiple￨U￨JJ￨O￨- transmission￨L￨NN￨O￨- modes￨L￨NNS￨O￨- Multiple￨U￨JJ￨O￨- infectious￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- Model￨U￨NNP￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- each￨L￨DT￨O￨- behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- different￨L￨JJ￨O￨A .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- tolerance￨L￨NN￨O￨A parameter￨L￨NN￨O￨- is￨L￨VBZ￨O￨- smaller￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- cascading￨L￨VBG￨O￨- failure￨L￨NN￨O￨- cuts￨L￨NNS￨O￨- off￨L￨NN￨O￨- abundant￨L￨JJ￨O￨- of￨L￨IN￨O￨- paths￨L￨NNS￨O￨- and￨L￨CC￨O￨- blocks￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- locally￨L￨RB￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- tolerance￨L￨NN￨O￨A parameter￨L￨NN￨O￨- is￨L￨VBZ￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- out￨L￨IN￨O￨- and￨L￨CC￨O￨- infects￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- tolerance￨L￨NN￨O￨A parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- out￨L￨RB￨O￨- and￨L￨CC￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cascading￨L￨VBG￨O￨- failure￨L￨NN￨O￨A also￨L￨RB￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- failed￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- deliver￨L￨VB￨O￨- data￨L￨NNS￨O￨- properly￨L￨RB￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- deliver￨L￨VB￨O￨- copies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- properly￨L￨RB￨O￨- .￨L￨.￨O￨- +–￨L￨:￨O￨- Epidemic￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- cascading￨L￨VBG￨O￨- failure￨L￨NN￨O￨A are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- over￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- methodology￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- computation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- final￨L￨JJ￨O￨A size￨L￨NN￨O￨A distributions￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- Markovian￨U￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Black￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Bailey￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- 1953￨L￨CD￨DATE￨- ;￨L￨:￨O￨- 1975￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- Neuts￨U￨NNS￨O￨- and￨L￨CC￨O￨- Li￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1996￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- superior￨L￨JJ￨O￨- ,￨L￨,￨O￨- being￨L￨VBG￨O￨- both￨L￨CC￨O￨- numerically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- and￨L￨CC￨O￨- computationally￨L￨RB￨O￨- efficient￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- algorithms￨L￨NNS￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- physically￨L￨RB￨O￨- transparent￨L￨JJ￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- allow￨L￨VB￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- extend￨L￨VB￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- phase-type￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- another￨L￨DT￨O￨- with￨L￨IN￨O￨- waning￨L￨VBG￨O￨A immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A size￨L￨NN￨O￨A distribution￨L￨NN￨O￨- gives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- eac￨L￨NN￨O￨- h￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- final￨L￨JJ￨O￨A size￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- w￨L￨VBP￨O￨- ho￨L￨NN￨O￨- have￨L￨VBP￨O￨- experienced￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- an￨L￨DT￨O￨- SIRS-type￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- account￨L￨NN￨O￨- for￨L￨IN￨O￨- behavioural￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- simultaneous￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Stability￨U￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨NN￨O￨- steady￨L￨JJ￨O￨- states￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- provides￨L￨VBZ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- potential￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨A .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- by￨L￨IN￨O￨- fleeing￨L￨VBG￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- area￨L￨NN￨O￨- the￨L￨DT￨O￨- people￨L￨NNS￨O￨- carried￨L￨VBD￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- infecting￨L￨VBG￨O￨- other￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- awareness￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨A prompted￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- first-hand￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Mixture-based￨U￨JJ￨MISC￨- Modeling￨U￨NN￨O￨- of￨L￨IN￨O￨- Spatially￨U￨RB￨O￨- Correlated￨U￨JJ￨O￨- Interference￨U￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨ORGANIZATION￨- Field￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Interferers￨U￨NNP￨ORGANIZATION￨- Arindam￨U￨NNP￨ORGANIZATION￨- Ghosh￨U￨NNP￨ORGANIZATION￨- Centre￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Development￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Telematics￨U￨NNPS￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- C-DOT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Bengaluru￨U￨NN￨O￨- ,￨L￨,￨O￨- Karnataka￨U￨NNP￨LOCATION￨- -￨L￨:￨O￨- 560100￨L￨CD￨NUMBER￨- Email￨U￨VB￨O￨- :￨L￨:￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- As￨U￨IN￨O￨- the￨L￨DT￨O￨- interference￨L￨NN￨O￨- in￨L￨IN￨O￨- PPP￨U￨NNP￨ORGANIZATION￨- based￨L￨VBN￨O￨- wireless￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- spatial￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- ,￨L￨,￨O￨- any￨L￨DT￨O￨- joint￨L￨JJ￨O￨A analysis￨L￨NN￨O￨- involving￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- integrations￨L￨NNS￨O￨- over￨L￨IN￨O￨- R2￨U￨NN￨O￨- spatial￨L￨JJ￨O￨- points￨L￨NNS￨O￨- either￨L￨CC￨O￨- end￨L￨VB￨O￨- up￨L￨RP￨O￨- with￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- or￨L￨CC￨O￨- become￨L￨VB￨O￨- analytically￨L￨RB￨O￨- too￨L￨RB￨O￨- intractable￨L￨JJ￨O￨- .￨L￨.￨O￨- +Index￨U￨NNP￨O￨- Terms￨U￨NNS￨O￨- —￨L￨:￨O￨- Poisson￨U￨NN￨PERSON￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- interference￨L￨NN￨O￨- ,￨L￨,￨O￨- correlation￨L￨NN￨O￨- ,￨L￨,￨O￨- mixture￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- joint￨L￨JJ￨O￨A CCDF￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- plots￨L￨NNS￨O￨- are￨L￨VBP￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- tightly￨L￨RB￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- PPP-based￨U￨JJ￨MISC￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- tightness￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- λ￨L￨NN￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- interferer￨L￨NN￨O￨- intensity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- exponent￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- by￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- the￨L￨DT￨O￨- joint￨L￨JJ￨O￨A CCDF￨U￨NN￨O￨- of￨L￨IN￨O￨- SIRs￨U￨NNS￨O￨- at￨L￨IN￨O￨- N￨U￨NN￨O￨- arbitrary￨L￨JJ￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- perfect￨L￨JJ￨O￨A simulation￨L￨NN￨O￨- algorithms￨L￨NNS￨O￨- for￨L￨IN￨O￨- locally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- dominated￨L￨VBN￨O￨- coupling￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- apply￨L￨VB￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- contexts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- coupling￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- (￨L￨-LRB-￨O￨- CFTP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- dominated￨L￨VBD￨O￨- CFTP￨U￨NNP￨O￨- ,￨L￨,￨O￨- exact￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- ,￨L￨,￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- ,￨L￨,￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- Monte￨U￨NNP￨LOCATION￨- Carlo￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- perfect￨L￨JJ￨O￨A simulation￨L￨NN￨O￨- ,￨L￨,￨O￨- Papangelou￨U￨NN￨O￨- conditional￨L￨JJ￨O￨- intensity￨L￨NN￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- birth-and-death￨L￨NN￨O￨- process￨L￨NN￨O￨- AMS￨U￨NNP￨O￨- subject￨L￨JJ￨O￨- classification￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- 62M30￨L￨NNP￨O￨- ,￨L￨,￨O￨- 60G55￨L￨NNP￨O￨- ,￨L￨,￨O￨- 60K35￨L￨NNP￨O￨- a￨L￨DT￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Medicine￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Addenbrooke￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨ORGANIZATION￨- Hospital￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hills￨U￨NNP￨LOCATION￨- Road￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Cambridge￨U￨NNP￨CITY￨- CB2￨U￨NN￨O￨- 0QQ￨L￨NN￨O￨- ;￨L￨:￨O￨- b￨L￨NN￨O￨- Smith￨U￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Enterprise￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Environment￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hayes￨U￨NNP￨ORGANIZATION￨- House￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 75￨L￨CD￨NUMBER￨- George￨U￨NNP￨CITY￨- Street￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Oxford￨U￨NNP￨O￨- OX1￨U￨NN￨O￨- 2BQ￨L￨NN￨O￨- ;￨L￨:￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- M￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- M￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- method￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- perfect￨L￨JJ￨O￨A simulation￨L￨NN￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- shows￨L￨VBZ￨O￨- promising￨L￨JJ￨O￨- results￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- which￨L￨WDT￨O￨- threshold￨L￨NN￨O￨- coefficients￨L￨NNS￨O￨- independently￨L￨RB￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- diffusion￨L￨NN￨O￨- on￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- known￨L￨JJ￨O￨- overlapping￨L￨VBG￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A ,￨L￨,￨O￨- by￨L￨IN￨O￨- analysing￨L￨VBG￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- contagion￨L￨NN￨O￨- on￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +5￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- diffusion￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨VBP￨O￨- replicate￨L￨VB￨O￨- and￨L￨CC￨O￨- extend￨L￨VB￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- non-overlapping￨L￨JJ￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- study￨L￨VB￨O￨- diffusion￨L￨NN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- overlapping￨L￨VBG￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A .￨L￨.￨O￨- +Both￨U￨CC￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨A node￨L￨NN￨O￨- states￨L￨NNS￨O￨- are￨L￨VBP￨O￨- specified￨L￨VBN￨O￨- by￨L￨IN￨O￨- Z￨U￨NN￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- ESM￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- §￨L￨SYM￨O￨- I￨U￨PRP￨O￨- for￨L￨IN￨O￨- further￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- contained￨L￨VBN￨O￨- in￨L￨IN￨O￨- Z￨U￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- directed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Motifs￨U￨NNS￨O￨- may￨L￨MD￨O￨- encode￨L￨VB￨O￨- intrinsic￨L￨JJ￨O￨A node￨L￨NN￨O￨- states￨L￨NNS￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- relevant￨L￨JJ￨O￨- information￨L￨NN￨O￨- ;￨L￨:￨O￨- further￨L￨RB￨O￨- details￨L￨NNS￨O￨- and￨L￨CC￨O￨- examples￨L￨NNS￨O￨- are￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- throughout￨L￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- ESM￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- §￨L￨NNP￨O￨- II￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- (￨L￨-LRB-￨O￨- Sec.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- modelling￨L￨NN￨O￨- scheme￨L￨NN￨O￨- where￨L￨WRB￨O￨- network￨L￨NN￨O￨- theory￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- accounts￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- elements￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- birth-death￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- models￨L￨NNS￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- motifs￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- attached￨L￨VBN￨O￨- together￨L￨RB￨O￨- to￨L￨TO￨O￨- form￨L￨VB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- vector￨L￨NN￨O￨A X￨U￨NN￨O￨- =￨L￨JJ￨O￨- x￨L￨CC￨O￨- enumerates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- available￨L￨JJ￨O￨- building￨L￨NN￨O￨- blocks￨L￨NNS￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- prior￨L￨JJ￨O￨- information￨L￨NN￨O￨- Y￨U￨NN￨O￨- specifies￨L￨NNS￨O￨- how￨L￨WRB￨O￨- such￨L￨JJ￨O￨- blocks￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- attached￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- vector￨L￨NN￨O￨A x￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- integers￨L￨NNS￨O￨- specifying￨L￨VBG￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- times￨L￨NNS￨O￨- different￨L￨JJ￨O￨- motifs￨L￨NNS￨O￨- appear￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Role￨U￨NN￨O￨- of￨L￨IN￨O￨- word-of-mouth￨L￨NN￨O￨- for￨L￨IN￨O￨- programs￨L￨NNS￨O￨- of￨L￨IN￨O￨- voluntary￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- game-theoretic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- Samit￨U￨NNP￨PERSON￨- Bhattacharyya￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- ∗￨L￨CD￨NUMBER￨- †￨L￨CD￨NUMBER￨- Chris￨U￨NNP￨PERSON￨- Bauch￨U￨NNP￨PERSON￨- ‡￨L￨NNP￨O￨- and￨L￨CC￨O￨- Romulus￨U￨NNP￨O￨- Breban￨U￨NNP￨O￨- §￨L￨NNP￨O￨- September￨U￨NNP￨DATE￨- 18￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- Abstract￨U￨NNP￨O￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- synergetic￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- between￨L￨IN￨O￨- word-of-mouth￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- WoM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- voluntary￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- combine￨L￨VBP￨O￨- a￨L￨DT￨O￨- game-theoretic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- WoM￨U￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- program￨L￨NN￨O￨- of￨L￨IN￨O￨- voluntary￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- synergetic￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- between￨L￨IN￨O￨- WoM￨U￨NN￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- voluntary￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- evaluate￨L￨VBP￨O￨- and￨L￨CC￨O￨- compare￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- what￨L￨WP￨O￨- WoM￨U￨NNP￨O￨- disseminates￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- vaccine￨L￨NN￨O￨- advertising￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- occur￨L￨VB￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- ongoing￨L￨JJ￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- status￨L￨NN￨O￨A ,￨L￨,￨O￨- notably￨L￨RB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +WoM￨U￨NN￨O￨- disseminates￨L￨VBZ￨O￨- stories￨L￨NNS￨O￨- on￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- scares￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- status￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- may￨L￨MD￨O￨- go￨L￨VB￨O￨- both￨L￨DT￨O￨- ways￨L￨NNS￨O￨- .￨L￨.￨O￨- +INTRODUCTION￨U￨NN￨O￨- The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- NadarayaWatson￨U￨NNP￨O￨- estimator￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- regression￨L￨NN￨O￨- function￨L￨NN￨O￨- f￨L￨FW￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- n￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- given￨L￨VBN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- semiparametric￨L￨JJ￨O￨- regression￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Yn￨U￨NN￨O￨- =￨L￨JJ￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- θ￨L￨NN￨O￨- Xn￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- εn￨L￨NN￨O￨- where￨L￨WRB￨O￨- (￨L￨-LRB-￨O￨- Xn￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- and￨L￨CC￨O￨- identically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- random￨L￨JJ￨O￨- vectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- Rp￨U￨NN￨MISC￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- driven￨L￨VBN￨O￨- noise￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- εn￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- martingale￨L￨NN￨O￨- difference￨L￨NN￨O￨- sequence￨L￨NN￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- Xn￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- make￨L￨VBP￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- recursive￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sliced￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- regression￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- originally￨L￨RB￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Li￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Duan￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Li￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- θ￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- the￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- regression￨L￨NN￨O￨- function￨L￨NN￨O￨- f￨L￨FW￨O￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- recursive￨L￨JJ￨O￨- Nadaraya-Watson￨U￨NN￨MISC￨- estimator￨L￨NN￨O￨A which￨L￨WDT￨O￨- takes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- θ￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- situation￨L￨NN￨O￨- without￨L￨IN￨O￨- any￨L￨DT￨O￨- parameter￨L￨NN￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- almost￨L￨RB￨O￨- sure￨L￨JJ￨O￨- convergence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Nadaraya-Watson￨U￨NNP￨MISC￨- estimator￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- was￨L￨VBD￨O￨- proved￨L￨VBN￨O￨- by￨L￨IN￨O￨- Noda￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- asymptotic￨L￨JJ￨O￨- normality￨L￨NN￨O￨- was￨L￨VBD￨O￨- established￨L￨VBN￨O￨- by￨L￨IN￨O￨- Schuster￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Last￨U￨JJ￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- numerically￨L￨RB￨O￨- the￨L￨DT￨O￨- indeces￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- STOCs￨U￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- considerations￨L￨NNS￨O￨A for￨L￨IN￨O￨- some￨L￨DT￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- make￨L￨VB￨O￨- some￨L￨DT￨O￨- discussions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- cycles￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- ;￨L￨:￨O￨- Small￨U￨JJ￨O￨- world￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- Scale￨U￨NNP￨O￨- free￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- cycle￨L￨NN￨O￨- ,￨L￨,￨O￨- propagation￨L￨NN￨O￨A ,￨L￨,￨O￨- Eurer￨U￨NNP￨O￨- ’s￨L￨POS￨O￨- Polyhedron￨U￨NNP￨O￨- Theorem￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Milgram￨U￨NNP￨PERSON￨- has￨L￨VBZ￨O￨- made￨L￨VBN￨O￨- a￨L￨DT￨O￨- great￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- by￨L￨IN￨O￨- advocating￨L￨VBG￨O￨- ”￨L￨''￨O￨- Six￨U￨CD￨NUMBER￨- Degrees￨U￨NNS￨O￨- of￨L￨IN￨O￨- Separation￨U￨NN￨O￨- ”￨L￨''￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Thanks￨U￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- recursion￨L￨NN￨O￨- relation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- can￨L￨MD￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- STOC￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- celebrated￨L￨JJ￨O￨- ”￨L￨''￨O￨- Euler￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- polyhedron￨L￨NN￨O￨- formula￨L￨NN￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- applicable￨L￨JJ￨O￨A to￨L￨TO￨O￨- planar￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Indeces￨U￨NNS￨O￨- for￨L￨IN￨O￨- propagation￨L￨NN￨O￨A We￨U￨PRP￨O￨- first￨L￨VBD￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- generation￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- initiate￨L￨VBP￨O￨- a￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- clustered￨L￨VBN￨O￨A multi-layer￨L￨JJ￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- all￨L￨DT￨O￨- constituent￨L￨NN￨O￨- layers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- information￨L￨NN￨O￨A propagates￨L￨VBZ￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- information￨L￨NN￨O￨- transmissibility￨L￨NN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- give￨L￨VBP￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- cases￨L￨NNS￨O￨- where￨L￨WRB￨O￨- information￨L￨NN￨O￨- star￨L￨NN￨O￨- ts￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- individual￨L￨NN￨O￨- and￨L￨CC￨O￨- reaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- e-Epidemic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SusceptibleInfectious-Recovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- save￨L￨VB￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- let￨L￨VB￨O￨- it￨L￨PRP￨O￨- survive￨L￨VB￨O￨A after￨L￨IN￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- collaboration￨L￨NN￨O￨- and￨L￨CC￨O￨- transmitting￨L￨VBG￨O￨- crucial￨L￨JJ￨O￨- information￨L￨NN￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- monitoring-related￨L￨JJ￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- survive￨L￨VB￨O￨A .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- takes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- natural￨L￨JJ￨O￨A death￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- crashing￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- birth￨L￨NN￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- authors￨L￨NNS￨O￨- discussed￨L￨VBD￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨A populations￨L￨NNS￨O￨A through￨L￨IN￨O￨- several￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- that￨L￨DT￨O￨- purpose￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- and￨L￨CC￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- epidemic-domain￨L￨NN￨O￨- inspired￨L￨VBD￨O￨A approach￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- survivability￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- IoT￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- quantity￨L￨NN￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproductive￨L￨JJ￨O￨A ratio￨L￨NN￨O￨A R0￨U￨NN￨O￨- —￨L￨:￨O￨- Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- will￨L￨MD￨O￨- experience￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- verbally￨L￨RB￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- infected￨L￨JJ￨O￨- per￨L￨IN￨O￨- primary￨L￨JJ￨O￨- case￨L￨NN￨O￨- early￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- a￨L￨DT￨O￨- two-dimensional￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- susceptible-infectious-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- making￨L￨VBG￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- time-scale￨L￨JJ￨O￨- separation￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- distinction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- between￨L￨IN￨O￨- susceptible-infectious-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- recovery￨L￨NN￨O￨A returns￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptible-infectious-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- recovery￨L￨NN￨O￨- removes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- further￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- former￨L￨JJ￨O￨- being￨L￨VBG￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- other￨L￨JJ￨O￨- than￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Similarly￨U￨RB￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- earliest￨L￨JJS￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- much￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- applied￨L￨VBN￨O￨- modeling￨L￨NN￨O￨- that￨L￨WDT￨O￨- followed￨L￨VBD￨O￨- was￨L￨VBD￨O￨- deterministic￨L￨JJ￨O￨A and￨L￨CC￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- non-linear￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- low-dimensional￨L￨JJ￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- accurate￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- for￨L￨IN￨O￨- cases￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- time-scale￨L￨NN￨O￨- separation￨L￨NN￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- too￨L￨RB￨O￨- pronounced￨L￨JJ￨O￨- ,￨L￨,￨O￨- provided￨L￨VBD￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- degree￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- households￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- —￨L￨:￨O￨- governing￨L￨VBG￨O￨- within-household￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- between-household￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- —￨L￨:￨O￨- from￨L￨IN￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- day￨L￨NN￨DATE￨- upon￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- became￨L￨VBD￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨A in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- occurred￨L￨VBD￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- available￨L￨JJ￨O￨- from￨L￨IN￨O￨- first￨L￨JJ￨O￨- few￨L￨JJ￨O￨- hundred￨L￨CD￨NUMBER￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNPS￨O￨- household￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- ·￨L￨CD￨NUMBER￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- ·￨L￨VBZ￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- ·￨L￨NN￨O￨- between-household￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- First￨U￨JJ￨ORDINAL￨- few￨L￨JJ￨O￨- hundred￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- FF100￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- studies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- data￨L￨NNS￨O￨- collection￨L￨NN￨O￨- exercises￨L￨NNS￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mathematical￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Adelaide￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Adelaide￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- SA￨U￨NNP￨O￨- 5005￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- E-mail￨U￨NN￨O￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- Bayesian￨U￨NNP￨O￨- Markov￨U￨NNP￨O￨- Chain￨U￨NNP￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- a￨L￨DT￨O￨- joint￨L￨JJ￨O￨- posterior￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨A reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- work￨L￨NN￨O￨- inferred￨L￨VBD￨O￨- within-household￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- household￨L￨NN￨O￨A stratified￨L￨VBD￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- works￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- first￨L￨NN￨O￨- order￨L￨NN￨O￨- reflections￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- paths￨L￨NNS￨O￨A from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- point￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- using￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- reflector￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- second￨L￨JJ￨ORDINAL￨- order￨L￨NN￨O￨- reflections￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- paths￨L￨NNS￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- point￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- using￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- reflector￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- features￨L￨NNS￨O￨- at￨L￨IN￨O￨- millimeter￨L￨JJ￨O￨- wave￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- by￨L￨IN￨O￨- metallic￨L￨JJ￨O￨- objects￨L￨NNS￨O￨- .￨L￨.￨O￨- +8￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 7￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨JJ￨O￨- —￨L￨:￨O￨- The￨U￨DT￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- user￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- mmwave￨L￨NN￨O￨- system￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- line-of-sight￨L￨JJ￨O￨- paths￨L￨NNS￨O￨A or￨L￨CC￨O￨- reflected￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- from￨L￨IN￨O￨- any￨L￨DT￨O￨- base￨L￨NN￨O￨- station￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- later￨L￨JJ￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- finds￨L￨NNS￨O￨- that￨L￨WDT￨O￨- well-known￨L￨JJ￨O￨- lossy￨L￨JJ￨O￨- objects￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- human￨L￨JJ￨O￨- body￨L￨NN￨O￨- and￨L￨CC￨O￨- concrete￨L￨NN￨O￨- are￨L￨VBP￨O￨- good￨L￨JJ￨O￨- reflectors￨L￨NNS￨O￨- at￨L￨IN￨O￨- mmWave￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨A ,￨L￨,￨O￨- enabling￨L￨VBG￨O￨- the￨L￨DT￨O￨- receiver￨L￨NN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- secondary￨L￨JJ￨O￨- reflections￨L￨NNS￨O￨- for￨L￨IN￨O￨- non-line-of-sight￨L￨JJ￨O￨- communication￨L￨NN￨O￨- .￨L￨.￨O￨- +Blockages￨U￨NNS￨O￨- are￨L￨VBP￨O￨- objects￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- obstruction￨L￨NN￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- path￨L￨NN￨O￨- ,￨L￨,￨O￨- LOS￨U￨NNP￨O￨- or￨L￨CC￨O￨- NLOS￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- base￨L￨NN￨O￨A station￨L￨NN￨O￨A and￨L￨CC￨O￨- a￨L￨DT￨O￨- user￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- these￨L￨DT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- reflect￨L￨JJ￨O￨- signals￨L￨NNS￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- reflection￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- is￨L￨VBZ￨O￨- zero￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- look￨L￨VBP￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- mmwave￨L￨NN￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- blockages￨L￨NNS￨O￨- and￨L￨CC￨O￨- reflectors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Estimating￨U￨VBG￨O￨- epidemic￨L￨JJ￨O￨- arrival￨L￨NN￨O￨A times￨L￨NNS￨O￨- using￨L￨VBG￨O￨- linear￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- theory￨L￨NN￨O￨- Lawrence￨U￨NNP￨PERSON￨- M.￨U￨NNP￨PERSON￨- Chen￨U￨NNP￨PERSON￨- ,1￨L￨CD￨NUMBER￨- Matt￨U￨NNP￨PERSON￨- Holzer￨U￨NNP￨PERSON￨- ,2￨L￨NN￨O￨- and￨L￨CC￨O￨- Anne￨U￨VB￨PERSON￨- Shapiro3￨U￨NN￨O￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Mathematics￨U￨NNP￨O￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Kansas￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Lawrence￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- KS￨U￨NN￨STATE_OR_PROVINCE￨- 66045￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- USA￨U￨NNP￨ORGANIZATION￨- 2Department￨L￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mathematical￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- George￨U￨NNP￨ORGANIZATION￨- Mason￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Fairfax￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- VA￨U￨NNP￨STATE_OR_PROVINCE￨- 22030￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- 3Department￨L￨NNP￨O￨- of￨L￨IN￨O￨- Mathematics￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Statistics￨U￨NNPS￨O￨- ,￨L￨,￨O￨- Carleton￨U￨NNP￨PERSON￨- Col￨U￨NNP￨PERSON￨- lege￨L￨NN￨O￨- ,￨L￨,￨O￨- Northfield￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- MN￨U￨NN￨STATE_OR_PROVINCE￨- 55057￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- November￨U￨NNP￨DATE￨- 12￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- structured￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- worldwide￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- formulate￨L￨VB￨O￨- predictions￨L￨NNS￨O￨- for￨L￨IN￨O￨- arrival￨L￨NN￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- city￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- pathway￨L￨NN￨O￨- between￨L￨IN￨O￨- any￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- cities￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- dimensional￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- or￨L￨CC￨O￨- homogeneous￨L￨JJ￨O￨- tree￨L￨NN￨O￨- and￨L￨CC￨O￨- gives￨L￨VBZ￨O￨- a￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- prediction￨L￨NN￨O￨- for￨L￨IN￨O￨- arrival￨L￨NN￨O￨A times￨L￨NNS￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- specific￨L￨JJ￨O￨- network￨L￨NN￨O￨- features￨L￨NNS￨O￨- .￨L￨.￨O￨- +Making￨U￨VBG￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- determinacy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- spreading￨L￨VBG￨O￨- speeds￨L￨NNS￨O￨- and￨L￨CC￨O￨- arrival￨L￨NN￨O￨A times￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- linearized￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- unstable￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- these￨L￨DT￨O￨- to￨L￨TO￨O￨- arrival￨L￨NN￨O￨- times￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- arrival￨L￨NN￨O￨A times￨L￨NNS￨O￨- based￨L￨VBN￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- determinacy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- traveling￨L￨VBG￨O￨- fronts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Cascaded￨U￨VBN￨MISC￨- Regression￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- CR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- facial￨L￨JJ￨O￨- landmarks￨L￨NNS￨O￨- detection￨L￨NN￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- learn￨L￨VBP￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- descent￨L￨NN￨O￨- directions￨L￨NNS￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- cascaded￨L￨VBN￨O￨- regressors￨L￨NNS￨O￨- separately￨L￨RB￨O￨- trained￨L￨VBN￨O￨- in￨L￨IN￨O￨- coarse￨L￨JJ￨O￨A and￨L￨CC￨O￨- fine￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- .￨L￨.￨O￨- +Only￨U￨RB￨O￨- one￨L￨CD￨NUMBER￨- self-iterative￨L￨JJ￨O￨- regressor￨L￨NN￨O￨- is￨L￨VBZ￨O￨- trained￨L￨VBN￨O￨- to￨L￨TO￨O￨- learn￨L￨VB￨O￨- the￨L￨DT￨O￨- descent￨L￨NN￨O￨- directions￨L￨NNS￨O￨- for￨L￨IN￨O￨- samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- coarse￨L￨JJ￨O￨A stages￨L￨NNS￨O￨- to￨L￨TO￨O￨- fine￨L￨VB￨O￨- stages￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- iteratively￨L￨RB￨O￨- updated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- regressor￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- training￨L￨NN￨O￨- multiple￨L￨JJ￨O￨A regressors￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- lots￨L￨NNS￨O￨- of￨L￨IN￨O￨- computing￨L￨VBG￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- for￨L￨IN￨O￨- deep￨L￨JJ￨O￨- learning￨L￨NN￨O￨- based￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- experiments￨L￨NNS￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- 3.72￨L￨CD￨NUMBER￨- M￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- proposed￨L￨VBN￨O￨A method￨L￨NN￨O￨- achieves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- state-of-the-art￨L￨JJ￨O￨- performance￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨A Landmarks-Attention￨U￨NNP￨ORGANIZATION￨- Network￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- LAN￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- our￨L￨PRP$￨O￨- regressor￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- concurrently￨L￨RB￨O￨- learns￨L￨VBZ￨O￨- features￨L￨NNS￨O￨- around￨L￨IN￨O￨- each￨L￨DT￨O￨- landmark￨L￨NN￨O￨- and￨L￨CC￨O￨- obtains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- holistic￨L￨JJ￨O￨- location￨L￨NN￨O￨- increment￨L￨NN￨O￨- .￨L￨.￨O￨- +R0￨U￨NN￨O￨- FAILS￨U￨VBZ￨O￨- TO￨U￨TO￨O￨- PREDICT￨U￨NNP￨O￨- THE￨U￨DT￨O￨- OUTBREAK￨U￨NNP￨O￨- POTENTIAL￨U￨NNP￨O￨- IN￨U￨IN￨O￨- THE￨U￨DT￨O￨- PRESENCE￨U￨NN￨O￨- OF￨U￨IN￨O￨- NATURAL-BOOSTING￨U￨NNP￨O￨- IMMUNITY￨U￨NNP￨O￨- YUKIHIKO￨U￨NNP￨PERSON￨- NAKATA￨U￨NNP￨PERSON￨- AND￨U￨CC￨O￨- RYOSUKE￨U￨NNP￨PERSON￨- OMORI￨U￨NNP￨PERSON￨- A￨U￨NNP￨O￨- B￨U￨NNP￨O￨- S￨U￨NN￨O￨- TRAC￨U￨NNP￨MISC￨- T.￨U￨NNP￨MISC￨- Time￨U￨NNP￨MISC￨- varying￨L￨VBG￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- waning￨L￨VBG￨O￨- and￨L￨CC￨O￨- boosting￨L￨VBG￨O￨A immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- induce￨L￨VB￨O￨- rich￨L￨JJ￨O￨- long-term￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Decreased￨U￨VBN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- by￨L￨IN￨O￨- waning￨L￨VBG￨O￨- immunity￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- induces￨L￨VBZ￨O￨- re-emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- boosting￨L￨VBG￨O￨A immunity￨L￨NN￨O￨- by￨L￨IN￨O￨- re-vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- system￨L￨NN￨O￨- show￨L￨NN￨O￨- “￨L￨``￨O￨- the￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- takes￨L￨VBZ￨O￨- off￨L￨RP￨O￨- after￨L￨IN￨O￨- negative￨L￨JJ￨O￨- slope￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨A phase￨L￨NN￨O￨A of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- classification￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- no￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ”￨L￨''￨O￨- as￨L￨IN￨O￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- normal￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- as￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- basic￨L￨JJ￨O￨- findings￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- computational￨L￨JJ￨O￨- calculations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Malware￨U￨NN￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨A affecting￨L￨VBG￨O￨- availability￨L￨NN￨O￨- can￨L￨MD￨O￨- turn￨L￨VB￨O￨- around￨L￨RP￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- kinetic￨L￨JJ￨O￨- combat￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- resulting￨L￨VBG￨O￨- framework￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- model-based￨L￨JJ￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- malware￨L￨NN￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨A turn￨L￨VBP￨O￨- around￨L￨RP￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- kinetic￨L￨JJ￨O￨- combat￨L￨NN￨O￨- .￨L￨.￨O￨- +Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- analyzed￨L￨VBN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- malware￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- cyber￨L￨NN￨O￨- part￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨A as￨L￨RB￨O￨- well￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- game-like￨L￨JJ￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- kinetic￨L￨JJ￨O￨- combat￨L￨NN￨O￨- illustrates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨A of￨L￨IN￨O￨- malware￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- concise￨L￨JJ￨O￨- way￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- make￨L￨VB￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- more￨L￨RBR￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- employ￨L￨VBP￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- pmove￨L￨NN￨O￨- to￨L￨TO￨O￨- denote￨L￨VB￨O￨- its￨L￨PRP$￨O￨- moving￨L￨VBG￨O￨A probability￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- corresponds￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- small￨L￨JJ￨O￨- world￨L￨NN￨O￨A networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- these￨L￨DT￨O￨- simulations￨L￨NNS￨O￨- we￨L￨PRP￨O￨- see￨L￨VBP￨O￨- the￨L￨DT￨O￨- moving￨L￨VBG￨O￨A probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- world￨L￨NN￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- profound￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- velocity￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- quantitative￨L￨JJ￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- time￨L￨NN￨O￨- τ￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- initial￨L￨JJ￨O￨- stage￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨A exponentially￨L￨RB￨O￨- with￨L￨IN￨O￨- pmove￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- improved￨L￨VBD￨O￨- machine￨L￨NN￨O￨- technology￨L￨NN￨O￨- has￨L￨VBZ￨O￨- spread￨L￨VBN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- computationally￨L￨RB￨O￨- intensive￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨A a￨L￨DT￨O￨- great￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- simulation￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- M￨U￨NN￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- becoming￨L￨VBG￨O￨- more￨L￨RBR￨O￨- popular￨L￨JJ￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- matter￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- solve￨L￨VBP￨O￨A the￨L￨DT￨O￨- system￨L￨NN￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- Dynamical￨U￨JJ￨O￨- Monte￨U￨NNP￨O￨- Carlo￨U￨NNP￨O￨- technique￨L￨NN￨O￨- and￨L￨CC￨O￨- check￨L￨VB￨O￨- the￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- self-consistently￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Euler￨U￨NNP￨PERSON￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- M￨U￨NN￨O￨- C￨U￨NN￨O￨- studies￨L￨NNS￨O￨- hide￨L￨VBP￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- time-dependent￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- ,￨L￨,￨O￨- reporting￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- as￨L￨IN￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- integral￨L￨JJ￨O￨A Monte￨U￨NNP￨O￨- Carlo￨U￨NNP￨O￨- steps￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- M￨U￨NN￨O￨- C￨U￨NN￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- present￨L￨VB￨DATE￨- a￨L￨DT￨O￨- Dynamical￨U￨JJ￨O￨- Monte￨U￨NNP￨O￨- Carlo￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- DM￨U￨NN￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- simulation￨L￨NN￨O￨A of￨L￨IN￨O￨- markovian￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Ambiguities￨U￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- M￨U￨NN￨O￨- C￨U￨NN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- real￨L￨JJ￨O￨- time￨L￨NN￨O￨- preclude￨L￨VB￨O￨- rigorous￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- results￨L￨NNS￨O￨- between￨L￨IN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- experiment￨L￨NN￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- random￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- builds￨L￨VBZ￨O￨- on￨L￨IN￨O￨- previous￨L￨JJ￨O￨- research￨L￨NN￨O￨- by￨L￨IN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- occur￨L￨VBP￨O￨- in￨L￨IN￨O￨- random￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- significant￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨A .￨L￨.￨O￨- +An￨U￨DT￨O￨- alternative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨A network￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- heterogeneous￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- a￨L￨DT￨O￨- trend￨L￨NN￨O￨A change￨L￨NN￨O￨- in￨L￨IN￨O￨- cross-border￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- compartment￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- meta-population￨L￨JJ￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- detecting￨L￨VBG￨O￨- a￨L￨DT￨O￨- trend￨L￨NN￨O￨A change￨L￨NN￨O￨- in￨L￨IN￨O￨- cross-border￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- task￨L￨NN￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- interest￨L￨NN￨O￨- to￨L￨TO￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- movements￨L￨NNS￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- change￨L￨VB￨O￨A at￨L￨IN￨O￨- all￨L￨DT￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- flu￨L￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- .￨L￨.￨O￨- +T￨U￨NN￨O￨- h￨L￨NN￨O￨- i￨L￨FW￨O￨- s￨L￨VBZ￨O￨- m￨L￨NN￨O￨- e￨L￨SYM￨O￨- a￨L￨DT￨O￨- n￨L￨NN￨O￨- s￨L￨VBZ￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- a￨L￨DT￨O￨- t￨L￨NN￨O￨- m￨L￨NN￨O￨- o￨L￨NN￨O￨- r￨L￨NN￨O￨- e￨L￨SYM￨O￨- l￨L￨NN￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- k￨L￨NN￨O￨- s￨L￨VBZ￨O￨- a￨L￨DT￨O￨- r￨L￨NN￨O￨- e￨L￨SYM￨O￨- a￨L￨DT￨O￨- c￨L￨NN￨O￨- t￨L￨NN￨O￨- i￨L￨FW￨O￨- v￨L￨LS￨O￨- e￨L￨SYM￨O￨- a￨L￨DT￨O￨- t￨L￨NN￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- e￨L￨SYM￨O￨- e￨L￨SYM￨O￨- n￨L￨NN￨O￨- d￨L￨NN￨O￨- c￨L￨NN￨O￨- o￨L￨NN￨O￨- m￨L￨NN￨O￨- p￨L￨NN￨O￨- a￨L￨DT￨O￨- r￨L￨NN￨O￨- e￨L￨SYM￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- o￨L￨NN￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- e￨L￨SYM￨O￨- b￨L￨SYM￨O￨- e￨L￨SYM￨O￨- g￨L￨NN￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- n￨L￨NN￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- g￨L￨NN￨O￨- ,￨L￨,￨O￨- w￨L￨NN￨O￨- h￨L￨NN￨O￨- i￨L￨FW￨O￨- c￨L￨NN￨O￨- h￨L￨NN￨O￨- i￨L￨FW￨O￨- s￨L￨VBZ￨O￨- n￨L￨NN￨O￨- a￨L￨DT￨O￨- t￨L￨NN￨O￨- u￨L￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- l￨L￨NN￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- e￨L￨SYM￨O￨- c￨L￨SYM￨O￨- a￨L￨DT￨O￨- s￨L￨NNS￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- e￨L￨SYM￨O￨- d￨L￨FW￨O￨- a￨L￨DT￨O￨- t￨L￨NN￨O￨- a￨L￨DT￨O￨- r￨L￨NN￨O￨- e￨L￨SYM￨O￨- p￨L￨NN￨O￨- r￨L￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- e￨L￨SYM￨O￨- n￨L￨NN￨O￨- t￨L￨NN￨O￨- s￨L￨VBZ￨O￨- a￨L￨DT￨O￨- g￨L￨NN￨O￨- r￨L￨NN￨O￨- o￨L￨NN￨O￨- w￨L￨NN￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- g￨L￨NN￨O￨- c￨L￨NN￨O￨- o￨L￨NN￨O￨- m￨L￨NN￨O￨- m￨L￨NN￨O￨- u￨L￨NN￨O￨- n￨L￨NN￨O￨- i￨L￨FW￨O￨- t￨L￨NN￨O￨- y￨L￨NN￨O￨- o￨L￨NN￨O￨- f￨L￨FW￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- d￨L￨NN￨O￨- i￨L￨FW￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- d￨L￨FW￨O￨- u￨L￨FW￨O￨- a￨L￨DT￨O￨- l￨L￨NN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- w￨L￨NN￨O￨- h￨L￨NN￨O￨- i￨L￨FW￨O￨- c￨L￨NN￨O￨- h￨L￨NN￨O￨- i￨L￨FW￨O￨- s￨L￨VBZ￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- e￨L￨SYM￨O￨- c￨L￨SYM￨O￨- a￨L￨DT￨O￨- s￨L￨NNS￨O￨- e￨L￨SYM￨O￨- f￨L￨FW￨O￨- o￨L￨NN￨O￨- r￨L￨NN￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- e￨L￨SYM￨O￨- The￨U￨DT￨O￨- link￨L￨NN￨O￨- turnover￨L￨NN￨O￨A picture￨L￨NN￨O￨- and￨L￨CC￨O￨- reference￨L￨NN￨O￨- data￨L￨NNS￨O￨- In￨U￨IN￨O￨- th￨L￨DT￨O￨- e￨L￨SYM￨O￨- link￨L￨NN￨O￨- turnover￨L￨NN￨O￨- picture￨L￨NN￨O￨- ,￨L￨,￨O￨- link￨L￨NN￨O￨- s￨L￨NNS￨O￨- are￨L￨VBP￨O￨- born￨L￨VBN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- active￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- while￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- die￨L￨VB￨O￨- .￨L￨.￨O￨- +S￨U￨NN￨O￨- i￨L￨FW￨O￨- m￨L￨NN￨O￨- i￨L￨FW￨O￨- l￨L￨NN￨O￨- a￨L￨DT￨O￨- r￨L￨NN￨O￨- l￨L￨NN￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- w￨L￨NN￨O￨- e￨L￨SYM￨O￨- a￨L￨DT￨O￨- l￨L￨NN￨O￨- s￨L￨VBZ￨O￨- o￨L￨NN￨O￨- s￨L￨NNS￨O￨- h￨L￨NN￨O￨- i￨L￨FW￨O￨- f￨L￨FW￨O￨- t￨L￨NN￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- e￨L￨SYM￨O￨- l￨L￨NN￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- k￨L￨NN￨O￨- s￨L￨VBZ￨O￨- t￨L￨NN￨O￨- o￨L￨NN￨O￨- a￨L￨DT￨O￨- l￨L￨NN￨O￨- l￨L￨NN￨O￨- e￨L￨SYM￨O￨- n￨L￨NN￨O￨- d￨L￨NN￨O￨- a￨L￨DT￨O￨- t￨L￨NN￨O￨- t￨L￨NN￨O￨- h￨L￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- a￨L￨DT￨O￨- m￨L￨NN￨O￨- e￨L￨SYM￨O￨- t￨L￨NN￨O￨- i￨L￨FW￨O￨- m￨L￨NN￨O￨- e￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- e￨L￨SYM￨O￨- p￨L￨NN￨O￨- l￨L￨NN￨O￨- a￨L￨DT￨O￨- c￨L￨NN￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- g￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- +￨L￨CC￨O￨- +￨L￨CC￨O￨- …￨L￨:￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- We￨U￨PRP￨O￨- run￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- and￨L￨CC￨O￨- reference￨L￨NN￨O￨A temporal￨L￨JJ￨O￨- network￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- as￨L￨IN￨O￨- some￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- Ω￨U￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- difference￨L￨NN￨O￨- with￨L￨IN￨O￨- most￨L￨JJS￨O￨- existing￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- allow￨L￨VBP￨O￨- very￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- observation￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- unobserved￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- state￨L￨NN￨O￨- observations￨L￨NNS￨O￨A made￨L￨VBN￨O￨- at￨L￨IN￨O￨- different￨L￨NN￨O￨- or￨L￨CC￨O￨- unknown￨L￨JJ￨O￨- times￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- times￨L￨NNS￨O￨- ,￨L￨,￨O￨- possibly￨L￨RB￨O￨- mixed￨L￨VBN￨O￨- together￨L￨RB￨O￨- .￨L￨.￨O￨- +Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- via￨L￨IN￨O￨- Belief￨U￨NNP￨O￨- Propagation￨U￨NN￨O￨- Fabrizio￨U￨NNP￨O￨- Altarelli￨U￨NNP￨O￨- ,1￨L￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Alfredo￨U￨NNP￨PERSON￨- Braunstein￨U￨NNP￨PERSON￨- ,1￨L￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Luca￨U￨NNP￨PERSON￨- Dall￨U￨NNP￨PERSON￨- ’￨L￨POS￨O￨- Asta￨U￨NNP￨ORGANIZATION￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Alejandro￨U￨NNP￨PERSON￨- Lage-Castellanos￨U￨NNP￨PERSON￨- ,1￨L￨NN￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Riccardo￨U￨NNP￨PERSON￨- Zecchina1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- 1DISAT￨L￨NN￨O￨- and￨L￨CC￨O￨- Center￨U￨NN￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Computational￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Politecnico￨U￨NNP￨ORGANIZATION￨- di￨L￨NNP￨ORGANIZATION￨- Torino￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Corso￨U￨NNP￨PERSON￨- Duca￨U￨NNP￨PERSON￨- degli￨L￨NNP￨O￨- Abruzzi￨U￨NNP￨ORGANIZATION￨- 24￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10129￨L￨CD￨NUMBER￨- Torino￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- 2Col￨L￨NN￨O￨- legio￨L￨NN￨O￨- Carlo￨U￨NNP￨PERSON￨- Alberto￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Via￨U￨NNP￨O￨- Real￨U￨NNP￨O￨- Col￨U￨NNP￨O￨- legio￨L￨NN￨O￨- 30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10024￨L￨CD￨NUMBER￨- Moncalieri￨U￨NNP￨O￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- 3Human￨L￨NNP￨O￨- Genetics￨U￨NNP￨ORGANIZATION￨- Foundation￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Via￨U￨NNP￨O￨- Nizza￨U￨NNP￨PERSON￨- 52￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10126￨L￨CD￨NUMBER￨- Torino￨U￨NNP￨O￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- 4Physics￨L￨NNPS￨O￨- Faculty￨U￨NNP￨O￨- ,￨L￨,￨O￨- Havana￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- San￨U￨NNP￨CITY￨- Lazaro￨U￨NNP￨CITY￨- y￨L￨NN￨O￨- L￨U￨NN￨O￨- ,￨L￨,￨O￨- 10400￨L￨CD￨NUMBER￨- Habana￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Cuba￨U￨NNP￨COUNTRY￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- several￨L￨JJ￨O￨- bayesian￨L￨JJ￨O￨A inference￨L￨NN￨O￨A problems￨L￨NNS￨O￨- for￨L￨IN￨O￨- irreversible￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- physics￨L￨NN￨O￨- viewpoint￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- most￨L￨JJS￨O￨- inverse￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- ,￨L￨,￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- seed￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenging￨L￨JJ￨O￨- problem￨L￨NN￨O￨- even￨L￨RB￨O￨- for￨L￨IN￨O￨- simple￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨A models￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- zero￨L￨CD￨NUMBER￨- patient￨L￨NN￨O￨- ”￨L￨''￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- SIR￨U￨NN￨O￨- or￨L￨CC￨O￨- SI￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- snapshot￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- later￨L￨JJ￨O￨- unknown￨L￨JJ￨O￨A time￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- equations￨L￨NNS￨O￨- which￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- given￨L￨VBN￨O￨- some￨L￨DT￨O￨- observations￨L￨NNS￨O￨A .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- real-time￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- large￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- static￨L￨JJ￨O￨- and￨L￨CC￨O￨- locally￨L￨RB￨O￨- unclustered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- computation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Malthusian￨U￨JJ￨MISC￨- parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- exponential￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- general￨L￨JJ￨TITLE￨- non-Markovian￨L￨JJ￨MISC￨- SIR￨U￨NN￨MISC￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- focus￨L￨VB￨O￨- our￨L￨PRP$￨O￨- attention￨L￨NN￨O￨- on￨L￨IN￨O￨- arguably￨L￨RB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- piece￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- temporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- Malthusian￨U￨JJ￨MISC￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- real-time￨L￨JJ￨O￨- growth￨L￨NN￨O￨A rate￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- quantity￨L￨NN￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- models￨L￨NNS￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- takes￨L￨VBZ￨O￨- off￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- large￨L￨JJ￨O￨- enough￨L￨RB￨O￨- that￨L￨IN￨O￨- its￨L￨PRP$￨O￨- reduction￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- ignored￨L￨VBN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- analytical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- either￨L￨RB￨O￨- been￨L￨VBN￨O￨- derived￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- specific￨L￨NN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Markovian￨U￨JJ￨MISC￨- SIR￨U￨NN￨MISC￨- model￨L￨NN￨TITLE￨- involving￨L￨VBG￨O￨- constant￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨A rates￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- e.g￨L￨FW￨O￨- .￨L￨.￨O￨- +Throughout￨U￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- contact￨L￨NN￨O￨A to￨L￨TO￨O￨- mean￨L￨VB￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ‘￨L￨``￨O￨- suf￨L￨SYM￨O￨- -￨L￨:￨O￨- ficiently￨L￨RB￨O￨- intense￨L￨JJ￨O￨- ’￨L￨''￨O￨- to￨L￨TO￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- whenever￨L￨WRB￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- that￨L￨WDT￨O￨- makes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- exponentially￨L￨RB￨O￨- decaying￨L￨VBG￨O￨- distributions￨L￨NNS￨O￨- with￨L￨IN￨O￨- characteristic￨L￨JJ￨O￨A times￨L￨NNS￨O￨- τI￨L￨NN￨O￨- and￨L￨CC￨O￨- τR￨L￨NN￨O￨- respectively￨L￨RB￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- local￨L￨JJ￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- Eqs￨U￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- other￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- use￨L￨VB￨O￨- characteristic￨L￨JJ￨O￨A times￨L￨NNS￨O￨- :￨L￨:￨O￨- τI￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- during￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- agent￨L￨NN￨O￨- stays￨L￨VBZ￨O￨- in￨L￨IN￨O￨- category￨L￨NN￨O￨- I￨U￨NN￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- τR￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- Dirac-delta￨U￨NN￨O￨- distributions￨L￨NNS￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- δ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- H￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- δ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τR￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represent￨L￨VBP￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- and￨L￨CC￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- last￨L￨JJ￨O￨- exactly￨L￨RB￨O￨- τI￨L￨NN￨O￨- and￨L￨CC￨O￨- τR￨L￨NN￨O￨- respectively￨L￨RB￨O￨- :￨L￨:￨O￨- ds￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨A =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- β￨L￨NN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- di￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- τ0￨L￨NN￨O￨- =￨L￨JJ￨O￨- τI￨L￨NN￨O￨- +￨L￨CC￨O￨- τR￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- showed￨L￨VBD￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- linear￨L￨JJ￨O￨- stability￨L￨NN￨O￨A analysis￨L￨NN￨O￨A and￨L￨CC￨O￨- numerical￨L￨JJ￨O￨- computation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- oscillations￨L￨NNS￨O￨- appear￨L￨VBP￨O￨- as￨L￨IN￨O￨- Hopf￨U￨NN￨PERSON￨- bifurcations￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- .￨L￨.￨O￨- +So￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- transition￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨A behavior￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- τi￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- is￨L￨VBZ￨O￨- usual￨L￨JJ￨O￨- in￨L￨IN￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- related￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- states￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sub-critical￨L￨JJ￨O￨- √￨L￨NN￨O￨- regime￨L￨NN￨O￨- for￨L￨IN￨O￨- LPC￨U￨NN￨O￨- random￨L￨JJ￨O￨A graphs￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- of￨L￨IN￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- n￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n2/3￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- regime￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- are￨L￨VBP￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Hazard￨U￨NN￨O￨- matrix￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- homogeneous￨L￨JJ￨O￨- random￨L￨JJ￨O￨A graphs￨L￨NNS￨O￨A G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- removal￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- fully￨L￨RB￨O￨- connected￨L￨VBN￨O￨- graph￨L￨NN￨O￨- with￨L￨IN￨O￨- n￨L￨NN￨O￨- vertices￨L￨NNS￨O￨- occurs￨L￨VBZ￨O￨- independently￨L￨RB￨O￨- for￨L￨IN￨O￨- every￨L￨DT￨O￨- edge￨L￨NN￨O￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- probability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- Erd￨U￨NNP￨O￨- ¨￨L￨CD￨NUMBER￨- os￨L￨NNS￨O￨- and￨L￨CC￨O￨- Renyi￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- occured￨L￨VBD￨O￨- for￨L￨IN￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- pn￨L￨NN￨O￨- =￨L￨JJ￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- references￨L￨NNS￨O￨- contain￨L￨VBP￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptotic￨L￨JJ￨O￨- results￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- when￨L￨WRB￨O￨- n￨L￨NN￨O￨- →￨L￨SYM￨O￨- ∞￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- upper￨L￨JJ￨O￨A bounds￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- connected￨L￨JJ￨O￨- components￨L￨NNS￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- upper￨L￨JJ￨O￨- bounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- γ0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ρn￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- o￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- γ0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ρn￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- NumericCitation￨U￨NN￨O￨- function￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Definition￨U￨NNP￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- bound￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- met￨L￨VBN￨O￨- for￨L￨IN￨O￨- particular￨L￨JJ￨O￨- random￨L￨JJ￨O￨A graphs￨L￨NNS￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- random￨L￨JJ￨O￨A graphs￨L￨NNS￨O￨A with￨L￨IN￨O￨- n￨L￨NN￨O￨- vertices￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- most￨L￨JJS￨O￨- a￨L￨DT￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- ρn￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- average￨L￨NN￨O￨- a￨L￨DT￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- highlight￨L￨VBP￨O￨- the￨L￨DT￨O￨- strong￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- NJP￨U￨NN￨O￨- with￨L￨IN￨O￨- classical￨L￨JJ￨O￨- wireless￨L￨JJ￨O￨A network￨L￨NN￨O￨- design￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- recommended￨L￨VBN￨O￨- by￨L￨IN￨O￨- regulatory￨L￨JJ￨O￨- bodies￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- adopt￨L￨VBP￨O￨- a￨L￨DT￨O￨- testpoint￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- signal-to-interference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- quantities￨L￨NNS￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- jamming￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- refining￨L￨VBG￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- 2￨L￨LS￨NUMBER￨- .￨L￨.￨O￨- +Keywords￨U￨NNPS￨O￨- Wireless￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- ·￨L￨NNP￨O￨- Network￨U￨NNP￨O￨- Jamming￨U￨NNP￨O￨- ·￨L￨SYM￨O￨- Integer￨U￨NNP￨O￨- Programming￨U￨NNP￨O￨- ·￨L￨NNP￨O￨- RHS￨U￨NNP￨O￨- Uncertainty￨U￨NN￨O￨- ·￨L￨NN￨O￨- Multiband￨U￨NNP￨O￨- Robust￨U￨NNP￨O￨- Optimization￨U￨NNP￨O￨- ·￨L￨NNP￨O￨- Robustness￨U￨NNP￨O￨- Cuts￨U￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- Wireless￨U￨NNP￨O￨- network￨L￨NN￨O￨- jamming￨L￨VBG￨O￨- consists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- compromising￨L￨VBG￨O￨- the￨L￨DT￨O￨- functionality￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- wireless￨L￨JJ￨O￨A network￨L￨NN￨O￨- by￨L￨IN￨O￨- activating￨L￨VBG￨O￨- jamming￨L￨VBG￨O￨- devices￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- jammers￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- disrupt￨L￨VBP￨O￨- network￨L￨NN￨O￨- communications￨L￨NNS￨O￨- by￨L￨IN￨O￨- emitting￨L￨VBG￨O￨- interfering￨L￨VBG￨O￨- signals￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- frequencies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- suppose￨L￨VBP￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- balance￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- testpoint￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- original￨L￨JJ￨O￨A Robust￨U￨JJ￨O￨- Optimization￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- RO￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- estimated￨L￨VBN￨O￨- deviations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- uncertain￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- jamming￨L￨NN￨O￨- problem￨L￨NN￨O￨- and￨L￨CC￨O￨- tackle￨L￨VB￨O￨- the￨L￨DT￨O￨- peculiar￨L￨JJ￨O￨- right-hand-side￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RHS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- uncertainty￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- original￨L￨JJ￨O￨- robust￨L￨JJ￨O￨A cutting-plane￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- drawing￨L￨VBG￨O￨- inspiration￨L￨NN￨O￨- from￨L￨IN￨O￨- Multiband￨U￨NNP￨O￨- Robust￨U￨NNP￨O￨- Optimization￨U￨NNP￨O￨- .￨L￨.￨O￨- +in￨L￨IN￨O￨- an￨L￨DT￨O￨- attempt￨L￨NN￨O￨- to￨L￨TO￨O￨- raise￨L￨VB￨O￨- The￨U￨DT￨O￨- Wireless￨U￨NNP￨O￨- Network￨U￨NNP￨O￨- Jamming￨U￨NNP￨O￨- Problem￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- NJP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- optimally￨L￨RB￨O￨- placing￨L￨VBG￨O￨- and￨L￨CC￨O￨- configuring￨L￨VBG￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- jammers￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- interdict￨L￨VB￨O￨- communications￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- wireless￨L￨JJ￨O￨A network￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- damage￨L￨NN￨O￨A ,￨L￨,￨O￨- economic￨L￨JJ￨O￨- losses￨L￨NNS￨O￨- ,￨L￨,￨O￨- antivirus￨L￨NN￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- individual-level￨L￨JJ￨O￨- delayed￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- damage￨L￨NN￨O￨A inflicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- losses￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- for￨L￨IN￨O￨- developing￨L￨VBG￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- time￨L￨NN￨O￨- the￨L￨DT￨O￨- antivirus-developing￨L￨JJ￨O￨- cost￨L￨NN￨O￨- is￨L￨VBZ￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- when￨L￨WRB￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- damage￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- major￨L￨JJ￨O￨- concern￨L￨NN￨O￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- damage￨L￨NN￨O￨A inflicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- some￨L￨DT￨O￨- virus￨L￨NN￨O￨A spreading￨L￨NN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- incorporate￨L￨VBP￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- appearance￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- release￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- comparatively￨L￨RB￨O￨- analyse￨L￨VBP￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- WKB￨U￨NN￨O￨- and￨L￨CC￨O￨- Fokker-Planck￨U￨NN￨PERSON￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- typical￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- population￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- logistic￨L￨JJ￨O￨A growth￨L￨NN￨O￨A ,￨L￨,￨O￨- endemic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- predator-prey￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- competitive￨L￨JJ￨O￨- Lotka-Volterra￨U￨NNP￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- large￨L￨JJ￨O￨- but￨L￨CC￨O￨- finite￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- weak￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨A stochasticity￨L￨NN￨O￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- random￨L￨JJ￨O￨- birth￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- events￨L￨NNS￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- population￨L￨NN￨O￨- extinction￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- studying￨L￨VBG￨O￨- such￨L￨JJ￨O￨- physical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- Wentzel-Kramers-Brillouin￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- WKB￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Fokker-Planck￨U￨JJ￨MISC￨- methods￨L￨NNS￨O￨A ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- similar￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mean￨L￨NN￨O￨- extinction￨L￨NN￨O￨A time￨L￨NN￨O￨A strongly￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- fixed￨L￨JJ￨O￨- point￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNPS￨MISC￨- Demographic￨U￨JJ￨MISC￨- stochasticity￨L￨NN￨O￨- ,￨L￨,￨O￨- Fokker-Planck￨U￨JJ￨PERSON￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- Mean￨U￨NN￨O￨- extinction￨L￨NN￨O￨A time￨L￨NN￨O￨A ,￨L￨,￨O￨- WKB￨U￨NN￨O￨- 8￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- l￨L￨NN￨O￨- u￨L￨NN￨O￨- J￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- letter￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- going￨L￨VBG￨O￨- into￨L￨IN￨O￨- any￨L￨DT￨O￨- particular￨L￨JJ￨O￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discover￨L￨VBP￨O￨- a￨L￨DT￨O￨- useful￨L￨JJ￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨A processes￨L￨VBZ￨O￨A describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- locations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- BSs￨U￨NNS￨O￨- and￨L￨CC￨O￨- users￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- power-law￨L￨NN￨O￨- pathloss￨L￨NN￨O￨- function￨L￨NN￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- meta￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cellular￨L￨JJ￨O￨- network￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- principle￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- endow￨L￨VB￨O￨- the￨L￨DT￨O￨- locations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- users￨L￨NNS￨O￨- and￨L￨CC￨O￨- base￨L￨NN￨O￨- stations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- BSs￨U￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- distributions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- them￨L￨PRP￨O￨- as￨L￨IN￨O￨- point￨L￨NN￨O￨A processes￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- processes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- performance￨L￨NN￨O￨- metrics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- spatially￨L￨RB￨O￨- averaged￨L￨VBD￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- signal-to-interference-plus-noise￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SINR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- distribution￨L￨NN￨O￨- averaged￨L￨VBD￨O￨- over￨L￨IN￨O￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- 0￨L￨CD￨DATE￨- 8￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- letter￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- cellular￨L￨JJ￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- users￨L￨NNS￨O￨- and￨L￨CC￨O￨- BSs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- distributed￨L￨VBN￨O￨- as￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- general￨L￨JJ￨TITLE￨- point￨L￨NN￨O￨A processes￨L￨NNS￨O￨A that￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- coupled￨L￨VBN￨O￨- ,￨L￨,￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- pathloss￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- follow￨L￨VB￨O￨- a￨L￨DT￨O￨- multi-slope￨L￨JJ￨O￨- power-law￨L￨NN￨O￨- pathloss￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- fading￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- power￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- independent￨L￨JJ￨RELIGION￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- links￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- setup￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨VBP￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- contours￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathloss￨L￨NN￨O￨- function￨L￨NN￨O￨- and￨L￨CC￨O￨- BS￨U￨NN￨O￨- and￨L￨CC￨O￨- user￨L￨NN￨O￨- point￨L￨NN￨O￨A processes￨L￨NNS￨O￨A .￨L￨.￨O￨- +same￨L￨JJ￨O￨- meta￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- Index￨U￨NNP￨O￨- Terms￨U￨NNS￨O￨- —￨L￨:￨O￨- Stochastic￨U￨JJ￨O￨- geometry￨L￨NN￨O￨- ,￨L￨,￨O￨- Poisson￨U￨NNP￨PERSON￨- cluster￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨A process￨L￨NN￨O￨A ,￨L￨,￨O￨- cellular￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- equi-coverage￨L￨JJ￨O￨- contours￨L￨NNS￨O￨- .￨L￨.￨O￨- +Initial￨U￨JJ￨O￨- attempts￨L￨NNS￨O￨- towards￨L￨IN￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- post-combining￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- equivalently￨L￨RB￨O￨- the￨L￨DT￨O￨- MRC￨U￨NNP￨ORGANIZATION￨- outage/success￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- spatially￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- interference￨L￨NN￨O￨A include￨L￨VBP￨O￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- interference￨L￨NN￨O￨- field￨L￨NN￨O￨- as￨L￨IN￨O￨- PPP￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- employ￨L￨VB￨O￨- tools￨L￨NNS￨O￨- from￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- geometry￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mixture￨L￨NN￨O￨A parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- tuned￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- matching￨L￨NN￨O￨- of￨L￨IN￨O￨- joint￨L￨JJ￨O￨- Signal-to-Interference￨U￨NNP￨O￨- Ratio￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- statistics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- accurate￨L￨JJ￨O￨- mixture-based￨L￨JJ￨O￨- result￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- DNN-based￨U￨JJ￨MISC￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- speech￨L￨NN￨O￨- enhancement￨L￨NN￨O￨A ,￨L￨,￨O￨- neural￨L￨JJ￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- fully-connected￨L￨JJ￨O￨- layers￨L￨NNS￨O￨- acted￨L￨VBD￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- mapping￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- spectrogram￨L￨NN￨O￨- fragment￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- noisy￨L￨JJ￨O￨- speech￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- spectrogram￨L￨NN￨O￨- frame￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- context￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- spectrogram￨L￨NN￨O￨- frame￨L￨NN￨O￨- of￨L￨IN￨O￨- enhanced￨L￨VBN￨O￨- speech￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Convolutional￨U￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- CNNs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- speech￨L￨NN￨O￨- enhancement￨L￨NN￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- combining￨L￨VBG￨O￨- convolutional￨L￨JJ￨O￨- and￨L￨CC￨O￨- fully￨L￨RB￨O￨- connected￨L￨VBN￨O￨- layers￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- binary￨L￨JJ￨O￨- mask￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IBM￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 8￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- StethoMe￨U￨NN￨O￨- R￨U￨NN￨O￨- Poznan￨U￨NNP￨CITY￨- Poland￨U￨NNP￨COUNTRY￨- ABSTRACT￨U￨NN￨O￨- When￨U￨WRB￨O￨- designing￨L￨VBG￨O￨- fully-convolutional￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A network￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- between￨L￨IN￨O￨- receptive￨L￨JJ￨O￨- field￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- of￨L￨IN￨O￨- features￨L￨NNS￨O￨- in￨L￨IN￨O￨- deeper￨L￨JJR￨O￨- layers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨MISC￨- U-net￨U￨NNP￨MISC￨- architecture￨L￨NN￨O￨A brought￨L￨VBD￨O￨- better￨L￨JJR￨O￨- singing￨L￨NN￨O￨- voice￨L￨NN￨O￨- separation￨L￨NN￨O￨- quality￨L￨NN￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- without￨L￨IN￨O￨- skip￨L￨VB￨O￨- connections￨L￨NNS￨O￨- .￨L￨.￨O￨- +Complementary￨U￨JJ￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- geometry-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- user￨L￨NN￨O￨A and￨L￨CC￨O￨- BS￨U￨NN￨O￨- locations￨L￨NNS￨O￨- as￨L￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- and￨L￨CC￨O￨- homogeneous￨L￨JJ￨O￨- Poisson￨U￨NN￨PERSON￨- point￨L￨NN￨O￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PPPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- gained￨L￨VBN￨O￨- prominence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- few￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- captures￨L￨VBZ￨O￨- both￨L￨CC￨O￨- non-uniformity￨L￨JJ￨O￨- and￨L￨CC￨O￨- coupling￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- BS￨U￨NN￨O￨- and￨L￨CC￨O￨- user￨L￨NN￨O￨A locations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- studies￨L￨NNS￨O￨- usually￨L￨RB￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- regarding￨L￨VBG￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- defense￨L￨NN￨O￨A gene￨L￨NN￨O￨- expression￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- as￨L￨IN￨O￨- species￨L￨NNS￨O￨- diverge￨L￨VBP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- P.￨U￨NNP￨O￨- Divergence￨U￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- PR10￨U￨NN￨O￨- expression￨L￨NN￨O￨A was￨L￨VBD￨O￨- most￨L￨RBS￨O￨- striking￨L￨JJ￨O￨- between￨L￨IN￨O￨- P.￨U￨NNP￨O￨- Two￨U￨CD￨NUMBER￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- multigene￨L￨JJ￨O￨- family￨L￨NN￨O￨- ,￨L￨,￨O￨- designated￨L￨VBN￨O￨- PR10￨U￨NN￨O￨- .1￨L￨NN￨NUMBER￨- and￨L￨CC￨O￨- PR10￨U￨NN￨O￨- .2￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- strongly-expressed￨L￨JJ￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- Fusarium￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- PR10￨U￨NN￨O￨- .3￨L￨NN￨NUMBER￨- gene￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- weakly￨L￨RB￨O￨- expressed￨L￨VBN￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- Pisum￨U￨NNP￨O￨- species￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- applied￨L￨VBN￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- overcome￨L￨VB￨O￨- the￨L￨DT￨O￨- adverse￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- tumor￨L￨NN￨CAUSE_OF_DEATH￨- cell￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A progression￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- oncolytic￨L￨JJ￨O￨- virus￨L￨NN￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- .￨L￨.￨O￨- +BACKGROUND￨U￨NN￨O￨- :￨L￨:￨O￨- One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- ensure￨L￨VBP￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A robustness￨L￨NN￨O￨- is￨L￨VBZ￨O￨- tumor￨L￨NN￨CAUSE_OF_DEATH￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- tumor￨L￨NN￨CAUSE_OF_DEATH￨- cells￨L￨NNS￨O￨- dynamics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- when￨L￨WRB￨O￨- studying￨L￨VBG￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- .￨L￨.￨O￨- +RESULTS￨U￨NNS￨O￨- :￨L￨:￨O￨- Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- a￨L￨DT￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- naturally￨L￨RB￨O￨- takes￨L￨VBZ￨O￨- stock￨L￨NN￨O￨- of￨L￨IN￨O￨- inherent￨L￨JJ￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A cell￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- illustrate￨L￨VB￨O￨- it￨L￨PRP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- tumor￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- oncolytic￨L￨JJ￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +Heterogeneity￨U￨NN￨O￨- in￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- tumor￨L￨NN￨CAUSE_OF_DEATH￨- cell￨L￨NN￨O￨A susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- virus￨L￨NN￨O￨- replication￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- complex￨L￨NN￨O￨- ,￨L￨,￨O￨- time-dependent￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- tumor￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- several￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- absent￨L￨JJ￨O￨- in￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A recurrence￨L￨NN￨O￨- ,￨L￨,￨O￨- tumor￨L￨NN￨CAUSE_OF_DEATH￨- dormancy￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- appear￨L￨VBP￨O￨- in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- setting￨L￨NN￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- several￨L￨JJ￨O￨- hypotheses￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- persister￨L￨NN￨O￨- formation￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- failure￨L￨NN￨O￨A of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- protocols￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- consistency￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- hypotheses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- over￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- antibiotics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- amplified￨L￨VBN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- chromosomal-resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- becoming￨L￨VBG￨O￨- increasingly￨L￨RB￨O￨- clear￨L￨JJ￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- other￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- protect￨L￨VBP￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- bacteria￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- noted￨L￨VBN￨O￨- that￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- planktonic￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A also￨L￨RB￨O￨- contain￨L￨VBP￨O￨- these￨L￨DT￨O￨- highly￨L￨RB￨O￨- tolerant￨L￨JJ￨O￨- or￨L￨CC￨O￨- persister￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- senescence￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- chemostat￨L￨NN￨O￨- and￨L￨CC￨O￨- biofilm￨L￨NN￨O￨- settings￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- first￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- briefly￨L￨VBP￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- collection￨L￨NN￨O￨- platform￨L￨NN￨O￨- and￨L￨CC￨O￨- our￨L￨PRP$￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- II￨U￨CD￨NUMBER￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- III￨U￨CD￨NUMBER￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- salient￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- aggregated￨L￨VBN￨O￨A on￨L￨IN￨O￨- time￨L￨NN￨O￨- windows￨L￨NNS￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spreading￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- markedly￨L￨RB￨O￨- different￨L￨JJ￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- conference￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- museum￨L￨NN￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- strongly￨L￨RB￨O￨- impacted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- causal￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- studying￨L￨VBG￨O￨- empirically￨L￨RB￨O￨- and￨L￨CC￨O￨- analytically￨L￨RB￨O￨- different￨L￨JJ￨O￨- characteristic￨L￨JJ￨O￨- relay￨L￨NN￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- relevant￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- respective￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- reference￨L￨NN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- for￨L￨IN￨O￨- removing￨L￨VBG￨O￨- selected￨L￨VBN￨O￨- time-domain￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨A one￨L￨CD￨NUMBER￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- perform￨L￨VBP￨O￨- a￨L￨DT￨O￨- multi-scale￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- pinpoint￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- timings￨L￨NNS￨O￨- of￨L￨IN￨O￨- event￨L￨NN￨O￨- sequences￨L￨NNS￨O￨A on￨L￨IN￨O￨- individual￨L￨JJ￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- correlations￨L￨NNS￨O￨- with￨L￨IN￨O￨- neighboring￨L￨VBG￨O￨- sequences￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- pathways￨L￨NNS￨O￨- taken￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- network-scale￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- temporal￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- approach￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- event￨L￨NN￨O￨- sequences￨L￨NNS￨O￨A are￨L￨VBP￨O￨- randomized￨L￨VBN￨O￨- or￨L￨CC￨O￨- randomly￨L￨RB￨O￨- reshuffled￨L￨VBN￨O￨- to￨L￨TO￨O￨- remove￨L￨VB￨O￨- time-domain￨L￨JJ￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- correlations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Whole￨U￨JJ￨O￨- event￨L￨NN￨O￨- sequences￨L￨NNS￨O￨A with￨L￨IN￨O￨- time￨L￨NN￨O￨- stamps￨L￨NNS￨O￨- are￨L￨VBP￨O￨- randomly￨L￨RB￨O￨- exchanged￨L￨VBN￨O￨- between￨L￨IN￨O￨- links￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- weights￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- events￨L￨NNS￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- weak￨L￨JJ￨O￨- ties￨L￨NNS￨O￨A are￨L￨VBP￨O￨- settled￨L￨VBN￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- arrival￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- displays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- diametrically￨L￨RB￨O￨- opposed￨L￨VBN￨O￨- changing￨L￨VBG￨O￨- trend￨L￨NN￨O￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- seed￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- bridgeness￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- seed￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨VBP￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- dif￨L￨NN￨O￨- ferent￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- weak￨L￨JJ￨O￨- ties￨L￨NNS￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- variabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- arrival￨L￨NN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- find￨L￨NN￨O￨- t￨L￨NN￨O￨- hat￨L￨NN￨O￨- the￨L￨DT￨O￨- bridgeness￨L￨NN￨O￨- with￨L￨IN￨O￨- small￨L￨JJ￨O￨- degree￨L￨NN￨O￨- can￨L￨MD￨O￨- enhance￨L￨VB￨O￨- the￨L￨DT￨O￨- predictability￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- arrival￨L￨NN￨O￨A time￨L￨NN￨O￨- always￨L￨RB￨O￨- marks￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- reversal￨L￨NN￨O￨- trend￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- implies￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- impossible￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- accurately￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- weak￨L￨JJ￨O￨- ties￨L￨NNS￨O￨A and￨L￨CC￨O￨- weak￨L￨JJ￨O￨- tie￨L￨JJ￨O￨- number￨L￨NN￨O￨- influence￨L￨NN￨O￨- the￨L￨DT￨O￨- predictability￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- numerically￨L￨RB￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- bridgeness￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- modularity￨L￨NN￨O￨- play￨L￨VBP￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- predictability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +Efficient￨U￨JJ￨O￨- local￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- change￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- Yilei￨U￨NNP￨O￨- Bu1￨U￨NN￨O￨- ,￨L￨,￨O￨- Steve￨U￨NNP￨PERSON￨- Gregory1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Harriet￨U￨NNP￨PERSON￨- Mills2￨U￨NNP￨PERSON￨- 1￨L￨CD￨NUMBER￨- Dept.￨U￨NNP￨O￨- It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- relatively￨L￨RB￨O￨- densely￨L￨RB￨O￨- connected￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- change￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- only￨L￨RB￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- becomes￨L￨VBZ￨O￨- ill￨L￨JJ￨O￨- or￨L￨CC￨O￨- aware￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- strategies￨L￨NNS￨O￨- can￨L￨MD￨O￨- substantially￨L￨RB￨O￨- reduce￨L￨VB￨O￨A epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- avoided￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A ,￨L￨,￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- employed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- vertex￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- vertices￨L￨NNS￨O￨A represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- over￨L￨IN￨O￨- which￨L￨WDT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- may￨L￨MD￨O￨- occur￨L￨VB￨O￨- .￨L￨.￨O￨- +Apart￨U￨RB￨O￨- from￨L￨IN￨O￨- purely￨L￨RB￨O￨- symptom￨L￨NN￨O￨- based￨L￨VBN￨O￨- ,￨L￨,￨O￨- presumptive￨L￨JJ￨O￨- diagnosis￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- diagnostic￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- currently￨L￨RB￨DATE￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- antigen-based￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasites￨L￨NNS￨O￨- using￨L￨VBG￨O￨- rapid￨L￨JJ￨O￨- diagnostic￨L￨JJ￨O￨- tests￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- RDT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- red￨L￨JJ￨O￨- blood￨L￨NN￨O￨A cells￨L￨NNS￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨- smears￨L￨NNS￨O￨- .1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- detection￨L￨NN￨O￨- limits￨L￨NNS￨O￨- of￨L￨IN￨O￨- RDT￨U￨NN￨O￨- and￨L￨CC￨O￨- light￨L￨NN￨O￨- microscopy￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- reported￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- approximately￨L￨RB￨O￨- 100￨L￨CD￨NUMBER￨- parasites/µL￨L￨NN￨O￨- and￨L￨CC￨O￨- 5-50￨L￨CD￨NUMBER￨- parasites/µL￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .1,5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Both￨U￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- sub￨L￨JJ￨O￨- ject￨L￨NN￨O￨- to￨L￨TO￨O￨- inherent￨L￨JJ￨O￨- limitations￨L￨NNS￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- although￨L￨IN￨O￨- RDTs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- becoming￨L￨VBG￨O￨- more￨L￨RBR￨O￨- affordable￨L￨JJ￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- parasitemia￨L￨NN￨O￨- and￨L￨CC￨O￨- presently￨L￨RB￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- possess￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- low-level￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- very￨L￨RB￨O￨- common￨L￨JJ￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- visual￨L￨JJ￨O￨- inspection￨L￨NN￨O￨- of￨L￨IN￨O￨- blood￨L￨NN￨O￨- smears￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- labor￨L￨NN￨O￨- intensive￨L￨JJ￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- recent￨L￨JJ￨O￨- study￨L￨NN￨O￨- using￨L￨VBG￨O￨- synthetic￨L￨JJ￨O￨- hemozoin￨L￨NN￨O￨- crystals￨L￨NNS￨O￨- suspended￨L￨VBN￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A demonstrated￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- rotating-crystal￨L￨JJ￨O￨- magneto-optical￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- MO￨U￨NNP￨DURATION￨- )￨L￨-RRB-￨O￨- diagnostic￨L￨JJ￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- detect￨L￨VB￨O￨- hemozoin￨L￨NN￨O￨- concentrations￨L￨NNS￨O￨- down￨L￨IN￨O￨- to￨L￨TO￨O￨- 15￨L￨CD￨NUMBER￨- pg/µL￨L￨NN￨O￨- .15￨L￨CD￨NUMBER￨- This￨U￨DT￨O￨- threshold￨L￨NN￨O￨- concentration￨L￨NN￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- parasite￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- ≤￨L￨CD￨NUMBER￨- 30￨L￨CD￨NUMBER￨- parasites/µL￨L￨NN￨O￨- in￨L￨IN￨O￨- infected￨L￨JJ￨O￨- blood￨L￨NN￨O￨- provided￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- hemozoin￨L￨NN￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- parasites￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- released￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- lysed￨L￨JJ￨O￨- cell￨L￨NN￨O￨- suspension￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- two￨L￨CD￨NUMBER￨- parasite￨L￨JJ￨O￨- cultures￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- containing￨L￨VBG￨O￨- mostly￨L￨RB￨O￨- ring￨L￨NN￨O￨- stages￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨JJ￨O￨- life￨L￨NN￨O￨- cycle￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- novel￨L￨JJ￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- detect￨L￨VB￨O￨- parasite￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- as￨L￨RB￨O￨- low￨L￨JJ￨O￨- as￨L￨IN￨O￨- ∼￨L￨CD￨NUMBER￨- 40￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- ∼￨L￨CD￨NUMBER￨- 10￨L￨CD￨NUMBER￨- parasites￨L￨NNS￨O￨- per￨L￨IN￨O￨- microliter￨L￨NN￨O￨- of￨L￨IN￨O￨- blood￨L￨NN￨O￨A for￨L￨IN￨O￨- ring￨L￨NN￨O￨- and￨L￨CC￨O￨- schizont￨L￨NN￨O￨- stage￨L￨NN￨O￨- parasites￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Intraerythrocytic￨U￨JJ￨MISC￨- hemozoin￨L￨NN￨O￨- content￨L￨NN￨O￨- is￨L￨VBZ￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- maturity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- blood￨L￨NN￨O￨A stage￨L￨NN￨O￨- parasites￨L￨NNS￨O￨- ;￨L￨:￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- least￨L￨JJS￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- hemozoin￨L￨NN￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- erythrocytes￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- ring￨L￨NN￨O￨- stage￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- amount￨L￨NN￨O￨- during￨L￨IN￨O￨- Typeset￨U￨NNP￨O￨- by￨L￨IN￨O￨- REVTEX￨U￨NNP￨ORGANIZATION￨- 2￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- schizont￨L￨NN￨O￨- stage￨L￨NN￨O￨- .20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- hemozoin￨L￨NN￨O￨- concentration￨L￨NN￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- human￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨JJ￨O￨- stage￨L￨NN￨O￨- distribution￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- the￨L￨DT￨O￨- blood￨L￨NN￨O￨- sample￨L￨NN￨O￨- was￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- magneto-optical￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- MO￨U￨NNP￨DURATION￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- high-sensitivity￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- pigment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- hemozoin￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- crystals￨L￨NNS￨O￨- via￨L￨IN￨O￨- their￨L￨PRP$￨O￨- magnetically￨L￨RB￨O￨- induced￨L￨VBN￨O￨- rotation￨L￨NN￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mechanism-based￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- consideration￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨A adherence￨L￨NN￨O￨- ,￨L￨,￨O￨- interacted￨L￨VBD￨O￨- by￨L￨IN￨O￨- virus￨L￨NN￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- drug￨L￨NN￨O￨- and￨L￨CC￨O￨- baseline￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- virologic￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- after￨L￨IN￨O￨- initiation￨L￨NN￨O￨- of￨L￨IN￨O￨- therapy￨L￨NN￨O￨- .￨L￨.￨O￨- +5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- No.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 551￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 577￨L￨CD￨NUMBER￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.1214￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 10-AOAS376￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- DYNAMIC￨U￨NNP￨O￨- BAYESIAN￨U￨NNP￨O￨- NONLINEAR￨U￨NNP￨O￨- MIXED-EFFECTS￨U￨NNP￨O￨- MODEL￨U￨NNP￨TITLE￨- OF￨U￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- RESPONSE￨U￨NN￨O￨- INCORPORATING￨U￨VBG￨O￨- MEDICATION￨U￨NN￨O￨- ADHERENCE￨U￨NN￨O￨- ,￨L￨,￨O￨- DRUG￨U￨NN￨O￨- RESISTANCE￨U￨NN￨O￨- AND￨U￨CC￨O￨- COVARIATES1￨U￨NN￨O￨- By￨U￨IN￨O￨- Yangxin￨U￨NN￨PERSON￨- Huang￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hulin￨U￨NNP￨PERSON￨- Wu￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jeanne￨U￨NNP￨PERSON￨- Holden-Wiltse￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Edward￨U￨NNP￨ORGANIZATION￨- P.￨U￨NNP￨ORGANIZATION￨- Medication￨U￨NNP￨ORGANIZATION￨- adherence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- predictor￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- ARV￨U￨NN￨ORGANIZATION￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- determinant￨L￨NN￨O￨A of￨L￨IN￨O￨- adherence￨L￨NN￨O￨- rate￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- medication￨L￨NN￨O￨- event￨L￨NN￨O￨- monitoring￨L￨NN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MEMS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- virologic￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- primary￨L￨JJ￨O￨- ob￨L￨NN￨O￨- jective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- summary￨L￨NN￨O￨- determinants￨L￨NNS￨O￨- of￨L￨IN￨O￨- MEMS￨U￨NN￨O￨- adherence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- on￨L￨IN￨O￨- virologic￨L￨JJ￨O￨- response￨L￨NN￨O￨A measured￨L￨VBN￨O￨- repeatedly￨L￨RB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- HIV-infected￨U￨JJ￨O￨- patients￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- fully￨L￨RB￨O￨- integrates￨L￨VBZ￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- ,￨L￨,￨O￨- MEMS￨U￨NN￨O￨- adherence￨L￨NN￨O￨- ,￨L￨,￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨- and￨L￨CC￨O￨- baseline￨L￨NN￨O￨- covariates￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- fit￨L￨NN￨O￨- with￨L￨IN￨O￨- theoretical￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- tail￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- tick￨L￨NN￨O￨- infestation￨L￨NN￨O￨- pattern￨L￨NN￨O￨- on￨L￨IN￨O￨- mice￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- better￨L￨JJR￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- PL￨U￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analysed￨L￨VBD￨O￨- a￨L￨DT￨O￨- 9-year￨L￨JJ￨DURATION￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- Ixodes￨U￨NNP￨O￨- ricinus￨L￨NN￨O￨- ticks￨L￨VBZ￨O￨- feeding￨L￨VBG￨O￨- on￨L￨IN￨O￨- Apodemus￨U￨NN￨MISC￨- flavicol￨L￨NN￨O￨- lis￨L￨NN￨O￨- mice￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- main￨L￨JJ￨O￨- reservoir-competent￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- tick-borne￨L￨JJ￨O￨- encephalitis￨L￨NN￨O￨- ,￨L￨,￨O￨- TBE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- sampled￨L￨VBN￨O￨- in￨L￨IN￨O￨- Trentino￨U￨NN￨LOCATION￨- (￨L￨-LRB-￨O￨- Northern￨U￨NN￨LOCATION￨- Italy￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Model￨U￨NNP￨TITLE￨- simulations￨L￨NNS￨O￨- indicated￨L￨VBD￨O￨A different￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- when￨L￨WRB￨O￨- considering￨L￨VBG￨O￨- different￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- laws￨L￨NNS￨O￨- of￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- among￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- tail￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- per￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- theoretical￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- :￨L￨:￨O￨- Negative￨U￨JJ￨O￨- Binomial￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- NB￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Poisson-LogNormal￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- PoiLN￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Power-Law￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- PL￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Running￨U￨VBG￨O￨- He￨U￨PRP￨O￨- ad￨L￨NN￨O￨- :￨L￨:￨O￨- Personalized￨U￨VBN￨O￨- Inflamma￨U￨NN￨O￨- t￨L￨NN￨O￨- io￨L￨NN￨O￨- n￨L￨NN￨O￨- Model￨U￨NNP￨TITLE￨- for￨L￨IN￨O￨- Young￨U￨NNP￨O￨- Men￨U￨NNP￨O￨- ABSTRACT￨U￨NN￨O￨- –￨L￨:￨O￨- The￨U￨DT￨O￨- initia￨L￨FW￨O￨- l￨L￨NN￨O￨- reaction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- body￨L￨NN￨O￨- to￨L￨TO￨O￨- pathogenic￨L￨JJ￨O￨- microbia￨L￨NN￨O￨- l￨L￨NN￨O￨- infect￨L￨VB￨O￨- io￨L￨NN￨O￨- n￨L￨NN￨O￨- or￨L￨CC￨O￨- severe￨L￨JJ￨O￨- tissue￨L￨NN￨O￨- trauma￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- acute￨L￨JJ￨O￨- inflammatory￨L￨JJ￨O￨A response￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- we￨L￨PRP￨O￨- soon￨L￨RB￨O￨- explain￨L￨VBP￨O￨- in￨L￨IN￨O￨- more￨L￨JJR￨O￨- detail￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- quantity￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- frog￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- finite￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- aforementioned￨L￨JJ￨O￨- walks￨L￨VBZ￨O￨- they￨L￨PRP￨O￨- pick￨L￨VBP￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- every￨L￨DT￨O￨- vertex￨L￨NN￨O￨- is￨L￨VBZ￨O￨- visited￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- particle￨L￨NN￨O￨A before￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- 2.1￨L￨CD￨NUMBER￨- Tori￨U￨NNP￨O￨- We￨U￨PRP￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- n-cycle￨L￨JJ￨O￨- graph￨L￨NN￨O￨- by￨L￨IN￨O￨- Cn￨U￨NN￨MISC￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- walks￨L￨VBZ￨O￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- frog￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- profile￨L￨NN￨O￨- of￨L￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- Poisson￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- particles￨L￨NNS￨O￨- per￨L￨IN￨O￨- site￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- additional￨L￨JJ￨O￨- active￨L￨JJ￨O￨- particle￨L￨NN￨O￨A planted￨L￨VBN￨O￨- at￨L￨IN￨O￨- some￨L￨DT￨O￨- vertex￨L￨NN￨O￨- o￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- connected￨L￨JJ￨O￨- simple￨L￨JJ￨O￨- graph￨L￨NN￨O￨- G￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- throughout￨L￨IN￨O￨- we￨L￨PRP￨O￨- allow￨L￨VBP￨O￨- the￨L￨DT￨O￨- particle￨L￨NN￨O￨A density￨L￨NN￨O￨- λ￨L￨NN￨O￨- to￨L￨TO￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- n￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- d￨L￨NN￨O￨- >￨L￨RBR￨O￨- 2￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Td￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- smaller￨L￨JJR￨O￨- order￨L￨NN￨O￨- terms￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- λ￨L￨NN￨O￨- =￨L￨JJ￨O￨- λn￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- next￨L￨JJ￨O￨- theorem￨L￨NN￨O￨- asserts￨L￨VBZ￨O￨- that￨L￨IN￨O￨- as￨L￨RB￨O￨- long￨L￨JJ￨O￨- as￨L￨IN￨O￨- λnn￨L￨NN￨O￨- ≫￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- Cn￨U￨NN￨MISC￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- particle￨L￨NN￨O￨A density￨L￨NN￨O￨- λn￨L￨NN￨O￨- is￨L￨VBZ￨O￨- w.h.p.￨L￨VBN￨O￨- 2￨L￨CD￨NUMBER￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- log2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- λnn￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- this￨L￨DT￨O￨- follows￨L￨VBZ￨O￨- from￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Cn￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- >￨L￨JJR￨O￨- cλ￨L￨NN￨O￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- only￨L￨RB￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- range￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- when￨L￨WRB￨O￨- valid￨L￨JJ￨O￨- offers￨L￨NNS￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- than￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Cn￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- unusually￨L￨RB￨O￨- small￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- graph￨L￨NN￨O￨- is￨L￨VBZ￨O￨- either￨L￨CC￨O￨- a￨L￨DT￨O￨- regular￨L￨JJ￨O￨- expander￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- d-dimensional￨L￨JJ￨O￨- torus￨L￨NN￨O￨- of￨L￨IN￨O￨- side￨L￨NN￨O￨- length￨L￨NN￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- d￨L￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Td￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨A behavior￨L￨NN￨O￨A of￨L￨IN￨O￨- S￨U￨NN￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- factor￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- idealized￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- concurrent￨L￨JJ￨O￨- partnerships￨L￨NNS￨O￨A leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- substantially￨L￨RB￨O￨- faster￨L￨JJR￨O￨- growth￨L￨NN￨O￨- and￨L￨CC￨O￨- higher￨L￨JJR￨O￨- equilibrium￨L￨NN￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- regions￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- concurrent￨L￨JJ￨O￨- partnerships￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- very￨L￨RB￨O￨- little￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +Sexual￨U￨JJ￨O￨- partnerships￨L￨NNS￨O￨A that￨L￨WDT￨O￨- overlap￨L￨VBP￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- concurrent￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- play￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- precise￨L￨JJ￨O￨- effect￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- models￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- partnerships￨L￨NNS￨O￨A change￨L￨VBP￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- enter￨L￨VBP￨O￨- and￨L￨CC￨O￨- leave￨L￨VBP￨O￨- the￨L￨DT￨O￨- at-risk￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- primary￨L￨JJ￨O￨- technical￨L￨JJ￨O￨- difficulties￨L￨NNS￨O￨- addressed￨L￨VBD￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- treatment￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- means￨L￨NN￨O￨- of￨L￨IN￨O￨- tractably￨L￨RB￨O￨- approximating￨L￨VBG￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- designed￨L￨VBN￨O￨- approximation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- robust￨L￨JJ￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- error￨L￨NN￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- applied￨L￨JJ￨O￨- moment￨L￨NN￨O￨- closure￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- guaranteeing￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- designed￨L￨VBN￨O￨- controller￨L￨NN￨TITLE￨- causes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- closed-loop￨L￨JJ￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- drive￨L￨VB￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- quickly￨L￨RB￨O￨- .￨L￨.￨O￨- +Robust￨U￨JJ￨O￨- Economic￨U￨JJ￨O￨- Model￨U￨NNP￨TITLE￨- Predictive￨U￨NNP￨O￨- Control￨U￨NNP￨O￨- of￨L￨IN￨O￨- Continuous-time￨U￨JJ￨O￨- Epidemic￨U￨JJ￨O￨- Processes￨U￨NNS￨O￨- Nicholas￨U￨NNP￨PERSON￨- J.￨U￨NNP￨PERSON￨- Pappas￨U￨NNP￨PERSON￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- robust￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- predictive￨L￨JJ￨O￨- controller￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- containment￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- SusceptibleExposed-Infected-Vigilant￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SE￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- V￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨A processes￨L￨NNS￨O￨A which￨L￨WDT￨O￨- drives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- quickly￨L￨RB￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- control￨L￨NN￨O￨- resources￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- significant￨L￨JJ￨O￨- in￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- addresses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- efficiently￨L￨RB￨O￨- controlling￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- without￨L￨IN￨O￨- relying￨L￨VBG￨O￨- on￨L￨IN￨O￨- mean-field￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- issue￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨A processes￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- approach￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- predictive￨L￨JJ￨O￨A controller￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- which￨L￨WDT￨O￨- controls￨L￨VBZ￨O￨- the￨L￨DT￨O￨- statistics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- directly￨L￨RB￨O￨- by￨L￨IN￨O￨- varying￨L￨VBG￨O￨- the￨L￨DT￨O￨- processes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- spreading￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- AdPMCMC￨U￨NN￨MISC￨- algorithm￨L￨NN￨O￨- samples￨L￨NNS￨O￨- complex￨L￨NN￨O￨- ,￨L￨,￨O￨- high-dimensional￨L￨JJ￨O￨- spaces￨L￨NNS￨O￨- ef￨L￨NN￨O￨- ficiently￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- superior￨L￨JJ￨O￨- to￨L￨TO￨O￨- standard￨L￨JJ￨O￨- Gibbs￨U￨NNP￨PERSON￨- or￨L￨CC￨O￨- Metropolis￨U￨NNP￨O￨- Hastings￨U￨NNP￨O￨- algorithms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- converge￨L￨VB￨O￨- very￨L￨RB￨O￨- slowly￨L￨RB￨O￨- when￨L￨WRB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- non-linear￨L￨JJ￨O￨- state￨L￨NN￨O￨A space￨L￨NN￨O￨A ecological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- advanced￨L￨JJ￨O￨- Par￨U￨NN￨O￨- ticle￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- algorithm￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- sampling￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- non-linear￨L￨JJ￨O￨- state￨L￨NN￨O￨A space￨L￨NN￨O￨A models￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- this￨L￨DT￨O￨- novel￨L￨JJ￨O￨A methodology￨L￨NN￨O￨- to￨L￨TO￨O￨- five￨L￨VB￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- strong￨L￨JJ￨O￨- and￨L￨CC￨O￨- weak￨L￨JJ￨O￨- Allee￨U￨JJ￨MISC￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- test￨L￨NN￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- ef￨L￨VB￨O￨- ficiently￨L￨RB￨O￨- sample￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- surface￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Utilising￨U￨VBG￨O￨- real￨L￨JJ￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- synthetically￨L￨RB￨O￨- generated￨L￨VBN￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- observation￨L￨NN￨O￨- noise￨L￨NN￨O￨- and￨L￨CC￨O￨- process￨L￨NN￨O￨- error￨L￨NN￨O￨- may￨L￨MD￨O￨- frustrate￨L￨VB￨O￨- effor￨L￨NN￨O￨- ts￨L￨NNS￨O￨- to￨L￨TO￨O￨- choose￨L￨VB￨O￨A between￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Ecological￨U￨NNP￨O￨- non-linear￨L￨JJ￨O￨- state￨L￨NN￨O￨A space￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- via￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- particle￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- AdPMCMC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- Gareth￨U￨NNP￨PERSON￨- W￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- short-term￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨DURATION￨- month￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- long-term￨L￨JJ￨O￨- virological￨L￨JJ￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- ARV￨U￨NN￨ORGANIZATION￨- treatment￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- difficulty￨L￨NN￨O￨- of￨L￨IN￨O￨- establishing￨L￨VBG￨O￨- a￨L￨DT￨O￨- relationship￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- response￨L￨NN￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- drug￨L￨NN￨O￨A exposure￨L￨NN￨O￨- and￨L￨CC￨O￨- drug￨L￨NN￨O￨- susceptibility￨L￨NN￨O￨- during￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- No.￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1384￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1408￨L￨CD￨DATE￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.1214￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 08-AOAS192￨L￨NN￨O￨- c￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- MODELING￨U￨NNP￨O￨- LONG-TERM￨U￨JJ￨O￨- LONGITUDINAL￨U￨NNP￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- DYNAMICS￨U￨NNS￨O￨- WITH￨U￨IN￨O￨- APPLICATION￨U￨NN￨O￨- TO￨U￨TO￨O￨- AN￨U￨DT￨O￨- AIDS￨U￨NN￨CAUSE_OF_DEATH￨- CLINICAL￨U￨NN￨O￨- STUDY￨U￨NN￨O￨- By￨U￨IN￨O￨- Yangxin￨U￨NN￨O￨- Huang1￨U￨NN￨O￨- and￨L￨CC￨O￨- Tao￨U￨NNP￨ORGANIZATION￨- Lu￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- South￨U￨NNP￨ORGANIZATION￨- Florida￨U￨NNP￨ORGANIZATION￨- A￨U￨NNP￨O￨- virologic￨L￨JJ￨O￨- marker￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- RNA￨U￨NN￨O￨- copies￨L￨NNS￨O￨- or￨L￨CC￨O￨- viral￨L￨JJ￨O￨A load￨L￨NN￨O￨A ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- currently￨L￨RB￨DATE￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- antiretroviral￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- ARV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- therapies￨L￨NNS￨O￨- in￨L￨IN￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- clinical￨L￨JJ￨O￨- trials￨L￨NNS￨O￨- .￨L￨.￨O￨- +Sampling￨U￨VBG￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- quasistationary￨L￨JJ￨O￨- regime￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- regular￨L￨JJ￨O￨- and￨L￨CC￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Renan￨U￨NNP￨O￨- S.￨U￨NNP￨O￨- Ferreira1￨U￨NNP￨O￨- 1Departamento￨L￨NNP￨O￨- de￨L￨IN￨O￨- F´ısica￨U￨NNP￨O￨- ,￨L￨,￨O￨- Universidade￨U￨NNP￨ORGANIZATION￨- Federal￨U￨NNP￨ORGANIZATION￨- de￨L￨NNP￨ORGANIZATION￨- Vi￨U￨NNP￨ORGANIZATION￨- ¸￨L￨NNP￨O￨- cosa￨L￨NN￨O￨- ,￨L￨,￨O￨- 36570-900￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Vi￨U￨NNP￨O￨- ¸￨L￨NNP￨O￨- cosa￨L￨NN￨O￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- A￨U￨NNP￨O￨- ma￨L￨NN￨O￨- jor￨L￨NN￨O￨- hurdle￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- will￨L￨MD￨O￨- unavoidably￨L￨RB￨O￨- visit￨L￨VB￨O￨- an￨L￨DT￨O￨- absorbing￨L￨NN￨O￨A ,￨L￨,￨O￨- disease-free￨L￨JJ￨O￨- state￨L￨NN￨O￨- at￨L￨IN￨O￨- sufficiently￨L￨RB￨O￨- long￨L￨JJ￨O￨- times￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- finite￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- epidemics￨L￨NNS￨O￨- evolves￨L￨VBZ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- QS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SQS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- constrained￨L￨VBN￨O￨- to￨L￨TO￨O￨- active￨L￨JJ￨O￨- configurations￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- reflecting￨L￨NN￨O￨- boundary￨L￨NN￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RBC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- returns￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pre-absorbing￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hub￨L￨NN￨O￨- reactivation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HR￨U￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- connected￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reactivated￨L￨VBN￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- visit￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- absorbing￨L￨VBG￨O￨A state￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- different￨L￨JJ￨O￨- quasistationary￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- QS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- simulation￨L￨NN￨O￨- methods￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- absorbing￨L￨VBG￨O￨A states￨L￨NNS￨O￨- are￨L￨VBP￨O￨- suitably￨L￨RB￨O￨- handled￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- thermodynamical￨L￨JJ￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- the￨L￨DT￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CP￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- regular￨L￨JJ￨O￨A and￨L￨CC￨O￨- scale￨L￨NN￨O￨- free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- such￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- covering￨L￨VBG￨O￨- an￨L￨DT￨O￨- extremely￨L￨RB￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- applications￨L￨NNS￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- recently￨L￨RB￨DATE￨- shown￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- exhibit￨L￨VB￨O￨- scale-free￨L￨JJ￨O￨- character￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- connectivity￨L￨NN￨O￨A distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- obey￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- mass￨L￨NN￨O￨- M￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- q￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- exponent￨L￨NN￨O￨- γ￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- investigate￨L￨VB￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- M￨U￨NN￨O￨- ,￨L￨,￨O￨- We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- dense￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- this￨L￨DT￨O￨- function￨L￨NN￨O￨A is￨L￨VBZ￨O￨- bimodal￨L￨JJ￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- for￨L￨IN￨O￨- sparse￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- smoothly￨L￨RB￨O￨- decreasing￨L￨VBG￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- distinction￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- being￨L￨VBG￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- q￨L￨NN￨O￨- .￨L￨.￨O￨- +Collective￨U￨JJ￨O￨- Synchronization￨U￨NN￨O￨- Induced￨U￨VBN￨O￨- by￨L￨IN￨O￨- Epidemic￨U￨NNP￨ORGANIZATION￨- Dynamics￨U￨NNP￨ORGANIZATION￨- on￨L￨IN￨ORGANIZATION￨- Complex￨U￨NN￨ORGANIZATION￨- Networks￨U￨NNP￨ORGANIZATION￨- with￨L￨IN￨O￨- Communities￨U￨NNPS￨O￨- Gang￨U￨NN￨O￨- Yan1￨U￨NN￨O￨- ,￨L￨,￨O￨- Zhong-Qian￨U￨JJ￨O￨- Fu1￨U￨NN￨O￨- ,￨L￨,￨O￨- ∗￨L￨CD￨NUMBER￨- Jie￨U￨NN￨O￨- Ren2￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Wen-Xu￨U￨NN￨O￨- Wang2￨U￨NN￨O￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Electronic￨U￨JJ￨ORGANIZATION￨- Science￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hefei￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Anhui￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- 230026￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P.R.China￨U￨NNP￨O￨- 2Nonlinear￨L￨NNP￨O￨- Science￨U￨NNP￨O￨- Center￨U￨NNP￨O￨- and￨L￨CC￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Modern￨U￨NNP￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- China￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Hefei￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Anhui￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- 230026￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P.R.China￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- October￨U￨NNP￨DATE￨- 17￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Much￨U￨JJ￨O￨- recent￨L￨JJ￨O￨- empirical￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- ubiquitous￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- numerical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- at￨L￨IN￨O￨- Qc￨U￨NN￨O￨- ≃￨L￨CD￨NUMBER￨- 0.835￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- global￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A to￨L￨TO￨O￨- desynchronization￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨- is￨L￨VBZ￨O￨- weakened￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- intermediately￨L￨RB￨O￨- large￨L￨JJ￨O￨- Q.￨U￨NNP￨O￨- Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- determined￨L￨VBN￨O￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- show￨L￨VBP￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- within￨L￨IN￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- between￨L￨IN￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- Letter￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- growth￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- tunable￨L￨JJ￨O￨- strength￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- noted￨L￨VBN￨O￨- by￨L￨IN￨O￨- Q￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- community￨L￨NN￨O￨- strength￨L￨NN￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- collective￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- SIRS￨U￨NNP￨O￨- epidemiological￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- intend￨L￨VBP￨O￨- to￨L￨TO￨O￨- fill￨L￨VB￨O￨- this￨L￨DT￨O￨- gap￨L￨NN￨O￨- by￨L￨IN￨O￨- investigating￨L￨VBG￨O￨- synchronization￨L￨NN￨O￨A behavior￨L￨NN￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- various￨L￨JJ￨O￨- strength￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- noted￨L￨VBN￨O￨- by￨L￨IN￨O￨- Q￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- observed￨L￨VBN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨A have￨L￨VBP￨O￨- hierarchical￨L￨JJ￨O￨- and￨L￨CC￨O￨- modular￨L￨JJ￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- dense￨L￨JJ￨O￨- substructure￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- departments￨L￨NNS￨O￨- ,￨L￨,￨O￨- wards￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- rooms￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- globally￨L￨RB￨O￨- but￨L￨CC￨O￨- only￨L￨RB￨O￨- loosely￨L￨RB￨O￨- connected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- reveal￨L￨VB￨O￨- extremely￨L￨RB￨O￨- right-skewed￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +Intervention￨U￨NN￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- restrict￨L￨VBP￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- medical￨L￨JJ￨O￨A doctors￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- visits￨L￨NNS￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- wards￨L￨NNS￨O￨- shrink￨L￨VB￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- more￨L￨RBR￨O￨- than￨L￨IN￨O￨- intervention￨L￨NN￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- directly￨L￨RB￨O￨- protect￨L￨VBP￨O￨- patients￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- isolating￨L￨VBG￨O￨- patients￨L￨NNS￨O￨- in￨L￨IN￨O￨- single￨L￨JJ￨O￨- rooms￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- simulate￨L￨VBP￨O￨- stochastic￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- observations￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- hospital￨L￨NN￨O￨A in￨L￨IN￨O￨- Tokyo￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- effective￨L￨JJ￨O￨- containment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- against￨L￨IN￨O￨- nosocomial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Diseases￨U￨NNS￨CAUSE_OF_DEATH￨- spread￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- great￨L￨JJ￨O￨- extent￨L￨NN￨O￨- with￨L￨IN￨O￨- larger￨L￨JJR￨O￨- probability￨L￨NN￨O￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- maintains￨L￨VBZ￨O￨- is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- workers￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- medical￨L￨JJ￨O￨A doctors￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- main￨L￨JJ￨O￨- vectors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- transmitters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- relation￨L￨NN￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- branching￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- in￨L￨IN￨O￨- queueing￨L￨VBG￨O￨- theory￨L￨NN￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- M￨U￨NN￨O￨- /￨L￨:￨O￨- G/1￨U￨NN￨O￨- queues￨L￨NNS￨O￨- and￨L￨CC￨O￨- birth￨L￨NN￨O￨- death￨L￨NN￨O￨- processes￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- combined￨L￨VBN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- results￨L￨VBZ￨O￨- from￨L￨IN￨O￨- queueing￨L￨VBG￨O￨- theory￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- vice￨L￨NN￨O￨- versa￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- deal￨L￨VBP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- at￨L￨IN￨O￨- detection￨L￨NN￨O￨A ,￨L￨,￨O￨- by￨L￨IN￨O￨- exploring￨L￨VBG￨O￨- an￨L￨DT￨O￨- obvious￨L￨JJ￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- so￨L￨RB￨O￨- well-known￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- queueing￨L￨VBG￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- moment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- detected￨L￨VBN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- moment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- on￨L￨IN￨O￨- queueing￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- geometrically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- multi-sample￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Ewens￨U￨NNP￨O￨- Sampling￨U￨NNP￨O￨- Formula￨U￨NNP￨O￨- forms￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- procedure￨L￨NN￨O￨- for￨L￨IN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨A reference￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- statistics￨L￨NNS￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Ewens￨U￨NNP￨O￨- Sampling￨U￨NNP￨O￨- Formula￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- forms￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- procedure￨L￨NN￨O￨- for￨L￨IN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨A reference￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- statistics￨L￨NNS￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- .￨L￨.￨O￨- +Key￨U￨NN￨O￨- words￨L￨NNS￨O￨- :￨L￨:￨O￨- network￨L￨NN￨O￨- reconstruction￨L￨NN￨O￨A ,￨L￨,￨O￨- set￨L￨VBN￨O￨- covering￨L￨VBG￨O￨- ,￨L￨,￨O￨- temporal￨L￨JJ￨O￨- data￨L￨NNS￨O￨- mining￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- There￨U￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- increasing￨L￨VBG￨O￨- interest￨L￨NN￨O￨- over￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- reconstructing￨L￨VBG￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- streams￨L￨NNS￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- they￨L￨PRP￨O￨- produce￨L￨VBP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- here￨L￨RB￨O￨- address￨L￨VBP￨O￨- the￨L￨DT￨O￨- challenge￨L￨NN￨O￨- of￨L￨IN￨O￨- reconstructing￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- data￨L￨NNS￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- stochastic￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- occurring￨L￨VBG￨O￨- on￨L￨IN￨O￨- directed￨L￨VBN￨O￨A networks￨L￨NNS￨O￨A and￨L￨CC￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- ‘￨L￨``￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ’￨L￨''￨O￨- is￨L￨VBZ￨O￨- propagated￨L￨VBN￨O￨- from￨L￨IN￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- LeaderRank￨U￨NNP￨O￨- performs￨L￨VBZ￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- LeaderRank￨U￨NNP￨O￨- in￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- aspects￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- out￨L￨RP￨O￨- more￨L￨JJR￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- tolerance￨L￨NN￨O￨- to￨L￨TO￨O￨- noisy￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- robustness￨L￨NN￨O￨- to￨L￨TO￨O￨- intentional￨L￨JJ￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- and￨L￨CC￨O￨- practical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- similar￨L￨JJ￨O￨- Preprint￨U￨NNP￨O￨- submitted￨L￨VBD￨O￨- to￨L￨TO￨O￨- Elsevier￨U￨NNP￨O￨- methods￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- in￨L￨IN￨O￨- ranking￨L￨JJ￨O￨- scientists￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- publications￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- athletes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- finding￨L￨VBG￨O￨- influential￨L￨JJ￨O￨- directors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- immunization￨L￨NN￨O￨- on￨L￨IN￨O￨- large-degree￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- influential￨L￨JJ￨O￨A )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- efficient￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Key￨U￨NN￨O￨- words￨L￨NNS￨O￨- :￨L￨:￨O￨- Social￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- ,￨L￨,￨O￨- Influential￨U￨NNP￨O￨- Spreader￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- LeaderRank￨U￨NNP￨O￨- ,￨L￨,￨O￨- Random￨U￨NNP￨ORGANIZATION￨- Walk￨U￨VBP￨ORGANIZATION￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- The￨U￨DT￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- attract￨L￨VBP￨O￨- increasing￨L￨VBG￨O￨- attention￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- researchers￨L￨NNS￨O￨- tried￨L￨VBD￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨A the￨L￨DT￨O￨- reason￨L￨NN￨O￨- why￨L￨WRB￨O￨- information￨L￨NN￨O￨- spread￨L￨NN￨O￨- so￨L￨RB￨O￨- quickly￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- decelerate￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Via￨U￨NNP￨O￨- assigning￨L￨VBG￨O￨- degree-dependent￨L￨JJ￨O￨- weights￨L￨NNS￨O￨- onto￨L￨IN￨O￨- links￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- ground￨L￨NN￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- variant￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- ranking￨L￨JJ￨O￨A algorithm￨L￨NN￨O￨- named￨L￨VBN￨O￨- LeaderRank￨U￨NNP￨O￨- [￨L￨-LRB-￨O￨- L￨U￨NNP￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- aggregation￨L￨NN￨O￨A the￨L￨DT￨O￨- regions￨L￨NNS￨O￨- become￨L￨VBP￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- with￨L￨IN￨O￨- aggregated￨L￨JJ￨O￨- user￨L￨NN￨O￨- counts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- directed￨L￨VBN￨O￨- and￨L￨CC￨O￨- weighted￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- respective￨L￨JJ￨O￨- sums￨L￨NNS￨O￨- of￨L￨IN￨O￨- user￨L￨NN￨O￨- level￨L￨NN￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +2.2￨L￨CD￨NUMBER￨- Regional￨U￨NNP￨O￨- Twitter￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- The￨U￨DT￨O￨- aggregation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- user-level￨L￨JJ￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- regional￨L￨JJ￨O￨A one￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- division￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- into￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- geopolitical￨L￨JJ￨O￨- units￨L￨NNS￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- a￨L￨DT￨O￨- k-shell￨L￨NN￨O￨- decomposition￨L￨NN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- core-periphery￨L￨JJ￨O￨- structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- revealed￨L￨VBN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- modified￨L￨JJ￨O￨- Regional-SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- consider￨L￨VBP￨O￨- basic￨L￨JJ￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- aggregated￨L￨JJ￨O￨- regional￨L￨JJ￨O￨A Twitter￨U￨NNP￨ORGANIZATION￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- communication￨L￨NN￨O￨- between￨L￨IN￨O￨- geopolitical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- aggregation￨L￨NN￨O￨A of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- different￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- connections￨L￨NNS￨O￨- we￨L￨PRP￨O￨- create￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- communication￨L￨NN￨O￨- networks￨L￨NNS￨O￨- between￨L￨IN￨O￨- geopolitical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- mention￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- M￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- follower￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- F￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Bhattacharjee￨U￨NNP￨ORGANIZATION￨- †￨L￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Bhubaneswar￨U￨NNP￨CITY￨- 751￨L￨CD￨NUMBER￨- 005￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- India￨U￨NNP￨COUNTRY￨- The￨U￨NNP￨O￨- force￨L￨NN￨O￨A induced￨L￨VBD￨O￨- unzipping￨L￨JJ￨O￨- transition￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- double￨L￨JJ￨O￨- stranded￨L￨JJ￨O￨- DNA￨U￨NN￨MISC￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- purely￨L￨RB￨O￨- thermodynamic￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- different￨L￨JJ￨O￨- source￨L￨NN￨O￨A detection￨L￨NN￨O￨- estimators￨L￨NNS￨O￨- for￨L￨IN￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- vary￨L￨VBP￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- assumptions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- locally￨L￨RB￨O￨- tree-like￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NNP￨O￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- both￨L￨DT￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- mean-field-like￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- node￨L￨NN￨O￨- independence￨L￨NN￨O￨- approximation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- tree-like￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨A likelihoods￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Epidemiologists￨U￨NNS￨O￨- detect￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- source￨L￨NN￨O￨A or￨L￨CC￨O￨- the￨L￨DT￨O￨- patient-zero￨L￨NN￨O￨- either￨L￨CC￨O￨- by￨L￨IN￨O￨- analysing￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- strains￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- time-demanding￨L￨JJ￨O￨- or￨L￨CC￨O￨- try￨L￨VB￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- backtracking￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +remove￨L￨VB￨O￨- the￨L￨DT￨O￨- independence￨L￨NN￨O￨- assumption￨L￨NN￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨- passing￨L￨NN￨O￨- method￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- tree-like￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- exact￨L￨JJ￨O￨- analytic￨L￨JJ￨O￨- calculations￨L￨NNS￨O￨- and￨L￨CC￨O￨- Monte￨U￨NNP￨LOCATION￨- Carlo￨U￨NNP￨LOCATION￨- estimators￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- detectability￨L￨NN￨O￨- limits￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- primarily￨L￨RB￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨A process￨L￨NN￨O￨A characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- analytical￨L￨JJ￨O￨- result￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- adapting￨L￨VBG￨O￨- an￨L￨DT￨O￨- ALOHA￨U￨NN￨O￨- protocol￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- throughput￨L￨NN￨O￨- is￨L￨VBZ￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- scheduling￨L￨VBG￨O￨- all￨L￨DT￨O￨- concurrently￨L￨RB￨O￨- transmitting￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- work￨L￨VB￨O￨- in￨L￨IN￨O￨- either￨L￨CC￨O￨- FD￨U￨NN￨O￨- mode￨L￨NN￨O￨A or￨L￨CC￨O￨- HD￨U￨NN￨O￨- mode￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- condition￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- downside￨L￨NN￨O￨- of￨L￨IN￨O￨- FD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- will￨L￨MD￨O￨- inevitably￨L￨RB￨O￨- cause￨L￨VB￨O￨- extra￨L￨JJ￨O￨- interference￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- half-duplex￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- HD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- wireless￨L￨JJ￨O￨A network￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- both￨L￨DT￨O￨- HD￨U￨NN￨O￨- and￨L￨CC￨O￨- FD￨U￨NN￨O￨- capabilities￨L￨NNS￨O￨- and￨L￨CC￨O￨- derive￨L￨VB￨O￨- and￨L￨CC￨O￨- optimize￨L￨VB￨O￨- the￨L￨DT￨O￨- throughput￨L￨NN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- the￨L￨DT￨O￨- Signal￨U￨NN￨O￨- to￨L￨TO￨O￨- Interference￨U￨NN￨O￨- Ratio￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- requirements￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- macro-cell￨L￨NN￨O￨- and￨L￨CC￨O￨- D2D￨U￨NN￨O￨- communications￨L￨NNS￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- geometrical￨L￨JJ￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- guard￨L￨NN￨TITLE￨- distances￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- D2D￨U￨NN￨O￨- user￨L￨NN￨O￨- equipment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DUE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- base￨L￨NN￨O￨- station￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmitting￨L￨VBG￨O￨- cellular￨L￨JJ￨O￨- user￨L￨NN￨O￨- equipment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CUE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- communicating￨L￨VBG￨O￨- D2D￨U￨NN￨O￨- pairs￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- uplink￨L￨NN￨O￨- resource￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reused￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- believe￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- obtained￨L￨VBN￨O￨- results￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- useful￨L￨JJ￨O￨- guidelines￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- deployment￨L￨NN￨O￨- of￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- cellular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- underlaying￨L￨VBG￨O￨- D2D￨U￨NN￨O￨- communications￨L￨NNS￨O￨A .￨L￨.￨O￨- +By￨U￨IN￨O￨- utilizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- guard￨L￨NN￨TITLE￨- distances￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- then￨L￨RB￨O￨- derive￨L￨VBP￨O￨- the￨L￨DT￨O￨- bounds￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- throughput￨L￨NN￨O￨- improvement￨L￨NN￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- D2D￨U￨NN￨O￨- communications￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- cell￨L￨NN￨O￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- Device-to-device￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- D2D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- communications￨L￨NNS￨O￨A in￨L￨IN￨O￨- cellular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- promising￨L￨JJ￨O￨- technologies￨L￨NNS￨O￨- for￨L￨IN￨O￨- improving￨L￨VBG￨O￨- network￨L￨NN￨O￨- throughput￨L￨NN￨O￨- ,￨L￨,￨O￨- spectrum￨L￨NN￨O￨- ef￨L￨NN￨O￨- ficiency￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- delay￨L￨NN￨O￨- .￨L￨.￨O￨- +Index￨U￨NNP￨O￨- Terms￨U￨NNS￨O￨- —￨L￨:￨O￨- Device-to-device￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- D2D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- communications￨L￨NNS￨O￨A ,￨L￨,￨O￨- uplink￨L￨NN￨O￨- reuse￨L￨NN￨O￨- ,￨L￨,￨O￨- throughput￨L￨NN￨O￨- ,￨L￨,￨O￨- guard￨L￨NN￨TITLE￨- distances￨L￨NNS￨O￨- ,￨L￨,￨O￨- circle￨L￨NN￨O￨- packing￨L￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- and￨L￨CC￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- attention￨L￨NN￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- ground￨L￨NN￨O￨- truth￨L￨NN￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- functional￨L￨JJ￨O￨- de￨L￨FW￨O￨- finition￨L￨FW￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- encoded￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- while￨L￨IN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- rely￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- detection￨L￨NN￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- uncover￨L￨VB￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- basic￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- random￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- where￨L￨WRB￨O￨- target￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- picked￨L￨VBN￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨A topology￨L￨NN￨O￨A .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨A can￨L￨MD￨O￨- diffuse￨L￨VB￨O￨- their￨L￨PRP$￨O￨- in￨L￨IN￨O￨- fluence￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- faster￨L￨RBR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- ones￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- targeted￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨A with￨L￨IN￨O￨- high￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- in￨L￨IN￨O￨- fluential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- Epidemic￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- denote￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- attracted￨L￨VBN￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- attention￨L￨NN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- experiments￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- fully￨L￨RB￨O￨- mixed￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨A distribution￨L￨NN￨O￨- on￨L￨IN￨O￨- edges￨L￨NNS￨O￨- would￨L￨MD￨O￨- not￨L￨RB￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- results￨L￨NNS￨O￨- once￨L￨IN￨DATE￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- weight￨L￨NN￨O￨- of￨L￨IN￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- fixed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- perform￨L￨VBP￨O￨- detailed￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- representative￨L￨JJ￨TITLE￨- metrics￨L￨NNS￨O￨- ,￨L￨,￨O￨- outbreak￨L￨NN￨O￨- threshold￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨A prevalence￨L￨NN￨O￨A ,￨L￨,￨O￨- on￨L￨IN￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- minimizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effort￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- sufficiently￨L￨JJ￨O￨- small￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- monotonically￨L￨RB￨O￨- decreasing￨L￨VBG￨O￨- ;￨L￨:￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Nash-equilibria￨U￨NN￨MISC￨- strategies￨L￨NNS￨O￨- where￨L￨WRB￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- simultaneously￨L￨RB￨O￨- minimize￨L￨VBP￨O￨- the￨L￨DT￨O￨- joint￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- versus￨L￨CC￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Typically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ob￨L￨NN￨O￨- jective￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- define￨L￨VB￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨A strategy￨L￨NN￨O￨- by￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- effort/cost￨L￨NN￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- can￨L￨MD￨O￨- give￨L￨VB￨O￨- rise￨L￨VB￨O￨- to￨L￨TO￨O￨- particularly￨L￨RB￨O￨- interesting￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- non-homogeneous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- vaccination￨L￨NN￨O￨A strategy￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- risk-groups￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- time-dependent￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- d’￨L￨NNP￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- specific￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- explicit￨L￨JJ￨O￨- formulas￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Nash￨U￨NNP￨PERSON￨- vaccination￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- current￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- time-dependent￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A when￨L￨WRB￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- periodic￨L￨JJ￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- comparing￨L￨VBG￨O￨- these￨L￨DT￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- user-average￨L￨JJ￨O￨- spectral￨L￨JJ￨O￨- ef￨L￨NN￨O￨- ficiency￨L￨NN￨O￨- ,￨L￨,￨O￨- small￨L￨JJ￨O￨- -￨L￨:￨O￨- cell￨L￨NN￨O￨A densi￨L￨NN￨O￨- fication￨L￨NN￨O￨- is￨L￨VBZ￨O￨- favorable￨L￨JJ￨O￨- in￨L￨IN￨O￨- crowded￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- with￨L￨IN￨O￨- moderate￨L￨JJ￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- user￨L￨NN￨O￨- density￨L￨NN￨O￨- and￨L￨CC￨O￨- massive￨L￨JJ￨O￨- MIMO￨U￨NN￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- user￨L￨NN￨O￨- density￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- this￨L￨DT￨O￨- complex￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- bus￨L￨NN￨O￨- networks￨L￨NNS￨O￨- for￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- Indian￨U￨JJ￨NATIONALITY￨- cities￨L￨NNS￨O￨- using￨L￨VBG￨O￨- SI￨U￨NNP￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Various￨U￨JJ￨O￨- complex￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- percolation￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨A of￨L￨IN￨O￨- blackouts￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- memes￨L￨NNS￨O￨- ,￨L￨,￨O￨- ideas￨L￨NNS￨O￨- and￨L￨CC￨O￨- opinions￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modelled￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- exploit￨L￨VBP￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- aspect￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- their￨L￨PRP$￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- diffusion￨L￨NN￨O￨A process￨L￨NN￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- identify￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨A which￨L￨WDT￨O￨- help￨L￨VBP￨O￨- us￨L￨PRP￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- by￨L￨IN￨O￨- developing￨L￨VBG￨O￨- node-based￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Methodology￨U￨NNP￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- bus￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- ma￨L￨NN￨O￨- jor￨L￨NN￨O￨- Indian￨U￨JJ￨NATIONALITY￨- cities￨L￨NNS￨O￨A ,￨L￨,￨O￨- namely￨L￨RB￨O￨- Ahmedabad￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- ABN￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Chennai￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- CBN￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Delhi￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- DBN￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Hyderabad￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- HBN￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Kolkata￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- KBN￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Mumbai￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- MBN￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- objective￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- sentinel￨L￨NN￨O￨A surveillance￨L￨NN￨O￨A —￨L￨:￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- detection￨L￨NN￨O￨- or￨L￨CC￨O￨- extinction￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- detection￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- detection￨L￨NN￨O￨- .￨L￨.￨O￨- +Objective￨U￨NN￨O￨- measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- sentinel￨L￨NN￨O￨A surveillance￨L￨NN￨O￨A in￨L￨IN￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- Petter￨U￨NNP￨ORGANIZATION￨- Holme￨U￨NNP￨ORGANIZATION￨- ∗￨L￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Innovative￨U￨JJ￨ORGANIZATION￨- Research￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Tokyo￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Nagatsuta-cho￨U￨JJ￨O￨- 4259￨L￨CD￨DATE￨- ,￨L￨,￨O￨- Midori-ku￨U￨NN￨O￨- ,￨L￨,￨O￨- Yokohama￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Kanagawa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- 226-8503￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- Assume￨U￨VB￨O￨- one￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- determining￨L￨VBG￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infectious￨L￨JJ￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- by￨L￨IN￨O￨- probing￨L￨VBG￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- optimizing￨L￨VBG￨O￨- sentinel￨L￨NN￨O￨A surveillance￨L￨NN￨O￨A in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- probe￨L￨VB￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- discovered￨L￨VBN￨O￨- early￨L￨JJ￨O￨- or￨L￨CC￨O￨- reliably￨L￨RB￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- find￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- that￨L￨WDT￨O￨- predicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- objective￨L￨JJ￨O￨A measures￨L￨NNS￨O￨- —￨L￨:￨O￨- that￨L￨IN￨O￨- depends￨L￨VBZ￨O￨- both￨L￨DT￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NN￨O￨- set￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- objective￨L￨JJ￨O￨A measures￨L￨NNS￨O￨- can￨L￨MD￨O￨- rank￨L￨VB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- very￨L￨RB￨O￨- differently￨L￨RB￨O￨- .￨L￨.￨O￨- +Importantly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- early￨L￨JJ￨O￨- short-time￨L￨JJ￨O￨- asynchrony￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- consistent￨L￨JJ￨O￨- precursor￨L￨NN￨O￨- to￨L￨TO￨O￨- future￨L￨JJ￨DATE￨- persistence￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- provide￨L￨VB￨O￨- valuable￨L￨JJ￨O￨- early￨L￨JJ￨O￨- warnings￨L￨NNS￨O￨- for￨L￨IN￨O￨- sustained￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- patch￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- persistent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- region￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- another￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- range￨L￨NN￨O￨- .￨L￨.￨O￨- +So￨U￨IN￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- stage￨L￨NN￨O￨A ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- stage￨L￨NN￨O￨- ,￨L￨,￨O￨- onto￨L￨IN￨O￨- the￨L￨DT￨O￨- refractory￨L￨JJ￨O￨- stage￨L￨NN￨O￨- and￨L￨CC￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- →￨L￨VBP￨O￨- R￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- cycle￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- key￨L￨JJ￨O￨- result￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- higher￨L￨JJR￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- synchronization￨L￨NN￨O￨A ,￨L￨,￨O￨- both￨L￨CC￨O￨- globally￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- locally￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- neighborhoods￨L￨NNS￨O￨- ,￨L￨,￨O￨- hinders￨L￨VBZ￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- transient￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A can￨L￨MD￨O￨- help￨L￨VB￨O￨- anticipate￨L￨VB￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- recent￨L￨JJ￨O￨- works￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- analyzed￨L￨VBN￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- user￨L￨NN￨O￨A process￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- scenario￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- BSs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- PPP￨U￨NNP￨ORGANIZATION￨- distributed￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- users￨L￨NNS￨O￨- are￨L￨VBP￨O￨- uniformly￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- Voronoi￨U￨NNP￨O￨- cell￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- BS￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- system￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- analytical￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- UL￨U￨NN￨O￨- signal￨L￨NN￨O￨- to￨L￨TO￨O￨- interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- average￨L￨JJ￨O￨- spectral￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- user￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Subjective￨U￨JJ￨O￨- listening￨L￨VBG￨O￨- tests￨L￨NNS￨O￨- reveal￨L￨VBP￨O￨- that￨L￨IN￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- cost￨L￨NN￨O￨- functions￨L￨NNS￨O￨- help￨L￨VBP￨O￨- achieve￨L￨VB￨O￨- superior￨L￨JJ￨O￨- separation￨L￨NN￨O￨A performance￨L￨NN￨O￨- as￨L￨IN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- stand-alone￨L￨JJ￨O￨- MSE￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- SDR￨U￨NN￨O￨- costs￨L￨NNS￨O￨- .￨L￨.￨O￨- +6￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 8￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- Recent￨U￨JJ￨O￨- neural￨L￨JJ￨O￨- network￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- source￨L￨NN￨O￨- separation￨L￨NN￨O￨A attempt￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- audio￨L￨NN￨O￨- signals￨L￨NNS￨O￨- by￨L￨IN￨O￨- processing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- waveforms￨L￨NNS￨O￨- directly￨L￨RB￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- loss￨L￨NN￨O￨- functions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- BSS￨U￨NNS￨ORGANIZATION￨- _￨L￨VBP￨O￨- Eval￨U￨JJ￨O￨- and￨L￨CC￨O￨- perceptual￨L￨JJ￨O￨- metrics￨L￨NNS￨O￨- like￨L￨IN￨O￨- source￨L￨NN￨O￨A to￨L￨TO￨O￨- distortion￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SDR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- source￨L￨NN￨O￨- to￨L￨TO￨O￨- interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- source￨L￨NN￨O￨- to￨L￨TO￨O￨- artifact￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SAR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- short-time￨L￨JJ￨O￨- objective￨L￨JJ￨O￨- intelligibility￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- STOI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- and￨L￨CC￨O￨- experiment￨L￨NN￨O￨- with￨L￨IN￨O￨- new￨L￨JJ￨O￨- loss￨L￨NN￨O￨- functions￨L￨NNS￨O￨- for￨L￨IN￨O￨- end-to-end￨L￨JJ￨O￨- source￨L￨NN￨O￨- separation￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- numerically￨L￨RB￨O￨- study￨L￨VB￨O￨- how￨L￨WRB￨O￨- other￨L￨JJ￨O￨- hazard￨L￨NN￨O￨- functions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Weibull￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- loglogistic￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- provide￨L￨VBP￨O￨- qualitative￨L￨JJ￨O￨- different￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨A evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- traditional￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- setting￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- a￨L￨DT￨O￨- fluid￨L￨NN￨O￨- limit￨L￨NN￨O￨A that￨L￨WDT￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- o.d.e.￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- o.d.e.￨L￨NN￨O￨- approximation￨L￨NN￨O￨- and￨L￨CC￨O￨- derive￨L￨VB￨O￨- explicit￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- trajectory￨L￨NN￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨A under￨L￨IN￨O￨- the￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨JJ￨O￨A distribution￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- o.d.e.￨L￨NN￨O￨- via￨L￨IN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- example￨L￨NN￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- set￨L￨VBN￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- newly￨L￨RB￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- aggregated￨L￨VBN￨O￨- by￨L￨IN￨O￨- week￨L￨NN￨DURATION￨- is￨L￨VBZ￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- POMP￨U￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- Markovian￨U￨JJ￨MISC￨- SIR￨U￨NN￨MISC￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- chapter￨L￨NN￨O￨- discusses￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- perform￨L￨VB￨O￨- likelihood-based￨L￨JJ￨O￨- inference￨L￨NN￨O￨- for￨L￨IN￨O￨- partially￨L￨RB￨O￨A observed￨L￨VBN￨O￨- Markov￨U￨NNP￨PERSON￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- easy￨L￨JJ￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- is￨L￨VBZ￨O￨- intractable￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- inference￨L￨NN￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨JJ￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- only￨L￨RB￨O￨- partially￨L￨RB￨O￨A observed￨L￨VBN￨O￨- e.g.￨L￨FW￨O￨- in￨L￨IN￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- incidences￨L￨NNS￨O￨- in￨L￨IN￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- periods￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- example￨L￨NN￨O￨- illustrates￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- extensions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- and￨L￨CC￨O￨- over-dispersion￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- observation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- analysing￨L￨VBG￨O￨A routinely￨L￨RB￨O￨- collected￨L￨VBN￨O￨- rotavirus￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJS￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- chapter￨L￨NN￨O￨- reviews￨L￨VBZ￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- background￨L￨NN￨O￨- of￨L￨IN￨O￨- inference￨L￨NN￨O￨- for￨L￨IN￨O￨- partially￨L￨RB￨O￨A observed￨L￨VBN￨O￨- Markov￨U￨NNP￨PERSON￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- POMP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- via￨L￨IN￨O￨- iterated￨L￨JJ￨O￨- filtering￨L￨NN￨O￨- .￨L￨.￨O￨- +Wroclaw￨U￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- cite￨L￨VBP￨O￨- was￨L￨VBD￨O￨- very￨L￨RB￨O￨- important￨L￨JJ￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- statistics￨L￨NNS￨O￨- from￨L￨IN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A epidemic￨L￨JJ￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- Bernoulli￨U￨NNP￨PERSON￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- few￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- and￨L￨CC￨O￨- few￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨A .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- and￨L￨CC￨O￨- behavior￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- valuable￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- unfolding￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- H1N1￨U￨NN￨O￨- pandemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- clear￨L￨JJ￨O￨- that￨L￨IN￨O￨- societal￨L￨JJ￨O￨- reactions￨L￨NNS￨O￨- coupling￨L￨NN￨O￨A behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- substantial￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- thus￨L￨RB￨O￨- defining￨L￨VBG￨O￨- limitations￨L￨NNS￨O￨- of￨L￨IN￨O￨- most￨L￨JJS￨O￨- current￨L￨JJ￨DATE￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- relatively￨L￨RB￨O￨- little￨L￨JJ￨O￨- systematic￨L￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- coupled￨L￨JJ￨O￨- behavior-disease￨L￨NN￨O￨- models￨L￨NNS￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- close￨L￨VB￨O￨- the￨L￨DT￨O￨- feedback￨L￨NN￨O￨- loop￨L￨NN￨O￨- between￨L￨IN￨O￨- behavioral￨L￨JJ￨O￨A changes￨L￨NNS￨O￨- triggered￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- perception￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- itself￨L￨PRP￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- models￨L￨NNS￨O￨- lacking￨L￨VBG￨O￨- this￨L￨DT￨O￨- coupling￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- extremely￨L￨RB￨O￨- successful￨L￨JJ￨O￨- in￨L￨IN￨O￨- mild￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- obviously￨L￨RB￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- of￨L￨IN￨O￨- limited￨L￨JJ￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- situations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- social￨L￨JJ￨O￨- disruption￨L￨NN￨O￨- or￨L￨CC￨O￨- behavioral￨L￨JJ￨O￨A alterations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- induced￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- by￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transition￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in/out￨L￨JJ￨O￨- of￨L￨IN￨O￨- behavioral￨L￨JJ￨O￨A classes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- rich￨L￨JJ￨O￨- phase￨L￨NN￨O￨- space￨L￨NN￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- peaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- tipping￨L￨VBG￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- DMP￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- exclusively￨L￨RB￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- one-way￨L￨JJ￨O￨- state￨L￨NN￨O￨- changes￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨A to￨L￨TO￨O￨- models￨L￨NNS￨O￨- like￨L￨IN￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infectious-susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- SIRS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infectious-recovered-susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- can￨L￨MD￨O￨- return￨L￨VB￨O￨- to￨L￨TO￨O￨- previously￨L￨RB￨DATE￨- inhabited￨L￨VBN￨O￨- states￨L￨NNS￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- many￨L￨JJ￨O￨- real-world￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- can￨L￨MD￨O￨- exhibit￨L￨VB￨O￨- such￨L￨JJ￨O￨- recurrent￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- DMP￨U￨NN￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- complex￨L￨NN￨O￨- ,￨L￨,￨O￨- recurrent￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Generalized￨U￨NNP￨O￨- individual-based￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- vulnerability￨L￨NN￨O￨A assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- correlated￨L￨VBN￨O￨- scale-free￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- Mina￨U￨NNP￨PERSON￨- Youssef￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Caterina￨U￨NNP￨PERSON￨- Scoglio￨U￨NNP￨PERSON￨- K-State￨U￨NNP￨PERSON￨- Epicenter￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electrical￨U￨JJ￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Computer￨U￨NNP￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Kansas￨U￨NNP￨ORGANIZATION￨- State￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Manhattan￨U￨NNP￨ORGANIZATION￨- KS￨U￨NN￨ORGANIZATION￨- 66506￨L￨CD￨NUMBER￨- Many￨U￨JJ￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- vulnerability￨L￨NN￨O￨- to￨L￨TO￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- such￨L￨JJ￨O￨- vulnerability￨L￨NN￨O￨- relates￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- employ￨L￨VBP￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- measure￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨A of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- applied￨L￨VBN￨O￨- on￨L￨IN￨O￨- structured￨L￨JJ￨O￨- networks￨L￨NNS￨O￨A considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- new￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- capable￨L￨JJ￨O￨A of￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Hybrid￨U￨NN￨O￨- models￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- effective￨L￨JJ￨O￨- means￨L￨NNS￨O￨- for￨L￨IN￨O￨- complex￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- action￨L￨NN￨O￨- and￨L￨CC￨O￨- dosage￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- drug￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- therapy￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- meaningfully￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- classically￨L￨RB￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- fashion￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- scheduling￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨A treatment￨L￨NN￨O￨- discretely￨L￨RB￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- predictive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- biomedicine￨L￨NN￨O￨- require￨L￨VBP￨O￨- a￨L￨DT￨O￨- multiscale￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- molecule-cell-tissue-organ-body￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- heterogeneous￨L￨JJ￨O￨- methodologies￨L￨NNS￨O￨A are￨L￨VBP￨O￨- often￨L￨RB￨O￨- employed￨L￨VBN￨O￨- for￨L￨IN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- an￨L￨DT￨O￨- algebraic￨L￨JJ￨O￨- language￨L￨NN￨O￨- for￨L￨IN￨O￨- specifying￨L￨VBG￨O￨- general￨L￨JJ￨TITLE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- processes￨L￨NNS￨O￨- and￨L￨CC￨O￨- multiple￨L￨JJ￨O￨- treatments￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- semantics￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- hybrid￨L￨NN￨O￨A dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- derived￨L￨VBN￨O￨- .￨L￨.￨O￨- +Disease￨U￨NN￨CAUSE_OF_DEATH￨- processes￨L￨NNS￨O￨- as￨L￨IN￨O￨- hybrid￨L￨JJ￨O￨A dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- Pietro￨U￨NNP￨PERSON￨- Li￨U￨NNP￨PERSON￨- `￨L￨``￨O￨- o￨L￨NN￨O￨- Computer￨U￨NN￨ORGANIZATION￨- Laboratory￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Cambridge￨U￨NNP￨ORGANIZATION￨- Cambridge￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- Emanuela￨U￨NNP￨ORGANIZATION￨- Merelli￨U￨NNP￨ORGANIZATION￨- Nicola￨U￨NNP￨ORGANIZATION￨- Paoletti￨U￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- Computer￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- Division￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Camerino￨U￨NNP￨ORGANIZATION￨- Camerino￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- IT￨U￨NNP￨O￨- We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- hybrid￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- potentialities￨L￨NNS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- are￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨A study￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- its￨L￨PRP$￨O￨- applicability￨L￨NN￨O￨- on￨L￨IN￨O￨- osteomyelitis￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- bone￨L￨NN￨O￨- remodelling￨L￨NN￨O￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨NN￨O￨- and￨L￨CC￨O￨- multiscale￨L￨JJ￨O￨- manner￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- both￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- and￨L￨CC￨O￨- static￨L￨JJ￨O￨A small-world￨L￨JJ￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- suppression￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- dependence￨L￨NN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- finite-size￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- known￨L￨VBN￨O￨- for￨L￨IN￨O￨- regular￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- network￨L￨NN￨O￨- was￨L￨VBD￨O￨- constructed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- 2-dimensional￨L￨JJ￨O￨- Watts-Strogatz￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 500￨L￨CD￨NUMBER￨A ×￨L￨NN￨O￨- 500￨L￨CD￨NUMBER￨- square￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- with￨L￨IN￨O￨- additional￨L￨JJ￨O￨- shortcuts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- rewiring￨L￨VBG￨O￨- shortcuts￨L￨NNS￨O￨- in￨L￨IN￨O￨- every￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- result￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨- small￨L￨JJ￨O￨A world￨L￨NN￨O￨A with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- shortcuts￨L￨NNS￨O￨- increased￨L￨VBN￨O￨- by￨L￨IN￨O￨- 20.7￨L￨CD￨PERCENT￨- ±￨L￨CD￨PERCENT￨- 1.4￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- qualitative￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- stays￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- static￨L￨JJ￨O￨A and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- small-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- similarity￨L￨NN￨O￨- between￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨A marketing￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- communications￨L￨NNS￨O￨- strategy￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- remain￨L￨VBP￨O￨- largely￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- marketing￨L￨NN￨O￨- specific￨L￨NN￨O￨- field￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SusceptibleInfected-Recovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨A marketing￨L￨NN￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- marketing￨L￨NN￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- message￨L￨NN￨O￨- is￨L￨VBZ￨O￨- viral￨L￨JJ￨O￨A when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- broadly￨L￨RB￨O￨- sent￨L￨VBN￨O￨- and￨L￨CC￨O￨- received￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- market￨L￨NN￨O￨- through￨L￨IN￨O￨- person-to-person￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- viral￨L￨JJ￨O￨A marketing￨L￨NN￨O￨- ,￨L￨,￨O￨- word-of-mouth￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- seed￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +References￨U￨NNS￨O￨- devoted￨L￨VBN￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- or￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- much￨L￨RB￨O￨- too￨L￨RB￨O￨- numerous￨L￨JJ￨O￨- for￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- being￨L￨VBG￨O￨- listed￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- refer￨L￨VB￨O￨- to￨L￨TO￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- recent￨L￨JJ￨O￨- accounts￨L￨NNS￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨A modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- comprehensively￨L￨RB￨O￨- presented￨L￨VBN￨O￨- and￨L￨CC￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- mobility￨L￨NN￨O￨- can￨L￨MD￨O￨- pronouncedly￨L￨RB￨O￨- promote￨L￨VB￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- extinction￨L￨NN￨O￨- domain￨L￨NN￨O￨A to￨L￨TO￨O￨- persistence￨L￨NN￨O￨- domain￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spirals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- wavelength￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- increasing￨L￨VBG￨O￨- and￨L￨CC￨O￨- ultimately￨L￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- will￨L￨MD￨O￨- saturate￨L￨VB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- value￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- observe￨L￨VBP￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- trade-offs￨L￨NNS￨O￨- of￨L￨IN￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- time￨L￨NN￨O￨- having￨L￨VBG￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- that￨L￨IN￨O￨- local￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- will￨L￨MD￨O￨- play￨L￨VB￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ma￨L￨NN￨O￨- jority￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ’￨L￨POS￨O￨- interactions￨L￨NNS￨O￨- particularly￨L￨RB￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- occurs￨L￨VBZ￨O￨A through￨L￨IN￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- opposite￨L￨JJ￨O￨- with￨L￨IN￨O￨- present￨L￨JJ￨DATE￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- explicit￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A is￨L￨VBZ￨O￨- limited￨L￨VBN￨O￨- by￨L￨IN￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- recent￨L￨JJ￨O￨- models￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- interactions￨L￨NNS￨O￨A between￨L￨IN￨O￨- local￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- may￨L￨MD￨O￨- generate￨L￨VB￨O￨- complex￨L￨NN￨O￨- spatial￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- by￨L￨IN￨O￨- dispersal￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- all￨L￨DT￨O￨- other￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- CSMA￨U￨NNP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- PPP￨U￨NN￨O￨- or￨L￨CC￨O￨- ALOHA￨U￨NN￨ORGANIZATION￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- cluster￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmitting￨L￨VBG￨O￨- set￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- Poisson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- difficulties￨L￨NNS￨O￨- of￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- non-Poisson￨L￨JJ￨MISC￨- point￨L￨NN￨O￨A processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- c￨L￨NN￨O￨- annot￨L￨NN￨O￨- be￨L￨VB￨O￨- expected￨L￨VBN￨O￨- that￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- closed-form￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- result￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- outage￨L￨NN￨O￨- probability￨L￨NN￨O￨- approaches￨L￨VBZ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- interferers￨L￨NNS￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- κ￨L￨NN￨O￨- assumes￨L￨VBZ￨O￨- values￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- κ￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- α/2￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- practical￨L￨JJ￨O￨- MAC￨U￨NNP￨ORGANIZATION￨- protocols￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- exponent￨L￨NN￨O￨A .￨L￨.￨O￨- +—￨L￨:￨O￨- Outage￨U￨NN￨O￨- probabilities￨L￨NNS￨O￨- in￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- various￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- MAC￨U￨NNP￨ORGANIZATION￨- scheme￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨A ,￨L￨,￨O￨- fading￨L￨JJ￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- success￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- outage￨L￨NN￨O￨- probability￨L￨NN￨O￨- characterization￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- introduced￨L￨VBN￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- coordination￨L￨NN￨O￨- level￨L￨NN￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- MAC￨U￨NNP￨ORGANIZATION￨- as￨L￨IN￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- interference￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +scaling￨L￨VBG￨O￨- exponent￨L￨JJ￨O￨A κ￨L￨NN￨O￨- introduced￨L￨VBN￨O￨- γ￨L￨NN￨O￨- ηκ￨L￨NN￨O￨- η￨L￨NN￨O￨- Index￨U￨NN￨O￨- Terms￨U￨NNS￨O￨- —￨L￨:￨O￨- Ad￨U￨NN￨O￨- hoc￨L￨FW￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- outage￨L￨NN￨O￨- ,￨L￨,￨O￨- ference￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- role￨L￨NN￨O￨- played￨L￨VBN￨O￨- by￨L￨IN￨O￨- this￨L￨DT￨O￨- internal￨L￨JJ￨O￨- noise￨L￨NN￨O￨A ,￨L￨,￨O￨- arising￨L￨VBG￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- of￨L￨IN￨O￨- sustained￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- prey-predator￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- master￨L￨JJ￨O￨- equation￨L￨NN￨O￨- approach￨L￨NN￨O￨- by￨L￨IN￨O￨- McKane￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Newman￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mechanism￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- of￨L￨IN￨O￨- sustained￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- analysed￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- framework￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- which￨L￨WDT￨O￨- concentrates￨L￨VBZ￨O￨- on￨L￨IN￨O￨- external￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- noise￨L￨NN￨O￨A source￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- non-normality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- linearised￨L￨VBN￨O￨- drift￨L￨NN￨O￨- matrix￨L￨NN￨O￨- ,￨L￨,￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- violation￨L￨NN￨O￨- of￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- balance￨L￨NN￨O￨- ,￨L￨,￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- enhanced￨L￨VBN￨O￨- fluctuations￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- amplitudes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨A coherence￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- simply￨L￨RB￨O￨- understood￨L￨VBN￨O￨- as￨L￨IN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- non-monotonic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- |￨L￨CD￨NUMBER￨- Im￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- Re￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- with￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- noise￨L￨NN￨O￨A approximation￨L￨NN￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- coherence￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- predicted￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- purely￨L￨RB￨O￨- deterministic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +A.￨U￨NN￨O￨- Background￨U￨NNP￨O￨- and￨L￨CC￨O￨- Related￨U￨JJ￨O￨- Work￨U￨NN￨O￨- Among￨U￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- PPP￨U￨NN￨ORGANIZATION￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- locations￨L￨NNS￨O￨- i￨L￨FW￨O￨- n￨L￨NN￨O￨- a￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- outage￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- users￨L￨NNS￨O￨- uniformly￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- bounded￨L￨JJ￨O￨- area￨L￨NN￨O￨- A￨U￨DT￨O￨- ⊂￨L￨SYM￨O￨- R2￨U￨NN￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- channel￨L￨NN￨O￨- fading￨L￨JJ￨O￨A ,￨L￨,￨O￨- by￨L￨IN￨O￨- scaling￨L￨VBG￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- n￨L￨NN￨O￨- appropriately￨L￨RB￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- sharp￨L￨JJ￨O￨- tradeoff￨L￨NN￨O￨- between￨L￨IN￨O￨- tractability￨L￨NN￨O￨- –￨L￨:￨O￨- requiring￨L￨VBG￨O￨A essentially￨L￨RB￨O￨- an￨L￨DT￨O￨- interference-agnostic￨L￨JJ￨O￨- ALOHA￨U￨NNP￨O￨- multiple￨L￨JJ￨O￨- access￨L￨NN￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MAC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- protocol￨L￨NN￨O￨- that￨L￨WDT￨O￨- preserves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- independence￨L￨NN￨O￨- –￨L￨:￨O￨- and￨L￨CC￨O￨- optimality/generality￨L￨NN￨O￨- ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- more￨L￨JJR￨O￨- intellige￨L￨NN￨O￨- nt￨L￨NNS￨O￨- MAC￨U￨NNP￨ORGANIZATION￨- protocols￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- characterized￨L￨VBN￨O￨- despite￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- dependence￨L￨NN￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- requiring￨L￨VBG￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- general￨L￨JJ￨TITLE￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +K.￨U￨NNP￨PERSON￨- Ganti￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Date￨U￨NNP￨O￨- revised￨L￨VBD￨O￨- :￨L￨:￨O￨- August￨U￨NNP￨DATE￨- 15￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- 2￨L￨CD￨NUMBER￨- Considerable￨U￨JJ￨O￨- recent￨L￨JJ￨O￨- interest￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- user￨L￨NN￨O￨- geometry￨L￨NN￨O￨- –￨L￨:￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- locations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmitters￨L￨NNS￨O￨- and￨L￨CC￨O￨- receivers￨L￨NNS￨O￨- –￨L￨:￨O￨- has￨L￨VBZ￨O￨- on￨L￨IN￨O￨- fundamental￨L￨JJ￨O￨- metri￨L￨NN￨O￨- cs￨L￨NNS￨O￨- of￨L￨IN￨O￨- wireless￨L￨JJ￨O￨A network￨L￨NN￨O￨- performance￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- for￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- node￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- fading￨L￨JJ￨O￨A statistics￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- Ps￨U￨NNS￨O￨- ∼￨L￨VBP￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- ηκ￨L￨NN￨O￨- for￨L￨IN￨O￨- η￨L￨NN￨O￨- →￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- provide￨L￨VBP￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- γ￨L￨NN￨O￨- and￨L￨CC￨O￨- κ￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- outage￨L￨NN￨O￨- and￨L￨CC￨O￨- TC￨U￨NN￨ORGANIZATION￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- distributed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨ORGANIZATION￨- cluster￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- results￨L￨VBZ￨O￨- from￨L￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- clustering￨L￨NN￨O￨- applied￨L￨VBD￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨ORGANIZATION￨- point￨L￨NN￨O￨A process￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- marks￨L￨NNS￨O￨- in￨L￨IN￨O￨- epigenetic￨L￨JJ￨O￨- silencing￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stable￨L￨JJ￨O￨- bivalent￨L￨JJ￨O￨- chromatin￨L￨NN￨O￨- state￨L￨NN￨O￨- Swagatam￨U￨NNP￨ORGANIZATION￨- Mukhopadhyay￨U￨NNP￨ORGANIZATION￨- Cold￨U￨NNP￨ORGANIZATION￨- Spring￨U￨NNP￨ORGANIZATION￨- Harbor￨U￨NNP￨ORGANIZATION￨- Laboratory￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Cold￨U￨NNP￨O￨- Spring￨U￨NNP￨DATE￨- Harbor￨U￨NNP￨O￨- ,￨L￨,￨O￨- NY￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- USA￨U￨NNP￨ORGANIZATION￨- Anirvan￨U￨NNP￨ORGANIZATION￨- M.￨U￨NNP￨ORGANIZATION￨- Besides￨U￨IN￨O￨- the￨L￨DT￨O￨- silenced￨L￨VBN￨O￨- and￨L￨CC￨O￨- transcriptionally￨L￨RB￨O￨- active￨L￨JJ￨O￨A fate￨L￨NN￨O￨- of￨L￨IN￨O￨- chromatin￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- state￨L￨NN￨O￨- with￨L￨IN￨O￨- bivalent￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- active￨L￨JJ￨O￨- and￨L￨CC￨O￨- silencing￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- marks￨L￨NNS￨O￨- under￨L￨IN￨O￨- certain￨L￨JJ￨O￨- perturbations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- knock-out￨L￨JJ￨O￨- mutations￨L￨NNS￨O￨- ,￨L￨,￨O￨- inhibition￨L￨NN￨O￨- or￨L￨CC￨O￨- enhancement￨L￨NN￨O￨- of￨L￨IN￨O￨- enzymatic￨L￨JJ￨O￨- activity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- Sir￨U￨NNP￨O￨- protein￨L￨NN￨O￨- recruitment￨L￨NN￨O￨A ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- and￨L￨CC￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- silenced￨L￨VBN￨O￨- regions￨L￨NNS￨O￨- in￨L￨IN￨O￨- commonly-studied￨L￨JJ￨O￨- mutants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- sas2￨L￨NN￨O￨- ∆￨L￨NN￨O￨- ,￨L￨,￨O￨- dot1￨L￨NN￨O￨- ∆￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- illuminating￨L￨VBG￨O￨- the￨L￨DT￨O￨- controversial￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- Dot1￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- systems￨L￨NNS￨O￨- biology￨L￨NN￨O￨- of￨L￨IN￨O￨- yeast￨L￨NN￨O￨- silencing￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- standard￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- silencing￨L￨NN￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- feedback￨L￨NN￨O￨- ,￨L￨,￨O￨- mediated￨L￨VBN￨O￨- by￨L￨IN￨O￨- chromatin￨L￨NN￨O￨- modifications￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- deacetylation￨L￨NN￨O￨- of￨L￨IN￨O￨- histone￨L￨NN￨O￨- residues￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- enhanced￨L￨VBN￨O￨- recruitment￨L￨NN￨O￨A of￨L￨IN￨O￨- chromatin￨L￨NN￨O￨- modifiers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Silent￨U￨JJ￨O￨- Information￨U￨NN￨O￨- Regulator￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- silencing￨L￨NN￨O￨- in￨L￨IN￨O￨- budding￨L￨VBG￨O￨- yeast￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- epigenetics￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- contributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ordering￨L￨VBG￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- coverage￨L￨NN￨O￨A probability￨L￨NN￨O￨A and￨L￨CC￨O￨- per￨L￨IN￨O￨- user￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- closed￨L￨JJ￨O￨- form￨L￨NN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- BS￨U￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- considered￨L￨VBN￨O￨- techniques￨L￨NNS￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- novel￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- from￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- orders￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- upper￨L￨JJ￨O￨- bounds￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨O￨- BS￨U￨NNP￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- spectral￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ASE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- No.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 477￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 522￨L￨CD￨NUMBER￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.1214￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 13-AAP1000￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- VIRAL￨U￨JJ￨O￨- PROCESSES￨U￨NNS￨O￨- BY￨U￨IN￨O￨- RANDOM￨U￨NNP￨O￨- WALKS￨U￨VBZ￨O￨- ON￨U￨IN￨O￨- RANDOM￨U￨NNP￨O￨- REGULAR￨U￨NNP￨O￨- GRAPHS￨U￨NNP￨O￨- By￨U￨IN￨O￨- Mohammed￨U￨NNP￨PERSON￨- Abdullah1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Colin￨U￨NNP￨PERSON￨- Cooper￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Moez￨U￨NNP￨ORGANIZATION￨- Draief1￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Birmingham￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- King￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- Col￨U￨NNP￨O￨- lege￨L￨NN￨O￨- London￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Imperial￨U￨NNP￨ORGANIZATION￨- Col￨U￨NNP￨ORGANIZATION￨- lege￨L￨NN￨O￨- London￨U￨NNP￨CITY￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- carried￨L￨VBN￨O￨- by￨L￨IN￨O￨- k￨L￨NN￨O￨- particles￨L￨NNS￨O￨- making￨L￨VBG￨O￨- independent￨L￨JJ￨RELIGION￨- random￨L￨JJ￨O￨- walks￨L￨VBZ￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- regular￨L￨JJ￨O￨- graph￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- give￨L￨VBP￨O￨- an￨L￨DT￨O￨- edge-weighted￨L￨JJ￨O￨- graph￨L￨NN￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- standard￨L￨JJ￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- Erd˝os￨U￨NNS￨O￨- –￨L￨:￨O￨- R´enyi￨U￨NN￨O￨- random￨L￨JJ￨O￨A graphs￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- particle￨L￨NN￨O￨- set￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- give￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- thresholds￨L￨NNS￨O￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- subcritical￨L￨JJ￨O￨- regime￨L￨NN￨O￨- ,￨L￨,￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ln￨L￨NN￨O￨A k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- particles￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- similarity￨L￨NN￨O￨- between￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨A marketing￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- communications￨L￨NNS￨O￨- strategy￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- remain￨L￨VBP￨O￨- largely￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- marketing￨L￨NN￨O￨- specific￨L￨NN￨O￨- field￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SusceptibleInfected-Recovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨A marketing￨L￨NN￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- marketing￨L￨NN￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- message￨L￨NN￨O￨- is￨L￨VBZ￨O￨- viral￨L￨JJ￨O￨A when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- broadly￨L￨RB￨O￨- sent￨L￨VBN￨O￨- and￨L￨CC￨O￨- received￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- market￨L￨NN￨O￨- through￨L￨IN￨O￨- person-to-person￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Viral￨U￨JJ￨O￨- marketing￨L￨NN￨O￨- as￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A ,￨L￨,￨O￨- Proceedings￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 955￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Contagion￨U￨NN￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨- and￨L￨CC￨O￨- activity￨L￨NN￨O￨- driven￨L￨VBN￨O￨- coupling￨L￨NN￨O￨A networks￨L￨NNS￨O￨- Yanjun￨U￨NNP￨PERSON￨- Lei￨U￨NNP￨PERSON￨- 1,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Xin￨U￨NNP￨PERSON￨- Jiang2￨U￨NNP￨PERSON￨- ,3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ∗￨L￨CD￨NUMBER￨- Quantong￨U￨NNP￨O￨- Guo￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yifang￨U￨NNP￨PERSON￨- Ma1￨U￨NN￨O￨- ,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Meng￨U￨NNP￨O￨- Li2￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Zhiming￨U￨NNP￨O￨- Zheng1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- School￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mathematical￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Peking￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Beijing￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- 100871￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 2LMIB￨L￨NNP￨O￨- &￨L￨CC￨O￨- School￨U￨NNP￨O￨- of￨L￨IN￨O￨- Mathematics￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Systems￨U￨NNPS￨O￨- Science￨U￨NNP￨O￨- ,￨L￨,￨O￨- Beihang￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Beijing￨U￨NNP￨CITY￨- 100191￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- 3Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Engineering￨U￨NNP￨O￨- Sciences￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Applied￨U￨NNP￨O￨- Mathematics￨U￨NNP￨O￨- ,￨L￨,￨O￨- Northwestern￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Evanston￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- 4Center￨L￨NNP￨O￨- IL￨U￨NN￨STATE_OR_PROVINCE￨- 60208￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- USA￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Complex￨U￨JJ￨ORGANIZATION￨- Network￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Physics￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- Northeastern￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Boston￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- MA￨U￨NNP￨STATE_OR_PROVINCE￨- 02115￨L￨CD￨DATE￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Dated￨U￨NNP￨O￨- :￨L￨:￨O￨- December￨U￨NNP￨DATE￨- 8￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- are￨L￨VBP￨O￨- common￨L￨JJ￨O￨- coexistent￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- thresholds￨L￨NNS￨O￨- of￨L￨IN￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- on￨L￨IN￨O￨- SADC￨U￨NNP￨ORGANIZATION￨- both￨L￨CC￨O￨- analytically￨L￨RB￨O￨- and￨L￨CC￨O￨- numerically￨L￨RB￨O￨- with￨L￨IN￨O￨- various￨L￨JJ￨O￨- coupling￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- strong￨L￨JJ￨O￨- structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- or￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨- and￨L￨CC￨O￨- activity￨L￨NN￨O￨- driven￨L￨VBN￨O￨- coupling￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- SADC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- between￨L￨IN￨O￨- static￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- strong￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- weak￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Theoretical￨U￨JJ￨O￨- thresholds￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- SADC￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- both￨L￨DT￨O￨- recover￨L￨VB￨O￨- and￨L￨CC￨O￨- generalize￨L￨VB￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- in￨L￨IN￨O￨- static￨L￨JJ￨O￨A and￨L￨CC￨O￨- time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- static￨L￨JJ￨O￨A and￨L￨CC￨O￨- time-varying￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- ;￨L￨:￨O￨- Configuration￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- Branching￨U￨VBG￨O￨- process￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- 1.1￨L￨CD￨NUMBER￨- Background￨U￨NNP￨O￨- Models￨U￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- have￨L￨VBP￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- relatively￨L￨RB￨O￨- modest￨L￨JJ￨O￨- beginnings￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Bailey￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- rich￨L￨JJ￨O￨- domain￨L￨NN￨O￨- of￨L￨IN￨O￨- applicability￨L￨NN￨O￨- covering￨L￨VBG￨O￨A the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- spectrum￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- ,￨L￨,￨O￨- animal￨L￨NN￨O￨- and￨L￨CC￨O￨- plant￨L￨NN￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- informing￨L￨VBG￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- questions￨L￨NNS￨O￨- from￨L￨IN￨O￨- viral￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- policy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Heesterbeek￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- closed-form￨L￨JJ￨O￨- analytic￨L￨JJ￨O￨A expressions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- and￨L￨CC￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- write￨L￨VB￨O￨- down￨L￨RP￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- extinction￨L￨NN￨O￨- by￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- numerically￨L￨RB￨O￨- fast￨L￨RB￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- Monte￨U￨NNP￨LOCATION￨- Carlo￨U￨NNP￨LOCATION￨- simulation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- theoretical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- configuration￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- popular￨L￨JJ￨O￨- choice￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- specify￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- that￨L￨DT￨O￨- are￨L￨VBP￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- analytic￨L￨JJ￨O￨- results￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Molloy￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Reed￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- Newman￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- real-time￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Markovian￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- configuration￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A network￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- multitype￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨A equations￨L￨NNS￨O￨A that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- Asymptotic￨U￨JJ￨O￨- Behavior￨U￨NN￨O￨- of￨L￨IN￨O￨- Ultra-Densification￨U￨NNP￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- Bounded￨U￨JJ￨MISC￨- Dual-Slope￨U￨NN￨MISC￨- Path￨U￨NN￨MISC￨- Loss￨U￨NN￨MISC￨- Model￨U￨NNP￨TITLE￨- Yanpeng￨U￨NNP￨PERSON￨- Yang￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jihong￨U￨NNP￨LOCATION￨- Park￨U￨NNP￨LOCATION￨- †￨L￨NN￨O￨- and￨L￨CC￨O￨- Ki￨U￨NN￨ORGANIZATION￨- Won￨U￨NNP￨ORGANIZATION￨- Sung￨U￨NNP￨ORGANIZATION￨- KTH￨U￨NNP￨ORGANIZATION￨- Royal￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Technology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- Stockholm￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Sweden￨U￨NNP￨COUNTRY￨- E-mail￨U￨NN￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- †￨L￨SYM￨O￨- Dept.￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 7￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- densification￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- downlink￨L￨NN￨O￨- signal-to-interference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- coverage￨L￨NN￨O￨A probability￨L￨NN￨O￨A and￨L￨CC￨O￨- network￨L￨NN￨O￨- area￨L￨NN￨O￨- spectral￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ASE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- geometry￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- an￨L￨DT￨O￨- integral￨L￨JJ￨O￨- expression￨L￨NN￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- closed-form￨L￨JJ￨O￨- bounds￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨A probability￨L￨NN￨O￨A and￨L￨CC￨O￨- ASE￨U￨NN￨MISC￨- ,￨L￨,￨O￨- validated￨L￨VBN￨O￨- by￨L￨IN￨O￨- simulation￨L￨NN￨O￨- results￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- coverage￨L￨NN￨O￨A probability￨L￨NN￨O￨A and￨L￨CC￨O￨- ASE￨U￨NN￨O￨- have￨L￨VBP￨O￨- non-zero￨L￨JJ￨O￨- convergence￨L￨NN￨O￨- in￨L￨IN￨O￨- asymptotic￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- unless￨L￨IN￨O￨- UE￨U￨NN￨LOCATION￨- density￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- full￨L￨JJ￨O￨- load￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- sophisticated￨L￨JJ￨O￨- bounded￨L￨VBN￨O￨A dual-slope￨L￨JJ￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- practical￨L￨JJ￨O￨- user￨L￨NN￨O￨- equipment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- UE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- densities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- incorporated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- never￨L￨RB￨O￨- been￨L￨VBN￨O￨- jointly￨L￨RB￨O￨- considered￨L￨VBN￨O￨- before￨L￨IN￨O￨- .￨L￨.￨O￨- +Related￨U￨JJ￨O￨- Works￨U￨NNP￨O￨- and￨L￨CC￨O￨- Motivation￨U￨NNP￨O￨- the￨L￨DT￨O￨- scalability￨L￨NN￨O￨- a￨L￨DT￨O￨- of￨L￨IN￨O￨- co-SF￨L￨NN￨O￨- interference￨L￨NN￨O￨A ,￨L￨,￨O￨- inter-SF￨L￨JJ￨O￨- interference￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- In￨U￨IN￨O￨- general￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- LoRa￨U￨NNP￨LOCATION￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- :￨L￨:￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- unruly￨L￨JJ￨O￨- same￨L￨JJ￨O￨- channel￨L￨NN￨O￨- transmissions￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- SF￨U￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- restrict￨L￨VB￨O￨- the￨L￨DT￨O￨- scalability￨L￨NN￨O￨- in￨L￨IN￨O￨- plausible￨L￨JJ￨O￨- high-density￨L￨JJ￨O￨- deployments￨L￨NNS￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- desired￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- below￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- stems￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- imperfect￨L￨JJ￨O￨- orthogonality￨L￨NN￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- SFs￨U￨NNS￨O￨- and￨L￨CC￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissions￨L￨NNS￨O￨- from￨L￨IN￨O￨- different￨L￨JJ￨O￨- SFs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- completely￨L￨RB￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- adjacent￨L￨JJ￨O￨- SFs￨U￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- requiring￨L￨VBG￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- protection￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- duty￨L￨NN￨O￨- cycle￨L￨NN￨O￨- as￨L￨RB￨O￨- low￨L￨JJ￨O￨- as￨L￨IN￨O￨- 0.33￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- performance￨L￨NN￨O￨- under￨L￨IN￨O￨- co-SF￨L￨NN￨O￨- interference￨L￨NN￨O￨A alone￨L￨RB￨O￨- is￨L￨VBZ￨O￨- considerably￨L￨RB￨O￨- optimistic￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- inter-SF￨L￨JJ￨O￨- interference￨L￨NN￨O￨- unveils￨L￨VBZ￨O￨- a￨L￨DT￨O￨- further￨L￨JJ￨O￨- drop￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- 15￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- for￨L￨IN￨O￨- 1500￨L￨CD￨DATE￨- devices￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- LoRa￨U￨NN￨O￨- channel￨L￨NN￨O￨- .￨L￨.￨O￨- +Index￨U￨NNP￨O￨- Terms￨U￨NNS￨O￨- —￨L￨:￨O￨- Low￨U￨JJ￨O￨- power￨L￨NN￨O￨- wide￨L￨JJ￨O￨- area￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- LoRaWAN￨U￨NN￨O￨- ,￨L￨,￨O￨- interference￨L￨NN￨O￨A analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- fading￨L￨JJ￨O￨- channels￨L￨NNS￨O￨- IN￨U￨IN￨O￨- TRODUC￨U￨NN￨MISC￨- T￨U￨NN￨O￨- ION￨U￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single-cell￨L￨JJ￨O￨- LoRa￨U￨NN￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- interference￨L￨NN￨O￨A among￨L￨IN￨O￨- transmissions￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- SF￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- co-SF￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- different￨L￨JJ￨O￨- SFs￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- inter-SF￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- surprising￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- phenomenon￨L￨NN￨O￨- :￨L￨:￨O￨- on￨L￨IN￨O￨- trees￨L￨NNS￨O￨- which￨L￨WDT￨O￨- grow￨L￨VBP￨O￨A faster￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- line￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- estimator￨L￨NN￨O￨- always￨L￨RB￨O￨- has￨L￨VBZ￨O￨- non-trivial￨L￨JJ￨O￨- detection￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- on￨L￨IN￨O￨- trees￨L￨NNS￨O￨- that￨L￨WDT￨O￨- grow￨L￨VBP￨O￨- like￨L￨IN￨O￨- a￨L￨DT￨O￨- line￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- probability￨L￨NN￨O￨- will￨L￨MD￨O￨- go￨L￨VB￨O￨- to￨L￨TO￨O￨- 0￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- grows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- essence￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- situations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- and￨L￨CC￨O￨- prevent￨L￨VB￨O￨- 1￨L￨CD￨NUMBER￨- these￨L￨DT￨O￨- network￨L￨NN￨O￨- risks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- limited￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- rumor￨L￨NN￨O￨- infected￨L￨JJ￨O￨- ’￨L￨''￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- simulations￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- rumor￨L￨NN￨O￨A centrality￨L￨NN￨O￨- outperforms￨L￨VBZ￨O￨- distance￨L￨NN￨O￨- centrality￨L￨NN￨O￨- in￨L￨IN￨O￨- finding￨L￨VBG￨O￨- rumor￨L￨NN￨O￨- sources￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- tree-like￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- on￨L￨IN￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A center￨L￨NN￨O￨- and￨L￨CC￨O￨- distance￨L￨NN￨O￨- center￨L￨NN￨O￨- are￨L￨VBP￨O￨- equivalent￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- on￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- differ￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- model￨L￨VBP￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- variant￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- popular￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- construct￨L￨VB￨O￨- an￨L￨DT￨O￨- estimator￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- source￨L￨NN￨O￨- .￨L￨.￨O￨- +Rectal￨U￨JJ￨O￨- tumour￨L￨NN￨O￨- segmentation￨L￨NN￨O￨- in￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- contrast-enhanced￨L￨JJ￨O￨- MRI￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- DCE-MRI￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenging￨L￨JJ￨O￨- task￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- automated￨L￨VBN￨O￨- and￨L￨CC￨O￨- consistent￨L￨JJ￨O￨- method￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- highly￨L￨RB￨O￨- desirable￨L￨JJ￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- patient￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- from￨L￨IN￨O￨- tissue￨L￨NN￨O￨- contrast￨L￨NN￨O￨- enhancement￨L￨NN￨O￨A characteristics￨L￨NNS￨O￨- –￨L￨:￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- routine￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- practice￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- framework￨L￨NN￨O￨- is￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- automate￨L￨VB￨O￨- DCE-MRI￨U￨NN￨O￨- tumour￨L￨NN￨O￨- segmentation￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- :￨L￨:￨O￨- perfusion-supervoxels￨L￨NNS￨O￨- to￨L￨TO￨O￨- over-segment￨L￨NN￨O￨- and￨L￨CC￨O￨- classify￨L￨VB￨O￨- DCE-MRI￨U￨NN￨O￨- volumes￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- contrast￨L￨NN￨O￨- enhancement￨L￨NN￨O￨A characteristics￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- pieces-of-parts￨L￨NNS￨O￨- graphical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- adds￨L￨VBZ￨O￨- global￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- anatomic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- constraints￨L￨NNS￨O￨- that￨L￨WDT￨O￨- further￨L￨RB￨O￨- refine￨L￨VBP￨O￨- the￨L￨DT￨O￨- supervoxel￨L￨NN￨O￨- components￨L￨NNS￨O￨- that￨L￨WDT￨O￨- comprise￨L￨VBP￨O￨- the￨L￨DT￨O￨- tumour￨L￨NN￨O￨- .￨L￨.￨O￨- +Creating￨U￨VBG￨O￨- a￨L￨DT￨O￨- binary￨L￨JJ￨O￨- tumour￨L￨NN￨O￨- segmentation￨L￨NN￨O￨- ,￨L￨,￨O￨- 21￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 23￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- segmented￨L￨JJ￨O￨- correctly￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- median￨L￨JJ￨O￨- Dice￨U￨NN￨O￨- similarity￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DSC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- 0.63￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- inter-rater￨L￨JJ￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- challenging￨L￨JJ￨O￨- task￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- framework￨L￨NN￨O￨- achieves￨L￨VBZ￨O￨- promising￨L￨JJ￨O￨A results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- underexplored￨L￨JJ￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- rectal￨L￨JJ￨O￨- tumour￨L￨NN￨O￨- segmentation￨L￨NN￨O￨- in￨L￨IN￨O￨- DCE-MRI￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- DCE-MRI￨U￨NN￨O￨- and￨L￨CC￨O￨- supervoxel￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- segmentation￨L￨NN￨O￨- problems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Parts-based￨U￨JJ￨MISC￨- graphical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- supervoxel￨L￨NN￨O￨- ,￨L￨,￨O￨- classification￨L￨NN￨O￨A ,￨L￨,￨O￨- segmentation￨L￨NN￨O￨- ,￨L￨,￨O￨- DCE-MRI￨U￨NN￨O￨- ,￨L￨,￨O￨- rectal￨L￨JJ￨O￨- tumour￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- key￨L￨JJ￨O￨- intermediate￨L￨JJ￨O￨- step￨L￨NN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- distance￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- lead￨L￨VBP￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- tractable￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- enable￨L￨VBP￨O￨- the￨L￨DT￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- classical￨L￨JJ￨O￨- and￨L￨CC￨O￨- currently￨L￨RB￨DATE￨- trending￨L￨VBG￨O￨- problems￨L￨NNS￨O￨- in￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- transmitting￨L￨VBG￨O￨A nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- confined￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- area￨L￨NN￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- from￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- prior￨L￨JJ￨O￨- works￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- BPP￨U￨NNP￨ORGANIZATION￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- serving￨L￨VBG￨O￨- transmitter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TX￨U￨NNP￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- located￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- distance￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- reference￨L￨NN￨O￨- receiver￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- general￨L￨JJ￨TITLE￨- TX-selection￨U￨NN￨O￨- policies￨L￨NNS￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- uniform￨L￨JJ￨O￨- TX-selection￨U￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- serving￨L￨VBG￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- chosen￨L￨VBN￨O￨- uniformly￨L￨RB￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- amongst￨L￨IN￨O￨- transmitting￨L￨VBG￨O￨A nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- k-closest￨L￨JJS￨O￨- TX-selection￨U￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- serving￨L￨VBG￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- k￨L￨NN￨O￨- th￨L￨DT￨O￨- closest￨L￨JJS￨O￨- node￨L￨NN￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- transmitting￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- reference￨L￨NN￨O￨- receiver￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- the￨L￨DT￨O￨- so￨L￨RB￨O￨- called￨L￨VBN￨O￨- nearest￨L￨JJS￨O￨- neighbor￨L￨NN￨O￨- connectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +Modeling￨U￨VBG￨O￨- the￨L￨DT￨O￨- locations￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- binomial￨L￨JJ￨O￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BPP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrarily-located￨L￨JJ￨O￨- reference￨L￨NN￨O￨- receiver￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- wireless￨L￨JJ￨O￨A network￨L￨NN￨O￨- .￨L￨.￨O￨- +Index￨U￨NNP￨ORGANIZATION￨- Terms￨U￨NNS￨ORGANIZATION￨- Binomial￨U￨JJ￨ORGANIZATION￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- finite￨L￨JJ￨O￨- wireless￨L￨JJ￨O￨A network￨L￨NN￨O￨- ,￨L￨,￨O￨- k-coverage￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- optimal￨L￨JJ￨O￨- cache￨L￨NN￨O￨- placement￨L￨NN￨O￨- ,￨L￨,￨O￨- selection￨L￨NN￨O￨- combining￨L￨VBG￨O￨- scheme￨L￨NN￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- geometry￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- warning￨L￨NN￨O￨- correlated￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- her￨L￨PRP$￨O￨- updating￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- prior￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- decision￨L￨NN￨O￨A is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- analyst￨L￨NN￨TITLE￨- 's￨L￨POS￨O￨- observation￨L￨NN￨O￨- and￨L￨CC￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- signals￨L￨NNS￨O￨- ,￨L￨,￨O￨- independent￨L￨JJ￨RELIGION￨- or￨L￨CC￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- article￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- this￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- perception￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- preferences￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- principal￨L￨JJ￨TITLE￨- decision￨L￨NN￨O￨A maker￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- analyst￨L￨NN￨TITLE￨- 's￨L￨POS￨O￨- dynamic￨L￨JJ￨O￨- warning￨L￨NN￨O￨- decision￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- warning￨L￨NN￨O￨- decision￨L￨NN￨O￨A also￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- analyst￨L￨NN￨TITLE￨- 's￨L￨POS￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- crisis￨L￨NN￨O￨- '￨L￨POS￨O￨- lead￨L￨JJ￨O￨- time￨L￨NN￨O￨- needed￨L￨VBN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- response￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- crucial￨L￨JJ￨O￨- property￨L￨NN￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- ,￨L￨,￨O￨- white￨L￨JJ￨O￨A cells￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- cells￨L￨NNS￨O￨- containing￨L￨VBG￨O￨- white￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- only￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- will￨L￨MD￨O￨- never￨L￨RB￨O￨- be￨L￨VB￨O￨- adjacent￨L￨JJ￨O￨- to￨L￨TO￨O￨- black￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- always￨L￨RB￨O￨- a￨L￨DT￨O￨- red￨L￨JJ￨O￨- wave￨L￨NN￨O￨- working￨L￨VBG￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- black￨L￨JJ￨O￨- region￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- white￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- make￨L￨VBP￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- grid￨L￨NN￨O￨- partition￨L￨NN￨O￨- of￨L￨IN￨O￨- S￨U￨NN￨O￨- into￨L￨IN￨O￨- cells￨L￨NNS￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- Θ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- define￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- states￨L￨NNS￨O￨- a￨L￨DT￨O￨- cell￨L￨NN￨O￨- can￨L￨MD￨O￨- assume￨L￨VB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- red￨L￨JJ￨O￨- ,￨L￨,￨O￨- white￨L￨JJ￨O￨A and￨L￨CC￨O￨- black￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- inside￨L￨IN￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- (￨L￨-LRB-￨O￨- parsimonious￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- k-flooding￨L￨NN￨O￨- protocol￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- white￨L￨JJ￨O￨A agent￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- informed￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- will￨L￨MD￨O￨- remain￨L￨VB￨O￨- red￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- so￨L￨RB￨O￨- active￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- k￨L￨NN￨O￨- time￨L￨NN￨O￨- steps￨L￨NNS￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- ,￨L￨,￨O￨- every￨L￨DT￨O￨- agent￨L￨NN￨O￨- performs￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- step￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- and￨L￨CC￨O￨- every￨L￨DT￨O￨- red￨L￨JJ￨O￨- agent￨L￨NN￨O￨- informs￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- infects￨L￨VBZ￨O￨- )￨L￨-RRB-￨O￨- all￨L￨DT￨O￨- white￨L￨JJ￨O￨A agents￨L￨NNS￨O￨- lying￨L￨VBG￨O￨- within￨L￨IN￨O￨- distance￨L￨NN￨O￨- R￨U￨NN￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- Geometric￨U￨JJ￨MISC￨- Random-Walk￨U￨NNP￨MISC￨- Model￨U￨NNP￨TITLE￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- agents￨L￨NNS￨O￨A perform￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- random￨L￨JJ￨O￨- walks￨L￨VBZ￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- bounded￨L￨VBN￨O￨- plane￨L￨NN￨O￨- region￨L￨NN￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- presented￨L￨VBN￨O￨- above￨L￨IN￨O￨- clearly￨L￨RB￨O￨- illustrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- ranking￨L￨JJ￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- epidemic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- regime￨L￨NN￨O￨A of￨L￨IN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spreading￨L￨NN￨O￨A on￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- ranked￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- epidemic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- scattering￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- points￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- plot￨L￨NN￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- vividly￨L￨RB￨O￨- demonstrates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ranking￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- regime￨L￨NN￨O￨A .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- originates￨L￨VBZ￨O￨- in￨L￨IN￨O￨- node￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- position￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- node￨L￨NN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- respective￨L￨JJ￨O￨- stars￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- regime￨L￨NN￨O￨A of￨L￨IN￨O￨- sufficiently￨L￨RB￨O￨- large￨L￨JJ￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Speci￨U￨NNP￨O￨- fically￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- set-up￨L￨NN￨O￨- :￨L￨:￨O￨- There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- physical￨L￨JJ￨O￨A information￨L￨NN￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- information￨L￨NN￨O￨- spreads￨L￨VBZ￨O￨- amongst￨L￨IN￨O￨- people￨L￨NNS￨O￨- through￨L￨IN￨O￨- conventional￨L￨JJ￨O￨- communication￨L￨NN￨O￨- media￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- face-to-face￨L￨JJ￨O￨- communication￨L￨NN￨O￨- ,￨L￨,￨O￨- phone￨L￨NN￨O￨- calls￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- conjoint￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- physical￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- information￨L￨NN￨O￨- spreads￨L￨VBZ￨O￨- via￨L￨IN￨O￨- web￨L￨NN￨O￨- sites￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Facebook￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Twitter￨U￨NNP￨O￨- ,￨L￨,￨O￨- FriendFeed￨U￨NNP￨O￨- ,￨L￨,￨O￨- YouTube￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- piecewise￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- sequential￨L￨JJ￨O￨A importance￨L￨NN￨O￨- sampling/resampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- pcSIR￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- aims￨L￨VBZ￨O￨- at￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- particle￨L￨NN￨O￨- filters￨L￨NNS￨O￨- by￨L￨IN￨O￨- approximating￨L￨VBG￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- mixture￨L￨NN￨O￨- of￨L￨IN￨O￨- uniform￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- over￨L￨IN￨O￨- pre-defined￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- or￨L￨CC￨O￨- bins￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- upper￨L￨JJ￨O￨- bounds￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- approximation￨L￨NN￨O￨- error￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- so-obtained￨L￨JJ￨O￨- piecewise￨L￨NN￨O￨- constant￨L￨JJ￨O￨- function￨L￨NN￨O￨- representation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- analyze￨L￨VB￨O￨- how￨L￨WRB￨O￨- bin￨L￨NN￨O￨- size￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- tracking￨L￨NN￨O￨A accuracy￨L￨NN￨O￨- and￨L￨CC￨O￨- runtime￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- pcSIR￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- computational￨L￨JJ￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- while￨L￨IN￨O￨- providing￨L￨VBG￨O￨- tracking￨L￨NN￨O￨A accuracy￨L￨NN￨O￨- comparable￨L￨JJ￨O￨- to￨L￨TO￨O￨- standard￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- .￨L￨.￨O￨- +Further￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- numerically￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- pcSIR￨L￨NN￨O￨- approximation￨L￨NN￨O￨- error￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- sequential￨L￨JJ￨O￨A importance￨L￨NN￨O￨- sampling/resampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- bin￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- decreased￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- idea￨L￨NN￨O￨- behind￨L￨IN￨O￨- pcSIR￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- group￨L￨NN￨O￨- particles￨L￨NNS￨O￨A in￨L￨IN￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- creating￨L￨VBG￨O￨- bins￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- each￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- particles￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- representative￨L￨NN￨TITLE￨- particle￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- consider￨L￨VB￨O￨- a￨L￨DT￨O￨- single-type￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- and￨L￨CC￨O￨- identically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- iid￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- lifetimes￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- variable￨L￨JJ￨O￨- Q￨U￨NNP￨O￨- having￨L￨VBG￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- specified￨L￨VBD￨O￨- ,￨L￨,￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- whilst￨L￨IN￨O￨- alive￨L￨JJ￨O￨- ,￨L￨,￨O￨- give￨L￨VB￨O￨- birth￨L￨NN￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- Poisson￨U￨NNP￨PERSON￨- point￨L￨NN￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- continuous-time￨L￨JJ￨O￨- birth-death￨L￨JJ￨O￨- type￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- and￨L￨CC￨O￨- identically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- lifetimes￨L￨NNS￨O￨- ,￨L￨,￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- variable￨L￨JJ￨O￨- Q￨U￨NNP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- E￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- Q￨U￨NNP￨O￨- ]￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨A rate￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- currently￨L￨RB￨DATE￨- in￨L￨IN￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- has￨L￨VBZ￨O￨- size￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- n￨L￨NN￨O￨- is￨L￨VBZ￨O￨- α￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formally￨L￨RB￨O￨- introduce￨L￨VB￨O￨- the￨L￨DT￨O￨- generic￨L￨JJ￨O￨- birth-death￨L￨JJ￨O￨- type￨L￨NN￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- birth￨L￨NN￨O￨A rate￨L￨NN￨O￨- α￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- n￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- introduce￨L￨VB￨O￨- regeneration￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- α￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- λn￨L￨NN￨O￨- being￨L￨VBG￨O￨- a￨L￨DT￨O￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- λn￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- N￨U￨NN￨O￨- which￨L￨WDT￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- →￨L￨NN￨O￨- infective￨L￨JJ￨O￨- →￨L￨NN￨O￨- susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneously￨L￨RB￨O￨- mixing￨L￨VBG￨O￨- community￨L￨NN￨O￨- of￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- as￨L￨IN￨O￨- Khintchine￨U￨NNP￨PERSON￨- foresaw￨L￨VBD￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- approximate￨L￨JJ￨O￨- ergodicity￨L￨NN￨O￨- holds￨L￨VBZ￨O￨- good￨L￨JJ￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- measurable￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- having￨L￨VBG￨O￨- particular￨L￨JJ￨O￨- physical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- degrees￨L￨NNS￨O￨A of￨L￨IN￨O￨- freedom￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- auto-correlation￨L￨NN￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- auto-correlation￨L￨NN￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- realisations￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- without￨L￨IN￨O￨- justification￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ergodic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Khintchine￨U￨NNP￨PERSON￨- made￨L￨VBD￨O￨- some￨L￨DT￨O￨- visionary￨L￨JJ￨O￨- conjectures￨L￨NNS￨O￨- about￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- degrees￨L￨NNS￨O￨A of￨L￨IN￨O￨- freedom￨L￨NN￨O￨- which￨L￨WDT￨O￨- would￨L￨MD￨O￨- justify￨L￨VB￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- ergodicity￨L￨NN￨O￨- ,￨L￨,￨O￨- approximately￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- conclusions￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- Hamiltonian￨U￨JJ￨IDEOLOGY￨- H￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- |￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- |￨L￨SYM￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- |￨L￨SYM￨O￨- q￨L￨SYM￨O￨- |￨L￨SYM￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- p￨L￨NN￨O￨- and￨L￨CC￨O￨- q￨L￨NN￨O￨- are￨L￨VBP￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1-dimensional￨L￨JJ￨O￨- vectors￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- collection￨L￨NN￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- uncoupled￨L￨VBD￨O￨- harmonic￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- oscillators￨L￨NNS￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- since￨L￨IN￨O￨- ˙p￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- ∂￨L￨NN￨O￨- H￨U￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- and￨L￨CC￨O￨- ˙q￨L￨NN￨O￨- =￨L￨JJ￨O￨- ∂￨L￨NN￨O￨- H￨U￨NN￨O￨- ∂￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A if￨L￨IN￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- q￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- generate￨L￨VBP￨O￨- batting￨L￨NN￨O￨- partnership￨L￨NN￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BPN￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨A teams￨L￨NNS￨O￨- and￨L￨CC￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- clustering￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- average￨L￨JJ￨O￨- shortest￨L￨JJS￨O￨- path￨L￨NN￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- them￨L￨PRP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- Erd￨U￨NNP￨MISC￨- ¨￨L￨SYM￨MISC￨- os-R￨L￨NN￨MISC￨- ´￨L￨''￨O￨- enyi￨L￨FW￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +6￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Advances￨U￨NNS￨O￨- in￨L￨IN￨O￨- Complex￨U￨JJ￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- c￨L￨NN￨ORGANIZATION￨- World￨U￨NNP￨ORGANIZATION￨- Scientific￨U￨NNP￨ORGANIZATION￨- Publishing￨U￨NNP￨ORGANIZATION￨- Company￨U￨NNP￨ORGANIZATION￨- Complex￨U￨JJ￨ORGANIZATION￨- Network￨U￨NNP￨ORGANIZATION￨- Analysis￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- Cricket￨U￨NNP￨O￨- :￨L￨:￨O￨- Community￨U￨NNP￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- player￨L￨NN￨O￨- ’s￨L￨POS￨O￨- role￨L￨NN￨O￨- and￨L￨CC￨O￨- performance￨L￨NN￨O￨A index￨L￨NN￨O￨- Satyam￨U￨NNP￨ORGANIZATION￨- Mukherjee￨U￨NNP￨ORGANIZATION￨- Kel￨U￨NNP￨ORGANIZATION￨- logg￨L￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Management￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Northwestern￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- Evanston￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- IL￨U￨NN￨ORGANIZATION￨- United￨U￨NNP￨ORGANIZATION￨- States￨U￨NNPS￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- America￨U￨NNP￨ORGANIZATION￨- This￨U￨DT￨O￨- paper￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- interaction￨L￨NN￨O￨- within￨L￨IN￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- sport￨L￨NN￨O￨- teams.We￨L￨NN￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- of￨L￨IN￨O￨- batsmen￨L￨NNS￨O￨- in￨L￨IN￨O￨- International￨U￨NNP￨O￨- Cricket￨U￨NNP￨O￨- matches￨L￨VBZ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extend￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨A ,￨L￨,￨O￨- relative￨L￨JJ￨O￨- importance￨L￨NN￨O￨- and￨L￨CC￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- removing￨L￨VBG￨O￨- a￨L￨DT￨O￨- player￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- team￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- scores￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- observe￨L￨VBP￨O￨- that￨L￨IN￨O￨- Sir￨U￨NNP￨O￨- DG￨U￨NNS￨PERSON￨- Bradman￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- batsman￨L￨NN￨O￨- in￨L￨IN￨O￨- Cricket￨U￨NNP￨O￨- history￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- occupy￨L￨VB￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- position￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- −￨L￨IN￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- connector￨L￨NN￨O￨- hub￨L￨NN￨O￨A .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- further￨L￨JJ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- decoupled￨L￨JJ￨O￨- association￨L￨NN￨O￨A —￨L￨:￨O￨- employing￨L￨VBG￨O￨- differing￨L￨VBG￨O￨- association￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- uplink￨L￨NN￨O￨- and￨L￨CC￨O￨- downlink￨L￨NN￨O￨- —￨L￨:￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- significant￨L￨JJ￨O￨- improvement￨L￨NN￨O￨- in￨L￨IN￨O￨- joint￨L￨JJ￨O￨- uplink-downlink￨L￨JJ￨O￨- rate￨L￨NN￨O￨- coverage￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- coupled￨L￨JJ￨O￨- association￨L￨NN￨O￨- in￨L￨IN￨O￨- HCNs￨U￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- accurate￨L￨JJ￨O￨- and￨L￨CC￨O￨- tractable￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- uplink￨L￨NN￨O￨- SINR￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- rate￨L￨NN￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- multi-tier￨L￨JJ￨O￨- HCN￨U￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- association￨L￨NN￨O￨A rules￨L￨NNS￨O￨- and￨L￨CC￨O￨- power￨L￨NN￨O￨- control￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- sharp￨L￨JJ￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- downlink￨L￨NN￨O￨- ,￨L￨,￨O￨- minimum￨L￨JJ￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- association￨L￨NN￨O￨A is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- for￨L￨IN￨O￨- uplink￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- minimum￨L￨JJ￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- association￨L￨NN￨O￨A and￨L￨CC￨O￨- full￨L￨JJ￨O￨- channel￨L￨NN￨O￨- inversion￨L￨NN￨O￨- ,￨L￨,￨O￨- uplink￨L￨NN￨O￨- SIR￨U￨NN￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- invariant￨L￨JJ￨O￨- of￨L￨IN￨O￨- infrastructure￨L￨NN￨O￨- density￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- formulating￨L￨VBG￨O￨- and￨L￨CC￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- utility￨L￨NN￨O￨- maximization￨L￨NN￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- user￨L￨NN￨O￨- association￨L￨NN￨O￨- bias￨L￨NN￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- spectrum￨L￨NN￨O￨A partition￨L￨NN￨O￨- ratios￨L￨NNS￨O￨- are￨L￨VBP￨O￨- analytically￨L￨RB￨O￨- obtained￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- multi-tier￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- uplink￨L￨NN￨O￨- under￨L￨IN￨O￨- spectrum￨L￨NN￨O￨A sharing￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- all￨L￨DT￨O￨- tiers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- target￨L￨NN￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- distance-based￨L￨JJ￨O￨- user￨L￨NN￨O￨- association￨L￨NN￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- path￨L￨NN￨O￨- loss￨L￨NN￨O￨- and￨L￨CC￨O￨- power￨L￨NN￨O￨- control￨L￨NN￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- joint￨L￨JJ￨O￨- user￨L￨NN￨O￨- association￨L￨NN￨O￨- and￨L￨CC￨O￨- spectrum￨L￨NN￨O￨A allocation￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- for￨L￨IN￨O￨- multi-tier￨L￨JJ￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- HetNets￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- downlink￨L￨NN￨O￨- and￨L￨CC￨O￨- uplink￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- interference-limited￨L￨JJ￨O￨- regime￨L￨NN￨O￨- .￨L￨.￨O￨- +Users￨U￨NNS￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- base-stations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- BSs￨U￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- biased￨L￨VBN￨O￨- downlink￨L￨NN￨O￨A received￨L￨VBD￨O￨- power￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- mapping￨L￨VBG￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- eigenvalue￨L￨NN￨O￨A problem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- transition￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvalue￨L￨NN￨O￨- spectra￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- supra-contact￨L￨JJ￨O￨- tensor￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- spreading￨L￨NN￨O￨- rates￨L￨NNS￨O￨- :￨L￨:￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- layer￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- comparable￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- rate￨L￨NN￨O￨- across￨L￨IN￨O￨- layers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- spectra￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- layer￨L￨NN￨TITLE￨- merge￨L￨VBP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- between￨L￨IN￨O￨- layers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- results￨L￨NNS￨O￨- from￨L￨IN￨O￨- extensive￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- considering￨L￨VBG￨O￨- multiplex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- scale-free￨L￨NN￨O￨- and￨L￨CC￨O￨- scale-rich￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- ,￨L￨,￨O￨- computing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- respective￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- approach￨L￨NN￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- inverse￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- leading￨L￨VBG￨O￨- eigenvalue￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- result￨L￨NN￨O￨- was￨L￨VBD￨O￨- also￨L￨RB￨O￨- obtained￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- ap￨L￨NN￨O￨- -￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- e￨L￨SYM￨O￨- D￨U￨NN￨O￨- 6￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- h￨L￨NN￨O￨- p￨L￨NN￨O￨- -￨L￨:￨O￨- c￨L￨NN￨O￨- o￨L￨NN￨O￨- s￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vast￨L￨JJ￨O￨- ma￨L￨NN￨O￨- jority￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- works￨L￨NNS￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- single-layered￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- real￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- interconnectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- multilayer￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- multilayer￨L￨JJ￨O￨A network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- fourth-order￨L￨JJ￨O￨- adjacency￨L￨NN￨O￨- tensor￨L￨NN￨O￨- M￨U￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- Rn￨U￨NN￨O￨- ×￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- ×￨L￨NN￨O￨- m￨L￨NN￨O￨- ×￨L￨NN￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- represent￨L￨VB￨O￨- several￨L￨JJ￨O￨- relations￨L￨NNS￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- α￨L￨NN￨O￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- Aα￨U￨NN￨O￨- β￨L￨NN￨O￨- Aγ￨U￨NN￨O￨- β￨L￨NN￨O￨- Aγ￨U￨NN￨O￨- m￨L￨NN￨O￨- m￨L￨NN￨O￨- ˜h￨L￨NN￨O￨- ,￨L￨,￨O￨- ˜k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- M￨U￨NN￨O￨- α˜δ￨L￨NN￨O￨- β￨L￨NN￨O￨- ˜γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- =￨L￨JJ￨O￨- n￨L￨NN￨O￨- C￨U￨NN￨O￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ˜h˜k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- ˜δ￨L￨NN￨O￨- ˜γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ˜h˜k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- wij￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ˜h˜k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- α˜δ￨L￨NN￨O￨- β￨L￨NN￨O￨- ˜γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ij￨L￨NN￨O￨- ˜h˜k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ˜h￨L￨NN￨O￨- ,￨L￨,￨O￨- ˜k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- i￨L￨LS￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ˜δ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ˜h˜k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨CD￨NUMBER￨- Rm￨U￨NN￨O￨- ×￨L￨NN￨O￨- m￨L￨NN￨O￨- and￨L￨CC￨O￨- E￨U￨NN￨O￨- α˜δ￨L￨NN￨O￨- β￨L￨NN￨O￨- ˜γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ij￨L￨NN￨O￨- ˜h˜k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨CD￨NUMBER￨- Rn￨U￨NN￨O￨- ×￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- ×￨L￨NN￨O￨- m￨L￨NN￨O￨- ×￨L￨NN￨O￨- m￨L￨NN￨O￨- where￨L￨WRB￨O￨- E￨U￨NN￨O￨- ˜γ￨L￨NN￨O￨- indicate￨L￨VBP￨O￨- the￨L￨DT￨O￨- tensor￨L￨NN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- respective￨L￨JJ￨O￨- canonical￨L￨JJ￨O￨- basis￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- rigourously￨L￨RB￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bus￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- ma￨L￨NN￨O￨- jor￨L￨NN￨O￨- Indian￨U￨JJ￨NATIONALITY￨- cities￨L￨NNS￨O￨- as￨L￨IN￨O￨- graphs￨L￨NNS￨O￨- in￨L￨IN￨O￨- Land￨U￨NNP￨O￨- P￨U￨NN￨O￨- -￨L￨:￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- tools￨L￨NNS￨O￨- from￨L￨IN￨O￨- network￨L￨NN￨O￨A science￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- common￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- small-world￨L￨JJ￨O￨- property￨L￨NN￨O￨- and￨L￨CC￨O￨- heavy￨L￨JJ￨O￨- tails￨L￨NNS￨O￨- in￨L￨IN￨O￨- degree-distribution￨L￨JJ￨O￨- plots￨L￨NNS￨O￨- are￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨A studied￨L￨VBN￨O￨A .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- analysis￨L￨NN￨O￨- further￨L￨RB￨O￨- reveals￨L￨VBZ￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- spectrum￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨A topologies￨L￨NNS￨O￨A arising￨L￨VBG￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- preferential￨L￨JJ￨O￨- and￨L￨CC￨O￨- random￨L￨JJ￨O￨- attachment￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- extend￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨A using￨L￨VBG￨O￨- SI￨U￨NNP￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- Complex￨U￨JJ￨O￨- networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- Power-laws￨U￨NNS￨MISC￨- ,￨L￨,￨O￨- Self-similarity￨U￨NN￨O￨- ,￨L￨,￨O￨- Small-world￨U￨JJ￨MISC￨- phenomenon￨L￨NN￨O￨- ,￨L￨,￨O￨- Transportation￨U￨NNP￨ORGANIZATION￨- networks￨L￨NNS￨ORGANIZATION￨- 5￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- e￨L￨SYM￨O￨- D￨U￨NN￨O￨- 8￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- h￨L￨NN￨O￨- p￨L￨NN￨O￨- -￨L￨:￨O￨- c￨L￨NN￨O￨- o￨L￨NN￨O￨- s￨L￨NNS￨O￨- .￨L￨.￨O￨- +Delay-Optimal￨U￨NNP￨ORGANIZATION￨- Biased￨U￨NNP￨ORGANIZATION￨- User￨U￨NN￨ORGANIZATION￨- Association￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨ORGANIZATION￨- Heterogeneous￨U￨JJ￨ORGANIZATION￨- Networks￨U￨NNP￨ORGANIZATION￨- Fancheng￨U￨NNP￨ORGANIZATION￨- Kong￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Xinghua￨U￨NNP￨PERSON￨- Sun￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Member￨U￨NNP￨O￨- ,￨L￨,￨O￨- IEEE￨U￨NNP￨O￨- ,￨L￨,￨O￨- Victor￨U￨NNP￨ORGANIZATION￨- C.￨U￨NNP￨ORGANIZATION￨- 1￨L￨CD￨DATE￨- 0￨L￨CD￨DATE￨- 7￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- :￨L￨:￨O￨- v￨L￨LS￨O￨- i￨L￨FW￨O￨- X￨U￨NN￨O￨- r￨L￨NN￨O￨- a￨L￨DT￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- In￨U￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- HetNets￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- load￨L￨NN￨O￨- balancing￨L￨NN￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- tiers￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- effectively￨L￨RB￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- biased￨L￨VBN￨O￨A user￨L￨NN￨O￨- association￨L￨NN￨O￨- scheme￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- user￨L￨NN￨O￨- chooses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- associate￨L￨VB￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- base￨L￨NN￨O￨- station￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- biased￨L￨VBN￨O￨- received￨L￨VBD￨O￨- power￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨A limit￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- real-time￨L￨JJ￨O￨- service￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- by￨L￨IN￨O￨- properly￨L￨RB￨O￨- tuning￨L￨NN￨O￨- the￨L￨DT￨O￨- biasing￨L￨VBG￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- tier￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- further￨L￨JJ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- mean￨L￨VB￨O￨- queuing￨L￨VBG￨O￨- delay￨L￨NN￨O￨A might￨L￨MD￨O￨- be￨L￨VB￨O￨- improved￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- deterioration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- signal-to-interference￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- indicates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- performance￨L￨NN￨O￨- tradeoff￨L￨NN￨O￨- between￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-real-time￨L￨JJ￨O￨- traffic￨L￨NN￨O￨- in￨L￨IN￨O￨- HetNets￨U￨NNS￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- that￨L￨DT￨O￨- basis￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- mean￨L￨VB￨O￨- queuing￨L￨VBG￨O￨- delay￨L￨NN￨O￨A .￨L￨.￨O￨- +Uplink￨U￨NNP￨O￨- Performance￨U￨NNP￨O￨- Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Drone￨U￨NNP￨O￨- Cell￨U￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Random￨U￨JJ￨MISC￨- Field￨U￨NN￨MISC￨- of￨L￨IN￨MISC￨- Ground￨U￨NN￨MISC￨- Interferers￨U￨NNP￨MISC￨- Mohammad￨U￨NNP￨PERSON￨- Mahdi￨U￨NNP￨PERSON￨- Azari1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Fernando￨U￨NNP￨PERSON￨- Rosas2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Alessandro￨U￨NNP￨PERSON￨- Chiumento1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Amir￨U￨NNP￨PERSON￨- Ligata4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Sofie￨U￨NNP￨O￨- Pollin1￨U￨NN￨O￨- 1Department￨L￨NN￨O￨- of￨L￨IN￨O￨- Electrical￨U￨JJ￨O￨- Engineering￨U￨NNP￨O￨- ,￨L￨,￨O￨- KU￨U￨NNP￨LOCATION￨- Leuven￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Belgium￨U￨NNP￨COUNTRY￨- 2￨L￨CD￨NUMBER￨- Centre￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Complexity￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Mathematics￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Imperial￨U￨NNP￨ORGANIZATION￨- College￨U￨NNP￨ORGANIZATION￨- London￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- 3￨L￨NNP￨NUMBER￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Electrical￨U￨JJ￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Electronic￨U￨JJ￨ORGANIZATION￨- Engineering￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Imperial￨U￨NNP￨ORGANIZATION￨- College￨U￨NNP￨ORGANIZATION￨- London￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- 4Motive￨L￨NNP￨O￨- Customer￨U￨NN￨ORGANIZATION￨- Experience￨U￨NN￨ORGANIZATION￨- Solutions￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- Applications￨U￨NNS￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Analytics￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Nokia￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Belgium￨U￨NNP￨COUNTRY￨- Email￨U￨VB￨O￨- :￨L￨:￨O￨- Abstract￨U￨NNP￨O￨- —￨L￨:￨O￨- Aerial￨U￨JJ￨O￨- base￨L￨NN￨O￨A stations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- promising￨L￨JJ￨O￨- technology￨L￨NN￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- capabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- communication￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- this￨L￨DT￨O￨- issue￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- interference￨L￨NN￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- coexisting￨L￨VBG￨O￨- ground￨L￨NN￨O￨A networks￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- aerial￨L￨JJ￨O￨- link￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- uplink￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- aerial￨L￨JJ￨O￨- cell￨L￨NN￨O￨- served￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- drone￨L￨NN￨O￨- base￨L￨NN￨O￨- station￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- coverage￨L￨NN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- drone￨L￨NN￨O￨- base￨L￨NN￨O￨A station￨L￨NN￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- a￨L￨DT￨O￨- promising￨L￨JJ￨O￨- technology￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- properly￨L￨RB￨O￨- dimensioned￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- given￨L￨VBN￨O￨- density￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interferers￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- considering￨L￨VBG￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- ground￨L￨NN￨O￨A interferers￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- characterize￨L￨VBP￨O￨- the￨L￨DT￨O￨- aggregate￨L￨JJ￨O￨- interference￨L￨NN￨O￨- experienced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- drone￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- drone￨L￨NN￨O￨- obtains￨L￨VBZ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- line-of-sight￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LoS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- high￨L￨JJ￨O￨- altitudes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- counteracted￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- vulnerability￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- interference￨L￨NN￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- ground￨L￨NN￨O￨A .￨L￨.￨O￨- +An￨U￨DT￨O￨- investigation￨L￨NN￨O￨- was￨L￨VBD￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- if￨L￨IN￨O￨- XDR￨U￨NN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- occurring￨L￨VBG￨O￨- elsewhere￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- province￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- hypotheses￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- rise￨L￨NN￨O￨- in￨L￨IN￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- view￨L￨NN￨O￨- to￨L￨TO￨O￨- developing￨L￨VBG￨O￨- a￨L￨DT￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- MDR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- multi-drug￨L￨JJ￨O￨- resistant￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- XDR￨U￨NN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- province￨L￨NN￨O￨- and￨L￨CC￨O￨- elsewhere￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- worst￨L￨JJS￨O￨- affected￨L￨VBN￨O￨- districts￨L￨NNS￨O￨- were￨L￨VBD￨O￨- uMzinyathi￨L￨NN￨O￨- where￨L￨WRB￨O￨- 226￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 4.1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- 5522￨L￨CD￨NUMBER￨- notified￨L￨VBN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- MDR￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- 120￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 53￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- extensively￨L￨RB￨O￨- drug￨L￨NN￨O￨A resistant￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- XDR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- uMkhanyakude￨L￨NN￨O￨- where￨L￨WRB￨O￨- 337￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 4.8￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- 6991￨L￨CD￨NUMBER￨- notified￨L￨VBN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- MDR￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- only￨L￨RB￨O￨- four￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- XDR￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- districts￨L￨NNS￨O￨A were￨L￨VBD￨O￨- compiled￨L￨VBN￨O￨- and￨L￨CC￨O￨- culture￨L￨NN￨O￨- taking￨L￨VBG￨O￨- practices￨L￨NNS￨O￨- were￨L￨VBD￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- MDR￨U￨NN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keywords￨U￨NNS￨O￨- :￨L￨:￨O￨- prion￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- rabbit￨L￨NN￨O￨- prion￨L￨NN￨O￨- protein￨L￨NN￨O￨A wild-type￨L￨JJ￨O￨- and￨L￨CC￨O￨- mutants￨L￨NNS￨O￨- ;￨L￨:￨O￨- X-ray￨U￨NN￨O￨- and￨L￨CC￨O￨- NMR￨U￨NN￨O￨- structures￨L￨NNS￨O￨- ;￨L￨:￨O￨- molecular￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- study￨L￨NN￨O￨- ;￨L￨:￨O￨- loop￨L￨NN￨O￨- β2-α2￨L￨NN￨O￨- ;￨L￨:￨O￨- salt￨L￨NN￨O￨- bridge￨L￨NN￨O￨- ;￨L￨:￨O￨- drug￨L￨NN￨O￨- target￨L￨NN￨O￨- Abbreviations￨U￨NNS￨O￨- :￨L￨:￨O￨- PrPC￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- soluble￨L￨JJ￨O￨- normal￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- prion￨L￨NN￨O￨- protein￨L￨NN￨O￨- ;￨L￨:￨O￨- RaPrPC￨U￨NN￨O￨- ,￨L￨,￨O￨- rabbit￨L￨NN￨O￨- PrPC￨U￨NN￨O￨- ;￨L￨:￨O￨- PrPSc￨U￨NN￨O￨- ,￨L￨,￨O￨- insoluble￨L￨JJ￨O￨- abnormally￨L￨RB￨O￨- folded￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- prions￨L￨NNS￨O￨- ;￨L￨:￨O￨- BSE￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- bovine￨L￨JJ￨O￨- spongiform￨L￨NN￨O￨- encephalopathy￨L￨NN￨O￨- ;￨L￨:￨O￨- TSE￨U￨NNP￨O￨- ,￨L￨,￨O￨- Transmissible￨U￨JJ￨MISC￨- Spongiform￨U￨NNP￨MISC￨- Encephalopathy￨U￨NNP￨MISC￨- ;￨L￨:￨MISC￨- CJD￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Creutzfeldt-Jakob￨U￨NNP￨MISC￨- Disease￨U￨NNP￨CAUSE_OF_DEATH￨- ;￨L￨:￨MISC￨- vCJD￨L￨NN￨MISC￨- ,￨L￨,￨O￨- variant￨L￨JJ￨O￨- Creutzfeldt-Jakob￨U￨NN￨MISC￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- SB￨U￨NN￨O￨- ,￨L￨,￨O￨- salt￨L￨NN￨O￨- bridge￨L￨NN￨O￨- ;￨L￨:￨O￨- HB￨U￨NN￨O￨- ,￨L￨,￨O￨- hydrogen￨L￨NN￨O￨- bond￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- saPMCA￨L￨NN￨O￨- ,￨L￨,￨O￨- serial￨L￨NN￨O￨- automated￨L￨VBN￨O￨- protein￨L￨NN￨O￨- misfolding￨L￨NN￨O￨- cyclic￨L￨JJ￨O￨- amplification￨L￨NN￨O￨- ;￨L￨:￨O￨- PDB￨U￨NNP￨ORGANIZATION￨- Bank￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- protein￨L￨NN￨O￨- data￨L￨NNS￨O￨- bank￨L￨NN￨O￨- ;￨L￨:￨O￨- H1￨U￨NN￨O￨- or￨L￨CC￨O￨- α1￨L￨NN￨O￨- ,￨L￨,￨O￨- α-Helix￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- H2￨U￨NN￨O￨- or￨L￨CC￨O￨- α2￨L￨NN￨O￨- ,￨L￨,￨O￨- α-Helix2￨L￨NN￨O￨- ;￨L￨:￨O￨- H3￨U￨NN￨O￨- or￨L￨CC￨O￨- α3￨L￨NN￨O￨- ,￨L￨,￨O￨- α-Helix￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- β1￨L￨NN￨O￨- ,￨L￨,￨O￨- β-strand￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- β2￨L￨NN￨O￨- ,￨L￨,￨O￨- β-strand￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- MD￨U￨NN￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- Molecular￨U￨JJ￨ORGANIZATION￨- Dynamics￨U￨NNPS￨ORGANIZATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- MD￨U￨NN￨STATE_OR_PROVINCE￨- simulation￨L￨NN￨O￨- materials￨L￨NNS￨O￨- and￨L￨CC￨O￨- MD￨U￨NN￨STATE_OR_PROVINCE￨- reproducible￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- X-ray￨U￨NN￨O￨- and￨L￨CC￨O￨- NMR￨U￨NN￨O￨- structures￨L￨NNS￨O￨- of￨L￨IN￨O￨- RaPrPC￨U￨NN￨O￨- wild-type￨L￨JJ￨O￨- are￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- in￨L￨IN￨O￨- next￨L￨JJ￨O￨- section￨L￨NN￨O￨- ,￨L￨,￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- discussion￨L￨NN￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- MD￨U￨NN￨STATE_OR_PROVINCE￨- trajectory￨L￨NN￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SB￨U￨NN￨O￨- between￨L￨IN￨O￨- ASP177￨U￨NN￨O￨- and￨L￨CC￨O￨- ARG163￨U￨NN￨O￨- linking￨L￨VBG￨O￨- the￨L￨DT￨O￨- β2-α2￨L￨NN￨O￨- loop￨L￨NN￨O￨A and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- discussions￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- NMR￨U￨NN￨O￨- structure￨L￨NN￨O￨- RaPrPC￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 124-228￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- temperature￨L￨NN￨O￨A is￨L￨VBZ￨O￨- 298￨L￨CD￨NUMBER￨- K￨U￨NN￨O￨- ,￨L￨,￨O￨- pH￨L￨NN￨COUNTRY￨- value￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 4.5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- pressure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 1￨L￨CD￨NUMBER￨- ATM￨U￨NNP￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- X-ray￨U￨NN￨O￨- structure￨L￨NN￨O￨- RaPrPC￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 126￨L￨CD￨NUMBER￨- -￨L￨:￨O￨- 230￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- resolution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 1.60￨L￨CD￨NUMBER￨- Å￨U￨NN￨O￨- ,￨L￨,￨O￨- R-value￨U￨NN￨O￨- is￨L￨VBZ￨O￨- 0.161￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- R-free￨U￨NN￨O￨- is￨L￨VBZ￨O￨- 0.218￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- temperature￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 100￨L￨CD￨NUMBER￨- K￨U￨NN￨O￨- ,￨L￨,￨O￨- pH￨L￨NN￨COUNTRY￨- value￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 6.5￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- ,￨L￨,￨O￨- possibly￨L￨RB￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- pH￨L￨NN￨COUNTRY￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- X-ray￨U￨NN￨O￨- structure￨L￨NN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- observe￨L￨VB￨O￨- the￨L￨DT￨O￨- SB￨U￨NN￨O￨- Asp177-Arg163￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- O-N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- NMR￨U￨NN￨O￨- structure￨L￨NN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- controls￨L￨NNS￨O￨- and￨L￨CC￨O￨- present￨L￨JJ￨DATE￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- Erd￨U￨NNP￨MISC￨- ˝os￨L￨SYM￨MISC￨- -￨L￨:￨O￨- R￨U￨NN￨O￨- ´￨L￨''￨O￨- enyi￨L￨NN￨O￨A and￨L￨CC￨O￨- scale￨L￨NN￨O￨- free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- more￨L￨JJR￨O￨- resource￨L￨NN￨O￨- is￨L￨VBZ￨O￨- allocated￨L￨VBN￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- scale￨L￨NN￨O￨- free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- but￨L￨CC￨O￨- medium￨L￨NN￨O￨- degree￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- Erd￨U￨NNP￨O￨- ˝os￨L￨SYM￨O￨- -￨L￨:￨O￨- R￨U￨NN￨O￨- ´￨L￨''￨O￨- enyi￨L￨FW￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- solution￨L￨NN￨O￨- optimally￨L￨RB￨O￨- allocates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- scarce￨L￨JJ￨O￨- resource￨L￨NN￨O￨A over￨L￨IN￨O￨- the￨L￨DT￨O￨- campaign￨L￨NN￨O￨- duration￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- class￨L￨NN￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Direct￨U￨JJ￨O￨- recruit￨L￨VB￨O￨- ment￨L￨NN￨O￨- and￨L￨CC￨O￨- word-of-mouth￨L￨NN￨O￨- incentives￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- accelerate￨L￨VB￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- controls￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- We￨U￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨A problem￨L￨NN￨O￨A of￨L￨IN￨O￨- maximizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- information￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +—￨L￨:￨O￨- We￨U￨PRP￨O￨- model￨L￨VBP￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- formulate￨L￨VB￨O￨- a￨L￨DT￨O￨- problem￨L￨NN￨O￨- to￨L￨TO￨O￨- jointly￨L￨RB￨O￨- optimize￨L￨VB￨O￨- seeds￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- varying￨L￨VBG￨O￨- resource￨L￨NN￨O￨A allocation￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- duration￨L￨NN￨O￨- campa￨L￨NN￨O￨- ign￨L￨NN￨O￨- running￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- formulation￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- pagerank￨L￨NN￨O￨- ,￨L￨,￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- closeness￨L￨NN￨O￨- and￨L￨CC￨O￨- betweenness￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- maximizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- message￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- an￨L￨DT￨O￨- objective￨L￨JJ￨O￨- function￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reward￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- informed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- deadline￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- aggregated￨L￨JJ￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- applying￨L￨VBG￨O￨- controls￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- advertising￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- campaign￨L￨NN￨O￨A duration￨L￨NN￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- grouped￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- centrality￨L￨NN￨O￨- measure￨L￨NN￨O￨- and￨L￨CC￨O￨- each￨L￨DT￨O￨- group￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- fluenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- externa￨L￨NN￨O￨- l￨L￨NN￨O￨- control￨L￨NN￨O￨- function￨L￨NN￨O￨- —￨L￨:￨O￨- implemented￨L￨VBN￨O￨- through￨L￨IN￨O￨- advertisements￨L￨NNS￨O￨- —￨L￨:￨O￨- du￨L￨NNP￨O￨- ring￨L￨NN￨O￨- the￨L￨DT￨O￨- campaign￨L￨NN￨O￨A duration￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- targets￨L￨NNS￨O￨- central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- resource￨L￨NN￨O￨A is￨L￨VBZ￨O￨- scarce￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- non-central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- targeted￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- resource￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- abundance￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rapid￨L￨JJ￨O￨- decline￨L￨NN￨O￨- in￨L￨IN￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- analytical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- and￨L￨CC￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- and￨L￨CC￨O￨- synthetic￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- within￨L￨IN￨O￨- 3￨L￨LS￨NUMBER￨- -￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- generations￨L￨NNS￨O￨- contrasts￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- expectation￨L￨NN￨O￨- of￨L￨IN￨O￨- invariant￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- obeying￨L￨VBG￨O￨- exponential￨L￨JJ￨O￨A growth￨L￨NN￨O￨A .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- growth￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- growth￨L￨NN￨O￨- profile￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- explicit￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- .￨L￨.￨O￨- +Existing￨U￨VBG￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- generally￨L￨RB￨O￨- assume￨L￨VB￨O￨- exponential￨L￨JJ￨O￨A growth￨L￨NN￨O￨A in￨L￨IN￨O￨- case￨L￨NN￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- few￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- generations￨L￨NNS￨O￨- ,￨L￨,￨O￨- before￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- depletion￨L￨NN￨O￨- sets￨L￨NNS￨O￨- in￨L￨IN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- both￨L￨DT￨O￨- readily￨L￨RB￨O￨- available￨L￨JJ￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- valuable￨L￨JJ￨O￨- information￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- and￨L￨CC￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- and￨L￨CC￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨O￨A .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- links￨L￨VBZ￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- unobserved￨L￨JJ￨O￨- influenza￨L￨NN￨O￨A transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- severe￨L￨JJ￨O￨- influenza￨L￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- admission￨L￨NN￨O￨- to￨L￨TO￨O￨- intensive￨L￨JJ￨O￨A care￨L￨NN￨O￨- given￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- monitoring￨L￨VBG￨O￨- purposes￨L￨NNS￨O￨- ,￨L￨,￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- severe￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨O￨A in￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- are￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- weekly￨L￨JJ￨SET￨- to￨L￨TO￨O￨- Public￨U￨NNP￨LOCATION￨- Health￨U￨NNP￨LOCATION￨- England￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- admissions￨L￨NNS￨O￨- data￨L￨NNS￨O￨- allows￨L￨VBZ￨O￨- reconstruction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨A transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- revealing￨L￨VBG￨O￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- noticeable￨L￨JJ￨O￨- eff￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Benchmarking￨U￨VBG￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- against￨L￨IN￨O￨- in￨L￨FW￨O￨- vivo￨L￨FW￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨- experimental￨L￨JJ￨O￨- programme￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- bacteria￨L￨NNS￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- improving￨L￨VBG￨O￨- treatment￨L￨NN￨O￨- outcome￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- predicts￨L￨VBZ￨O￨- that￨L￨IN￨O￨- inhibitor￨L￨NN￨O￨- treatment￨L￨NN￨O￨A can￨L￨MD￨O￨- not￨L￨RB￨O￨- eliminate￨L￨VB￨O￨- the￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨- burden￨L￨NN￨O￨- when￨L￨WRB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- isolation￨L￨NN￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- regular￨L￨JJ￨O￨- or￨L￨CC￨O￨- continuous￨L￨JJ￨O￨- debridement￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exudate￨L￨NN￨O￨- ,￨L￨,￨O￨- elimination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- theoretically￨L￨RB￨O￨- possible￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- and￨L￨CC￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- anti-adhesion￨L￨JJ￨O￨- therapy￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- burn￨L￨VBP￨O￨- wounds￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- improving￨L￨VBG￨O￨- treatment￨L￨NN￨O￨- outcome￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨- burden￨L￨NN￨O￨- ,￨L￨,￨O￨- inhibitor￨L￨NN￨O￨- treatment￨L￨NN￨O￨A operates￨L￨VBZ￨O￨- both￨L￨CC￨O￨- by￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- bacteria￨L￨NNS￨O￨- from￨L￨IN￨O￨- binding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epithelium￨L￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- flux￨L￨NN￨O￨- of￨L￨IN￨O￨- daughter￨L￨NN￨O￨- cells￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epithelium￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- exudate￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- formulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- inhibitor￨L￨NN￨O￨- treatment￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- Pseudomonas￨U￨FW￨O￨- aeruginosa￨L￨FW￨O￨- burn￨L￨VBP￨O￨- wound￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- rat￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨JJ￨ORDINAL￨- order￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- found￨L￨VBN￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- few￨L￨JJ￨O￨- short￨L￨JJ￨O￨- but￨L￨CC￨O￨- many￨L￨JJ￨O￨- long￨L￨JJ￨O￨- loops￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- No￨U￨DT￨O￨- first￨L￨NN￨O￨- order￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- on￨L￨IN￨O￨- trees￨L￨NNS￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- 2-d￨L￨JJ￨O￨- lattices￨L￨NNS￨O￨A with￨L￨IN￨O￨- local￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- They￨U￨PRP￨O￨- do￨L￨VBP￨O￨- exist￨L￨VB￨O￨- on￨L￨IN￨O￨- Erd˝os￨U￨NNS￨O￨- -￨L￨:￨O￨- R´enyi￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ER￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- lattices￨L￨NNS￨O￨- with￨L￨IN￨O￨- d￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- 2-d￨L￨JJ￨O￨- lattices￨L￨NNS￨O￨- with￨L￨IN￨O￨- sufficiently￨L￨JJ￨O￨- long-ranged￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- On￨U￨IN￨O￨- 3-d￨L￨JJ￨O￨- lattices￨L￨NNS￨O￨- with￨L￨IN￨O￨- local￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- ;￨L￨:￨O￨- d-dimensional￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- While￨U￨IN￨O￨- single￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- seeds￨L￨NNS￨O￨- can￨L￨MD￨O￨- always￨L￨RB￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- infinite￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- regular￨L￨JJ￨O￨- lattices￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- ER￨U￨NN￨O￨- networks￨L￨NNS￨O￨- one￨L￨CD￨NUMBER￨- sometimes￨L￨RB￨O￨- needs￨L￨VBZ￨O￨- finite￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- In￨U￨IN￨O￨- all￨L￨DT￨O￨- cases￨L￨NNS￨O￨- the￨L￨DT￨O￨- first￨L￨NN￨O￨- order￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- actually￨L￨RB￨O￨- “￨L￨``￨O￨- hybrid￨L￨NN￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- they￨L￨PRP￨O￨- display￨L￨VBP￨O￨- also￨L￨RB￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- scaling￨L￨VBG￨O￨- usually￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- second￨L￨JJ￨ORDINAL￨- order￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- basic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- show￨L￨VBP￨O￨- continuous￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- second￨L￨JJ￨ORDINAL￨- order￨L￨NN￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- transitions￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- starting￨L￨VBG￨O￨- ∗￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infinitesimal￨L￨JJ￨O￨- “￨L￨``￨O￨- seed￨L￨NN￨O￨- ”￨L￨''￨O￨- density￨L￨NN￨O￨- just￨L￨RB￨O￨- above￨L￨IN￨O￨- threshold￨L￨NN￨O￨- never￨L￨RB￨O￨- reaches￨L￨VBZ￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- an￨L￨DT￨O￨- infinitesimal￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- spite￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- first￨L￨NN￨O￨- order￨L￨NN￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨A were￨L￨VBD￨O￨- found￨L￨VBN￨O￨- there￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- only￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- finite￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- evaluate￨L￨VBP￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- traditional￨L￨JJ￨O￨- information￨L￨NN￨O￨A propagation￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- S￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- R￨U￨NN￨O￨- or￨L￨CC￨O￨- I￨U￨PRP￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- perform￨L￨VB￨O￨- analysis￨L￨NN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- artificial￨L￨JJ￨O￨- and￨L￨CC￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- +￨L￨CC￨O￨- ,￨L￨,￨O￨- Facebook￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- roads￨L￨NNS￨O￨- map￨L￨VBP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- curiosity￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨A spreading￨L￨NN￨O￨A in￨L￨IN￨O￨- all￨L￨DT￨O￨- networks￨L￨NNS￨O￨- as￨L￨IN￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- without￨L￨IN￨O￨- curiosity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- increase￨L￨NN￨O￨- is￨L￨VBZ￨O￨- larger￨L￨JJR￨O￨- in￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- the￨L￨DT￨O￨- establishment￨L￨NN￨O￨- of￨L￨IN￨O￨- Network￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNPS￨ORGANIZATION￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- more￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- for￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A as￨L￨IN￨O￨- social￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- processes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- proposes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- information￨L￨NN￨O￨A propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- curiosity￨L￨NN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- evolves￨L￨VBZ￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Mathematically￨U￨RB￨O￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- just￨L￨RB￨O￨- the￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- λ￨L￨NN￨O￨- must￨L￨MD￨O￨- satisfy￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- gamma-distributed￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨A periods￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- further￨L￨JJ￨O￨- details￨L￨NNS￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- Protocol￨U￨NNP￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- and￨L￨CC￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- modify￨L￨VBP￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- still￨L￨RB￨O￨- incorporating￨L￨VBG￨O￨- gamma-distributed￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨A periods￨L￨NNS￨O￨A .￨L￨.￨O￨- +While￨U￨IN￨O￨- mathematically￨L￨RB￨O￨- very￨L￨RB￨O￨- convenient￨L￨JJ￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- assumption￨L￨NN￨O￨- gives￨L￨VBZ￨O￨- rise￨L￨NN￨O￨- to￨L￨TO￨O￨- exponentially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨A periods￨L￨NNS￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- epidemiologically￨L￨RB￨O￨- unrealistic￨L￨JJ￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- unrealistic￨L￨JJ￨O￨- yet￨L￨RB￨O￨- almost￨L￨RB￨O￨- ubiquitous￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- embedded￨L￨VBN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨A periods￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- are￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1A￨L￨NN￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- some￨L￨DT￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- latent￨L￨JJ￨O￨A and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- threat￨L￨NN￨O￨- posed￨L￨VBN￨O￨- by￨L￨IN￨O￨- deliberate￨L￨JJ￨O￨- release￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- foot￨L￨NN￨O￨- and￨L￨CC￨O￨- mouth￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- FMD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- containing￨L￨VBG￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- the￨L￨DT￨O￨- preface￨L￨NN￨O￨- :￨L￨:￨O￨- "￨L￨``￨O￨- This￨U￨DT￨O￨- volume￨L￨NN￨O￨- brings￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- selected￨L￨VBN￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- experts￨L￨NNS￨O￨- from￨L￨IN￨O￨- various￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- begun￨L￨VBN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- tackle￨L￨VB￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- challenges￨L￨NNS￨O￨- raised￨L￨VBN￨O￨- in￨L￨IN￨O￨- biosurveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- agroterrorism￨L￨NN￨O￨- ,￨L￨,￨O￨- bioterror￨L￨NN￨O￨- response￨L￨NN￨O￨- logistics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deliberate￨L￨JJ￨O￨- release￨L￨NN￨O￨A of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- forces￨L￨NNS￨O￨- that￨L￨WDT￨O￨- maintain￨L￨VBP￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- terror￨L￨NN￨O￨- .￨L￨.￨O￨- "￨L￨''￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- introductory￨L￨JJ￨O￨- preface￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- book￨L￨NN￨O￨- and￨L￨CC￨O￨- ten￨L￨CD￨NUMBER￨- chapters￨L￨NNS￨O￨- presenting￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- bioterrorism￨L￨NN￨O￨- The￨U￨DT￨O￨- 1st￨L￨JJ￨ORDINAL￨- chapter￨L￨NN￨O￨- ,￨L￨,￨O￨- "￨L￨``￨O￨- Challenges￨U￨NNS￨O￨- for￨L￨IN￨O￨- Discrete￨U￨NNP￨O￨- Mathematics￨U￨NNP￨O￨- and￨L￨CC￨O￨- Theoretical￨U￨NNP￨O￨- Computer￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Defense￨U￨NN￨O￨- against￨L￨IN￨O￨- Bioterrorism￨U￨NNP￨MISC￨- "￨L￨''￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- overview￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- approaches￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- mathematics￨L￨NN￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- computer￨L￨NN￨O￨A science￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- bioterrorism￨L￨NN￨O￨- issues￨L￨NNS￨O￨- .￨L￨.￨O￨- +"￨L￨``￨O￨- These￨U￨DT￨O￨- tools￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- seem￨L￨VBP￨O￨- very￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- to￨L￨TO￨O￨- epidemiological￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- defense￨L￨NN￨O￨A against￨L￨IN￨O￨- bioterrorism￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- very￨L￨RB￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- among￨L￨IN￨O￨- those￨L￨DT￨O￨- working￨L￨VBG￨O￨- on￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- "￨L￨''￨O￨- +The￨U￨DT￨O￨- ultimate￨L￨JJ￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- STEM￨U￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- platform￨L￨NN￨O￨- powerful￨L￨JJ￨O￨A enough￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- modelling￨L￨VBG￨O￨- scenarios￨L￨NNS￨O￨- and￨L￨CC￨O￨- extensible￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- researchers￨L￨NNS￨O￨- to￨L￨TO￨O￨- combine￨L￨VB￨O￨- their￨L￨PRP$￨O￨- efforts￨L￨NNS￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- exceptionally￨L￨RB￨O￨- good￨L￨JJ￨O￨- models.Prior￨L￨NN￨O￨- to￨L￨TO￨O￨- STEM￨U￨NN￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- previous￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- systems￨L￨NNS￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- being￨L￨VBG￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- "￨L￨``￨O￨- well￨L￨RB￨O￨- mixed￨L￨JJ￨O￨- "￨L￨''￨O￨- and￨L￨CC￨O￨- either￨L￨CC￨O￨- not￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- zero￨L￨CD￨NUMBER￨- dimensional￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- geographically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- manner￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ultimate￨L￨JJ￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- STEM￨U￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- platform￨L￨NN￨O￨- powerful￨L￨JJ￨O￨A enough￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- modelling￨L￨VBG￨O￨- scenarios￨L￨NNS￨O￨- and￨L￨CC￨O￨- extensible￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- researchers￨L￨NNS￨O￨- to￨L￨TO￨O￨- combine￨L￨VB￨O￨- their￨L￨PRP$￨O￨- efforts￨L￨NNS￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- exceptionally￨L￨RB￨O￨- good￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methodology￨U￨NN￨O￨- Open￨U￨VB￨O￨- Access￨U￨NN￨O￨- An￨U￨DT￨O￨- extensible￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨A systemDaniel￨L￨NNP￨O￨- Alexander￨U￨NNP￨O￨- Ford1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- James￨U￨NNP￨PERSON￨- H￨U￨NNP￨PERSON￨- Kaufman1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Iris￨U￨NNP￨O￨- Eiron1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 5:4￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Ford￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2006Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- This￨U￨DT￨O￨- paper￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Spatiotemporal￨U￨NNP￨O￨- Epidemiological￨U￨NNP￨O￨- Modeller￨U￨NNP￨TITLE￨- (￨L￨-LRB-￨O￨- STEM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- extensible￨L￨JJ￨O￨- software￨L￨NN￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- affecting￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- geographically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- locations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- STEM￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- powerful￨L￨JJ￨O￨A modelling￨L￨NN￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- researchers￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- scenarios￨L￨NNS￨O￨- with￨L￨IN￨O￨- unmixed￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- uniformly￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- multiple￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- that￨L￨DT￨O￨- are￨L￨VBP￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- allows￨L￨VBZ￨O￨- simulated￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- multiple￨L￨JJ￨O￨A population￨L￨NN￨O￨- types￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Humans￨U￨NNS￨O￨- and￨L￨CC￨O￨- Ducks￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- being￨L￨VBG￨O￨- simultaneously￨L￨RB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Software￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- An￨U￨DT￨O￨- object￨L￨NN￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- hypothetical￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- –￨L￨:￨O￨- EpiFlexBrian￨U￨JJ￨O￨- Hanley1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 3:32￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Hanley￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2006Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 09￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- EpiFlex￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- flexible￨L￨JJ￨O￨- ,￨L￨,￨O￨- easy￨L￨JJ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- computer￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- computer￨L￨NN￨O￨- ,￨L￨,￨O￨- intended￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- operated￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- user￨L￨NN￨O￨- who￨L￨WP￨O￨- need￨L￨VBP￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- expert￨L￨NN￨O￨- .￨L￨.￨O￨- +EpiFlex￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- evaluated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- results￨L￨NNS￨O￨- from￨L￨IN￨O￨- modeling￨L￨NN￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- comparing￨L￨VBG￨O￨- them￨L￨PRP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- .￨L￨.￨O￨- +EpiFlex￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- object-oriented￨L￨JJ￨O￨- Monte￨U￨NNP￨LOCATION￨- Carlo￨U￨NNP￨LOCATION￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- allocating￨L￨VBG￨O￨- entities￨L￨NNS￨O￨- to￨L￨TO￨O￨- correspond￨L￨VB￨O￨- to￨L￨TO￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- vectors￨L￨NNS￨O￨- ,￨L￨,￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- locations￨L￨NNS￨O￨A that￨L￨WDT￨O￨- hosts￨L￨NNS￨O￨- may￨L￨MD￨O￨- inhabit￨L￨VB￨O￨- .￨L￨.￨O￨- +EpiFlex￨U￨NNP￨O￨- defines￨L￨VBZ￨O￨- eight￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- contact￨L￨NN￨O￨- types￨L￨NNS￨O￨A available￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Contacts￨U￨NNS￨O￨- occur￨L￨VBP￨O￨- inside￨L￨IN￨O￨- locations￨L￨NNS￨O￨A within￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- strategy￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- limited￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- failure￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- to￨L￨TO￨O￨- yield￨L￨VB￨O￨- adequate￨L￨JJ￨O￨- protection￨L￨NN￨O￨- for￨L￨IN￨O￨- high-risk￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- lesser￨L￨JJR￨O￨- roles￨L￨NNS￨O￨- played￨L￨VBN￨O￨- by￨L￨IN￨O￨- infants￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- elderly￨L￨JJ￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- —￨L￨:￨O￨- they￨L￨PRP￨O￨- typically￨L￨RB￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- introduce￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- into￨L￨IN￨O￨- households￨L￨NNS￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- social￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- realistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- urban￨L￨JJ￨O￨- setting￨L￨NN￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- mortality-based￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- target￨L￨VBP￨O￨A high-risk￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- morbidity-based￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- target￨L￨VBP￨O￨- demographics￨L￨NNS￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2005￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- shortage￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨ORGANIZATION￨- States￨U￨NNPS￨ORGANIZATION￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- restricted￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- most￨L￨RBS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- hospitalization￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- —￨L￨:￨O￨- healthy￨L￨JJ￨O￨- infants￨L￨NNS￨O￨A ,￨L￨,￨O￨- elderly￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- chronic￨L￨JJ￨O￨- illnesses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- contains￨L￨VBZ￨O￨- undirected￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reflect￨L￨VBP￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨A of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- either￨L￨DT￨O￨- direction￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- directed￨L￨VBD￨O￨- edges￨L￨NNS￨O￨- that￨L￨WDT￨O￨- indicate￨L￨VBP￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- person￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- reverse￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- tools￨L￨NNS￨O￨- from￨L￨IN￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A epidemiology￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- spectrum￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- when￨L￨WRB￨O￨- vaccine￨L￨NN￨O￨- supplies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- .￨L￨.￨O￨- +Contact￨U￨NN￨O￨- tracing￨L￨VBG￨O￨A will￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- earlier￨L￨JJR￨O￨- prevention￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- quarantine￨L￨NN￨O￨- of￨L￨IN￨O￨- traced￨L￨VBN￨O￨- infecteds￨L￨NNS￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- uncontrolled￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- R￨U￨NN￨O￨- to￨L￨TO￨O￨- R￨U￨NN￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- R￨U￨NN￨O￨- is￨L￨VBZ￨O￨- distinct￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- isolation￨L￨NN￨O￨- and￨L￨CC￨O￨- quarantine￨L￨NN￨O￨- which￨L￨WDT￨O￨- reduce￨L￨VB￨O￨- c.￨L￨NNP￨O￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- insight￨L￨NN￨O￨- has￨L￨VBZ￨O￨- yet￨L￨RB￨O￨- been￨L￨VBN￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- R￨U￨NN￨O￨- in￨L￨IN￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- time-related￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- tracing￨L￨VBG￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- symptom-based￨L￨JJ￨O￨- detection￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- delays￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tracing￨L￨VBG￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Contact￨U￨NN￨O￨- tracing￨L￨VBG￨O￨A of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infecteds￨L￨NNS￨O￨- works￨L￨VBZ￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- level￨L￨NN￨O￨- :￨L￨:￨O￨- treatment￨L￨NN￨O￨- or￨L￨CC￨O￨- quarantine￨L￨NN￨O￨- of￨L￨IN￨O￨- contactees￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- by￨L￨IN￨O￨- contact￨L￨NN￨O￨- we￨L￨PRP￨O￨- mean￨L￨VBP￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- event￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- contactee￨L￨NN￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- contacted￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- effective￨L￨JJ￨O￨- because￨L￨IN￨O￨- unidentified￨L￨JJ￨O￨- infecteds￨L￨NNS￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- among￨L￨IN￨O￨- contactees￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- efficient￨L￨JJ￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- resources￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- directed￨L￨VBN￨O￨- towards￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- type￨L￨NN￨O￨- is￨L￨VBZ￨O￨- single-step￨L￨JJ￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- all￨L￨DT￨O￨- traceable￨L￨JJ￨O￨- contactees￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨- case￨L￨NN￨O￨- are￨L￨VBP￨O￨- quarantined￨L￨VBN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- tracing￨L￨VBG￨O￨- only￨L￨RB￨O￨- continues￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- undiscovered￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- quarantined￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- detected￨L￨VBN￨O￨- itself￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NNP￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- type￨L￨NN￨O￨- is￨L￨VBZ￨O￨- iterative￨L￨JJ￨O￨- tracing￨L￨VBG￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- tracing￨L￨VBG￨O￨- of￨L￨IN￨O￨- traceable￨L￨JJ￨O￨- contactees￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- continued￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- whole￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- infecteds￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- linked￨L￨VBN￨O￨- through￨L￨IN￨O￨- traceable￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- quarantined￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NNP￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Emerging￨U￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- considered￨L￨VBN￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- framework￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- repeated￨L￨VBN￨O￨- introductions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- novel￨L￨JJ￨O￨- ”￨L￨''￨O￨- pathogen￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨A population￨L￨NN￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- of￨L￨IN￨O￨- attempts￨L￨NNS￨O￨- to￨L￨TO￨O￨- prophylactically￨L￨RB￨O￨- vaccinate￨L￨VB￨O￨- populations￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- spillover￨L￨NN￨O￨- ,￨L￨,￨O￨- requires￨L￨VBZ￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- pathogen-free￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- comprising￨L￨VBG￨O￨- both￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- acquired￨L￨VBN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- here￨L￨RB￨O￨- as￨L￨IN￨O￨- “￨L￨``￨O￨- partially￨L￨RB￨O￨- immune￨L￨JJ￨O￨- ”￨L￨''￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- introduction￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- naïve￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨A population￨L￨NN￨O￨A is￨L￨VBZ￨O￨- self-limiting￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- explosion￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- depleted￨L￨VBN￨O￨- to￨L￨TO￨O￨- such￨L￨PDT￨O￨- an￨L￨DT￨O￨- extent￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- trajectory￨L￨NN￨O￨- dips￨L￨NNS￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- never￨L￨RB￨O￨- completely￨L￨RB￨O￨- disappears￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- I￨U￨CD￨NUMBER￨- <<￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- as￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- which￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- whether￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- exhibit￨L￨VB￨O￨- this￨L￨DT￨O￨- behavior￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ρ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- grey￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- 50,000￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- demonstrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- which￨L￨WDT￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- (￨L￨-LRB-￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- I1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- persistence￨L￨NN￨O￨- upon￨L￨IN￨O￨- reintroduction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- *￨L￨SYM￨O￨- >￨L￨JJR￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- turnover￨L￨NN￨O￨- between￨L￨IN￨O￨- pathogen￨L￨NN￨O￨A extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- reintroduction￨L￨NN￨O￨- .￨L￨.￨O￨- +R￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- naïve￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨A population￨L￨NN￨O￨A ;￨L￨:￨O￨- ρ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- adamantanes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- M2￨U￨NN￨O￨- inhibitors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- NIs￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- predict￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- resistant￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- suffer￨L￨VBP￨O￨- little￨L￨JJ￨O￨- or￨L￨CC￨O￨- no￨L￨DT￨O￨- fitness￨L￨NN￨O￨- deficit￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- reductions￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmissibility￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- sensitive￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- resistant￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- could￨L￨MD￨O￨- spread￨L￨VB￨O￨- ,￨L￨,￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- use￨L￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- that￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- fitness￨L￨NN￨O￨- cost￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- runs￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- values￨L￨NNS￨O￨- are￨L￨VBP￨O￨- exactly￨L￨RB￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- higher￨L￨JJR￨O￨- but￨L￨CC￨O￨- nonpharmaceutical￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨- ,￨L￨,￨O￨- mask￨L￨NN￨O￨- wearing￨L￨VBG￨O￨- ,￨L￨,￨O￨- quarantine￨L￨NN￨O￨- and￨L￨CC￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- and/or￨L￨CC￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- prestockpiled￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- with￨L￨IN￨O￨- partial￨L￨JJ￨O￨- effectiveness￨L￨NN￨O￨- have￨L￨VBP￨O￨- reduced￨L￨VBN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- resistant￨L￨JJ￨O￨A and￨L￨CC￨O￨- sensitive￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- resistant￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- have￨L￨VBP￨O￨- appeared￨L￨VBN￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- other￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- use￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- sufficiently￨L￨RB￨O￨- strong￨L￨JJ￨O￨- selective￨L￨JJ￨O￨- force￨L￨NN￨O￨- to￨L￨TO￨O￨- offset￨L￨VB￨O￨- the￨L￨DT￨O￨- ”￨L￨''￨O￨- fitness￨L￨NN￨O￨- cost￨L￨NN￨O￨- ”￨L￨''￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- What￨U￨WP￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- and￨L￨CC￨O￨- prophylaxis￨L￨NN￨O￨A in￨L￨IN￨O￨- selecting￨L￨VBG￨O￨- for￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- given￨L￨VBN￨O￨- that￨L￨IN￨O￨- treatment￨L￨NN￨O￨- generates￨L￨VBZ￨O￨- de￨L￨FW￨O￨- novo￨L￨FW￨O￨- resistance￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- rate￨L￨NN￨O￨- than￨L￨IN￨O￨- prophylaxis￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- prophylaxis￨L￨NN￨O￨- blocks￨L￨VBZ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- drug-sensitive￨L￨JJ￨O￨- strain￨L￨NN￨O￨- more￨L￨RBR￨O￨- effectively￨L￨RB￨O￨- than￨L￨IN￨O￨- treatment￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Either￨U￨CC￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- prophylaxis￨L￨NN￨O￨A of￨L￨IN￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- reduces￨L￨VBZ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- sensitive￨L￨JJ￨O￨- strain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- green￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- red￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- somewhat￨L￨RB￨O￨- more￨L￨JJR￨O￨- resistance￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- prophylaxis￨L￨NN￨O￨- than￨L￨IN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- that￨L￨IN￨O￨- resistance￨L￨NN￨O￨- will￨L￨MD￨O￨- emerge￨L￨VB￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 0.2￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- treatment￨L￨NN￨O￨- and￨L￨CC￨O￨- 0.02￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- prophylaxis￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- track￨L￨VBP￨O￨- both￨L￨DT￨O￨- individual-level￨L￨JJ￨O￨- decisions￨L￨NNS￨O￨A and￨L￨CC￨O￨- population-level￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- yearly￨L￨JJ￨SET￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- level￨L￨NN￨O￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- ;￨L￨:￨O￨- where￨L￨WRB￨O￨- prevalence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- modeling￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- decisions￨L￨NNS￨O￨A made￨L￨VBN￨O￨- by￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- through￨L￨IN￨O￨- voluntary￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- protective￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- lasts￨L￨VBZ￨O￨- less￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- one￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- must￨L￨MD￨O￨- decide￨L￨VB￨O￨- every￨L￨DT￨SET￨- year￨L￨NN￨SET￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- participate￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- voluntary￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- model￨L￨VBP￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- 's￨L￨POS￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- making￨L￨VBG￨O￨- yearly￨L￨JJ￨SET￨- vaccination￨L￨NN￨O￨- decisions￨L￨NNS￨O￨A as￨L￨IN￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- trial￨L￨NN￨O￨- and￨L￨CC￨O￨- error￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- construct￨L￨VBP￨O￨- an￨L￨DT￨O￨- individual-level￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- cognition￨L￨NN￨O￨- and￨L￨CC￨O￨- behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- link￨L￨NN￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- vaccination￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Inspired￨U￨VBN￨O￨- by￨L￨IN￨O￨- questions￨L￨NNS￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- policy￨L￨NN￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- core￨L￨NN￨O￨- ”￨L￨''￨O￨- group￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- particularly￨L￨RB￨O￨- effective￨L￨JJ￨O￨- at￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- distinct￨L￨JJ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- victim￨L￨NN￨O￨- ”￨L￨''￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- vulnerable￨L￨JJ￨O￨A ”￨L￨''￨O￨- group￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- vulnerable￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- although￨L￨IN￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- more￨L￨RBR￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- ,￨L￨,￨O￨- switching￨L￨VBG￨O￨- vaccine￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- vulnerable￨L￨JJ￨O￨A group￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- group￨L￨NN￨O￨- first￨L￨JJ￨ORDINAL￨- increases￨L￨NNS￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vulnerable￨L￨JJ￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- fewer￨L￨JJR￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- directly￨L￨RB￨O￨- protected￨L￨VBN￨O￨- .￨L￨.￨O￨- +Inspired￨U￨VBN￨O￨- by￨L￨IN￨O￨- recent￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- about￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccines￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- allowed￨L￨VBD￨O￨- the￨L￨DT￨O￨- protective￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- higher￨L￨JJR￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vulnerable￨L￨JJ￨O￨A group￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- more￨L￨JJR￨O￨- vaccine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- allocated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- turning￨L￨VBG￨O￨- point￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reached￨L￨VBN￨O￨- after￨L￨IN￨O￨- which￨L￨WDT￨O￨- fewer￨L￨JJR￨O￨- vulnerable￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- sharply￨L￨RB￨O￨- reduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- illustration￨L￨NN￨O￨- purposes￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- allocate￨L￨VB￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- actively￨L￨RB￨O￨- mixing￨L￨VBG￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- schoolchildren￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- vulnerable￨L￨JJ￨O￨A population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- elderly￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- @Risk￨L￨NN￨HANDLE￨- model￨L￨NN￨TITLE￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- domestic￨L￨JJ￨O￨A spread￨L￨NN￨O￨- in-between￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- national￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- herds￨L￨NNS￨O￨- from￨L￨IN￨O￨- animals￨L￨NNS￨O￨- imported￨L￨VBN￨O￨- from￨L￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- sanitary￨L￨JJ￨O￨- status￨L￨NN￨O￨- comparable￨L￨JJ￨O￨- to￨L￨TO￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- or￨L￨CC￨O￨- lower￨L￨JJR￨O￨- sanitary￨L￨JJ￨O￨- status￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- summary￨L￨NN￨O￨- sheet￨L￨NN￨O￨- which￨L￨WDT￨O￨- summed￨L￨VBD￨O￨- up￨L￨RP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- resulting￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- herds￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pathways￨L￨NNS￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- the￨L￨DT￨O￨- pre-survey￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- domestic￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Methodology￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨O￨- A￨U￨DT￨O￨- stochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- repeated￨L￨JJ￨O￨- national￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨A to￨L￨TO￨O￨- document￨L￨VB￨O￨- freedom￨L￨NN￨O￨- from￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- herpesvirus￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- BoHV-1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infectionLea￨L￨NN￨O￨- Knopf1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Heinzpeter￨U￨NNP￨O￨- Schwermer1￨U￨NN￨O￨- and￨L￨CC￨O￨- Katharina￨U￨NNP￨PERSON￨- DC￨U￨NNP￨STATE_OR_PROVINCE￨- Stärk1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 3:10￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Knopf￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2007Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 03￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- International￨U￨NNP￨O￨- trade￨L￨NN￨O￨- regulations￨L￨NNS￨O￨- require￨L￨VBP￨O￨- that￨L￨IN￨O￨- countries￨L￨NNS￨O￨- document￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- livestock￨L￨NN￨O￨- 's￨L￨POS￨O￨- sanitary￨L￨JJ￨O￨- status￨L￨NN￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- and￨L￨CC￨O￨- freedom￨L￨NN￨O￨- from￨L￨IN￨O￨- specific￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- provided￨L￨VBD￨O￨- that￨L￨IN￨O￨- import￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- sensitivity￨L￨NN￨O￨- analysis￨L￨NN￨O￨- revealed￨L￨VBD￨O￨- that￨L￨IN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- undetected￨L￨JJ￨O￨- domestic￨L￨JJ￨O￨A herds￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- multiplicative￨L￨JJ￨O￨- between-survey-spread￨L￨NN￨O￨- factor￨L￨NN￨O￨- were￨L￨VBD￨O￨- most￨L￨RBS￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- pre-survey￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- freedom￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- consecutive￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- was￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- from￨L￨IN￨O￨- undetected￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- domestic￨L￨JJ￨O￨A population￨L￨NN￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- imported￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Undetected￨U￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- domestic￨L￨JJ￨O￨A population￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- surveys￨L￨NNS￨O￨- gained￨L￨VBD￨O￨- more￨L￨RBR￨O￨- importance￨L￨NN￨O￨- than￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- animals￨L￨NNS￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- import￨L￨NN￨O￨- pathway￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simple￨L￨JJ￨O￨- transformation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- equations￨L￨NNS￨O￨- reveals￨L￨VBZ￨O￨- a￨L￨DT￨O￨- scaling￨L￨VBG￨O￨- relationship￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- birth￨L￨NN￨O￨A rate￨L￨NN￨O￨A B￨U￨NN￨O￨- →￨L￨NN￨O￨- B￨U￨NN￨O￨- ′￨L￨CD￨NUMBER￨- produce￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- proportionate￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Earn￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- will￨L￨MD￨O￨- remain￨L￨VB￨O￨- invariant￨L￨JJ￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- scaled￨L￨VBN￨O￨- proportionately￨L￨RB￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- return￨L￨VB￨O￨- to￨L￨TO￨O￨- later￨L￨RB￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- persistence￨L￨NN￨O￨- with￨L￨IN￨O￨- birth￨L￨NN￨O￨A rate￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- possible￨L￨JJ￨O￨- standard￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- equal￨L￨JJ￨O￨- birth￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- powerful￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- birth￨L￨NN￨O￨A rate￨L￨NN￨O￨A on￨L￨IN￨O￨- persistence￨L￨NN￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- seasonality￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- modify￨L￨VBP￨O￨- this￨L￨DT￨O￨- picture￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- potentially￨L￨RB￨O￨- significant￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- long-lasting￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- results￨L￨NNS￨O￨- in￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- being￨L￨VBG￨O￨- a￨L￨DT￨O￨- predominantly￨L￨RB￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- intimately￨L￨RB￨O￨- connects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨A process￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- how￨L￨WRB￨O￨- stochastic￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- scales￨L￨NNS￨O￨- with￨L￨IN￨O￨- birth￨L￨NN￨O￨A rate￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- .￨L￨.￨O￨- +Heterogeneities￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- increase￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- transmissibility￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- per￨L￨IN￨O￨- potentially￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨- or￨L￨CC￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- subpopulation￨L￨NN￨O￨- confer￨L￨VBP￨O￨- advantages￨L￨NNS￨O￨- to￨L￨TO￨O￨- pathogens￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- exploit￨L￨VB￨O￨A them￨L￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- average￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- ,￨L￨,￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- higher￨L￨JJR￨O￨- R0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- adaptive￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ”￨L￨''￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- maximization￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- also￨L￨RB￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- initially￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- exploit￨L￨VB￨O￨A heterogeneities￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- will￨L￨MD￨O￨- always￨L￨RB￨O￨- be￨L￨VB￨O￨- favoured￨L￨VBN￨O￨- over￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- that￨L￨WDT￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- an￨L￨DT￨O￨- evolving￨L￨VBG￨O￨- pathogen￨L￨NN￨O￨- will￨L￨MD￨O￨- only￨L￨RB￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- exploit￨L￨VB￨O￨A R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- R0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- maximization￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- successful￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infected￨L￨JJ￨O￨A individual￨L￨NN￨O￨A into￨L￨IN￨O￨- a￨L￨DT￨O￨- wholly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- will￨L￨MD￨O￨- on￨L￨IN￨O￨- average￨L￨JJ￨O￨- result￨L￨NN￨O￨- in￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- other￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- science￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- made￨L￨VBN￨O￨- tremendous￨L￨JJ￨O￨- progress￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- several￨L￨JJ￨DATE￨- decades￨L￨NNS￨DATE￨- thanks￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- part￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- advances￨L￨NNS￨O￨- in￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- biology￨L￨NN￨O￨- ,￨L￨,￨O￨- immunology￨L￨NN￨O￨- ,￨L￨,￨O￨- medicine￨L￨NN￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- eradication￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- parasites￨L￨NNS￨O￨- in￨L￨IN￨O￨- wildlife￨L￨NN￨O￨A relies￨L￨VBZ￨O￨- very￨L￨RB￨O￨- often￨L￨RB￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- culling￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- to￨L￨TO￨O￨- push￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- invasion￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- historically￨L￨RB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- different￨L￨JJ￨O￨- domestic￨L￨JJ￨O￨A and￨L￨CC￨O￨- wildlife￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- or￨L￨CC￨O￨- removing￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- for￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- badgers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- foot-and-mouth￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- avian￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- waterfowl￨L￨NN￨O￨- birds￨L￨NNS￨O￨- and￨L￨CC￨O￨- poultry￨L￨NN￨O￨- in￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- classical￨L￨JJ￨O￨- swine￨L￨NNS￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- boars￨L￨NNS￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- anecdotal￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- by￨L￨IN￨O￨- age/stage￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- implication￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- variation￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨- reservoirs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- limited￨L￨JJ￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- domestic￨L￨JJ￨O￨A animals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Historically￨U￨NNP￨O￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- considered￨L￨VBN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- well-mixed￨L￨JJ￨O￨- with￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A among￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Seroepidemiological￨U￨JJ￨O￨- surveys￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- reliable￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- experience￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- Salmaso￨U￨FW￨MISC￨- et￨L￨FW￨MISC￨- al￨L￨FW￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- when￨L￨WRB￨O￨- considering￨L￨VBG￨O￨- historic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- continuing￨L￨VBG￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- representative￨L￨NN￨TITLE￨- programmes￨L￨NNS￨O￨- of￨L￨IN￨O￨- serological￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- reliance￨L￨NN￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- placed￨L￨VBN￨O￨- upon￨L￨IN￨O￨- case￨L￨NN￨O￨- notification￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- time.To￨L￨NN￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A with￨L￨IN￨O￨- much￨L￨RB￨O￨- important￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- having￨L￨VBG￨O￨- been￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- long￨L￨JJ￨O￨- data￨L￨NNS￨O￨- series￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- national￨L￨JJ￨O￨A policy￨L￨NN￨O￨- makers￨L￨NNS￨O￨- must￨L￨MD￨O￨- possess￨L￨VB￨O￨- data￨L￨NNS￨O￨- which￨L￨WDT￨O￨- reflect￨L￨VBP￨O￨- as￨L￨IN￨O￨- closely￨L￨RB￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- scale￨L￨NN￨O￨- and￨L￨CC￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- allowing￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- policy￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- tuned￨L￨VBN￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- maximum￨L￨JJ￨O￨- impact.Optimisation￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- programme￨L￨NN￨O￨- design￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- greatly￨L￨RB￨O￨- facilitated￨L￨VBN￨O￨- through￨L￨IN￨O￨- insights￨L￨NNS￨O￨- gained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- A￨U￨DT￨O￨- corrected￨L￨JJ￨O￨- national￨L￨JJ￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- is￨L￨VBZ￨O￨- calculated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- based￨L￨VBN￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- equality￨L￨NN￨O￨- between￨L￨IN￨O￨- births￨L￨NNS￨O￨- and￨L￨CC￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- ;￨L￨:￨O￨- under-reporting￨L￨VBG￨O￨- estimates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- Italian￨U￨JJ￨NATIONALITY￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- poor￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- reporting￨L￨VBG￨O￨A in￨L￨IN￨O￨- Southern￨U￨NNP￨LOCATION￨- Italy￨U￨NNP￨COUNTRY￨- are￨L￨VBP￨O￨- confirmed￨L￨VBN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- because￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- becomes￨L￨VBZ￨O￨- activated￨L￨VBN￨O￨- upon￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- strain￨L￨NN￨O￨A ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- hard￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- strain￨L￨NN￨O￨- to￨L￨TO￨O￨- enter￨L￨VB￨O￨- and/or￨L￨CC￨O￨- replicate￨L￨VB￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- physically￨L￨RB￨O￨- removed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- dying￨L￨VBG￨O￨- or￨L￨CC￨O￨- staying￨L￨VBG￨O￨- at￨L￨IN￨O￨- home￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- strain￨L￨NN￨O￨A is￨L￨VBZ￨O￨- removed￨L￨VBN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- focuses￨L￨VBZ￨O￨- first￨L￨RB￨ORDINAL￨- on￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- estimators￨L￨NNS￨O￨- for￨L￨IN￨O￨- individual￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- on￨L￨IN￨O￨- household￨L￨NN￨O￨A reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- on￨L￨IN￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- individual￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- roughly￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- someone￨L￨NN￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- can￨L￨MD￨O￨- infect￨L￨VB￨O￨- over￨L￨IN￨O￨- their￨L￨PRP$￨O￨- entire￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- lifespan￨L￨NN￨O￨- ;￨L￨:￨O￨- as￨L￨IN￨O￨- I￨U￨PRP￨O￨- will￨L￨MD￨O￨- show￨L￨VB￨O￨- below￨L￨IN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- several￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- of￨L￨IN￨O￨- defining￨L￨VBG￨O￨- this￨L￨DT￨O￨- more￨L￨RBR￨O￨- precisely￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- analysis￨L￨NN￨O￨- presented￨L￨VBN￨O￨- here￨L￨RB￨O￨- will￨L￨MD￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- new￨L￨JJ￨O￨- estimators￨L￨NNS￨O￨- for￨L￨IN￨O￨- individual￨L￨JJ￨O￨- and￨L￨CC￨O￨- household￨L￨NN￨O￨A reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- *￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨A provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- laboratory￨L￨NN￨O￨- ”￨L￨''￨O￨- within￨L￨IN￨O￨- which￨L￨WDT￨O￨- key￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- ,￨L￨,￨O￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- or￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- studied￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- household￨L￨NN￨O￨A reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- here￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- households￨L￨NNS￨O￨- a￨L￨DT￨O￨- household￨L￨NN￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- can￨L￨MD￨O￨- infect￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- out￨L￨RP￨O￨- statistical￨L￨JJ￨O￨- similarities￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- donations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A from￨L￨IN￨O￨- donor￨L￨NN￨O￨- organizations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- DH￨U￨NNP￨O￨- ,￨L￨,￨O￨- AH￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- GK￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- summarized￨L￨VBN￨O￨- in￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- DH￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- compared￨L￨VBD￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- donations￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- interval￨L￨NN￨O￨- of￨L￨IN￨O￨- six￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- tsunami￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- finding￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- confirmed￨L￨VBN￨O￨- also￨L￨RB￨O￨- for￨L￨IN￨O￨- another￨L￨DT￨O￨- German￨U￨JJ￨NATIONALITY￨- donor￨L￨NN￨O￨- organization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- AH￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- collected￨L￨VBN￨O￨- ten￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- less￨L￨RBR￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨A of￨L￨IN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- donations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- donations￨L￨NNS￨O￨- coincide￨L￨VBP￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- later￨L￨RB￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- donations￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨A of￨L￨IN￨O￨- frequencies￨L￨NNS￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- μ￨L￨NN￨O￨- and￨L￨CC￨O￨- τ￨L￨NN￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- °￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- *￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- donations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Presentation￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- We￨U￨PRP￨O￨- hypothesize￨L￨VBP￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- moratorium￨L￨NN￨O￨- ,￨L￨,￨O￨- poultry￨L￨NN￨O￨A segregation￨L￨NN￨O￨- and￨L￨CC￨O￨- targeted￨L￨VBN￨O￨- vaccination￨L￨NN￨O￨- if￨L￨IN￨O￨- successfully￨L￨RB￨O￨- adapted￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- affected￨L￨JJ￨O￨- district￨L￨NN￨O￨- or￨L￨CC￨O￨- province￨L￨NN￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- geographical￨L￨JJ￨O￨- region￨L￨NN￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- endemicity￨L￨NN￨O￨- would￨L￨MD￨O￨- set￨L￨VB￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Averting￨U￨VBG￨O￨- a￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- successful￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- endemicity￨L￨NN￨O￨- ,￨L￨,￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨A and￨L￨CC￨O￨- occasional￨L￨JJ￨O￨- spillage￨L￨NN￨O￨- into￨L￨IN￨O￨- human￨L￨JJ￨O￨- which￨L￨WDT￨O￨- carries￨L￨VBZ￨O￨- a￨L￨DT￨O￨- case-fatality￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- over￨L￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +Systematic￨U￨JJ￨O￨- surveillance￨L￨NN￨O￨- in￨L￨IN￨O￨- southern￨L￨JJ￨O￨- China￨U￨NNP￨COUNTRY￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- ducks￨L￨NNS￨O￨- and￨L￨CC￨O￨- geese￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- reservoirs￨L￨NNS￨O￨- which￨L￨WDT￨O￨- transmit￨L￨VBP￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- chickens￨L￨NNS￨O￨- ,￨L￨,￨O￨- minor￨L￨JJ￨O￨- poultry￨L￨NN￨O￨A and￨L￨CC￨O￨- even￨L￨RB￨O￨- migratory￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- .￨L￨.￨O￨- +Backyard￨U￨NN￨O￨- farms￨L￨NNS￨O￨- will￨L￨MD￨O￨- then￨L￨RB￨O￨- be￨L￨VB￨O￨- re-populated￨L￨VBN￨O￨- by￨L￨IN￨O￨- hatchlings￨L￨NNS￨O￨- from￨L￨IN￨O￨- virus-free￨L￨JJ￨O￨- chickens￨L￨NNS￨O￨- and￨L￨CC￨O￨- minor￨L￨JJ￨O￨- poultry￨L￨NN￨O￨A only￨L￨RB￨O￨- .￨L￨.￨O￨- +Targeted￨U￨VBN￨O￨- immunization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ducks￨L￨NNS￨O￨- and￨L￨CC￨O￨- geese￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- industrial￨L￨JJ￨O￨- farms￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- chickens￨L￨NNS￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- strictly￨L￨RB￨O￨- implemented￨L￨VBN￨O￨- as￨L￨IN￨O￨- blanket￨L￨NN￨O￨- immunization￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- backyard￨L￨NN￨O￨- poultry￨L￨NN￨O￨A is￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- impossible￨L￨JJ￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Predictability￨U￨NN￨MISC￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- pathways￨L￨NNS￨O￨- in￨L￨IN￨O￨- global￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- SARS￨U￨NNP￨MISC￨- case￨L￨NN￨O￨- studyVittoria￨L￨NN￨O￨- Colizza1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Alain￨U￨NNP￨PERSON￨- Barrat1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Marc￨U￨NNP￨PERSON￨- Barthélemy3￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Alessandro￨U￨NNP￨PERSON￨- Vespignani4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 5:34￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Colizza￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2007Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- global￨L￨JJ￨O￨A spread￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- severe￨L￨JJ￨O￨- acute￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SARS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- clearly￨L￨RB￨O￨- shown￨L￨VBN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- long-range￨L￨JJ￨O￨- transportation￨L￨NN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- predictability￨L￨NN￨O￨- offered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- quantitatively￨L￨RB￨O￨- analyzed￨L￨VBN￨O￨- and￨L￨CC￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- appearance￨L￨NN￨O￨- of￨L￨IN￨O￨- robust￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- pathways￨L￨NNS￨O￨A that￨L￨WDT￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- probable￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- stochastic￨L￨JJ￨O￨- meta-population￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- actual￨L￨JJ￨O￨- travel￨L￨NN￨O￨- and￨L￨CC￨O￨- census￨L￨NN￨O￨A data￨L￨NNS￨O￨- among￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- 100￨L￨CD￨NUMBER￨- urban￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- 220￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- predictive￨L￨JJ￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A spread￨L￨NN￨O￨A of￨L￨IN￨O￨- SARS￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- allows￨L￨VBZ￨O￨- probabilistic￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- country￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨A and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- magnitude￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- formulate￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A effected￨L￨VBN￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- time￨L￨NN￨O￨- during￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- develop￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- after￨L￨IN￨O￨- that￨L￨DT￨O￨- time￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- vector￨L￨NN￨O￨- can￨L￨MD￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- human￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- categories￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- parameter￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨- parameter￨L￨NN￨O￨- giving￨L￨VBG￨O￨A the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infectives￨L￨NNS￨O￨- become￨L￨VBP￨O￨- immune￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- natural￨L￨JJ￨O￨- birth￨L￨NN￨O￨- ,￨L￨,￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- yielded￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- distributed￨L￨VBN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A :￨L￨:￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- satisfies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- pulse￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- repeated￨L￨VBN￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- defined￨L￨VBN￨O￨- age￨L￨NN￨O￨- range￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- strategy￨L￨NN￨O￨A to￨L￨TO￨O￨- control￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- A￨U￨NNP￨O￨- double￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SARS￨U￨NNP￨MISC￨- propagationTuen￨L￨NNP￨MISC￨- Wai￨U￨NNP￨MISC￨- Ng1Email￨U￨NN￨MISC￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Gabriel￨U￨NNP￨PERSON￨- Turinici2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Antoine￨U￨NNP￨PERSON￨- Danchin4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 3:19￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Ng￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2003Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- An￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Severe￨U￨JJ￨O￨- Acute￨U￨JJ￨O￨- Respiratory￨U￨JJ￨O￨- Syndrome￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SARS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- coronavirus￨L￨NN￨O￨- has￨L￨VBZ￨O￨- spread￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Guangdong￨U￨NNP￨STATE_OR_PROVINCE￨- province￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- puzzling￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- apparently￨L￨RB￨O￨A classical￨L￨JJ￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- onset￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- became￨L￨VBD￨O￨- puzzling￨L￨JJ￨O￨- after￨L￨IN￨O￨- an￨L￨DT￨O￨- estate￨L￨NN￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- was￨L￨VBD￨O￨- affected￨L￨VBN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- huge￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- apparently￨L￨RB￨O￨- causing￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- report￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- first￨L￨RB￨ORDINAL￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Susceptible-Infected-Removed￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- involving￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- superimposed￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- spread￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- SARS￨U￨NNP￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Epigrass￨U￨NN￨MISC￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networksFlávio￨L￨NN￨O￨- C￨U￨NN￨O￨- Coelho1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Oswaldo￨U￨NNP￨PERSON￨- G￨U￨NNP￨O￨- Cruz1￨U￨NN￨O￨- and￨L￨CC￨O￨- Cláudia￨U￨NN￨O￨- T￨U￨NN￨O￨- Codeço1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 3:3￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Coelho￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2008Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨DT￨O￨- construction￨L￨NN￨O￨A of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- those￨L￨DT￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- daunting￨L￨JJ￨O￨- task￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- parameterization￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨A software￨L￨NN￨O￨- ,￨L￨,￨O￨- Epigrass￨U￨NN￨LOCATION￨- ,￨L￨,￨O￨- aimed￨L￨VBN￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- designing￨L￨VBG￨O￨- and￨L￨CC￨O￨- simulating￨L￨VBG￨O￨- network-epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- any￨L￨DT￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- Epigrass￨U￨NN￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- greatly￨L￨RB￨O￨- the￨L￨DT￨O￨- construction￨L￨NN￨O￨A ,￨L￨,￨O￨- simulation￨L￨NN￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- A￨U￨DT￨O￨- Network￨U￨NNP￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- directly￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- bus-transportation￨L￨JJ￨O￨- network￨L￨NN￨O￨A connecting￨L￨VBG￨O￨- mid-size￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +All￨U￨PDT￨O￨- this￨L￨DT￨O￨- just￨L￨RB￨O￨A to￨L￨TO￨O￨- construct￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- it￨L￨PRP￨O￨- still￨L￨RB￨O￨- has￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- simulated￨L￨JJ￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- ran￨L￨VBD￨O￨- gravity￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- simulations￨L￨NNS￨O￨- for￨L￨IN￨O￨- twenty-one￨L￨CD￨NUMBER￨- consecutive￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- with￨L￨IN￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- 26￨L￨CD￨NUMBER￨- biweeks￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- test￨L￨VB￨O￨- the￨L￨DT￨O￨- null￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- persistence￨L￨NN￨O￨A and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- coastal￨L￨JJ￨O￨- towns￨L￨NNS￨O￨- and￨L￨CC￨O￨- non-coastal￨L￨JJ￨O￨- towns￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- size￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- similar￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- into￨L￨IN￨O￨- our￨L￨PRP$￨O￨- artificial￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- and￨L￨CC￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- 's￨L￨POS￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- ‘￨L￨``￨O￨- edge￨L￨NN￨O￨A ’￨L￨''￨O￨- towns￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- equivalent￨L￨JJ￨O￨- ‘￨L￨``￨O￨- non-edge￨L￨JJ￨O￨- ’￨L￨''￨O￨- towns￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- always￨L￨RB￨O￨- predicts￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- correlation￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- fadeout￨L￨NN￨O￨- rate￨L￨NN￨O￨- between￨L￨IN￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨A town￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- town￨L￨NN￨O￨- than￨L￨IN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- inland￨L￨RB￨O￨- town￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- town￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- structural￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cattle￨L￨NNS￨O￨A contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- movements￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- quasi-persistent￨L￨JJ￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- movements￨L￨NNS￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- short￨L￨JJ￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- 4￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- persistent￨L￨JJ￨O￨- through￨L￨IN￨O￨- that￨L￨DT￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨O￨- Construction￨U￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- intrinsic￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- structure￨L￨NN￨O￨- from￨L￨IN￨O￨- UK￨U￨NNP￨COUNTRY￨- cattle￨L￨NNS￨O￨A movement￨L￨NN￨O￨- dataM￨L￨NNP￨O￨- Fred￨U￨NNP￨O￨- Heath1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Matthew￨U￨NNP￨PERSON￨- C￨U￨NNP￨O￨- Vernon1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Cerian￨U￨JJ￨MISC￨- R￨U￨NN￨MISC￨- Webb1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 4:11￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Heath￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2008Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- national￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- for￨L￨IN￨O￨- recording￨L￨VBG￨O￨- the￨L￨DT￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- between￨L￨IN￨O￨- agricultural￨L￨JJ￨O￨- holdings￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- has￨L￨VBZ￨O￨- enabled￨L￨VBN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- parameterisation￨L￨NN￨O￨- of￨L￨IN￨O￨- network-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- data￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- form￨L￨VB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- cattle-holding￨L￨NN￨O￨- location￨L￨NN￨O￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- node￨L￨NN￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- formed￨L￨VBN￨O￨- if￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A between￨L￨IN￨O￨- them￨L￨PRP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- selected￨L￨VBN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Two￨U￨CD￨NUMBER￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- constructed￨L￨VBN￨O￨- assuming￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- 7-day￨L￨JJ￨DURATION￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- 14-day￨L￨JJ￨DURATION￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨A using￨L￨VBG￨O￨- British￨U￨JJ￨ORGANIZATION￨- Cattle￨U￨NNP￨ORGANIZATION￨- Movement￨U￨NNP￨ORGANIZATION￨- Service￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- BCMS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- contrast￨L￨VBP￨O￨- in￨L￨IN￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨- new￨L￨JJ￨O￨- human￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- avian￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Vietnam￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- reported￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨- isolate￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- H3N2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2005￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Methods￨U￨NNS￨O￨- for￨L￨IN￨O￨- “￨L￨``￨O￨- Data￨U￨NNP￨O￨- Sources￨U￨NNS￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- likely￨L￨RB￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- avian￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- complete￨L￨JJ￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- would￨L￨MD￨O￨- imply￨L￨VB￨O￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- likely￨L￨JJ￨O￨- R￨U￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- human￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- suggest￨L￨VBP￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- an￨L￨DT￨O￨- emerging￨L￨VBG￨O￨A infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- case￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- very￨L￨RB￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- alternate￨L￨JJ￨O￨- short￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- with￨L￨IN￨O￨- long￨L￨JJ￨O￨- quiet￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- an￨L￨DT￨O￨- emerging￨L￨VBG￨O￨A infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- incipient￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- is￨L￨VBZ￨O￨- adapting￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- becomes￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- quantitative￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- established￨L￨VBN￨O￨- human￨L￨JJ￨O￨A pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- standard￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- or￨L￨CC￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- classified￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- once￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- nodes￨L￨NNS￨O￨- ‘￨L￨``￨O￨- triggering￨L￨VBG￨O￨- ’￨L￨''￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A (￨L￨-LRB-￨O￨- T￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- being￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- immediately￨L￨RB￨O￨- isolated￨L￨VBN￨O￨- and￨L￨CC￨O￨- initiate￨L￨VB￨O￨- tracing￨L￨VBG￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- finally￨L￨RB￨O￨- ,￨L￨,￨O￨- removed￨L￨VBD￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- no￨L￨RB￨O￨- longer￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- initiate￨L￨VB￨O￨- tracing￨L￨VBG￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- initial￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- from￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- to￨L￨TO￨O￨- power￨L￨NN￨O￨A law￨L￨NN￨O￨A if￨L￨IN￨O￨- non-random￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- small-world￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- power-law￨L￨NN￨O￨- exponent￨L￨NN￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- node￨L￨NN￨O￨- distance￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- epizootic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- usefully￨L￨RB￨O￨- modelled￨L￨VBN￨O￨- as￨L￨IN￨O￨- nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- links￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- potentially￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨A levels￨L￨NNS￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- avoiding￨L￨VBG￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- modified￨L￨VBD￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- integrate￨L￨VB￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- acquired￨L￨VBN￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- boosting￨L￨VBG￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- attenuated￨L￨VBN￨O￨- re-infections￨L￨NNS￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- occurs￨L￨VBZ￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- falls￨L￨VBZ￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- protective￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- purpose￨L￨NN￨O￨- here￨L￨RB￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- evolves￨L￨VBZ￨O￨- with￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- circulation￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- only￨L￨RB￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- individual￨L￨JJ￨O￨- suffering￨L￨VBG￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- constant￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- pathogen￨L￨NN￨O￨- exposure￨L￨NN￨O￨A .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨A rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogenic￨L￨JJ￨O￨- agent￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- denote￨L￨VBP￨O￨- φ￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- “￨L￨``￨O￨- avoiders￨L￨NNS￨O￨- ”￨L￨''￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- “￨L￨``￨O￨- normal￨L￨JJ￨O￨A ”￨L￨''￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +“￨L￨``￨O￨- Avoiders￨U￨NNP￨O￨- ”￨L￨''￨O￨- are￨L￨VBP￨O￨- less￨L￨RBR￨O￨- often￨L￨RB￨O￨- infected￨L￨JJ￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- “￨L￨``￨O￨- normal￨L￨JJ￨O￨A ”￨L￨''￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- avoid￨L￨VB￨O￨- all￨L￨DT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- mathematically￨L￨RB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonally￨L￨RB￨O￨- reproducing￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- induce￨L￨VBP￨O￨A a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- no￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- chronically￨L￨RB￨O￨- reduce￨L￨VB￨O￨- fecundity￨L￨NN￨O￨- ,￨L￨,￨O￨- following￨L￨VBG￨O￨- recovery￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- address￨L￨VB￨O￨- whether￨L￨IN￨O￨- microparasitic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- regulate￨L￨VB￨O￨- or￨L￨CC￨O￨- induce￨L￨VB￨O￨A multiyear￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- in￨L￨IN￨O￨- seasonally￨L￨RB￨O￨- reproducing￨L￨VBG￨O￨- populations￨L￨NNS￨O￨- by￨L￨IN￨O￨- influencing￨L￨VBG￨O￨- reproductive￨L￨JJ￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- reproductive￨L￨JJ￨O￨- output￨L￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- theoretical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- already￨L￨RB￨O￨- illustrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- macro￨L￨NN￨O￨- and￨L￨CC￨O￨- microparasitic￨L￨JJ￨O￨- infection-induced￨L￨JJ￨O￨- reductions￨L￨NNS￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- fecundity￨L￨NN￨O￨- can￨L￨MD￨O￨- destabilize￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- sufficiently￨L￨RB￨O￨- to￨L￨TO￨O￨- induce￨L￨VB￨O￨A multiyear￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- was￨L￨VBD￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- population￨L￨NN￨O￨- densities￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- Kielder￨U￨NNP￨LOCATION￨- Forest￨U￨NNP￨LOCATION￨- field￨L￨NN￨O￨- voles￨L￨NNS￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- this￨L￨DT￨O￨- could￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- multiyear￨L￨JJ￨O￨- population￨L￨NN￨O￨- cycles￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Smith￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨JJR￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- answer￨L￨VB￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- or￨L￨CC￨O￨- global￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- routes￨L￨NNS￨O￨A of￨L￨IN￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- heterogenous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- some￨L￨DT￨O￨- new￨L￨JJ￨O￨- results￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- given￨L￨VBN￨O￨- previously.The￨L￨NNP￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- routes￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- see￨L￨VB￨O￨- d'Onofrio￨L￨NNP￨O￨- A￨U￨DT￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- note￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network-based￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Pastor-Satorras￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- considered￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- degrees￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- factor￨L￨NN￨O￨- Θ￨U￨NN￨O￨- =￨L￨JJ￨O￨- ∑￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- m￨L￨NN￨O￨- a￨L￨DT￨O￨- x￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- ′￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- k￨L￨NN￨O￨- ′￨L￨CD￨NUMBER￨- @￨L￨SYM￨O￨- @￨L￨SYM￨O￨- +￨L￨CC￨O￨- =￨L￨JJ￨O￨- feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi￨L￨NN￨O￨- =￨L￨JJ￨O￨- xH8viVGI8Gi￨L￨NN￨O￨- =￨L￨JJ￨O￨- hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI￨L￨NN￨O￨- +￨L￨CC￨O￨- fsY￨L￨NN￨O￨- =￨L￨JJ￨O￨- rqGqVepae9pg0db9vqaiVgFr0xfr￨L￨NN￨O￨- =￨L￨JJ￨O￨- xfr￨L￨NN￨O￨- =￨L￨JJ￨O￨- @￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- here￨L￨RB￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- '￨L￨''￨O￨- |￨L￨SYM￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- '￨L￨''￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- max￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- k￨L￨NN￨O￨- '￨L￨''￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- '￨L￨''￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- stand￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- emanating￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- points￨L￨NNS￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Now￨U￨RB￨DATE￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- :￨L￨:￨O￨- d￨L￨NN￨O￨- I￨U￨PRP￨O￨- k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- k￨L￨NN￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- λ￨L￨NN￨O￨- k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- I￨U￨PRP￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Θ￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- …￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- −￨L￨SYM￨O￨- p￨L￨NN￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- I￨U￨PRP￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- k￨L￨NN￨O￨- Θ￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- @￨L￨SYM￨O￨- @￨L￨SYM￨O￨- +￨L￨CC￨O￨- =￨L￨JJ￨O￨- feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi￨L￨NN￨O￨- =￨L￨JJ￨O￨- xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI￨L￨NN￨O￨- +￨L￨CC￨O￨- fsY￨L￨NN￨O￨- =￨L￨JJ￨O￨- rqGqVepae9pg0db9vqaiVgFr0xfr￨L￨NN￨O￨- =￨L￨JJ￨O￨- xfr￨L￨NN￨O￨- =￨L￨JJ￨O￨- @￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ...￨L￨:￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- max￨L￨NN￨O￨A and￨L￨CC￨O￨- where￨L￨WRB￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- unity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- p￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- gives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- routes￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Zhou￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- argue￨L￨VBP￨O￨- that￨L￨IN￨O￨- Θ￨U￨NN￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- another￨L￨DT￨O￨- form￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- let￨L￨VBP￨O￨- Θ￨U￨NN￨O￨- =￨L￨JJ￨O￨- ∑￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- m￨L￨NN￨O￨- a￨L￨DT￨O￨- x￨L￨NN￨O￨- U￨U￨NNP￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- ′￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- k￨L￨NN￨O￨- ′￨L￨NN￨O￨- k￨L￨NN￨O￨- ′￨L￨CD￨NUMBER￨- @￨L￨SYM￨O￨- @￨L￨SYM￨O￨- +￨L￨CC￨O￨- =￨L￨JJ￨O￨- feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi￨L￨NN￨O￨- =￨L￨JJ￨O￨- xH8viVGI8Gi￨L￨NN￨O￨- =￨L￨JJ￨O￨- hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI￨L￨NN￨O￨- +￨L￨CC￨O￨- fsY￨L￨NN￨O￨- =￨L￨JJ￨O￨- rqGqVepae9pg0db9vqaiVgFr0xfr￨L￨NN￨O￨- =￨L￨JJ￨O￨- xfr￨L￨NN￨O￨- =￨L￨JJ￨O￨- @￨L￨SYM￨O￨- ,￨L￨,￨O￨- just￨L￨RB￨O￨- because￨L￨IN￨O￨- every￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- capability￨L￨NN￨O￨A U￨U￨NN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- other￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- mortality￨L￨NN￨O￨A date￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PMD￨U￨NN￨O￨- =￨L￨JJ￨O￨- the￨L￨DT￨O￨- date￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- was￨L￨VBD￨O￨- reached￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- DOE￨U￨NNP￨O￨- =￨L￨JJ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- days￨L￨NNS￨DURATION￨- during￨L￨IN￨O￨- which￨L￨WDT￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- carcasses￨L￨NNS￨O￨- were￨L￨VBD￨O￨- found￨L￨VBN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- fixed￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- PMD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- regions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- data￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- came￨L￨VBD￨O￨- into￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individual￨L￨NN￨O￨- would￨L￨MD￨O￨- infect￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- naïve￨L￨JJ￨O￨- population￨L￨NN￨O￨- during￨L￨IN￨O￨- its￨L￨PRP$￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- mortality￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- dying￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- local￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- swept￨L￨VBD￨O￨- through￨L￨IN￨O￨- European￨U￨JJ￨NATIONALITY￨- seal￨L￨NN￨O￨- populations￨L￨NNS￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- unusual￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- mortality￨L￨NN￨O￨A attributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- PDV￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- location￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- island￨L￨NN￨O￨- of￨L￨IN￨O￨- Anholt￨U￨NNP￨LOCATION￨- in￨L￨IN￨O￨- Denmark￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- started￨L￨VBD￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- were￨L￨VBD￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- either￨L￨CC￨O￨- case￨L￨NN￨O￨- mortality￨L￨NN￨O￨A or￨L￨CC￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- NumericCitation￨U￨NN￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- case￨L￨NN￨O￨- mortality￨L￨NN￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- explanation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- regional￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- was￨L￨VBD￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- low￨L￨JJ￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- regions￨L￨NNS￨O￨A ,￨L￨,￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- difference￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- The￨U￨DT￨O￨- geosimulation￨L￨NN￨O￨- of￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Nile￨U￨NNP￨LOCATION￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- multi-agent￨L￨JJ￨O￨- and￨L￨CC￨O￨- climate￨L￨NN￨O￨- sensitive￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- risk￨L￨NN￨O￨- management￨L￨NN￨O￨- in￨L￨IN￨O￨- public￨L￨JJ￨O￨- healthMondher￨L￨NN￨O￨- Bouden1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Bernard￨U￨NNP￨PERSON￨- Moulin1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Pierre￨U￨NNP￨PERSON￨- Gosselin2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 7:35￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Bouden￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2008Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨A Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- West￨U￨NNP￨LOCATION￨- Nile￨U￨NNP￨LOCATION￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- WNV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epizooty￨L￨NN￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- to￨L￨TO￨O￨- build￨L￨VB￨O￨- and￨L￨CC￨O￨- operate￨L￨VB￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- North￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- simulation￨L￨NN￨O￨- takes￨L￨VBZ￨O￨- place￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- virtual￨L￨JJ￨O￨- mapping￨L￨NN￨O￨- environment￨L￨NN￨O￨- representing￨L￨VBG￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- administrative￨L￨JJ￨O￨- territory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- province￨L￨NN￨O￨- ,￨L￨,￨O￨- state￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- under￨L￨IN￨O￨- various￨L￨JJ￨O￨- climate￨L￨NN￨O￨A scenarios￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- larviciding￨L￨VBG￨O￨- at￨L￨IN￨O￨- scales￨L￨NNS￨O￨- of￨L￨IN￨O￨- 1/20￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- smaller￨L￨JJR￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Multi-Agent￨U￨JJ￨MISC￨- GeoSimulation￨U￨NN￨MISC￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- selected￨L￨VBN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- simulates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨A and￨L￨CC￨O￨- birds￨L￨NNS￨O￨- over￨L￨IN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- WNV￨U￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- After￨U￨IN￨O￨- setting￨L￨VBG￨O￨- some￨L￨DT￨O￨- hypotheses￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- conceptual￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- system￨L￨NN￨O￨- architecture￨L￨NN￨O￨- were￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A and￨L￨CC￨O￨- interactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- genus￨L￨NNS￨O￨- Culex￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- American￨U￨JJ￨NATIONALITY￨- crows￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- were￨L￨VBD￨O￨- chosen￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- actors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A ,￨L￨,￨O￨- an￨L￨DT￨O￨- operational￨L￨JJ￨O￨- prototype￨L￨NN￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Southern￨U￨NNP￨MISC￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- Quebec￨U￨NNP￨STATE_OR_PROVINCE￨- (￨L￨-LRB-￨O￨- Canada￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- choose￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- between￨L￨IN￨O￨- 0.1￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 0.15￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- casual￨L￨JJ￨O￨- contact￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- per￨L￨IN￨O￨- shift￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- among￨L￨IN￨O￨- patients￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- HCW￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 23￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- observed￨L￨VBN￨O￨- influenza-like-illness￨L￨NN￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- moderate￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- few￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- trials￨L￨NNS￨O￨- have￨L￨VBP￨O￨- indeed￨L￨RB￨O￨- demonstrated￨L￨VBN￨O￨- protective￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- intervention￨L￨NN￨O￨- for￨L￨IN￨O￨- patients￨L￨NNS￨O￨A in￨L￨IN￨O￨- nursing￨L￨NN￨O￨- homes￨L￨NNS￨O￨- at￨L￨IN￨O￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- HCW￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- uptake￨L￨NN￨O￨- rates￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- elucidate￨L￨VB￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- HCW￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- patient￨L￨NN￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- department￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- uptake￨L￨NN￨O￨- among￨L￨IN￨O￨- patients￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- elderly￨L￨JJ￨O￨- nursing￨L￨NN￨O￨- home￨L￨NN￨O￨- patients￨L￨NNS￨O￨A the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- against￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- significantly￨L￨RB￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- propose￨L￨VBP￨O￨- to￨L￨TO￨O￨- disentangle￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- effect￨L￨NN￨O￨- modifiers￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- nursing￨L￨NN￨O￨- home￨L￨NN￨O￨A department￨L￨NN￨O￨- under￨L￨IN￨O￨- various￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- institutional￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aims￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- were￨L￨VBD￨O￨- :￨L￨:￨O￨- Produce￨U￨VB￨O￨- techniques￨L￨NNS￨O￨- to￨L￨TO￨O￨- link￨L￨VB￨O￨- IID￨U￨NN￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨A with￨L￨IN￨O￨- area￨L￨NN￨O￨- based￨L￨VBN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- socio-economic￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- land-use￨L￨NN￨O￨- types￨L￨NNS￨O￨- and￨L￨CC￨O￨- water￨L￨NN￨O￨- supply￨L￨NN￨O￨- quality￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Wales￨U￨NNP￨LOCATION￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- collated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Health￨U￨NNP￨ORGANIZATION￨- Protection￨U￨NNP￨ORGANIZATION￨- Agency￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Centre￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Infections￨U￨NNPS￨ORGANIZATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- contain￨L￨VBP￨O￨- additional￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- specimen￨L￨NN￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- sex￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- laboratory￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- was￨L￨VBD￨O￨- analysed￨L￨VBN￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- had￨L￨VBD￨O￨- reported￨L￨VBN￨O￨A recent￨L￨JJ￨O￨- foreign￨L￨JJ￨O￨- travel￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- cryptosporidiosis￨L￨NN￨O￨- in￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Wales￨U￨NNP￨LOCATION￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- usefulness￨L￨NN￨O￨- of￨L￨IN￨O￨- IID￨U￨NN￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨A for￨L￨IN￨O￨- exploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- factors￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- geography￨L￨NN￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- ascertainment￨L￨NN￨O￨- bias￨L￨NN￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- when￨L￨WRB￨O￨- using￨L￨VBG￨O￨- national￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨A on￨L￨IN￨O￨- cryptosporidiosis￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- IID￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Wales￨U￨NNP￨LOCATION￨- for￨L￨IN￨O￨- every￨L￨DT￨O￨- positive￨L￨JJ￨O￨- cryptosporidiosis￨L￨NN￨O￨- case￨L￨NN￨O￨- reported￨L￨VBD￨O￨- to￨L￨TO￨O￨- national￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨A there￨L￨EX￨O￨- are￨L￨VBP￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 7.4￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- movement￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- movements￨L￨NNS￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- simulated￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- processes￨L￨NNS￨O￨- were￨L￨VBD￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- suitability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- network￨L￨NN￨O￨- representations￨L￨NNS￨O￨A .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- adopted￨L￨VBD￨O￨- an￨L￨DT￨O￨- alternative￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- generic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- simple￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- cattle￨L￨NNS￨O￨A movements￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- connections￨L￨NNS￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- discrete-time￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- run￨L￨VBP￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- network￨L￨NN￨O￨- representations￨L￨NNS￨O￨A measured￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- static￨L￨JJ￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- network￨L￨NN￨O￨- representations￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- 's￨L￨POS￨O￨- cattle￨L￨NNS￨O￨- herd￨L￨NN￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- network￨L￨NN￨O￨- representation￨L￨NN￨O￨- was￨L￨VBD￨O￨- constructed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- manner￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- only￨L￨RB￨O￨- movements￨L￨NNS￨O￨A from￨L￨IN￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- either￨L￨CC￨O￨- 7￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- 28￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- problem￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- include￨L￨VB￨O￨- prevalence-dependent￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- assume￨L￨VB￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- depressive￨L￨JJ￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- -￨L￨:￨O￨- protective￨L￨JJ￨O￨A self-isolation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- sequestration￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- being￨L￨VBG￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- .￨L￨.￨O￨- +Henri￨U￨NNP￨PERSON￨- Poincare￨U￨NNP￨PERSON￨- In￨U￨IN￨O￨- classical￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- –￨L￨:￨O￨- the￨L￨DT￨O￨- tradition￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨A equations￨L￨NNS￨O￨- with￨L￨IN￨O￨- perfect￨L￨JJ￨O￨- mixing￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- mass￨L￨JJ￨O￨- action￨L￨NN￨O￨- kinetics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- Kermack-McKendrick￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- –￨L￨:￨O￨- individuals￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- adapt￨L￨VB￨O￨- their￨L￨PRP$￨O￨- contact￨L￨NN￨O￨- behavior￨L￨NN￨O￨- during￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- introduced￨L￨VBN￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- expand￨L￨VBP￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- response￨L￨NN￨O￨- repertoire￨L￨NN￨O￨- of￨L￨IN￨O￨- agents￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- fear￨L￨NN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- both￨L￨CC￨O￨- flight￨L￨NN￨O￨- and￨L￨CC￨O￨- protective￨L￨JJ￨O￨A self-isolation￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- seems￨L￨VBZ￨O￨- ill-suited￨L￨JJ￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- cases￨L￨NNS￨O￨- where￨L￨WRB￨O￨- endogenous￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- fear￨L￨NN￨O￨- inspire￨L￨VB￨O￨- widespread￨L￨JJ￨O￨- adaptations￨L￨NNS￨O￨- unrelated￨L￨JJ￨O￨- to￨L￨TO￨O￨- prevalence￨L￨NN￨O￨A .￨L￨.￨O￨- +As￨U￨IN￨O￨- two￨L￨CD￨NUMBER￨- terms￨L￨NNS￨O￨- with￨L￨IN￨O￨- similar￨L￨JJ￨O￨- meanings￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- throughout￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- will￨L￨MD￨O￨- clarify￨L￨VB￨O￨- the￨L￨DT￨O￨- distinctions￨L￨NNS￨O￨- :￨L￨:￨O￨- Herd￨U￨VB￨O￨- Immunity￨U￨NN￨O￨- Threshold￨U￨NN￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- overall￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- when￨L￨WRB￨O￨- these￨L￨DT￨O￨- vaccinations￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- per￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- to￨L￨TO￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- VPD￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Outbreak￨U￨NN￨O￨- Response￨U￨NN￨O￨- Immunization￨U￨NN￨O￨- Threshold￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ORIT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- per￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- to￨L￨TO￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- causing￨L￨VBG￨O￨- the￨L￨DT￨O￨- cessation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- immunizing￨L￨VBG￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- persons￨L￨NNS￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- gradually￨L￨RB￨O￨- stop￨L￨VB￨O￨A an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- control￨L￨NN￨O￨- agency￨L￨NN￨O￨- can￨L￨MD￨O￨- save￨L￨VB￨O￨- vaccines￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- later￨L￨JJ￨O￨- date￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- immunize￨L￨VB￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- persons￨L￨NNS￨O￨- to￨L￨TO￨O￨- stop￨L￨VB￨O￨A an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- control￨L￨NN￨O￨- agency￨L￨NN￨O￨- must￨L￨MD￨O￨- have￨L￨VB￨O￨- advance￨L￨NN￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- approximation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- ORIT￨U￨NNP￨O￨- .￨L￨.￨O￨- +Kimura￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- provided￨L￨VBN￨O￨- us￨L￨PRP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- null￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- against￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- create￨L￨VB￨O￨- interesting￨L￨JJ￨O￨- alternative￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- molecular￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- variation￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- far￨L￨RB￨O￨- too￨L￨RB￨O￨- simple￨L￨JJ￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- pathogen￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨A .￨L￨.￨O￨- +They￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- all￨L￨DT￨O￨- new￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- continuously￨L￨RB￨O￨- created￨L￨VBN￨O￨- are￨L￨VBP￨O￨- selectively￨L￨RB￨O￨- equivalent￨L￨JJ￨O￨- then￨L￨RB￨O￨- diversity￨L￨NN￨O￨A increases￨L￨VBZ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- U￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- extant￨L￨JJ￨O￨- lineages￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- Poisson￨U￨NNP￨PERSON￨- distributed￨L￨VBN￨O￨- with￨L￨IN￨O￨- mean￨L￨JJ￨O￨- Ut￨U￨NN￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- the￨L￨DT￨O￨- powerful￨L￨JJ￨O￨- tool￨L￨NN￨O￨- of￨L￨IN￨O￨- coalescent￨L￨JJ￨O￨- theory￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- pathogen￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨A but￨L￨CC￨O￨- have￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- populations￨L￨NNS￨O￨- follow￨L￨VBP￨O￨- the￨L￨DT￨O￨- Wright-Fisher￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- unstructured￨L￨JJ￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- fluctuates￨L￨VBZ￨O￨- in￨L￨IN￨O￨- size￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- proposed￨L￨VBN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- different￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- types￨L￨NNS￨O￨- and￨L￨CC￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- geographical￨L￨JJ￨O￨- maps￨L￨NNS￨O￨- with￨L￨IN￨O￨- marked￨L￨JJ￨O￨- population￨L￨NN￨O￨- densities￨L￨NNS￨O￨- and￨L￨CC￨O￨- enables￨L￨VBZ￨O￨A the￨L￨DT￨O￨- modeler￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- change￨L￨VB￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- framework￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- cellular￨L￨JJ￨O￨- automaton￨L￨NN￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- enables￨L￨VBZ￨O￨A the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- parametrizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- individual￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- geographical￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- densities￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨A are￨L￨VBP￨O￨- accessible￨L￨JJ￨O￨- at￨L￨IN￨O￨- every￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- facilitates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- exploration￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- patterns￨L￨NNS￨O￨- using￨L￨VBG￨O￨- statistics￨L￨NNS￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- mining￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- individual￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- e.g.￨L￨FW￨O￨- touching￨L￨VBG￨O￨- ,￨L￨,￨O￨- eating￨L￨VBG￨O￨- ,￨L￨,￨O￨- breathing￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sexual￨L￨JJ￨O￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- furthermore￨L￨RB￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- can￨L￨MD￨O￨- contract￨L￨VB￨O￨- a￨L￨DT￨O￨- germ￨L￨NN￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- animal￨L￨NN￨O￨- .￨L￨.￨O￨- +Setting￨U￨VBG￨O￨- the￨L￨DT￨O￨- unit￨L￨NN￨O￨- cost￨L￨NN￨O￨A to￨L￨TO￨O￨- be￨L￨VB￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- for￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- cost￨L￨NN￨O￨- per￨L￨IN￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- repeated￨L￨VBN￨O￨- forward￨L￨RB￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- total￨L￨JJ￨O￨- cost￨L￨NN￨O￨- over￨L￨IN￨O￨- 40￨L￨CD￨NUMBER￨- time￨L￨NN￨O￨- steps￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- approximately￨L￨RB￨O￨- 2100￨L￨CD￨DATE￨- cost￨L￨NN￨O￨- units￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- attributable￨L￨JJ￨O￨- entirely￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- until￨L￨IN￨O￨- recovery￨L￨NN￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Monte￨U￨NNP￨MISC￨- Carlo-based￨U￨JJ￨MISC￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- becomes￨L￨VBZ￨O￨- straightforward￨L￨JJ￨O￨- to￨L￨TO￨O￨- couple￨L￨VB￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- with￨L￨IN￨O￨- Bayesian￨U￨JJ￨O￨- procedures￨L￨NNS￨O￨- for￨L￨IN￨O￨- performing￨L￨VBG￨O￨- on-line￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- propagating￨L￨VBG￨O￨- parameter￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨- through￨L￨IN￨O￨- to￨L￨TO￨O￨- policy￨L￨NN￨O￨A decisions￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- policies￨L￨NNS￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- this￨L￨DT￨O￨- framework￨L￨NN￨O￨- are￨L￨VBP￨O￨- optimal￨L￨JJ￨O￨- in￨L￨IN￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- minimize￨L￨VBP￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- cost￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- adaptive￨L￨JJ￨O￨- in￨L￨IN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- policy￨L￨NN￨O￨- changes￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨- variable￨L￨JJ￨O￨- stop￨L￨NN￨O￨- time￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- by￨L￨IN￨O￨- searching￨L￨VBG￨O￨- the￨L￨DT￨O￨- policy￨L￨NN￨O￨- space￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- fractions-to-vaccinate￨L￨JJ￨O￨- and￨L￨CC￨O￨- stopping￨L￨VBG￨O￨- thresholds￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- policy￨L￨NN￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- frequently￨L￨RB￨O￨- produces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- lowest￨L￨JJS￨O￨- expected￨L￨VBN￨O￨- cost￨L￨NN￨O￨A .￨L￨.￨O￨- +By￨U￨IN￨O￨- conditioning￨L￨NN￨O￨- on￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- and￨L￨CC￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- Monte￨U￨NNP￨LOCATION￨- Carlo￨U￨NNP￨LOCATION￨- simulation￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- total￨L￨JJ￨O￨- accrued￨L￨VBN￨O￨- cost￨L￨NN￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- 60￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 180￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- was￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- local￨L￨JJ￨O￨- case￨L￨NN￨O￨- until￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- only￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- dose￨L￨NN￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- seroconversion￨L￨NN￨O￨- occurring￨L￨VBG￨O￨- 21￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- and￨L￨CC￨ORDINAL￨- second￨L￨JJ￨ORDINAL￨- doses￨L￨NNS￨O￨- were￨L￨VBD￨O￨- given￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- note￨L￨NN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 2-dose￨L￨JJ￨O￨- program￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccinees￨L￨NNS￨O￨- achieve￨L￨VBP￨O￨- 1-and￨L￨JJ￨O￨- 2-dose￨L￨JJ￨O￨- protection￨L￨NN￨O￨- in￨L￨IN￨O￨- sequence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- dose￨L￨NN￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- that￨L￨WDT￨O￨- protects￨L￨VBZ￨O￨- against￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- reduces￨L￨VBZ￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- this￨L￨DT￨O￨- finding￨L￨NN￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- published￨L￨VBN￨O￨- trials￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨DATE￨- second￨L￨NN￨DATE￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- 1-and￨L￨JJ￨O￨- 2-dose￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- matched￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- susceptible-exposed-infectious-removed￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- delay￨L￨NN￨O￨A to￨L￨TO￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- seroconversion￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- seasonal￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- normalized￨L￨VBN￨O￨- difference￨L￨NN￨O￨- vegetation￨L￨NN￨O￨- index￨L￨NN￨O￨- –￨L￨:￨O￨- NDVI￨U￨NNP￨O￨- –￨L￨:￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- forage￨L￨NN￨O￨- availability￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- how￨L￨WRB￨O￨- seasonal￨L￨JJ￨O￨- variability￨L￨NN￨O￨A might￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- FMD￨U￨NN￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Sirca￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- FMD￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- feral￨L￨JJ￨O￨- pig￨L￨NN￨O￨A populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Queensland￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- feral￨L￨JJ￨O￨- pig￨L￨NN￨O￨- and￨L￨CC￨O￨- wild￨L￨JJ￨O￨- deer￨L￨NNS￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Texas￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- Plasmodium￨U￨NN￨O￨- falciparum￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1994￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2006￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Plasmodium￨U￨NN￨O￨- vivax￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1999￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2006￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- Perú￨U￨NNP￨COUNTRY￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- in￨L￨IN￨O￨- conjunction￨L￨NN￨O￨- with￨L￨IN￨O￨- associated￨L￨VBN￨O￨- demographic￨L￨JJ￨O￨- ,￨L￨,￨O￨- geographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- climatological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- analysed￨L￨VBN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- significant￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨A heterogeneity￨L￨NN￨O￨A was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- across￨L￨IN￨O￨- jungle￨L￨NN￨O￨- ,￨L￨,￨O￨- mountain￨L￨NN￨O￨- and￨L￨CC￨O￨- coastal￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- with￨L￨IN￨O￨- slightly￨L￨RB￨O￨- higher￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- for￨L￨IN￨O￨- P.￨U￨NNP￨O￨- vivax￨L￨NN￨O￨- than￨L￨IN￨O￨- P.￨U￨NNP￨O￨- falciparum￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- declining￨L￨VBG￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- across￨L￨IN￨O￨- geographic￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- species￨L￨NNS￨O￨- were￨L￨VBD￨O￨- significantly￨L￨RB￨O￨- synchronized￨L￨VBN￨O￨- in￨L￨IN￨O￨- coastal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- ρ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- <￨L￨VBG￨O￨- 0.0001￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- jungle￨L￨NN￨O￨- regions￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- ρ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.76￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- <￨L￨VBG￨O￨- 0.0001￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- in￨L￨IN￨O￨- mountain￨L￨NN￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Modeling￨U￨VBG￨MISC￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- pandemics￨L￨NNS￨O￨- :￨L￨:￨O￨- insights￨L￨NNS￨O￨A into￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- of￨L￨IN￨O￨- swine￨L￨NNS￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Brian￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Coburn1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Bradley￨U￨NNP￨PERSON￨- G￨U￨NNP￨O￨- Wagner1￨U￨NN￨O￨- and￨L￨CC￨O￨- Sally￨U￨NNP￨PERSON￨- Blower1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:30￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Blower￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2009Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 02￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- AbstractHere￨U￨NNP￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- modeling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- discuss￨L￨VB￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- currently￨L￨RB￨DATE￨- circulating￨L￨VBG￨O￨- novel￨L￨JJ￨O￨- strain￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- formerly￨L￨RB￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- swine￨L￨NNS￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- modeling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- discuss￨L￨VB￨O￨- how￨L￨WRB￨O￨- results￨L￨NNS￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- insights￨L￨NNS￨O￨A into￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- currently￨L￨RB￨DATE￨- circulating￨L￨VBG￨O￨- strain￨L￨NN￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- modeling￨L￨NN￨O￨- cross-species￨L￨NNS￨O￨- transmission￨L￨NN￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza.KeywordsInfluenzaAvian￨L￨JJ￨MISC￨- InfluenzaBasic￨U￨NNP￨MISC￨- Reproduction￨U￨NNP￨MISC￨- NumberInfluenza￨U￨NNP￨MISC￨- EpidemicBiomedical￨U￨NNP￨MISC￨- Intervention￨U￨NN￨MISC￨- IntroductionMathematical￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- spatial-temporal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- should￨L￨MD￨O￨- simultaneously￨L￨RB￨O￨- track￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- bird￨L￨NN￨O￨- ,￨L￨,￨O￨- pig￨L￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- basic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- InfluenzaThe￨U￨NNP￨O￨- first￨L￨RB￨ORDINAL￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A epidemic￨L￨JJ￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- early￨L￨RB￨DATE￨- in￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- 20th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- by￨L￨IN￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- metapopulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- situations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- humans￨L￨NNS￨O￨- form￨L￨VBP￨O￨- static￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨A zoonotic￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- or￨L￨CC￨O￨- vector￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- study￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- static￨L￨JJ￨O￨- vector￨L￨NN￨O￨- populations￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨A humans￨L￨NNS￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- even￨L￨RB￨O￨- low￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- areas￨L￨NNS￨O￨- are￨L￨VBP￨O￨- prone￨L￨JJ￨O￨- to￨L￨TO￨O￨- dengue￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- if￨L￨IN￨O￨- local￨L￨JJ￨O￨- residents￨L￨NNS￨O￨- also￨L￨RB￨O￨- visit￨L￨VBP￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- shift￨L￨VBP￨O￨- focus￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨- and￨L￨CC￨O￨- mosquito￨L￨NN￨O￨- patchiness￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨- scale￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- that￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- mosquito￨L￨NN￨O￨A movement￨L￨NN￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- connecting￨L￨VBG￨O￨- such￨L￨JJ￨O￨- patches￨L￨NNS￨O￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨- reservoirs￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- disseminate￨L￨VB￨O￨- it￨L￨PRP￨O￨- widely￨L￨RB￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Objective￨U￨NN￨O￨- The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- approach￨L￨NN￨O￨- the￨L￨DT￨O￨- integrates￨L￨VBZ￨O￨- geographic￨L￨JJ￨O￨- information￨L￨NN￨O￨- systems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- GIS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- communicable￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- urban￨L￨JJ￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- interactions￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- geospatial￨L￨JJ￨O￨- context￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- An￨U￨DT￨O￨- agent-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- contagious￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreadLiliana￨L￨NN￨O￨- Perez1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Suzana￨U￨NNP￨O￨- Dragicevic1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 8:50￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Perez￨U￨NNP￨O￨- and￨L￨CC￨O￨- Dragicevic￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2009Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- communicable￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- inherent￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- importance￨L￨NN￨O￨- for￨L￨IN￨O￨- modern￨L￨JJ￨O￨- society￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- results￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- ratios￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible/infected￨L￨VBN￨O￨- in￨L￨IN￨O￨- specific￨L￨JJ￨O￨- time￨L￨NN￨O￨- frames￨L￨NNS￨O￨- and￨L￨CC￨O￨- urban￨L￨JJ￨O￨A environments￨L￨NNS￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- depict￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- interactions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- The￨U￨DT￨O￨- methodology￨L￨NN￨O￨- for￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- spatiotemporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- communicable￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- using￨L￨VBG￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- urban￨L￨JJ￨O￨- environment￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨A within￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- lead￨L￨NN￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- perform￨L￨VBP￨O￨- stationary￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- after￨L￨IN￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- finished￨L￨VBN￨O￨- commuting￨L￨VBG￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- SCFGs￨U￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- RDS￨U￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- recruitment￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- between￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- hidden￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- injection￨L￨NN￨O￨- drug￨L￨NN￨O￨- users￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IDUs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- Tijuana￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- México￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- non-random￨L￨JJ￨O￨- network￨L￨NN￨O￨- associations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- cross-tabulating￨L￨VBG￨O￨- attributes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- recruiter￨L￨NN￨TITLE￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- recruitee￨L￨NN￨O￨- ,￨L￨,￨O￨- analyzed￨L￨VBN￨O￨- using￨L￨VBG￨O￨- log-linear￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- generalized￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- symbol￨L￨NN￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- all￨L￨DT￨O￨- strings￨L￨NNS￨O￨- are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- initiation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- RDS￨U￨NN￨O￨- study￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- non-terminal￨L￨JJ￨O￨- symbols￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- respondents￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- recruitment￨L￨NN￨O￨A outcomes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- unresolved￨L￨JJ￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- terminal￨L￨JJ￨O￨- symbols￨L￨NNS￨O￨- for￨L￨IN￨O￨- respondents￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- recruitment￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- resolved￨L￨VBN￨O￨- .￨L￨.￨O￨- +Respondent-driven￨U￨JJ￨O￨- sampling￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- RDS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- offshoot￨L￨NN￨O￨- of￨L￨IN￨O￨- chain-referral￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- that￨L￨WDT￨O￨- implements￨L￨VBZ￨O￨- a￨L￨DT￨O￨- dual-incentive￨L￨JJ￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- incentive￨L￨NN￨O￨- for￨L￨IN￨O￨- participation￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- respondent￨L￨NN￨O￨- receives￨L￨VBZ￨O￨- additional￨L￨JJ￨O￨- rewards￨L￨NNS￨O￨- for￨L￨IN￨O￨- every￨L￨DT￨O￨- peer￨L￨VBP￨O￨- they￨L￨PRP￨O￨- recruit￨L￨VB￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +Thirdly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨A process￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- unobserved￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- respondents￨L￨NNS￨O￨- that￨L￨WDT￨O￨- might￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- directly￨L￨RB￨O￨- measurable￨L￨JJ￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- 's￨L￨POS￨O￨- disposition￨L￨NN￨O￨- to￨L￨TO￨O￨- recruit￨L￨VB￨O￨- their￨L￨PRP$￨O￨- peers￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- go￨L￨VBP￨O￨- on￨L￨IN￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- integral￨L￨JJ￨O￨- representation￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- loop￨L￨NN￨O￨A expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- action￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- establish￨L￨VB￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- result￨L￨NN￨O￨- for￨L￨IN￨O￨- computing￨L￨VBG￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- action.We￨L￨NN￨O￨- then￨L￨RB￨O￨- write￨L￨VB￨O￨- down￨L￨RP￨O￨- the￨L￨DT￨O￨- actions￨L￨NNS￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- 1-loop￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- usual￨L￨JJ￨O￨- moment-closure￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- before￨L￨IN￨O￨- summarizing￨L￨VBG￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- symmetrized￨L￨VBN￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- bugs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- identical￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- normalized￨L￨VBN￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- integrating￨L￨VBG￨O￨- out￨L￨RP￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- arguments￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- summing￨L￨VBG￨O￨- over￨L￨IN￨O￨- n￨L￨NN￨O￨- gives￨L￨VBZ￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- expectations￨L￨NNS￨O￨- of￨L￨IN￨O￨- observable￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- similarly￨L￨RB￨O￨- sums￨L￨NNS￨O￨- over￨L￨IN￨O￨- terms￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- n-bug￨L￨NN￨O￨- sector￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨A equation￨L￨NN￨O￨A must￨L￨MD￨O￨- be￨L￨VB￨O￨- specified￨L￨VBN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- n￨L￨NN￨O￨- separately￨L￨RB￨O￨- and￨L￨CC￨O￨- includes￨L￨VBZ￨O￨- clumsy￨L￨JJ￨O￨- symmetrization￨L￨NN￨O￨- operations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Expectation￨U￨NN￨O￨- values￨L￨NNS￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- as￨L￨IN￨O￨- above￨L￨RB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- local￨L￨JJ￨O￨- number￨L￨NN￨O￨- density￨L￨NN￨O￨- is￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- local￨L￨JJ￨O￨- number￨L￨NN￨O￨- operator￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨A equation￨L￨NN￨O￨A again￨L￨RB￨O￨- becomes￨L￨VBZ￨O￨- Eqn￨U￨NN￨O￨- .3￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- time￨L￨NN￨O￨- with￨L￨IN￨O￨- HamiltonianThis￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- simpler￨L￨JJR￨O￨- because￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- to￨L￨TO￨O￨- specify￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- possible￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- bugs￨L￨NNS￨O￨- separately￨L￨RB￨O￨- .￨L￨.￨O￨- +Functional￨U￨JJ￨O￨- differentiation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- action￨L￨NN￨O￨A yields￨L￨VBZ￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- fields￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- all￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- contend￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- RNA￨U￨NN￨O￨- virus￨L￨NN￨O￨- phylodynamics￨L￨NNS￨O￨- will￨L￨MD￨O￨- allow￨L￨VB￨O￨- more￨L￨RBR￨O￨- directed￨L￨VBN￨O￨- attempts￨L￨NNS￨O￨- at￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- facilitate￨L￨VB￨O￨- more￨L￨JJR￨O￨- accurate￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- newly￨L￨RB￨O￨- emerged￨L￨VBN￨O￨- viruses￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- assist￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- exhibit￨L￨VBP￨O￨- complex￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- dengue￨L￨NN￨O￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Such￨U￨PDT￨O￨- a￨L￨DT￨O￨- marriage￨L￨NN￨O￨- of￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- currently￨L￨RB￨DATE￨- only￨L￨RB￨O￨- potentially￨L￨RB￨O￨- possible￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- select￨L￨JJ￨O￨- few￨L￨JJ￨O￨- human￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- large￨L￨JJ￨O￨- genome￨L￨NN￨O￨A sequence￨L￨NN￨O￨- datasets￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- acquired￨L￨VBN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- here￨L￨RB￨O￨- fundamental￨L￨JJ￨O￨- gaps￨L￨NNS￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- remain￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- striking￨L￨JJ￨O￨- that￨L￨IN￨O￨- so￨L￨RB￨O￨- few￨L￨JJ￨O￨- complete￨L￨JJ￨O￨- genome￨L￨NN￨O￨A sequences￨L￨NNS￨O￨- are￨L￨VBP￨O￨- currently￨L￨RB￨DATE￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- in￨L￨IN￨O￨- exquisite￨L￨JJ￨O￨- detail￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- these￨L￨DT￨O￨- sequences￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- so￨L￨RB￨O￨- sparsely￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- full￨L￨JJ￨O￨- phylodynamic￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- been￨L￨VBN￨O￨- achieved￨L￨VBN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- this￨L￨DT￨O￨- genomic￨L￨JJ￨O￨- revolution￨L￨NN￨O￨- will￨L￨MD￨O￨- affect￨L￨VB￨O￨- all￨L￨DT￨O￨- microbes￨L￨NNS￨O￨- alike￨L￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- focus￨L￨NN￨O￨- here￨L￨RB￨O￨- is￨L￨VBZ￨O￨- on￨L￨IN￨O￨- RNA￨U￨NN￨O￨- viruses￨L￨NNS￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- rapidity￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- observable￨L￨JJ￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- observation￨L￨NN￨O￨- ,￨L￨,￨O￨- allows￨L￨VBZ￨O￨- phylodynamic￨L￨JJ￨O￨- inferences￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- with￨L￨IN￨O￨- great￨L￨JJ￨O￨- precision￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rapidity￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- genome￨L￨NN￨O￨A sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- generated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- swine-origin￨L￨JJ￨O￨- H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- virus￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- testament￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- technology￨L￨NN￨O￨- .￨L￨.￨O￨- +Surprisingly￨U￨RB￨O￨- ,￨L￨,￨O￨- certain￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- hierarchical￨L￨JJ￨O￨- modular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- contain￨L￨VBP￨O￨- enough￨L￨JJ￨O￨- topological￨L￨JJ￨O￨- cues￨L￨NNS￨O￨- for￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- both￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- patterns￨L￨NNS￨O￨- to￨L￨TO￨O￨- emerge￨L￨VB￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- dynamic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- switch￨L￨VB￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- modes￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- spontaneous￨L￨JJ￨O￨- node￨L￨NN￨O￨- activation￨L￨NN￨O￨- increases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- follow￨L￨VBP￨O￨- this￨L￨DT￨O￨- line￨L￨NN￨O￨- of￨L￨IN￨O￨- thought￨L￨NN￨O￨- and￨L￨CC￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- of￨L￨IN￨O￨- topology￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- excitable￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- currently￨L￨RB￨DATE￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- neuron￨L￨NN￨O￨- firing￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- graph￨L￨NN￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- hierarchical￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- excitable￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- use￨L￨VBP￨O￨- here￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Materials￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Methods￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨A and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- analyzed￨L￨VBN￨O￨- by￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- :￨L￨:￨O￨- waves￨L￨NNS￨O￨- propagating￨L￨VBG￨O￨- from￨L￨IN￨O￨- central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- module-based￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- analyzing￨L￨VBG￨O￨- these￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- modular￨L￨JJ￨O￨A graph￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- clusters￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- simultaneous￨L￨JJ￨O￨- excitations￨L￨NNS￨O￨- coincide￨L￨VBP￨O￨- well￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- modules￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- weak￨L￨JJ￨O￨- within￨L￨IN￨O￨- cluster￨L￨NN￨O￨- selection￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- selective￨L￨JJ￨O￨- sweeps￨L￨NNS￨O￨- that￨L￨WDT￨O￨- accompany￨L￨VBP￨O￨- antigenic￨L￨JJ￨O￨A clusters￨L￨NNS￨O￨- transition￨L￨NN￨O￨- are￨L￨VBP￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- recover￨L￨VB￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- HA￨U￨NNP￨O￨- interpandemic￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- finding￨L￨NN￨O￨- confirmed￨L￨VBN￨O￨- by￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- data￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Contrary￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- resorts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- gradual￨L￨JJ￨O￨- antigenic￨L￨JJ￨O￨A drift￨L￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- results￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- to￨L￨TO￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- serial￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- to￨L￨TO￨O￨- transitions￨L￨NNS￨O￨- provoked￨L￨VBN￨O￨- by￨L￨IN￨O￨- punctuated￨L￨VBN￨O￨- evolution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rare￨L￨JJ￨O￨- immune-escape￨L￨JJ￨O￨- mutants￨L￨NNS￨O￨- with￨L￨IN￨O￨- strong￨L￨JJ￨O￨- antigenic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- antigenic￨L￨JJ￨O￨A space￨L￨NN￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- a￨L￨DT￨O￨- self-organisation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- strains￨L￨NNS￨O￨- into￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- clusters￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨A clusters￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- degenerated￨L￨VBN￨O￨- genotype￨L￨NN￨O￨- to￨L￨TO￨O￨- phenotype￨L￨NN￨O￨- map￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- have￨L￨VBP￨O￨- confirmed￨L￨VBN￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨A clusters￨L￨NNS￨O￨- emerging￨L￨VBG￨O￨- and￨L￨CC￨O￨- replacing￨L￨VBG￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- every￨L￨DT￨SET￨- 2￨L￨CD￨SET￨- to￨L￨TO￨SET￨- 8￨L￨CD￨SET￨- years￨L￨NNS￨SET￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- critical￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- determined￨L￨VBD￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨A of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- slows￨L￨VBZ￨O￨- down￨L￨RP￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- dynamics.Comparing￨L￨VBG￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- removal￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- established￨L￨JJ￨O￨- hub￨L￨NN￨O￨- removal￨L￨NN￨O￨- we￨L￨PRP￨O￨- find￨L￨VBD￨O￨- that￨L￨IN￨O￨- removing￨L￨VBG￨O￨- selected￨L￨VBN￨O￨- edges￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- bigger￨L￨JJR￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- spreading￨L￨NN￨O￨- activity￨L￨NN￨O￨- with￨L￨IN￨O￨- significantly￨L￨RB￨O￨- lower￨L￨JJR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- removed￨L￨VBN￨O￨- connections￨L￨NNS￨O￨- .￨L￨.￨O￨- +Whereas￨U￨IN￨O￨- some￨L￨DT￨O￨- strategies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- computationally￨L￨RB￨O￨- costly￨L￨JJ￨O￨- for￨L￨IN￨O￨- large￨L￨JJ￨O￨- or￨L￨CC￨O￨- rapidly￨L￨RB￨O￨- evolving￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- edge￨L￨NN￨O￨- removal￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- as￨L￨RB￨O￨- fast￨L￨RB￨O￨- as￨L￨IN￨O￨- hub￨L￨NN￨O￨- removal￨L￨NN￨O￨- while￨L￨IN￨O￨- offering￨L￨VBG￨O￨- much￨L￨RB￨O￨- better￨L￨JJR￨O￨- spreading￨L￨NN￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Network￨U￨NNP￨O￨- spreading￨L￨VBG￨O￨A simulations￨L￨NNS￨O￨- starting￨L￨VBG￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- node￨L￨NN￨O￨- were￨L￨VBD￨O￨- summarized￨L￨VBN￨O￨- by￨L￨IN￨O￨- T1/2￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- steps￨L￨NNS￨O￨- for￨L￨IN￨O￨- infecting￨L￨VBG￨O￨- half￨L￨PDT￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Structural￨U￨JJ￨O￨- network￨L￨NN￨O￨- integrity￨L￨NN￨O￨- could￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- partially￨L￨RB￨O￨- inactivating￨L￨VBG￨O￨- specific￨L￨NN￨O￨- connections￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- edges￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- same￨L￨JJ￨O￨- calculations￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- typically￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wholly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- approximately￨L￨RB￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- effective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- partially￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨A population￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- eg.￨L￨RB￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- estimated￨L￨VBN￨O￨- as￨L￨IN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- previous￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- reasonable￨L￨JJ￨O￨- to￨L￨TO￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- much￨L￨JJ￨O￨- larger￨L￨JJR￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- than￨L￨IN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Understanding￨U￨VBG￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨A behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- sensitivity￨L￨NN￨O￨- to￨L￨TO￨O￨- parameters￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- forecasting￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- in￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- antigenic￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- mechanisms￨L￨NNS￨O￨- combine￨L￨VBP￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- complex￨L￨NN￨O￨- seasonal￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- featuring￨L￨VBG￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- annual￨L￨JJ￨SET￨A attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- and￨L￨CC￨O￨- alternating￨L￨VBG￨O￨- sequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- dominant￨L￨JJ￨O￨- annual￨L￨JJ￨SET￨- strains￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- parameters￨L￨NNS￨O￨- control￨L￨VBP￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- The￨U￨DT￨O￨- timescale￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- of￨L￨IN￨O￨- antigenically￨L￨RB￨O￨- new￨L￨JJ￨O￨- strains￨L￨NNS￨O￨A ,￨L￨,￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- mean￨L￨NN￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- D￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Model￨U￨NNP￨TITLE￨- Section￨U￨NNP￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- from￨L￨IN￨O￨- France￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- See￨U￨VB￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- indicate￨L￨VBP￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- deviation￨L￨NN￨O￨- for￨L￨IN￨O￨- AAR￨U￨NNP￨ORGANIZATION￨- across￨L￨IN￨O￨- successive￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- approx￨L￨RB￨O￨- 40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- employed￨L￨VBD￨O￨- advanced￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨A distribution￨L￨NN￨O￨- schedules￨L￨NNS￨O￨- that￨L￨WDT￨O￨- vary￨L￨VBP￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- release￨L￨NN￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- allocations￨L￨NNS￨O￨- to￨L￨TO￨O￨- states￨L￨NNS￨O￨- are￨L￨VBP￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- overall￨L￨JJ￨O￨- population￨L￨NN￨O￨- or￨L￨CC￨O￨- recent￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- U.S.￨U￨NNP￨COUNTRY￨- Government￨U￨NNP￨O￨- holds￨L￨VBZ￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- courses￨L￨NNS￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨A medications￨L￨NNS￨O￨- its￨L￨PRP$￨O￨- Strategic￨U￨NNP￨O￨- National￨U￨NNP￨O￨- Stockpile￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SNS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- published￨L￨VBN￨O￨- criteria￨L￨NNS￨O￨- for￨L￨IN￨O￨- sequential￨L￨JJ￨O￨- release￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- medications￨L￨NNS￨O￨- to￨L￨TO￨O￨- States￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Territories￨U￨NNPS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- worldwide￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- currently￨L￨RB￨DATE￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- A￨U￨NNP￨MISC￨- cost-utility￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- preadolescent￨L￨JJ￨O￨- Canadian￨U￨JJ￨NATIONALITY￨- femalesAndrea￨L￨NN￨O￨- M￨U￨NN￨O￨- Anonychuk￨U￨NN￨O￨- †￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Chris￨U￨NNP￨PERSON￨- T￨U￨NN￨PERSON￨- Bauch￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Maraki￨U￨NNP￨PERSON￨- Fikre￨U￨NNP￨PERSON￨- Merid4￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Georges￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Kriekinge5￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Nadia￨U￨NNP￨O￨- Demarteau5￨U￨NNP￨O￨- †￨L￨NNP￨O￨- Citation￨U￨NNP￨O￨- 9:401￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Anonychuk￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2009Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- Canadian￨U￨JJ￨NATIONALITY￨- women￨L￨NNS￨O￨- undergo￨L￨VBP￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- screening￨L￨NN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- once￨L￨RB￨DATE￨- every￨L￨DT￨SET￨- 3￨L￨CD￨SET￨- years￨L￨NNS￨SET￨- ,￨L￨,￨O￨- approximately￨L￨RB￨O￨- 1,300￨L￨CD￨NUMBER￨- women￨L￨NNS￨O￨- were￨L￨VBD￨O￨- diagnosed￨L￨VBN￨O￨- with￨L￨IN￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- approximately￨L￨RB￨O￨- 380￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Vaccinating￨U￨VBG￨O￨- 12-year￨L￨JJ￨DURATION￨- old￨L￨JJ￨DURATION￨- females￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 100,000￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- between￨L￨IN￨O￨- 390-633￨L￨CD￨NUMBER￨- undiscounted￨L￨JJ￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- 47￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- -77￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- 168-275￨L￨CD￨NUMBER￨- undiscounted￨L￨JJ￨O￨- deaths￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 48￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- -78￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- over￨L￨IN￨O￨- their￨L￨PRP$￨O￨- lifetime￨L￨NN￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- cross-protection￨L￨NN￨O￨- against￨L￨IN￨O￨- other￨L￨JJ￨O￨- oncogenic￨L￨JJ￨O￨- HPV￨U￨NN￨O￨- types￨L￨NNS￨O￨- were￨L￨VBD￨O￨- included￨L￨VBN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- a￨L￨DT￨O￨- healthcare￨L￨NN￨O￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- with￨L￨IN￨O￨- efficacy￨L￨NN￨O￨- against￨L￨IN￨O￨- HPV-16￨U￨NN￨O￨- /￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- cross-protection￨L￨NN￨O￨- against￨L￨IN￨O￨- other￨L￨JJ￨O￨- oncogenic￨L￨JJ￨O￨- HPV￨U￨NN￨O￨- types￨L￨NNS￨O￨- was￨L￨VBD￨O￨- evaluated￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- undergoing￨L￨VBG￨O￨- current￨L￨JJ￨DATE￨- screening￨L￨NN￨O￨A practices￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- base-case￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- included￨L￨VBD￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- screening￨L￨NN￨O￨A coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- 75￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- $￨L￨$￨MONEY￨- 135/dose￨L￨CD￨MONEY￨- for￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 3￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- discount￨L￨NN￨O￨- rate￨L￨NN￨O￨- on￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- health￨L￨NN￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- estimates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- and￨L￨CC￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- 12-year￨L￨JJ￨DURATION￨- old￨L￨JJ￨DURATION￨- Canadian￨U￨JJ￨NATIONALITY￨- females￨L￨NNS￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- AS04-adjuvanted￨U￨JJ￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- careful￨L￨JJ￨O￨- when￨L￨WRB￨O￨- using￨L￨VBG￨O￨- observed￨L￨VBN￨O￨- exponential￨L￨JJ￨O￨A growth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- quantify￨L￨VBP￨O￨- the￨L￨DT￨O￨- discrepancies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- arise.KeywordsBasic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Emerging￨U￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- Epidemics￨U￨NNS￨O￨- Mathematics￨U￨NNP￨O￨- Subject￨U￨NNP￨O￨- Classification￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 92B05￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- IntroductionThe￨U￨NNP￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- agent￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- typical￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- only￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mean￨L￨NN￨O￨- generation￨L￨NN￨O￨A interval￨L￨NN￨O￨A may￨L￨MD￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- formula￨L￨NN￨O￨- Equality￨U￨NN￨O￨- T￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- G￨U￨NN￨ORGANIZATION￨- }￨L￨-RRB-￨ORGANIZATION￨- Integral￨U￨JJ￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- limits￨L￨VBZ￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- rm￨L￨FW￨O￨- f￨L￨FW￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- x￨L￨CC￨O￨- Given￨U￨VBN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- increase￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- by￨L￨IN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- e￨L￨SYM￨O￨- rt￨L￨NN￨O￨- with￨L￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≃￨L￨CD￨NUMBER￨- N.￨U￨NNP￨O￨- +A￨U￨DT￨O￨- frequently￨L￨RB￨O￨- used￨L￨VBN￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- function￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- cumulative￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- approx￨L￨RB￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- T￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- G￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- r￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- T￨U￨NN￨O￨- G￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- mean￨L￨NN￨O￨- generation￨L￨NN￨O￨A interval￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +HeesterbeekOpen￨U￨NNP￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1.2￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 43￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractWe￨U￨NN￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- merit￨L￨NN￨O￨- of￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨JJ￨O￨- early￨L￨JJ￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- emerging￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- generation￨L￨NN￨O￨A interval￨L￨NN￨O￨A only￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- goals￨L￨NNS￨O￨- :￨L￨:￨O￨- To￨U￨TO￨O￨- model￨L￨VB￨O￨- a￨L￨DT￨O￨- possible￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- including￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- importation￨L￨NN￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- ;￨L￨:￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- case￨L￨NN￨O￨- detection￨L￨NN￨O￨- ,￨L￨,￨O￨- case￨L￨NN￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- quarantine￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- medication￨L￨NN￨O￨- for￨L￨IN￨O￨- therapy￨L￨NN￨O￨- and￨L￨CC￨O￨- post￨L￨NN￨O￨- exposure￨L￨NN￨O￨- prophylaxis￨L￨NN￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- effectiveness￨L￨NN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ;￨L￨:￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- possible￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- –￨L￨:￨O￨- if￨L￨IN￨O￨- known￨L￨VBN￨O￨- –￨L￨:￨O￨- favour￨L￨VBP￨O￨- the￨L￨DT￨O￨- adaptation￨L￨NN￨O￨- of￨L￨IN￨O￨- measures￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- termination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- an￨L￨DT￨O￨- R0￨U￨NN￨O￨- of￨L￨IN￨O￨- 1.58￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- after￨L￨IN￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- case￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- 10￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- 11￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- imported￨L￨VBN￨O￨A cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- compare￨L￨VBP￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- estimate￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- infected￨L￨VBN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- 4.3￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- infected￨L￨JJ￨O￨- 44.8￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- diseased￨L￨JJ￨O￨- 38.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- imported￨L￨VBN￨O￨A cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- other￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- and￨L￨CC￨O￨- include￨L￨VBP￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- ,￨L￨,￨O￨- isolation￨L￨NN￨O￨- and￨L￨CC￨O￨- quarantine￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- post￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- prophylaxis￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- considered￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- of￨L￨IN￨O￨- case￨L￨NN￨O￨- importation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- S1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- firstly￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- imported￨L￨VBN￨O￨A cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- (￨L￨-LRB-￨O￨- five￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- ten￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- secondly￨L￨RB￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- exponentially￨L￨RB￨O￨- growing￨L￨VBG￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- imported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- 120￨L￨CD￨NUMBER￨- imported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- strategy￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spill-over￨L￨NN￨O￨- from￨L￨IN￨O￨- imported￨L￨VBN￨O￨A cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- slow-down￨L￨NN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Routinely￨U￨RB￨O￨- collected￨L￨VBN￨O￨- data￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- influenza-like-illness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- reporting￨L￨NN￨O￨- from￨L￨IN￨O￨- sentinel￨L￨NN￨O￨A networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- physicians￨L￨NNS￨O￨- and￨L￨CC￨O￨- reported￨L￨VBD￨O￨- hospitalizations￨L￨NNS￨O￨- suffer￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- usual￨L￨JJ￨O￨- caveats￨L￨NNS￨O￨- of￨L￨IN￨O￨- discounting￨L￨VBG￨O￨- a￨L￨DT￨O￨- potentially￨L￨RB￨O￨- large￨L￨JJ￨O￨- unobserved￨L￨JJ￨O￨- subclinical￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- uncertain￨L￨JJ￨O￨- contextual￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- seeking￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- difficult￨L￨JJ￨O￨- etiologic￨L￨JJ￨O￨- interpretation￨L￨NN￨O￨- in￨L￨IN￨O￨- locations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- indeed￨L￨RB￨O￨- other￨L￨JJ￨O￨- upper￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- with￨L￨IN￨O￨- similar￨L￨JJ￨O￨- presentations￨L￨NNS￨O￨- ,￨L￨,￨O￨- co-circulate￨L￨JJ￨O￨- with￨L￨IN￨O￨- H1N1pdm￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- strain￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨DT￨O￨- H1N1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1pdm￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- highlighted￨L￨VBN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- investigation￨L￨NN￨O￨A and￨L￨CC￨O￨- population￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- support￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- decision￨L￨NN￨O￨- making￨L￨NN￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- independent￨L￨JJ￨RELIGION￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- that￨L￨WDT￨O￨- provided￨L￨VBD￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- isolates￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- discern￨L￨VB￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- strain￨L￨NN￨O￨- were￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- sentinel￨L￨NN￨O￨A surveillance￨L￨NN￨O￨- system￨L￨NN￨O￨- designed￨L￨VBN￨O￨- for￨L￨IN￨O￨- exactly￨L￨RB￨O￨- that￨L￨DT￨O￨- purpose￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Parameters￨U￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- investigation￨L￨NN￨O￨A data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- give￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- how￨L￨WRB￨O￨- underlying￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- will￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- Linear￨U￨JJ￨O￨- and￨L￨CC￨O￨- log-linear￨L￨JJ￨O￨- regression￨L￨NN￨O￨- of￨L￨IN￨O￨- guinea￨L￨NN￨COUNTRY￨- pig￨L￨NN￨O￨- airborne￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- on￨L￨IN￨O￨- specific￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- AH￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Log-linear￨U￨JJ￨MISC￨- regression￨L￨NN￨O￨- of￨L￨IN￨O￨- 1-hour￨L￨JJ￨DURATION￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- survival￨L￨NN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- on￨L￨IN￨O￨- specific￨L￨JJ￨O￨- humidity￨L￨NN￨O￨- ;￨L￨:￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Functional￨U￨JJ￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- and￨L￨CC￨O￨- per￨L￨IN￨O￨- Equation￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- d￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- 1972-2002￨L￨CD￨DURATION￨- daily￨L￨JJ￨SET￨- climatology￨L￨NN￨O￨- of￨L￨IN￨O￨- 2-meter￨L￨JJ￨O￨- above-ground￨L￨JJ￨O￨- NCEP-NCAR￨U￨NN￨O￨- reanalysis￨L￨NN￨O￨- specific￨L￨JJ￨O￨- humidity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- for￨L￨IN￨O￨- Arizona￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- Florida￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- Illinois￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- Washington￨U￨NNP￨STATE_OR_PROVINCE￨- state￨L￨NN￨O￨- ;￨L￨:￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- 1972-2002￨L￨CD￨DURATION￨- average￨L￨JJ￨O￨- daily￨L￨JJ￨SET￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨- humidity￨L￨NN￨O￨- climatology￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- best-fit￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- combination￨L￨NN￨O￨- from￨L￨IN￨O￨- SIRS￨U￨NNP￨O￨- simulations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- =￨L￨JJ￨O￨- 3.52￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- =￨L￨JJ￨O￨- 1.12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- functional￨L￨JJ￨O￨- form￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1c￨L￨NN￨O￨- and￨L￨CC￨O￨- Equation￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Average￨U￨JJ￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- wintertime￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 10￨L￨CD￨NUMBER￨- best-fit￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- shown￨L￨VBN￨O￨- for￨L￨IN￨O￨- 100￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- prior￨L￨RB￨O￨- through￨L￨IN￨O￨- 150￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- post￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- onset￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- minimum￨L￨NN￨O￨- 400￨L￨CD￨NUMBER￨- infections/day￨L￨NN￨O￨- during￨L￨IN￨O￨- 2￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- prior￨L￨RB￨O￨- ;￨L￨:￨O￨- minimum￨L￨JJ￨O￨- 5000￨L￨CD￨NUMBER￨- infections/day￨L￨NN￨O￨- at￨L￨IN￨DURATION￨- least￨L￨JJS￨DURATION￨- one￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- during￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- 30￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Annual￨U￨JJ￨SET￨- wintertime￨L￨NN￨O￨- mortality￨L￨NN￨O￨- peaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- evident￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- records￨L￨NNS￨O￨- of￨L￨IN￨O￨- excess￨L￨JJ￨O￨- pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- P&I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- robust￨L￨JJ￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- at￨L￨IN￨O￨- national￨L￨JJ￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NNP￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- similar￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- between￨L￨IN￨O￨- AH￨U￨NN￨O￨- and￨L￨CC￨O￨- airborne￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨A transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- laboratory￨L￨NN￨O￨- guinea￨L￨NN￨COUNTRY￨- pigs￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- transmission￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- markedly￨L￨RB￨O￨- as￨L￨IN￨O￨- AH￨U￨NN￨O￨- levels￨L￨NNS￨O￨- decrease￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- seasonal￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- favors￨L￨VBZ￨O￨- a￨L￨DT￨O￨- wintertime￨L￨JJ￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨A survival￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- seasonal￨L￨JJ￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- during￨L￨IN￨O￨- winter￨L￨NN￨DATE￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- can￨L￨MD￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- when￨L￨WRB￨O￨- daily￨L￨JJ￨SET￨- AH￨U￨NN￨O￨- conditions￨L￨NNS￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- modulate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨A .￨L￨.￨O￨- +Stochastic￨U￨JJ￨O￨- spatial￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- or￨L￨CC￨O￨- small￨L￨JJ￨O￨- communities￨L￨NNS￨O￨A are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- in￨L￨IN￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- more￨L￨JJR￨O￨- traditional￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- valuable￨L￨JJ￨O￨- tool￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- animals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Traditionally￨U￨RB￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- often￨L￨RB￨O￨- take￨L￨VBP￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- variables￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- broad￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- classes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- increased￨L￨VBN￨O￨- computational￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- previous￨L￨JJ￨O￨- implementations￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- parameterization￨L￨NN￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨A using￨L￨VBG￨O￨A the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- per￨L￨FW￨O￨- contact￨L￨NN￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- illustrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- utility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- refined￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- simulation￨L￨NN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- seeding￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Taiwan￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- an￨L￨DT￨O￨- algorithmic￨L￨JJ￨O￨- refinement￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- communities￨L￨NNS￨O￨A .￨L￨.￨O￨- +Issues￨U￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- exposure￨L￨NN￨O￨- and￨L￨CC￨O￨- diagnostic￨L￨JJ￨O￨A test￨L￨NN￨O￨- sensitivity￨L￨NN￨O￨- or￨L￨CC￨O￨- specificity￨L￨NN￨O￨- are￨L￨VBP￨O￨- fundamental￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨- to￨L￨TO￨O￨- epidemiologists￨L￨NNS￨O￨- when￨L￨WRB￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- their￨L￨PRP$￨O￨- intrinsic￨L￨JJ￨O￨- importance￨L￨NN￨O￨- is￨L￨VBZ￨O￨- currently￨L￨RB￨DATE￨- ignored￨L￨VBN￨O￨- in￨L￨IN￨O￨- quantitative￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- theory￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Heritabilities￨U￨NNS￨O￨- are￨L￨VBP￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- to￨L￨TO￨O￨- what￨L￨WP￨O￨- degree￨L￨NN￨O￨- the￨L￨DT￨O￨- expected￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- classification￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- healthy￨L￨JJ￨O￨A and￨L￨CC￨O￨- diseased￨L￨JJ￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- individual￨L￨JJ￨O￨- SNP￨U￨NN￨O￨- associations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- inferred￨L￨VBN￨O￨- from￨L￨IN￨O￨- departures￨L￨NNS￨O￨- of￨L￨IN￨O￨- SNP￨U￨NN￨ORGANIZATION￨- allele￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- from￨L￨IN￨O￨- their￨L￨PRP$￨O￨- expectations￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- categories￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- genetic￨L￨JJ￨O￨A associations￨L￨NNS￨O￨- uncovered￨L￨VBN￨O￨- by￨L￨IN￨O￨- such￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- will￨L￨MD￨O￨- indicate￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- genetic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- ‘￨L￨``￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resistance￨L￨NN￨O￨- ’￨L￨''￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- ‘￨L￨``￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resistance￨L￨NN￨O￨- ’￨L￨''￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- generically￨L￨RB￨O￨- to￨L￨TO￨O￨- cover￨L￨VB￨O￨- any￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- processes￨L￨NNS￨O￨- shown￨L￨VBN￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- being￨L￨VBG￨O￨- diagnosed￨L￨VBN￨O￨- as￨L￨IN￨O￨- diseased￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- and￨L￨CC￨O￨- diagnostic￨L￨JJ￨O￨A test￨L￨NN￨O￨- sensitivity￨L￨NN￨O￨- and￨L￨CC￨O￨- specificity￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- explored￨L￨VBN￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- are￨L￨VBP￨O￨- termed￨L￨VBN￨O￨- static￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +Specificity￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- diagnostic￨L￨JJ￨O￨A test￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- sensitivity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- diseased￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- diseased￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- test￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- simulate￨L￨VB￨O￨- several￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- can￨L￨MD￨O￨- either￨L￨RB￨O￨- change￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- change￨L￨VB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Briefly￨U￨RB￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- within￨L￨IN￨O￨- which￨L￨WDT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- random￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- section￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- 's￨L￨POS￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- simulated￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +FluTE￨U￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A across￨L￨IN￨O￨- major￨L￨JJ￨O￨- metropolitan￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- continental￨L￨JJ￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- .￨L￨.￨O￨- +FluTE￨U￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- pathogen￨L￨NN￨O￨- virulence￨L￨NN￨O￨- can￨L￨MD￨O￨- respond￨L￨VB￨O￨- positively￨L￨RB￨O￨- or￨L￨CC￨O￨- negatively￨L￨RB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- temperature￨L￨NN￨O￨- ,￨L￨,￨O￨- nutrient￨L￨JJ￨O￨- availability￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- habitat￨L￨NN￨O￨- quality￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- environmental￨L￨JJ￨O￨A conditions￨L￨NNS￨O￨- can￨L￨MD￨O￨- promote￨L￨VB￨O￨- physiological￨L￨JJ￨O￨- stress￨L￨NN￨O￨- that￨L￨WDT￨O￨- impairs￨L￨VBZ￨O￨- host￨L￨NN￨TITLE￨- immunity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- susceptibility￨L￨NN￨O￨- between￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- genotypes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Significant￨U￨JJ￨O￨- relationships￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- between￨L￨IN￨O￨- coral￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A prevalence￨L￨NN￨O￨A and￨L￨CC￨O￨- elevated￨L￨JJ￨O￨- water￨L￨NN￨O￨- temperatures￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- decline￨L￨NN￨O￨- in￨L￨IN￨O￨- water￨L￨NN￨O￨- quality￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- densities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- coral￨L￨NN￨O￨- bleaching￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨A factors￨L￨NNS￨O￨- on￨L￨IN￨O￨- coral￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- modes￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- intricate￨L￨JJ￨O￨- and￨L￨CC￨O￨- synergistic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Spatial￨U￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- coral￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- linked￨L￨VBN￨O￨- to￨L￨TO￨O￨- environmental￨L￨JJ￨O￨A conditions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Log-linear￨U￨JJ￨MISC￨- regression￨L￨NN￨O￨- of￨L￨IN￨O￨- guinea￨L￨NN￨COUNTRY￨- pig￨L￨NN￨O￨- airborne￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- on￨L￨IN￨O￨- specific￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- AH￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- log-linear￨L￨JJ￨O￨- regression￨L￨NN￨O￨- of￨L￨IN￨O￨- 1-h￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- survival￨L￨NN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- on￨L￨IN￨O￨- specific￨L￨JJ￨O￨- humidity￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- functional￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- q￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- per￨L￨IN￨O￨- Equation￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 1972￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2002￨L￨CD￨DATE￨- daily￨L￨JJ￨SET￨- climatology￨L￨NN￨O￨- of￨L￨IN￨O￨- 2-m￨L￨JJ￨O￨- above-ground￨L￨JJ￨O￨- NCEP-NCAR￨U￨NN￨O￨- reanalysis￨L￨NN￨O￨- specific￨L￨JJ￨O￨- humidity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- for￨L￨IN￨O￨- Arizona￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- Florida￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- Illinois￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Washington￨U￨NNP￨STATE_OR_PROVINCE￨- state￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 1972￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2002￨L￨CD￨DATE￨- average￨L￨JJ￨O￨- daily￨L￨JJ￨SET￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨- humidity￨L￨NN￨O￨- climatology￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- best-fit￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- combination￨L￨NN￨O￨- from￨L￨IN￨O￨- SIRS￨U￨NNP￨O￨- simulations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- 0max￨L￨NN￨O￨- =￨L￨JJ￨O￨- 3.52￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨DURATION￨- min￨L￨NN￨DURATION￨- =￨L￨JJ￨O￨- 1.12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- functional￨L￨JJ￨O￨- form￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1C￨L￨NN￨O￨- and￨L￨CC￨O￨- Equation￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- F￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- average￨L￨JJ￨O￨- R￨U￨NN￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- wintertime￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ten￨L￨CD￨NUMBER￨- best-fit￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- shown￨L￨VBN￨O￨- for￨L￨IN￨O￨- 100￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- through￨L￨IN￨O￨- 150￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- post￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- onset￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- minimum￨L￨NN￨O￨- 400￨L￨CD￨NUMBER￨- infections/day￨L￨NN￨O￨- during￨L￨IN￨O￨- 2￨L￨CD￨DURATION￨- wk￨L￨NN￨DURATION￨- prior￨L￨RB￨O￨- ;￨L￨:￨O￨- minimum￨L￨JJ￨O￨- 5,000￨L￨CD￨NUMBER￨- infections/day￨L￨NN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- 1￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- during￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- 30￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Annual￨U￨JJ￨SET￨- wintertime￨L￨NN￨O￨- mortality￨L￨NN￨O￨- peaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- evident￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- records￨L￨NNS￨O￨- of￨L￨IN￨O￨- excess￨L￨JJ￨O￨- pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- P&I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- robust￨L￨JJ￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- at￨L￨IN￨O￨- national￨L￨JJ￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NNP￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- wintertime￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A as￨L￨IN￨O￨- the￨L￨DT￨O￨- date￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- 2￨L￨CD￨DURATION￨- wk￨L￨NN￨DURATION￨- prior￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- excess￨L￨JJ￨O￨- P&I￨U￨NNP￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- at￨L￨IN￨O￨- or￨L￨CC￨O￨- above￨L￨IN￨O￨- a￨L￨DT￨O￨- prescribed￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- 0.01￨L￨CD￨NUMBER￨- deaths/100￨L￨NN￨O￨- ,000￨L￨CD￨NUMBER￨- people/day￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- seasonal￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- favors￨L￨VBZ￨O￨- a￨L￨DT￨O￨- wintertime￨L￨JJ￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨A survival￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- seasonal￨L￨JJ￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- during￨L￨IN￨O￨- winter￨L￨NN￨DATE￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- can￨L￨MD￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- when￨L￨WRB￨O￨- daily￨L￨JJ￨SET￨- AH￨U￨NN￨O￨- conditions￨L￨NNS￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- modulate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assumed￨L￨VBD￨O￨- higher￨L￨JJR￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- higher￨L￨JJR￨O￨- infectious￨L￨JJ￨O￨A contact￨L￨NN￨O￨A rates￨L￨NNS￨O￨- among￨L￨IN￨O￨- students￨L￨NNS￨O￨- than￨L￨IN￨O￨- among￨L￨IN￨O￨- faculty/staff￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- vaccination￨L￨NN￨O￨- would￨L￨MD￨O￨- prevent￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- vaccinated￨L￨VBN￨O￨- persons￨L￨NNS￨O￨- and￨L￨CC￨O￨- would￨L￨MD￨O￨- attenuate￨L￨VB￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- if￨L￨IN￨O￨- they￨L￨PRP￨O￨- became￨L￨VBD￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- infected￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- asymptomatic￨L￨JJ￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- shorter￨L￨JJR￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- lower￨L￨JJR￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- than￨L￨IN￨O￨- persons￨L￨NNS￨O￨- with￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conducted￨L￨VBD￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨VBN￨O￨- ,￨L￨,￨O￨- college￨L￨NN￨O￨- campus￨L￨NN￨O￨- setting￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- extending￨L￨VBG￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- holiday/break￨L￨NN￨O￨- schedule￨L￨NN￨O￨- on￨L￨IN￨O￨- these￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +How￨U￨WRB￨O￨- this￨L￨DT￨O￨- might￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨A within￨L￨IN￨O￨- closed￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- college￨L￨NN￨O￨- campuses￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- well￨L￨RB￨O￨- described￨L￨VBN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- unvaccinated￨L￨JJ￨O￨- student￨L￨NN￨TITLE￨- who￨L￨WP￨O￨- becomes￨L￨VBZ￨O￨- ill￨L￨JJ￨O￨- with￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨A contact￨L￨NN￨O￨A rate￨L￨NN￨O￨- of￨L￨IN￨O￨- 0.5￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- (￨L￨-LRB-￨O￨- ie￨L￨FW￨O￨- 17￨L￨CD￨NUMBER￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- *￨L￨SYM￨O￨- 0.03￨L￨CD￨NUMBER￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- per￨L￨IN￨O￨- contact￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- once￨L￨RB￨DATE￨- infected￨L￨VBN￨O￨- a￨L￨DT￨O￨- person￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- once￨L￨RB￨DATE￨- recovered￨L￨VBD￨O￨- the￨L￨DT￨O￨- person￨L￨NN￨O￨- is￨L￨VBZ￨O￨- immune￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A .￨L￨.￨O￨- +Having￨U￨VBG￨O￨- estimated￨L￨VBN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- then￨L￨RB￨O￨- proceed￨L￨VB￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- projections￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- differs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- mainly￨L￨RB￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- larger￨L￨JJR￨O￨- initial￨L￨JJ￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- although￨L￨IN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- argue￨L￨VBP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- other￨L￨JJ￨O￨- investigators￨L￨NNS￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- is￨L￨VBZ￨O￨- questionable￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- make￨L￨VB￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- more￨L￨RBR￨O￨- transparent￨L￨JJ￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- H1N1￨U￨NN￨O￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- several￨L￨JJ￨O￨- large-scale￨L￨JJ￨O￨- research￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- into￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A strain￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- follow￨L￨VBP￨O￨- this￨L￨DT￨O￨- path￨L￨NN￨O￨- by￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- known￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A epidemics￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- which￨L￨WDT￨O￨- fully￨L￨RB￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- equality￨L￨NN￨O￨- holds￨L￨VBZ￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- for￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- pandemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A strain￨L￨NN￨O￨- H1N1￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- measuring￨L￨VBG￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- provide￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- prediction￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- ,￨L￨,￨O￨- unless￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- independent￨L￨JJ￨RELIGION￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Five￨U￨CD￨NUMBER￨- epidemiologically￨L￨RB￨O￨- important￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- invasion￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨A basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- households￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- household￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- totally￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- determines￨L￨VBZ￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- may￨L￨MD￨O￨- successfully￨L￨RB￨O￨- invade￨L￨VB￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- called￨L￨VBN￨O￨- the￨L￨DT￨O￨- Malthusian￨U￨JJ￨MISC￨- parameter￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- quantity￨L￨NN￨O￨- generally￨L￨RB￨O￨- measured￨L￨VBN￨O￨- for￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨- offspring￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- households￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- seeded￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- –￨L￨:￨O￨- the￨L￨DT￨O￨- expectation￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- random￨L￨JJ￨O￨- variable￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- amongst￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- of￨L￨IN￨O￨- households￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- transient￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- proceed￨L￨VB￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- this￨L￨DT￨O￨- methodology￨L￨NN￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- structured￨L￨JJ￨O￨- households￨L￨NNS￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- household￨L￨NN￨O￨A size￨L￨NN￨O￨- ,￨L￨,￨O￨- within-and￨L￨NN￨O￨- between-household￨L￨NN￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- waning￨L￨VBG￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- distribution￨L￨NN￨O￨- on￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- household￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- basic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- :￨L￨:￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- a￨L￨DT￨O￨- between-household￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- each￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨A generates￨L￨VBZ￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- straightforward￨L￨JJ￨O￨- Bayesian￨U￨JJ￨MISC￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- for￨L￨IN￨O￨- small￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- purely￨L￨RB￨O￨- demographic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- break￨L￨VBP￨O￨- down￨L￨RP￨O￨- for￨L￨IN￨O￨- large￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Beskos￨U￨NNP￨LOCATION￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- environmental￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- non-negligible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Bretó￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- advances￨L￨NNS￨O￨- in￨L￨IN￨O￨- statistical￨L￨JJ￨O￨A algorithms￨L￨NNS￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- hardware￨L￨NN￨O￨- have￨L￨VBP￨O￨- made￨L￨VBN￨O￨- it￨L￨PRP￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- tailor￨L￨VB￨O￨- statistical￨L￨JJ￨O￨- methodology￨L￨NN￨O￨- directly￨L￨RB￨O￨- to￨L￨TO￨O￨- questions￨L￨NNS￨O￨- of￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- interest￨L￨NN￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- expanded￨L￨VBN￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- confronted￨L￨VBN￨O￨- with￨L￨IN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Even￨U￨RB￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- useful￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- nonlinear￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stochasticity￨L￨NN￨O￨A can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- ignored￨L￨VBN￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- predictable￨L￨JJ￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- great￨L￨JJ￨O￨- deal￨L￨NN￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- techniques￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- mechanistic￨L￨JJ￨O￨A models￨L￨NNS￨O￨A to￨L￨TO￨O￨- time-series￨L￨JJ￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Bjø￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Bjørnstad￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- Finkenstädt￨U￨NNP￨O￨- ;￨L￨:￨O￨- Grenfell￨U￨NNP￨ORGANIZATION￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Clark￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Bjø￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Beskos￨U￨NNP￨O￨- ;￨L￨:￨O￨- Cook￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Cauchemez￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Ferrari￨U￨NNP￨ORGANIZATION￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨A stochastic￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- arising￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- proved￨L￨VBN￨O￨- relatively￨L￨RB￨O￨- recalcitrant￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- biologically￨L￨RB￨O￨- realistic￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- forcing￨L￨VBG￨O￨- amplitude￨L￨NN￨O￨A δ￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- immunity￨L￨NN￨O￨- loss￨L￨NN￨O￨- rate￨L￨NN￨O￨- ρ￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- term￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- vectorial￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- C0￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- IR￨U￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- subharmonic￨L￨JJ￨O￨- resonances￨L￨NNS￨O￨- are￨L￨VBP￨O￨- excited￨L￨VBN￨O￨- under￨L￨IN￨O￨- conditions￨L￨NNS￨O￨- of￨L￨IN￨O￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- amplitude￨L￨NN￨O￨A forcing￨L￨VBG￨O￨- and￨L￨CC￨O￨- short￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Deterministic￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- comprising￨L￨VBG￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- aspects￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- of￨L￨IN￨O￨- relevance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- potentially￨L￨RB￨O￨- or￨L￨CC￨O￨- in￨L￨IN￨O￨- reality￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- Dependence￨U￨NN￨O￨- of￨L￨IN￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- on￨L￨IN￨O￨- other￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- gives￨L￨VBZ￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- Simplified￨U￨VBN￨O￨- model￨L￨NN￨TITLE￨- yields￨L￨NNS￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- interplay￨L￨NN￨O￨- of￨L￨IN￨O￨- horizontal￨L￨JJ￨O￨- and￨L￨CC￨O￨- vertical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- scrapie￨L￨NN￨O￨- Stochastic￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- within-flock￨L￨NN￨O￨- transmission￨L￨NN￨O￨- Analytical￨U￨NNP￨O￨- calculations￨L￨NNS￨O￨- using￨L￨VBG￨O￨- branching-process￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- and￨L￨CC￨O￨- Numerical￨U￨JJ￨O￨- calculation￨L￨NN￨O￨- using￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- simulations￨L￨NNS￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- extinction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- likely￨L￨RB￨O￨- when￨L￨WRB￨O￨- late-stage￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- Presence￨U￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- extinction￨L￨NN￨O￨- Mean￨U￨NN￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- 1.5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- Infectiousness￨U￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- becomes￨L￨VBZ￨O￨- appreciable￨L￨JJ￨O￨- at￨L￨IN￨O￨- early￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- incubation￨L￨NN￨O￨- Difficult￨U￨NNP￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- values￨L￨NNS￨O￨- Mathematical￨U￨JJ￨O￨- expression￨L￨NN￨O￨- for￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- Sensitivity￨U￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- various￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- Reduction￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- allele￨L￨NN￨O￨- reduces￨L￨VBZ￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- most￨L￨RBS￨O￨- effectively￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- allele￨L￨NN￨O￨- is￨L￨VBZ￨O￨- recessive￨L￨JJ￨O￨- Inbreeding￨U￨NNP￨O￨- may￨L￨MD￨O￨- increase￨L￨VB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- allele￨L￨NN￨O￨- is￨L￨VBZ￨O￨- recessive￨L￨JJ￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- Point￨U￨NN￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Cheviot￨U￨NNP￨CITY￨- sheep￨L￨NN￨O￨A is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 3.9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Model￨U￨NNP￨TITLE￨- reproduces￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- allele￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- and￨L￨CC￨O￨- total￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- remaining￨L￨VBG￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- Indication￨U￨NN￨O￨- that￨L￨WDT￨O￨- older￨L￨JJR￨O￨- animals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- reduced￨L￨VBN￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- scrapie￨L￨VB￨O￨- Three￨U￨CD￨NUMBER￨- main￨L￨JJ￨O￨- observed￨L￨VBN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- :￨L￨:￨O￨- sporadic￨L￨JJ￨O￨- ,￨L￨,￨O￨- endemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reproduced￨L￨VBN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- parameter￨L￨NN￨O￨- settings￨L￨NNS￨O￨- Model￨U￨NNP￨TITLE￨- results￨L￨VBZ￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- overall￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- primarily￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- composition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- flock￨L￨NN￨O￨- Outbreak￨U￨NN￨O￨- type￨L￨NN￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- mainly￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨- management￨L￨NN￨O￨- practices￨L￨NNS￨O￨- Develop￨U￨VBP￨O￨- within-flock￨L￨JJ￨O￨- scrapie￨L￨NN￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- assisting￨L￨VBG￨O￨- the￨L￨DT￨O￨- interpretation￨L￨NN￨O￨- of￨L￨IN￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- Use￨U￨VBP￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- Scrapie￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- of￨L￨IN￨O￨- long￨L￨JJ￨O￨- duration￨L￨NN￨O￨- Will￨U￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- susceptible￨L￨JJ￨O￨- allele￨L￨NN￨O￨- frequency￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Partial-differential￨U￨JJ￨MISC￨- equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- within-flock￨L￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- Applied￨U￨NNP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Romanov￨U￨NNP￨LOCATION￨- sheep￨L￨NN￨O￨- The￨U￨DT￨O￨- observed￨L￨VBN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonality￨L￨NN￨O￨- in￨L￨IN￨O￨- incidence￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- accounted￨L￨VBN￨O￨- for￨L￨IN￨O￨- by￨L￨IN￨O￨- seasonality￨L￨NN￨O￨- in￨L￨IN￨O￨- demography￨L￨NN￨O￨- alone￨L￨RB￨O￨- Provides￨U￨VBZ￨O￨- support￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- during￨L￨IN￨O￨- lambing￨L￨VBG￨O￨- Partial-differential￨U￨JJ￨MISC￨- equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- within-flock￨L￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- Parameter￨U￨NN￨O￨- values￨L￨NNS￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- In￨U￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- flock￨L￨NN￨O￨- ,￨L￨,￨O￨- scrapie￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨DURATION￨- decades￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- genotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- become￨L￨VB￨O￨- endemic￨L￨JJ￨O￨- if￨L￨IN￨O￨- carrier￨L￨NN￨O￨- genotypes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- present￨L￨JJ￨DATE￨- In￨U￨IN￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- flock￨L￨NN￨O￨- ,￨L￨,￨O￨- endemic￨L￨JJ￨O￨- scrapie￨L￨NN￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- carriers￨L￨NNS￨O￨- Control￨U￨VBP￨O￨- measures￨L￨NNS￨O￨- currently￨L￨RB￨DATE￨- or￨L￨CC￨O￨- likely￨L￨RB￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- available￨L￨JJ￨O￨- may￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- but￨L￨CC￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- fully￨L￨RB￨O￨- effective￨L￨JJ￨O￨- only￨L￨RB￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- Model￨U￨NNP￨TITLE￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- key￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- long￨L￨JJ￨O￨- duration￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ages￨L￨NNS￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- Many￨U￨JJ￨O￨- infected￨L￨JJ￨O￨- sheep￨L￨NN￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- survive￨L￨VB￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- clinical￨L￨JJ￨O￨- signs￨L￨NNS￨O￨- Most￨U￨JJS￨O￨- cases￨L￨NNS￨O￨- arise￨L￨VBP￨O￨- through￨L￨IN￨O￨- horizontal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- Strong￨U￨JJ￨O￨- selection￨L￨NN￨O￨- against￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- genotypes￨L￨NNS￨O￨- References￨U￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- superscript￨L￨JJ￨O￨- use￨L￨NN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- approach￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- Hagenaars￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Current￨U￨NNP￨DATE￨- crisis￨L￨NN￨O￨- or￨L￨CC￨O￨- artifact￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- :￨L￨:￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- rebound￨L￨NN￨O￨- chlamydia￨L￨NN￨O￨A rates￨L￨NNS￨O￨- from￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- modellingDavid￨L￨NN￨O￨- M￨U￨NN￨O￨- Vickers￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Nathaniel￨U￨NN￨PERSON￨- D￨U￨NN￨PERSON￨- Osgood￨U￨NN￨PERSON￨- †￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- †￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- 10:70￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Vickers￨U￨NNP￨O￨- and￨L￨CC￨O￨- Osgood￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2010Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- After￨U￨IN￨O￨- initially￨L￨RB￨O￨- falling￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- face￨L￨NN￨O￨- of￨L￨IN￨O￨- intensified￨L￨VBN￨O￨- control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- ,￨L￨,￨O￨- reported￨L￨VBD￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- chlamydia￨L￨NN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- developed￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- are￨L￨VBP￨O￨- rising￨L￨VBG￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- all￨L￨DT￨O￨- models￨L￨NNS￨O￨- examined￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- repeatedly￨L￨RB￨O￨- highlighted￨L￨VBD￨O￨- that￨L￨IN￨O￨- increased￨L￨VBN￨O￨- testing￨L￨NN￨O￨- volumes￨L￨NNS￨O￨- ,￨L￨,￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- and￨L￨CC￨O￨- specificity￨L￨NN￨O￨- of￨L￨IN￨O￨- testing￨L￨NN￨O￨- technologies￨L￨NNS￨O￨- ,￨L￨,￨O￨- sexual￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- truncated￨L￨VBN￨O￨- immunological￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- brought￨L￨VBD￨O￨- about￨L￨RB￨O￨- by￨L￨IN￨O￨- treatment￨L￨NN￨O￨- can￨L￨MD￨O￨- ,￨L￨,￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- observed￨L￨VBN￨O￨- chlamydia￨L￨NN￨O￨A case￨L￨NN￨O￨- notifications￨L￨NNS￨O￨- .￨L￨.￨O￨- +Calibration￨U￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- observed￨L￨VBN￨O￨- 25-year￨L￨JJ￨DURATION￨- case￨L￨NN￨O￨- notification￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- being￨L￨VBG￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- testing￨L￨NN￨O￨- records￨L￨NNS￨O￨- ,￨L￨,￨O￨- placed￨L￨VBN￨O￨- constraints￨L￨NNS￨O￨- on￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- allowed￨L￨VBN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- approximation￨L￨NN￨O￨- of￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨A prevalence￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- This￨U￨DT￨O￨- study￨L￨NN￨O￨- integrated￨L￨VBN￨O￨- 25-year￨L￨JJ￨DURATION￨- testing￨L￨NN￨O￨A volume￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Canadian￨U￨JJ￨NATIONALITY￨- province￨L￨NN￨O￨- of￨L￨IN￨O￨- Saskatchewan￨U￨NNP￨STATE_OR_PROVINCE￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- susceptible-infected-treated-susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- three￨L￨CD￨NUMBER￨- susceptible-infected-treated-removed￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Introduction￨U￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- program￨L￨NN￨O￨A was￨L￨VBD￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- greater￨L￨JJR￨O￨- overall￨L￨JJ￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- and￨L￨CC￨O￨- working-age￨L￨JJ￨O￨- adults￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- greater￨L￨JJR￨O￨- reductions￨L￨NNS￨O￨- in￨L￨IN￨O￨- influenza-associated￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- provinces￨L￨NNS￨O￨- that￨L￨WDT￨O￨- maintained￨L￨VBD￨O￨- targeted￨L￨JJ￨O￨- programs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Worldwide￨U￨NNP￨O￨- ,￨L￨,￨O￨- annual￨L￨JJ￨SET￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- cause￨L￨NN￨O￨- significant￨L￨JJ￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- impose￨L￨VB￨O￨- a￨L￨DT￨O￨- considerable￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- burden￨L￨NN￨O￨- on￨L￨IN￨O￨- society￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨A care￨L￨NN￨O￨A costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- lost￨L￨VBD￨O￨- productivity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- economic￨L￨JJ￨O￨- evaluation￨L￨NN￨O￨- was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- health￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- and￨L￨CC￨O￨- costs￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- universal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- continuation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- program￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- (￨L￨-LRB-￨O￨- 12.16￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- province￨L￨NN￨O￨- of￨L￨IN￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- Canada￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- initiated￨L￨VBD￨O￨- a￨L￨DT￨O￨- universal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- immunization￨L￨NN￨O￨- program￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- UIIP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- free￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccines￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨DURATION￨- mo￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- or￨L￨CC￨O￨- older￨L￨JJR￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- findings￨L￨NNS￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- provinces￨L￨NNS￨O￨- and￨L￨CC￨O￨- territories￨L￨NNS￨O￨- in￨L￨IN￨O￨- Canada￨U￨NNP￨COUNTRY￨- offer￨L￨VBP￨O￨- free￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccinations￨L￨NNS￨O￨- for￨L￨IN￨O￨- those￨L￨DT￨O￨- 65￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- or￨L￨CC￨O￨- older￨L￨JJR￨O￨- ,￨L￨,￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- chronic￨L￨JJ￨O￨- medical￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- health￨L￨NN￨O￨A care￨L￨NN￨O￨A workers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Targeted￨U￨VBN￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- Immunization￨U￨NNP￨O￨- Program￨U￨NNP￨O￨- ,￨L￨,￨O￨- TIIP￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Technical￨U￨NNP￨O￨- advance￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- An￨U￨DT￨MISC￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A theory￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- non-pharmaceutical￨L￨JJ￨O￨- interventionsFeng￨L￨NN￨O￨- Lin1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Kumar￨U￨NNP￨PERSON￨- Muthuraman2￨U￨NN￨O￨- and￨L￨CC￨O￨- Mark￨U￨NNP￨O￨- Lawley1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 10:32￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Lin￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2010Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Non-pharmaceutical￨U￨JJ￨MISC￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- NPI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- line￨L￨NN￨O￨- of￨L￨IN￨O￨- defense￨L￨NN￨O￨- against￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- perform￨L￨VBP￨O￨- a￨L￨DT￨O￨- multivariate￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨- analysis￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Latin￨U￨NNP￨O￨- Hypercube￨U￨NNP￨O￨- Sampling￨U￨VBG￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- input￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A policy￨L￨NN￨O￨- .￨L￨.￨O￨- +Optimal￨U￨JJ￨O￨- control￨L￨NN￨O￨A theory￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- balancing￨L￨NN￨O￨- competing￨L￨VBG￨O￨- objectives￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- NPI￨U￨NN￨ORGANIZATION￨- cost￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- expected￨L￨VBN￨O￨- person-days￨L￨NNS￨O￨- lost￨L￨VBD￨O￨A from￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- related￨L￨JJ￨O￨- deaths￨L￨NNS￨O￨- and￨L￨CC￨O￨- NPI￨U￨NN￨ORGANIZATION￨- implementations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A on￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemiologic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- triggers￨L￨NNS￨O￨- for￨L￨IN￨O￨- NPI￨U￨NNP￨ORGANIZATION￨- implementation￨L￨NN￨O￨- .￨L￨.￨O￨- +Contact￨U￨NN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- fat-tailed￨L￨JJ￨O￨- degree￨L￨NN￨O￨A distributions￨L￨NNS￨O￨A ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- extraordinarily￨L￨RB￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- R0￨U￨NN￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- would￨L￨MD￨O￨- expect￨L￨VB￨O￨- from￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- highly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- makes￨L￨VBZ￨O￨- them￨L￨PRP￨O￨- an￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- target￨L￨NN￨O￨- for￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- quantity￨L￨NN￨O￨- central￨L￨JJ￨O￨- to￨L￨TO￨O￨- developing￨L￨VBG￨O￨- intervention￨L￨NN￨O￨- measures￨L￨NNS￨O￨- or￨L￨CC￨O￨- immunization￨L￨NN￨O￨- programs￨L￨NNS￨O￨- ,￨L￨,￨O￨- depends￨L￨VBZ￨O￨- crucially￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- demonstration￨L￨NN￨O￨- that￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- show￨L￨VBP￨O￨- significant￨L￨JJ￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- social￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- homophily￨L￨NN￨O￨- and￨L￨CC￨O￨- transitivity￨L￨NN￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- highly￨L￨RB￨O￨- clustered￨L￨VBN￨O￨- and￨L￨CC￨O￨- modular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- microstructures￨L￨NNS￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- only￨L￨RB￨O￨- recently￨L￨RB￨DATE￨- started￨L￨VBD￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- their￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- been￨L￨VBN￨O￨- ignored￨L￨VBN￨O￨- .￨L￨.￨O￨- +Community￨U￨NNP￨O￨- structure￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- members￨L￨NNS￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- dense￨L￨JJ￨O￨- than￨L￨IN￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +KeywordsAcute￨U￨NNP￨O￨- Otitis￨U￨NNP￨MISC￨- MediumInvasive￨U￨NNP￨MISC￨- Pneumococcal￨U￨JJ￨MISC￨- DiseasePneumococcal￨U￨JJ￨MISC￨- SerotypesPneumococcal￨U￨JJ￨MISC￨- CarriagePCV7￨U￨NN￨MISC￨- Vaccination￨U￨NN￨MISC￨- BackgroundDespite￨U￨NN￨MISC￨- the￨L￨DT￨O￨- considerable￨L￨JJ￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- Streptococcus￨U￨NN￨MISC￨- pneumoniae￨L￨FW￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- 7-valent￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨A conjugate￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PCV7￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- routine￨L￨JJ￨O￨- immunisation￨L￨NN￨O￨- schedules￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- yet￨L￨RB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- launched￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- low-income￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- where￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- needed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Dynamic￨U￨NNP￨MISC￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨A carriage￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Heptavalent￨U￨JJ￨O￨- Pneumococcal￨U￨JJ￨O￨- Conjugate￨U￨NN￨O￨- Vaccine￨U￨NN￨O￨- on￨L￨IN￨O￨- invasive￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨- diseaseAlessia￨L￨NN￨O￨- Melegaro1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yoon￨U￨NNP￨PERSON￨- Hong￨U￨NNP￨PERSON￨- Choi2Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Robert￨U￨NNP￨PERSON￨- George2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- W￨U￨NNP￨O￨- John￨U￨NNP￨PERSON￨- Edmunds2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Elizabeth￨U￨NNP￨PERSON￨- Miller2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Nigel￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Gay1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 10:90￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Melegaro￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2010Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- 7-valent￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨- conjugate￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- national￨L￨JJ￨O￨- immunisation￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- of￨L￨IN￨O￨- most￨L￨JJS￨O￨- industrialised￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- and￨L￨CC￨O￨- recently￨L￨RB￨DATE￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- African￨U￨JJ￨NATIONALITY￨- GAVI￨U￨NN￨ORGANIZATION￨- eligible￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Rwanda￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- The￨U￨DT￨O￨- Gambia￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Method￨U￨NN￨O￨- A￨U￨NN￨O￨- dynamic￨L￨NN￨O￨- ,￨L￨,￨O￨- age-structured￨L￨JJ￨O￨- ,￨L￨,￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Streptococcus￨U￨NN￨O￨- pneumoniae￨L￨FW￨O￨- transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- PCV7￨U￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- invasive￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- serotype￨L￨NN￨O￨- replacement￨L￨NN￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Model￨U￨NNP￨TITLE￨- projections￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- serotype￨L￨NN￨O￨- replacement￨L￨NN￨O￨A plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- PCV7￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- programme￨L￨NN￨O￨- and￨L￨CC￨O￨- could￨L￨MD￨O￨- reduce￨L￨VB￨O￨- ,￨L￨,￨O￨- negate￨L￨VB￨O￨- or￨L￨CC￨O￨- outweigh￨L￨VB￨O￨- its￨L￨PRP$￨O￨- beneficial￨L￨JJ￨O￨- impact￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- competition￨L￨NN￨O￨- parameter￨L￨NN￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- post-vaccination￨L￨JJ￨O￨- experience￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- infant￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- programme￨L￨NN￨O￨A would￨L￨MD￨O￨- prevent￨L￨VB￨O￨- 39,000￨L￨CD￨NUMBER￨- IPD￨U￨NNP￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- 20￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- PCV7￨U￨NN￨O￨- introduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- attempt￨L￨NN￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- this￨L￨DT￨O￨- deficiency￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- sexual￨L￨JJ￨O￨- partnerships￨L￨NNS￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- “￨L￨``￨O￨- pair￨L￨NN￨O￨- models￨L￨NNS￨O￨- ”￨L￨''￨O￨- and￨L￨CC￨O￨- “￨L￨``￨O￨- pair￨L￨NN￨O￨- approximations￨L￨NNS￨O￨- ”￨L￨''￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Traditionally￨U￨RB￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- one-sex￨L￨NN￨O￨- or￨L￨CC￨O￨- heterosexual￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- partnerships￨L￨NNS￨O￨A are￨L￨VBP￨O￨- instantaneous￨L￨JJ￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- duration￨L￨NN￨O￨- :￨L￨:￨O￨- each￨L￨DT￨O￨- new￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- contact￨L￨NN￨O￨- is￨L￨VBZ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- person￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 25,31￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 34￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- STIs￨U￨NNS￨O￨- like￨L￨IN￨O￨- HPV￨U￨NN￨O￨- spread￨L￨NN￨O￨- sexually￨L￨RB￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- including￨L￨VBG￨O￨- partnerships￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- potentially￨L￨RB￨O￨- bias￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- projections￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- they￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- SI￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infected￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- :￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- every￨L￨DT￨O￨- contact￨L￨NN￨O￨- is￨L￨VBZ￨O￨- instantaneous￨L￨JJ￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- partner￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- pair￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonzero￨L￨NN￨O￨- partnership￨L￨NN￨O￨- length￨L￨NN￨O￨- .￨L￨.￨O￨- +Carcinogenic￨U￨JJ￨O￨- HPV￨U￨NN￨O￨- types￨L￨NNS￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- prevalent￨L￨JJ￨O￨- in￨L￨IN￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- women￨L￨NNS￨O￨A ,￨L￨,￨O￨- infecting￨L￨VBG￨O￨- about￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- women￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Theoretical￨U￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- stimulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- agent-based￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- simulations￨L￨NNS￨O￨- indicating￨L￨VBG￨O￨- that￨L￨IN￨O￨- small￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- behavior￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- large￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Further￨U￨JJ￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- argued￨L￨VBN￨O￨- that￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A can￨L￨MD￨O￨- arrest￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- if￨L￨IN￨O￨- started￨L￨VBN￨O￨- quickly￨L￨RB￨O￨- and￨L￨CC￨O￨- maintained￨L￨VBD￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- long￨L￨JJ￨O￨- period￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Compartmental￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A by￨L￨IN￨O￨- including￨L￨VBG￨O￨- states￨L￨NNS￨O￨- that￨L￨WDT￨O￨- represent￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- employing￨L￨VBG￨O￨- specific￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- setting￨L￨NN￨O￨- by￨L￨IN￨O￨- prescribing￨L￨VBG￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- proximity￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Whereas￨U￨IN￨O￨- previous￨L￨JJ￨O￨- hypotheses￨L￨NNS￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- source-sink￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- East￨U￨NNP￨O￨- and￨L￨CC￨O￨- Southeast￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- E-SE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Asia￨U￨NNP￨CITY￨- seeds￨L￨NNS￨O￨- annual￨L￨JJ￨SET￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- temperate￨L￨JJ￨O￨- latitudes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- often￨L￨RB￨O￨- circulate￨L￨VBP￨O￨- outside￨L￨JJ￨O￨- Asia￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- sustained￨L￨VBN￨O￨- by￨L￨IN￨O￨- complex￨L￨JJ￨O￨- migration￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Influenza￨U￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- endemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- particular￨L￨JJ￨O￨- region￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- but￨L￨CC￨O￨- appears￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- dynamically￨L￨RB￨O￨- sustained￨L￨VBN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- will￨L￨NN￨O￨- sweep￨L￨NN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- fade￨L￨VB￨O￨- out￨L￨RP￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- be￨L￨VB￨O￨- reseeded￨L￨VBN￨O￨- by￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- region￨L￨NN￨O￨- 's￨L￨POS￨O￨- local￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- the￨L￨DT￨DATE￨- following￨L￨JJ￨DATE￨- year￨L￨NN￨DATE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- genetic￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- among￨L￨IN￨O￨- viral￨L￨JJ￨O￨- samples￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- structured￨L￨JJ￨O￨- coalescent￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- genealogical￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- connecting￨L￨VBG￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- reproducing￨L￨VBG￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- migration￨L￨NN￨O￨- between￨L￨IN￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- persist￨L￨VB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- no￨L￨DT￨O￨- particular￨L￨JJ￨O￨- region￨L￨NN￨O￨A serves￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- simpler￨L￨JJR￨O￨- setting￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- detailed￨L￨JJ￨O￨- exploration￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- between￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- connected￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨A ,￨L￨,￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- travel￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- residence￨L￨NN￨O￨- of￨L￨IN￨O￨- travelers￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- relevance￨L￨NN￨O￨- to￨L￨TO￨O￨- large￨L￨JJ￨O￨- and￨L￨CC￨O￨- small￨L￨JJ￨O￨- centers￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aims￨L￨NNS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- were￨L￨VBD￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨A in￨L￨IN￨O￨- slowing￨L￨VBG￨O￨- the￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- restrictions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- Australia￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- predictions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨A and￨L￨CC￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Australia￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- resultant￨L￨JJ￨O￨- spread￨L￨NN￨O￨- to￨L￨TO￨O￨- Melbourne￨U￨NNP￨CITY￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨A were￨L￨VBD￨O￨- simulated￨L￨JJ￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- anticipate￨L￨VBP￨O￨- six￨L￨CD￨NUMBER￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- challenges￨L￨NNS￨O￨- and￨L￨CC￨O￨- identify￨L￨VBP￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- decision￨L￨NN￨O￨- making￨L￨NN￨O￨- :￨L￨:￨O￨- Measuring￨U￨VBG￨O￨- age-specific￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- accurately￨L￨RB￨O￨- quantifying￨L￨VBG￨O￨A severity￨L￨NN￨O￨- ;￨L￨:￨O￨- improving￨L￨VBG￨O￨- treatment￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- for￨L￨IN￨O￨- severe￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ;￨L￨:￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- ;￨L￨:￨O￨- capturing￨L￨VBG￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- on￨L￨IN￨O￨- mortality￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- rapidly￨L￨RB￨O￨- identifying￨L￨VBG￨O￨- and￨L￨CC￨O￨- responding￨L￨VBG￨O￨- to￨L￨TO￨O￨- antigenic￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- strain￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A/H1N1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- pandemic￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- 2009￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- H1N1pdm￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- highlighted￨L￨VBN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- investigations￨L￨NNS￨O￨A and￨L￨CC￨O￨- population￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- support￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- decision￨L￨NN￨O￨- making￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- organizations￨L￨NNS￨O￨- in￨L￨IN￨O￨- several￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- undertook￨L￨VBD￨O￨- detailed￨L￨JJ￨O￨- case￨L￨NN￨O￨- investigations￨L￨NNS￨O￨A to￨L￨TO￨O￨- build￨L￨VB￨O￨- databases￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- few￨L￨JJ￨O￨- hundred￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- include￨L￨VBP￨O￨- laboratory￨L￨NN￨O￨- confirmation￨L￨NN￨O￨- status￨L￨NN￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- relative￨L￨JJ￨O￨- severity￨L￨NN￨O￨- ,￨L￨,￨O￨- exposure￨L￨NN￨O￨- history￨L￨NN￨O￨- ,￨L￨,￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- history￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- First￨U￨NNP￨ORDINAL￨- Few￨U￨JJ￨O￨- Hundred￨U￨NNP￨NUMBER￨- project￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Continuing￨U￨VBG￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- H1N1pdm￨U￨NN￨O￨- cases￨L￨NNS￨O￨- will￨L￨MD￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- clear￨L￨JJ￨O￨- picture￨L￨NN￨O￨- of￨L￨IN￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- during￨L￨IN￨O￨- population-wide￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- behavior￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- school￨L￨NN￨O￨- vacations￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- nonpharmaceutical￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨A .￨L￨.￨O￨- +Parameters￨U￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- investigation￨L￨NN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- give￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- how￨L￨WRB￨O￨- underlying￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- will￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- used￨L￨VBD￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- for￨L￨IN￨O￨- viral￨L￨JJ￨O￨- phylodynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- coalescent￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- genealogical￨L￨JJ￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- changes￨L￨VBZ￨O￨- size￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- fashion￨L￨NN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- relative￨L￨JJ￨O￨- size￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- ν￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- measured￨L￨VBN￨O￨- in￨L￨IN￨O￨- generations￨L￨NNS￨O￨- ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- and￨L￨CC￨O￨- going￨L￨VBG￨O￨- backwards￨L￨RB￨O￨- .￨L￨.￨O￨- +Sophisticated￨U￨JJ￨O￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- which￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- time-stamped￨L￨JJ￨O￨- phylogenies￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- viral￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Drummond￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- conjunction￨L￨NN￨O￨- with￨L￨IN￨O￨- coalescent￨L￨JJ￨O￨A models￨L￨NNS￨O￨- borrowed￨L￨VBN￨O￨- from￨L￨IN￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Pybus￨U￨NNP￨O￨- ;￨L￨:￨O￨- Drummond￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- different￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- genealogical￨L￨JJ￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- taxa￨L￨NN￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- changes￨L￨VBZ￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- deterministically￨L￨RB￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- simple￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescence￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- directly￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- absolute￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- ;￨L￨:￨O￨- Volz￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- whether￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- conditions￨L￨NNS￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- coalescence￨L￨NN￨O￨- rate￨L￨NN￨O￨- may￨L￨MD￨O￨- indeed￨L￨RB￨O￨- reflect￨L￨VB￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- effective￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ’￨L￨POS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- coalescence￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- classical￨L￨JJ￨O￨- population￨L￨NN￨O￨A genetics￨L￨NNS￨O￨A models￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analyse￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- differ￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- particular￨L￨JJ￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- traits￨L￨NNS￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- xf￨L￨NN￨O￨- in￨L￨IN￨O￨- females￨L￨NNS￨O￨A and￨L￨CC￨O￨- xm￨L￨NN￨O￨- in￨L￨IN￨O￨- males￨L￨NNS￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- both￨L￨DT￨O￨- sexes￨L￨NNS￨O￨- obey￨L￨VBP￨O￨- identical￨L￨JJ￨O￨- trade-off￨L￨NN￨O￨- functions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- electronic￨L￨JJ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- appendix￨L￨NN￨O￨- S6￨U￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- sex-specific￨L￨JJ￨O￨- trade-off￨L￨NN￨O￨- functions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Following￨U￨VBG￨O￨- the￨L￨DT￨O￨- terminology￨L￨NN￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- Boots￨U￨NNP￨O￨- ,￨L￨,￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- defence￨L￨NN￨O￨- that￨L￨WDT￨O￨- reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- fecundity￨L￨NN￨O￨- during￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- tolerance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- defence￨L￨NN￨O￨- that￨L￨WDT￨O￨- restores￨L￨VBZ￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- 's￨L￨POS￨O￨- fitness￨L￨NN￨O￨- without￨L￨IN￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- 's￨L￨POS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- recent￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Stoehr￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Kokko￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- 2006￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- between￨L￨IN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- survival￨L￨NN￨O￨- and￨L￨CC￨O￨- reproduction￨L￨NN￨O￨- in￨L￨IN￨O￨- males￨L￨NNS￨O￨- and￨L￨CC￨O￨- females￨L￨NNS￨O￨A ,￨L￨,￨O￨- under￨L￨IN￨O￨- varying￨L￨VBG￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- selection￨L￨NN￨O￨- by￨L￨IN￨O￨- females￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- genetic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- embedded￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- classical￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- acquired￨L￨VBN￨O￨- immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- figure￨L￨NN￨O￨- 1b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- subscripts￨L￨NNS￨O￨- f￨L￨LS￨O￨- and￨L￨CC￨O￨- m￨L￨NN￨O￨- represent￨L￨VBP￨O￨- females￨L￨NNS￨O￨A and￨L￨CC￨O￨- males￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- j￨L￨FW￨O￨- are￨L￨VBP￨O￨- placeholders￨L￨NNS￨O￨- for￨L￨IN￨O￨- genotypes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- alleles￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- locus￨L￨NN￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- xf￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- dummy￨L￨NN￨O￨- trait￨L￨NN￨O￨- that￨L￨WDT￨O￨- affects￨L￨VBZ￨O￨- both￨L￨DT￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- life￨L￨NN￨O￨- history￨L￨NN￨O￨- in￨L￨IN￨O￨- females￨L￨NNS￨O￨A only￨L￨RB￨O￨- .￨L￨.￨O￨- +Subtracting￨U￨VBG￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- E￨U￨NN￨O￨- →￨L￨NN￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- median￨L￨JJ￨O￨- time￨L￨NN￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- birds￨L￨NNS￨O￨A to￨L￨TO￨O￨- become￨L￨VB￨O￨- exposed/infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- slightly￨L￨RB￨O￨- longer￨L￨RBR￨O￨- for￨L￨IN￨O￨- HP￨U￨NNP￨O￨- than￨L￨IN￨O￨- LP￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 0.48￨L￨CD￨NUMBER￨- vs.￨L￨CC￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- on￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- during￨L￨IN￨O￨- AI￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- compare￨L￨VBP￨O￨- LPAI￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- HPAI￨U￨NN￨ORGANIZATION￨- outbreak￨L￨NN￨O￨- predictions￨L￨NNS￨O￨- to￨L￨TO￨O￨- field￨L￨NN￨O￨- observations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- bird￨L￨NN￨O￨- mortality￨L￨NN￨O￨A and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- age-composition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Susceptible￨U￨JJ￨O￨- birds￨L￨NNS￨O￨A exposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- contact￨L￨NN￨O￨- to￨L￨TO￨O￨- LPAI-inoculated￨U￨JJ￨O￨- birds￨L￨NNS￨O￨- became￨L￨VBD￨O￨- infectious￨L￨JJ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- slower￨L￨JJR￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- median￨L￨JJ￨O￨- time￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1.50￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- HPAI-inoculated￨U￨JJ￨O￨- birds￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 0.76￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Parameters￨U￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- published￨L￨VBN￨O￨- laboratory￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- trials￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- Anseriform￨U￨JJ￨O￨- species￨L￨NNS￨O￨- and￨L￨CC￨O￨- AI￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extended￨L￨VBD￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- wild￨L￨JJ￨O￨- bird￨L￨NN￨O￨- populations￨L￨NNS￨O￨- by￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A contact￨L￨NN￨O￨A with￨L￨IN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- bird-to-bird￨L￨NN￨O￨- or￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- contact￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- using￨L￨VBG￨O￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- waterfowl￨L￨NN￨O￨- surveys￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- -9￨L￨CD￨NUMBER￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- pre-existing￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- protection￨L￨NN￨O￨- ,￨L￨,￨O￨- presumably￨L￨RB￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- prior￨L￨JJ￨O￨A exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- limited￨L￨VBN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- attack-rate￨L￨NN￨O￨- in￨L￨IN￨O￨- urban￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- waning￨L￨VBG￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- protection￨L￨NN￨O￨- likely￨L￨JJ￨O￨- contributed￨L￨VBD￨O￨- to￨L￨TO￨O￨- recurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- waves￨L￨NNS￨O￨- in￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- cities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- modelled￨L￨VBD￨O￨- all￨L￨PDT￨O￨- these￨L￨DT￨O￨- possibilities￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- best￨L￨JJS￨O￨- explain￨L￨VBP￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- repeat￨L￨NN￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- 24,706￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- potentially￨L￨RB￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- summer￨L￨NN￨DATE￨A ,￨L￨,￨O￨- autumn￨L￨NN￨DATE￨- and￨L￨CC￨O￨- winter￨L￨NN￨DATE￨- waves￨L￨NNS￨O￨- in￨L￨IN￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- -9￨L￨CD￨NUMBER￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- -9￨L￨CD￨NUMBER￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 2009￨L￨CD￨DATE￨- pandemic￨L￨NN￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- limited￨L￨VBN￨O￨- by￨L￨IN￨O￨- immunity￨L￨NN￨O￨- from￨L￨IN￨O￨- prior￨L￨JJ￨O￨A exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Before￨U￨IN￨O￨- the￨L￨DT￨O￨- summer￨L￨NN￨DATE￨- wave￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- that￨L￨IN￨O￨- only￨L￨RB￨O￨- 52￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- persons￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- credibility￨L￨NN￨O￨- estimates￨L￨VBZ￨O￨- 41-66￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- remainder￨L￨NN￨O￨- protected￨L￨VBN￨O￨- by￨L￨IN￨O￨- prior￨L￨JJ￨O￨A immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- -9￨L￨CD￨NUMBER￨- were￨L￨VBD￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- cities￨L￨NNS￨O￨- ,￨L￨,￨O￨- presumably￨L￨RB￨O￨- because￨L￨IN￨O￨- prior￨L￨JJ￨O￨A immunity￨L￨NN￨O￨- was￨L￨VBD￨O￨- less￨L￨RBR￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- infrequent￨L￨JJ￨O￨- prior￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- suggest￨L￨VBP￨O￨- this￨L￨DT￨O￨- observation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- unrecognised￨L￨JJ￨O￨- establishment￨L￨NN￨O￨- of￨L￨IN￨O￨- community￨L￨NN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- pH1N1￨L￨NN￨O￨- in￨L￨IN￨O￨- Victoria￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- in￨L￨IN￨O￨- WA￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- around￨L￨IN￨O￨- or￨L￨CC￨O￨- before￨L￨IN￨O￨- 26￨L￨CD￨DATE￨- April￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- agencies￨L￨NNS￨O￨- and￨L￨CC￨O￨- laboratories￨L￨NNS￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- Australian￨U￨JJ￨NATIONALITY￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- territories￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- “￨L￨``￨O￨- jurisdictions￨L￨NNS￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- commenced￨L￨VBD￨O￨- investigating￨L￨VBG￨O￨- and￨L￨CC￨O￨- testing￨L￨VBG￨O￨- incoming￨L￨JJ￨O￨- travellers￨L￨NNS￨O￨- with￨L￨IN￨O￨- influenza-like￨L￨JJ￨O￨- illnesses￨L￨NNS￨O￨- from￨L￨IN￨O￨- North￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- for￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- confirmed￨L￨VBN￨O￨A case￨L￨NN￨O￨- in￨L￨IN￨O￨- Australia￨U￨NNP￨COUNTRY￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 2009￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- pH1N1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- recorded￨L￨VBN￨O￨- in￨L￨IN￨O￨- Queensland￨U￨NNP￨LOCATION￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- returned￨L￨VBN￨O￨- traveller￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- (￨L￨-LRB-￨O￨- US￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- almost￨L￨RB￨O￨- four￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- confirmed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- on￨L￨IN￨O￨- 15￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Victoria￨U￨NNP￨CITY￨- confirmed￨L￨VBD￨O￨A its￨L￨PRP$￨O￨- first￨L￨JJ￨ORDINAL￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- traveller￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- on￨L￨IN￨O￨- 20￨L￨CD￨DATE￨- May￨U￨NNP￨DATE￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- Western￨U￨NNP￨LOCATION￨- Australia￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- WA￨U￨NNP￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- notified￨L￨VBN￨O￨- on￨L￨IN￨O￨- 24￨L￨CD￨DATE￨- May￨U￨NNP￨DATE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- traveller￨L￨NN￨O￨- returned￨L￨VBD￨O￨- from￨L￨IN￨O￨- Canada￨U￨NNP￨COUNTRY￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- help￨L￨VB￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- answers￨L￨NNS￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- questions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- an￨L￨DT￨O￨- agent‐based￨L￨JJ￨O￨- computer￨L￨NN￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- Allegheny￨U￨NNP￨LOCATION￨- County￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- PA￨U￨NN￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- its￨L￨PRP$￨O￨- health￨L￨NN￨O￨A care￨L￨NN￨O￨A system￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- Susceptible￨U￨NNP￨O￨- –￨L￨:￨O￨- Infected￨U￨JJ￨O￨- –￨L￨:￨O￨- Recovered￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- and￨L￨CC￨O￨- simulates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- of￨L￨IN￨O￨- hospital‐based￨L￨JJ￨O￨- HCWs￨U￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- workplaces￨L￨NNS￨O￨- ,￨L￨,￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- households￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- community￨L￨NN￨O￨- activities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- policy￨L￨NN￨O￨- makers￨L￨NNS￨O￨- ,￨L￨,￨O￨- hospital￨L￨NN￨O￨A administrators￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- decision￨L￨NN￨O￨- makers￨L￨NNS￨O￨- may￨L￨MD￨O￨- need￨L￨VB￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- HCWs￨U￨NNS￨O￨- may￨L￨MD￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- HCWs￨U￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- each￨L￨DT￨O￨- HCW￨U￨NN￨O￨- should￨L￨MD￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- soon￨L￨RB￨O￨- HCWs￨U￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- protected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- varying￨L￨VBG￨O￨- HCW￨U￨NNP￨O￨- compliance￨L￨NN￨O￨- with￨L￨IN￨O￨- protective￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- agent‐based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Allegheny￨U￨NNP￨LOCATION￨- County￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- PA￨U￨NN￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- finds￨L￨VBZ￨O￨- that￨L￨IN￨O￨- protecting￨L￨VBG￨O￨- hospital‐based￨L￨JJ￨O￨- health￨L￨NN￨O￨A care￨L￨NN￨O￨A workers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- HCWs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- before￨L￨IN￨O￨- or￨L￨CC￨O￨- early￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- will￨L￨MD￨O￨- reduce￨L￨VB￨O￨- absenteeism￨L￨NN￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- whole￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- infected￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- visit￨L￨NN￨O￨- health￨L￨NN￨O￨A care￨L￨NN￨O￨A facilities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- HCFs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- will￨L￨MD￨O￨- interact￨L￨VB￨O￨- closely￨L￨RB￨O￨- with￨L￨IN￨O￨- HCWs￨U￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- will￨L￨MD￨O￨- interact￨L￨VB￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- uninfected￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- ,￨L￨,￨O￨- colleagues￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- family￨L￨NN￨O￨- members￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- mitigation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- developed￨L￨VBD￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- survey￨L￨NN￨O￨- campaign￨L￨NN￨O￨- conducted￨L￨VBN￨O￨- in￨L￨IN￨O￨- rural￨L￨JJ￨O￨A Clay￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Kearny￨U￨NNP￨CITY￨- counties￨L￨NNS￨O￨- in￨L￨IN￨O￨- Kansas￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- such￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- immunization￨L￨NN￨O￨A wherein￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- having￨L￨VBG￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- connectivity￨L￨NN￨O￨- were￨L￨VBD￨O￨- deemed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- critical￨L￨JJ￨O￨- for￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- those￨L￨DT￨O￨- highly￨L￨RB￨O￨- connected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- were￨L￨VBD￨O￨- chosen￨L￨VBN￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- these￨L￨DT￨O￨- responses￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rural￨L￨JJ￨O￨A community￨L￨NN￨O￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- survey￨L￨NN￨O￨- respondents￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- connected￨L￨VBN￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- links￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- respondents￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rural￨L￨JJ￨O￨A communities￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- interesting￨L￨JJ￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- it￨L￨PRP￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- stability￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- epidemic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- localized￨L￨JJ￨O￨- immunization￨L￨NN￨O￨A methods￨L￨NNS￨O￨- include￨L￨VBP￨O￨- targeting￨L￨VBG￨O￨- acquaintances￨L￨NNS￨O￨- of￨L￨IN￨O￨- randomly￨L￨RB￨O￨- selected￨L￨VBN￨O￨- people￨L￨NNS￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- estimated￨L￨VBN￨O￨- contact￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- cofeeding￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- ticks￨L￨NNS￨O￨- to￨L￨TO￨O￨- feed￨L￨VB￨O￨A in￨L￨RP￨O￨- close￨L￨JJ￨O￨- proximity￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- tick￨L￨VB￨O￨- activity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- seasonal￨L￨JJ￨O￨- in￨L￨IN￨O￨- temperate￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- tick￨L￨NN￨O￨- activity￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- tick-borne￨L￨JJ￨O￨- flaviviruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Understanding￨U￨VBG￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- driving￨L￨VBG￨O￨- POWV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ultimately￨L￨RB￨O￨- its￨L￨PRP$￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- and￨L￨CC￨O￨- risk￨L￨VB￨O￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- requires￨L￨VBZ￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- examination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- tick￨L￨NN￨O￨- vector￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨A populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Cofeeding￨U￨VBG￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- potentially￨L￨RB￨O￨- effective￨L￨JJ￨O￨- because￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- show￨L￨VBP￨O￨- aggregated￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- among￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- individuals￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- 75￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- feed￨L￨NN￨O￨A on￨L￨IN￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Simulation￨U￨NN￨O￨- studies￨L￨NNS￨O￨- illustrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- contact￨L￨NN￨O￨A tracing￨L￨VBG￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- measure￨L￨NN￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- less￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- than￨L￨IN￨O￨- random￨L￨JJ￨O￨- screening￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- perhaps￨L￨RB￨O￨- less￨L￨JJR￨O￨- costly￨L￨JJ￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- ideal￨L￨JJ￨O￨- for￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- programs￨L￨NNS￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- less￨L￨JJR￨O￨- resources￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- could￨L￨MD￨O￨- significantly￨L￨RB￨O￨- change￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- program￨L￨NN￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- factor￨L￨NN￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- measure￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- eventual￨L￨JJ￨O￨- eradication￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Modeling￨U￨VBG￨MISC￨- secondary￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- contact￨L￨NN￨O￨A tracing￨L￨VBG￨O￨A :￨L￨:￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- intervention￨L￨NN￨O￨- in￨L￨IN￨O￨- CubaYing-Hen￨U￨JJ￨O￨- Hsieh1￨U￨NN￨O￨- ,￨L￨,￨O￨- Yun-Shih￨U￨JJ￨O￨- Wang2￨U￨NN￨O￨- ,￨L￨,￨O￨- Hector￨U￨NNP￨PERSON￨- de￨L￨IN￨O￨- Arazoza3￨U￨NNP￨O￨- and￨L￨CC￨O￨- Rachid￨U￨NNP￨O￨- Lounes4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 10:194￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Hsieh￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2010Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Universal￨U￨NNP￨MISC￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- testing/treatment￨L￨NN￨O￨- program￨L￨NN￨O￨- has￨L￨VBZ￨O￨- currently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨- and￨L￨CC￨O￨- debated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- useful￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- not￨L￨RB￨O￨- without￨L￨IN￨O￨- practical￨L￨JJ￨O￨- issues￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- feasibility￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- implemented￨L￨VBN￨O￨- program￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- contact￨L￨NN￨O￨A tracing￨L￨VBG￨O￨A for￨L￨IN￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infectives￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- suitably￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- remedy￨L￨VB￨O￨- inadequacies￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- universal￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- testing￨L￨NN￨O￨- program￨L￨NN￨O￨- when￨L￨WRB￨O￨- designing￨L￨VBG￨O￨- timely￨L￨JJ￨O￨- and￨L￨CC￨O￨- effective￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- which￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV-infectives￨U￨NNS￨O￨- through￨L￨IN￨O￨- contact￨L￨NN￨O￨A tracing￨L￨VBG￨O￨A of￨L￨IN￨O￨- known￨L￨JJ￨O￨- infectives￨L￨NNS￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- detections￨L￨NNS￨O￨- through￨L￨IN￨O￨- other￨L￨JJ￨O￨- means￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- random￨L￨JJ￨O￨- screening￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- individual￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- local￨L￨JJ￨O￨- information￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- status￨L￨NN￨O￨A of￨L￨IN￨O￨- acquaintances￨L￨NNS￨O￨- ,￨L￨,￨O￨- partners￨L￨NNS￨O￨- ,￨L￨,￨O￨- relatives￨L￨NNS￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- ,￨L￨,￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- individual￨L￨JJ￨O￨- preventive￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- condoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- face￨L￨NN￨O￨- masks￨L￨NNS￨O￨- or￨L￨CC￨O￨- prophylactic￨L￨NN￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- avoidance￨L￨NN￨O￨- of￨L￨IN￨O￨- visiting￨L￨VBG￨O￨- specific￨L￨JJ￨O￨- web-pages￨L￨NNS￨O￨- ,￨L￨,￨O￨- staying￨L￨VBG￨O￨- away￨L￨RB￨O￨- from￨L￨IN￨O￨- public￨L￨JJ￨O￨- places￨L￨NNS￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- bias￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- organization￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- paths￨L￨NNS￨O￨- along￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- analytical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- which￨L￨WDT￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- finite￨L￨JJ￨O￨A adaptive￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- ultimately￨L￨RB￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Contrary￨U￨JJ￨O￨- to￨L￨TO￨O￨- current￨L￨JJ￨DATE￨- models￨L￨NNS￨O￨- though￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Discussion￨U￨NNP￨O￨- Section￨U￨NNP￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- dynamical￨L￨JJ￨O￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- variable￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- overall￨L￨JJ￨O￨A links￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Infection￨U￨NN￨CAUSE_OF_DEATH￨- occurs￨L￨VBZ￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- whose￨L￨WP$￨O￨- structure￨L￨NN￨O￨- may￨L￨MD￨O￨- change￨L￨VB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- 's￨L￨POS￨O￨- health￨L￨NN￨O￨- status￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- par￨L￨NN￨O￨- with￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- studies￨L￨NNS￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨A and￨L￨CC￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- national￨L￨JJ￨O￨- scientific￨L￨JJ￨O￨- and￨L￨CC￨O￨- academic￨L￨JJ￨O￨- community￨L￨NN￨O￨- has￨L￨VBZ￨O￨- issued￨L￨VBN￨O￨- repeated￨L￨VBN￨O￨- clarion￨L￨NN￨O￨- calls￨L￨VBZ￨O￨- for￨L￨IN￨O￨- revising￨L￨VBG￨O￨- college￨L￨NN￨O￨- biology￨L￨NN￨O￨A curricula￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- preparation￨L￨NN￨O￨- for￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- life￨L￨NN￨O￨- scientists￨L￨NNS￨O￨- to￨L￨TO￨O￨- reflect￨L￨VB￨O￨- the￨L￨DT￨O￨- tools￨L￨NNS￨O￨- and￨L￨CC￨O￨- practices￨L￨NNS￨O￨- of￨L￨IN￨O￨- science￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- HHMI-funded￨U￨JJ￨O￨- mini-grant￨L￨NN￨O￨- ,￨L￨,￨O￨- led￨L￨VBN￨O￨- by￨L￨IN￨O￨- Karl￨U￨NNP￨PERSON￨- Joplin￨U￨NNP￨PERSON￨- of￨L￨IN￨O￨- East￨U￨NNP￨ORGANIZATION￨- Tennessee￨U￨NNP￨ORGANIZATION￨- State￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- ETSU￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- 30￨L￨CD￨NUMBER￨- institutions￨L￨NNS￨O￨- joined￨L￨VBD￨O￨- in￨L￨IN￨O￨- planning￨L￨VBG￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- summer￨L￨NN￨DATE￨- institutes￨L￨NN￨O￨- and￨L￨CC￨O￨- workshops￨L￨NNS￨O￨- to￨L￨TO￨O￨- document￨L￨VB￨O￨- progress￨L￨NN￨O￨- toward￨L￨IN￨O￨- and￨L￨CC￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- challenges￨L￨NNS￨O￨- of￨L￨IN￨O￨- implementing￨L￨VBG￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- quantitative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- undergraduate￨L￨JJ￨O￨- biology￨L￨NN￨O￨A education￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- calls￨L￨VBZ￨O￨- for￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- biomedical￨L￨JJ￨O￨- researchers￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- better￨L￨JJR￨O￨- educated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- ,￨L￨,￨O￨- physical￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- molecular￨L￨JJ￨O￨- bases￨L￨NNS￨O￨- of￨L￨IN￨O￨- biology￨L￨NN￨O￨A and￨L￨CC￨O￨- urges￨L￨VBZ￨O￨- better￨L￨JJR￨O￨- integration￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- disciplines￨L￨NNS￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- meeting￨L￨NN￨O￨- included￨L￨VBD￨O￨- invited￨L￨VBN￨O￨- speakers￨L￨NNS￨O￨- who￨L￨WP￨O￨- addressed￨L￨VBD￨O￨- new￨L￨JJ￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- life￨L￨NN￨O￨- sciences￨L￨NNS￨O￨- or￨L￨CC￨O￨- mathematics￨L￨NNS￨O￨- ,￨L￨,￨O￨- invited￨L￨VBN￨O￨- education￨L￨NN￨O￨A presentations￨L￨NNS￨O￨- to￨L￨TO￨O￨- illustrate￨L￨VB￨O￨- biomath￨L￨NN￨O￨- collaborations￨L￨NNS￨O￨- ,￨L￨,￨O￨- workshops￨L￨NNS￨O￨- and￨L￨CC￨O￨- discussions￨L￨NNS￨O￨- on￨L￨IN￨O￨- key￨L￨JJ￨O￨- issues￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- contributed￨L￨VBD￨O￨- posters￨L￨NNS￨O￨- and￨L￨CC￨O￨- presentations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Howard￨U￨NNP￨ORGANIZATION￨- Hughes￨U￨NNP￨ORGANIZATION￨- Medical￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- HHMI￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- Program￨U￨NNP￨O￨- Directors￨U￨NNS￨O￨- Meeting￨U￨VBG￨O￨- ,￨L￨,￨O￨- participants￨L￨NNS￨O￨- from￨L￨IN￨O￨- HHMI-funded￨U￨JJ￨MISC￨- institutions￨L￨NNS￨O￨- with￨L￨IN￨O￨- interests￨L￨NNS￨O￨- in￨L￨IN￨O￨- interdisciplinary￨L￨JJ￨O￨- curriculum￨L￨NN￨O￨- reform￨L￨NN￨O￨- established￨L￨VBD￨O￨- a￨L￨DT￨O￨- consortium￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- ,￨L￨,￨O￨- implement￨L￨VB￨O￨- ,￨L￨,￨O￨- develop￨L￨VB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- disseminate￨L￨VB￨O￨- best￨L￨JJS￨O￨- practices￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- integration￨L￨NN￨O￨- of￨L￨IN￨O￨- math￨L￨NN￨O￨- and￨L￨CC￨O￨- biology￨L￨NN￨O￨A .￨L￨.￨O￨- +Similarly￨U￨RB￨O￨- ,￨L￨,￨O￨- working￨L￨VBG￨O￨- with￨L￨IN￨O￨- manipulatives￨L￨NNS￨O￨- helps￨L￨VBZ￨O￨- students￨L￨NNS￨O￨A develop￨L￨VB￨O￨- problem-solving￨L￨JJ￨O￨- and￨L￨CC￨O￨- critical-thinking￨L￨JJ￨O￨- skills￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- increases￨L￨NNS￨O￨- students￨L￨NNS￨O￨- '￨L￨POS￨O￨- sense￨L￨NN￨O￨- of￨L￨IN￨O￨- responsibility￨L￨NN￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- learning￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- emphasizes￨L￨VBZ￨O￨- intuitive￨L￨JJ￨O￨- ,￨L￨,￨O￨- long-term￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- course￨L￨NN￨O￨- material￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- also￨L￨RB￨O￨- see￨L￨VBP￨O￨- Jungck￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- meta-analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- 60￨L￨CD￨NUMBER￨- research￨L￨NN￨O￨- studies￨L￨NNS￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- consistent￨L￨JJ￨O￨- and￨L￨CC￨O￨- knowledgeable￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- manipulatives￨L￨NNS￨O￨- improves￨L￨VBZ￨O￨- both￨L￨CC￨O￨- students￨L￨NNS￨O￨A '￨L￨POS￨O￨- mathematical￨L￨JJ￨O￨- achievement￨L￨NN￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- attitudes￨L￨NNS￨O￨- toward￨L￨IN￨O￨- mathematics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- appropriate￨L￨JJ￨O￨- classroom￨L￨NN￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- manipulatives￨L￨NNS￨O￨- both￨L￨CC￨O￨- broadens￨L￨VBZ￨O￨- and￨L￨CC￨O￨- deepens￨L￨VBZ￨O￨- students￨L￨NNS￨O￨A '￨L￨POS￨O￨- learning￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- group￨L￨NN￨O￨- work￨L￨NN￨O￨- with￨L￨IN￨O￨- manipulatives￨L￨NNS￨O￨- transforms￨L￨VBZ￨O￨- mathematical￨L￨JJ￨O￨- problem￨L￨NN￨O￨- solving￨L￨VBG￨O￨A into￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- activity￨L￨NN￨O￨- ,￨L￨,￨O￨- decreasing￨L￨VBG￨O￨- student￨L￨NN￨TITLE￨- anxiety￨L￨NN￨O￨- and￨L￨CC￨O￨- increasing￨L￨VBG￨O￨- engagement￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- demonstrate￨L￨VB￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨A such￨L￨PDT￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- hands-on￨L￨JJ￨O￨- exercise￨L￨NN￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- iteration￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- four￨L￨CD￨NUMBER￨- successive￨L￨JJ￨O￨- semesters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- heuristics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- sensu￨L￨NN￨O￨- Starfield￨U￨NN￨LOCATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- plausible￨L￨JJ￨O￨- or￨L￨CC￨O￨- reasonable￨L￨JJ￨O￨- approach￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- es￨L￨NNS￨O￨- ]￨L￨-RRB-￨O￨- …￨L￨:￨O￨- often￨L￨RB￨O￨- proved￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- ,￨L￨,￨O￨- rule￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- ]￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- thumb￨L￨NN￨O￨- ”￨L￨''￨O￨- for￨L￨IN￨O￨- designing￨L￨VBG￨O￨- and￨L￨CC￨O￨- implementing￨L￨VBG￨O￨- a￨L￨DT￨O￨- course￨L￨NN￨O￨- that￨L￨WDT￨O￨- emphasized￨L￨VBD￨O￨- both￨L￨DT￨O￨- content￨L￨NN￨O￨- and￨L￨CC￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- cooperative￨L￨JJ￨O￨- learning￨L￨NN￨O￨A .￨L￨.￨O￨- +An￨U￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- >￨L￨JJR￨O￨- 190￨L￨CD￨NUMBER￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- Johnson￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- strongly￨L￨RB￨O￨- demonstrates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- emphasizing￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- cooperative￨L￨JJ￨O￨- learning￨L￨NN￨O￨A increases￨L￨VBZ￨O￨- students￨L￨NNS￨O￨- '￨L￨POS￨O￨- academic￨L￨JJ￨O￨- achievement￨L￨NN￨O￨- ,￨L￨,￨O￨- higher-level￨L￨JJ￨O￨- reasoning￨L￨NN￨O￨- ,￨L￨,￨O￨- retention￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- motivation￨L￨NN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- competitive￨L￨JJ￨O￨- or￨L￨CC￨O￨- individual￨L￨JJ￨O￨- learning￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- published￨L￨VBN￨O￨- general￨L￨JJ￨TITLE￨- prescriptive￨L￨JJ￨O￨- models￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- implementing￨L￨VBG￨O￨- cooperative￨L￨JJ￨O￨- learning￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Johnson￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Tanner￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- had￨L￨VBD￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- built￨L￨VBN￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Biology￨U￨NNP￨ORGANIZATION￨- 's￨L￨POS￨O￨- objectives￨L￨NNS￨O￨- :￨L￨:￨O￨- to￨L￨TO￨O￨- teach￨L￨VB￨O￨- students￨L￨NNS￨O￨A models￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- modeling￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- efforts￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- ,￨L￨,￨O￨- statistical￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- training￨L￨NN￨O￨- of￨L￨IN￨O￨- undergraduates￨L￨NNS￨O￨- in￨L￨IN￨O￨- life￨L￨NN￨O￨- science￨L￨NN￨O￨A majors￨L￨NNS￨O￨- at￨L￨IN￨O￨- Emory￨U￨NNP￨ORGANIZATION￨- College￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Mathematics￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Computer￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Biology￨U￨NNP￨O￨- Departments￨U￨NNP￨O￨- both￨L￨CC￨O￨- offer￨L￨VBP￨O￨- courses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- mathematical￨L￨JJ￨O￨- ,￨L￨,￨O￨- statistical￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- instruction￨L￨NN￨O￨- for￨L￨IN￨O￨- life￨L￨NN￨O￨- science￨L￨NN￨O￨A majors￨L￨NNS￨O￨- at￨L￨IN￨O￨- Emory￨U￨NNP￨ORGANIZATION￨- College￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- provides￨L￨VBZ￨O￨- the￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- training￨L￨NN￨O￨- needed￨L￨VBN￨O￨- by￨L￨IN￨O￨- all￨L￨DT￨O￨- life￨L￨NN￨O￨- science￨L￨NN￨O￨A students￨L￨NNS￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- required￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Biology￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨O￨- its￨L￨PRP$￨O￨- Bachelor￨U￨NN￨TITLE￨- of￨L￨IN￨O￨- Science￨U￨NNP￨O￨- program￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- introductory￨L￨JJ￨O￨- mathematics￨L￨NN￨O￨- sequence￨L￨NN￨O￨- for￨L￨IN￨O￨- life￨L￨NN￨O￨- science￨L￨NN￨O￨A majors￨L￨NNS￨O￨- ,￨L￨,￨O￨- Mathematics￨U￨NNS￨O￨- 115/116-Life￨L￨JJ￨O￨- Science￨U￨NN￨O￨- Calculus￨U￨NN￨O￨- 1/2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- addresses￨L￨NNS￨O￨- two￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- themes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- for￨L￨IN￨O￨- density-independent￨L￨JJ￨O￨- growth￨L￨NN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- modelled￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- geometric￨L￨JJ￨O￨- Brownian￨U￨JJ￨MISC￨- motion￨L￨NN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- For￨U￨IN￨O￨- density-dependent￨L￨JJ￨O￨- growth￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- modelled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- σ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Imax￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- dz￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Gaussian￨U￨JJ￨MISC￨- distributed￨L￨VBN￨O￨- Wiener￨U￨NNP￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- mean￨L￨NN￨O￨- and￨L￨CC￨O￨- infinitesimal￨L￨JJ￨O￨- variance￨L￨NN￨O￨- dt￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- background￨L￨NN￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- electronic￨L￨JJ￨O￨A supplementary￨L￨JJ￨O￨A material￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- every￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- increase￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- exponential￨L￨JJ￨O￨- and￨L￨CC￨O￨- logistic￨L￨JJ￨O￨- increase￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨A ,￨L￨,￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- where￨L￨WRB￨O￨- p￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- monetary￨L￨JJ￨O￨- gain￨L￨NN￨O￨- in￨L￨IN￨O￨- yield￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevented￨L￨VBN￨O￨- by￨L￨IN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- scaled￨L￨VBN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- averted￨L￨VBN￨O￨- by￨L￨IN￨O￨- treatment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- electronic￨L￨JJ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- net￨L￨JJ￨O￨- gain￨L￨NN￨O￨- from￨L￨IN￨O￨- treatment￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- at￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- *￨L￨SYM￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- costs￨L￨NNS￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- *￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- wish￨L￨VBP￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- option￨L￨NN￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- where￨L￨WRB￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- net￨L￨JJ￨O￨- benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- under￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- and￨L￨CC￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- discount￨L￨NN￨O￨- rate￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- conventionally￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- economic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- expenditure￨L￨NN￨O￨- today￨L￨NN￨DATE￨- has￨L￨VBZ￨O￨- greater￨L￨JJR￨O￨- weighting￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- expenditure￨L￨NN￨O￨- at￨L￨IN￨O￨- some￨L￨DT￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- flexibility￨L￨NN￨O￨- in￨L￨IN￨O￨- choosing￨L￨VBG￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨A in￨L￨IN￨O￨- combination￨L￨NN￨O￨- with￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- irreversibility￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- costs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- creates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- value￨L￨NN￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- option￨L￨NN￨O￨- value￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- finance￨L￨NN￨O￨- literature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- presented￨L￨VBN￨O￨- here￨L￨RB￨O￨- give￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨A for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- agricultural￨L￨JJ￨O￨- landscape￨L￨NN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- natural￨L￨JJ￨O￨- plant￨L￨NN￨O￨- and￨L￨CC￨O￨- animal￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- coinfections￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- common￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- is￨L￨VBZ￨O￨- limited￨L￨VBN￨O￨- ,￨L￨,￨O￨- influences￨L￨VBZ￨O￨- of￨L￨IN￨O￨- nutritional￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- cofactors￨L￨NNS￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- may￨L￨MD￨O￨- more￨L￨RBR￨O￨- often￨L￨RB￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- norm￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- exception.Stratified￨L￨JJ￨O￨- models￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- subpopulations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- stratification￨L￨NN￨O￨- by￨L￨IN￨O￨- sex￨L￨NN￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- risk￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- tailored￨L￨VBN￨O￨- to￨L￨TO￨O￨- particular￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨A populations￨L￨NNS￨O￨A and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- cofactors￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- latter￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- substantive￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- impacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- a￨L￨DT￨O￨- "￨L￨``￨O￨- simplest￨L￨JJS￨O￨- possible￨L￨JJ￨O￨- "￨L￨''￨O￨- model￨L￨NN￨TITLE￨- built￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- classical￨L￨JJ￨O￨- Susceptible-Infected￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- framework￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- how￨L￨WRB￨O￨- cofactors￨L￨NNS￨O￨- can￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- fate￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- additional￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- "￨L￨``￨O￨- simplest￨L￨JJS￨O￨- possible￨L￨JJ￨O￨- "￨L￨''￨O￨- demographic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- cofactors￨L￨NNS￨O￨- :￨L￨:￨O￨- that￨L￨IN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- bearing￨L￨VBG￨O￨- the￨L￨DT￨O￨- cofactor￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨DT￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- acquisition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- but￨L￨CC￨O￨- carries￨L￨VBZ￨O￨- the￨L￨DT￨O￨- cofactor￨L￨NN￨O￨- .￨L￨.￨O￨- +Host￨U￨NN￨TITLE￨- populations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- differ￨L￨VBP￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- often￨L￨RB￨O￨- differ￨L￨VBP￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- ecological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- indirectly￨L￨RB￨O￨- affect￨L￨VBP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- as￨L￨IN￨O￨- well.Cofactors￨L￨NNS￨O￨- can￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- ways￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- cofactors￨L￨NNS￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- primary￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- shifting￨L￨VBG￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- non-endemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- endemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reversing￨L￨VBG￨O￨- demographic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- bears￨L￨VBZ￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- demographic￨L￨JJ￨O￨- decline￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- identify￨L￨VB￨O￨- vaccine￨L￨NN￨O￨- allocation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- greatest￨L￨JJS￨O￨- potential￨L￨NN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- morbidity￨L￨NN￨O￨A and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- studied￨L￨VBD￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- population￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- whose￨L￨WP$￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- from￨L￨IN￨O￨- observed￨L￨VBN￨O￨- proportions￨L￨NNS￨O￨- infected￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- interpersonal￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- weighted￨L￨VBN￨O￨- by￨L￨IN￨O￨- duration￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- added￨L￨VBD￨O￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- age-specific￨L￨JJ￨O￨- efficacy￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Govaert￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- conducted￨L￨VBD￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- randomized￨L￨NN￨O￨- ,￨L￨,￨O￨- double-blind￨L￨JJ￨O￨- ,￨L￨,￨O￨- placebo-controlled￨L￨JJ￨O￨- trial￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- morbidity￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- circulating￨L￨VBG￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- shifting￨L￨VBG￨O￨- and￨L￨CC￨O￨- drifting￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- merits￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- schoolchildren￨L￨NNS￨O￨- against￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- partly￨L￨RB￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- elderly￨L￨JJ￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- argued￨L￨VBN￨O￨- from￨L￨IN￨O￨- community-intervention￨L￨JJ￨O￨- trials￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- natural￨L￨JJ￨O￨- experiments￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- individual-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- 's￨L￨POS￨O￨- disease-induced￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- either￨L￨RB￨O￨- quotients￨L￨NNS￨O￨- of￨L￨IN￨O￨- deaths￨L￨NNS￨O￨- attributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A NumericCitation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- mortalities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- problems￨L￨NNS￨O￨- have￨L￨VBP￨O￨- affected￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨- availability￨L￨NN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A seasons￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- ;￨L￨:￨O￨- these￨L￨DT￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- varied￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- experiments￨L￨NNS￨O￨A :￨L￨:￨O￨- The￨U￨DT￨O￨- simulation￨L￨NN￨O￨- starts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- with￨L￨IN￨O￨- 50￨L￨CD￨NUMBER￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- divided￨L￨VBN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- The￨U￨DT￨O￨- base-line￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- is￨L￨VBZ￨O￨- calibrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- age￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- as￨L￨IN￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- New￨U￨NNP￨COUNTRY￨- Zealand￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- 0-19￨L￨NN￨O￨- =￨L￨JJ￨O￨- 64￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 20-59￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 32￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 60￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- =￨L￨JJ￨O￨- 4￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- The￨U￨DT￨O￨- base-line￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- is￨L￨VBZ￨O￨- calibrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- mild￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- investigating￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- following￨L￨VBG￨O￨- values￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- start￨L￨NN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- set￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Swedish￨U￨JJ￨NATIONALITY￨- vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- One￨U￨CD￨NUMBER￨- vaccine￨L￨NN￨O￨- dose￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- administered￨L￨VBN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- for￨L￨IN￨O￨- people￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- 6￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- 13￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- who￨L￨WP￨O￨- will￨L￨MD￨O￨- receive￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- doses￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- ,￨L￨,￨O￨- VirSim￨U￨NNP￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- main￨L￨JJ￨O￨- goals￨L￨NNS￨O￨- in￨L￨IN￨O￨- mind￨L￨NN￨O￨- :￨L￨:￨O￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- available￨L￨JJ￨O￨- population￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- specific￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- to￨L￨TO￨O￨- extend￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- Graphical￨U￨NNP￨O￨- User￨U￨NN￨O￨- Interface￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- GUI￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- easy￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- of￨L￨IN￨O￨- simulation￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- VirSim￨U￨NNP￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨- environment￨L￨NN￨O￨- AnyLogic.Three￨U￨NN￨O￨- identical￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- created￨L￨VBN￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- representing￨L￨VBG￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨A group￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- and￨L￨CC￨O￨- within￨L￨IN￨O￨- age-groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- vaccination￨L￨NN￨O￨- doses￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- administered￨L￨VBN￨O￨- at￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- pace￨L￨NN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- takes￨L￨VBZ￨O￨- 7￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- dose￨L￨NN￨O￨- Vaccine￨U￨NN￨O￨- effectiveness￨L￨NN￨O￨- :￨L￨:￨O￨- One￨U￨CD￨NUMBER￨- dose￨L￨NN￨O￨- :￨L￨:￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- become￨L￨VBN￨O￨- fully￨L￨RB￨O￨- immune￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- for￨L￨IN￨O￨- people￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- 60￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- become￨L￨VBN￨O￨- fully￨L￨RB￨O￨- immune￨L￨JJ￨O￨- Two￨U￨CD￨NUMBER￨- doses￨L￨NNS￨O￨- :￨L￨:￨O￨- 85￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- become￨L￨VBN￨O￨- fully￨L￨RB￨O￨- immune￨L￨JJ￨O￨- Five￨U￨CD￨NUMBER￨- different￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- experiments￨L￨NNS￨O￨A were￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- was￨L￨VBD￨O￨- varied￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- reductions￨L￨NNS￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- age-groups￨L￨NNS￨O￨- were￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- :￨L￨:￨O￨- Contacts￨U￨NNS￨O￨- within￨L￨IN￨O￨- population￨L￨NN￨O￨- 0-19￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- reduced￨L￨VBN￨O￨- with￨L￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Contacts￨U￨NNS￨O￨- between￨L￨IN￨O￨- population￨L￨NN￨O￨- 0-19￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 20-59￨L￨CD￨DATE￨- are￨L￨VBP￨O￨- reduced￨L￨VBN￨O￨- with￨L￨IN￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Contacts￨U￨NNS￨O￨- between￨L￨IN￨O￨- population￨L￨NN￨O￨- 0-19￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 60￨L￨CD￨NUMBER￨- plus￨L￨CC￨O￨- are￨L￨VBP￨O￨- reduced￨L￨VBN￨O￨- with￨L￨IN￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Three￨U￨CD￨NUMBER￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- experiments￨L￨NNS￨O￨A were￨L￨VBD￨O￨- run￨L￨VBN￨O￨- ;￨L￨:￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- closure￨L￨NN￨O￨- times￨L￨NNS￨O￨- were￨L￨VBD￨O￨- 7￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- 21￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- 28￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- experiments￨L￨NNS￨O￨A ,￨L￨,￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- ,￨L￨,￨O￨- following￨L￨VBG￨O￨- values￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- :￨L￨:￨O￨- Initialization￨U￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- schools￨L￨NNS￨O￨- close￨L￨RB￨O￨- when￨L￨WRB￨O￨- 1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- 0-19￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- emergence￨L￨NN￨O￨- per￨L￨IN￨O￨- introduction￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨A population￨L￨NN￨O￨A ,￨L￨,￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mutation￨L￨NN￨O￨- rate￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- adapts￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- concentrate￨L￨VBP￨O￨- here￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨A population￨L￨NN￨O￨A ,￨L￨,￨O￨- an￨L￨DT￨O￨- area￨L￨NN￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- hitherto￨L￨RB￨O￨- received￨L￨VBN￨O￨- little￨L￨JJ￨O￨- attention￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- adapting￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +Computationally￨U￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- fully￨L￨RB￨O￨- adapted￨L￨VBN￨O￨- strain￨L￨NN￨O￨- to￨L￨TO￨O￨- distinguish￨L￨VB￨O￨- between￨L￨IN￨O￨- emergence￨L￨NN￨O￨A and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- situations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨A population￨L￨NN￨O￨A is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- small￨L￨JJ￨O￨- we￨L￨PRP￨O￨- relax￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- emergence￨L￨NN￨O￨- threshold￨L￨NN￨O￨- to￨L￨TO￨O￨- smaller￨L￨JJR￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- as￨L￨IN￨O￨- some￨L￨DT￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- below￨L￨IN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- new￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- studied￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- ignored￨L￨VBD￨O￨- spatial￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨A population￨L￨NN￨O￨A structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- plant￨L￨NN￨O￨- parasites￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- widely￨L￨RB￨O￨- accepted￨L￨VBN￨O￨- gene-for-gene￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- predicts￨L￨VBZ￨O￨- that￨L￨DT￨O￨- successful￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resistance￨L￨NN￨O￨- is￨L￨VBZ￨O￨- triggered￨L￨VBN￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- resistance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- gene￨L￨NN￨O￨A product￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- plant￨L￨NN￨O￨- recognizes￨L￨VBZ￨O￨- ,￨L￨,￨O￨- directly￨L￨RB￨O￨- or￨L￨CC￨O￨- indirectly￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- avirulence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Avr￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- gene￨L￨NN￨O￨- product￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- circumvented￨L￨VBD￨O￨- this￨L￨DT￨O￨- difficulty￨L￨NN￨O￨- by￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- fitness￨L￨NN￨O￨A traits￨L￨NNS￨O￨- in￨L￨IN￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- Phytophthora￨U￨NNP￨LOCATION￨- infestans￨L￨NNS￨O￨- isolates￨L￨NNS￨O￨- sharing￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- multilocus￨L￨NN￨O￨- fingerprint￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- differing￨L￨VBG￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- virulence/avirulence￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- statistically￨L￨RB￨O￨- significant￨L￨JJ￨O￨- fitness￨L￨NN￨O￨- cost￨L￨NN￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- isolates￨L￨NNS￨O￨- virulent￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- R10￨U￨NN￨MISC￨- resistance￨L￨NN￨O￨- gene￨L￨NN￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- adolescents￨L￨NNS￨O￨- or￨L￨CC￨O￨- adults￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- that￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- indirectly￨L￨RB￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- protection￨L￨NN￨O￨- of￨L￨IN￨O￨- young￨L￨JJ￨O￨- vulnerable￨L￨JJ￨O￨- infants￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- often￨L￨RB￨O￨- go￨L￨VBP￨O￨- by￨L￨IN￨O￨- unnoticed￨L￨JJ￨O￨- in￨L￨IN￨O￨- adolescents￨L￨NNS￨O￨- and￨L￨CC￨O￨- adults￨L￨NNS￨O￨- ,￨L￨,￨O￨- partly￨L￨RB￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- misdiagnosed￨L￨JJ￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- by￨L￨IN￨O￨- clinicians￨L￨NNS￨O￨- and￨L￨CC￨O￨- partly￨L￨RB￨O￨- as￨L￨IN￨O￨- many￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- remain￨L￨VBP￨O￨- asymptomatic￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- probably￨L￨RB￨O￨- is￨L￨VBZ￨O￨- much￨L￨JJ￨O￨- larger￨L￨JJR￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- underreporting￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- generally￨L￨RB￨O￨- recognized￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- serious￨L￨JJ￨O￨- problem￨L￨NN￨O￨- beyond￨L￨IN￨O￨- childhood￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- significant￨L￨JJ￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- costs￨L￨NNS￨O￨- in￨L￨IN￨O￨- adolescents￨L￨NNS￨O￨- and￨L￨CC￨O￨- adults￨L￨NNS￨O￨- with￨L￨IN￨O￨- productivity￨L￨NN￨O￨- losses￨L￨NNS￨O￨- comprising￨L￨VBG￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- costs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- schedule￨L￨NN￨O￨- consisted￨L￨VBD￨O￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- doses￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- cell￨L￨NN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- currently￨L￨RB￨DATE￨- at￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- booster￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- at￨L￨IN￨O￨- 11￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Currently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Germany￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- France￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Canada￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- already￨L￨RB￨O￨- incorporated￨L￨VBN￨O￨- an￨L￨DT￨O￨- adolescent￨L￨JJ￨O￨- booster￨L￨NN￨O￨- dose￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- acellular￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- their￨L￨PRP$￨O￨- immunization￨L￨NN￨O￨- program￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Ross￨U￨NNP￨PERSON￨- recognized￨L￨VBD￨O￨- that￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- makes￨L￨VBZ￨O￨- intuitive￨L￨JJ￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- trajectory￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- intervention￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨A difficult￨L￨JJ￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- not￨L￨RB￨O￨- impossible￨L￨JJ￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- help￨L￨VBP￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- facilitate￨L￨VBP￨O￨- comparisons￨L￨NNS￨O￨- among￨L￨IN￨O￨- competing￨L￨VBG￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A that￨L￨WDT￨O￨- can￨L￨MD￨O￨- inform￨L￨VB￨O￨- policy￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- review￨L￨VBP￨O￨- the￨L￨DT￨O￨- areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- most￨L￨RBS￨O￨- useful￨L￨JJ￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- drug￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- vector￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- alternative￨L￨JJ￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- cost-effectiveness￨L￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- realistic￨L￨JJ￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- then￨L￨RB￨O￨- improves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- specifically￨L￨RB￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨A further￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- conditions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- influence￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- thresholds￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- selective￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- can￨L￨MD￨O￨- act￨L￨VB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- refuge￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- wild￨L￨JJ￨O￨- type￨L￨NN￨O￨- ,￨L￨,￨O￨- non-resistant￨L￨JJ￨O￨- ,￨L￨,￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- so￨L￨RB￨O￨- doing￨L￨VBG￨O￨- ,￨L￨,￨O￨- oppose￨L￨VBP￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨A at￨L￨IN￨O￨- high￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- levels￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- shifts￨L￨NNS￨O￨- towards￨L￨IN￨O￨- providing￨L￨VBG￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- refuge￨L￨NN￨O￨- .￨L￨.￨O￨- +Analytical￨U￨NNP￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- simulations￨L￨NNS￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- at￨L￨IN￨O￨- low￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- settings￨L￨NNS￨O￨- changes￨L￨NNS￨O￨- increase￨L￨VBP￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- acts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- encourage￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- further￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- beyond￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- shown￨L￨VBN￨O￨- by￨L￨IN￨O￨- Klein￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Numerous￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- addressed￨L￨VBN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- and￨L￨CC￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨A from￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- perspective￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- :￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- recent￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- propose￨L￨VBP￨O￨- that￨L￨IN￨O￨- low￨L￨JJ￨O￨- ,￨L￨,￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- high￨L￨JJ￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- would￨L￨MD￨O￨- favor￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Conjunctival￨U￨JJ￨O￨- swabs￨L￨NNS￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 4,436￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- living￨L￨VBG￨O￨- in￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- endemic￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- had￨L￨VBD￨O￨- not￨L￨RB￨O￨- received￨L￨VBN￨O￨- prior￨L￨RB￨O￨- interventions￨L￨NNS￨O￨A for￨L￨IN￨O￨- trachoma￨L￨NN￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨O￨- and￨L￨CC￨O￨- East￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- Upper￨U￨NNP￨LOCATION￨- Saloum￨U￨NNP￨LOCATION￨- District￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Jali￨U￨NNP￨PERSON￨- village￨L￨NN￨O￨- in￨L￨IN￨O￨- The￨U￨DT￨O￨- Gambia￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- Kahe￨U￨NNP￨LOCATION￨- Mpya￨U￨NNP￨LOCATION￨- sub-village￨L￨NN￨O￨- and￨L￨CC￨O￨- Maindi￨U￨NN￨LOCATION￨- village￨L￨NN￨O￨- in￨L￨IN￨O￨- Tanzania￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- assessed￨L￨VBN￨O￨- using￨L￨VBG￨O￨- Polymerase￨U￨NNP￨O￨- Chain￨U￨NNP￨O￨- Reaction￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- PCR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- amplification￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- target￨L￨NN￨O￨- sequence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- cryptic￨L￨JJ￨O￨- plasmid￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bacterium￨L￨NN￨O￨- C￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- calculate￨L￨VBP￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- household￨L￨NN￨O￨A treatment￨L￨NN￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- MDA￨U￨NN￨ORGANIZATION￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- previously￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- household￨L￨NN￨O￨A was￨L￨VBD￨O￨- assigned￨L￨VBN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- by￨L￨IN￨O￨- sampling￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- Bernoulli￨U￨NNP￨ORGANIZATION￨- distribution￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- household￨L￨NN￨O￨- having￨L￨VBG￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- individual￨L￨NN￨O￨- with￨L￨IN￨O￨- active￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- taken￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- household￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +MDA￨U￨NN￨ORGANIZATION￨- is￨L￨VBZ￨O￨- advocated￨L￨VBN￨O￨- because￨L￨IN￨O￨- screening￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- cost-effective￨L￨JJ￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- poor￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- active￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- well￨L￨RB￨O￨- studied￨L￨VBN￨O￨- are￨L￨VBP￨O￨- classic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- like￨L￨IN￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- microbial￨L￨JJ￨O￨A infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- network-structured￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- move￨L￨VBP￨O￨- from￨L￨IN￨O￨- ‘￨L￨``￨O￨- susceptible￨L￨JJ￨O￨- ’￨L￨''￨O￨- (￨L￨-LRB-￨O￨- non-adopter￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- adopter￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- state￨L￨NN￨O￨- by￨L￨IN￨O￨- adopting￨L￨VBG￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- product￨L￨NN￨O￨- or￨L￨CC￨O￨- idea￨L￨NN￨O￨- ,￨L￨,￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- both￨L￨CC￨O￨- social￨L￨JJ￨O￨A and￨L￨CC￨O￨- non-social￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- recovery￨L￨NN￨O￨- ;￨L￨:￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- innovation￨L￨NN￨O￨A adoptions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- permanent￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- never￨L￨RB￨O￨- move￨L￨VBP￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +Stochastic￨U￨JJ￨O￨- spatial￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- or￨L￨CC￨O￨- small￨L￨JJ￨O￨- communities￨L￨NNS￨O￨A are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- in￨L￨IN￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- more￨L￨JJR￨O￨- traditional￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- valuable￨L￨JJ￨O￨- tool￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- animals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Traditionally￨U￨RB￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- often￨L￨RB￨O￨- take￨L￨VBP￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- variables￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- broad￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- classes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- incorporates￨L￨VBZ￨O￨- epidemiological￨L￨JJ￨O￨- attributes￨L￨NNS￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- computer￨L￨NN￨O￨- generated￨L￨VBD￨O￨- mock￨L￨JJ￨O￨- population￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A viruses￨L￨NNS￨O￨A .￨L￨.￨O￨- +Each￨U￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- member￨L￨NN￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- five￨L￨CD￨NUMBER￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨A throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- belong￨L￨VB￨O￨- to￨L￨TO￨O￨- several￨L￨JJ￨O￨- contact￨L￨NN￨O￨- groups￨L￨NNS￨O￨- simultaneously￨L￨RB￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- an￨L￨DT￨O￨- algorithmic￨L￨JJ￨O￨- refinement￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- communities￨L￨NNS￨O￨A .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- resilience￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- fail￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- cascade￨L￨NN￨O￨A .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- preliminary￨L￨JJ￨O￨- task￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- cascade￨L￨NN￨O￨A resilience￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- different￨L￨JJ￨O￨- domains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Dark￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- therefore￨L￨RB￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- operate￨L￨VB￨O￨- in￨L￨IN￨O￨- conditions￨L￨NNS￨O￨- of￨L￨IN￨O￨- intense￨L￨JJ￨O￨- cascade￨L￨NN￨O￨A pressure￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- figure￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- figure￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A if￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- were￨L￨VBD￨O￨- to￨L￨TO￨O￨- start￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 20￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 40￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 60￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 80￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- 90￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- for￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- hospitalizations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- left￨L￨JJ￨O￨- panel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- right￨L￨JJ￨O￨- panel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- minimize￨L￨VBP￨O￨- mortality￨L￨NN￨O￨- or￨L￨CC￨O￨- hospitalizations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- that￨L￨WDT￨O￨- gives￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A given￨L￨VBN￨O￨- a￨L￨DT￨O￨- starting￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- supply￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- vaccine￨L￨NN￨O￨A supplies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- ,￨L￨,￨O￨- vaccinating￨L￨VBG￨O￨- the￨L￨DT￨O￨- high-transmission￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- school￨L￨NN￨O￨- children￨L￨NNS￨O￨- or￨L￨CC￨O￨- young￨L￨JJ￨O￨- adults￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- proven￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- doing￨L￨VBG￨O￨- so￨L￨RB￨O￨- the￨L￨DT￨O￨- groups￨L￨NNS￨O￨- at￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- indirectly￨L￨RB￨O￨- protected￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- enough￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A to￨L￨TO￨O￨- cover￨L￨VB￨O￨- only￨L￨RB￨O￨- two￨L￨CD￨PERCENT￨- percent￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- DC￨U￨NN￨STATE_OR_PROVINCE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- strategy￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- cases￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- allocate￨L￨VB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- high-risk￨L￨JJ￨O￨- children￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 93￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- coverage￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- when￨L￨WRB￨O￨- vaccination￨L￨NN￨O￨- begins￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- figure￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Volume￨U￨NN￨O￨- 6￨L￨CD￨NUMBER￨- Supplement￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Computational￨U￨NNP￨O￨- Vaccinology￨U￨NNP￨O￨- :￨L￨:￨O￨- State-of-the-art￨U￨JJ￨O￨- Assessments￨U￨NNS￨MISC￨- Review￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Models￨U￨NNS￨MISC￨- of￨L￨IN￨MISC￨- RNA￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- designSamuel￨L￨NN￨O￨- Ojosnegros1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Niko￨U￨NNP￨PERSON￨- Beerenwinkel1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 6￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Suppl￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- S5￨U￨NN￨O￨- ©￨L￨SYM￨O￨- Beerenwinkel￨U￨NNP￨O￨- and￨L￨CC￨O￨- Ojosnegros￨U￨NNP￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2010Published￨L￨NNP￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractViruses￨U￨NNP￨O￨- are￨L￨VBP￨O￨- fast￨L￨JJ￨O￨- evolving￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- that￨L￨WDT￨O￨- continuously￨L￨RB￨O￨- adapt￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- highly￨L￨RB￨O￨- variable￨L￨JJ￨O￨- environments￨L￨NNS￨O￨- they￨L￨PRP￨O￨- live￨L￨VBP￨O￨- and￨L￨CC￨O￨- reproduce￨L￨VBP￨O￨A in￨L￨IN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- review￨L￨VBP￨O￨- several￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- addressed￨L￨VBN￨O￨- quantitatively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- computational￨L￨JJ￨O￨A methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- vaccine￨L￨NN￨O￨- design.KeywordsHuman￨L￨NNP￨O￨- Immunodeficiency￨U￨NN￨O￨- VirusInfluenzaHuman￨U￨NNP￨O￨- Leukocyte￨U￨NN￨O￨- AntigenViral￨U￨NNP￨O￨- EvolutionVaccine￨U￨NNP￨O￨- Design￨U￨NNP￨O￨- ReviewViruses￨U￨NNP￨O￨- are￨L￨VBP￨O￨- intracellular￨L￨JJ￨O￨- parasites￨L￨NNS￨O￨- that￨L￨WDT￨O￨- need￨L￨VBP￨O￨- the￨L￨DT￨O￨- cellular￨L￨JJ￨O￨- machinery￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Computational￨U￨JJ￨O￨- techniques￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- broadened￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- picture￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- has￨L￨VBZ￨O￨- contributed￨L￨VBN￨O￨- substantially￨L￨RB￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- progress￨L￨NN￨O￨- in￨L￨IN￨O￨- unraveling￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- replication￨L￨NN￨O￨A ,￨L￨,￨O￨- fitness￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- virulence￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- piece￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- development￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- viral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- selection￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccinations￨L￨NNS￨O￨- or￨L￨CC￨O￨- rational￨L￨JJ￨O￨- attenuation￨L￨NN￨O￨- of￨L￨IN￨O￨- viruses￨L￨NNS￨O￨A .￨L￨.￨O￨- +Viruses￨U￨NNS￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- RNA￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- exist￨L￨VBP￨O￨- in￨L￨IN￨O￨- genetically￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- error-prone￨L￨JJ￨O￨- replication￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- these￨L￨DT￨O￨- approaches￨L￨NNS￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- approach￨L￨NN￨O￨- considers￨L￨VBZ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- transient￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- situations￨L￨NNS￨O￨- ,￨L￨,￨O￨- current￨L￨JJ￨DATE￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- strive￨L￨VBP￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- integrated￨L￨JJ￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- both￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- stages￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A network￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- transmission￨L￨NN￨O￨A network￨L￨NN￨O￨A topology￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- restrict￨L￨VB￨O￨- ourselves￨L￨PRP￨O￨- to￨L￨TO￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- agents￨L￨NNS￨O￨- that￨L￨WDT￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- either￨L￨CC￨O￨- immunity￨L￨NN￨O￨- or￨L￨CC￨O￨- death￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- only￨L￨RB￨O￨- once￨L￨RB￨DATE￨- .￨L￨.￨O￨- +Network-based￨U￨JJ￨MISC￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- 's￨L￨POS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A network￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- 's￨L￨POS￨O￨- degree￨L￨NN￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- notation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemicNatasha￨L￨NN￨O￨- L￨U￨NN￨O￨- Tilston￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Ken￨U￨NNP￨PERSON￨- TD￨U￨NNP￨O￨- Eames￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Daniela￨U￨NNP￨PERSON￨- Paolotti2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Toby￨U￨NNP￨PERSON￨- Ealden1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- W￨U￨NNP￨O￨- John￨U￨NNP￨PERSON￨- Edmunds￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 1Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- †￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 10:650￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Tilston￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2010Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Internet-based￨U￨JJ￨MISC￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨A influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- advantages￨L￨NNS￨O￨- over￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- physician-based￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- reporting￨L￨VBG￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- monitor￨L￨VB￨O￨- a￨L￨DT￨O￨- wider￨L￨JJR￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- including￨L￨VBG￨O￨- those￨L￨DT￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- seek￨L￨VB￨O￨- care￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compared￨L￨VBD￨O￨- the￨L￨DT￨O￨- recorded￨L￨VBN￨O￨A ILI￨U￨NN￨O￨- incidence￨L￨NN￨O￨- with￨L￨IN￨O￨- physician-recorded￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- using￨L￨VBG￨O￨- different￨L￨JJ￨O￨- ILI￨U￨NN￨O￨- definitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- alternative￨L￨JJ￨O￨- denominator￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- on￨L￨IN￨O￨- incidence￨L￨NN￨O￨A estimates￨L￨NNS￨O￨- was￨L￨VBD￨O￨- explored￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- four￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- fitness￨L￨NN￨O￨A traits￨L￨NNS￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- vary￨L￨VB￨O￨- independently￨L￨RB￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- transmissibility￨L￨NN￨O￨- from￨L￨IN￨O￨- human￨L￨JJ￨O￨- to￨L￨TO￨O￨- mosquito￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- through￨L￨IN￨O￨- increased￨L￨VBN￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- longer￨L￨RBR￨O￨- life-expectancy￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- DENV2￨U￨NN￨O￨- ′￨L￨NN￨O￨- to￨L￨TO￨O￨- emulate￨L￨VB￨O￨- a￨L￨DT￨O￨- shorter￨L￨JJR￨O￨- extrinsic￨L￨JJ￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EIP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- longer￨L￨RBR￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- enhancement￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- system￨L￨NN￨O￨- can￨L￨MD￨O￨- then￨L￨RB￨O￨- be￨L￨VB￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- either￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- temporarily￨L￨RB￨O￨- immune￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- from￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- DENV1￨U￨NN￨O￨- ,￨L￨,￨O￨- DENV2￨U￨NN￨O￨- ,￨L￨,￨O￨- DENV2￨U￨NN￨O￨- ′￨L￨NN￨O￨- ,￨L￨,￨O￨- DENV3￨U￨NN￨O￨- or￨L￨CC￨O￨- DENV4￨U￨NN￨O￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- serotype￨L￨NN￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- asWe￨L￨NN￨O￨- denote￨L￨VBP￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨A biting￨L￨VBG￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- vector-to-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- respective￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- cross-immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- humans￨L￨NNS￨O￨- to￨L￨TO￨O￨- mosquitoes￨L￨NNS￨O￨- given￨L￨VBN￨O￨- as￨L￨IN￨O￨- In￨U￨IN￨O￨- accordance￨L￨NN￨O￨- with￨L￨IN￨O￨- our￨L￨PRP$￨O￨- previous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- antibody-dependent￨L￨JJ￨O￨- enhancement￨L￨NN￨O￨A acts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- both￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- and￨L￨CC￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- heterologous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- values￨L￨NNS￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- replacement￨L￨NN￨O￨- events￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- genotypes￨L￨NNS￨O￨- of￨L￨IN￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- fitness￨L￨NN￨O￨A differences￨L￨NNS￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- for￨L￨IN￨O￨- displacement￨L￨NN￨O￨- ,￨L￨,￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- interfere￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- serotype￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- this￨L￨DT￨O￨- genotype￨L￨NN￨O￨- replaced￨L￨VBD￨O￨- the￨L￨DT￨O￨- Asian/American￨U￨NNP￨MISC￨- type￨L￨NN￨O￨- would￨L￨MD￨O￨- suggest￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- fitness￨L￨NN￨O￨A advantage￨L￨NN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- resident￨L￨JJ￨O￨- genotype￨L￨NN￨O￨- but￨L￨CC￨O￨- possibly￨L￨RB￨O￨- also￨L￨RB￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- circulating￨L￨VBG￨O￨- serotypes￨L￨NNS￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- no￨L￨DT￨O￨- discernible￨L￨JJ￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- before￨L￨IN￨O￨- or￨L￨CC￨O￨- after￨L￨IN￨O￨- fixation￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- genealogy￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- parasites￨L￨NNS￨O￨- must￨L￨MD￨O￨- fit￨L￨VB￨O￨- inside￨L￨IN￨O￨A the￨L￨DT￨O￨- tree￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- forms￨L￨VBZ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨NN￨O￨- spreads￨L￨VBZ￨O￨- from￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- tree￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- must￨L￨MD￨O￨- fit￨L￨VB￨O￨- inside￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- 's￨L￨POS￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- model￨L￨VB￨O￨- heterogeneity￨L￨NN￨O￨A in￨L￨IN￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- represent￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- as￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- that￨L￨WDT￨O￨- links￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨ORGANIZATION￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- elimination￨L￨NN￨O￨A guidelines￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- valuable￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- control￨L￨NN￨O￨- to￨L￨TO￨O￨- elimination￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- suggested￨L￨VBN￨O￨- interventions￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- frame￨L￨NN￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- elimination￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- settings￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- numerous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨A including￨L￨VBG￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- insecticide￨L￨NN￨O￨- treated￨L￨VBN￨O￨- nets￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ITNS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- artemisinin￨L￨NN￨O￨- combination￨L￨NN￨O￨- therapy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ACT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- case￨L￨NN￨O￨- management￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- vaccines￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- in￨L￨IN￨O￨- specific￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- usually￨L￨RB￨O￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- world￨L￨NN￨O￨- countries￨L￨NNS￨O￨- would￨L￨MD￨O￨- deploy￨L￨VB￨O￨- an￨L￨DT￨O￨- integrated￨L￨VBN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- program￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨A which￨L￨WDT￨O￨- target￨L￨VBP￨O￨- different￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- chances￨L￨NNS￨O￨- of￨L￨IN￨O￨- success￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- discrete-time￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- Plasmodium￨U￨NN￨O￨- falciparum￨L￨NN￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- selected￨L￨VBN￨O￨- interventions￨L￨NNS￨O￨A in￨L￨IN￨O￨- low￨L￨JJ￨O￨- to￨L￨TO￨O￨- moderate￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- long￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- patterns￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- practical￨L￨JJ￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨A well￨L￨RB￨O￨- enough￨L￨RB￨O￨- to￨L￨TO￨O￨- guide￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- manage￨L￨VB￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- stratified￨L￨VBN￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨- only￨L￨RB￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- matrices￨L￨NNS￨O￨A whose￨L￨WP$￨O￨- entries￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- i￨L￨FW￨O￨- have￨L￨VBP￨O￨- with￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- j￨L￨NN￨O￨- ,￨L￨,￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Survey￨U￨NN￨O￨- respondents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- then￨L￨RB￨O￨- asked￨L￨VBN￨O￨- to￨L￨TO￨O￨- record￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- diary￨L￨NN￨O￨- relevant￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- they￨L￨PRP￨O￨- had￨L￨VBD￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨- assigned￨L￨VBN￨O￨- day￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- occurred￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- home￨L￨NN￨O￨- ,￨L￨,￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- public￨L￨JJ￨O￨- transportation￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- matrices￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- “￨L￨``￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- ”￨L￨''￨O￨- matrices￨L￨NNS￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- transportation￨L￨NN￨O￨- surveys￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- time￨L￨NN￨O￨- use￨L￨VBP￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- increasingly￨L￨RB￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- drawback￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- use￨L￨VBP￨O￨A data￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- usually￨L￨RB￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- give￨L￨VB￨O￨- direct￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- respondents￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- they￨L￨PRP￨O￨- spent￨L￨VBD￨O￨- in￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- critical￨L￨JJ￨O￨- aspect￨L￨NN￨O￨- common￨L￨JJ￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- parameterization￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- how￨L￨WRB￨O￨- people￨L￨NNS￨O￨- socially￨L￨RB￨O￨- mix￨L￨VBP￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- modeling￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- universal￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨A that￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- short-term￨L￨JJ￨O￨- protection￨L￨NN￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- small￨L￨JJ￨O￨- frequent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- universal￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- that￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- long-term￨L￨JJ￨O￨- protection￨L￨NN￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- severe￨L￨JJ￨O￨- infrequent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Influenza￨U￨NN￨CAUSE_OF_DEATH￨- vaccines￨L￨NNS￨O￨A that￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- short-term￨L￨JJ￨O￨- protection￨L￨NN￨O￨- maintain￨L￨VBP￨O￨- risk￨L￨NN￨O￨- awareness￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- result￨L￨NN￨O￨- in￨L￨IN￨O￨- stable￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +Vaccines￨U￨NNS￨O￨- that￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- long-term￨L￨JJ￨O￨- protection￨L￨NN￨O￨A could￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- substantial￨L￨JJ￨O￨- drops￨L￨NNS￨O￨- in￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- should￨L￨MD￨O￨- therefore￨L￨RB￨O￨- include￨L￨VB￨O￨- an￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- epidemic￨L￨JJ￨O￨- risk￨L￨NN￨O￨- awareness￨L￨NN￨O￨- programs￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Findings￨U￨NNS￨O￨- To￨U￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- universal￨L￨JJ￨O￨- long-term￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- vaccines￨L￨NNS￨O￨A on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- linked￨L￨VBD￨O￨- human￨L￨JJ￨O￨- cognition￨L￨NN￨O￨- and￨L￨CC￨O￨- memory￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- are￨L￨VBP￨O￨- kept￨L￨VBN￨O￨- high￨L￨JJ￨O￨- over￨L￨IN￨O￨- many￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- epidemics￨L￨NNS￨O￨- will￨L￨MD￨O￨- stay￨L￨VB￨O￨- small￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- score-based￨L￨JJ￨O￨- BN￨U￨NN￨O￨- learning￨L￨VBG￨O￨- algorithms￨L￨NNS￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- score￨L￨NN￨O￨- functions￨L￨NNS￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- several￨L￨JJ￨O￨- BN￨U￨NNP￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- VE￨U￨NNP￨O￨- trial￨L￨NN￨O￨- dataset￨L￨NN￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- naïve￨L￨JJ￨O￨- Bayes￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- and￨L￨CC￨O￨- evaluated￨L￨VBD￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BN￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- compact￨L￨JJ￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- VE￨U￨NNP￨O￨- trial￨L￨NN￨O￨- dataset￨L￨NN￨O￨A for￨L￨IN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- ABS￨U￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- policy￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- BN￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- encodes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- joint￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- over￨L￨IN￨O￨- all￨L￨DT￨O￨- dataset￨L￨NN￨O￨A variables￨L￨NNS￨O￨- .￨L￨.￨O￨- +VE￨U￨NNP￨O￨- conditioned￨L￨VBN￨O￨- on￨L￨IN￨O￨- any￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- covariates￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- BN￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- VE￨U￨NNP￨O￨- trial￨L￨NN￨O￨- dataset￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- position￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- units￨L￨NNS￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- change￨L￨VB￨O￨- significantly￨L￨RB￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- cells￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- tissue￨L￨NN￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- viral￨L￨JJ￨O￨- or￨L￨CC￨O￨- bacterial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- trees￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- forest￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- organisms￨L￨NNS￨O￨- carrying￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- moving￨L￨VBG￨O￨- around￨L￨RB￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- are￨L￨VBP￨O￨- acquiring￨L￨VBG￨O￨- new￨L￨JJ￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- connections￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- perhaps￨L￨RB￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- common￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- involving￨L￨VBG￨O￨- long￨L￨JJ￨O￨- distance￨L￨NN￨O￨- flights￨L￨NNS￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- removing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- culture￨L￨NN￨O￨- medium￨L￨NN￨O￨- we￨L￨PRP￨O￨- obtained￨L￨VBD￨O￨- an￨L￨DT￨O￨- extensive￨L￨JJ￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- images￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- developing￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- growing￨L￨VBG￨O￨- clusters￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A ;￨L￨:￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- experimental￨L￨JJ￨O￨- setup￨L￨NN￨O￨- was￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- tissue￨L￨NN￨O￨- cell￨L￨NN￨O￨- culture￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- confluent￨L￨JJ￨O￨- monolayer￨L￨NN￨O￨- of￨L￨IN￨O￨- astrocytes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- exposed￨L￨VBN￨O￨- uniformly￨L￨RB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- recombinant￨L￨JJ￨O￨- pseudorabies￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PRV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Ba-DupGreen￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- BDG￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- expresses￨L￨VBZ￨O￨- green￨L￨JJ￨O￨- fluorescent￨L￨JJ￨O￨- protein￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GFP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A with￨L￨IN￨O￨- immediate￨L￨JJ￨O￨- early￨L￨JJ￨O￨- kinetics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- chosen￨L￨VBN￨O￨- astrocytes￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cell￨L￨NN￨O￨- types￨L￨NNS￨O￨- examined￨L￨VBN￨O￨- in￨L￨IN￨O￨- preliminary￨L￨JJ￨O￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- these￨L￨DT￨O￨- cells￨L￨NNS￨O￨A show￨L￨VBP￨O￨- restricted￨L￨JJ￨O￨- release￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- interconnected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- compromised￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- experimental￨L￨JJ￨O￨- images￨L￨NNS￨O￨- also￨L￨RB￨O￨- displayed￨L￨VBD￨O￨- features￨L￨NNS￨O￨- very￨L￨RB￨O￨- much￨L￨RB￨O￨- like￨L￨IN￨O￨- percolation￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- cluster￨L￨NN￨O￨A had￨L￨VBD￨O￨- a￨L￨DT￨O￨- well￨L￨RB￨O￨- defined￨L￨VBN￨O￨- fractal￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cluster￨L￨NN￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- function￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- algebraically￨L￨RB￨O￨- decaying￨L￨JJ￨O￨- function￨L￨NN￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- modifications￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- and￨L￨CC￨ORDINAL￨- second￨L￨JJ￨ORDINAL￨- waves￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- antivirals￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- summer￨L￨NN￨DATE￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- explicitly￨L￨RB￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- acquired￨L￨VBN￨O￨- immunity￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨A we￨L￨PRP￨O￨- also￨L￨RB￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- summer￨L￨NN￨DATE￨- school￨L￨NN￨O￨- closures￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- both￨L￨DT￨O￨- waves￨L￨NNS￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- acquired￨L￨VBN￨O￨- immunity￨L￨NN￨O￨- from￨L￨IN￨O￨- previous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- either￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strain￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨A that￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- delineated￨L￨VBN￨O￨- by￨L￨IN￨O￨- immune￨L￨JJ￨O￨- status￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Immunity￨U￨NN￨O￨- gained￨L￨VBD￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨A or￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- will￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- using￨L￨VBG￨O￨- detailed￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- Georgia￨U￨NNP￨STATE_OR_PROVINCE￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- how￨L￨WRB￨O￨- various￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- mass￨L￨NN￨O￨- gatherings￨L￨NNS￨O￨- and￨L￨CC￨O￨- holiday￨L￨NN￨O￨- traveling￨L￨VBG￨O￨A ,￨L￨,￨O￨- may￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- gatherings￨L￨NNS￨O￨- and￨L￨CC￨O￨- holiday￨L￨NN￨O￨- traveling￨L￨VBG￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- computational￨L￨JJ￨O￨- modelPengyi￨L￨NN￨O￨- Shi1￨U￨NN￨O￨- ,￨L￨,￨O￨- Pinar￨U￨NNP￨PERSON￨- Keskinocak1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Julie￨U￨NNP￨PERSON￨- L￨U￨NNP￨O￨- Swann1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Bruce￨U￨NNP￨O￨- Y￨U￨NN￨O￨- Lee2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 10:778￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Shi￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2010Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- concerns￨L￨NNS￨O￨- arose￨L￨VBD￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- negative￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- mass￨L￨JJ￨O￨- public￨L￨JJ￨O￨- gatherings￨L￨NNS￨O￨- and￨L￨CC￨O￨- travel￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +Various￨U￨JJ￨O￨- scenarios￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mass￨L￨NN￨O￨- gatherings￨L￨NNS￨O￨- or￨L￨CC￨O￨- traveling￨L￨VBG￨O￨A period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- range￨L￨NN￨O￨- :￨L￨:￨O￨- 0.5￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- 5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- attending￨L￨VBG￨O￨- the￨L￨DT￨O￨- mass￨L￨NN￨O￨- gathering￨L￨NN￨O￨- events￨L￨NNS￨O￨- or￨L￨CC￨O￨- on￨L￨IN￨O￨- travel￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- range￨L￨NN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- to￨L￨TO￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- R0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1.5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1.8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- explored￨L￨VBN￨O￨- .￨L￨.￨O￨- +Conversely￨U￨RB￨O￨- ,￨L￨,￨O￨- mass￨L￨NN￨O￨- traveling￨L￨VBG￨O￨A or￨L￨CC￨O￨- gatherings￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- little￨L￨JJ￨O￨- effect￨L￨NN￨O￨- when￨L￨WRB￨O￨- occurring￨L￨VBG￨O￨- much￨L￨RB￨O￨- earlier￨L￨RBR￨O￨- or￨L￨CC￨O￨- later￨L￨RBR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- more￨L￨JJR￨DATE￨- than￨L￨IN￨DATE￨- 40￨L￨CD￨DATE￨- days￨L￨NNS￨DATE￨- earlier￨L￨RBR￨DATE￨- or￨L￨CC￨O￨- 20￨L￨CD￨DATE￨- days￨L￨NNS￨DATE￨- later￨L￨RB￨DATE￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1.5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Mass￨U￨JJ￨STATE_OR_PROVINCE￨- gatherings￨L￨NNS￨O￨- that￨L￨WDT￨O￨- occur￨L￨VBP￨O￨- within￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨A can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- as￨L￨RB￨O￨- high￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- relative￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- even￨L￨RB￨O￨- worse￨L￨JJR￨O￨- impacts￨L￨NNS￨O￨- on￨L￨IN￨O￨- local￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- and￨L￨CC￨O￨- travelers￨L￨NNS￨O￨- '￨L￨POS￨O￨- families￨L￨NNS￨O￨- .￨L￨.￨O￨- +Key￨U￨NN￨O￨- policy￨L￨NN￨O￨- statements￨L￨NNS￨O￨- have￨L￨VBP￨O￨- called￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- evidence-based￨L￨JJ￨O￨- policy￨L￨NN￨O￨- for￨L￨IN￨O￨- effectively￨L￨RB￨O￨- deploying￨L￨VBG￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- antiviral￨L￨JJ￨O￨A stockpile￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- limited￨L￨JJ￨O￨- or￨L￨CC￨O￨- costly￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- to￨L￨TO￨O￨- limit￨L￨VB￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- from￨L￨IN￨O￨- pH1N1￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- brief￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- involves￨L￨VBZ￨O￨- running￨L￨VBG￨O￨- a￨L￨DT￨O￨- structured￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- optimization￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- choice￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- policy￨L￨NN￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- policy￨L￨NN￨O￨- goal￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- that￨L￨WDT￨O￨- efficiently￨L￨RB￨O￨- searches￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- spaces￨L￨NNS￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- U.S.￨U￨NNP￨COUNTRY￨- antiviral￨L￨JJ￨O￨A stockpile￨L￨NN￨O￨- against￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- widespread￨L￨JJ￨O￨- and￨L￨CC￨O￨- effective￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- May￨U￨NNP￨DATE￨- 6￨L￨CD￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- U.S.￨U￨NNP￨ORGANIZATION￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- had￨L￨VBD￨O￨- distributed￨L￨VBN￨O￨- 11￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- 50￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- antiviral￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- courses￨L￨NNS￨O￨- held￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- federal￨L￨JJ￨O￨- portion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Strategic￨U￨NNP￨O￨- National￨U￨NNP￨O￨- Stockpile￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SNS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- recipients￨L￨NNS￨O￨- had￨L￨VBD￨O￨- local￨L￨JJ￨O￨- stockpiles￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- allowed￨L￨VBD￨O￨- the￨L￨DT￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- to￨L￨TO￨O￨- exceed￨L￨VB￨O￨- the￨L￨DT￨O￨- pre-determined￨L￨JJ￨O￨- target￨L￨NN￨O￨- of￨L￨IN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- 31￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- treatment￨L￨NN￨O￨- courses￨L￨NNS￨O￨- of￨L￨IN￨O￨- oseltamivir￨L￨NN￨O￨- and￨L￨CC￨O￨- zanamivir￨L￨NN￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- acceleration￨L￨NN￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- couple￨L￨VBP￨O￨- a￨L￨DT￨O￨- fast￨L￨RB￨O￨- ,￨L￨,￨O￨- scalable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- adaptable￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- cities￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- (￨L￨-LRB-￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- million￨L￨CD￨NUMBER￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- binormal￨L￨JJ￨O￨- mixture￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- was￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- log10-transformed￨L￨JJ￨O￨- corrected￨L￨VBN￨O￨- OD-values￨U￨NNS￨O￨- for￨L￨IN￨O￨- wild￨L￨JJ￨O￨- boar￨L￨NN￨O￨- up￨L￨IN￨DURATION￨- to￨L￨TO￨DURATION￨- 20￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 722￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- cut-off￨L￨JJ￨O￨- value￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- correctly￨L￨RB￨O￨- scored￨L￨VBN￨O￨- animals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- highest￨L￨JJS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- accompanying￨L￨VBG￨O￨- sensitivity￨L￨NN￨O￨- and￨L￨CC￨O￨- specificity￨L￨NN￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- appropriate￨L￨JJ￨O￨- reference￨L￨NN￨O￨- sera￨L￨NNS￨O￨- a￨L￨DT￨O￨- cut-off￨L￨JJ￨O￨- value￨L￨NN￨O￨- was￨L￨VBD￨O￨- selected￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- binormal￨L￨JJ￨O￨- mixture￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- fitted￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- log-transformed￨L￨JJ￨O￨- optical￨L￨JJ￨O￨- density-values￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- score￨L￨VB￨O￨- wild￨L￨JJ￨O￨- boar￨L￨NN￨O￨- positive￨L￨JJ￨O￨- or￨L￨CC￨O￨- negative￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- age-dependent￨L￨JJ￨O￨- seroprevalence￨L￨NN￨O￨- was￨L￨VBD￨O￨- additionally￨L￨RB￨O￨- estimated￨L￨VBN￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- mixture￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- per￨L￨IN￨O￨- age￨L￨NN￨O￨- category￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- interpreted￨L￨VBN￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- various￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- cut-off￨L￨JJ￨O￨- value￨L￨NN￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- binormal￨L￨JJ￨O￨- mixture￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- subsequently￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- score￨L￨VB￨O￨- wild￨L￨JJ￨O￨- boar￨L￨NN￨O￨- as￨L￨IN￨O￨- positive￨L￨JJ￨O￨- or￨L￨CC￨O￨- negative￨L￨JJ￨O￨- .￨L￨.￨O￨- +Analysis￨U￨NN￨O￨- was￨L￨VBD￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- wild￨L￨JJ￨O￨A boar￨L￨NN￨O￨- up￨L￨IN￨DURATION￨- to￨L￨TO￨DURATION￨- 20￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- initial￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- including￨L￨VBG￨O￨- all￨L￨DT￨O￨- wild￨L￨JJ￨O￨- boar￨L￨NN￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- satisfactorily￨L￨RB￨O￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- local￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A of￨L￨IN￨O￨- distribution￨L￨NN￨O￨- d￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- having￨L￨VBG￨O￨- k￨L￨NN￨O￨- network￨L￨NN￨O￨- contacts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- ϕ￨L￨VBP￨O￨- that￨L￨IN￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- triangles￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- all￨L￨DT￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- triples￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- types￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- lines￨L￨NNS￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- or￨L￨CC￨O￨- without￨L￨IN￨O￨- a￨L￨DT￨O￨- transitive￨L￨JJ￨O￨- link￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- assortativity￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- as￨L￨IN￨O￨- captured￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- matrixwhere￨L￨NN￨O￨- n̄￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- compares￨L￨VBZ￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- if￨L￨IN￨O￨- half-links￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- closure￨L￨NN￨O￨- scheme￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- acting￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨A equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- produces￨L￨VBZ￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- ODE￨U￨NN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 5M￨L￨NN￨O￨- +￨L￨CC￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- M￨U￨NN￨O￨- independent￨L￨JJ￨RELIGION￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- SIR￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- quickly￨L￨RB￨O￨- outstrip￨L￨VB￨O￨- even￨L￨RB￨O￨- modern￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- for￨L￨IN￨O￨- graphs￨L￨NNS￨O￨- with￨L￨IN￨O￨- ‘￨L￨``￨O￨- fat￨L￨JJ￨O￨- tailed￨L￨VBD￨O￨- ’￨L￨''￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- M￨U￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- .￨L￨.￨O￨- +Closure￨U￨NN￨O￨- schemes￨L￨NNS￨O￨- for￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨A models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- essentially￨L￨RB￨O￨- standard￨L￨JJ￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- presented￨L￨VBN￨O￨- for￨L￨IN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- significant￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- but￨L￨CC￨O￨- with￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- degree￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- for￨L￨IN￨O￨- unclustered￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- degree￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- now￨L￨RB￨DATE￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- other￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- pairwise￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- discussing￨L￨VBG￨O￨- the￨L￨DT￨O￨- reasoning￨L￨NN￨O￨- behind￨L￨IN￨O￨- each￨L￨DT￨O￨- assumption￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- validity￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- federal￨L￨JJ￨O￨- mandates￨L￨NNS￨O￨- minimize￨L￨VBP￨O￨- these￨L￨DT￨O￨- effects￨L￨NNS￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- recurring￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- like￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- whose￨L￨WP$￨O￨- control￨L￨NN￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- voluntary￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- predicts￨L￨VBZ￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- mutual￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- between￨L￨IN￨O￨- behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- high￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- season￨L￨NN￨O￨- may￨L￨MD￨O￨- increase￨L￨VB￨O￨- future￨L￨JJ￨DATE￨A vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- lowering￨L￨VBG￨O￨- future￨L￨JJ￨DATE￨- prevalence￨L￨NN￨O￨- ;￨L￨:￨O￨- conversely￨L￨RB￨O￨- low￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- may￨L￨MD￨O￨- decrease￨L￨VB￨O￨- future￨L￨JJ￨DATE￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- ultimately￨L￨RB￨O￨- increases￨L￨VBZ￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- contact￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- prior￨L￨JJ￨O￨- seasons￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- remembered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- make￨L￨VBP￨O￨- vaccination￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- explicit￨L￨JJ￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- that￨L￨WDT￨O￨- experiences￨L￨VBZ￨O￨- seasonal￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- cobwebbing￨L￨VBG￨O￨- NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- oscillatory￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- elderly￨L￨JJ￨O￨- have￨L￨VBP￨O￨- high￨L￨JJ￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- developing￨L￨VBG￨O￨- severe￨L￨JJ￨O￨- or￨L￨CC￨O￨- fatal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- when￨L￨WRB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨A at￨L￨IN￨O￨- high￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- ;￨L￨:￨O￨- younger￨L￨JJR￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- perceive￨L￨VBP￨O￨- lower￨L￨JJR￨O￨- risks￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- less￨L￨JJR￨O￨- incentive￨L￨NN￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- several￨L￨JJ￨O￨- explanations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- discrepancy￨L￨NN￨O￨- between￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- predicted￨L￨VBN￨O￨- oscillations￨L￨NNS￨O￨- dampen￨L￨VBP￨O￨- when￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- make￨L￨VBP￨O￨- vaccination￨L￨NN￨O￨A decisions￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- prior￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- experience￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- reason￨L￨NN￨O￨- to￨L￨TO￨O￨- anticipate￨L￨VB￨O￨- episodic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- for￨L￨IN￨O￨- rubella￨L￨NN￨O￨A :￨L￨:￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- for￨L￨IN￨O￨- rubella￨L￨NN￨O￨- are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- low￨L￨JJ￨O￨- —￨L￨:￨O￨- particularly￨L￨RB￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- childhood￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- pertussiss￨L￨NN￨O￨- —￨L￨:￨O￨- typically￨L￨RB￨O￨- between￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 8￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- transient￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- alone￨L￨RB￨O￨- may￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- variable￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- across￨L￨IN￨O￨- years￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- re-colonization￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- CCS￨U￨NN￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- important￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- age￨L￨NN￨O￨A incidence￨L￨NN￨O￨- curves￨L￨NNS￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- such￨L￨JJ￨O￨- episodic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- may￨L￨MD￨O￨- allow￨L￨VB￨O￨- leakage￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- older￨L￨JJR￨O￨- age￨L￨NN￨O￨- classes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- this￨L￨DT￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- indirectly￨L￨RB￨O￨- observed￨L￨VBN￨O￨- burden￨L￨NN￨O￨- as￨L￨IN￨O￨- inferred￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- rubella￨L￨NN￨O￨A cases￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- in￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- aged￨L￨VBN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 15￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 175￨L￨CD￨NUMBER￨- provinces￨L￨NNS￨O￨- .￨L￨.￨O￨- +Routine￨U￨JJ￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- aged￨L￨JJ￨O￨A 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2005￨L￨CD￨DATE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- coverage￨L￨NN￨O￨- during￨L￨IN￨O￨- this￨L￨DT￨O￨- period￨L￨NN￨O￨- was￨L￨VBD￨O￨- low￨L￨JJ￨O￨- and￨L￨CC￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 4￨L￨CD￨MONEY￨- per￨L￨IN￨MONEY￨- cent￨L￨NN￨MONEY￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- this￨L￨DT￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- FOI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- across￨L￨IN￨O￨- Peru￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infer￨L￨VBP￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- burden￨L￨NN￨O￨A of￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- Peruvian￨U￨JJ￨NATIONALITY￨- context￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- diagnostic￨L￨JJ￨O￨A strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- logistical￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- services￨L￨NNS￨O￨- sector￨L￨NN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Australian￨U￨JJ￨NATIONALITY￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- A￨U￨NNP￨MISC￨- H1N1￨U￨NN￨O￨- 2009￨L￨CD￨DATE￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- similar￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- order￨L￨NN￨O￨- of￨L￨IN￨O￨- magnitude￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- developed￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- extended￨L￨VBN￨O￨- an￨L￨DT￨O￨- existing￨L￨VBG￨O￨- Susceptible￨U￨NNP￨O￨- Exposed￨U￨VBN￨O￨- Infectious￨U￨JJ￨O￨- Recovered￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- presentations￨L￨NNS￨O￨- at￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- hospitals￨L￨NNS￨O￨- ,￨L￨,￨O￨- GP￨U￨NN￨O￨- s￨L￨NNS￨O￨- and￨L￨CC￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- clinics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- diagnosis￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- available￨L￨JJ￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- location￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- finite￨L￨JJ￨O￨- diagnostic￨L￨JJ￨O￨A and￨L￨CC￨O￨- antiviral￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- capacities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- response￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- pandemic￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- world-wide￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- antiviral￨L￨JJ￨O￨A intervention￨L￨NN￨O￨- strategy￨L￨NN￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- future￨L￨JJ￨DATE￨- pandemic￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- uncertain￨L￨JJ￨O￨- and￨L￨CC￨O￨- requires￨L￨VBZ￨O￨- further￨L￨JJ￨O￨- investigation￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- diagnostic￨L￨JJ￨O￨A strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- antiviral￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- PCRtests￨U￨NN￨O￨- until￨L￨IN￨O￨- lab￨L￨NN￨O￨- diagnostic￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- exceeded￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- use￨L￨VB￨O￨- syndromic￨L￨JJ￨O￨- diagnosis￨L￨NN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- powerful￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- decision￨L￨NN￨O￨- making￨L￨VBG￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- pre-planning￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- knowing￨L￨VBG￨O￨- in￨L￨IN￨O￨- advance￨L￨NN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- spontaneous￨L￨JJ￨O￨A behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- would￨L￨MD￨O￨- greatly￨L￨RB￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- predictive￨L￨JJ￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2010￨L￨CD￨DATE￨- Influenza-Like￨U￨NNP￨O￨- Illness￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- Italy￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- reported￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- national￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- plausible￨L￨JJ￨O￨- that￨L￨IN￨O￨- spontaneous￨L￨JJ￨O￨A behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- played￨L￨VBN￨O￨- a￨L￨DT￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- contributing￨L￨VBG￨O￨- to￨L￨TO￨O￨- change￨L￨VB￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- potential￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- epidemic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- explicitly￨L￨RB￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spontaneous￨L￨JJ￨O￨A response￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- payoff￨L￨NN￨O￨- functions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- triggered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- vice￨L￨NN￨O￨- versa￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- evolutionary￨L￨JJ￨O￨- game￨L￨NN￨O￨- theory￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- rich￨L￨JJ￨O￨- and￨L￨CC￨O￨- natural￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- human￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨A changes￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission￨L￨NN￨O￨A process￨L￨NN￨O￨A is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Susceptible-Infective-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- adopt￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- mutually￨L￨RB￨O￨- exclusive￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- normal￨L￨JJ￨O￨- ”￨L￨''￨O￨- and￨L￨CC￨O￨- “￨L￨``￨O￨- altered￨L￨JJ￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- perceived￨L￨VBN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- by￨L￨IN￨O￨- policy￨L￨NN￨O￨- makers￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- intervention￨L￨NN￨O￨A measures￨L￨NNS￨O￨- implemented￨L￨VBN￨O￨- as￨L￨RB￨O￨- early￨L￨RB￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- the￨L￨DT￨O￨- better￨L￨JJR￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- mitigation￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨JJ￨O￨A public￨L￨JJ￨O￨- health￨L￨NN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- and￨L￨CC￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- lowered￨L￨VBD￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- reduced￨L￨VBN￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- case￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- current￨L￨JJ￨DATE￨- scrapie￨L￨NN￨O￨- control￨L￨NN￨O￨- regulation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- European￨U￨NNP￨ORGANIZATION￨- Union￨U￨NNP￨ORGANIZATION￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- minimum￨L￨JJ￨O￨- requirements￨L￨NNS￨O￨- :￨L￨:￨O￨- culling￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- animals￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- genotype￨L￨NN￨O￨- in￨L￨IN￨O￨- infected￨L￨JJ￨O￨- flocks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- if￨L￨IN￨O￨- no￨L￨DT￨O￨- genetic￨L￨JJ￨O￨- testing￨L￨NN￨O￨- is￨L￨VBZ￨O￨- done￨L￨VBN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- animals￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- culled￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- genetic￨L￨JJ￨O￨- testing￨L￨NN￨O￨- of￨L￨IN￨O￨- rams￨L￨NNS￨O￨- intended￨L￨VBN￨O￨- for￨L￨IN￨O￨- breeding￨L￨VBG￨O￨A in￨L￨IN￨O￨- scrapie-free￨L￨JJ￨O￨- flocks￨L￨NNS￨O￨- of￨L￨IN￨O￨- "￨L￨``￨O￨- high￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- merit￨L￨NN￨O￨- "￨L￨''￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- culling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- rams￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- EC￨U￨NN￨ORGANIZATION￨- Regulation￨U￨NN￨O￨- No￨U￨DT￨O￨- 999/2001￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- under￨L￨IN￨O￨- field￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- how￨L￨WRB￨O￨- a￨L￨DT￨O￨- breeding￨L￨VBG￨O￨A programme￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- selecting￨L￨VBG￨O￨- rams￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- genotype￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- classical￨L￨JJ￨O￨- scrapie￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- were￨L￨VBD￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- flocks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- confirmed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- scrapie￨L￨NN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- individual￨L￨JJ￨O￨- identification￨L￨NN￨O￨- and￨L￨CC￨O￨- registration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- animals￨L￨NNS￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- perspective￨L￨NN￨O￨- of￨L￨IN￨O￨- continuation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- flock￨L￨NN￨O￨- for￨L￨IN￨O￨- at￨L￨IN￨DURATION￨- least￨L￨JJS￨DURATION￨- five￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- sale￨L￨NN￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- over￨L￨IN￨O￨- six￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- we￨L￨PRP￨O￨- recruited￨L￨VBD￨O￨- six￨L￨CD￨NUMBER￨- scrapie-affected￨L￨JJ￨O￨- commercially-run￨L￨JJ￨O￨- sheep￨L￨NN￨O￨- flocks￨L￨NNS￨O￨- into￨L￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- willing￨L￨JJ￨O￨- to￨L￨TO￨O￨- join￨L￨VB￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- initially￨L￨RB￨O￨- voluntary￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- breeding￨L￨VBG￨O￨A programme￨L￨NN￨O￨- .￨L￨.￨O￨- +Both￨U￨CC￨O￨- the￨L￨DT￨O￨- genotype￨L￨NN￨O￨A distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- scrapie￨L￨NN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- flocks￨L￨NNS￨O￨- was￨L￨VBD￨O￨- monitored￨L￨VBN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- 4￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- 6￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- maintained￨L￨VBN￨O￨- by￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- cooperative￨L￨JJ￨O￨A plasmid￨L￨NN￨O￨- carriers￨L￨NNS￨O￨- dominate￨L￨VBP￨O￨- other￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- and￨L￨CC￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- defector￨L￨NN￨O￨- plasmids￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- engineer￨L￨VBP￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- survival￨L￨NN￨O￨- by￨L￨IN￨O￨- virtue￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- higher￨L￨JJR￨O￨- productivity￨L￨NN￨O￨- and￨L￨CC￨O￨- horizontal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- Smith￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- model￨L￨NN￨TITLE￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- plasmids￨L￨NNS￨O￨- that￨L￨WDT￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- code￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- good￨L￨NN￨O￨- could￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- or￨L￨CC￨O￨- arise￨L￨VB￨O￨- through￨L￨IN￨O￨- mutation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- could￨L￨MD￨O￨- outcompete￨L￨VB￨O￨- the￨L￨DT￨O￨- cooperative￨L￨JJ￨O￨A plasmid￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- start￨L￨VBP￨O￨- by￨L￨IN￨O￨- imagining￨L￨VBG￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- defectors￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- rare￨L￨JJ￨O￨- mobile￨L￨JJ￨TITLE￨- element￨L￨NN￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- contains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- gene￨L￨NN￨O￨- coding￨L￨VBG￨O￨- for￨L￨IN￨O￨- cooperative￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨A assumes￨L￨VBZ￨O￨A that￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- well-mixed￨L￨JJ￨O￨- and￨L￨CC￨O￨- all￨L￨DT￨O￨- D￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- equal￨L￨JJ￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- m￨L￨NN￨O￨- plasmid￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- via￨L￨IN￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- 1￨L￨CD￨NUMBER￨- reveals￨L￨VBZ￨O￨- that￨L￨IN￨O￨- cooperative￨L￨JJ￨O￨A plasmid￨L￨NN￨O￨- carriers￨L￨NNS￨O￨- can￨L￨MD￨O￨- invade￨L￨VB￨O￨- a￨L￨DT￨O￨- pure￨L￨JJ￨O￨- defection￨L￨NN￨O￨- equilibrium￨L￨NN￨O￨- D￨U￨NN￨O￨- *￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- D￨U￨NN￨O￨- *￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- β￨L￨NN￨O￨- >￨L￨JJR￨O￨- s￨L￨NNS￨O￨- +￨L￨CC￨O￨- v￨L￨LS￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- Rm0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- illustrate￨L￨VB￨O￨- this￨L￨DT￨O￨- argument￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- probabilistic￨L￨JJ￨O￨- setting￨L￨NN￨O￨- wherein￨L￨WRB￨O￨- infectious￨L￨JJ￨O￨- encounters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- pure￨L￨JJ￨O￨- birth￨L￨NN￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- form￨L￨NN￨O￨- proposed￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- by￨L￨IN￨O￨- Liu￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- later￨L￨RB￨O￨- analyzed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Hethcote￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Van￨U￨NNP￨PERSON￨- Den￨U￨NNP￨PERSON￨- Driessche￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Liu￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hethcote￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Van￨U￨NNP￨PERSON￨- Den￨U￨NNP￨PERSON￨- Driessche￨U￨NNP￨PERSON￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A as￨L￨IN￨O￨- the￨L￨DT￨O￨- LHD￨U￨NNP￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- LHD￨U￨NN￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- qualitatively￨L￨RB￨O￨- different￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- ones￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- plethora￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- carefully￨L￨RB￨O￨- analyzed￨L￨VBN￨O￨A NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- confronted￨L￨VBN￨O￨- with￨L￨IN￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- biomathematics￨L￨NNS￨O￨- and￨L￨CC￨O￨- ecology￨L￨NN￨O￨- literatures￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Theoretical￨U￨JJ￨O￨- basis￨L￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- short-lasting￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peakRyosuke￨L￨NN￨O￨- Omori1￨U￨NN￨O￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Hiroshi￨U￨NNP￨PERSON￨- Nishiura2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 8:2￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Omori￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Nishiura￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- While￨U￨IN￨O￨- many￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- preparedness￨L￨NN￨O￨- plans￨L￨NNS￨O￨- have￨L￨VBP￨O￨- promoted￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- effort￨L￨NN￨O￨A to￨L￨TO￨O￨- lower￨L￨JJR￨O￨- and￨L￨CC￨O￨- delay￨L￨VB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨- ,￨L￨,￨O￨- analytical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- required￨L￨VBN￨O￨- control￨L￨NN￨O￨- effort￨L￨NN￨O￨- and￨L￨CC￨O￨- making￨L￨VBG￨O￨- statistical￨L￨JJ￨O￨- inferences￨L￨NNS￨O￨- have￨L￨VBP￨O￨- yet￨L￨RB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- sought￨L￨VBN￨O￨- .￨L￨.￨O￨- +[￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- most￨L￨RBS￨O￨- notably￨L￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- the￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics.Although￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- aided￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- expected￨L￨VBN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- analytical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- objectively￨L￨RB￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- required￨L￨VBN￨O￨- control￨L￨NN￨O￨- effort￨L￨NN￨O￨A and￨L￨CC￨O￨- that￨L￨IN￨O￨- make￨L￨VBP￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- empirically￨L￨RB￨O￨- observed￨L￨VBN￨O￨- delay￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- yet￨L￨RB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- developed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- offer￨L￨VBP￨O￨- methodological￨L￨JJ￨O￨- avenues￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- objectively￨L￨RB￨O￨- estimate￨L￨VB￨O￨- required￨L￨VBN￨O￨- control￨L￨NN￨O￨- effort￨L￨NN￨O￨A to￨L￨TO￨O￨- lower￨L￨JJR￨O￨- and￨L￨CC￨O￨- delay￨L￨VB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- this￨L￨DT￨O￨- issue￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- basis￨L￨NN￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- early￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨A ,￨L￨,￨O￨- employing￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- analytical￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- for￨L￨IN￨O￨- magnitude￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨A ,￨L￨,￨O￨- employing￨L￨VBG￨O￨- approximate￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- and￨L￨CC￨O￨- logarithmic-form￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- .￨L￨.￨O￨- +Disease￨U￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- from￨L￨IN￨O￨- reefs￨L￨NNS￨O￨- in￨L￨IN￨O￨- regions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- ranged￨L￨VBD￨O￨- from￨L￨IN￨O￨- heavily￨L￨RB￨O￨- populated￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- potentially￨L￨RB￨O￨- more￨L￨RBR￨O￨- intensely￨L￨RB￨O￨- impacted￨L￨VBN￨O￨- by￨L￨IN￨O￨- local￨L￨JJ￨O￨- stressors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- Hawaiian￨U￨JJ￨LOCATION￨- Islands￨U￨NNPS￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- Central￨U￨NNP￨LOCATION￨- Philippines￨U￨NNPS￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- relatively￨L￨RB￨O￨- pristine￨L￨JJ￨O￨- remote￨L￨JJ￨O￨- reefs￨L￨NNS￨O￨- with￨L￨IN￨O￨- minimal￨L￨JJ￨O￨- direct￨L￨JJ￨O￨- human￨L￨JJ￨O￨- impact￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- still￨L￨RB￨O￨- vulnerable￨L￨JJ￨O￨- to￨L￨TO￨O￨- global￨L￨JJ￨O￨A stressors￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Palmyra￨U￨NNP￨LOCATION￨- Atoll￨U￨NNP￨LOCATION￨- National￨U￨NNP￨LOCATION￨- Wildlife￨U￨NNP￨LOCATION￨- Refuge￨U￨NNP￨LOCATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- northern￨L￨JJ￨O￨- Line￨U￨NNP￨O￨- Islands￨U￨NNPS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- step￨L￨NN￨O￨- towards￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- statistical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- over￨L￨IN￨O￨- small￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- individual￨L￨JJ￨O￨- reefs￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨A multiple￨L￨JJ￨O￨- coral￨L￨NN￨O￨- disease-environment￨L￨NN￨O￨- associations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Coral￨U￨NN￨O￨- reefs￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- biologically￨L￨RB￨O￨- diverse￨L￨JJ￨O￨- ecosystems￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- planet￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- these￨L￨DT￨O￨- important￨L￨JJ￨O￨- habitats￨L￨NNS￨O￨- are￨L￨VBP￨O￨- declining￨L￨VBG￨O￨- worldwide￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- overexploitation￨L￨NN￨O￨- ,￨L￨,￨O￨- land-based￨L￨JJ￨O￨- pollution￨L￨NN￨O￨- ,￨L￨,￨O￨- global￨L￨JJ￨O￨A climate￨L￨NN￨O￨- change￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Coral￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- increases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- local￨L￨JJ￨O￨- anthropogenic￨L￨JJ￨O￨- stressors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- poor￨L￨JJ￨O￨- water￨L￨NN￨O￨- quality￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- global￨L￨JJ￨O￨A stressors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- sea-surface￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- anomalies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- resultant￨L￨JJ￨O￨- coral￨L￨NN￨O￨- bleaching￨L￨NN￨O￨- events￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- statistical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨A the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- coral￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Acropora￨U￨NNP￨O￨- growth￨L￨NN￨O￨- anomalies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- AGAs￨U￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Porites￨U￨NNP￨O￨- growth￨L￨NN￨O￨- anomalies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PGAs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- Indo-Pacific￨U￨JJ￨MISC￨- region￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- population￨L￨NN￨O￨- dataset￨L￨NN￨O￨- choice￨L￨NN￨O￨- on￨L￨IN￨O￨- estimates￨L￨NNS￨O￨A of￨L￨IN￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- diseaseAndrew￨L￨NN￨O￨- J￨U￨NN￨O￨- Tatem1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Nicholas￨U￨NNP￨PERSON￨- Campiz1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Peter￨U￨NNP￨PERSON￨- W￨U￨NNP￨PERSON￨- Gething4￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Robert￨U￨NNP￨PERSON￨- W￨U￨NNP￨PERSON￨- Snow5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Catherine￨U￨NNP￨PERSON￨- Linard4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 9:4￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Tatem￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- spatial￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- being￨L￨VBG￨O￨- undertaken￨L￨VBN￨O￨- for￨L￨IN￨O￨- health￨L￨NN￨O￨- services￨L￨NNS￨O￨- planning￨L￨VBG￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- monitoring￨L￨NN￨O￨- ,￨L￨,￨O￨- implementation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- evaluation￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- quantify￨L￨VBP￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- effects￨L￨NNS￨O￨- using￨L￨VBG￨O￨- global￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PAR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- P.￨U￨FW￨O￨- falciparum￨L￨FW￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- endemicity￨L￨NN￨O￨A enabled￨L￨VBD￨O￨- the￨L￨DT￨O￨- testing￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- gridded￨L￨JJ￨O￨- population￨L￨NN￨O￨- datasets￨L￨NNS￨O￨- for￨L￨IN￨O￨- providing￨L￨VBG￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- PAR￨U￨NN￨O￨- by￨L￨IN￨O￨- endemicity￨L￨NN￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +Where￨U￨WRB￨O￨- risks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- heterogeneous￨L￨JJ￨O￨- in￨L￨IN￨O￨- space￨L￨NN￨O￨- or￨L￨CC￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- person-to-person￨L￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨A population￨L￨NN￨O￨A distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risks￨L￨NNS￨O￨- ,￨L￨,￨O￨- burdens￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- different￨L￨JJ￨O￨- modeled￨L￨VBN￨O￨- human￨L￨JJ￨O￨A population￨L￨NN￨O￨A distribution￨L￨NN￨O￨- datasets￨L￨NNS￨O￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- and￨L￨CC￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- disparities￨L￨NNS￨O￨- among￨L￨IN￨O￨- them￨L￨PRP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- enumerating￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burdens￨L￨NNS￨O￨- and￨L￨CC￨O￨- populations￨L￨NNS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- systematically￨L￨RB￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Real-time￨U￨JJ￨MISC￨- forecasting￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- H1N1-2009￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Hiroshi￨U￨NNP￨O￨- Nishiura1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 10:15￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Nishiura￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Real-time￨U￨JJ￨MISC￨- forecasting￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- those￨L￨DT￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- likelihood-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- understudied￨L￨VBN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨A stochastic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- and￨L￨CC￨O￨- conditional￨L￨JJ￨O￨- measurement￨L￨NN￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- and￨L￨CC￨O￨- applied￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- H1N1-2009￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- vast￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- quantitative￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- effort￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- devoted￨L￨VBN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- inverse￨L￨JJ￨O￨- problem￨L￨NN￨O￨- methodology￨L￨NN￨O￨- which￨L￨WDT￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- estimations￨L￨NNS￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- building￨L￨NN￨O￨- imposes￨L￨VBZ￨O￨- strong￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- future￨L￨JJ￨DATE￨- prediction￨L￨NN￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- area￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- understudied￨L￨VBN￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- and￨L￨CC￨O￨- long-term￨L￨JJ￨O￨- prediction￨L￨NN￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- yet￨L￨RB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- sought￨L￨VBN￨O￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨A incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- greatly￨L￨RB￨O￨- improved￨L￨VBN￨O￨- at￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨- with￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- points￨L￨NNS￨O￨- falling￨L￨VBG￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨- bounds￨L￨NNS￨O￨- .￨L￨.￨O￨- +Software￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨DT￨MISC￨- GLEaMviz￨U￨NN￨MISC￨- computational￨L￨JJ￨O￨- tool￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- publicly￨L￨RB￨O￨- available￨L￨JJ￨O￨- software￨L￨NN￨O￨A to￨L￨TO￨O￨- explore￨L￨VB￨O￨- realistic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- scaleWouter￨L￨NN￨O￨- Van￨U￨NNP￨O￨- den￨L￨NN￨O￨- Broeck1￨U￨NN￨O￨- ,￨L￨,￨O￨- Corrado￨U￨NNP￨PERSON￨- Gioannini1Email￨U￨NNP￨PERSON￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Bruno￨U￨NNP￨PERSON￨- Gonçalves2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Marco￨U￨NNP￨PERSON￨- Quaggiotto1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Vittoria￨U￨NNP￨PERSON￨- Colizza5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Alessandro￨U￨NNP￨PERSON￨- Vespignani2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 11:37￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Broeck￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- simulation￨L￨NN￨O￨- engine￨L￨NN￨O￨- leverages￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Global￨U￨JJ￨O￨- Epidemic￨U￨JJ￨O￨- and￨L￨CC￨O￨- Mobility￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- GLEaM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- scheme￨L￨NN￨O￨- that￨L￨WDT￨O￨- integrates￨L￨VBZ￨O￨- worldwide￨L￨JJ￨O￨- high-resolution￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨A data￨L￨NNS￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- scale￨L￨NN￨O￨- .￨L￨.￨O￨- +Much￨U￨JJ￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- sophisticated￨L￨JJ￨O￨- data-driven￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- realistic￨L￨JJ￨O￨A computer-based￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- "￨L￨``￨O￨- GLEaMviz￨U￨NN￨O￨- "￨L￨''￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- publicly￨L￨RB￨O￨- available￨L￨JJ￨O￨- software￨L￨NN￨O￨A system￨L￨NN￨O￨- that￨L￨WDT￨O￨- simulates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- human-to-human￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- GLEaMviz￨U￨NN￨O￨- tool￨L￨NN￨O￨A comprises￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- components￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- client￨L￨NN￨O￨- application￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proxy￨L￨NN￨O￨- middleware￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- engine￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- research￨L￨NN￨O￨- under￨L￨IN￨O￨- survey￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- deals￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- developing￨L￨VBG￨O￨- probabilistic￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- levels￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- such￨L￨JJ￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- main￨L￨JJ￨O￨- target￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- extra￨L￨JJ￨O￨- vaccinated￨L￨VBN￨O￨- to￨L￨TO￨O￨- guarantee￨L￨VB￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- led￨L￨VBD￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- idea￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- original￨L￨JJ￨O￨- paper￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- suggest￨L￨VB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- by￨L￨IN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- continuous-time￨L￨JJ￨O￨- branching￨L￨VBG￨O￨A processes￨L￨NNS￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- firstly￨L￨RB￨O￨- we￨L￨PRP￨O￨- established￨L￨VBD￨O￨- stochastic￨L￨JJ￨O￨- monotonicity￨L￨NN￨O￨- and￨L￨CC￨O￨- continuity￨L￨NN￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- survives￨L￨VBZ￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- BHBP￨U￨NN￨O￨- and￨L￨CC￨O￨- SBP￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- level￨L￨NN￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- Bellman￨U￨NNP￨PERSON￨- –￨L￨:￨O￨- Harris￨U￨NNP￨PERSON￨- branching￨L￨VBG￨O￨A processes￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- BHBP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- epidemics￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- society-wide￨L￨JJ￨O￨- phenomenon￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- structure￨L￨NN￨O￨- at￨L￨IN￨O￨- all￨L￨DT￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- need￨L￨VBP￨O￨- population-level￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- network￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- STI￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Geography￨U￨NN￨O￨- leaves￨L￨VBZ￨O￨- several￨L￨JJ￨O￨- imprints￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A ,￨L￨,￨O￨- making￨L￨VBG￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- graph￨L￨NN￨O￨- distances￨L￨NNS￨O￨- ;￨L￨:￨O￨- it￨L￨PRP￨O￨- also￨L￨RB￨O￨- creates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- clusters￨L￨NNS￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- densely￨L￨RB￨O￨- populated￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- data￨L￨NNS￨O￨- set￨L￨VBN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- just￨L￨RB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- probably￨L￨RB￨O￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- substantial￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Internet-mediated￨U￨JJ￨MISC￨- escort￨L￨NN￨TITLE￨- business￨L￨NN￨O￨- of￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Sexual￨U￨JJ￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A have￨L￨VBP￨O￨- temporal￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- both￨L￨CC￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Five￨U￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- alternatives￨L￨NNS￨O￨- for￨L￨IN￨O￨- targeting￨L￨VBG￨O￨A unvaccinated￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- randomly￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- shown￨L￨VBN￨O￨- as￨L￨IN￨O￨- ‘￨L￨``￨O￨- 1￨L￨CD￨NUMBER￨- ’￨L￨''￨O￨- and￨L￨CC￨O￨- white￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- ‘￨L￨``￨O￨- S￨U￨NN￨O￨- ’￨L￨''￨O￨- and￨L￨CC￨O￨- green￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- ‘￨L￨``￨O￨- I￨U￨PRP￨O￨- ’￨L￨''￨O￨- and￨L￨CC￨O￨- red￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- ‘￨L￨``￨O￨- R￨U￨NN￨O￨- ’￨L￨''￨O￨- and￨L￨CC￨O￨- grey￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- never￨L￨RB￨O￨- optimal￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- district￨L￨NN￨O￨- .￨L￨.￨O￨- +Vector-borne￨U￨JJ￨O￨- and￨L￨CC￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- transmitted￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- frequency-dependent￨L￨JJ￨O￨- manner￨L￨NN￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨A density￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- partners￨L￨NNS￨O￨- or￨L￨CC￨O￨- vector￨L￨NN￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- split￨L￨VBN￨O￨- into￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- sections￨L￨NNS￨O￨- which￨L￨WDT￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- relevant￨L￨JJ￨O￨- to￨L￨TO￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- multitude￨L￨NN￨O￨- of￨L￨IN￨O￨- ways￨L￨NNS￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- characterised￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- either￨L￨CC￨O￨- infer￨L￨VBP￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨A network￨L￨NN￨O￨- structure￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- realised￨L￨VBN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- simulation￨L￨NN￨O￨- and￨L￨CC￨O￨- analytical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A network￨L￨NN￨O￨A allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- following￨L￨VBG￨O￨- invasion￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- aims￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- likely￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A network￨L￨NN￨O￨A connections￨L￨NNS￨O￨- from￨L￨IN￨O￨- known￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- treat￨L￨VB￨O￨- or￨L￨CC￨O￨- contain￨L￨VB￨O￨- their￨L￨PRP$￨O￨- contacts￨L￨NNS￨O￨- thereby￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- connections￨L￨NNS￨O￨A between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- propagate￨L￨VB￨O￨- naturally￨L￨RB￨O￨- define￨L￨VB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- generated￨L￨VBN￨O￨- provides￨L￨VBZ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- minor￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- negligible￨L￨JJ￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- ceases￨L￨VBZ￨O￨- because￨L￨IN￨O￨- infected￨L￨JJ￨O￨- persons￨L￨NNS￨O￨A fail￨L￨VBP￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- any￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- major￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- ceases￨L￨VBZ￨O￨- because￨L￨IN￨O￨- infected￨L￨JJ￨O￨- persons￨L￨NNS￨O￨A make￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- .￨L￨.￨O￨- +Directed￨U￨NNP￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- call￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- percolation￨L￨NN￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- EPNs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- “￨L￨``￨O￨- Susceptible-Infected-Removed￨U￨JJ￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- “￨L￨``￨O￨- Susceptible-Exposed-Infectious-Removed￨U￨NNP￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- persons￨L￨NNS￨O￨A infected￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- infected￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- obtain￨L￨VB￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- can￨L￨MD￨O￨- rather￨L￨RB￨O￨- easily￨L￨RB￨O￨- self-report￨L￨JJ￨O￨- contact￨L￨NN￨O￨- data￨L￨NNS￨O￨- quickly￨L￨RB￨O￨- and￨L￨CC￨O￨- efficiently￨L￨RB￨O￨- through￨L￨IN￨O￨- contact￨L￨NN￨O￨A tracing￨L￨VBG￨O￨A or￨L￨CC￨O￨- contact￨L￨NN￨O￨- diaries￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- clever￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- of￨L￨IN￨O￨- using￨L￨VBG￨O￨- proxies￨L￨NNS￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- mining￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- flu-related￨L￨JJ￨O￨- internet￨L￨NN￨O￨- queries￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- using￨L￨VBG￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨- locations￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- proxy￨L￨NN￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨- or￨L￨CC￨O￨- contact-tracing￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Conventional￨U￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- include￨L￨VBP￨O￨- a￨L￨DT￨O￨- repertoire￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- :￨L￨:￨O￨- traditional￨L￨JJ￨O￨- mean￨L￨JJ￨O￨- field￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- compartmental￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- metapopulation￨L￨NN￨O￨- ,￨L￨,￨O￨- lattice-based￨L￨JJ￨O￨- ,￨L￨,￨O￨- reaction-diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨A models￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- advantages￨L￨NNS￨O￨- over￨L￨IN￨O￨- traditional￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- underused￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- animal￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- these￨L￨DT￨O￨- reasons￨L￨NNS￨O￨- ,￨L￨,￨O￨- network￨L￨NN￨O￨- techniques￨L￨NNS￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- increasingly￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- network￨L￨NN￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- inherently￨L￨RB￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- modeling￨L￨NN￨O￨A tools￨L￨NNS￨O￨- .￨L￨.￨O￨- +Journal￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- International￨U￨NNP￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- Society￨U￨NNP￨O￨- Volume￨U￨NN￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Commentary￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- A￨U￨DT￨DURATION￨- decade￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- research￨L￨NN￨O￨- yields￨L￨NNS￨O￨- considerable￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- concurrency￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- Sawers￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Stillwaggon￨U￨NNP￨ORGANIZATION￨- Steven￨U￨NNP￨ORGANIZATION￨- M￨U￨NN￨ORGANIZATION￨- Goodreau￨U￨NNP￨ORGANIZATION￨- E-mail￨U￨NN￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Anthropology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Washington￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- WA￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- 98195￨L￨CD￨NUMBER￨- USASearch￨U￨NN￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- papers￨L￨NNS￨O￨- by￨L￨IN￨O￨- this￨L￨DT￨O￨- author￨L￨NN￨TITLE￨- Steven￨U￨NNP￨PERSON￨- M￨U￨NNP￨O￨- Goodreau￨U￨NNP￨ORGANIZATION￨- E-mail￨U￨NN￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Anthropology￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Washington￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- WA￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- 98195￨L￨CD￨NUMBER￨- USASearch￨U￨NN￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- papers￨L￨NNS￨O￨- by￨L￨IN￨O￨- this￨L￨DT￨O￨- author￨L￨NN￨TITLE￨- First￨U￨JJ￨ORDINAL￨- published￨L￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Cited￨U￨VBN￨O￨- by￨L￨IN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- AboutSectionsPDFPDF￨U￨NN￨O￨- ToolsRequest￨U￨NNP￨O￨- permissionExport￨L￨NNP￨O￨- citationAdd￨L￨NN￨O￨- to￨L￨TO￨O￨- favoritesTrack￨L￨NN￨O￨- citation￨L￨NN￨O￨- Share￨U￨NN￨O￨- Give￨U￨VB￨O￨- accessShare￨L￨NN￨O￨- full￨L￨JJ￨O￨- text￨L￨NN￨O￨A accessShare￨L￨NN￨O￨- full￨L￨JJ￨O￨- text￨L￨NN￨O￨- accessPlease￨L￨NN￨O￨- review￨L￨NN￨O￨- our￨L￨PRP$￨O￨- Terms￨U￨NNS￨O￨- and￨L￨CC￨O￨- Conditions￨U￨NNS￨O￨- of￨L￨IN￨O￨- Use￨U￨NN￨O￨- and￨L￨CC￨O￨- check￨L￨NN￨O￨- box￨L￨NN￨O￨- below￨L￨IN￨O￨- to￨L￨TO￨O￨- share￨L￨VB￨O￨- full-text￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- article.I￨L￨NN￨O￨- have￨L￨VBP￨O￨- read￨L￨VBN￨O￨- and￨L￨CC￨O￨- accept￨L￨VB￨O￨- the￨L￨DT￨O￨- Wiley￨U￨NNP￨ORGANIZATION￨- Online￨U￨NNP￨ORGANIZATION￨- Library￨U￨NNP￨ORGANIZATION￨- Terms￨U￨NNS￨ORGANIZATION￨- and￨L￨CC￨O￨- Conditions￨U￨NNS￨O￨- of￨L￨IN￨O￨- Use.Shareable￨U￨JJ￨O￨- LinkUse￨U￨NNP￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- below￨L￨IN￨O￨- to￨L￨TO￨O￨- share￨L￨VB￨O￨- a￨L￨DT￨O￨- full-text￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- with￨L￨IN￨O￨- your￨L￨PRP$￨O￨- friends￨L￨NNS￨O￨- and￨L￨CC￨O￨- colleagues￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- Morris￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Kretzschmar￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- initial￨L￨JJ￨O￨- work￨L￨NN￨O￨- helped￨L￨VBD￨O￨- clarify￨L￨VB￨O￨- how￨L￨WRB￨O￨- existing￨L￨VBG￨O￨- modelling￨L￨NN￨O￨- methods￨L￨NNS￨O￨- could￨L￨MD￨O￨- not￨L￨RB￨O￨- easily￨L￨RB￨O￨- or￨L￨CC￨O￨- thoroughly￨L￨RB￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- concurrency￨L￨NN￨O￨- hypothesis￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- have￨L￨VBP￨O￨- seen￨L￨VBN￨O￨- considerable￨L￨JJ￨O￨A methodological￨L￨JJ￨O￨- development￨L￨NN￨O￨- to￨L￨TO￨O￨- remedy￨L￨VB￨O￨- this￨L￨DT￨O￨- situation￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- argue￨L￨VBP￨O￨- that￨L￨IN￨O￨- neither￨L￨CC￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨A work￨L￨NN￨O￨- nor￨L￨CC￨O￨- the￨L￨DT￨O￨- behavioural￨L￨JJ￨O￨- data￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- convincing￨L￨JJ￨O￨- picture￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- relational￨L￨JJ￨O￨- concurrency￨L￨NN￨O￨- in￨L￨IN￨O￨- explaining￨L￨VBG￨O￨- national￨L￨JJ￨O￨- or￨L￨CC￨O￨- regional￨L￨JJ￨O￨- disparities￨L￨NNS￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- this￨L￨DT￨O￨- argument￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- reader￨L￨NN￨TITLE￨- might￨L￨MD￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- no￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- papers￨L￨NNS￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- concurrency￨L￨NN￨O￨- since￨L￨IN￨O￨- these￨L￨DT￨O￨- early￨L￨JJ￨O￨- works￨L￨NNS￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- then￨L￨RB￨O￨- call￨L￨VB￨O￨- for￨L￨IN￨O￨- “￨L￨``￨O￨- an￨L￨DT￨O￨- end￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- a￨L￨DT￨O￨- moratorium￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- kind￨L￨NN￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- modelling￨L￨NN￨O￨A or￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- relational￨L￨JJ￨O￨- concurrency￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Effectiveness￨U￨NN￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- and￨L￨CC￨O￨- tolerance￨L￨NN￨O￨A to￨L￨TO￨O￨- infectionJohann￨L￨NN￨O￨- C￨U￨NN￨O￨- Detilleux1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 43:9￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Detilleux￨U￨NN￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Tolerance￨U￨NN￨O￨- and￨L￨CC￨O￨- resistance￨L￨NN￨O￨- provide￨L￨VBP￨O￨- animals￨L￨NNS￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- fight￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- exhibit￨L￨VB￨O￨- different￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- individual￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- tolerance￨L￨NN￨O￨A and￨L￨CC￨O￨- resistance￨L￨NN￨O￨- is￨L￨VBZ￨O￨- evaluated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- these￨L￨DT￨O￨- imputed￨L￨JJ￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- higher￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- tolerance￨L￨NN￨O￨A should￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- than￨L￨IN￨O￨- increased￨L￨VBN￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- in￨L￨IN￨O￨- commercial￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- The￨U￨DT￨O￨- paper￨L￨NN￨O￨- proposes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- simultaneously￨L￨RB￨O￨- describe￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- between￨L￨IN￨O￨- animals￨L￨NNS￨O￨A ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- within￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- performances￨L￨NNS￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- hosts￨L￨NNS￨O￨- have￨L￨VBP￨O￨- evolved￨L￨VBN￨O￨- resistance￨L￨NN￨O￨- and￨L￨CC￨O￨- tolerance￨L￨NN￨O￨A defenses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- breeders￨L￨NNS￨O￨- may￨L￨MD￨O￨- choose￨L￨VB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- progenitors￨L￨NNS￨O￨- ,￨L￨,￨O￨- animals￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- tolerance￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- both￨L￨DT￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- Fig.￨U￨NN￨O￨- 1B￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨A cases￨L￨NNS￨O￨A ,￨L￨,￨O￨- W￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Basically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨A cases￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- among￨L￨IN￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- Y￨U￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- y￨L￨NN￨O￨- over￨L￨IN￨O￨- all￨L￨DT￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨A cases￨L￨NNS￨O￨A ,￨L￨,￨O￨- Y￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- selection￨L￨NN￨O￨- gradient￨L￨NN￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- depend￨L￨VB￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- monomorphic￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A experienced￨L￨VBN￨O￨- by￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- q￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- empty￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- around￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- body￨L￨NN￨O￨- of￨L￨IN￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- suggested￨L￨VBN￨O￨- that￨L￨IN￨O￨- “￨L￨``￨O￨- prudent￨L￨JJ￨O￨- ”￨L￨''￨O￨- pathogens￨L￨NNS￨O￨A are￨L￨VBP￨O￨- selected￨L￨VBN￨O￨- for￨L￨IN￨O￨- in￨L￨IN￨O￨- viscous￨L￨JJ￨O￨- populatons￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- spatially￨L￨RB￨O￨- structured￨L￨VBN￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- occur￨L￨VBP￨O￨- locally￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Rand￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ,2000￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Kamo￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- defining￨L￨VBG￨O￨- parasite￨L￨NN￨O￨A fitness￨L￨NN￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- virulence￨L￨NN￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- evolve￨L￨VBP￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨NN￨O￨- 's￨L￨POS￨O￨- strategy￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- exploitation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- clear￨L￨JJ￨O￨- that￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨- theory￨L￨NN￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- parasite￨L￨JJ￨O￨A life￨L￨NN￨O￨- histories￨L￨NNS￨O￨- since￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- shaped￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- co-evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Dieckmann￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- Box￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Appendix￨U￨NNP￨O￨- S1￨U￨NN￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- decouple￨L￨VB￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨A structuring￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- effectively￨L￨RB￨O￨- partitions￨L￨VBZ￨O￨- the￨L￨DT￨O￨- selective￨L￨JJ￨O￨- pressures￨L￨NNS￨O￨- on￨L￨IN￨O￨- parasitic￨L￨JJ￨O￨- traits￨L￨NNS￨O￨- between￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- brief￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- coupled￨L￨VBN￨O￨- ,￨L￨,￨O￨- nonlinear￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- stratifications￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- gender￨L￨NN￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- sexual￨L￨JJ￨O￨- activity￨L￨NN￨O￨- ,￨L￨,￨O￨- PrEP￨U￨NN￨O￨- use￨L￨NN￨O￨- status￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- on/off￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible/infected￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- drug￨L￨NN￨O￨A susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- extended￨L￨VBD￨O￨- our￨L￨PRP$￨O￨- published￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- by￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- detailed￨L￨JJ￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- transmitted￨L￨VBD￨O￨- and￨L￨CC￨O￨- acquired￨L￨VBD￨O￨- ,￨L￨,￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- PrEP￨U￨NN￨O￨- as￨L￨IN￨O￨- outlined￨L￨VBN￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- parameter￨L￨NN￨O￨- assignments￨L￨NNS￨O￨- listed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- therefore￨L￨RB￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- orally￨L￨RB￨O￨- administered￨L￨VBN￨O￨- PrEP￨U￨NN￨O￨- on￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- through￨L￨IN￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- PrEP￨U￨NN￨O￨- implementation￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +Insight￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- needed￨L￨VBN￨O￨- into￨L￨IN￨O￨- factors￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- from￨L￨IN￨O￨- PrEP￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- respect￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- its￨L￨PRP$￨O￨- evolutionary￨L￨JJ￨O￨A impact.The￨L￨NN￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- is￨L￨VBZ￨O￨- expanded￨L￨VBN￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- multiple￨L￨JJ￨O￨- virus￨L￨NN￨O￨- strains￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- evolutionary￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A viruses￨L￨NNS￨O￨A are￨L￨VBP￨O￨- complicated￨L￨VBN￨O￨- the￨L￨DT￨O￨- frequent￨L￨JJ￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- reassortment￨L￨NN￨O￨- events￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- two￨L￨CD￨NUMBER￨- virus￨L￨NN￨O￨- strains￨L￨NNS￨O￨- co-infecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- exchange￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- strain￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- overlap￨L￨VBP￨O￨- between￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- evolutionary￨L￨JJ￨O￨A time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- immune￨L￨JJ￨O￨- drift￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- mutation￨L￨NN￨O￨- rate￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- make￨L￨VB￨O￨- it￨L￨PRP￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- integrate￨L￨VB￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- strain￨L￨NN￨O￨- space￨L￨NN￨O￨- into￨L￨IN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Software￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- An￨U￨DT￨MISC￨- Agent-Based￨U￨JJ￨MISC￨- Model￨U￨NNP￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- evolutionary￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- virusesBenjamin￨L￨NNP￨O￨- Roche1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- John￨U￨NNP￨PERSON￨- M￨U￨NNP￨O￨- Drake3￨U￨NN￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Pejman￨U￨NNP￨PERSON￨- Rohani1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 12:87￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Roche￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- A￨U￨NNP￨O￨- viruses￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- complex￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mammalian￨L￨JJ￨O￨- and￨L￨CC￨O￨- avian￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- step￨L￨NN￨O￨- toward￨L￨IN￨O￨- the￨L￨DT￨O￨- improvement￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- among￨L￨IN￨O￨- wild￨L￨JJ￨O￨A waterbirds.KeywordsH5N1￨L￨NN￨O￨- wild￨L￨JJ￨O￨- waterbirds￨L￨NNS￨O￨- Lake￨U￨NNP￨O￨- Constance￨U￨NNP￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- Introduction￨U￨NN￨O￨- Highly￨U￨RB￨O￨- pathogenic￨L￨JJ￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HPAI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- H5N1￨U￨NN￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- of￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 200￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2004￨L￨CD￨DATE￨- alone￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- regularly￨L￨RB￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨- waterbirds￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- waterbirds￨L￨NNS￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- wild￨L￨JJ￨O￨A waterbird￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- three￨L￨CD￨NUMBER￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- predict￨L￨VBP￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 1.6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- ended￨L￨VBD￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- migration￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- wild￨L￨JJ￨O￨A waterbirds￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- winter￨L￨NN￨DATE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- simple￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- this￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨A waterbirds￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- H5N1￨U￨NN￨O￨- virus￨L￨NN￨O￨- was￨L￨VBD￨O￨- confirmed￨L￨VBN￨O￨- in￨L￨IN￨O￨- 82￨L￨CD￨NUMBER￨- dead￨L￨JJ￨O￨- wild￨L￨JJ￨O￨A waterbirds￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- shores￨L￨NNS￨O￨- of￨L￨IN￨O￨- Lake￨U￨NNP￨LOCATION￨- Constance￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- The￨U￨DT￨O￨- goals￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- were￨L￨VBD￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- among￨L￨IN￨O￨- early￨L￨JJ￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- total￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- timing￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- utility￨L￨NN￨O￨- of￨L￨IN￨O￨- specific￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- variation￨L￨NN￨O￨- among￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- RSV￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨A curves￨L￨NNS￨O￨A .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Modeling￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- pediatric￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨- syncytial￨L￨NN￨O￨- virus￨L￨NN￨O￨- seasonal￨L￨JJ￨O￨A epidemicsMolly￨L￨NN￨O￨- Leecaster1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Per￨U￨IN￨O￨- Gesteland2￨U￨NN￨O￨- ,￨L￨,￨O￨- Tom￨U￨NNP￨PERSON￨- Greene1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Nephi￨U￨NNP￨PERSON￨- Walton2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Adi￨U￨NNP￨PERSON￨- Gundlapalli1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Robert￨U￨NNP￨PERSON￨- Rolfs3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Carrie￨U￨NNP￨PERSON￨- Byington2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Matthew￨U￨NNP￨PERSON￨- Samore1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 11:105￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Leecaster￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Seasonal￨U￨NNP￨O￨- respiratory￨L￨JJ￨O￨- syncytial￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RSV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- annually￨L￨RB￨SET￨- in￨L￨IN￨O￨- temperate￨L￨JJ￨O￨- climates￨L￨NNS￨O￨- and￨L￨CC￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- significant￨L￨JJ￨O￨- pediatric￨L￨JJ￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- increased￨L￨VBD￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- costs￨L￨NNS￨O￨- .￨L￨.￨O￨- +Simple￨U￨JJ￨O￨- linear￨L￨JJ￨O￨- regression￨L￨NN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- epidemic￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- days￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- peak￨L￨VB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- length￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- exponential￨L￨JJ￨O￨A growth￨L￨NN￨O￨A calculated￨L￨VBN￨O￨- from￨L￨IN￨O￨- four￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- daily￨L￨JJ￨SET￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- fit￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- parameter￨L￨NN￨O￨- estimated￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- among￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- RSV￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨A curves￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- modeling￨L￨NN￨O￨- results￨L￨VBZ￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- start￨L￨NN￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- parameter￨L￨NN￨O￨- co-varied￨L￨VBD￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Onset￨U￨NNP￨MISC￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- :￨L￨:￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- swine￨L￨NNS￨O￨A flu￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- IsraelUri￨U￨NNP￨MISC￨- Roll1￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Rami￨U￨NNP￨PERSON￨- Yaari2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Guy￨U￨NNP￨O￨- Katriel1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Oren￨U￨NNP￨PERSON￨- Barnea1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Lewi￨U￨NNP￨PERSON￨- Stone1Email￨U￨NNP￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Ella￨U￨NNP￨PERSON￨- Mendelson3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Michal￨U￨NNP￨PERSON￨- Mandelboim￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Amit￨U￨NNP￨PERSON￨- Huppert￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 6￨L￨CD￨NUMBER￨- †￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 11:92￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Roll￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- swine￨L￨NNS￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- H1N1￨U￨NN￨O￨- first￨L￨RB￨ORDINAL￨- identified￨L￨VBN￨O￨- in￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- spread￨L￨VBD￨O￨- rapidly￨L￨RB￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- globe￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- fastest￨L￨JJS￨O￨- moving￨L￨VBG￨O￨- pandemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- history￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- and￨L￨CC￨O￨- characterized￨L￨VBD￨O￨- fundamental￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- in￨L￨IN￨O￨- Israel￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- effective￨L￨JJ￨O￨A reproductive￨L￨JJ￨O￨A number￨L￨NN￨O￨- ,￨L￨,￨O￨- age-class￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- at-risk￨L￨JJ￨O￨- social￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- sexes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- effective￨L￨JJ￨O￨A reproductive￨L￨JJ￨O￨A number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- e￨L￨SYM￨O￨- =￨L￨JJ￨O￨- 1.06￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- age-class￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- skewed￨L￨JJ￨O￨- towards￨L￨IN￨O￨- ages￨L￨NNS￨O￨- 18-25￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- at-risk￨L￨JJ￨O￨- social￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- soldiers￨L￨NNS￨O￨- and￨L￨CC￨O￨- ultra￨L￨NN￨O￨- Orthodox￨U￨NNP￨RELIGION￨- Jews￨U￨NNPS￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- significant￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- sexes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- skewed￨L￨JJ￨O￨- towards￨L￨IN￨O￨- males￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A spread￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- coastal￨L￨JJ￨O￨- plain￨L￨NN￨O￨- of￨L￨IN￨O￨- Israel￨U￨NNP￨COUNTRY￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- higher￨L￨JJR￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- more￨L￨JJR￨O￨- densely￨L￨RB￨O￨- populated￨L￨JJ￨O￨- sub-districts￨L￨NNS￨O￨- with￨L￨IN￨O￨- higher￨L￨JJR￨O￨- income￨L￨NN￨O￨- households￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBD￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- dataset￨L￨NN￨O￨- from￨L￨IN￨O￨- Israel￨U￨NNP￨COUNTRY￨- on￨L￨IN￨O￨- all￨L￨DT￨O￨- confirmed￨L￨VBD￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- between￨L￨IN￨O￨- April￨U￨NNP￨DATE￨- 26￨L￨CD￨DATE￨- to￨L￨TO￨O￨- July￨U￨NNP￨DATE￨- 7￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2009￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- most￨L￨RBS￨O￨- swine￨L￨NNS￨O￨A flu￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- literature￨L￨NN￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- developing￨L￨VBG￨O￨- exact￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- parameter￨L￨NN￨O￨A estimation￨L￨NN￨O￨A ,￨L￨,￨O￨- requiring￨L￨VBG￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- hand￨L￨NN￨O￨- .￨L￨.￨O￨- +Proper￨U￨JJ￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- uncertainty￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- under￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- scrutiny￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- parameter￨L￨NN￨O￨A estimation￨L￨NN￨O￨A and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- calibration￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Parameter￨U￨NN￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- allow￨L￨VBP￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- theory￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- help￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- estimate￨L￨NN￨O￨- data￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- directly￨L￨RB￨O￨- observed￨L￨VBN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- help￨L￨NN￨O￨- of￨L￨IN￨O￨- theory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- parameter￨L￨NN￨O￨A estimation￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- parameter￨L￨NN￨O￨A estimation￨L￨NN￨O￨A in￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +coli￨L￨NN￨O￨- O157￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- Scottish￨U￨JJ￨NATIONALITY￨- cattle￨L￨NNS￨O￨A farms￨L￨NNS￨O￨- ,￨L￨,￨O￨- individual-based￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- metapopulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Zhang￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- coli￨L￨FW￨O￨- O157￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- Scottish￨U￨JJ￨NATIONALITY￨- cattle￨L￨NNS￨O￨- farms￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- most￨L￨RBS￨O￨- parsimoniously￨L￨RB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- described￨L￨VBN￨O￨- below￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- §￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Infection￨U￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A farms￨L￨NNS￨O￨- with￨L￨IN￨O￨- E.￨U￨NNP￨O￨- Both￨U￨CC￨O￨- reported￨L￨VBD￨O￨- ca￨L￨MD￨O￨- 20￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- cent￨L￨NN￨O￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- farms￨L￨NNS￨O￨- were￨L￨VBD￨O￨- affected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- together￨L￨RB￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- reached￨L￨VBN￨O￨- some￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +coli￨L￨NN￨O￨- O157￨U￨NN￨O￨- is￨L￨VBZ￨O￨- spread￨L￨VBN￨O￨- among￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A farms￨L￨NNS￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- it￨L￨PRP￨O￨- persists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- cattle￨L￨NNS￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 5￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- iterated￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- various￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1.3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1.4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1.5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 1.6￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- R0￨U￨NN￨O￨- onthe￨L￨NN￨O￨- potential￨L￨JJ￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- time-course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨- Jaipur￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- keeping￨L￨VBG￨O￨A the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- 1/γ￨L￨CD￨NUMBER￨- constant￨L￨JJ￨O￨- at￨L￨IN￨O￨- 3￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- increase￨L￨NN￨O￨- depend￨L￨VBP￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- one￨L￨CD￨NUMBER￨- case￨L￨NN￨O￨- generates￨L￨VBZ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- entirely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨A population￨L￨NN￨O￨A ,￨L￨,￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- so-called￨L￨JJ￨O￨- scale￨L￨NN￨O￨- free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A diverges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- pathogen￨L￨NN￨O￨- also￨L￨RB￨O￨- diverges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- approaches￨L￨NNS￨O￨- zero￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- meaning￨L￨NN￨O￨- even￨L￨RB￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- very￨L￨RB￨O￨- low￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- cause￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- profoundly￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- network￨L￨NN￨O￨- properties￨L￨NNS￨O￨- –￨L￨:￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transitivity￨L￨NN￨O￨- or￨L￨CC￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- within￨L￨IN￨O￨- households￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- designed￨L￨VBN￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- easily￨L￨RB￨O￨- tune￨L￨VB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cliques￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- clique￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- connected￨L￨VBN￨O￨- subgraph￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- structured￨L￨VBN￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- using￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- straightforward￨L￨JJ￨O￨A generalizations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- a￨L￨DT￨O￨- versatile￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- extensive￨L￨JJ￨O￨- exploration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interactive￨L￨JJ￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- clustering￨L￨NN￨O￨- and￨L￨CC￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- random￨L￨JJ￨O￨- spontaneous￨L￨JJ￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- resting￨L￨VBG￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- large￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- demonstrate￨L￨VBP￨O￨- oscillatory￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- with￨L￨IN￨O￨- complex￨L￨JJ￨O￨- spatio-temporal￨L￨JJ￨O￨- activity￨L￨NN￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- interacting￨L￨VBG￨O￨- waves￨L￨NNS￨O￨A .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- excitable￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamical￨L￨JJ￨O￨- states￨L￨NNS￨O￨- propagate￨L￨VB￨O￨A through￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- both￨L￨CC￨O￨- temporally￨L￨RB￨O￨- and￨L￨CC￨O￨- spatially￨L￨RB￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- waves￨L￨NNS￨O￨- and￨L￨CC￨O￨- more￨L￨JJR￨O￨- complex￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- excitable￨L￨JJ￨O￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- that￨L￨IN￨O￨- active￨L￨JJ￨O￨- state￨L￨NN￨O￨- can￨L￨MD￨O￨- arise￨L￨VB￨O￨- and￨L￨CC￨O￨- propagate￨L￨VB￨O￨A from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- if￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- sufficiently￨L￨RB￨O￨- large￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- emanating￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- degree￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- variable￨L￨NN￨O￨- with￨L￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- mean￨L￨VB￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- single￨L￨JJ￨O￨- active￨L￨JJ￨O￨A node￨L￨NN￨O￨- may￨L￨MD￨O￨- generate￨L￨VB￨O￨- an￨L￨DT￨O￨- expanding￨L￨VBG￨O￨- circular￨L￨JJ￨O￨- wave￨L￨NN￨O￨- of￨L￨IN￨O￨- excitation￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- network￨L￨NN￨O￨- connectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- enough￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- sense￨L￨NN￨O￨- ,￨L￨,￨O￨- voluntary￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- itself￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- dilemma￨L￨NN￨O￨- :￨L￨:￨O￨- vaccinated￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨A can￨L￨MD￨O￨- escape￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- cost￨L￨NN￨O￨- partly￨L￨RB￨O￨- incurred￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- side￨L￨NN￨O￨- effects￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- unvaccinated￨L￨JJ￨O￨- can￨L￨NN￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- protected￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- without￨L￨IN￨O￨- paying￨L￨VBG￨O￨- anything￨L￨NN￨O￨- provided￨L￨VBD￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- season￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- parts￨L￨NNS￨O￨- :￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- comprises￨L￨VBZ￨O￨- effectively￨L￨RB￨O￨- vaccinated￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- is￨L￨VBZ￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- ones￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- vaccinations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- effective￨L￨JJ￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- perceived￨L￨VBN￨O￨- efficacy￨L￨NN￨O￨A of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- psychological￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- determinant￨L￨NN￨O￨- role￨L￨NN￨O￨- since￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- adjust￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- strategic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- perceptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- become￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- effectively￨L￨RB￨O￨- vaccinated￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨A have￨L￨VBP￨O￨- a￨L￨DT￨O￨- perfect￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- its￨L￨PRP$￨O￨- proximal￨L￨JJ￨O￨- origins￨L￨NNS￨O￨- in￨L￨IN￨O￨- overly￨L￨RB￨O￨- complex￨L￨JJ￨O￨- credit￨L￨NN￨O￨- instruments￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- crisis￨L￨NN￨O￨- initially￨L￨RB￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- tightening￨L￨NN￨O￨- of￨L￨IN￨O￨- private￨L￨JJ￨O￨- sector￨L￨NN￨O￨- credit￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ultimately￨L￨RB￨O￨- the￨L￨DT￨O￨- collapse￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- financial￨L￨JJ￨O￨- institutions￨L￨NNS￨O￨- ,￨L￨,￨O￨- sharp￨L￨JJ￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- public￨L￨JJ￨O￨- sector￨L￨NN￨O￨- debt￨L￨NN￨O￨- and￨L￨CC￨O￨- declines￨L￨VBZ￨O￨- in￨L￨IN￨O￨- global￨L￨JJ￨O￨- trade￨L￨NN￨O￨- ,￨L￨,￨O￨- markedly￨L￨RB￨O￨- lower￨L￨JJR￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- cases￨L￨NNS￨O￨- negative￨L￨JJ￨O￨- GDP￨U￨NNP￨O￨- growth￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- rising￨L￨VBG￨O￨- unemployment￨L￨NN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- industrialised￨L￨JJ￨O￨- countries￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Inevitably￨U￨RB￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- concerns￨L￨NNS￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- raised￨L￨VBN￨O￨- that￨L￨IN￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- and￨L￨CC￨O￨- will￨L￨MD￨O￨- continue￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- adversely￨L￨RB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- budgetary￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- recession￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Marked￨U￨JJ￨O￨- rises￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- during￨L￨IN￨O￨- previous￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- crises￨L￨NNS￨O￨- and￨L￨CC￨O￨- downturns￨L￨NNS￨O￨- raise￨L￨VBP￨O￨- concerns￨L￨NNS￨O￨A about￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- situation￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- countries￨L￨NNS￨O￨A have￨L￨VBP￨O￨- cut￨L￨VBN￨O￨- budgets￨L￨NNS￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- risking￨L￨VBG￨O￨- disruption￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- and/or￨L￨CC￨O￨- the￨L￨DT￨O￨- exacerbation￨L￨NN￨O￨- of￨L￨IN￨O￨- drug-resistance￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Even￨U￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- economic￨L￨JJ￨O￨A crisis￨L￨NN￨O￨- or￨L￨CC￨O￨- downturn￨L￨NN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- disproportionately￨L￨RB￨O￨- affect￨L￨VBP￨O￨- vulnerable￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Far-Western￨U￨NNP￨LOCATION￨- Nepal￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- labor￨L￨NN￨O￨- migration￨L￨NN￨O￨A to￨L￨TO￨O￨- IndiaNaveen￨U￨NNP￨O￨- K￨U￨NNP￨O￨- Vaidya1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Jianhong￨U￨NNP￨PERSON￨- Wu3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 11:310￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Vaidya￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Wu￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Because￨U￨IN￨O￨- of￨L￨IN￨O￨- limited￨L￨JJ￨O￨- work￨L￨NN￨O￨- opportunities￨L￨NNS￨O￨- in￨L￨IN￨O￨- Nepal￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- open-border￨L￨NN￨O￨- provision￨L￨NN￨O￨- between￨L￨IN￨O￨- Nepal￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- labor￨L￨NN￨O￨- migration￨L￨NN￨O￨- of￨L￨IN￨O￨- males￨L￨NNS￨O￨- from￨L￨IN￨O￨- Far-Western￨U￨NNP￨LOCATION￨- Nepal￨U￨NNP￨COUNTRY￨- to￨L￨TO￨O￨- India￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- common￨L￨JJ￨O￨- .￨L￨.￨O￨- +Unsafe￨U￨JJ￨O￨- sexual￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- migrants￨L￨NNS￨O￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- frequent￨L￨JJ￨O￨- visits￨L￨NNS￨O￨A to￨L￨TO￨O￨- brothels￨L￨NNS￨O￨- ,￨L￨,￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- among￨L￨IN￨O￨- them￨L￨PRP￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- upon￨L￨IN￨O￨- their￨L￨PRP$￨O￨- return￨L￨NN￨O￨- home￨L￨NN￨O￨- to￨L￨TO￨O￨- Nepal￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- back￨L￨NN￨O￨- and￨L￨CC￨O￨- forth￨L￨RB￨O￨A mobility￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- labor-migrants￨L￨NNS￨O￨- to￨L￨TO￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- among￨L￨IN￨O￨- migrants￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- Far-Western￨U￨NNP￨LOCATION￨- Nepal￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- An￨U￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- Far-Western￨U￨NNP￨LOCATION￨- Nepal￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Xu￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Ma￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Noble￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- delayed￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- diffusionwith￨L￨NN￨O￨- initial￨L￨JJ￨O￨- conditionsIn￨L￨NN￨O￨- problem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- denote￨L￨VB￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- bounded￨L￨JJ￨O￨- domain￨L￨NN￨O￨- in￨L￨IN￨O￨- with￨L￨IN￨O￨- smooth￨L￨JJ￨O￨- boundary￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Xu￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ma￨U￨NNP￨PERSON￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rateBy￨L￨NN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- characteristic￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨A of￨L￨IN￨O￨- travelling￨L￨VBG￨O￨- wave￨L￨NN￨O￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- reaction-diffusion￨L￨NN￨O￨- equations￨L￨NNS￨O￨- with￨L￨IN￨O￨- delays￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- sub-and￨L￨JJ￨O￨- supersolution￨L￨NN￨O￨- technique￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- Atkinson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Reuter￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- semigroups￨L￨NNS￨O￨- ,￨L￨,￨O￨- Saccomandi￨U￨FW￨O￨- NumericCitation￨U￨NN￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨A and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- inhomogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- nonlocal￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨A of￨L￨IN￨O￨- travelling￨L￨VBG￨O￨- wave￨L￨NN￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 0.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- leadership￨L￨NN￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- fundamentally￨L￨RB￨O￨- different￨L￨JJ￨O￨- as￨L￨IN￨O￨- personal￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- are￨L￨VBP￨O￨- quickly￨L￨RB￨O￨- evolving￨L￨VBG￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- makes￨L￨VBZ￨O￨- adaptability￨L￨NN￨O￨- essential￨L￨JJ￨O￨- for￨L￨IN￨O￨- ranking￨L￨JJ￨O￨- users￨L￨NNS￨O￨A .￨L￨.￨O￨- +By￨U￨IN￨O￨- conducting￨L￨VBG￨O￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- see￨L￨VB￨O￨- how￨L￨WRB￨O￨- ranking￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- identify￨L￨VBP￨O￨- influential￨L￨JJ￨O￨- users￨L￨NNS￨O￨A in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Interested￨U￨VBN￨O￨- readers￨L￨NNS￨O￨- may￨L￨MD￨O￨- try￨L￨VB￨O￨- the￨L￨DT￨O￨- webpage￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- implement￨L￨VBP￨O￨- LeaderRank￨U￨NNP￨O￨- to￨L￨TO￨O￨- rank￨L￨VB￨O￨- users￨L￨NNS￨O￨A in￨L￨IN￨O￨- In￨U￨IN￨O￨- many￨L￨JJ￨O￨- online￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- ,￨L￨,￨O￨- users￨L￨NNS￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- select￨L￨VB￨O￨- other￨L￨JJ￨O￨- users￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- their￨L￨PRP$￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- LeaderRank￨U￨NNP￨O￨- algorithm￨L￨NN￨O￨- outperforms￨L￨VBZ￨O￨- PageRank￨U￨NNP￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- users￨L￨NNS￨O￨A who￨L￨WP￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- quick￨L￨JJ￨O￨- and￨L￨CC￨O￨- wide￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- useful￨L￨JJ￨O￨- items￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- U.S.￨U￨NNP￨COUNTRY￨- domestic￨L￨JJ￨O￨- air￨L￨NN￨O￨- transportation￨L￨NN￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- construct￨L￨VBP￨O￨- a￨L￨DT￨O￨- fine-grained￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- scalings￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recognize￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- broad￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infrastructure￨L￨NN￨O￨A plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- temporal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- take￨L￨VBP￨O￨- the￨L￨DT￨O￨- scenarios￨L￨NNS￨O￨- of￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- contain￨L￨VBP￨O￨- sufficient￨L￨JJ￨O￨- spatiotemporal￨L￨JJ￨O￨- information￨L￨NN￨O￨- making￨L￨VBG￨O￨- it￨L￨PRP￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- visualize￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- scalings￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- inherent￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- formation￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Zipf￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- law￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- Heaps￨U￨NNP￨O￨- '￨L￨POS￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- laboratory￨L￨NN￨O￨- confirmed￨L￨VBD￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- naturally￨L￨RB￨O￨- shaped￨L￨VBN￨O￨- to￨L￨TO￨O￨- coexist￨L￨VB￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- at￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- U.S.￨U￨NNP￨COUNTRY￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- crossover￨L￨NN￨O￨- comes￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- inconsistency￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- keeps￨L￨VBZ￨O￨- on￨L￨IN￨O￨- prevailing￨L￨VBG￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- Heaps￨U￨NNP￨O￨- '￨L￨POS￨O￨- law￨L￨NN￨O￨- still￨L￨RB￨O￨- exists￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- disappearance￨L￨NN￨O￨- of￨L￨IN￨O￨- strict￨L￨JJ￨O￨- Zipf￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- law￨L￨NN￨O￨- .￨L￨.￨O￨- +G.K.￨U￨NNP￨PERSON￨- Zipf￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- sixty￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- ago￨L￨RB￨DATE￨- ,￨L￨,￨O￨- found￨L￨VBD￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨A distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- of￨L￨IN￨O￨- words￨L￨NNS￨O￨- within￨L￨IN￨O￨- different￨L￨JJ￨O￨- written￨L￨VBN￨O￨- texts￨L￨NNS￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- were￨L￨VBD￨O￨- plotted￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- descending￨L￨VBG￨O￨- order￨L￨NN￨O￨- against￨L￨IN￨O￨- their￨L￨PRP$￨O￨- rank￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- improved￨L￨VBN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- Simon￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- was￨L￨VBD￨O￨- put￨L￨VBN￨O￨- forward￨L￨RB￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Zipf￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- law￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- deemed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Heaps￨U￨NNP￨O￨- '￨L￨POS￨O￨- law￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- A￨U￨DT￨MISC￨- single￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- commercial￨L￨JJ￨O￨- broilers￨L￨NNS￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- reduce￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- highly￨L￨RB￨O￨- pathogenic￨L￨JJ￨O￨A avian￨L￨JJ￨O￨- influenzaOkti￨L￨NN￨O￨- Poetri1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Annemarie￨U￨NNP￨PERSON￨- Bouma2Email￨U￨NNP￨PERSON￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Ivo￨U￨NNP￨PERSON￨- Claassen3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Guus￨U￨NNP￨PERSON￨- Koch3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Retno￨U￨NNP￨O￨- Soejoedono1￨U￨NN￨O￨- ,￨L￨,￨O￨- Arjan￨U￨NNP￨PERSON￨- Stegeman2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Michiel￨U￨NNP￨PERSON￨- van￨L￨NNP￨O￨- Boven4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 42:74￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Poetri￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractVaccination￨U￨NNP￨O￨- of￨L￨IN￨O￨- chickens￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- routine￨L￨JJ￨O￨- practice￨L￨NN￨O￨- in￨L￨IN￨O￨- Asian￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- H5N1￨U￨NN￨O￨- highly￨L￨RB￨O￨- pathogenic￨L￨JJ￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- HPAI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- endemically￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- these￨L￨DT￨O￨- experiments￨L￨NNS￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ~￨L￨NN￨O￨- 1.0￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ~￨L￨NN￨O￨- 3.3￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ~￨L￨NN￨O￨- 1.4￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- similar￨L￨JJ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- were￨L￨VBD￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ~￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- generation￨L￨NN￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ~￨L￨NN￨O￨- 1.4￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- inoculation￨L￨NN￨O￨- was￨L￨VBD￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 28th￨L￨JJ￨DATE￨- day￨L￨NN￨DATE￨A of￨L￨IN￨O￨- life￨L￨NN￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- efficient￨L￨JJ￨O￨- in￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- birds￨L￨NNS￨O￨- vaccinated￨L￨VBN￨O￨- at￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- or￨L￨CC￨O￨- tenth￨L￨NN￨DATE￨- day￨L￨NN￨DATE￨- of￨L￨IN￨O￨- life￨L￨NN￨O￨- .￨L￨.￨O￨- +Experiments￨U￨NNS￨O￨- 1-3￨L￨CD￨NUMBER￨- were￨L￨VBD￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- with￨L￨IN￨O￨- four-week-old￨L￨JJ￨DURATION￨- birds￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- unvaccinated￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- at￨L￨IN￨O￨- day￨L￨NN￨DURATION￨A 1￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- at￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- 10￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- whether￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨A HPAI￨U￨NNP￨ORGANIZATION￨- H5N1￨U￨NN￨O￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- broiler￨L￨NN￨O￨- chickens￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- meningitis￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- empirically￨L￨RB￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- grow￨L￨VB￨O￨- rapidly￨L￨RB￨O￨- with￨L￨IN￨O￨- population-size￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Aimed￨U￨VBN￨O￨- at￨L￨IN￨O￨- modeling￨L￨NN￨O￨- accidental￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- shed￨L￨VB￨O￨- some￨L￨DT￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- reasons￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- scale￨L￨NN￨O￨A invariance￨L￨NN￨O￨- in￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- Stollenwerk￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jansen￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- coworkers￨L￨NNS￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- and￨L￨CC￨O￨- elegant￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- as￨L￨IN￨O￨- power-laws￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- any￨L￨DT￨O￨- apparent￨L￨JJ￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- fine￨L￨JJ￨O￨- tuning￨L￨NN￨O￨- –￨L￨:￨O￨- i.e.￨L￨FW￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- generically￨L￨RB￨O￨- scale￨L￨NN￨O￨A invariant￨L￨JJ￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Conversely￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- tail￨L￨NN￨O￨A is￨L￨VBZ￨O￨- enriched￨L￨VBN￨O￨- for￨L￨IN￨O￨- known￨L￨JJ￨O￨- anti-neoplastic￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 2b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 25￨L￨CD￨NUMBER￨- lowest￨L￨JJS￨O￨- S￨U￨NN￨O￨- scores￨L￨NNS￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- known￨L￨VBN￨O￨- chemotherapeutic￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- selectively￨L￨RB￨O￨- toxic￨L￨JJ￨O￨- to￨L￨TO￨O￨- cells￨L￨NNS￨O￨- rapidly￨L￨RB￨O￨- proliferating￨L￨VBG￨O￨- in￨L￨IN￨O￨- glucose￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Supplementary￨U￨NNP￨O￨- Table￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- online￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- utilize￨L￨VBP￨O￨- a￨L￨DT￨O￨- nutrient-sensitized￨L￨JJ￨O￨- screening￨L￨NN￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- that￨L￨WDT￨O￨- toggle￨L￨VBP￨O￨- cellular￨L￨JJ￨O￨- energy￨L￨NN￨O￨- metabolism￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- selective￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- cell￨L￨NN￨O￨A growth￨L￨NN￨O￨- and￨L￨CC￨O￨- viability￨L￨NN￨O￨- in￨L￨IN￨O￨- glucose￨L￨NN￨O￨- versus￨L￨CC￨O￨- galactose￨L￨NN￨O￨- media￨L￨NNS￨O￨- .￨L￨.￨O￨- +Reassuringly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- upper￨L￨JJ￨O￨- tail￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- distribution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 2b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- enriched￨L￨VBN￨O￨- for￨L￨IN￨O￨- known￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨- chain￨L￨NN￨O￨- and￨L￨CC￨O￨- OXPHOS￨U￨NN￨O￨- inhibitors￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- top￨L￨JJ￨O￨- 25￨L￨CD￨NUMBER￨- compounds￨L￨NNS￨O￨- include￨L￨VBP￨O￨- 20￨L￨CD￨NUMBER￨- compounds￨L￨NNS￨O￨- previously￨L￨RB￨DATE￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- disrupt￨L￨VB￨O￨- respiration￨L￨NN￨O￨- by￨L￨IN￨O￨- directly￨L￨RB￨O￨- interrupting￨L￨VBG￨O￨- or￨L￨CC￨O￨- uncoupling￨L￨NN￨O￨- electron￨L￨NN￨O￨- transport￨L￨NN￨O￨- from￨L￨IN￨O￨- ATP￨U￨NN￨O￨- synthesis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Supplementary￨U￨NNP￨O￨- Table￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- online￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- the￨L￨DT￨O￨- proliferation￨L￨NN￨O￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- higher￨L￨JJR￨O￨- for￨L￨IN￨O￨- cells￨L￨NNS￨O￨- grown￨L￨VBN￨O￨- in￨L￨IN￨O￨- glucose￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- galactose￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Supplementary￨U￨JJ￨O￨- Fig.￨U￨NN￨O￨- 3b￨L￨NN￨O￨- online￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- normalized￨L￨VBN￨O￨- cell￨L￨NN￨O￨A number￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- nutrient￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- screening￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- chemical￨L￨NN￨O￨- library￨L￨NN￨O￨- for￨L￨IN￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- that￨L￨WDT￨O￨- selectively￨L￨RB￨O￨- inhibit￨L￨VBP￨O￨- cell￨L￨NN￨O￨A growth￨L￨NN￨O￨- and￨L￨CC￨O￨- proliferation￨L￨NN￨O￨- in￨L￨IN￨O￨- galactose￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- glucose￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- FDA￨U￨NNP￨ORGANIZATION￨- approved￨L￨VBD￨O￨- compounds￨L￨NNS￨O￨- that￨L￨WDT￨O￨- redirect￨L￨VBP￨O￨- oxidative￨L￨JJ￨O￨- metabolism￨L￨NN￨O￨- to￨L￨TO￨O￨- glycolysis￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨DATE￨- second￨L￨JJ￨DATE￨- year￨L￨NN￨DATE￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- establishment￨L￨NN￨O￨- of￨L￨IN￨O￨- People￨U￨NNS￨LOCATION￨- 's￨L￨POS￨LOCATION￨- Republic￨U￨NN￨COUNTRY￨- of￨L￨IN￨COUNTRY￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- rabies￨L￨NNP￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- II￨U￨CD￨NUMBER￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- National￨U￨NNP￨MISC￨- Stationary￨U￨NNP￨MISC￨- Notifiable￨U￨JJ￨MISC￨- Communicable￨U￨JJ￨MISC￨- Diseases￨U￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨MISC￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- rabies￨L￨NNP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- archived￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Chinese￨U￨JJ￨ORGANIZATION￨- Center￨U￨NN￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +All￨U￨DT￨O￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- mammals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- rabies￨L￨NNP￨O￨A virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- dogs￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- carrier￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- rabies￨L￨NNP￨O￨- deaths￨L￨NNS￨O￨- worldwide￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,255￨L￨CD￨NUMBER￨- human￨L￨JJ￨O￨- rabies￨L￨NNP￨O￨A cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- 2,037￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +Human￨U￨JJ￨O￨- rabies￨L￨NNP￨O￨A in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- was￨L￨VBD￨O￨- first￨L￨RB￨ORDINAL￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- about￨L￨IN￨DATE￨- 556￨L￨CD￨DATE￨- BC￨U￨NN￨DATE￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- persisted￨L￨VBN￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- 2500￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- communities￨L￨NNS￨O￨A could￨L￨MD￨O￨- help￨L￨VB￨O￨- identifying￨L￨VBG￨O￨- which￨L￨WDT￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- introducing￨L￨VBG￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨- we￨L￨PRP￨O￨- contrast￨L￨VBP￨O￨- how￨L￨WRB￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- behaviour￨L￨NN￨O￨- could￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- between￨L￨IN￨O￨- communities￨L￨NNS￨O￨A with￨L￨IN￨O￨- varying￨L￨VBG￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- focus￨L￨NN￨O￨- in￨L￨IN￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- designing￨L￨VBG￨O￨- algorithms￨L￨NNS￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- detection￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- ignored￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- computer-generated￨L￨JJ￨O￨- network￨L￨NN￨O￨- :￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- communities￨L￨NNS￨O￨A of￨L￨IN￨O￨- varying￨L￨VBG￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- connectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- risk￨L￨NN￨O￨- aversion￨L￨NN￨O￨- to￨L￨TO￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- at￨L￨IN￨O￨- varicella￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- decrease￨L￨VB￨O￨- in￨L￨IN￨O￨- successively￨L￨RB￨O￨- born￨L￨VBN￨O￨A children￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- household￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- risk￨L￨NN￨O￨- followed￨L￨VBD￨O￨- after￨L￨IN￨O￨- school￨L￨NN￨O￨- enrolment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first-born￨L￨JJ￨O￨- child￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- was￨L￨VBD￨O￨- smaller￨L￨JJR￨O￨- in￨L￨IN￨O￨- less￨L￨JJR￨O￨- densely￨L￨RB￨O￨- populated￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- computational￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- have￨L￨VBP￨O￨- increasingly￨L￨RB￨O￨- tried￨L￨VBN￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- describe￨L￨VBP￨O￨- places￨L￨NNS￨O￨- where￨L￨WRB￨O￨- population￨L￨NN￨O￨- mix￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- occur￨L￨VBP￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- detailed￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- median￨L￨JJ￨O￨A age￨L￨NN￨O￨- at￨L￨IN￨O￨- varicella￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- smaller￨L￨JJR￨O￨- in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- where￨L￨WRB￨O￨- more￨L￨RBR￨O￨- children￨L￨NNS￨O￨- attend￨L￨VBP￨O￨- pre-school￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- explanation￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- factors￨L￨NNS￨O￨- shaping￨L￨VBG￨O￨- the￨L￨DT￨O￨- possibilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨A ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- household￨L￨NN￨O￨- structure￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- schools￨L￨NNS￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- behaviours￨L￨NNS￨O￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- from￨L￨IN￨O￨- OECD￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- median￨L￨JJ￨O￨A age￨L￨NN￨O￨- at￨L￨IN￨O￨- varicella￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- strategy￨L￨NN￨O￨- involves￨L￨VBZ￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- severe￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- using￨L￨VBG￨O￨- incidences￨L￨NNS￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- common￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- sharing￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- fragmenting￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- into￨L￨IN￨O￨- disconnected￨L￨VBN￨O￨- pieces￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- partitioning￨L￨NN￨O￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- multiple￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- play￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- common￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- circulating￨L￨VBG￨O￨- in￨L￨IN￨O￨- society￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- censorships￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- to￨L￨TO￨O￨- emulate￨L￨VB￨O￨- the￨L￨DT￨O￨- low￨L￨JJ￨O￨- reporting￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- common￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- censored￨L￨VBN￨O￨- incidences￨L￨NNS￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- generating￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨A S￨U￨NN￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- mitigate￨L￨VB￨O￨- new￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- fragment￨L￨NN￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- commuting￨L￨VBG￨O￨- process￨L￨NN￨O￨- τ￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- consider￨L￨VB￨O￨- a￨L￨DT￨O￨- quasi-stationary￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- mixed￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- stationary￨L￨JJ￨O￨- values￨L￨NNS￨O￨- :￨L￨:￨O￨- These￨U￨DT￨O￨- expressions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- Methods￨U￨NNS￨O￨- section￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- allow￨L￨VBP￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨A k￨L￨NN￨O￨- as￨L￨IN￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- had￨L￨VBD￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- N￨U￨NN￨O￨- ≪￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- neighboring￨L￨VBG￨O￨- subpopulation￨L￨NN￨O￨- k￨L￨NN￨O￨- ′￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- quasi-stationary￨L￨JJ￨O￨- state￨L￨NN￨O￨- reached￨L￨VBD￨O￨- whenever￨L￨WRB￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- studying￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- τ￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- particle-network￨L￨JJ￨O￨- framework￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- subpopulation￨L￨NN￨O￨A network￨L￨NN￨O￨- with￨L￨IN￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- denote￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- subpopulations￨L￨NNS￨O￨- with￨L￨IN￨O￨- k￨L￨NN￨O￨- connections￨L￨NNS￨O￨- by￨L￨IN￨O￨- V.￨U￨NNP￨O￨- For￨U￨IN￨O￨- the￨L￨DT￨O￨- sake￨L￨NN￨O￨- of￨L￨IN￨O￨- analysis￨L￨NN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- follows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- functional￨L￨JJ￨O￨- form￨L￨NN￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- N̄k￨U￨NN￨O￨- /￨L￨:￨O￨- 〈￨L￨SYM￨O￨- k￨L￨NN￨O￨- 〉￨L￨NN￨O￨- where￨L￨WRB￨O￨- N̄￨U￨NN￨O￨- =￨L￨JJ￨O￨- ∑￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- per￨L￨IN￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- approach￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨A network￨L￨NN￨O￨- analytically￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- mixing￨L￨VBG￨O￨- subpopulations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨- k￨L￨NN￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- subpopulation￨L￨NN￨O￨- k￨L￨NN￨O￨- ′￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- expression￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- stationary￨L￨JJ￨O￨A population￨L￨NN￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- random￨L￨JJ￨O￨- diffusive￨L￨JJ￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- along￨L￨IN￨O￨- each￨L￨DT￨O￨- link￨L￨NN￨O￨- leaving￨L￨VBG￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- 1/k￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- wave-speed￨L￨NN￨O￨- was￨L￨VBD￨O￨- calculated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- convex￨L￨NN￨O￨A hull￨L￨NN￨O￨- method￨L￨NN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- square￨L￨JJ￨O￨- root￨L￨NN￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- polygon￨L￨NNP￨O￨- encompassing￨L￨VBG￨O￨- ABCDE￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- black￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- square￨L￨JJ￨O￨- root￨L￨NN￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- polygon￨L￨NNP￨O￨- encompassing￨L￨VBG￨O￨- ABCD￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- red￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- locations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- convex￨L￨NN￨O￨- hull￨L￨NN￨O￨- method￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- transects￨L￨NNS￨O￨- from￨L￨IN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ultrafine￨L￨NN￨O￨- dashed￨L￨VBN￨O￨- and￨L￨CC￨O￨- dash-dotted￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- intersecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- polygon￨L￨NNP￨O￨- ABCDE￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transect￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dash-dotted￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- intersecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- polygon￨L￨NNP￨O￨- ABCD￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- boundary￨L￨NN￨O￨- displacement￨L￨NN￨O￨- method￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- AC￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- AB￨U￨NNP￨STATE_OR_PROVINCE￨- (￨L￨-LRB-￨O￨- maximum￨L￨JJ￨O￨- distance￨L￨NN￨O￨- method￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- divided￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- elapsed￨L￨VBN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Estimated￨U￨VBN￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- WNV￨U￨NNP￨O￨- spread￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- black￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- meters￨L￨NNS￨O￨- d￨L￨NN￨O￨- −￨L￨SYM￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- convex￨L￨NN￨O￨A hull￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- circles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- boundary￨L￨NN￨O￨- displacement￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- symbol￨L￨NN￨O￨- X￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- distance￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- crosses￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- mean￨L￨VB￨O￨- daily￨L￨JJ￨SET￨- temperature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- blue￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- daily￨L￨JJ￨SET￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- red￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- asymptotically￨L￨RB￨O￨- constant￨L￨JJ￨O￨- wave-speeds￨L￨NNS￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- environment￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- accelerating￨L￨VBG￨O￨- spread￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- occasional￨L￨JJ￨O￨- long￨L￨JJ￨O￨- distance￨L￨NN￨O￨A dispersal￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- continental￨L￨JJ￨O￨- scale￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- WNV￨U￨NN￨O￨- in￨L￨IN￨O￨- New￨U￨NNP￨CITY￨- York￨U￨NNP￨CITY￨- City￨U￨NNP￨CITY￨- nearly￨L￨RB￨O￨- always￨L￨RB￨O￨- decelerated￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- hypothesized￨L￨VBD￨O￨- that￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- urban￨L￨JJ￨O￨- environments￨L￨NNS￨O￨- gives￨L￨VBZ￨O￨- rise￨L￨NN￨O￨- to￨L￨TO￨O￨- decelerating￨L￨VBG￨O￨- waves￨L￨NNS￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- inhibition￨L￨NN￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- locations￨L￨NNS￨O￨- unfavourable￨L￨JJ￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- emphasize￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- decelerating￨L￨VBG￨O￨- waves￨L￨NNS￨O￨A we￨L￨PRP￨O￨- hypothesize￨L￨VBP￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- environmental￨L￨JJ￨O￨- or￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- gradients￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- fungal￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- infecting￨L￨VBG￨O￨- plants￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- solely￨L￨RB￨O￨- to￨L￨TO￨O￨- endogenous￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- caregiver￨L￨NN￨O￨- case￨L￨NN￨O￨- every￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨- person￨L￨NN￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- primary￨L￨JJ￨O￨- caregiver￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- who￨L￨WP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- every￨L￨DT￨O￨- other￨L￨JJ￨O￨- person￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- recommended￨L￨VBN￨O￨- by￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- agencies￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- case￨L￨NN￨O￨- every￨L￨DT￨O￨- person￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- whether￨L￨IN￨O￨- sick￨L￨JJ￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- every￨L￨DT￨O￨- other￨L￨JJ￨O￨- person￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨A ,￨L￨,￨O￨- as￨L￨RB￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- complete￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- extreme￨L￨JJ￨O￨- possibilities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- household￨L￨NN￨O￨A :￨L￨:￨O￨- full￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- single￨L￨JJ￨O￨- caregiver￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- simulations￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- of￨L￨IN￨O￨- household￨L￨NN￨O￨A transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- contact￨L￨VB￨O￨- structures￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨A world￨L￨NN￨O￨A parameter￨L￨NN￨O￨- strongly￨L￨RB￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- distance￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- seems￨L￨VBZ￨O￨- plausible￨L￨JJ￨O￨- that￨L￨IN￨O￨- given￨L￨VBN￨O￨- bacterial￨L￨JJ￨O￨- isolates￨L￨NNS￨O￨- sampled￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨NN￨NUMBER￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- some￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨- world￨L￨NN￨O￨- parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- simulates￨L￨VBZ￨O￨- MLST￨U￨NNP￨ORGANIZATION￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- commensal￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- spreading￨L￨VBG￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- linked￨L￨VBN￨O￨- together￨L￨RB￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨- generated￨L￨VBN￨O￨- small￨L￨JJ￨O￨A world￨L￨NN￨O￨A network￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- “￨L￨``￨O￨- U￨U￨NNP￨O￨- shape￨L￨NN￨O￨- ”￨L￨''￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨- discordant￨L￨JJ￨O￨- alleles￨L￨NNS￨O￨- previously￨L￨RB￨DATE￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- commensal￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- only￨L￨RB￨O￨- occurs￨L￨VBZ￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨- world￨L￨NN￨O￨- parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨A world￨L￨NN￨O￨A parameter￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- structured￨L￨JJ￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- these￨L￨DT￨O￨- results￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- highly￨L￨RB￨O￨- structured￨L￨VBN￨O￨- populations￨L￨NNS￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- localized￨L￨JJ￨O￨- pockets￨L￨NNS￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- overrepresentation￨L￨NN￨O￨- of￨L￨IN￨O￨- low￨L￨JJ￨O￨- discordance￨L￨NN￨O￨- pairs￨L￨NNS￨O￨- –￨L￨:￨O￨- recent￨L￨JJ￨O￨- ,￨L￨,￨O￨- local￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- –￨L￨:￨O￨- and￨L￨CC￨O￨- maximally￨L￨RB￨O￨- discordant￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨- comparisons￨L￨NNS￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- pockets￨L￨NNS￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- separated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Distributions￨U￨NNS￨O￨- of￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- discordant￨L￨JJ￨O￨- alleles￨L￨NNS￨O￨- drawn￨L￨VBN￨O￨- from￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- various￨L￨JJ￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨A world￨L￨NN￨O￨A parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- summarize￨L￨VB￨O￨- MLST￨U￨NNP￨ORGANIZATION￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- isolates￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨A distances￨L￨NNS￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- discordant￨L￨JJ￨O￨- alleles￨L￨NNS￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- and￨L￨CC￨O￨- behavior￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- valuable￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- unfolding￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- H1N1￨U￨NN￨O￨- pandemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- clear￨L￨JJ￨O￨- that￨L￨IN￨O￨- societal￨L￨JJ￨O￨- reactions￨L￨NNS￨O￨- coupling￨L￨NN￨O￨- behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- substantial￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- NumericCitation￨U￨NN￨MISC￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- thus￨L￨RB￨O￨- defining￨L￨VBG￨O￨- limitations￨L￨NNS￨O￨- of￨L￨IN￨O￨- most￨L￨JJS￨O￨- current￨L￨JJ￨DATE￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- recent￨L￨JJ￨O￨- attempts￨L￨NNS￨O￨- have￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- self-induced￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨A changes￨L￨NNS￨O￨A individuals￨L￨NNS￨O￨- adopt￨L￨VBP￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- self-initiate￨L￨VBP￨O￨- behavioral￨L￨JJ￨O￨A changes￨L￨NNS￨O￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- concern￨L￨NN￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- eventual￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨A changes￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- some￨L￨DT￨O￨- approaches￨L￨NNS￨O￨A individual￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- were￨L￨VBD￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- modifying￨L￨VBG￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- turned￨L￨VBN￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- inhomogeneous￨L￨JJ￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- characterized￨L￨VBN￨O￨A by￨L￨IN￨O￨- modular￨L￨JJ￨O￨- or￨L￨CC￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- separate￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- bridges￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- more￨L￨JJR￨O￨- and￨L￨CC￨O￨- stronger￨L￨JJR￨O￨- links￨L￨NNS￨O￨- within￨L￨IN￨O￨- communities￨L￨NNS￨O￨- than￨L￨IN￨O￨- between￨L￨IN￨O￨- communities￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- accordance￨L￨NN￨O￨- with￨L￨IN￨O￨- Granovetter￨U￨NN￨PERSON￨- 's￨L￨POS￨O￨- “￨L￨``￨O￨- The￨U￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- weak￨L￨JJ￨O￨- ties￨L￨NNS￨O￨- ”￨L￨''￨O￨- hypothesis￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- corroborated￨L￨VBN￨O￨- later￨L￨RB￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- bursty￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- characterized￨L￨VBN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- heavy￨L￨JJ￨O￨- tailed￨L￨VBD￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- inter-event￨L￨JJ￨O￨- times￨L￨NNS￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- between￨L￨IN￨O￨- consecutive￨L￨JJ￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- shows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- power-law￨L￨NN￨O￨- decay￨L￨NN￨O￨- as￨L￨IN￨O￨- with￨L￨IN￨O￨- or￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- MPC￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- email￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- interaction￨L￨NN￨O￨- structure￨L￨NN￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- social￨L￨JJ￨O￨- data￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- the￨L￨DT￨O￨- concepts￨L￨NNS￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- relationships￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨A ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- is￨L￨VBZ￨O￨- characterized￨L￨VBN￨O￨A by￨L￨IN￨O￨- a￨L￨DT￨O￨- weight￨L￨NN￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- or￨L￨CC￨O￨- closeness￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- MPC￨U￨NNP￨ORGANIZATION￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- aggregate￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- calls￨L￨NNS￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Few￨U￨JJ￨O￨- epidemics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- ever￨L￨RB￨O￨- observed￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- moment￨L￨NN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- enters￨L￨VBZ￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨A population￨L￨NN￨O￨A ,￨L￨,￨O￨- so￨L￨RB￨O￨- calculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- concept￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- otherwise￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨A population￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- invade￨L￨VB￨O￨A an￨L￨DT￨O￨- otherwise￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- persist￨L￨VBP￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- successfully￨L￨RB￨O￨- invade￨L￨VB￨O￨- and￨L￨CC￨O￨- will￨L￨MD￨O￨- die￨L￨VB￨O￨- out￨L￨RP￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- few￨L￨JJ￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- agree￨L￨VBP￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- and￨L￨CC￨O￨- few￨L￨JJ￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- produce￨L￨VBP￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- measurement￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Understanding￨U￨VBG￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- drive￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨- –￨L￨:￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- strain￨L￨NN￨O￨- polymorphic￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- –￨L￨:￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- affect￨L￨VBP￨O￨- interpretation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A data￨L￨NNS￨O￨A NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- clinical￨L￨JJ￨O￨- case￨L￨NN￨O￨- management￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨- ,￨L￨,￨O￨- selection￨L￨NN￨O￨- and￨L￨CC￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Formal￨U￨JJ￨O￨- confrontation￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- putative￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- for￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- interactions￨L￨NNS￨O￨A directly￨L￨RB￨O￨- with￨L￨IN￨O￨- data￨L￨NNS￨O￨- may￨L￨MD￨O￨- enable￨L￨VB￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- effectively￨L￨RB￨O￨- harvest￨L￨VB￨O￨- the￨L￨DT￨O￨- data￨L￨NN￨O￨- 's￨L￨POS￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- effectively￨L￨RB￨O￨- and￨L￨CC￨O￨- reliably￨L￨RB￨O￨- distinguish￨L￨VB￨O￨- among￨L￨IN￨O￨- competing￨L￨VBG￨O￨- hypotheses￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- their￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- impact￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- world￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- interactions￨L￨NNS￨O￨A would￨L￨MD￨O￨- be￨L￨VB￨O￨- quantified￨L￨VBN￨O￨- from￨L￨IN￨O￨- individual-level￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- histories￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- natural￨L￨JJ￨O￨- habitats￨L￨NNS￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- dengue￨L￨NN￨O￨- ,￨L￨,￨O￨- immune-mediated￨L￨JJ￨O￨- serotype￨L￨NN￨O￨- interactions￨L￨NNS￨O￨A may￨L￨MD￨O￨- be￨L￨VB￨O￨- both￨L￨CC￨O￨- competitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- cooperative￨L￨JJ￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- since￨L￨IN￨O￨- previous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- feasibility￨L￨NN￨O￨- of￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- likelihood-based￨L￨JJ￨O￨- inference￨L￨NN￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- interactions￨L￨NNS￨O￨- from￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A data￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- conventional￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ring￨L￨NN￨O￨- culling￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- new￨L￨JJ￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- risk￨L￨NN￨O￨- based￨L￨VBN￨O￨- culling￨L￨NN￨O￨- can￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- farms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- culled￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- culled￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- farms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- zoonosis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- vast￨L￨JJ￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- phylodynamic￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- inferred￨L￨VBN￨O￨- past￨L￨JJ￨DATE￨- dynamics￨L￨NNS￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨A phenomenological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- genealogies￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- smaller￨L￨JJR￨O￨- body￨L￨NN￨O￨- of￨L￨IN￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- fitting￨L￨JJ￨O￨- mechanistic￨L￨JJ￨O￨- population￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Fitting￨U￨JJ￨O￨- simple￨L￨JJ￨O￨- parametric￨L￨JJ￨O￨- models￨L￨NNS￨O￨- like￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨A to￨L￨TO￨O￨- genealogies￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- provide￨L￨VBP￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- emergence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- especially￨L￨RB￨O￨- true￨L￨JJ￨O￨- when￨L￨WRB￨O￨- fitting￨L￨JJ￨O￨A models￨L￨NNS￨O￨- to￨L￨TO￨O￨- long-term￨L￨JJ￨O￨- data￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- stochasticity￨L￨NN￨O￨- can￨L￨MD￨O￨- accrue￨L￨VB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- cause￨L￨VB￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- deviate￨L￨VB￨O￨- widely￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- expectations￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- coalescence￨L￨NN￨O￨- times￨L￨NNS￨O￨A over￨L￨IN￨O￨- a￨L￨DT￨O￨- genealogy￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Past￨U￨JJ￨DATE￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- inferred￨L￨VBN￨O￨- by￨L￨IN￨O￨- specifying￨L￨VBG￨O￨- a￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- fitting￨L￨JJ￨O￨A it￨L￨PRP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- genealogy￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- along￨L￨IN￨O￨- these￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- was￨L￨VBD￨O￨- simulated￨L￨JJ￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Exposed￨U￨VBN￨O￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨O￨- ,￨L￨,￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨A defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- collected￨L￨VBN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- aggregated￨L￨JJ￨O￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- temporal￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Simulation￨U￨NNP￨MISC￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨A contact￨L￨NN￨O￨A network￨L￨NN￨O￨- of￨L￨IN￨O￨- conference￨L￨NN￨O￨- attendeesJuliette￨L￨NN￨O￨- Stehlé1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Nicolas￨U￨NNP￨PERSON￨- Voirin2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Alain￨U￨NNP￨PERSON￨- Barrat1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ciro￨U￨NNP￨PERSON￨- Cattuto4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Vittoria￨U￨NNP￨PERSON￨- Colizza5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Lorenzo￨U￨NNP￨PERSON￨- Isella4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Corinne￨U￨NNP￨PERSON￨- Régis3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jean-François￨U￨NNP￨O￨- Pinton8￨U￨NNP￨O￨- ,￨L￨,￨O￨- Nagham￨U￨NNP￨O￨- Khanafer2￨U￨NNP￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Wouter￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- den￨L￨NN￨O￨- Broeck4￨U￨NN￨O￨- and￨L￨CC￨O￨- Philippe￨U￨NNP￨PERSON￨- Vanhems2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 9:87￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Stehlé￨U￨FW￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- crucially￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- much￨L￨JJ￨O￨- larger￨L￨JJR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨A than￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- value￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- and￨L￨CC￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- well-identified￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- all￨L￨DT￨O￨- have￨L￨VBP￨O￨- important￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aimed￨L￨VBD￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- data-driven￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨A contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- temporal￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- shaping￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 88￨L￨CD￨NUMBER￨- KeywordsFinal￨U￨NNP￨MISC￨- NumberDisease￨U￨NNP￨MISC￨- SpreadContact￨U￨NNP￨MISC￨- NetworkInfectious￨U￨NNP￨MISC￨- PeriodContact￨U￨NNP￨MISC￨- Pattern￨U￨NNP￨MISC￨- BackgroundThe￨U￨NNP￨MISC￨- pattern￨L￨NN￨O￨A of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- determinant￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Mitigating￨U￨JJ￨MISC￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- given￨L￨VBN￨O￨- constraints￨L￨NNS￨O￨- in￨L￨IN￨O￨- stockpile￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- daily￨L￨JJ￨SET￨A administration￨L￨NN￨O￨- capacityMaytee￨L￨NN￨O￨- Cruz-Aponte1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Erin￨U￨NN￨PERSON￨- C￨U￨NN￨O￨- McKiernan1￨U￨NN￨O￨- ,￨L￨,￨O￨- 4Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Marco￨U￨NNP￨O￨- A￨U￨NNP￨O￨- Herrera-Valdez1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 11:207￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Cruz-Aponte￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- viruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- parameter￨L￨NN￨O￨- regimes￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- duration￨L￨NN￨O￨- and￨L￨CC￨O￨- daily￨L￨JJ￨SET￨- supply￨L￨NN￨O￨- limit￨L￨NN￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- non-proportional￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- predicts￨L￨VBZ￨O￨- smaller￨L￨JJR￨O￨- epidemics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- peak￨L￨VBP￨O￨- later￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- may￨L￨MD￨O￨- last￨L￨RB￨O￨- longer￨L￨RB￨O￨- ,￨L￨,￨O￨- than￨L￨IN￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proportional￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- existing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- employ￨L￨VBP￨O￨- several￨L￨JJ￨O￨- questionable￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- proportional￨L￨JJ￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- proportional￨L￨JJ￨O￨A and￨L￨CC￨O￨- non-proportional￨L￨JJ￨O￨- models￨L￨NNS￨O￨- behave￨L￨VBP￨O￨- similarly￨L￨RB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- different￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- analysed￨L￨VBN￨O￨- here￨L￨RB￨O￨- were￨L￨VBD￨O￨- weekly￨L￨JJ￨SET￨- case￨L￨NN￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- laboratory-confirmed￨L￨JJ￨O￨- H1N1pdm￨U￨NN￨O￨- or￨L￨CC￨O￨- influenza-like-illness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- by￨L￨IN￨O￨- age-group￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- period￨L￨NN￨O￨- for￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- Southern￨U￨NNP￨MISC￨- hemisphere￨L￨NN￨O￨- countries￨L￨NNS￨O￨- and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Argentina￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- -￨L￨:￨O￨- whole￨L￨JJ￨O￨- country￨L￨NN￨O￨A and￨L￨CC￨O￨- Victoria￨U￨NNP￨CITY￨- -￨L￨:￨O￨- ,￨L￨,￨O￨- Bolivia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Chile￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- New￨U￨NNP￨COUNTRY￨- Zealand￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- South￨U￨NNP￨COUNTRY￨- Africa￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- stratification￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- H1N1pdm￨U￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- country-associated￨L￨JJ￨O￨- age-groups￨L￨NNS￨O￨- were￨L￨VBD￨O￨- broken￨L￨VBN￨O￨- down￨L￨RP￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- Argentina￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 49￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 50￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 59￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ≥￨L￨CD￨NUMBER￨- 60￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨A )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Australia￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 49￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 50￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 64￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ≥￨L￨CD￨NUMBER￨- 65￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Victoria￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 49￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 50￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 64￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ≥￨L￨CD￨NUMBER￨- 65￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Bolivia￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 44￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 45￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 49￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ≥￨L￨CD￨NUMBER￨- 50￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Brazil￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 49￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 50￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 59￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ≥￨L￨CD￨NUMBER￨- 60￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Chile￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 54￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 55￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 64￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ≥￨L￨CD￨NUMBER￨- 65￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- New￨U￨NNP￨COUNTRY￨- Zealand￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 49￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 50￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 59￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ≥￨L￨CD￨NUMBER￨- 60￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- South￨U￨NNP￨COUNTRY￨- Africa￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 49￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 50￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 64￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ≥￨L￨CD￨NUMBER￨- 65￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- ,￨L￨,￨O￨- weekly￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- either￨L￨DT￨O￨- laboratory￨L￨NN￨O￨A confirmed￨L￨VBD￨O￨A H1N1pdm￨U￨NN￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- H1N1CC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Argentina￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Bolivia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Chile￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- New￨U￨NNP￨COUNTRY￨- Zealand￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- South￨U￨NNP￨COUNTRY￨- Africa￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- influenza-like-illness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Australia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Chile￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- New￨U￨NNP￨COUNTRY￨- Zealand￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Victoria￨U￨NNP￨CITY￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- pandemic￨L￨NN￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- opportunity￨L￨NN￨O￨- for￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- setting￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- countries￨L￨NNS￨O￨A with￨L￨IN￨O￨- different￨L￨JJ￨O￨- population￨L￨NN￨O￨- structures￨L￨NNS￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +Dynamic￨U￨NNP￨O￨- health￨L￨NN￨O￨- policies￨L￨NNS￨O￨A make￨L￨VBP￨O￨- real-time￨L￨JJ￨O￨- recommendations￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- changing￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- characteristics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- levels￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- immune￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- resource￨L￨NN￨O￨- constraints￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- vaccines￨L￨NNS￨O￨- ,￨L￨,￨O￨- antimicrobial￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- personnel￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- budget￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- these￨L￨DT￨O￨- approaches￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- which￨L￨WDT￨O￨- baseline￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- may￨L￨MD￨O￨- best￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- generally￨L￨RB￨O￨- structured￨L￨VBN￨O￨- to￨L￨TO￨O￨- assist￨L￨VB￨O￨- real-time￨L￨JJ￨O￨- decision￨L￨NN￨O￨- making￨L￨VBG￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- recommendations￨L￨NNS￨O￨A as￨L￨IN￨O￨- new￨L￨JJ￨O￨- data￨L￨NNS￨O￨- become￨L￨VBP￨O￨- available￨L￨JJ￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- policies￨L￨NNS￨O￨A allow￨L￨VBP￨O￨- decision-makers￨L￨NNS￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- cumulative￨L￨JJ￨O￨- real-time￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- current￨L￨JJ￨DATE￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- resource￨L￨NN￨O￨- availability￨L￨NN￨O￨- to￨L￨TO￨O￨- guide￨L￨VB￨O￨- their￨L￨PRP$￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- particular￨L￨JJ￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- existing￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- optimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- use￨L￨VBP￨O￨- simulation￨L￨NN￨O￨- or￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- pre-determined￨L￨JJ￨O￨- health￨L￨NN￨O￨- policies￨L￨NNS￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- health￨L￨NN￨O￨- policies￨L￨NNS￨O￨A for￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- allocation￨L￨NN￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- without￨L￨IN￨O￨- explicitly￨L￨RB￨O￨- considering￨L￨VBG￨O￨- interventions￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- employed￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- evidence￨L￨NN￨O￨- synthesis￨L￨NN￨O￨- drawing￨L￨VBG￨O￨- upon￨L￨IN￨O￨- ideas￨L￨NNS￨O￨- of￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- incidence￨L￨NN￨O￨- from￨L￨IN￨O￨- serial￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- extending￨L￨VBG￨O￨- this￨L￨DT￨O￨- to￨L￨TO￨O￨- inference￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- these￨L￨DT￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- serial￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- a￨L￨DT￨O￨- multistate￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- diagnosis￨L￨NN￨O￨A ,￨L￨,￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- diagnosis￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- develop￨L￨VBP￨O￨- the￨L￨DT￨O￨- multistate￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- parameterizing￨L￨VBG￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- given￨L￨VBN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- further￨L￨RB￨O￨- developed￨L￨VBD￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- from￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- prevalence￨L￨NN￨O￨A ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- of￨L￨IN￨O￨- undiagnosed￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- dynamic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- multistate￨L￨NN￨O￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- incidence￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- these￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- exploratory￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- as￨L￨IN￨O￨- candidate￨L￨NN￨TITLE￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- optimality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Materials￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Methods￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- preferential￨L￨JJ￨O￨A treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- infected￨L￨JJ￨O￨- sub-population￨L￨NN￨O￨- -￨L￨:￨O￨- to￨L￨TO￨O￨- equalize￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- regions￨L￨NNS￨O￨- as￨L￨IN￨O￨- fast￨L￨JJ￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- and￨L￨CC￨O￨- thereafter￨L￨RB￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- each￨L￨DT￨O￨- region￨L￨NN￨O￨- equally￨L￨RB￨O￨- ;￨L￨:￨O￨- preferential￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- less￨L￨JJR￨O￨- infected￨L￨JJ￨O￨- sub-population￨L￨NN￨O￨- -￨L￨:￨O￨- initially￨L￨RB￨O￨- ‘￨L￨``￨O￨- sacrificing￨L￨VBG￨O￨- ’￨L￨''￨O￨- the￨L￨DT￨O￨- sub-population￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- infecteds￨L￨NNS￨O￨- preferential￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- susceptible￨L￨JJ￨O￨- sub-population￨L￨NN￨O￨- -￨L￨:￨O￨- initially￨L￨RB￨O￨- ‘￨L￨``￨O￨- sacrificing￨L￨VBG￨O￨- ’￨L￨''￨O￨- the￨L￨DT￨O￨- sub-population￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- a￨L￨DT￨O￨- strategy￨L￨NN￨O￨- involving￨L￨VBG￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- switch￨L￨NN￨O￨- between￨L￨IN￨O￨- preferential￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- infected￨L￨JJ￨O￨- to￨L￨TO￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- less￨L￨JJR￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- susceptible￨L￨JJ￨O￨- sub-population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemiological￨L￨JJ￨O￨- intuition￨L￨NN￨O￨- underpinning￨L￨VBG￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- understood￨L￨VBN￨O￨- by￨L￨IN￨O￨- noting￨L￨VBG￨O￨- that￨L￨IN￨O￨- since￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- or￨L￨CC￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- preferential￨L￨JJ￨O￨A treatment￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- region￨L￨NN￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- giving￨L￨VBG￨O￨- preference￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- uncertainty￨L￨NN￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- done￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- melding￨L￨NN￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- hierarchical￨L￨JJ￨O￨- random￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- sampling￨L￨NN￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- .2￨L￨NN￨NUMBER￨- 3￨L￨CD￨NUMBER￨- This￨U￨DT￨O￨- method￨L￨NN￨O￨- was￨L￨VBD￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- projection￨L￨NN￨O￨- package￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EPP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- UNAIDS￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- download￨L￨NN￨O￨- from￨L￨IN￨O￨- This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- UNAIDS￨U￨NNP￨ORGANIZATION￨- Secretariat￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- by￨L￨IN￨O￨- national￨L￨JJ￨O￨- officials￨L￨NNS￨O￨- producing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- and￨L￨CC￨O￨- projections￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- EPP￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- uses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- removed￨L￨VBD￨O￨- epidemiological￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- population￨L￨NN￨O￨- change￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- adjustable￨L￨JJ￨O￨- input￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- t0￨L￨NN￨O￨- ,￨L￨,￨O￨- f0￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ϕ￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- t0￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- f0￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adult￨L￨JJ￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ϕ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- change￨L￨NN￨O￨- parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- Methods￨U￨NNS￨O￨- section￨L￨NN￨O￨- we￨L￨PRP￨O￨- review￨L￨VBP￨O￨- the￨L￨DT￨O￨- EPP￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- r￨L￨NN￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- outline￨L￨VB￨O￨- the￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- estimation￨L￨NN￨O￨- method￨L￨NN￨O￨A we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- EPP￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- worked￨L￨VBN￨O￨- well￨L￨RB￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- and￨L￨CC￨O￨- projecting￨L￨VBG￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨A in￨L￨IN￨O￨- most￨L￨JJS￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- some￨L￨DT￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- GTAP￨U￨NN￨O￨- strategy￨L￨NN￨O￨A ,￨L￨,￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- the￨L￨DT￨O￨- identified￨L￨VBN￨O￨- index￨L￨NN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- provide￨L￨VBP￨O￨- prophylaxis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- index￨L￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- predefined￨L￨JJ￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- groups￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- households￨L￨NNS￨O￨- ,￨L￨,￨O￨- workplaces￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- neighborhood￨L￨NN￨O￨- clusters￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- bottom-up￨L￨JJ￨O￨- strategy￨L￨NN￨O￨A depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- each￨L￨DT￨O￨- person￨L￨NN￨O￨- 's￨L￨POS￨O￨- private￨L￨JJ￨O￨- awareness￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- his/her￨L￨NN￨O￨- direct￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- top-down￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- public￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- school￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- census￨L￨NN￨O￨- block￨L￨NN￨O￨- group￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- human-to-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- incubation￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ring￨L￨NN￨O￨- strategy￨L￨NN￨O￨A ,￨L￨,￨O￨- GTAP￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- geographically￨L￨RB￨O￨- targeted￨L￨VBN￨O￨- antiviral￨L￨JJ￨O￨- prophylaxis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- strategy￨L￨NN￨O￨- or￨L￨CC￨O￨- another￨L￨DT￨O￨- similar￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- may￨L￨MD￨O￨- indeed￨L￨RB￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- effective￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- respond￨L￨VB￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- compared￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- measures￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- averted￨L￨VBD￨O￨- per￨L￨IN￨O￨- drug￨L￨NN￨O￨- course￨L￨NN￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- the￨L￨DT￨O￨- bottom-up￨L￨JJ￨O￨- strategy￨L￨NN￨O￨A ,￨L￨,￨O￨- antivirals￨L￨NNS￨O￨- can￨L￨MD￨O￨- drop￨L￨VB￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- low￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- experiments￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- replicable￨L￨JJ￨O￨- microcosm￨L￨NN￨O￨- lattice￨L￨NN￨O￨- systems￨L￨NNS￨O￨- as￨L￨IN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- SIR￨U￨NN￨O￨- soil-borne￨L￨JJ￨O￨- plant￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- succeeded￨L￨VBD￨O￨- in￨L￨IN￨O￨- validating￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- from￨L￨IN￨O￨- percolation￨L￨NN￨O￨- theory￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- that￨L￨IN￨O￨- invasion￨L￨NN￨O￨A and￨L￨CC￨O￨- threshold￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- for￨L￨IN￨O￨- SIR￨U￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- coincides￨L￨VBZ￨O￨- within￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- precision￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- bond-percolation￨L￨NN￨O￨- ”￨L￨''￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- Text￨U￨VB￨O￨- S1￨U￨NN￨O￨- for￨L￨IN￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Even￨U￨RB￨O￨- more￨L￨RBR￨O￨- important￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- succeeded￨L￨VBD￨O￨- in￨L￨IN￨O￨- addressing￨L￨VBG￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- question￨L￨NN￨O￨- :￨L￨:￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- any￨L￨DT￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- variability￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- invasion￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- important￨L￨JJ￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- findings￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- variability￨L￨NN￨O￨- can￨L￨MD￨O￨- affect￨L￨VB￨O￨- invasion￨L￨NN￨O￨A thresholds￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- can￨L￨MD￨O￨- invade￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- lattice￨L￨NN￨O￨- will￨L￨MD￨O￨- never￨L￨RB￨O￨- invade￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- there￨L￨EX￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- invasion￨L￨NN￨O￨A when￨L￨WRB￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- higher￨L￨JJR￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Percolation￨U￨NN￨O￨- theory￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- conceptual￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- “￨L￨``￨O￨- scaling￨L￨VBG￨O￨- up￨L￨RP￨O￨- ”￨L￨''￨O￨- from￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- between-host￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- scale￨L￨NN￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- invasion￨L￨NN￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- scale￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assigned￨L￨VBD￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- five￨L￨CD￨NUMBER￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- that￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- UK￨U￨NNP￨COUNTRY￨- matched￨L￨VBD￨O￨A early￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- UK￨U￨NNP￨COUNTRY￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- an￨L￨DT￨O￨- overall￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficients￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contexts￨L￨NNS￨O￨- matched￨L￨VBD￨O￨- that￨L￨IN￨O￨- estimated￨L￨VBN￨O￨- in￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- after￨L￨IN￨O￨- adding￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- age-dependent￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- 36￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- being￨L￨VBG￨O￨- transmitted￨L￨VBN￨O￨- in￨L￨IN￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- 31￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- households￨L￨NNS￨O￨- ,￨L￨,￨O￨- 9￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- workplaces￨L￨NNS￨O￨- and￨L￨CC￨O￨- 24￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- relevant￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- seen￨L￨VBN￨O￨- also￨L￨RB￨O￨- within￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- has￨L￨VBZ￨O￨- experienced￨L￨VBN￨O￨- a￨L￨DT￨O￨- substantial￨L￨JJ￨O￨- first￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- early￨L￨JJ￨DATE￨- summer￨L￨NN￨DATE￨A ,￨L￨,￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- autumn￨L￨NN￨DATE￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- all￨L￨DT￨O￨- other￨L￨JJ￨O￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- had￨L￨VBD￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- summer￨L￨NN￨DATE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- wave￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- autumn/winter￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- employing￨L￨VBG￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- structurally￨L￨RB￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- already￨L￨RB￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatiotemporal￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- geographic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- here￨L￨RB￨O￨- which￨L￨WDT￨O￨- factors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- geographical￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- extent￨L￨NN￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨A was￨L￨VBD￨O￨- predictable￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- H1N1pdm￨U￨NN￨O￨- in￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- overall￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- is￨L￨VBZ￨O￨- summarised￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NNP￨O￨- 1A￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- expected￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- summer￨L￨NN￨DATE￨A among￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- case￨L￨NN￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- predicted￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- simulations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- and￨L￨CC￨O￨- each￨L￨DT￨SET￨- week￨L￨NN￨SET￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- date￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- European￨U￨JJ￨NATIONALITY￨- country￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- correlates￨L￨VBZ￨O￨- significantly￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- travellers￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- from￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- US￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- model￨L￨JJ￨TITLE￨- output￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- longitude￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- West￨U￨NN￨O￨- to￨L￨TO￨O￨- East￨U￨NNP￨O￨- pattern￨L￨NN￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- all￨L￨DT￨O￨- available￨L￨JJ￨O￨- serial￨L￨NN￨O￨- cross-sectional￨L￨JJ￨O￨- serologic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- soon￨L￨RB￨O￨- we￨L￨PRP￨O￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- reliable￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- IAR￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- infection-hospitalization￨L￨NN￨O￨- probability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IHP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- hospitalization￨L￨NN￨O￨A if￨L￨IN￨O￨- infected￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- these￨L￨DT￨O￨- serologic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- available￨L￨JJ￨O￨- weekly￨L￨JJ￨SET￨- in￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- unfolded￨L￨VBD￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- pdmH1N1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- pandemic￨L￨NN￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- and￨L￨CC￨O￨- reliable￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmissibility￨L￨NN￨O￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- hospitalization￨L￨NN￨O￨A and￨L￨CC￨O￨- death￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- infected￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- novel￨L￨JJ￨O￨- virus￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- previously￨L￨RB￨DATE￨- reported￨L￨VBD￨O￨- pdmH1N1￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IAR￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨A estimates￨L￨NNS￨O￨- using￨L￨VBG￨O￨- only￨L￨RB￨O￨- serologic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- before￨L￨RB￨O￨- and￨L￨CC￨O￨- immediately￨L￨RB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- companion￨L￨NN￨TITLE￨- study￨L￨NN￨O￨- used￨L￨VBD￨O￨- paired￨L￨JJ￨O￨- sera￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- cohort￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- IAR￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨A profile￨L￨NN￨O￨- of￨L￨IN￨O￨- pdmH1N1￨L￨NN￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- specimens￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- from￨L￨IN￨O￨- larger￨L￨JJR￨O￨- cohorts￨L￨NNS￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- yielded￨L￨VBN￨O￨- more￨L￨RBR￨O￨- reliable￨L￨JJ￨O￨- severity￨L￨NN￨O￨- estimates￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- ,￨L￨,￨O￨- equivalently￨L￨RB￨O￨- multi-group-or￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- -￨L￨:￨O￨- )￨L￨-RRB-￨O￨- modeling￨L￨NN￨O￨- paradigm￨L￨NN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- builds￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- viewpoint￨L￨NN￨O￨- was￨L￨VBD￨O￨- motivated￨L￨VBN￨O￨- specifically￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- recognition￨L￨NN￨O￨A that￨L￨WDT￨O￨- spread￨L￨VBD￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- structured￨L￨JJ￨O￨- and￨L￨CC￨O￨- variable￨L￨JJ￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- control￨L￨NN￨O￨- capabilities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- targeted￨L￨VBN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- can￨L￨MD￨O￨- aid￨L￨VB￨O￨- practitioners￨L￨NNS￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- and￨L￨CC￨O￨- making￨L￨VBG￨O￨- explicit￨L￨JJ￨O￨- the￨L￨DT￨O￨- roles￨L￨NNS￨O￨- played￨L￨VBN￨O￨- by￨L￨IN￨O￨- various￨L￨JJ￨O￨- species￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- such￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- control￨L￨NN￨O￨A seems￨L￨VBZ￨O￨- germane￨L￨NN￨O￨- to￨L￨TO￨O￨- mitigation￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonoses￨L￨NNS￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- as￨L￨IN￨O￨- yet￨L￨RB￨O￨- have￨L￨VBP￨O￨- only￨L￨RB￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- using￨L￨VBG￨O￨- generic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- only￨L￨RB￨O￨- measured￨L￨VBN￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- measure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- considered￨L￨VBN￨O￨- surveillance￨L￨NN￨O￨- at￨L￨IN￨O￨- all￨L￨DT￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- group￨L￨NN￨O￨- has￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- heterogeneous￨L￨JJ￨O￨- control￨L￨NN￨O￨A resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- in￨L￨IN￨O￨- multi-group￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- virus￨L￨NN￨O￨- spread￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- A￨U￨NNP￨MISC￨- poisson￨L￨NN￨O￨A regression￨L￨NN￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- spatial￨L￨JJ￨O￨- autocorrelation￨L￨NN￨O￨- between￨L￨IN￨O￨- geographically￨L￨RB￨O￨- referenced￨L￨VBN￨O￨- observationsMohammadreza￨L￨NN￨O￨- Mohebbi1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Rory￨U￨NNP￨PERSON￨- Wolfe1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Damien￨U￨NNP￨PERSON￨- Jolley1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 11:133￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Mohebbi￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Analytic￨U￨NNP￨MISC￨- methods￨L￨NNS￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- observations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Distance-based￨U￨JJ￨O￨- and￨L￨CC￨O￨- neighbourhood-based￨L￨JJ￨O￨- autocorrelation￨L￨NN￨O￨- structures￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- defining￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨A random￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- pseudolikelihood￨L￨NN￨O￨- approach￨L￨NN￨O￨- was￨L￨VBD￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- residual￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨A dependence￨L￨NN￨O￨- was￨L￨VBD￨O￨- modelled￨L￨VBN￨O￨- ,￨L￨,￨O￨- point￨L￨NN￨O￨- and￨L￨CC￨O￨- interval￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- covariate￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- were￨L￨VBD￨O￨- different￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- nonspatial￨L￨JJ￨O￨- Poisson￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- following￨L￨VBG￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- SIR￨U￨NN￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Poisson￨U￨NNP￨PERSON￨- regression￨L￨NN￨O￨A with￨L￨IN￨O￨- agglomeration-specific￨L￨JJ￨O￨- nonspatial￨L￨JJ￨O￨- random￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Poisson￨U￨NNP￨PERSON￨- regression￨L￨NN￨O￨- with￨L￨IN￨O￨- agglomeration-specific￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- random￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- A￨U￨DT￨O￨- Gaussian￨U￨JJ￨MISC￨- semivariogram￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- 225￨L￨CD￨NUMBER￨- km￨L￨NN￨O￨- best￨L￨RB￨O￨- fit￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨A autocorrelation￨L￨NN￨O￨- in￨L￨IN￨O￨- agglomeration-level￨L￨JJ￨O￨- EC￨U￨NN￨ORGANIZATION￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- seven-valent￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨- conjugate￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PCV7￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- serotypes￨L￨NNS￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6B￨L￨NN￨O￨- ,￨L￨,￨O￨- 9V￨L￨NN￨O￨- ,￨L￨,￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 18C￨L￨NN￨O￨- ,￨L￨,￨O￨- 19F￨L￨NN￨O￨- and￨L￨CC￨O￨- 23F￨L￨NN￨O￨- was￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- routine￨L￨JJ￨O￨- childhood￨L￨NN￨O￨- immunisation￨L￨NN￨O￨- programme￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- (￨L￨-LRB-￨O￨- US￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- and￨L￨CC￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- VT￨U￨NNP￨STATE_OR_PROVINCE￨- IPD￨U￨NNP￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- with￨L￨IN￨O￨- little￨L￨JJ￨O￨- NVT￨U￨NN￨O￨- replacement￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- post-PCV7￨L￨JJ￨O￨- experience￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- the￨L￨DT￨O￨- national￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- IPD￨U￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- three￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- postPCV7￨L￨NN￨O￨- introduction￨L￨NN￨O￨- in￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Wales￨U￨NNP￨LOCATION￨- to￨L￨TO￨O￨- re-estimate￨L￨VB￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- predicted￨L￨VBD￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- VT￨U￨NNP￨STATE_OR_PROVINCE￨- IPD￨U￨NNP￨O￨- with￨L￨IN￨O￨- limited￨L￨JJ￨O￨- serotype￨L￨NN￨O￨- replacement￨L￨NN￨O￨A such￨L￨JJ￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- sustained￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- overall￨L￨JJ￨O￨- IPD￨U￨NN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- likely￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- PCV7￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- was￨L￨VBD￨O￨- initially￨L￨RB￨O￨- evaluated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A with￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- impact￨L￨NN￨O￨- parameterised￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- post-PCV7￨L￨JJ￨O￨- IPD￨U￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- re-parameterised￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- term￨L￨NN￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- PCV7￨U￨NN￨O￨- programme￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- VT￨U￨NN￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- NVT￨U￨NN￨O￨- IPD￨U￨NN￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨- in￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Wales￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- primarily￨L￨RB￨O￨- involves￨L￨VBZ￨O￨- applying￨L￨VBG￨O￨- health￨L￨NN￨O￨- resources￨L￨NNS￨O￨- to￨L￨TO￨O￨- affected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- medical￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- for￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- closure￨L￨NN￨O￨- of￨L￨IN￨O￨- affected￨L￨VBN￨O￨- workplaces/schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- travel￨L￨NN￨O￨- restriction￨L￨NN￨O￨- to￨L￨TO￨O￨- affected￨L￨VBN￨O￨- communities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- far￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- combined￨L￨JJ￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A and￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- preventive￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- little￨L￨JJ￨O￨- attention￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- issue￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- devising￨L￨VBG￨O￨- various￨L￨JJ￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A and￨L￨CC￨O￨- evaluating￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- effectiveness￨L￨NN￨O￨- ,￨L￨,￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- incorporated￨L￨VBN￨O￨- the￨L￨DT￨O￨- preventive￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- reality￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- preventive￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- also￨L￨RB￨O￨- reduces￨L￨VBZ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- takes￨L￨VBZ￨O￨- effect￨L￨NN￨O￨- concurrently￨L￨RB￨O￨- with￨L￨IN￨O￨- typical￨L￨JJ￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- most￨L￨JJS￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- passively￨L￨RB￨O￨- comply￨L￨VB￨O￨- with￨L￨IN￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- their￨L￨PRP$￨O￨- active￨L￨JJ￨O￨- prevention￨L￨NN￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- overlooked￨L￨VBN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- immunization￨L￨NN￨O￨- campaign￨L￨NN￨O￨- budget￨L￨NN￨O￨A re-allocation￨L￨NN￨O￨- on￨L￨IN￨O￨- global￨L￨JJ￨O￨- eradication￨L￨NN￨O￨- of￨L￨IN￨O￨- paediatric￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseasesTiffany￨L￨NN￨O￨- Fitzpatrick1￨U￨NN￨O￨- and￨L￨CC￨O￨- Chris￨U￨NNP￨PERSON￨- T￨U￨NN￨PERSON￨- Bauch1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 11:739￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Fitzpatrick￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Bauch￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- potential￨L￨JJ￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- coordinating￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- eradication￨L￨NN￨O￨- programs￨L￨NNS￨O￨- that￨L￨WDT￨O￨- use￨L￨VBP￨O￨- campaigns￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- supplementary￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIAs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- should￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- over-looked￨L￨JJ￨O￨- .￨L￨.￨O￨- +Herd￨U￨NN￨O￨- immunity￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- sequential￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- may￨L￨MD￨O￨- eradicate￨L￨VB￨O￨- several￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- faster￨L￨RBR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- non-adaptive￨L￨JJ￨O￨- "￨L￨``￨O￨- simultaneous￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- "￨L￨''￨O￨- of￨L￨IN￨O￨- dividing￨L￨VBG￨O￨- annual￨L￨JJ￨SET￨- budget￨L￨NN￨O￨A equally￨L￨RB￨O￨- among￨L￨IN￨O￨- eradication￨L￨NN￨O￨- programs￨L￨NNS￨O￨- for￨L￨IN￨O￨- those￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- objective￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- illustrate￨L￨VB￨O￨- how￨L￨WRB￨O￨- budget￨L￨NN￨O￨A allocation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- can￨L￨MD￨O￨- interact￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- eradication￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- budget￨L￨NN￨O￨- allocation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- coordinated￨L￨VBN￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- "￨L￨``￨O￨- sequential￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- "￨L￨''￨O￨- :￨L￨:￨O￨- first￨L￨RB￨ORDINAL￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- SIA￨U￨NNP￨ORGANIZATION￨- budget￨L￨NN￨O￨A is￨L￨VBZ￨O￨- dedicated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- eradication￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- once￨L￨RB￨DATE￨- that￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- eradicated￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- SIA￨U￨NNP￨ORGANIZATION￨- budget￨L￨NN￨O￨- is￨L￨VBZ￨O￨- re-focussed￨L￨JJ￨O￨- on￨L￨IN￨O￨- eradicating￨L￨VBG￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- major￨L￨JJ￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- conducted￨L￨VBN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- include￨L￨VBP￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- fogging￨L￨VBG￨O￨- ultra-low-volume￨L￨JJ￨O￨- insecticide￨L￨NN￨O￨A particles￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- insecticide￨L￨NN￨O￨- fogging￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- target￨L￨VBP￨O￨- adult￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- ;￨L￨:￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- chemical￨L￨NN￨O￨- and￨L￨CC￨O￨- biological￨L￨JJ￨O￨- controls￨L￨NNS￨O￨- for￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- larvae￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- containers￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- larval￨L￨JJ￨O￨- source￨L￨NN￨O￨- reduction￨L￨NN￨O￨- .￨L￨.￨O￨- +Newton￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Reiter￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- N&R￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- reported￨L￨VBD￨O￨- that￨L￨IN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- strongest￨L￨JJS￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- insecticide￨L￨NN￨O￨A fogging￨L￨NN￨O￨- in￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- dengue￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- when￨L￨WRB￨O￨- insecticides￨L￨NNS￨O￨- are￨L￨VBP￨O￨- applied￨L￨VBN￨O￨- several￨L￨JJ￨DURATION￨- days￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- peak￨L￨NN￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- had￨L￨VBD￨O￨- little￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- 6.8￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- prevented￨L￨VBD￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- dengue￨L￨JJ￨O￨- situation￨L￨NN￨O￨- ,￨L￨,￨O￨- seasonality￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- are￨L￨VBP￨O￨- critical￨L￨JJ￨O￨- determinants￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- that￨L￨WDT￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- consideration￨L￨NN￨O￨- when￨L￨WRB￨O￨- evaluating￨L￨VBG￨O￨- and￨L￨CC￨O￨- optimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- insecticide￨L￨NN￨O￨A fogging￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- studies￨L￨NNS￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- insecticide￨L￨NN￨O￨A fogging￨L￨NN￨O￨- might￨L￨MD￨O￨- differ￨L￨VB￨O￨- from￨L￨IN￨O￨- results￨L￨NNS￨O￨- reported￨L￨VBN￨O￨- by￨L￨IN￨O￨- N&R￨U￨NN￨ORGANIZATION￨- when￨L￨WRB￨O￨- also￨L￨RB￨O￨- considering￨L￨VBG￨O￨- seasonality￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- those￨L￨DT￨O￨- ,￨L￨,￨O￨- insecticide￨L￨NN￨O￨A fogging￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- commonly￨L￨RB￨O￨- implemented￨L￨VBN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- dengue￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- controversial￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- commonly￨L￨RB￨O￨- believed￨L￨VBN￨O￨- that￨L￨IN￨O￨- evolving￨L￨VBG￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- may￨L￨MD￨O￨- take￨L￨VB￨O￨- years￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- escape￨L￨VB￨O￨A population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- inter-wave￨L￨NN￨O￨- periods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- few￨L￨JJ￨DURATION￨- weeks￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- existing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- rather￨L￨RB￨O￨- phenomenological￨L￨JJ￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- endowed￨L￨VBN￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- interpretations￨L￨NNS￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- immune￨L￨JJ￨O￨- escape￨L￨NN￨CRIMINAL_CHARGE￨A by￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- drift￨L￨NN￨O￨- to￨L￨TO￨O￨- reinfection￨L￨NN￨O￨- by￨L￨IN￨O￨- immune￨L￨JJ￨O￨- deficiency￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- report￨L￨NN￨O￨- challenges￨L￨VBZ￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- confers￨L￨VBZ￨O￨- life-long￨L￨JJ￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- reinfection￨L￨NN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- strain￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- antigenically￨L￨RB￨O￨- variable￨L￨JJ￨O￨- RNA￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- status-based￨L￨JJ￨O￨- multi-strain￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- andwhere￨L￨JJ￨O￨- subscript￨L￨JJ￨O￨- i￨L￨FW￨O￨- denotes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- antigenic￨L￨JJ￨O￨- variant￨L￨NN￨O￨A ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- ν￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- σ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- cross-immunity￨L￨NN￨O￨- between￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- j￨L￨FW￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- most￨L￨JJS￨O￨- evolutionary￨L￨JJ￨O￨- multi-strain￨L￨JJ￨O￨- models￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- mutation￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- factor￨L￨NN￨O￨- thereof￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- here￨L￨RB￨O￨- more￨L￨RBR￨O￨- generally￨L￨RB￨O￨- allow￨L￨VB￨O￨- hW￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- antigenic￨L￨JJ￨O￨- variant￨L￨NN￨O￨A 's￨L￨POS￨O￨- age￨L￨NN￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- variant￨L￨NN￨O￨- 's￨L￨POS￨O￨- emergence￨L￨NN￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- variant￨L￨JJ￨O￨A Y￨U￨NN￨O￨- 's￨L￨POS￨O￨- frequency-dependent￨L￨JJ￨O￨- selective￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- variants￨L￨NNS￨O￨- X￨U￨NN￨O￨- and￨L￨CC￨O￨- Y￨U￨NN￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨- of￨L￨IN￨O￨- variant￨L￨JJ￨O￨- Y￨U￨NN￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- variant￨L￨JJ￨O￨- X￨U￨NN￨O￨- ,￨L￨,￨O￨- until￨L￨IN￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- variant￨L￨JJ￨O￨- X￨U￨NN￨O￨- is￨L￨VBZ￨O￨- lost￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- start￨L￨VBP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- antigenic￨L￨JJ￨O￨- variant￨L￨NN￨O￨A X￨U￨NN￨O￨- circulating￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- giving￨L￨VBG￨O￨- rise￨L￨NN￨O￨- to￨L￨TO￨O￨- new￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ‘￨L￨``￨O￨- offspring￨L￨NN￨O￨- variants￨L￨NNS￨O￨- ’￨L￨POS￨O￨- )￨L￨-RRB-￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dimensionless￨L￨JJ￨O￨- number￨L￨NN￨O￨- κ￨L￨NN￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- here￨L￨RB￨O￨- for￨L￨IN￨O￨- viral￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- its￨L￨PRP$￨O￨- value￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- players￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- fluid￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- pipe￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Reynolds￨U￨NNP￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- κ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- quarantine￨L￨NN￨O￨A is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- as￨L￨IN￨O￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- barrier￨L￨NN￨O￨- ”￨L￨''￨O￨- is￨L￨VBZ￨O￨- placed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- placed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- adjacent￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- site￨L￨NN￨O￨- percolation￨L￨NN￨O￨- for￨L￨IN￨O￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- bond￨L￨NN￨O￨- percolation￨L￨NN￨O￨- for￨L￨IN￨O￨- quarantine￨L￨NN￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- lattice￨L￨NN￨O￨- space16￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- prevention￨L￨NN￨O￨- p￨L￨NN￨O￨- and/or￨L￨CC￨O￨- quarantine￨L￨NN￨O￨A p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- effective￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Figs￨U￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- synergistic￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- quarantine￨L￨NN￨O￨A under￨L￨IN￨O￨- local￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- prevented￨L￨VBN￨O￨- site￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- person￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- completely￨L￨RB￨O￨- protected￨L￨VBN￨O￨- from￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- global￨L￨JJ￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨A that￨L￨WDT￨O￨- marks￨L￨VBZ￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- beyond￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- reaches￨L￨VBZ￨O￨- other￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- spreads￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- system￨L￨NN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- as￨L￨IN￨O￨- well1213￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- differs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- population￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +Ultimately￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- prevalence-based￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨A ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- subpopulations￨L￨NNS￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- does￨L￨VBZ￨O￨- depend￨L￨VB￨O￨- considerably￨L￨RB￨O￨- on￨L￨IN￨O￨- population￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- self-initiated￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- study￨L￨NN￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- reactions￨L￨NNS￨O￨- influence￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- subpopulation￨L￨NN￨O￨A consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- several￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- dynamical￨L￨JJ￨O￨- state￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- modeled￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- –￨L￨:￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- removed￨L￨VBN￨O￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- we￨L￨PRP￨O￨- assume￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- distributionwhere￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- per￨L￨IN￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨A network￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- include￨L￨VBP￨O￨- government￨L￨NN￨O￨- commitment￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- diagnosis￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- sputum-smear￨L￨JJ￨O￨- microscopy￨L￨NN￨O￨- tests￨L￨VBZ￨O￨- done￨L￨VBN￨O￨- on￨L￨IN￨O￨- patients￨L￨NNS￨O￨- who￨L￨WP￨O￨- actively￨L￨RB￨O￨- report￨L￨VBP￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- direct￨L￨JJ￨O￨- observation￨L￨NN￨O￨- short-course￨L￨NN￨O￨- chemotherapy￨L￨NN￨O￨- treatments￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- definite￨L￨JJ￨O￨- supply￨L￨NN￨O￨- of￨L￨IN￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- standardized￨L￨JJ￨O￨- reporting￨L￨NN￨O￨- and￨L￨CC￨O￨- recording￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨A outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Globally￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- recognized￨L￨VBN￨O￨- that￨L￨IN￨O￨- limited￨L￨JJ￨O￨- financial￨L￨JJ￨O￨- and￨L￨CC￨O￨- health￨L￨NN￨O￨- resources￨L￨NNS￨O￨- continue￨L￨VBP￨O￨- to￨L￨TO￨O￨- strain￨L￨VB￨O￨- efforts￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨A infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A like￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- condition￨L￨NN￨O￨- worsened￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- advent￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- International￨U￨NNP￨ORGANIZATION￨- Union￨U￨NNP￨ORGANIZATION￨- against￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- Lung￨U￨NN￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- IUATLD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- promote￨L￨VBP￨O￨- universal￨L￨JJ￨O￨- adoption￨L￨NN￨O￨- of￨L￨IN￨O￨- Directly￨U￨RB￨O￨- Observed￨U￨VBN￨O￨- Treatment￨U￨NN￨O￨- ,￨L￨,￨O￨- Short-Course￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- DOTS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- treatment￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- means￨L￨NN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- treatment￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- task￨L￨NN￨O￨- shifting￨L￨VBG￨O￨- in￨L￨IN￨O￨- DOTS￨U￨NNS￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨A TB￨U￨NN￨CAUSE_OF_DEATH￨- Susceptible-Infectious-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Model￨U￨NNP￨TITLE￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Correspondingly￨U￨RB￨O￨- ,￨L￨,￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- leading￨L￨VBG￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- mortality￨L￨NN￨O￨- among￨L￨IN￨O￨- persons￨L￨NNS￨O￨A infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- The￨U￨DT￨MISC￨- potential￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- highly￨L￨RB￨O￨- pathogenic￨L￨JJ￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- via￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- poultry￨L￨NN￨O￨- premises￨L￨NNS￨O￨A in￨L￨IN￨O￨- Great￨U￨JJ￨O￨- BritainJennifer￨U￨NN￨O￨- E￨U￨NN￨O￨- Dent1￨U￨NN￨O￨- ,￨L￨,￨O￨- 5Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Istvan￨U￨NNP￨PERSON￨- Z￨U￨NNP￨PERSON￨- Kiss3￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Rowland￨U￨NNP￨PERSON￨- R￨U￨NNP￨O￨- Kao4￨U￨NN￨O￨- and￨L￨CC￨O￨- Mark￨U￨NNP￨O￨- Arnold2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:59￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Dent￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Highly￨U￨RB￨O￨- pathogenic￨L￨JJ￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- HPAI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- viruses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- had￨L￨VBN￨O￨- devastating￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- poultry￨L￨NN￨O￨- industries￨L￨NNS￨O￨- worldwide￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- concern￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- HPAI￨U￨NN￨ORGANIZATION￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- poultry￨L￨NN￨O￨- industry￨L￨NN￨O￨- in￨L￨IN￨O￨- Great￨U￨NNP￨COUNTRY￨- Britain￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- GB￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Results￨U￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- whilst￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- that￨L￨IN￨O￨- HPAI￨U￨NN￨ORGANIZATION￨- virus￨L￨NN￨O￨- will￨L￨MD￨O￨- jump￨L￨VB￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- farms￨L￨NNS￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- ,￨L￨,￨O￨- movements￨L￨NNS￨O￨- made￨L￨VBN￨O￨- by￨L￨IN￨O￨- catching￨L￨VBG￨O￨- teams￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- fewer￨L￨JJR￨O￨- poultry￨L￨NN￨O￨- premises￨L￨NNS￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- situation￨L￨NN￨O￨- than￨L￨IN￨O￨- slaughterhouses￨L￨NNS￨O￨- and￨L￨CC￨O￨- company￨L￨NN￨O￨- personnel￨L￨NNS￨O￨- .￨L￨.￨O￨- +Final￨U￨JJ￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- was￨L￨VBD￨O￨- most￨L￨RBS￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- via￨L￨IN￨O￨- slaughterhouse-linked￨L￨JJ￨O￨- movements￨L￨NNS￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- onward￨L￨RB￨O￨- spread￨L￨VBN￨O￨- beyond￨L￨IN￨O￨- an￨L￨DT￨O￨- index￨L￨NN￨O￨- premises￨L￨NNS￨O￨A was￨L￨VBD￨O￨- most￨L￨RBS￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- company￨L￨NN￨O￨- personnel￨L￨NNS￨O￨- movements￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- predicted￨L￨VBD￨O￨- that￨L￨IN￨O￨- although￨L￨IN￨O￨- large￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- rare￨L￨JJ￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- occur￨L￨VB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- long￨L￨JJ￨O￨- distances￨L￨NNS￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- premises￨L￨NNS￨O￨A .￨L￨.￨O￨- +Movement￨U￨NNP￨O￨- records￨L￨NNS￨O￨- of￨L￨IN￨O￨- catching￨L￨VBG￨O￨- teams￨L￨NNS￨O￨- and￨L￨CC￨O￨- slaughterhouse￨L￨NN￨O￨- vehicles￨L￨NNS￨O￨- were￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- catching￨L￨VBG￨O￨- company￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- HPAI￨U￨NNP￨O￨- spread￨L￨NN￨O￨- between￨L￨IN￨O￨- farms￨L￨NNS￨O￨A serviced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- catching￨L￨VBG￨O￨- company￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- surrounding￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- geographic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- seem￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- sensitive￨L￨JJ￨O￨- for￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- asymptomatic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- antibody￨L￨NN￨O￨A tests￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- hypothesised￨L￨VBN￨O￨- that￨L￨IN￨O￨- PCR￨U￨NN￨O￨- of￨L￨IN￨O￨- peripheral￨L￨JJ￨O￨- blood￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- marker￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- positive￨L￨JJ￨O￨- after￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- before￨L￨IN￨O￨- antibody￨L￨NN￨O￨- seroconversion￨L￨NN￨O￨- takes￨L￨VBZ￨O￨- place￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- cellular￨L￨JJ￨O￨- and￨L￨CC￨O￨- humoral￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- Leishmania￨U￨NNP￨LOCATION￨- are￨L￨VBP￨O￨- diminished￨L￨VBN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- developing￨L￨VBG￨O￨- VL￨U￨NNP￨O￨- after￨L￨IN￨O￨- Leishmania￨U￨NNP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- failure￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- proceeded￨L￨VBD￨O￨- asymptomatically￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨A that￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- indicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- subscript￨L￨NN￨O￨- H￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- typically￨L￨RB￨O￨- passed￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- five￨L￨CD￨NUMBER￨- stages￨L￨NNS￨O￨- :￨L￨:￨O￨- :￨L￨:￨O￨- Susceptible￨U￨JJ￨O￨- stage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +donovani￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Indian￨U￨JJ￨NATIONALITY￨- subcontinent￨L￨NN￨O￨- and￨L￨CC￨O￨- extends￨L￨VBZ￨O￨A the￨L￨DT￨O￨- before-mentioned￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- findings￨L￨NNS￨O￨- with￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- quantifications￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- L￨U￨NN￨O￨- .￨L￨.￨O￨- +Hosts￨U￨NNS￨O￨- are￨L￨VBP￨O￨- DAT-negative￨U￨JJ￨O￨- but￨L￨CC￨O￨- still￨L￨RB￨O￨- LST-positive￨U￨JJ￨O￨- and￨L￨CC￨O￨- assumed￨L￨VBD￨O￨A to￨L￨TO￨O￨- be￨L￨VB￨O￨- protected￨L￨VBN￨O￨- against￨L￨IN￨O￨- re-infection￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- PrPres￨U￨NNP￨O￨- dissemination￨L￨NN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- non-neural￨L￨JJ￨O￨- tissues￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- lymphoreticular￨L￨JJ￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- placenta￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨A levels￨L￨NNS￨O￨A of￨L￨IN￨O￨- transmissibility￨L￨NN￨O￨- within￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- completely￨L￨RB￨O￨- understood￨L￨VBN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- highly￨L￨RB￨O￨- sensitive￨L￨JJ￨O￨- methodologies￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- allowed￨L￨VBN￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- PrPres￨U￨NNP￨O￨- in￨L￨IN￨O￨- samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- scrapie￨L￨NN￨O￨- animals￨L￨NNS￨O￨A that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- undetectable￨L￨JJ￨O￨- by￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- assays￨L￨NNS￨O￨- .￨L￨.￨O￨- +Placentas￨U￨NNS￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- may￨L￨MD￨O￨- harbor￨L￨VB￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- PrPres￨U￨NNP￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨A levels￨L￨NNS￨O￨A of￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- fetus￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- PrP￨U￨NN￨O￨- genotype￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- protein￨L￨NN￨O￨- misfolding￨L￨NN￨O￨- cyclic￨L￨JJ￨O￨- amplification￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PMCA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- technique￨L￨NN￨O￨- ,￨L￨,￨O￨- PrPres￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- detected￨L￨VBN￨O￨A in￨L￨IN￨O￨- milk￨L￨NN￨O￨- ,￨L￨,￨O￨- feces￨L￨NNS￨O￨- ,￨L￨,￨O￨- urine￨L￨NN￨O￨- ,￨L￨,￨O￨- saliva￨L￨NN￨O￨- and￨L￨CC￨O￨- blood￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Limited￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- detected￨L￨VBN￨O￨A infectivity￨L￨NN￨O￨- by￨L￨IN￨O￨- bioassay￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- PrPres￨U￨NNS￨O￨- by￨L￨IN￨O￨- conventional￨L￨JJ￨O￨- immunoassay￨L￨NN￨O￨- of￨L￨IN￨O￨- fetuses￨L￨NNS￨O￨- and￨L￨CC￨O￨- fetal￨L￨JJ￨O￨- fluids￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Understanding￨U￨VBG￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨A behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- sensitivity￨L￨NN￨O￨- to￨L￨TO￨O￨- parameters￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- forecasting￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- in￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- antigenic￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- features￨L￨NNS￨O￨- characterizing￨L￨VBG￨O￨- seasonal￨L￨JJ￨O￨A influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- incidence￨L￨NN￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- these￨L￨DT￨O￨- to￨L￨TO￨O￨- define￨L￨VB￨O￨- information￨L￨NN￨O￨- measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- mechanisms￨L￨NNS￨O￨- combine￨L￨VBP￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- complex￨L￨NN￨O￨- seasonal￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- featuring￨L￨VBG￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- annual￨L￨JJ￨SET￨A attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- AARs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- and￨L￨CC￨O￨- alternating￨L￨VBG￨O￨- sequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- dominant￨L￨JJ￨O￨- annual￨L￨JJ￨SET￨- subtypes￨L￨NNS￨O￨- and￨L￨CC￨O￨- strains￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Use￨U￨NN￨O￨- of￨L￨IN￨O￨- summary￨L￨NN￨O￨- statistics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- attempting￨L￨VBG￨O￨- to￨L￨TO￨O￨- directly￨L￨RB￨O￨- fit￨L￨VB￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- time-series￨L￨JJ￨O￨- data￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- adds￨L￨VBZ￨O￨- robustness￨L￨NN￨O￨- to￨L￨TO￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- reporting￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- much￨L￨JJ￨O￨- ILI￨U￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- even￨L￨RB￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- short-term￨L￨JJ￨O￨- fluctuation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Annual￨U￨JJ￨SET￨- periodic￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- causes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- oscillatory￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- illustrated￨L￨VBN￨O￨- by￨L￨IN￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Key￨U￨NN￨O￨- issues￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- limited￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- resources￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- STIs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- whether￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- as￨L￨IN￨O￨- effective￨L￨JJ￨O￨- for￨L￨IN￨O￨- males￨L￨NNS￨O￨- as￨L￨IN￨O￨- for￨L￨IN￨O￨- females￨L￨NNS￨O￨A ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- whether￨L￨IN￨O￨- directing￨L￨VBG￨O￨- interventions￨L￨NNS￨O￨- at￨L￨IN￨O￨- both￨L￨DT￨O￨- males￨L￨NNS￨O￨- and￨L￨CC￨O￨- females￨L￨NNS￨O￨- adds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- population-level￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- directing￨L￨VBG￨O￨- interventions￨L￨NNS￨O￨- at￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- sex￨L￨NN￨O￨- alone￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rationale￨L￨NN￨O￨- for￨L￨IN￨O￨- male￨L￨JJ￨O￨- inclusion￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- twofold￨L￨RB￨O￨- :￨L￨:￨O￨- men￨L￨NNS￨O￨- benefit￨L￨VBP￨O￨A directly￨L￨RB￨O￨- from￨L￨IN￨O￨- immunization￨L￨NN￨O￨- against￨L￨IN￨O￨- HPV-related￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- boys￨L￨NNS￨O￨- could￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- further￨L￨JJ￨O￨- decrease￨L￨VB￨O￨- the￨L￨DT￨O￨- circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨MISC￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- indirectly￨L￨RB￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- protection￨L￨NN￨O￨- of￨L￨IN￨O￨- women￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- allow￨L￨VBP￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- prophylactic￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- best￨L￨JJS￨O￨- distributed￨L￨VBN￨O￨- between￨L￨IN￨O￨- males￨L￨NNS￨O￨- and￨L￨CC￨O￨- females￨L￨NNS￨O￨A in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- lower￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- basic￨L￨JJ￨O￨- question￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- addressed￨L￨VBN￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- is￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- levels￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- effectively￨L￨RB￨O￨- reduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- stimulating￨L￨VBG￨O￨- vaccine￨L￨NN￨O￨- uptake￨L￨NN￨O￨- in￨L￨IN￨O￨- girls￨L￨NNS￨O￨- when￨L￨WRB￨O￨- female￨L￨JJ￨O￨A coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- by￨L￨IN￨O￨- extending￨L￨VBG￨O￨- coverage￨L￨NN￨O￨- to￨L￨TO￨O￨- males￨L￨NNS￨O￨- .￨L￨.￨O￨- +Inductive￨U￨JJ￨O￨- reasoning￨L￨NN￨O￨- games￨L￨NNS￨O￨- were￨L￨VBD￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨- assuming￨L￨VBG￨O￨- both￨L￨CC￨O￨- uniform￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- mixing￨L￨VBG￨O￨- through￨L￨IN￨O￨- complex￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- generalize￨L￨VBP￨O￨- previous￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- media￨L￨NNS￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- implicitly￨L￨RB￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +So￨U￨RB￨O￨- far￨L￨RB￨O￨- ,￨L￨,￨O￨- inductive￨L￨JJ￨O￨- reasoning￨L￨NN￨O￨- games￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨A assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- information￨L￨NN￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- individuals￨L￨NNS￨O￨- was￨L￨VBD￨O￨- whether￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- took￨L￨VBD￨O￨- place￨L￨NN￨O￨- .￨L￨.￨O￨- +Game￨U￨NNP￨O￨- theory￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- successfully￨L￨RB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- on￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- gets￨L￨VBZ￨O￨- vaccinated￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- conjectured￨L￨VBN￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- make￨L￨VBP￨O￨- repeated￨L￨VBN￨O￨- vaccination￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- expectations￨L￨NNS￨O￨- about￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- epidemics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- collective￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨A data￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- directed￨L￨VBN￨O￨- edges￨L￨NNS￨O￨- ,￨L￨,￨O￨- poses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- whether￨L￨IN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- phone￨L￨NN￨O￨- call￨L￨VB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- exchange￨L￨NN￨O￨- exhibits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- favored￨L￨JJ￨O￨- flow￨L￨NN￨O￨- direction￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- different￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- exclusively￨L￨RB￨O￨- active￨L￨JJ￨O￨- and￨L￨CC￨O￨- intentional￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- phone￨L￨NN￨O￨A calls￨L￨NNS￨O￨- made￨L￨VBN￨O￨- by￨L￨IN￨O￨- informed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- intended￨L￨VBN￨O￨- to￨L￨TO￨O￨- propagate￨L￨VB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- we￨L￨PRP￨O￨- think￨L￨VBP￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- rumor￨L￨NN￨O￨- being￨L￨VBG￨O￨- spread￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨A network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- phone￨L￨NN￨O￨- call￨L￨NN￨O￨- that￨L￨WDT￨O￨- involves￨L￨VBZ￨O￨- an￨L￨DT￨O￨- informed￨L￨VBN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- ignorant￨L￨JJ￨O￨- user￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- imagine￨L￨VB￨O￨- that￨L￨IN￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- communication￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- users￨L￨NNS￨O￨- are￨L￨VBP￨O￨- informed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- causality￨L￨NN￨O￨- trees￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- proxy￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- we￨L￨PRP￨O￨- need￨L￨VBP￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- time￨L￨NN￨O￨A scale￨L￨NN￨O￨A which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- controlled￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨A data￨L￨NNS￨O￨- ,￨L￨,￨O￨- A￨U￨DT￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- processed￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time-scale￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- here￨L￨RB￨O￨- =￨L￨JJ￨O￨- 150￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- causality￨L￨NN￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- .￨L￨.￨O￨- +Methodology￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- In￨U￨FW￨MISC￨- vitro￨L￨FW￨O￨- culture￨L￨NN￨O￨A of￨L￨IN￨O￨- Plasmodium￨U￨NN￨O￨- berghei-ANKA￨L￨NN￨O￨- maintains￨L￨VBZ￨O￨- infectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- mouse￨L￨NN￨O￨- erythrocytes￨L￨NNS￨O￨- inducing￨L￨VBG￨O￨- cerebral￨L￨JJ￨O￨- malariaRonan￨L￨NN￨O￨- Jambou1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Fatima￨U￨NNP￨PERSON￨- El-Assaad1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Valery￨U￨NNP￨PERSON￨- Combes1￨U￨NNP￨O￨- and￨L￨CC￨O￨- Georges￨U￨NNP￨PERSON￨- E￨U￨NNP￨O￨- Grau1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 10:346￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Jambou￨U￨FW￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- Plasmodium￨U￨NN￨O￨- berghei￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- murine￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- powerful￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- reverse￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- and￨L￨CC￨O￨- pathogenesis￨L￨NN￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- serial￨L￨NN￨O￨- interval￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- contracts￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Kenah￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- transmissions￨L￨NNS￨O￨A per￨L￨IN￨O￨- infected￨L￨JJ￨O￨- unit￨L￨NN￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- conventional￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- K￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- motivation￨L￨NN￨O￨- ,￨L￨,￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- X￨U￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- Y￨U￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- transmissions￨L￨NNS￨O￨A per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- is￨L￨VBZ￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- βX￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Y￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- more￨L￨JJR￨O￨- general￨L￨JJ￨TITLE￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- Y￨U￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- well￨L￨RB￨O￨- explored￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- perspective￨L￨NN￨O￨- of￨L￨IN￨O￨- coalescent￨L￨JJ￨O￨A theory￨L￨NN￨O￨- .￨L￨.￨O￨- +Birth￨U￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- change￨L￨VBP￨O￨- dramatically￨L￨RB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- strictly￨L￨RB￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- population￨L￨NN￨O￨A size￨L￨NN￨O￨A .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- conducted￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- human￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- motivation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- polyparasitism￨L￨NN￨O￨- being￨L￨VBG￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- urgency￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- clinical￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A potentially￨L￨RB￨O￨- interacting￨L￨VBG￨O￨- with￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- emerging￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- interactions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- such￨L￨JJ￨O￨- common￨L￨JJ￨O￨- risk￨L￨NN￨O￨A factors￨L￨NNS￨O￨A ,￨L￨,￨O￨- some￨L￨DT￨O￨- have￨L￨VBP￨O￨- long￨L￨RB￨O￨- been￨L￨VBN￨O￨- recognised￨L￨VBN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- behaviours￨L￨NNS￨O￨- for￨L￨IN￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- socio-economic￨L￨JJ￨O￨- status￨L￨NN￨O￨- for￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- particularly￨L￨RB￨O￨- prevalent￨L￨JJ￨O￨- in￨L￨IN￨O￨- poor￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- helminth￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- age￨L￨NN￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- confounding￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- can￨L￨MD￨O￨- create￨L￨VB￨O￨- statistical￨L￨JJ￨O￨- associations￨L￨NNS￨O￨- between￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A even￨L￨RB￨O￨- if￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- true￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- alter￨L￨VB￨O￨- conclusions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- interspecific￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- another￨L￨DT￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- risk￨L￨NN￨O￨A factors￨L￨NNS￨O￨A into￨L￨IN￨O￨- account￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- them￨L￨PRP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- logistic￨L￨JJ￨O￨- regression￨L￨NN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- parasite￨L￨NN￨O￨- B￨U￨NN￨O￨- status￨L￨NN￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- a￨L￨DT￨O￨- predictor￨L￨NN￨O￨- of￨L￨IN￨O￨- parasite￨L￨NN￨O￨- A￨U￨NN￨O￨- status￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Cryptic￨U￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- asymptomatic￨L￨JJ￨O￨- or￨L￨CC￨O￨- undetectable￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- long-distance￨L￨JJ￨O￨- dispersal￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- fat-tailed￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- transmissible￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- pests￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- two￨L￨CD￨NUMBER￨- serious￨L￨JJ￨O￨- impediments￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- organisms￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- only￨L￨RB￨O￨- become￨L￨VBP￨O￨- apparent￨L￨JJ￨O￨- once￨L￨RB￨DATE￨- symptoms￨L￨NNS￨O￨A develop￨L￨VBP￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- time￨L￨NN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- grown￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- new￨L￨JJ￨O￨- ,￨L￨,￨O￨- sometimes￨L￨RB￨O￨- distant￨L￨JJ￨O￨- foci￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- established￨L￨VBN￨O￨- through￨L￨IN￨O￨- long-distance￨L￨NN￨O￨- dispersal￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Without￨U￨IN￨O￨- this￨L￨DT￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- or￨L￨CC￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- at￨L￨IN￨O￨- later￨L￨JJ￨O￨- time￨L￨NN￨O￨- t1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- restricted￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- control￨L￨NN￨O￨- area￨L￨NN￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- symptoms￨L￨NNS￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- misses￨L￨VBZ￨O￨- out￨L￨RP￨O￨- cryptic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- around￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- possibly￨L￨RB￨O￨- within￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- barrier￨L￨NN￨O￨- treatment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- total￨L￨JJ￨O￨- removal￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ahead￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- front￨L￨NN￨O￨- ,￨L￨,￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- core￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- fail￨L￨VB￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- although￨L￨IN￨O￨- it￨L￨PRP￨O￨- might￨L￨MD￨O￨- delay￨L￨VB￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- disperse￨L￨VB￨O￨- over￨L￨IN￨O￨- distances￨L￨NNS￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- width￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- barrier￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- a￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- t2￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cryptic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- symptomatic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- continued￨L￨VBN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- area￨L￨NN￨O￨A ,￨L￨,￨O￨- expanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- focus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- back￨L￨RB￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- area￨L￨NN￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- still￨L￨RB￨O￨- contains￨L￨VBZ￨O￨- non-infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- effort￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- -￨L￨:￨O￨- Exposed￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- latent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- Infective￨U￨JJ￨O￨- -￨L￨:￨O￨- Removed￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- staged￨L￨VBD￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- infective￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- additional￨L￨JJ￨O￨- states￨L￨NNS￨O￨- for￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- exposed￨L￨JJ￨O￨- stage￨L￨NN￨O￨- were￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- with￨L￨IN￨O￨- infectivity￨L￨NN￨O￨A 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- full￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- viral￨L￨JJ￨O￨- shedding￨L￨VBG￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- increases￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- day￨L￨NN￨DURATION￨- following￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- perform￨L￨VB￨O￨- contrafactual￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A burden￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- unmitigated￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- strategy￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- stratified￨L￨VBD￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- and￨L￨CC￨O￨- antivirals￨L￨NNS￨O￨- into￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- age￨L￨NN￨O￨A groups￨L￨NNS￨O￨A :￨L￨:￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 64￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- 65￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- accordance￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- ILI￨U￨NN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pandemic￨L￨NN￨O￨A was￨L￨VBD￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- pandemic￨L￨JJ￨O￨- where￨L￨WRB￨O￨- antivirals￨L￨NNS￨O￨- and￨L￨CC￨O￨- vaccines￨L￨NNS￨O￨- were￨L￨VBD￨O￨- available￨L￨JJ￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- interest￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- intervention￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- assessed￨L￨VBD￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- quantified￨L￨VBD￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- triple￨L￨JJ￨O￨- reassortant￨L￨NN￨O￨- H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- naïve￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- pig￨L￨NN￨O￨A populations￨L￨NNS￨O￨- by￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- Susceptible-Infectious-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- fitted￨L￨VBN￨O￨- on￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- run￨L￨VBN￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- replicates￨L￨VBZ￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- replicate￨L￨VBP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- non-vaccinated￨L￨JJ￨O￨- pig￨L￨NN￨O￨- was￨L￨VBD￨O￨- placed￨L￨VBN￨O￨- with￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- contact￨L￨NN￨O￨- pigs￨L￨NNS￨O￨A for￨L￨IN￨O￨- two￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- evaluated￨L￨VBD￨O￨- daily￨L￨RB￨SET￨- by￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- individual￨L￨JJ￨O￨- nasal￨L￨JJ￨O￨- swabs￨L￨NNS￨O￨- by￨L￨IN￨O￨- RT-PCR￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- statistically￨L￨RB￨O￨- significant￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- groups￨L￨NNS￨O￨- where￨L￨WRB￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 0.39-2.09￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- HE￨U￨PRP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- HO￨U￨NN￨O￨- groups￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- Ro￨U￨NN￨MISC￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- 10.66￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 6.57-16.46￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- NV￨U￨NNP￨STATE_OR_PROVINCE￨- pigs￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- <￨L￨JJR￨O￨- 0.05￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- statistically￨L￨RB￨O￨- significant￨L￨JJ￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- R￨U￨NN￨O￨- estimates￨L￨NNS￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- between￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- and￨L￨CC￨O￨- non-vaccinated￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- <￨L￨JJR￨O￨- 0.05￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Namely￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- with￨L￨IN￨O￨- differing￨L￨VBG￨O￨- propensities￨L￨NNS￨O￨- to￨L￨TO￨O￨- adopt￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- early￨L￨JJ￨O￨- versus￨L￨CC￨O￨- late￨L￨JJ￨O￨- adopters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- preference￨L￨NN￨O￨- for￨L￨IN￨O￨- friendship￨L￨NN￨O￨- with￨L￨IN￨O￨- others￨L￨NNS￨O￨- who￨L￨WP￨O￨- share￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- tastes￨L￨NNS￨O￨- and￨L￨CC￨O￨- geographic￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- crucial￨L￨JJ￨O￨- features￨L￨NNS￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- describe￨L￨VB￨O￨- micro￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨- level￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- macro￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- national￨L￨JJ￨O￨- level￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- adoption￨L￨NN￨O￨A trends￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- informed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- colloquially￨L￨RB￨O￨- referred￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- adoption￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- micro-blogging￨L￨NN￨O￨- platform￨L￨NN￨O￨- ,￨L￨,￨O￨- Twitter￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- accumulation￨L￨NN￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨- in￨L￨IN￨O￨- cities￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- three￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- innovations￨L￨NNS￨O￨- literature￨L￨NN￨O￨- has￨L￨VBZ￨O￨- had￨L￨VBN￨O￨- made￨L￨VBN￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- similar￨L￨JJ￨O￨- frameworks￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- Bass￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- adoption￨L￨NN￨O￨A of￨L￨IN￨O￨- technologies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- feature￨L￨VBP￨O￨- considerable￨L￨JJ￨O￨- cost￨L￨NN￨O￨- and￨L￨CC￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- update￨L￨VBP￨O￨- and￨L￨CC￨O￨- unify￨L￨VBP￨O￨- traditional￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- technology￨L￨NN￨O￨- adoption￨L￨NN￨O￨A to￨L￨TO￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- reflect￨L￨VB￨O￨- the￨L￨DT￨O￨- novel￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- environments￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- spreading￨L￨NN￨O￨- now￨L￨RB￨DATE￨- occurs￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- endogenous￨L￨JJ￨O￨- mass￨L￨NN￨O￨- media￨L￨NNS￨O￨- that￨L￨WDT￨O￨- responds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- adoption￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨- while￨L￨IN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- influencing￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- adopt￨L￨VB￨O￨- an￨L￨DT￨O￨- innovation￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- 's￨L￨POS￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨A number￨L￨NN￨O￨A ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- each￨L￨DT￨O￨- case￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- pre-existing￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- related￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨A number￨L￨NN￨O￨A ,￨L￨,￨O￨- ,￨L￨,￨O￨- pertains￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- some￨L￨DT￨O￨- proportion￨L￨NN￨O￨- are￨L￨VBP￨O￨- already￨L￨RB￨O￨- immune￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Health￨U￨NNP￨ORGANIZATION￨- Protection￨U￨NNP￨ORGANIZATION￨- Agency￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- HPA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- monitored￨L￨VBD￨O￨- case￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- published￨L￨VBD￨O￨- its￨L￨PRP$￨O￨- findings￨L￨NNS￨O￨- online￨L￨NN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- ‘￨L￨``￨O￨- Weekly￨U￨NNP￨SET￨- Pandemic￨U￨NNP￨MISC￨- Flu￨U￨NNP￨CAUSE_OF_DEATH￨- Media￨U￨NNP￨MISC￨- Updates￨U￨NNP￨MISC￨- ’￨L￨POS￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- ‘￨L￨``￨O￨- Weekly￨U￨NNP￨SET￨- National￨U￨NNP￨MISC￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- Reports￨U￨NNP￨MISC￨- ’￨L￨POS￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- amounts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- English￨U￨NNP￨NATIONALITY￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- much￨L￨RB￨O￨- lower￨L￨JJR￨O￨- figure￨L￨NN￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- even￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨A number￨L￨NN￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- published￨L￨VBN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- this￨L￨DT￨O￨- time￨L￨NN￨O￨- HPA￨U￨NN￨ORGANIZATION￨- 's￨L￨POS￨O￨- estimates￨L￨NNS￨O￨- totalled￨L￨VBD￨O￨- cases￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨A in￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- simplest￨L￨JJS￨O￨- way￨L￨NN￨O￨- possible￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- transported￨L￨VBN￨O￨- by￨L￨IN￨O￨- wind￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- farm￨L￨NN￨O￨A directly￨L￨RB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- uninfected￨L￨JJ￨O￨- farm￨L￨NN￨O￨- as￨L￨IN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- plume￨L￨NN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- FMDV￨U￨NN￨O￨- spread￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- wind-borne￨L￨JJ￨O￨- dispersal￨L￨NN￨O￨- and￨L￨CC￨O￨- deposition￨L￨NN￨O￨- of￨L￨IN￨O￨- farm￨L￨NN￨O￨A dust￨L￨NN￨O￨- contaminated￨L￨VBN￨O￨- with￨L￨IN￨O￨- HPAI￨U￨NN￨ORGANIZATION￨- .￨L￨.￨O￨- +Quantifying￨U￨VBG￨O￨- this￨L￨DT￨O￨- reduction￨L￨NN￨O￨- and￨L￨CC￨O￨- determining￨L￨VBG￨O￨- how￨L￨WRB￨O￨- it￨L￨PRP￨O￨- might￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- mitigated￨L￨VBN￨O￨- through￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- dispensing￨L￨VBG￨O￨- schemes￨L￨NNS￨O￨- motivated￨L￨VBD￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- effort￨L￨NN￨O￨- reported￨L￨VBD￨O￨- here.Seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- have￨L￨VBP￨O￨- historically￨L￨RB￨O￨- targeted￨L￨VBN￨O￨- those￨L￨DT￨O￨- at￨L￨IN￨O￨- greatest￨L￨JJS￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- severe￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- --￨L￨:￨O￨- notably￨L￨RB￨O￨- the￨L￨DT￨O￨- very￨L￨RB￨O￨- young￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- elderly￨L￨JJ￨O￨- and￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- ages￨L￨NNS￨O￨- with￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- medical￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- their￨L￨PRP$￨O￨- close￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- workers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Proposed￨U￨VBN￨O￨- explanations￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- apparently￨L￨RB￨O￨- reduced￨L￨VBN￨O￨- susceptibility￨L￨NN￨O￨- in￨L￨IN￨O￨- older￨L￨JJR￨O￨A adults￨L￨NNS￨O￨- include￨L￨VBP￨O￨- pre-existing￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- prior￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- related￨L￨JJ￨O￨- H1N1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- accumulated￨L￨VBN￨O￨- cross-protection￨L￨NN￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- human￨L￨JJ￨O￨- H1N1￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- lifespan￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and/or￨L￨CC￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- younger￨L￨JJR￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- highly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- pH1N1￨L￨NN￨O￨- early￨L￨RB￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- than￨L￨IN￨O￨- older￨L￨JJR￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Regardless￨U￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reasons￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- vulnerability￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- observation￨L￨NN￨O￨- has￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨- and￨L￨CC￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- mitigation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- pH1N1￨L￨NN￨O￨- and￨L￨CC￨O￨- future￨L￨JJ￨DATE￨- pandemic￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- viruses.Vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- measure￨L￨NN￨O￨- and￨L￨CC￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- '￨L￨POS￨O￨- pandemic￨L￨JJ￨O￨- preparedness￨L￨NN￨O￨- plans￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- pandemic￨L￨JJ￨O￨A H1N1￨U￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Vancouver￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Canada￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- timing￨L￨NN￨O￨- is￨L￨VBZ￨O￨- everythingJessica￨L￨NN￨O￨- M￨U￨NN￨O￨- Conway1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ashleigh￨U￨NNP￨PERSON￨- R￨U￨NNP￨O￨- Tuite3￨U￨NN￨O￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- N￨U￨NNP￨PERSON￨- Fisman3￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Nathaniel￨U￨NNP￨PERSON￨- Hupert4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Rafael￨U￨NNP￨PERSON￨- Meza1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Bahman￨U￨NNP￨PERSON￨- Davoudi1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Krista￨U￨NNP￨PERSON￨- English1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- van￨L￨NN￨O￨- den￨L￨NN￨O￨- Driessche6￨U￨NN￨O￨- ,￨L￨,￨O￨- Fred￨U￨NNP￨PERSON￨- Brauer2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Junling￨U￨NN￨O￨- Ma6￨U￨NN￨O￨- ,￨L￨,￨O￨- Lauren￨U￨NNP￨PERSON￨- Ancel￨U￨NNP￨PERSON￨- Meyers7￨U￨NNP￨O￨- ,￨L￨,￨O￨- Marek￨U￨NN￨PERSON￨- Smieja8￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Amy￨U￨NNP￨PERSON￨- Greer3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Danuta￨U￨NNP￨PERSON￨- M￨U￨NNP￨O￨- Skowronski10￨U￨NN￨O￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- L￨U￨NNP￨PERSON￨- Buckeridge11￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jeffrey￨U￨NNP￨PERSON￨- C￨U￨NNP￨O￨- Kwong3￨U￨NN￨O￨- ,￨L￨,￨O￨- 13￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jianhong￨U￨NNP￨PERSON￨- Wu14￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Seyed￨U￨NNP￨PERSON￨- M￨U￨NNP￨PERSON￨- Moghadas14￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Daniel￨U￨NNP￨PERSON￨- Coombs2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Robert￨U￨NNP￨PERSON￨- C￨U￨NNP￨O￨- Brunham1￨U￨NN￨O￨- and￨L￨CC￨O￨- Babak￨U￨NNP￨PERSON￨- Pourbohloul1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 11:932￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Conway￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Much￨U￨JJ￨O￨- remains￨L￨NNS￨O￨- unknown￨L￨JJ￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- prioritization￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- pH1N1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 2009￨L￨CD￨DATE￨- virus￨L￨NN￨O￨- on￨L￨IN￨O￨- health￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨- that￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- schoolchildren￨L￨NNS￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- younger￨L￨JJR￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- are￨L￨VBP￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disproportionate￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- targeting￨L￨VBG￨O￨- these￨L￨DT￨O￨- groups￨L￨NNS￨O￨- would￨L￨MD￨O￨- indirectly￨L￨RB￨O￨- protect￨L￨VB￨O￨- at-risk￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Characterizing￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- interface￨L￨NN￨O￨- between￨L￨IN￨O￨- wild￨L￨JJ￨O￨A ducks￨L￨NNS￨O￨- and￨L￨CC￨O￨- poultry￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨- pathogensJulien￨L￨NN￨O￨- Cappelle1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Nicolas￨U￨NNP￨PERSON￨- Gaidet1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Samuel￨U￨NNP￨PERSON￨- A￨U￨NNP￨O￨- Iverson2￨U￨NN￨O￨- ,￨L￨,￨O￨- John￨U￨NNP￨PERSON￨- Y￨U￨NN￨PERSON￨- Takekawa2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Scott￨U￨NNP￨PERSON￨- H￨U￨NNP￨PERSON￨- Newman3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Bouba￨U￨NNP￨PERSON￨- Fofana4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Marius￨U￨NNP￨PERSON￨- Gilbert6￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 10:60￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Cappelle￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2011Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Characterizing￨U￨VBG￨O￨- the￨L￨DT￨O￨- interface￨L￨NN￨O￨- between￨L￨IN￨O￨- wild￨L￨JJ￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- animal￨L￨NN￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- recognized￨L￨VBN￨O￨- as￨L￨IN￨O￨- essential￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- EIDs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- integrated￨L￨VBD￨O￨- satellite￨L￨NN￨O￨- telemetry￨L￨NN￨O￨- ,￨L￨,￨O￨- remote￨L￨JJ￨O￨- sensing￨L￨VBG￨O￨- and￨L￨CC￨O￨- ground-based￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- indirect￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- wild￨L￨JJ￨O￨A and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- that￨L￨IN￨O￨- avian￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- Newcastle￨U￨JJ￨ORGANIZATION￨- viruses￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- transmitted￨L￨VBN￨O￨- between￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- to￨L￨TO￨O￨- poultry￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- between￨L￨IN￨O￨- wild￨L￨JJ￨O￨A and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- EIDs￨U￨NNS￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- modelled￨L￨VBD￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨A ducks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- 250-meter￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- and￨L￨CC￨O￨- 8-days￨L￨JJ￨DURATION￨- temporal￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- remotely-sensed￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- indicators￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Maxent￨U￨JJ￨MISC￨- niche￨L￨NN￨O￨- modelling￨L￨NN￨O￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- potential￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- between￨L￨IN￨O￨- wild￨L￨JJ￨O￨A ducks￨L￨NNS￨O￨- and￨L￨CC￨O￨- poultry￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- invasion￨L￨NN￨O￨A is￨L￨VBZ￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- successful￨L￨JJ￨O￨- in￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- totally￨L￨RB￨O￨- fail￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- observing￨L￨VBG￨O￨- a￨L￨DT￨O￨- failed￨L￨VBN￨O￨- invasion￨L￨NN￨O￨- in￨L￨IN￨O￨- nature￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- imply￨L￨VB￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- invasion￨L￨NN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- van￨L￨NN￨O￨- Kampen￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- system-size￨L￨JJ￨O￨- expansion￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- individual-based￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- stochastic￨L￨JJ￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- helped￨L￨VBN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨A amplification￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- early￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨A compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- recent￨L￨JJ￨O￨- spatially￨L￨RB￨O￨- structured￨L￨VBN￨O￨- stochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- impacted￨L￨VBN￨O￨- both￨L￨CC￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- planning￨L￨NN￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- both￨L￨DT￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- hotspot￨L￨NN￨O￨- radius￨L￨NN￨O￨A of￨L￨IN￨O￨- attraction￨L￨NN￨O￨- ,￨L￨,￨O￨- identified￨L￨VBD￨O￨- the￨L￨DT￨O￨- groups￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- explored￨L￨VBD￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- hotspots￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- investigate￨L￨VB￨O￨- these￨L￨DT￨O￨- transmission￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- exploring￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- closed￨L￨JJ￨O￨- population￨L￨NN￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- territorial￨L￨JJ￨O￨- social￨L￨JJ￨O￨- groups￨L￨NNS￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- hotspots￨L￨NNS￨O￨- influence￨L￨VBP￨O￨- group￨L￨NN￨O￨- movement￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- where￨L￨WRB￨O￨- direct￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- hotspot￨L￨NN￨O￨- itself￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- negligible￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- radius￨L￨NN￨O￨A of￨L￨IN￨O￨- attraction￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- was￨L￨VBD￨O￨- then￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- under￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- scenarios￨L￨NNS￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- groups￨L￨NNS￨O￨- including￨L￨VBG￨O￨- sick￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- travel￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- hotspot￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- these￨L￨DT￨O￨- groups￨L￨NNS￨O￨- still￨L￨RB￨O￨- travel￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- hotspot￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- groups￨L￨NNS￨O￨- gain￨L￨VB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- benefit￨L￨NN￨O￨- from￨L￨IN￨O￨- visiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- hotspot￨L￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- travel￨L￨NN￨O￨- cost￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- P￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- visit￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- eight￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- directly￨L￨RB￨O￨- neighbouring￨L￨VBG￨O￨- the￨L￨DT￨O￨- hotspot￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- hotspot￨L￨NN￨O￨- radius￨L￨NN￨O￨A of￨L￨IN￨O￨- attraction￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- between-group￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- both￨L￨DT￨O￨- between￨L￨IN￨O￨- groups￨L￨NNS￨O￨A having￨L￨VBG￨O￨- neighbouring￨L￨JJ￨O￨- territories￨L￨NNS￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- groups￨L￨NNS￨O￨- travelling￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- hotspot￨L￨NN￨O￨- and￨L￨CC￨O￨- groups￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- territories￨L￨NNS￨O￨- are￨L￨VBP￨O￨- crossed￨L￨VBN￨O￨- en￨L￨IN￨O￨- route￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨A presents￨L￨VBZ￨O￨A a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- throughout￨L￨IN￨O￨- a￨L￨DT￨O￨- realistic￨L￨JJ￨O￨- interconnection￨L￨NN￨O￨- network￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- actual￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- extract￨L￨VBP￨O￨- from￨L￨IN￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Lastly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- and￨L￨CC￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- adopting￨L￨VBG￨O￨- several￨L￨JJ￨O￨- different￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- policies￨L￨NNS￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- individual￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨A -￨L￨:￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- age-while￨L￨JJ￨O￨- others￨L￨NNS￨O￨- targeting￨L￨VBG￨O￨- the￨L￨DT￨O￨- super-connectors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- additionally￨L￨RB￨O￨- allow￨L￨VBP￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨A of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- customizing￨L￨VBG￨O￨- his￨L￨PRP$￨O￨- daily￨L￨JJ￨SET￨- interaction￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- by￨L￨IN￨O￨- making￨L￨VBG￨O￨- them￨L￨PRP￨O￨- time-dependent￨L￨JJ￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- purpose￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A spreads￨L￨VBZ￨O￨A depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Classical￨U￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- –￨L￨:￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- or￨L￨CC￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- interacts￨L￨VBZ￨O￨- with45￨L￨NN￨O￨- ,￨L￨,￨O￨- betweenness￨L￨NN￨O￨- centrality8￨L￨NN￨O￨- counting￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- shortest￨L￨JJS￨O￨- paths￨L￨NNS￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- eigenvector￨L￨NN￨O￨- centrality9￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- idea￨L￨NN￨O￨- that￨L￨IN￨O￨- relations￨L￨NNS￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- influential￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- confer￨L￨VBP￨O￨- greater￨L￨JJR￨O￨- importance￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- k-shell￨L￨NN￨O￨- decomposition10￨L￨NN￨O￨- that￨L￨WDT￨O￨- correlates￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- supercritical￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- originating￨L￨VBG￨O￨- in￨L￨IN￨O￨- specific￨L￨JJ￨O￨- nodes111213￨L￨NN￨O￨- –￨L￨:￨O￨- rely￨L￨VBP￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- an￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- indirectly￨L￨RB￨O￨- associated￨L￨VBN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- and￨L￨CC￨O￨- rigorous￨L￨JJ￨O￨- framework￨L￨NN￨O￨- where￨L￨WRB￨O￨- dynamical￨L￨JJ￨O￨- influence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨- both￨L￨CC￨O￨- on￨L￨IN￨O￨- directed￨L￨VBN￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- undirected￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- applies￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- families￨L￨NNS￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- models￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Ising￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- diffusive￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- voter￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- or￨L￨CC￨O￨- phase￨L￨NN￨O￨- coupled￨L￨VBN￨O￨- oscillators￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- influence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- how￨L￨WRB￨O￨- strongly￨L￨RB￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- 's￨L￨POS￨O￨- dynamical￨L￨JJ￨O￨- state￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- collective￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- explicitly￨L￨RB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- respect￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Laplacian-based￨U￨JJ￨MISC￨- centrality￨L￨NN￨O￨A measure141516￨L￨NN￨O￨- ,￨L￨,￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- PageRank17￨U￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- recently￨L￨RB￨DATE￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- specific￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Eimeria￨U￨FW￨O￨- stiedae￨L￨FW￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- causative￨L￨JJ￨O￨- agent￨L￨NN￨O￨- of￨L￨IN￨O￨- hepatic￨L￨JJ￨O￨- coccidiosis￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨A rabbits￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- severe￨L￨JJ￨O￨- hepatic￨L￨JJ￨O￨- injury￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- in￨L￨IN￨O￨- juveniles￨L￨NNS￨O￨- and￨L￨CC￨O￨- neonates￨L￨NNS￨O￨- .￨L￨.￨O￨- +F.￨U￨NNP￨O￨- tularensis￨L￨NN￨O￨- causes￨L￨VBZ￨O￨- serious￨L￨JJ￨O￨- septicemia￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- wild￨L￨JJ￨O￨A rodents￨L￨NNS￨O￨- and￨L￨CC￨O￨- lagomorphs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- rabbits￨L￨NNS￨O￨- and￨L￨CC￨O￨- hares￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- potentially￨L￨RB￨O￨- fatal￨L￨JJ￨O￨- ,￨L￨,￨O￨- multisystemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- no￨L￨DT￨O￨- gross￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- tularemia￨L￨NN￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- specimen￨L￨NN￨O￨- was￨L￨VBD￨O￨- treated￨L￨VBN￨O￨- as￨L￨IN￨O￨- potentially￨L￨RB￨O￨A infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- tularemia￨L￨NN￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- veterinarian￨L￨NN￨TITLE￨- requested￨L￨VBD￨O￨- F.￨U￨NNP￨O￨- +We￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- tularemia￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- rabbit￨L￨NN￨O￨- co-infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- E.￨U￨NNP￨O￨- stiedae￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- gross￨L￨JJ￨O￨- lesions￨L￨NNS￨O￨- of￨L￨IN￨O￨- hepatic￨L￨JJ￨O￨- coccidiosis￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- overshadowed￨L￨VBD￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- subtle￨L￨JJ￨O￨- tularemia￨L￨NN￨O￨- lesions￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨A structure￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- phylogenetic￨L￨JJ￨O￨- tree￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- perform￨L￨VBP￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- for￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- Erdös-Rényi￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- ER￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- Barabási-Albert￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- BA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- Watts-Strogatz￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- WS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- rewiring￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Methods￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- non-random￨L￨JJ￨O￨- mixing￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- contact￨L￨NN￨O￨A structure￨L￨NN￨O￨A are￨L￨VBP￨O￨- increasingly￨L￨RB￨O￨- being￨L￨VBG￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- populations￨L￨NNS￨O￨- spreading￨L￨VBG￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- various￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- phylogenetic￨L￨JJ￨O￨A trees￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- important￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- requirements￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- depend￨L￨VB￨O￨- sensitively￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A structure￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- results￨L￨NNS￨O￨- were￨L￨VBD￨O￨- published￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- POLYMOD￨U￨NN￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- survey￨L￨NN￨O￨- involving￨L￨VBG￨O￨- participants￨L￨NNS￨O￨- in￨L￨IN￨O￨- 8￨L￨CD￨NUMBER￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- described￨L￨VBD￨O￨- patterns￨L￨NNS￨O￨A of￨L￨IN￨O￨- social￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- tendency￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- mix￨L￨VB￨O￨- with￨L￨IN￨O￨- others￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- were￨L￨VBD￨O￨- between￨L￨IN￨O￨- children￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A terms￨L￨NNS￨O￨- and￨L￨CC￨O￨- holidays￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- school-age￨L￨JJ￨O￨- children￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- day-to-day￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- population-level￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- events￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- school￨L￨NN￨O￨A holidays￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- POLYMOD￨U￨NN￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- school￨L￨NN￨O￨A holidays￨L￨NNS￨O￨- ,￨L￨,￨O￨- demonstrating￨L￨VBG￨O￨- significant￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- during￨L￨IN￨O￨- holiday￨L￨NN￨O￨- periods￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- close-contact￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- explaining￨L￨VBG￨O￨- observed￨L￨VBN￨O￨- patterns￨L￨NNS￨O￨A of￨L￨IN￨O￨- incidence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- against￨L￨IN￨O￨- HPV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- represents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- decrease￨L￨VB￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- among￨L￨IN￨O￨- young￨L￨JJ￨O￨- women￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- cervical￨L￨JJ￨O￨- cancers￨L￨NNS￨O￨- usually￨L￨RB￨O￨- occur￨L￨VBP￨O￨- 15￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- HPV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- useful￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- an￨L￨DT￨O￨- expected￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- prophylactic￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- against￨L￨IN￨O￨- HPV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- France￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- highly￨L￨RB￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- women￨L￨NNS￨O￨A who￨L￨WP￨O￨- have￨L￨VBP￨O￨- never￨L￨RB￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- HPV￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- which￨L￨WDT￨O￨- matched￨L￨VBD￨O￨- HPV￨U￨NN￨O￨- 16/18￨L￨CD￨NUMBER￨- prevalence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- age-specific￨L￨JJ￨O￨- incidences￨L￨NNS￨O￨- of￨L￨IN￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A NumericCitation￨U￨NN￨O￨- was￨L￨VBD￨O￨- selected￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- French￨U￨JJ￨NATIONALITY￨- women￨L￨NNS￨O￨- .￨L￨.￨O￨- +That￨U￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- AR￨U￨NN￨STATE_OR_PROVINCE￨- is￨L￨VBZ￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- individual￨L￨JJ￨O￨- antibiotic￨L￨JJ￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- veterinary￨L￨JJ￨O￨- medicine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- programmes￨L￨NNS￨O￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- limiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A often￨L￨RB￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- restricting￨L￨VBG￨O￨- antibiotic￨L￨JJ￨O￨- use￨L￨NN￨O￨- and/or￨L￨CC￨O￨- choosing￨L￨VBG￨O￨- therapeutic￨L￨JJ￨O￨- options￨L￨NNS￨O￨- that￨L￨WDT￨O￨- minimize￨L￨VBP￨O￨- selection￨L￨NN￨O￨- for￨L￨IN￨O￨- resistance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A ,￨L￨,￨O￨- extending￨L￨VBG￨O￨- simple￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- reflect￨L￨VB￨O￨- competition￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- simple￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- colonization￨L￨NN￨O￨- inhibition￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- complex￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- resistance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- amplification￨L￨NN￨O￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- overgrowth￨L￨NN￨O￨- following￨L￨VBG￨O￨- antibiotic￨L￨JJ￨O￨- use￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- antibiotic￨L￨JJ￨O￨- use￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- AR￨U￨NN￨STATE_OR_PROVINCE￨- spread￨L￨NN￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- unresolved￨L￨JJ￨O￨- question￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- broader￨L￨JJR￨O￨- ecological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A among￨L￨IN￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relative￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- different￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- AR￨U￨NN￨STATE_OR_PROVINCE￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- across￨L￨IN￨O￨- communities￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A in￨L￨IN￨O￨- community￨L￨NN￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Studying￨U￨VBG￨O￨- population-level￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- shifts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- emphasis￨L￨NN￨O￨- from￨L￨IN￨O￨- individual￨L￨JJ￨O￨- use￨L￨NN￨O￨- to￨L￨TO￨O￨- overall￨L￨JJ￨O￨- antibiotic￨L￨JJ￨O￨- use￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- carry￨L￨VBP￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Sensitivity￨U￨NN￨O￨- analyses￨L￨NNS￨O￨- revealed￨L￨VBD￨O￨- that￨L￨IN￨O￨- herd￨L￨NN￨O￨- density￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- best￨L￨JJS￨O￨- estimate￨L￨NN￨O￨- 1-3￨L￨CD￨NUMBER￨- pigs￨L￨NNS￨O￨- km-2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- daily￨L￨JJ￨SET￨- herd￨L￨NN￨O￨- movement￨L￨NN￨O￨- distances￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- best￨L￨JJS￨O￨- estimate￨L￨NN￨O￨- approximately￨L￨RB￨O￨- 1￨L￨CD￨NUMBER￨- km￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- herds￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- best￨L￨JJS￨O￨- estimate￨L￨NN￨O￨- 0.75￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- related￨L￨JJ￨O￨- herd￨L￨NN￨O￨- mortality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- best￨L￨JJS￨O￨- estimate￨L￨NN￨O￨- 42￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- highly￨L￨RB￨O￨- influential￨L￨JJ￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- but￨L￨CC￨O￨- that￨L￨IN￨O￨- extraordinary￨L￨JJ￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- yearly￨L￨JJ￨SET￨- home￨L￨NN￨O￨- range￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pig￨L￨NN￨O￨A herd￨L￨NN￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- susceptible-exposed-infected-recovered￨L￨JJ￨O￨- process￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- simulates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- classical￨L￨JJ￨O￨- swine￨L￨NNS￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- documented￨L￨VBN￨O￨- ,￨L￨,￨O￨- large￨L￨JJ￨O￨- and￨L￨CC￨O￨- free￨L￨JJ￨O￨- living￨L￨NN￨O￨- wild￨L￨JJ￨O￨- pig￨L￨NN￨O￨A population￨L￨NN￨O￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- incursion￨L￨NN￨O￨- .￨L￨.￨O￨- +CSF￨U￨NN￨O￨- spread￨L￨NN￨O￨- at￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 9￨L￨CD￨NUMBER￨- km2￨L￨NN￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- <￨L￨JJR￨O￨- 2￨L￨CD￨NUMBER￨- herds￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- wave￨L￨NN￨O￨- along￨L￨IN￨O￨- contiguous￨L￨JJ￨O￨- habitat￨L￨NN￨O￨- for￨L￨IN￨O￨- several￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- before￨L￨IN￨O￨- dying￨L￨VBG￨O￨- out￨L￨RP￨O￨- (￨L￨-LRB-￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- arrived￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- contiguous￨L￨JJ￨O￨- sub-population￨L￨NN￨O￨- or￨L￨CC￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- density￨L￨NN￨O￨- wild￨L￨JJ￨O￨- pig￨L￨NN￨O￨A area￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Published￨U￨VBN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- wild￨L￨JJ￨O￨- pig￨L￨NN￨O￨A ecology￨L￨NN￨O￨- from￨L￨IN￨O￨- Australia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- international￨L￨JJ￨O￨- Classical￨U￨JJ￨MISC￨- Swine￨U￨NN￨MISC￨- Fever￨U￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- parameterise￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- AB￨U￨NNP￨STATE_OR_PROVINCE￨- methodology￨L￨NN￨O￨- ,￨L￨,￨O￨- individual￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- describing￨L￨VBG￨O￨- in-host￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasite￨L￨NN￨O￨A with￨L￨IN￨O￨- target￨L￨NN￨O￨- cells￨L￨NNS￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible/Infected/Removed￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- methodology￨L￨NN￨O￨A and￨L￨CC￨O￨- sometimes￨L￨RB￨O￨- aim￨L￨NN￨O￨- at￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- paper￨L￨NN￨O￨- describing￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- south-east￨L￨JJ￨O￨- Asia￨U￨NNP￨CITY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Mathematically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- and￨L￨CC￨O￨- run￨L￨VBN￨O￨- in￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- steps￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- 48￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- parasite￨L￨NN￨O￨A replication￨L￨NN￨O￨- cycle￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- its￨L￨PRP$￨O￨- secondary￨L￨JJ￨O￨- form￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- generally￨L￨RB￨O￨- involves￨L￨VBZ￨O￨- LIC￨U￨NN￨ORGANIZATION￨- values￨L￨NNS￨O￨- even￨L￨RB￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- those￨L￨DT￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- one.This￨L￨NN￨O￨- is￨L￨VBZ￨O￨- currently￨L￨RB￨DATE￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- field￨L￨NN￨O￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- primary￨L￨JJ￨O￨- haemochromatosis￨L￨NN￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- confirmed￨L￨VBN￨O￨- that￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- mutations￨L￨NNS￨O￨- ,￨L￨,￨O￨- widely￨L￨RB￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- conclusive￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- definitive￨L￨JJ￨O￨- diagnosis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- form￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- iron￨L￨NN￨O￨- chelating￨L￨NN￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- changing￨L￨VBG￨O￨- the￨L￨DT￨O￨- clinical￨L￨JJ￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease.Chemical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- liver￨L￨NN￨O￨A biopsy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- gold￨L￨JJ￨O￨- standard￨L￨NN￨O￨- ”￨L￨''￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- measurement￨L￨NN￨O￨- of￨L￨IN￨O￨- LIC￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- patients￨L￨NNS￨O￨- are￨L￨VBP￨O￨- resistant￨L￨JJ￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- invasive￨L￨JJ￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- moreover￨L￨RB￨O￨- ,￨L￨,￨O￨- results￨L￨VBZ￨O￨- vary￨L￨VBP￨O￨- widely￨L￨RB￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- coefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- quantification￨L￨NN￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- liver￨L￨NN￨O￨- biopsy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- from￨L￨IN￨O￨- 19￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- liver￨L￨NN￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- 40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- cirrhosis￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Various￨U￨JJ￨O￨- different￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- relaxometry￨L￨NN￨O￨- methods￨L￨NNS￨O￨- measuring￨L￨VBG￨O￨- absolute￨L￨JJ￨O￨- T2￨U￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- relaxometry￨L￨NN￨O￨- methods￨L￨NNS￨O￨- measuring￨L￨VBG￨O￨- T2￨U￨NN￨O￨- *￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- an￨L￨DT￨O￨- absolute￨L￨JJ￨O￨- value￨L￨NN￨O￨- but￨L￨CC￨O￨- measured￨L￨VBN￨O￨- with￨L￨IN￨O￨- gradient￨L￨NN￨O￨- echo￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- GRE￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- sequences￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- methods￨L￨NNS￨O￨- measuring￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- liver￨L￨NN￨O￨A and￨L￨CC￨O￨- other￨L￨JJ￨O￨- tissues￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- iron￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- generally￨L￨RB￨O￨- deposited￨L￨VBN￨O￨- ,￨L￨,￨O￨- usually￨L￨RB￨O￨- paraspinal￨L￨JJ￨O￨- muscles.For￨L￨NN￨O￨- MRI￨U￨NNP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- respond￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- challenges￨L￨NNS￨O￨- in￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- practice￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- there￨L￨RB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- universally￨L￨RB￨O￨- accepted￨L￨VBN￨O￨- MRI￨U￨NNP￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- accurate￨L￨JJ￨O￨- ,￨L￨,￨O￨- reproducible￨L￨JJ￨O￨- ,￨L￨,￨O￨- standardised￨L￨JJ￨O￨- and￨L￨CC￨O￨- widely￨L￨RB￨O￨- available.T2￨L￨NN￨O￨- relaxometry￨L￨NN￨O￨- methodsAssessment￨L￨NN￨O￨- of￨L￨IN￨O￨- iron￨L￨NN￨O￨- overload￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- decreases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- T2￨U￨NN￨O￨- relaxation￨L￨NN￨O￨- times￨L￨NNS￨O￨- induced￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- liver￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- paramagnetic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- iron￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- iron￨L￨NN￨O￨- overload￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- need￨L￨VBP￨O￨- a￨L￨DT￨O￨- reproducible￨L￨JJ￨O￨- ,￨L￨,￨O￨- standardised￨L￨JJ￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- can￨L￨MD￨O￨- easily￨L￨RB￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- ,￨L￨,￨O￨- widely￨L￨RB￨O￨- available.MethodsThis￨L￨JJ￨O￨- article￨L￨NN￨O￨- discusses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- MRI￨U￨NNP￨O￨- techniques￨L￨NNS￨O￨- and￨L￨CC￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- liver￨L￨NN￨O￨A iron￨L￨NN￨O￨- concentration￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- currently￨L￨RB￨DATE￨- available￨L￨JJ￨O￨- and￨L￨CC￨O￨- envisaged￨L￨VBD￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨DATE￨- near￨L￨JJ￨DATE￨- future￨L￨NN￨DATE￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- realistic￨L￨JJ￨O￨- perspective.ResultsT2￨L￨NN￨O￨- relaxometry￨L￨NN￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- than￨L￨IN￨O￨- signal￨L￨NN￨O￨- intensity￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- reproducible￨L￨JJ￨O￨- but￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- standardised￨L￨JJ￨O￨- or￨L￨CC￨O￨- widely￨L￨RB￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +d￨L￨NN￨O￨- Liver￨U￨NN￨O￨- with￨L￨IN￨O￨- very￨L￨RB￨O￨- high￨L￨JJ￨O￨- iron￨L￨NN￨O￨- overload￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- T2￨U￨NN￨O￨- *￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ms￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- Relaxometry￨U￨NN￨O￨- methods￨L￨NNS￨O￨- calculate￨L￨VBP￨O￨- T2￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- T2￨U￨NN￨O￨- *￨L￨SYM￨O￨- NumericCitation￨U￨NN￨O￨- by￨L￨IN￨O￨- fitting￨L￨NN￨O￨- a￨L￨DT￨O￨- decay￨L￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- signal￨L￨NN￨O￨- intensity￨L￨NN￨O￨- at￨L￨IN￨O￨- various￨L￨JJ￨O￨- echo￨L￨VBP￨O￨- times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- TEs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +b￨L￨NN￨O￨- Patient￨U￨NN￨O￨- with￨L￨IN￨O￨- iron￨L￨NN￨O￨- overload￨L￨NN￨O￨- with￨L￨IN￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- signal￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- echoes￨L￨NNS￨O￨- ;￨L￨:￨O￨- T2￨U￨NN￨O￨- *￨L￨NN￨O￨- =￨L￨JJ￨O￨- 2.1￨L￨CD￨NUMBER￨- ms￨L￨NNS￨O￨- Many￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- T2￨U￨NN￨O￨- and￨L￨CC￨O￨- T2￨U￨NN￨O￨- *￨L￨SYM￨O￨- values￨L￨NNS￨O￨- with￨L￨IN￨O￨- LIC￨U￨NN￨ORGANIZATION￨- measured￨L￨VBN￨O￨- in￨L￨IN￨O￨- liver￨L￨NN￨O￨A biopsies￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- LIC￨U￨NN￨ORGANIZATION￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- highly￨L￨RB￨O￨A connected￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- the￨L￨DT￨O￨- celebrated￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- originally￨L￨RB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- "￨L￨``￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- non-immune￨L￨JJ￨O￨- homogenously￨L￨RB￨O￨- mixing￨L￨VBG￨O￨- population￨L￨NN￨O￨- where￨L￨WRB￨O￨- no￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- taken￨L￨VBN￨O￨- "￨L￨''￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- longer￨L￨JJR￨O￨- predicts￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- computer￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨A with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- superimposed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- distinguish￨L￨VB￨O￨- between￨L￨IN￨O￨- close￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- comprising￨L￨VBG￨O￨- family￨L￨NN￨O￨- members￨L￨NNS￨O￨- and￨L￨CC￨O￨- close￨L￨JJ￨O￨- friends￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- easily￨L￨RB￨O￨- be￨L￨VB￨O￨- traced￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- casual￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- who￨L￨WP￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- worrisome￨L￨JJ￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- placed￨L￨VBN￨O￨- under￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Finding￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- removing￨L￨VBG￨O￨- highly￨L￨RB￨O￨A connected￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- using￨L￨VBG￨O￨- suboptimal￨L￨JJ￨O￨- vaccinesBeatriz￨L￨NN￨O￨- Vidondo1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Markus￨U￨NNP￨PERSON￨- Schwehm2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Andrea￨U￨NNP￨PERSON￨- Bühlmann1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Martin￨U￨NNP￨PERSON￨- Eichner3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 12:51￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Vidondo￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Social￨U￨NNP￨MISC￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- highly￨L￨RB￨O￨- skewed￨L￨JJ￨O￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vast￨L￨JJ￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- has￨L￨VBZ￨O￨- only￨L￨RB￨O￨- few￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- whereas￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- minority￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +And￨U￨CC￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- lessons￨L￨NNS￨O￨- draw￨L￨VBP￨O￨- on￨L￨IN￨O￨- skills￨L￨NNS￨O￨- and￨L￨CC￨O￨- concepts￨L￨NNS￨O￨- from￨L￨IN￨O￨- many￨L￨JJ￨O￨- fields￨L￨NNS￨O￨A in￨L￨IN￨O￨- biology￨L￨NN￨O￨- —￨L￨:￨O￨- from￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- biology￨L￨NN￨O￨- ,￨L￨,￨O￨- evolutionary￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- pathogen￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ecology￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- bioinformatics￨L￨NNS￨O￨- ,￨L￨,￨O￨- computational￨L￨JJ￨O￨- biology￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- statistics￨L￨NNS￨O￨- —￨L￨:￨O￨- this￨L￨DT￨O￨- exercise￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- array￨L￨NN￨O￨- of￨L￨IN￨O￨- life￨L￨NN￨O￨- sciences￨L￨NNS￨O￨- courses￨L￨NNS￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- the￨L￨DT￨O￨- exercise￨L￨NN￨O￨- ,￨L￨,￨O￨- dynamical￨L￨JJ￨O￨- epidemiologists￨L￨NNS￨O￨A developed￨L￨VBD￨O￨- empirical￨L￨JJ￨O￨- skills￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- study￨L￨NN￨O￨- design￨L￨NN￨O￨- and￨L￨CC￨O￨- learned￨L￨VBD￨O￨- concepts￨L￨NNS￨O￨- of￨L￨IN￨O￨- bias￨L￨NN￨O￨- while￨L￨IN￨O￨- classical￨L￨JJ￨O￨- epidemiologists￨L￨NNS￨O￨- were￨L￨VBD￨O￨- trained￨L￨VBN￨O￨- in￨L￨IN￨O￨- systems￨L￨NNS￨O￨- thinking￨L￨VBG￨O￨- and￨L￨CC￨O￨- began￨L￨VBD￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- as￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- hands-on￨L￨JJ￨O￨- ,￨L￨,￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- real-time￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- course￨L￨NN￨O￨- participants￨L￨NNS￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- realistic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- reporting￨L￨NN￨O￨- ,￨L￨,￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- and￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- ,￨L￨,￨O￨- stemming￨L￨VBG￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- traditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- pedagogical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- bridges￨L￨VBZ￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- distinction￨L￨NN￨O￨- between￨L￨IN￨O￨- classical￨L￨JJ￨O￨A and￨L￨CC￨O￨- dynamical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- at￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- educational￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- high￨L￨JJ￨O￨- school￨L￨NN￨O￨- to￨L￨TO￨O￨- graduate￨L￨VB￨O￨- level￨L￨NN￨O￨- courses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Modern￨U￨NNP￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- builds￨L￨VBZ￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- independently￨L￨RB￨O￨- developed￨L￨VBN￨O￨- fields￨L￨NNS￨O￨A :￨L￨:￨O￨- classical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +Active￨U￨JJ￨O￨- stimulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- low-level￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- result￨L￨VB￨O￨- from￨L￨IN￨O￨- social￨L￨JJ￨O￨- transfer￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨A individual￨L￨NN￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- nestmates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- suggested￨L￨VBN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- occurring￨L￨VBG￨O￨- during￨L￨IN￨O￨- “￨L￨``￨O￨- normal￨L￨JJ￨O￨- ”￨L￨''￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- byproduct￨L￨NN￨O￨- of￨L￨IN￨O￨- collective￨L￨JJ￨O￨- sanitary￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- allogrooming￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- individual￨L￨NN￨O￨- by￨L￨IN￨O￨- its￨L￨PRP$￨O￨- nestmates￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- described￨L￨VBN￨O￨- that￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- exposed￨L￨VBN￨O￨A to￨L￨TO￨O￨- fungal￨L￨JJ￨O￨- conidia￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- conidiospores￨L￨NNS￨O￨- ;￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- nestmate￨L￨NN￨O￨- ants￨L￨NNS￨O￨- when￨L￨WRB￨O￨- challenged￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- fungal￨L￨JJ￨O￨- dose￨L￨NN￨O￨- after￨L￨IN￨O￨- this￨L￨DT￨O￨- period￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- contact￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- colony￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- lower￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- nestmates￨L￨NNS￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- later￨L￨RB￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- observed￨L￨VBN￨O￨- protection￨L￨NN￨O￨- in￨L￨IN￨O￨- nestmates￨L￨NNS￨O￨- of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨A ants￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- active￨L￨JJ￨O￨- upregulation￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- following￨L￨VBG￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fungus-exposed￨L￨JJ￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- therefore￨L￨RB￨O￨- aimed￨L￨VBD￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- causes￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- immunisation￨L￨NN￨O￨- in￨L￨IN￨O￨- colonies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ant￨L￨NN￨O￨- Lasius￨U￨NN￨MISC￨- neglectus￨L￨NN￨O￨- after￨L￨IN￨O￨- exposure￨L￨NN￨O￨- of￨L￨IN￨O￨- single￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- entomopathogenic￨L￨JJ￨O￨- fungus￨L￨NN￨O￨- Metarhizium￨U￨NN￨O￨- anisopliae￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- natural￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨A of￨L￨IN￨O￨- ants￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- ease￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- statistical￨L￨JJ￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- Bayesian￨U￨NNP￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- MCMC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- computational￨L￨JJ￨O￨A statistics￨L￨NNS￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- ecological￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- resolution￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- issues￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- problems￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- largely￨L￨RB￨O￨- unresolved￨L￨JJ￨O￨- when￨L￨WRB￨O￨- fitting￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- ecological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- either￨L￨CC￨O￨- in￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- or￨L￨CC￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- large￨L￨JJ￨O￨- ecological￨L￨JJ￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- using￨L￨VBG￨O￨- likelihood￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- Bayesian￨U￨JJ￨MISC￨- MCMC￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- has￨L￨VBZ￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- data￨L￨NNS￨O￨A sets￨L￨NNS￨O￨A collected￨L￨VBN￨O￨- in￨L￨IN￨O￨- small￨L￨JJ￨O￨- closed￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- households￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- but￨L￨CC￨O￨- very￨L￨RB￨O￨- little￨L￨JJ￨O￨- into￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- computational￨L￨JJ￨O￨A methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- are￨L￨VBP￨O￨- largely￨L￨RB￨O￨- drawn￨L￨VBN￨O￨- from￨L￨IN￨O￨- recent￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- taken￨L￨VBN￨O￨- in￨L￨IN￨O￨- systems￨L￨NNS￨O￨- biology￨L￨NN￨O￨- for￨L￨IN￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- using￨L￨VBG￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approach￨L￨NN￨O￨- used￨L￨VBN￨O￨- here￨L￨RB￨O￨- includes￨L￨VBZ￨O￨- births￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- immigration￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- allows￨L￨VBZ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- inference￨L￨NN￨O￨A of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- algorithm￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- computational￨L￨JJ￨O￨A foundation￨L￨NN￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- Markovian￨U￨JJ￨MISC￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- social￨L￨JJ￨O￨- learning￨L￨NN￨O￨- and￨L￨CC￨O￨- feedback￨L￨NN￨O￨- fit￨L￨VBP￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A coverage￨L￨NN￨O￨A data￨L￨NNS￨O￨- quite￨L￨RB￨O￨- well￨L￨RB￨O￨- under￨L￨IN￨O￨- all￨L￨DT￨O￨- risk￨L￨NN￨O￨- evolution￨L￨NN￨O￨- curves￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- first￨L￨JJ￨ORDINAL￨- objective￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- behavior-incidence￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- social￨L￨JJ￨O￨- learning￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- feedback￨L￨NN￨O￨- can￨L￨MD￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A coverage￨L￨NN￨O￨A data￨L￨NNS￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- vaccine￨L￨NN￨O￨- scares￨L￨VBZ￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- competing￨L￨VBG￨O￨- explanations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- ignore￨L￨VBP￨O￨- social￨L￨JJ￨O￨- learning￨L￨NN￨O￨- and/or￨L￨CC￨O￨- feedback￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- allowed￨L￨VBD￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- behavior-prevalence￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- curve￨L￨NN￨O￨- #￨L￨#￨MONEY￨- 1￨L￨CD￨MONEY￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- data￨L￨NNS￨O￨- points￨L￨NNS￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A coverage￨L￨NN￨O￨A and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- fit￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- see￨L￨VB￨O￨- whether￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- predict￨L￨VB￨O￨- later￨L￨RB￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- fit￨L￨VBN￨O￨- >￨L￨JJR￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- behavior-incidence￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- again￨L￨RB￨O￨- achieves￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- AICc￨U￨NN￨O￨- score￨L￨NN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- cases￨L￨NNS￨O￨- except￨L￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- neither￨L￨CC￨O￨- social￨L￨JJ￨O￨- learning￨L￨NN￨O￨A nor￨L￨CC￨O￨- feedback￨L￨NN￨O￨- under￨L￨IN￨O￨- curve￨L￨NN￨O￨- #￨L￨#￨MONEY￨- 5￨L￨CD￨MONEY￨- (￨L￨-LRB-￨O￨- Supporting￨U￨VBG￨O￨- Information￨U￨NNP￨O￨- Figure￨U￨NNP￨O￨- S4￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- second￨L￨JJ￨ORDINAL￨- objective￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- could￨L￨MD￨O￨- predict￨L￨VB￨O￨- in￨L￨IN￨O￨- advance￨L￨NN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨A coverage￨L￨NN￨O￨A and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- as￨L￨IN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- vaccine￨L￨NN￨O￨- scares￨L￨VBZ￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- individual￨L￨NN￨O￨- 's￨L￨POS￨O￨- decision-making￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- vaccination￨L￨NN￨O￨- may￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- perceived￨L￨VBN￨O￨A risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccinating￨L￨VBG￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- all￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- networks￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- imitation￨L￨NN￨O￨- behavior￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨- when￨L￨WRB￨O￨- vaccines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- inexpensive￨L￨JJ￨O￨- and￨L￨CC￨O￨- decreases￨L￨VBZ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- when￨L￨WRB￨O￨- vaccines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- expensive￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- portion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- adopts￨L￨VBZ￨O￨- vaccination￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- payoff￨L￨NN￨O￨- maximization￨L￨NN￨O￨- ”￨L￨''￨O￨- strategy￨L￨NN￨O￨- that￨L￨WDT￨O￨- maximizes￨L￨VBZ￨O￨- their￨L￨PRP$￨O￨- perceived￨L￨VBN￨O￨A payoff￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- population￨L￨NN￨O￨- imitates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- choices￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- imitation￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- imitation￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- imitation￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneously￨L￨RB￨O￨- mixed￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- substrate￨L￨NN￨O￨- —￨L￨:￨O￨- statistically￨L￨RB￨O￨- described￨L￨VBN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- its￨L￨PRP$￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- vertex￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- q￨L￨VB￨O￨- other￨L￨JJ￨O￨- individuals4￨L￨NN￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- mean-field￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HMF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- approach9￨L￨NN￨O￨- assuming￨L￨VBG￨O￨- no￨L￨DT￨O￨- topological￨L￨JJ￨O￨- correlations10￨L￨NN￨O￨- and￨L￨CC￨O￨- neglecting￨L￨VBG￨O￨- dynamical￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- ,￨L￨,￨O￨- yields￨L￨NNS￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- inversely￨L￨RB￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- moment￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- 〈￨L￨CD￨NUMBER￨- q2￨L￨NN￨O￨- 〉￨L￨CD￨NUMBER￨- 111213￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +for￨L￨IN￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- finite￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- with￨L￨IN￨O￨- degrees￨L￨NNS￨O￨- distributed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- power-law19￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- threshold20Equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- vanishes￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨- limit￨L￨NN￨O￨- in￨L￨IN￨O￨- power-law￨L￨NN￨O￨- distributed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- q￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- growing￨L￨VBG￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨A size￨L￨NN￨O￨A N￨U￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- previous￨L￨JJ￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- SIS212223￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- result￨L￨NN￨O￨- has￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- been￨L￨VBN￨O￨- interpreted￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- leading￨L￨VBG￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hubs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- vertices￨L￨NNS￨O￨- with￨L￨IN￨O￨- largest￨L￨JJS￨O￨- degree￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- elements￨L￨NNS￨O￨- sustaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- whenever￨L￨WRB￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- sufficiently￨L￨RB￨O￨- large￨L￨JJ￨O￨- degree￨L￨NN￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- moment￨L￨NN￨O￨A 〈￨L￨CD￨NUMBER￨- q2￨L￨NN￨O￨- 〉￨L￨CD￨NUMBER￨- diverge￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- when￨L￨WRB￨O￨- γ￨L￨NN￨O￨- ≤￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 9￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- moment￨L￨NN￨O￨A therefore￨L￨RB￨O￨- diverges￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infinite￨L￨JJ￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- limit￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- when￨L￨WRB￨O￨- q￨L￨SYM￨O￨- →￨L￨SYM￨O￨- ∞￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- γ￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- vanishing￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- any￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- invade￨L￨VB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- whatever￨L￨WDT￨O￨- its￨L￨PRP$￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate1415￨L￨NN￨O￨- .￨L￨.￨O￨- +Inspired￨U￨VBN￨O￨- by￨L￨IN￨O￨- these￨L￨DT￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hub￨L￨NN￨O￨A and￨L￨CC￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- complex￨L￨JJ￨O￨- topologies￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- only￨L￨RB￨O￨- unvaccinated￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- turkey￨L￨NN￨COUNTRY￨- farms￨L￨NNS￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- samplings￨L￨NNS￨O￨- and￨L￨CC￨O￨- available￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- farm￨L￨NN￨O￨A size￨L￨NN￨O￨- ,￨L￨,￨O￨- mean￨L￨VB￨O￨- sampling￨L￨NN￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- mean￨L￨VB￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- detected￨L￨VBN￨O￨- by￨L￨IN￨O￨- active￨L￨JJ￨O￨- or￨L￨CC￨O￨- passive￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- easier￨L￨JJR￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- but￨L￨CC￨O￨- has￨L￨VBZ￨O￨- no￨L￨DT￨O￨- direct￨L￨JJ￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- Rh￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- detection￨L￨NN￨O￨A :￨L￨:￨O￨- an￨L￨DT￨O￨- Rh￨U￨NN￨O￨- of￨L￨IN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- at￨L￨IN￨O￨- detection￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- detected￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- stopped￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- early￨L￨JJ￨O￨- stage￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- brought￨L￨VBN￨O￨- under￨L￨IN￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- passive￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- detection￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- was￨L￨VBD￨O￨- sufficient￨L￨JJ￨O￨- for￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- clinical￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- farm￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- occurred￨L￨VBD￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- within-farm￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- reached￨L￨VBD￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- D￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- below￨L￨IN￨O￨- for￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- detection￨L￨NN￨O￨A could￨L￨MD￨O￨- occur￨L￨VB￨O￨- on￨L￨IN￨O￨- specific￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- 60￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 90￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨DURATION￨- 120￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- production￨L￨NN￨O￨- cycle￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- reference￨L￨NN￨O￨- strategy￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- propose￨L￨VB￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- method￨L￨NN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- employ￨L￨VB￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨A of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- while￨L￨IN￨O￨- conducting￨L￨VBG￨O￨- real-time￨L￨JJ￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- readily￨L￨RB￨O￨- available￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- datasets￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- initiated￨L￨VBD￨O￨- the￨L￨DT￨O￨- two-dose￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- first￨L￨JJ￨ORDINAL￨- and￨L￨CC￨ORDINAL￨- second￨L￨JJ￨ORDINAL￨- doses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- 12-24￨L￨CD￨NUMBER￨- months￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- before￨L￨IN￨O￨- entering￨L￨VBG￨O￨- primary￨L￨JJ￨O￨A schools￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- 6￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- vaccinated￨L￨VBN￨O￨- population￨L￨NN￨O￨- 1,12,13￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- little￨L￨JJ￨O￨- attempt￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨A jointly￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- popular￨L￨JJ￨O￨- technique￨L￨NN￨O￨- along￨L￨IN￨O￨- these￨L￨DT￨O￨- lines￨L￨NNS￨O￨- employs￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Krylov￨U￨NNP￨PERSON￨- subspace￨L￨NN￨O￨- approximation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- KSA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- that￨L￨WDT￨O￨- dramatically￨L￨RB￨O￨- reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- matrix￨L￨NN￨O￨- exponentiation￨L￨NN￨O￨- and￨L￨CC￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- attractive￨L￨JJ￨O￨- iterative￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨A equation￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨A equation￨L￨NN￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- approximation￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- system-size￨L￨JJ￨O￨- expansion￨L￨NN￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- van￨L￨NN￨O￨- Kampen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- system-size￨L￨JJ￨O￨- expansion￨L￨NN￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- produce￨L￨VB￨O￨- a￨L￨DT￨O￨- normal￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨A equation￨L￨NN￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨A equation￨L￨NN￨O￨A through￨L￨IN￨O￨- matrix￨L￨NN￨O￨- exponentiation￨L￨NN￨O￨- ;￨L￨:￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- bimodal￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- will￨L￨MD￨O￨- produce￨L￨VB￨O￨A erroneous￨L￨JJ￨O￨- results￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- directed￨L￨VBN￨O￨- network￨L￨NN￨O￨- considered￨L￨VBN￨O￨- here￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- connections￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- definite￨L￨JJ￨O￨- direction￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- them￨L￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- giant￨L￨JJ￨O￨- strong￨L￨JJ￨O￨- component￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- farms￨L￨NNS￨O￨A where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- forward￨L￨RB￨O￨- path￨L￨NN￨O￨- from￨L￨IN￨O￨- every￨L￨DT￨O￨- farm￨L￨NN￨O￨- to￨L￨TO￨O￨- every￨L￨DT￨O￨- other￨L￨JJ￨O￨- farm￨L￨NN￨O￨- –￨L￨:￨O￨- in￨L￨IN￨O￨- principle￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- movement￨L￨NN￨O￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- from￨L￨IN￨O￨- any￨L￨DT￨O￨- farm￨L￨NN￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- other￨L￨JJ￨O￨- farm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- possibly￨L￨RB￨O￨- via￨L￨IN￨O￨- intermediate￨L￨JJ￨O￨- farms￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- component￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- giant￨L￨JJ￨O￨A components￨L￨NNS￨O￨- using￨L￨VBG￨O￨- different￨L￨JJ￨O￨- observation￨L￨NN￨O￨- windows￨L￨NNS￨O￨- of￨L￨IN￨O￨- UK￨U￨NNP￨COUNTRY￨- cattle￨L￨NNS￨O￨- movements￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- previous￨L￨JJ￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- proxy￨L￨NN￨O￨- measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- cattle￨L￨NNS￨O￨- herd￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- calculate￨L￨VBP￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- giant￨L￨JJ￨O￨A weak￨L￨JJ￨O￨- and￨L￨CC￨O￨- strong￨L￨JJ￨O￨- components￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- observation￨L￨NN￨O￨- windows￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- 10-day￨L￨JJ￨DURATION￨- window￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- 28-day￨L￨JJ￨DURATION￨- window￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- year-long￨L￨JJ￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- naturally￨L￨RB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- reflecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- farms￨L￨NNS￨O￨A are￨L￨VBP￨O￨- only￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- when￨L￨WRB￨O￨- animals￨L￨NNS￨O￨- move￨L￨VBP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- weighted￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- reflecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- moving￨L￨VBG￨O￨- different￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- individual-based￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- farms￨L￨NNS￨O￨A that￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- to￨L￨TO￨O￨- transfer￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- farms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- early￨L￨JJ￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- neighborhood￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NV￨U￨NNP￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- protocol￨L￨NN￨O￨- —￨L￨:￨O￨- choose￨L￨VB￨O￨- a￨L￨DT￨O￨- person￨L￨NN￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- among￨L￨IN￨O￨- all￨L￨DT￨O￨- persons￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- contact￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- ask￨L￨VB￨O￨- her￨L￨PRP￨O￨- to￨L￨TO￨O￨- name￨L￨VB￨O￨- someone￨L￨NN￨O￨- she￨L￨PRP￨O￨- met￨L￨VBD￨O￨- ,￨L￨,￨O￨- vaccinate￨L￨VB￨O￨- this￨L￨DT￨O￨- other￨L￨JJ￨O￨- person￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- repeat￨L￨NN￨O￨- until￨L￨IN￨O￨- a￨L￨DT￨O￨- desired￨L￨VBN￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vertices￨L￨NNS￨O￨- are￨L￨VBP￨O￨- vaccinated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Human￨U￨JJ￨O￨- interaction￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- have￨L￨VBP￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- structure￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- utilized￨L￨VBN￨O￨- in￨L￨IN￨O￨- immunization￨L￨NN￨O￨- protocols￨L￨NNS￨O￨A than￨L￨IN￨O￨- merely￨L￨RB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- degrees￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- what￨L￨WP￨O￨- neighborhood￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- protocols￨L￨NNS￨O￨- build￨L￨VBP￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- idea￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- empirical￨L￨JJ￨O￨- contact￨L￨NN￨O￨- structures￨L￨NNS￨O￨- ,￨L￨,￨O￨- more￨L￨JJR￨O￨- or￨L￨CC￨O￨- less￨L￨JJR￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- over￨L￨IN￨O￨- which￨L￨WDT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- spread￨L￨VB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- important￨L￨JJ￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- temporal￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- static￨L￨JJ￨O￨A network￨L￨NN￨O￨A models￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- capture￨L￨VB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- overturn￨L￨VB￨O￨- of￨L￨IN￨O￨- relationships￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- is￨L￨VBZ￨O￨- active￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- never￨L￨RB￨O￨- again￨L￨RB￨O￨- after￨L￨IN￨O￨- this￨L￨DT￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- limited￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- balanced￨L￨JJ￨O￨- between￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- eradication￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- combined￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- time￨L￨NN￨O￨- until￨L￨IN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- rate￨L￨NN￨O￨- on￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- neighborhood￨L￨NN￨O￨A .￨L￨.￨O￨- +Addition￨U￨NN￨O￨- of￨L￨IN￨O￨- small￨L￨JJ￨O￨- world￨L￨NN￨O￨- links￨L￨NNS￨O￨- narrows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- scaling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- power￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- law￨L￨NN￨O￨- is￨L￨VBZ￨O￨- valid￨L￨JJ￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- scaling￨L￨NN￨O￨- persists￨L￨VBZ￨O￨- for￨L￨IN￨O￨- small￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- detection￨L￨NN￨O￨A and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- times￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- principal￨L￨JJ￨TITLE￨- objective￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- eradication￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- neighborhood￨L￨NN￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨A world￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- long￨L￨JJ￨O￨- range￨L￨NN￨O￨- links￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- added￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- regular￨L￨JJ￨O￨- network￨L￨NN￨O￨- described￨L￨VBN￨O￨- above￨L￨IN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- matches￨L￨VBZ￨O￨- the￨L￨DT￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- dispersal￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- so￨L￨IN￨O￨- the￨L￨DT￨O￨- larger￨L￨JJR￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- neighborhood￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- further￨L￨RBR￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- has￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- extended￨L￨VBN￨O￨- .￨L￨.￨O￨- +Theoretical￨U￨JJ￨O￨- considerations￨L￨NNS￨O￨- may￨L￨MD￨O￨- assume￨L￨VB￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- contact￨L￨NN￨O￨- pattern￨L￨NN￨O￨- with￨L￨IN￨O￨- equal￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- all￨L￨DT￨O￨- herds￨L￨NNS￨O￨A ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- mixing￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- MAM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- mixing￨L￨VBG￨O￨- heterogeneities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- spread￨L￨VBN￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- vectors￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- between￨L￨IN￨O￨- herds￨L￨NNS￨O￨A are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- livestock￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- movements￨L￨NNS￨O￨- may￨L￨MD￨O￨- however￨L￨RB￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- highly￨L￨RB￨O￨- directed￨L￨VBN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- herd￨L￨NN￨O￨- that￨L￨WDT￨O￨- sends￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- herds￨L￨NNS￨O￨A may￨L￨MD￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- receive￨L￨VB￨O￨- many￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Infected￨U￨JJ￨O￨- herds￨L￨NNS￨O￨A with￨L￨IN￨O￨- many￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- may￨L￨MD￨O￨- rapidly￨L￨RB￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- herds￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thereby￨L￨RB￨O￨- function￨L￨NN￨O￨- as￨L￨IN￨O￨- ‘￨L￨``￨O￨- super￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- ’￨L￨POS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Perhaps￨U￨RB￨O￨- most￨L￨RBS￨O￨- obvious￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- differ￨L￨VB￨O￨- between￨L￨IN￨O￨- herds￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- better￨L￨JJR￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- sink￨L￨NN￨O￨- vector￨L￨NN￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- critically￨L￨RB￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- health￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- highly￨L￨RB￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- despite￨L￨IN￨O￨- ongoing￨L￨JJ￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- where￨L￨WRB￨O￨- vectors￨L￨NNS￨O￨A are￨L￨VBP￨O￨- expanding￨L￨VBG￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- large￨L￨JJ￨O￨- body￨L￨NN￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- contributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨A ecology￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- pathogen￨L￨NN￨O￨- evolution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨- of￨L￨IN￨O￨- efficient￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- studies￨L￨NNS￨O￨- typically￨L￨RB￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- highly￨L￨RB￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- pathogens￨L￨NNS￨O￨- are￨L￨VBP￨O￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- large￨L￨JJ￨O￨- self-sustaining￨L￨JJ￨O￨- ‘￨L￨``￨O￨- source￨L￨NN￨O￨- ’￨L￨''￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- vectors￨L￨NNS￨O￨A of￨L￨IN￨O￨- human￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- mosquitoes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Anopheles￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Aedes￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- Culex￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- flies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Glossina￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- phlebotomines￨L￨NNS￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- triatomines￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Triatoma￨U￨NN￨O￨- infestans￨L￨NNS￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Rhodnius￨U￨NNP￨MISC￨- prolixus￨L￨NN￨MISC￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Clearly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fate￨L￨NN￨O￨- of￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- in￨L￨IN￨O￨- sink￨L￨NN￨O￨- vector￨L￨NN￨O￨A populations￨L￨NNS￨O￨- will￨L￨MD￨O￨- also￨L￨RB￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- ease￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- when￨L￨WRB￨O￨- contacts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- established￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- within-host￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +Sink￨U￨VB￨O￨- populations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- vectors￨L￨NNS￨O￨A of￨L￨IN￨O￨- human￨L￨JJ￨O￨- African￨U￨JJ￨NATIONALITY￨- trypanosomiasis￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Chagas￨U￨NNP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- research￨L￨NN￨O￨- papers￨L￨NNS￨O￨A which￨L￨WDT￨O￨- appear￨L￨VBP￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- issue￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- classified￨L￨VBN￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- categories￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- papers￨L￨NNS￨O￨- which￨L￨WDT￨O￨- discuss￨L￨VBP￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- nonlinear￨L￨JJ￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- analysis￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- others￨L￨NNS￨O￨- which￨L￨WDT￨O￨- present￨L￨VBP￨DATE￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- application￨L￨NN￨O￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- biology￨L￨NN￨O￨- and￨L￨CC￨O￨- medicine￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- interesting￨L￨JJ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- author￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- successfully￨L￨RB￨O￨- employed￨L￨VBN￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A data￨L￨NNS￨O￨- from￨L￨IN￨O￨- 60￨L￨CD￨NUMBER￨- UK￨U￨NNP￨COUNTRY￨- cities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Korhonen￨U￨NNP￨PERSON￨- contribute￨L￨VBP￨O￨- a￨L￨DT￨O￨- paper￨L￨NN￨O￨- on￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨A deformations￨L￨NNS￨O￨- of￨L￨IN￨O￨- cells￨L￨NNS￨O￨- during￨L￨IN￨O￨- micropipette￨L￨NN￨O￨- aspiration￨L￨NN￨O￨- procedure￨L￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- its￨L￨PRP$￨O￨- viscoelastic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +Free￨U￨NNP￨O￨- energy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- information￨L￨NN￨O￨- theoretic￨L￨JJ￨O￨- measure￨L￨NN￨O￨A that￨L￨WDT￨O￨- bounds￨L￨VBZ￨O￨- the￨L￨DT￨O￨- surprise￨L￨NN￨O￨- on￨L￨IN￨O￨- sampling￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- generative￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- paper￨L￨NN￨O￨A examines￨L￨VBZ￨O￨- a￨L￨DT￨O￨- neo-Hookean￨L￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- micropipette￨L￨NN￨O￨- aspiration￨L￨NN￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A and￨L￨CC￨O￨- virions￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- they￨L￨PRP￨O￨- fail￨L￨VBP￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- some￨L￨DT￨O￨- important￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- intrinsic￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- play￨L￨VBP￨O￨- a￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- role￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- regions￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A in￨L￨IN￨O￨- which￨L￨WDT￨O￨- drug￨L￨NN￨O￨- levels￨L￨NNS￨O￨- are￨L￨VBP￨O￨- low￨L￨JJ￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- in￨L￨IN￨O￨- those￨L￨DT￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- HCV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- considered￨L￨VBN￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- and￨L￨CC￨O￨- fluctuates￨L￨VBZ￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- fluctuation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- of￨L￨IN￨O￨- ∼￨L￨CD￨NUMBER￨- n.￨L￨NN￨O￨- +A￨U￨DT￨O￨- major￨L￨JJ￨O￨- characteristic￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- extinction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- time￨L￨NN￨O￨- -￨L￨:￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A reaches￨L￨VBZ￨O￨- zero￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- that￨L￨WDT￨O￨- describe￨L￨VBP￨O￨- spontaneous￨L￨JJ￨O￨- virus￨L￨NN￨O￨- extinction￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- relevant￨L￨JJ￨O￨- to￨L￨TO￨O￨- various￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- current￨L￨JJ￨DATE￨- available￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- on￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- prevention￨L￨NN￨O￨- program￨L￨NN￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- current￨L￨JJ￨DATE￨- spending￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- created￨L￨VBD￨O￨- an￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- generate￨L￨VB￨O￨- the￨L￨DT￨O￨- mathematically￨L￨RB￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- DHAP￨U￨NN￨ORGANIZATION￨- ’s￨L￨POS￨O￨- budget￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- allocation￨L￨NN￨O￨A of￨L￨IN￨O￨- DHAP￨U￨NN￨ORGANIZATION￨- ’s￨L￨POS￨O￨- budget￨L￨NN￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- focus￨L￨VB￨O￨- specifically￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- prevention￨L￨NN￨O￨- programs￨L￨NNS￨O￨- currently￨L￨RB￨DATE￨- funded￨L￨VBN￨O￨- by￨L￨IN￨O￨- DHAP￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- testing￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- counseling￨L￨NN￨O￨- and￨L￨CC￨O￨- education￨L￨NN￨O￨- programs￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- components￨L￨NNS￨O￨- that￨L￨WDT￨O￨- interact￨L￨VBP￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- projects￨L￨VBZ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- funding￨L￨NN￨O￨- allocation￨L￨NN￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- optimization￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- supplies￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- stopping￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- allocation￨L￨NN￨O￨- that￨L￨WDT￨O￨- yields￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fewest￨L￨JJS￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- projects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- allocation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- budget￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- estimated￨L￨VBN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HIV-infected￨U￨JJ￨MISC￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- aged￨L￨JJ￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 64￨L￨CD￨NUMBER￨A ,￨L￨,￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- high-risk￨L￨JJ￨O￨- population￨L￨NN￨O￨- subgroup￨L￨NN￨O￨- was￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- DHAP￨U￨NN￨ORGANIZATION￨- ’s￨L￨POS￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- adjustments￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- equivalent￨L￨JJ￨O￨- “￨L￨``￨O￨- positivity￨L￨NN￨O￨- ”￨L￨''￨O￨- measure￨L￨NN￨O￨- for￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- average￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- year￨L￨NN￨DURATION￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- above￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- T￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Once￨U￨RB￨DATE￨- again￨L￨RB￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- partner￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- T￨U￨NN￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- a￨L￨DT￨O￨- T￨U￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- no￨L￨DT￨O￨- effort￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- expended￨L￨VBN￨O￨- in￨L￨IN￨O￨- tracing￨L￨VBG￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relative￨L￨JJ￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- screening￨L￨NN￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- examined￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- below￨L￨IN￨O￨- which￨L￨WDT￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- becomes￨L￨VBZ￨O￨- cost￨L￨NN￨O￨- effective￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- NCSP￨U￨NN￨ORGANIZATION￨- targets￨L￨VBZ￨O￨- young￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- under￨L￨IN￨O￨- 25￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- outside￨L￨IN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- health￨L￨NN￨O￨- clinics￨L￨NNS￨O￨- ,￨L￨,￨O￨- screening￨L￨VBG￨O￨A individuals￨L￨NNS￨O￨- opportunistically￨L￨RB￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- visit￨L￨VBP￨O￨- other￨L￨JJ￨O￨- health￨L￨NN￨O￨- services￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Screening￨U￨VBG￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- quick￨L￨JJ￨O￨- ,￨L￨,￨O￨- easy￨L￨JJ￨O￨- ,￨L￨,￨O￨- noninvasive￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- someone￨L￨NN￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- effort￨L￨NN￨O￨A is￨L￨VBZ￨O￨- made￨L￨VBN￨O￨- to￨L￨TO￨O￨- offer￨L￨VB￨O￨- a￨L￨DT￨O￨- screen￨L￨NN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- previous￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- partners￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨A may￨L￨MD￨O￨- move￨L￨VB￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- class￨L￨NN￨O￨- either￨L￨CC￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- symptoms￨L￨NNS￨O￨- naturally￨L￨RB￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- d￨L￨NN￨O￨- or￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- screened￨L￨VBN￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- g￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- weak￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- absent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- outbreak￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- large￨L￨JJ￨O￨- enough￨L￨RB￨O￨- to￨L￨TO￨O￨- deplete￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- people￨L￨NNS￨O￨- below￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- level￨L￨NN￨O￨- below￨L￨IN￨O￨- which￨L￨WDT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- re-introduced￨L￨JJ￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- effective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- too￨L￨RB￨O￨- low￨L￨JJ￨O￨- to￨L￨TO￨O￨- cause￨L￨VB￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- black￨L￨JJ￨O￨- and￨L￨CC￨O￨- cyan￨L￨JJ￨O￨- lines￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨A is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- strong￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- that￨L￨IN￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- people￨L￨NNS￨O￨- remaining￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- enough￨L￨RB￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- (￨L￨-LRB-￨O￨- uncontrolled￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- outbreak￨L￨NN￨O￨- upon￨L￨IN￨O￨- re-introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- overall￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- that￨L￨IN￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- as￨L￨IN￨O￨- that￨L￨DT￨O￨- reached￨L￨VBN￨O￨- during￨L￨IN￨O￨- just￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- red￨L￨JJ￨O￨- line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- excess￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- beyond￨L￨IN￨O￨- those￨L￨DT￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- reach￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A level￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- termed￨L￨VBN￨O￨- ‘￨L￨``￨O￨- overshoot￨L￨NN￨O￨- ’￨L￨''￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- minimizes￨L￨VBZ￨O￨- this￨L￨DT￨O￨- overshoot￨L￨NN￨O￨- and￨L￨CC￨O￨- thereby￨L￨RB￨O￨- minimizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- over￨L￨IN￨O￨- all￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- that￨L￨WDT￨O￨- minimizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- overshoot￨L￨NN￨O￨- by￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- to￨L￨TO￨O￨- drop￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A level￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- outbreak￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- occur￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- green￨L￨JJ￨O￨- line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- national￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- scale￨L￨NN￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- modeling￨L￨NN￨O￨- platform￨L￨NN￨O￨- for￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- landscapes￨L￨NNS￨O￨- outside￨L￨IN￨O￨- human￨L￨JJ￨O￨- transportation￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- US￨U￨NNP￨COUNTRY￨- counties￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- adjacent￨L￨JJ￨O￨A counties￨L￨NNS￨O￨- weighted￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- crop￨L￨NN￨O￨- densities￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- landscape￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- density￨L￨NN￨O￨- levels￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- typical￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- spatial￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- locations￨L￨NNS￨O￨- or￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- ‘￨L￨``￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- encounters￨L￨NNS￨O￨- or￨L￨CC￨O￨- movement￨L￨NN￨O￨A between￨L￨IN￨O￨- any￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- link￨L￨NN￨O￨- ’￨L￨''￨O￨- that￨L￨WDT￨O￨- joins￨L￨VBZ￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Network￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- applications￨L￨NNS￨O￨- in￨L￨IN￨O￨- biology￨L￨NN￨O￨- have￨L￨VBP￨O￨- included￨L￨VBN￨O￨- movement￨L￨NN￨O￨A of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- among￨L￨IN￨O￨- habitat￨L￨NN￨O￨- patches￨L￨NNS￨O￨- and￨L￨CC￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- aggressiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- no￨L￨DT￨O￨- studies￨L￨NNS￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- have￨L￨VBP￨O￨- examined￨L￨VBN￨O￨- differences￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- response￨L￨NN￨O￨- by￨L￨IN￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- clonal￨L￨JJ￨O￨- lines￨L￨NNS￨O￨A of￨L￨IN￨O￨- fish￨L￨NN￨O￨- exhibiting￨L￨VBG￨O￨- susceptibility￨L￨NN￨O￨- or￨L￨CC￨O￨- resistance￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- background￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fish￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- modifications￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- mRNAs￨L￨NNS￨O￨- for￨L￨IN￨O￨- important￨L￨JJ￨O￨- cytokines￨L￨NNS￨O￨- ,￨L￨,￨O￨- sensors￨L￨NNS￨O￨- and￨L￨CC￨O￨- effector￨L￨NN￨O￨- genes￨L￨NNS￨O￨A by￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- step￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- fish￨L￨NN￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- further￨L￨RB￨O￨- dissect￨L￨VB￨O￨- the￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- genes￨L￨NNS￨O￨- in￨L￨FW￨O￨- vivo￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- identified￨L￨VBD￨O￨- resistant￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- among￨L￨IN￨O￨- a￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- established￨L￨VBN￨O￨- collection￨L￨NN￨O￨- of￨L￨IN￨O￨- rainbow￨L￨NN￨O￨- trout￨L￨NNS￨O￨- homozygous￨L￨JJ￨O￨- clonal￨L￨JJ￨O￨- lines￨L￨NNS￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +psychrophilum￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- resistant￨L￨JJ￨O￨A and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- fish￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- substantial￨L￨JJ￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- nutritional￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- added￨L￨VBN￨O￨- to￨L￨TO￨O￨- large-scale￨L￨JJ￨O￨- programs￨L￨NNS￨O￨- to￨L￨TO￨O￨- deliver￨L￨VB￨O￨- drug￨L￨NN￨O￨- treatments￨L￨NNS￨O￨- and￨L￨CC￨O￨- thereby￨L￨RB￨O￨- contribute￨L￨VBP￨O￨- ,￨L￨,￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- and￨L￨CC￨O￨- behavior￨L￨NN￨O￨- change￨L￨NN￨O￨- activities￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- controlling￨L￨VBG￨O￨- and￨L￨CC￨O￨- preventing￨L￨VBG￨O￨- NTDs￨U￨NNS￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- restoring￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- health.KeywordsNeglected￨L￨JJ￨O￨- tropical￨L￨JJ￨O￨A diseasescontrol￨L￨NN￨O￨- programsundernutritionmicronutrients￨L￨NNS￨O￨- IntroductionThe￨U￨NNP￨O￨- fundamental￨L￨JJ￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- organism￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- nutritional￨L￨JJ￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- nutrients￨L￨NNS￨O￨- needed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- organism￨L￨NN￨O￨- for￨L￨IN￨O￨- maintenance￨L￨NN￨O￨- ,￨L￨,￨O￨- growth￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reproduction￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Opinion￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- nutrition￨L￨NN￨O￨- in￨L￨IN￨O￨- integrated￨L￨JJ￨O￨- programs￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- neglected￨L￨VBN￨O￨- tropical￨L￨JJ￨O￨A diseasesAndrew￨L￨NN￨O￨- Hall1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yaobi￨U￨NNP￨O￨- Zhang2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Chad￨U￨NNP￨PERSON￨- MacArthur3￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Shawn￨U￨NNP￨PERSON￨- Baker2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 10:41￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Hall￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- AbstractThere￨U￨NNP￨O￨- are￨L￨VBP￨O￨- strong￨L￨JJ￨O￨- and￨L￨CC￨O￨- direct￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- undernutrition￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- organisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- diverse￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- labeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- neglected￨L￨VBN￨O￨- tropical￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- NTDs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- opinion￨L￨NN￨O￨A article￨L￨NN￨O￨- examines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- nutrition￨L￨NN￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- NTDs￨U￨NNS￨O￨- and￨L￨CC￨O￨- makes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- that￨L￨WDT￨O￨- mass￨L￨NN￨O￨- drug￨L￨NN￨O￨- treatment￨L￨NN￨O￨- -￨L￨:￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- currently￨L￨RB￨DATE￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- several￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- -￨L￨:￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- controlling￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- physical￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- .￨L￨.￨O￨- +Without￨U￨IN￨O￨- adequate￨L￨JJ￨O￨- energy￨L￨NN￨O￨- and￨L￨CC￨O￨- nutrients￨L￨NNS￨O￨- to￨L￨TO￨O￨- repair￨L￨VB￨O￨- damaged￨L￨JJ￨O￨- tissues￨L￨NNS￨O￨- or￨L￨CC￨O￨- recover￨L￨VB￨O￨- lost￨L￨VBN￨O￨- growth￨L￨NN￨O￨- and￨L￨CC￨O￨- development￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- evident￨L￨JJ￨O￨- quickly￨L￨RB￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨A may￨L￨MD￨O￨- be￨L￨VB￨O￨- not￨L￨RB￨O￨- appreciated￨L￨VBN￨O￨- by￨L￨IN￨O￨- beneficiaries￨L￨NNS￨O￨- ;￨L￨:￨O￨- while￨L￨IN￨O￨- vulnerability￨L￨NN￨O￨- to￨L￨TO￨O￨- reinfection￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +Undernutrition￨U￨NN￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- that￨L￨IN￨O￨- children￨L￨NNS￨O￨- will￨L￨MD￨O￨- die￨L￨VB￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- physical￨L￨JJ￨O￨- damage￨L￨NN￨O￨- ,￨L￨,￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- appetite￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- responses￨L￨NNS￨O￨- during￨L￨IN￨O￨- chronic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- contribute￨L￨VB￨O￨A substantially￨L￨RB￨O￨- to￨L￨TO￨O￨- undernutrition￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- popularity￨L￨NN￨O￨- of￨L￨IN￨O￨- baby￨L￨NN￨O￨- names￨L￨NNS￨O￨- was￨L￨VBD￨O￨- very￨L￨RB￨O￨- robust￨L￨JJ￨O￨- until￨L￨IN￨O￨- the￨L￨DT￨DATE￨- end￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- 18th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- NumericCitation￨U￨NN￨O￨- but￨L￨CC￨O￨- since￨L￨IN￨O￨- then￨L￨RB￨O￨- names￨L￨NNS￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- matter￨L￨NN￨O￨A of￨L￨IN￨O￨- fashion￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- involving￨L￨VBG￨O￨- growth￨L￨NN￨O￨- and￨L￨CC￨O￨- decline￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- few￨L￨JJ￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- suggested￨L￨VBN￨O￨- that￨L￨IN￨O￨- exogenous￨L￨JJ￨O￨- events￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- “￨L￨``￨O￨- contamination￨L￨NN￨O￨- ”￨L￨''￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- name￨L￨NN￨O￨- associated￨L￨VBN￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- notorious￨L￨JJ￨O￨- character￨L￨NN￨O￨- or￨L￨CC￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- popularity￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- name￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- movie￨L￨NN￨TITLE￨- star￨L￨NN￨TITLE￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- successful￨L￨JJ￨O￨- leader￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- play￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- names￨L￨NNS￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Baby￨U￨NNP￨O￨- names￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- particularly￨L￨RB￨O￨- suitable￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- cultural￨L￨JJ￨O￨A traits￨L￨NNS￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- names￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- attractiveness￨L￨NN￨O￨- will￨L￨MD￨O￨- not￨L￨RB￨O￨- score￨L￨VB￨O￨- the￨L￨DT￨O￨- very￨L￨RB￨O￨- same￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- babies￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨JJ￨O￨- year￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- decision￨L￨NN￨O￨A making￨L￨VBG￨O￨A process￨L￨NN￨O￨- by￨L￨IN￨O￨- each￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- parents￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- names￨L￨NNS￨O￨- varies￨L￨VBZ￨O￨A tremendously￨L￨RB￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- societies￨L￨NNS￨O￨- and￨L￨CC￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- interpretation￨L￨NN￨O￨- of￨L￨IN￨O￨- SNP￨U￨NN￨ORGANIZATION￨- association￨L￨NN￨O￨- studies￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- collection￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- suggest￨L￨VBP￨O￨- experimental￨L￨JJ￨O￨- designs￨L￨NNS￨O￨- for￨L￨IN￨O￨- genome￨L￨NN￨O￨A scans￨L￨NNS￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- perform￨L￨VB￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- classic￨L￨JJ￨O￨- matched￨L￨VBN￨O￨- case-control￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- issues￨L￨NNS￨O￨- yet￨L￨RB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- resolved￨L￨VBN￨O￨- .￨L￨.￨O￨- +Consider￨U￨VB￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- undergoing￨L￨VBG￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ;￨L￨:￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- known￨L￨JJ￨O￨- pedigrees￨L￨NNS￨O￨- or￨L￨CC￨O￨- reliable￨L￨JJ￨O￨- animal￨L￨NN￨O￨A identification￨L￨NN￨O￨- ,￨L￨,￨O￨- classification￨L￨NN￨O￨- of￨L￨IN￨O￨- DNA￨U￨NN￨O￨- as￨L￨IN￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- cases￨L￨NNS￨O￨- or￨L￨CC￨O￨- control￨L￨NN￨O￨- may￨L￨MD￨O￨- enable￨L￨VB￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- genomic￨L￨JJ￨O￨- predictors￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- principle￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- animal￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- breed￨L￨NN￨O￨- .￨L￨.￨O￨- +Disease￨U￨NN￨CAUSE_OF_DEATH￨- genetics￨L￨NNS￨O￨- studies￨L￨NNS￨O￨- typically￨L￨RB￨O￨- require￨L￨VBP￨O￨- observations￨L￨NNS￨O￨- on￨L￨IN￨O￨- many￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- genetic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- or￨L￨CC￨O￨- perform￨L￨VB￨O￨- a￨L￨DT￨O￨- genome￨L￨NN￨O￨A scan￨L￨VB￨O￨- of￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- power￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- reality￨L￨NN￨O￨- most￨L￨RBS￨O￨- field￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A data￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- collected￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- situation￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- changes￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- further￨L￨RB￨O￨- develop￨L￨VBP￨O￨- the￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨- to￨L￨TO￨O￨- interpret￨L￨VB￨O￨- field￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A data￨L￨NNS￨O￨A and￨L￨CC￨O￨- summarize￨L￨VB￨O￨- their￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- heritability￨L￨NN￨O￨- and￨L￨CC￨O￨- SNP￨U￨NN￨ORGANIZATION￨- association￨L￨NN￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- dominate￨L￨VBP￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- simulation￨L￨NN￨O￨- or￨L￨CC￨O￨- numerical￨L￨JJ￨O￨- integration￨L￨NN￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- strategies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- option￨L￨NN￨O￨- with￨L￨IN￨O￨- complex￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- game￨L￨NN￨O￨- theoretic￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- individual-level￨L￨JJ￨O￨- decisions￨L￨NNS￨O￨- with￨L￨IN￨O￨- nationally￨L￨RB￨O￨- optimal￨L￨JJ￨O￨A policy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- recently￨L￨RB￨DATE￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- from￨L￨IN￨O￨- control￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- minimise￨L￨VB￨O￨- some￨L￨DT￨O￨- associated￨L￨VBN￨O￨- cost￨L￨NN￨O￨- function￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- often￨L￨RB￨O￨- taken￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- integral￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- square￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccinate￨L￨JJ￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Four￨U￨CD￨NUMBER￨- main￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- dominate￨L￨VBP￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- desire￨L￨NN￨O￨- to￨L￨TO￨O￨- minimise￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- supply￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- administered￨L￨VBN￨O￨- prophylactically￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- related￨L￨JJ￨O￨- issue￨L￨NN￨O￨- of￨L￨IN￨O￨- minimising￨L￨VBG￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- on-going￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- highly￨L￨RB￨O￨- complex￨L￨JJ￨O￨- issue￨L￨NN￨O￨- of￨L￨IN￨O￨- distributing￨L￨VBG￨O￨- vaccine￨L￨NN￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- minimise￨L￨VB￨O￨- total￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- or￨L￨CC￨O￨- costs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- considered￨L￨VBN￨O￨- here￨L￨RB￨O￨- where￨L￨WRB￨O￨- prophylactic￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- targetted￨L￨VBN￨O￨- to￨L￨TO￨O￨- minimise￨L￨VB￨O￨- the￨L￨DT￨O￨- total￨L￨NN￨O￨- expected￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- adopt￨L￨VB￨O￨- a￨L￨DT￨O￨- far￨L￨RB￨O￨- simpler￨L￨JJR￨O￨- approach￨L￨NN￨O￨- and￨L￨CC￨O￨- goal￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- prophylactic￨L￨JJ￨O￨A distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- stockpile￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- between￨L￨IN￨O￨- various￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- considering￨L￨VBG￨O￨- prophylactic￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- vaccination￨L￨NN￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨- with￨L￨IN￨O￨- relative￨L￨JJ￨O￨- ease￨L￨NN￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- population￨L￨NN￨O￨- –￨L￨:￨O￨- and￨L￨CC￨O￨- more-over￨L￨JJR￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- precise￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- concerning￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- motivate￨L￨VB￨O￨- and￨L￨CC￨O￨- introduce￨L￨VB￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨A size￨L￨NN￨O￨A calculation￨L￨NN￨O￨- ;￨L￨:￨O￨- before￨L￨IN￨O￨- using￨L￨VBG￨O￨- this￨L￨DT￨O￨- quantity￨L￨NN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- policy￨L￨NN￨O￨- in￨L￨IN￨O￨- spatially￨L￨RB￨O￨- segregated￨L￨VBN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- single￨L￨JJ￨O￨- diagram￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- characterise￨L￨VB￨O￨- a￨L￨DT￨O￨- whole￨L￨JJ￨O￨- research￨L￨NN￨O￨- area￨L￨NN￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- just￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- -￨L￨:￨O￨- although￨L￨IN￨O￨- this￨L￨DT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- consistency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- causal￨L￨JJ￨O￨A relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- -￨L￨:￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- integrate￨L￨VB￨O￨- multiple￨L￨JJ￨O￨- datasets.Additional￨L￨JJ￨O￨- advantages￨L￨NNS￨O￨- of￨L￨IN￨O￨- system-wide￨L￨JJ￨O￨- models￨L￨NNS￨O￨- include￨L￨VBP￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- instrumental￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- -￨L￨:￨O￨- now￨L￨RB￨DATE￨- emerging￨L￨VBG￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- technique￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- mendelian￨L￨JJ￨O￨- randomisation￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- under-used￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exploitation￨L￨NN￨O￨- of￨L￨IN￨O￨- "￨L￨``￨O￨- natural￨L￨JJ￨O￨- experiments￨L￨NNS￨O￨- "￨L￨''￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- change￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- advantages￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- inferring￨L￨VBG￨O￨- causation￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- elucidation￨L￨NN￨O￨- of￨L￨IN￨O￨- feedback.KeywordsEpidemiological￨L￨JJ￨O￨- methodologyCausationDAGsDiagrammatic￨L￨JJ￨O￨- methodsInfectious￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- modelsWeb￨L￨NN￨O￨- of￨L￨IN￨O￨- causationInstrumental￨L￨JJ￨O￨- variablesChange￨L￨NN￨O￨- modelsFeedback￨L￨NN￨O￨- Introductory￨U￨JJ￨O￨- quotes￨L￨NNS￨O￨- "￨L￨``￨O￨- Could￨U￨MD￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- problems￨L￨NNS￨O￨- of￨L￨IN￨O￨- modern￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- ...￨L￨:￨O￨- +Transmitted￨U￨VBN￨O￨- causes￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- "￨L￨``￨O￨- causes￨L￨NNS￨O￨- of￨L￨IN￨O￨- causes￨L￨NNS￨O￨- "￨L￨''￨O￨- )￨L￨-RRB-￨O￨- tend￨L￨VBP￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- systematically￨L￨RB￨O￨- analysed.The￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- modelling￨L￨NN￨O￨- tradition￨L￨NN￨O￨- models￨L￨NNS￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- typically￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- exposure-health￨L￨NN￨O￨- relationship￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- determinants￨L￨NNS￨O￨- of￨L￨IN￨O￨- exposure￨L￨NN￨O￨- being￨L￨VBG￨O￨- considered￨L￨VBN￨O￨- at￨L￨IN￨O￨- individual￨L￨JJ￨O￨- and￨L￨CC￨O￨- group/ecological￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Confining￨U￨VBG￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- link￨L￨NN￨O￨- misses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- opportunity￨L￨NN￨O￨- to￨L￨TO￨O￨- discover￨L￨VB￨O￨- such￨L￨JJ￨O￨- properties.The￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- causal￨L￨JJ￨O￨A diagram￨L￨NN￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- works￨L￨VBZ￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- from￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- accurate￨L￨JJ￨O￨- modelization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- activity-driven￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- calls￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- interaction￨L￨NN￨O￨- processes￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- measurement￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- activity￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- agents￨L￨NNS￨O￨- forming￨L￨VBG￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- task￨L￨NN￨O￨- now￨L￨RB￨DATE￨- made￨L￨VBN￨O￨- possible￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- time-resolved￨L￨JJ￨O￨- ,￨L￨,￨O￨- high-quality￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- instantaneous￨L￨JJ￨O￨- activity￨L￨NN￨O￨- of￨L￨IN￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- agents￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- networks3334353637￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- limiting￨L￨VBG￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- evolving￨L￨VBG￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨A scale￨L￨NN￨O￨A much￨L￨JJ￨O￨- shorter￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- thus￨L￨RB￨O￨- effectively￨L￨RB￨O￨- disappearing￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- conveniently￨L￨RB￨O￨- replaced￨L￨VBN￨O￨- by￨L￨IN￨O￨- effective￨L￨JJ￨O￨- random￨L￨JJ￨O￨- couplings￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- time￨L￨NN￨O￨A scale￨L￨NN￨O￨A separation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- extremely￨L￨RB￨O￨- convenient￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- and￨L￨CC￨O￨- analytical￨L￨JJ￨O￨- tractability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- networks￨L￨NNS￨O￨- generally￨L￨RB￨O￨- evolve￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- time-scale￨L￨NN￨O￨- that￨L￨WDT￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- comparable￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- process272829303132￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- one￨L￨CD￨NUMBER￨- limit￨L￨NN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- as￨L￨IN￨O￨- quenched￨L￨VBN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- connectivity￨L￨NN￨O￨- pattern￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- evolving￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨A scale￨L￨NN￨O￨A that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- longer￨L￨RBR￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- itself￨L￨PRP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- often￨L￨RB￨O￨- displays￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- connections￨L￨NNS￨O￨- per￨L￨IN￨O￨- mobility￨L￨NN￨O￨- centre￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- whose￨L￨WP$￨O￨- corresponding￨L￨JJ￨O￨- geographic￨L￨JJ￨O￨- census￨L￨NN￨O￨- area￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- framework￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- broad￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- traffic￨L￨NN￨O￨- exchanged￨L￨VBN￨O￨- by￨L￨IN￨O￨- each￨L￨DT￨O￨- mobility￨L￨NN￨O￨- centre￨L￨NN￨O￨- or￨L￨CC￨O￨- flowing￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- origin￨L￨NN￨O￨- and￨L￨CC￨O￨- destination￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- prevailing￨L￨VBG￨O￨- view￨L￨NN￨O￨- among￨L￨IN￨O￨- modelers￨L￨NNS￨O￨- of￨L￨IN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- skewed￨L￨JJ￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- cases￨L￨NNS￨O￨- power-law￨L￨NN￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- risky￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- straightforward￨L￨JJ￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- inferences￨L￨NNS￨O￨- about￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- network￨L￨NN￨O￨- properties￨L￨NNS￨O￨- from￨L￨IN￨O￨- cluster￨L￨NN￨O￨A size￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Similar￨U￨JJ￨O￨- taxa￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- those￨L￨DT￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- acute￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- cluster￨L￨VB￨O￨A together￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- co-cluster￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- greater￨L￨JJR￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- recent￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- airline￨L￨NN￨O￨- network21￨L￨NN￨O￨- demonstrated￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- cohesiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- airline￨L￨NN￨O￨- network￨L￨NN￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- arise￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- in￨L￨IN￨O￨- fact￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- particular￨L￨JJ￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A which￨L￨WDT￨O￨- meant￨L￨VBD￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- lesser￨L￨JJR￨O￨- connected￨L￨JJ￨O￨- airports￨L￨NNS￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- central￨L￨JJ￨O￨- role￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- indicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- higher￨L￨JJR￨O￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- all-pairs￨L￨JJ￨O￨- shortest￨L￨JJS￨O￨- paths￨L￨NNS￨O￨- crossing￨L￨VBG￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- topological￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- airline￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- run￨L￨VBP￨O￨- simulations￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza22￨L￨NN￨O￨- 23￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- worldwide￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- commercial￨L￨JJ￨O￨- flights￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- for￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- traveling￨L￨VBG￨O￨- between￨L￨IN￨O￨- cities￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NNP￨O￨- 1A￨L￨NN￨O￨- with￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- City￨U￨NNP￨LOCATION￨- as￨L￨IN￨O￨- starting￨L￨VBG￨O￨- node￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- expand￨L￨VBP￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- finding￨L￨NN￨O￨- further￨L￨RB￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- individual￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- cities￨L￨NNS￨O￨- ,￨L￨,￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- their￨L￨PRP$￨O￨- targeted￨L￨VBN￨O￨- removal￨L￨NN￨O￨- can￨L￨MD￨O￨- improve￨L￨VB￨O￨- on￨L￨IN￨O￨- existing￨L￨VBG￨O￨- control￨L￨NN￨O￨- strategies5￨L￨NN￨O￨- for￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A on￨L￨IN￨O￨- this￨L￨DT￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Scale-free￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- highly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- hubs￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- having￨L￨VBG￨O￨- k￨L￨NN￨O￨- edges￨L￨NNS￨O￨A follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- k￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- 8￨L￨CD￨NUMBER￨- 9￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Structural￨U￨JJ￨O￨- network￨L￨NN￨O￨- integrity￨L￨NN￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- partially￨L￨RB￨O￨- inactivating￨L￨VBG￨O￨- specific￨L￨JJ￨O￨- connections￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- edges￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- nodes16￨L￨CD￨NUMBER￨- 17￨L￨CD￨DATE￨- 18￨L￨CD￨DATE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigated￨L￨VBD￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨A strategy￨L￨NN￨O￨A would￨L￨MD￨O￨- be￨L￨VB￨O￨- most￨L￨RBS￨O￨- cost￨L￨VB￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- benefit￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- resources￨L￨NNS￨O￨- spent￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- different￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- apply￨L￨VBP￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +Percentages￨U￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- vaccinated￨L￨VBN￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨A strategy￨L￨NN￨O￨A To￨U￨TO￨O￨- detect￨L￨VB￨O￨- whether￨L￨IN￨O￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- best￨L￨JJS￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- evaluated￨L￨VBD￨O￨- the￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- alternative￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- plausible￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- for￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- Kingdom￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- three￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨A that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- geographically￨L￨RB￨O￨- close￨L￨JJ￨O￨- and￨L￨CC￨O￨- culturally￨L￨RB￨O￨- similar￨L￨JJ￨O￨- but￨L￨CC￨O￨- differ￨L￨VBP￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Country￨U￨NN￨O￨- specific￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- and￨L￨CC￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- for￨L￨IN￨O￨- countries￨L￨NNS￨O￨A with￨L￨IN￨O￨- different￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- profiles￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- incremental￨L￨JJ￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- ratios￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- below￨L￨IN￨O￨- country￨L￨NN￨O￨- specific￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- scenarios￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- were￨L￨VBD￨O￨- cost￨L￨VBN￨O￨- effective￨L￨JJ￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Following￨U￨VBG￨O￨- inoculation￨L￨NN￨O￨- with￨L￨IN￨O￨- pine￨L￨VB￨O￨- wood￨L￨NN￨O￨- nematode￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- marked￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- trees￨L￨NNS￨O￨A in￨L￨IN￨O￨- transcript￨L￨NN￨O￨- diversity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- transcripts￨L￨NNS￨O￨- expressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- common￨L￨JJ￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- stress￨L￨NN￨O￨- response￨L￨NN￨O￨- and￨L￨CC￨O￨- defense￨L￨NN￨O￨- genes￨L￨NNS￨O￨- differed￨L￨VBD￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- transcripts￨L￨NNS￨O￨- were￨L￨VBD￨O￨- discriminative￨L￨JJ￨O￨- :￨L￨:￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- peptide￨L￨NN￨O￨- and￨L￨CC￨O￨- putative￨L￨JJ￨O￨- pathogenesis-related￨L￨JJ￨O￨- genes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- PR-1b￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- in￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- trees￨L￨NNS￨O￨A than￨L￨IN￨O￨- in￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- at￨L￨IN￨O￨- every￨L￨DT￨O￨- time￨L￨NN￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- PR-9￨U￨NN￨O￨- ,￨L￨,￨O￨- PR-10￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- cell￨L￨NN￨O￨- wall-related￨L￨JJ￨O￨- genes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- hydroxyproline-rich￨L￨JJ￨O￨- glycoprotein￨L￨NN￨O￨- precursor￨L￨NN￨O￨- and￨L￨CC￨O￨- extensin￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- higher￨L￨JJR￨O￨- in￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- at￨L￨IN￨O￨- 7￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 14￨L￨CD￨NUMBER￨- dpi￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- seven￨L￨CD￨NUMBER￨- subtractive￨L￨JJ￨O￨- suppression￨L￨NN￨O￨- hybridization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SSH￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- cDNA￨L￨NN￨O￨- libraries￨L￨NNS￨O￨- using￨L￨VBG￨O￨- time-course￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- of￨L￨IN￨O￨- trees￨L￨NNS￨O￨A inoculated￨L￨VBN￨O￨- with￨L￨IN￨O￨- pine￨L￨VBP￨O￨- wood￨L￨NN￨O￨- nematode￨L￨NN￨O￨- at￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- 7￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- post-inoculation￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- dpi￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- 14￨L￨CD￨NUMBER￨- dpi￨L￨NN￨O￨- in￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- assessed￨L￨VBN￨O￨- the￨L￨DT￨O￨- molecular￨L￨JJ￨O￨- genetics￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- transcriptional￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- ,￨L￨,￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- infection-induced￨L￨JJ￨O￨- physiological￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- or￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- trees￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- transcriptional￨L￨JJ￨O￨- components￨L￨NNS￨O￨- revealed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Gene￨U￨NNP￨O￨- Ontology￨U￨NNP￨O￨- classification￨L￨NN￨O￨- clearly￨L￨RB￨O￨- differed￨L￨VBD￨O￨- between￨L￨IN￨O￨- resistant￨L￨JJ￨O￨A and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- libraries￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- address￨L￨VBP￨O￨- this￨L￨DT￨O￨- question￨L￨NN￨O￨- by￨L￨IN￨O￨- developing￨L￨VBG￨O￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- contagion￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- geographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- traffic￨L￨NN￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- time-resolved￨L￨JJ￨O￨- collective￨L￨JJ￨O￨- transport￨L￨NN￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- that￨L￨WDT￨O￨- carry￨L￨VBP￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Taken￨U￨VBN￨O￨- together￨L￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- previous￨L￨JJ￨O￨- results￨L￨NNS￨O￨- reflect￨L￨VBP￨O￨- an￨L￨DT￨O￨- emphasis￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- late-time￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- contagion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- typically￨L￨RB￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- thresholds￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- “￨L￨``￨O￨- fermionic￨L￨JJ￨O￨- ”￨L￨''￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- “￨L￨``￨O￨- bosonic￨L￨JJ￨O￨- ”￨L￨''￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- leave￨L￨VBP￨O￨- open￨L￨JJ￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- what￨L￨WP￨O￨- the￨L￨DT￨O￨- early-time￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- that￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- mediated￨L￨VBN￨O￨- by￨L￨IN￨O￨- human￨L￨JJ￨O￨- travel￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- individual￨L￨JJ￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- far￨L￨RB￨O￨- from￨L￨IN￨O￨- being￨L￨VBG￨O￨- random￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- natural￨L￨JJ￨O￨- to￨L￨TO￨O￨- ask￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- non-Markovian￨L￨JJ￨MISC￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- contagion￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- selfish￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- behavior￨L￨NN￨O￨A can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- detrimental￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- society￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- whole￨L￨JJ￨O￨- by￨L￨IN￨O￨- inducing￨L￨VBG￨O￨- a￨L￨DT￨O￨- larger￨L￨JJR￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- price￨L￨NN￨O￨- of￨L￨IN￨O￨- anarchy￨L￨NN￨O￨- in￨L￨IN￨O￨- transportation￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- operates￨L￨VBZ￨O￨- also￨L￨RB￨O￨- during￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- recurrent￨L￨JJ￨O￨- mobility￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- return￨L￨NN￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- origin￨L￨NN￨O￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- otherwise￨L￨RB￨O￨- diffusive￨L￨JJ￨O￨- random-walk￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Timing￨U￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- low￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- coverage￨L￨NN￨O￨- rate￨L￨NN￨O￨- areas￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- resource-poor￨L￨JJ￨O￨- setting￨L￨VBG￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- sub-Saharan￨L￨JJ￨O￨- Africa￨U￨NNP￨LOCATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- sometimes￨L￨RB￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- operate￨L￨VB￨O￨- ‘￨L￨``￨O￨- reactively￨L￨RB￨O￨- ’￨L￨''￨O￨- after￨L￨IN￨O￨- major￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- begun￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- outbreak￨L￨NN￨O￨- response￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- need￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- supplemented￨L￨VBN￨O￨- by￨L￨IN￨O￨- palliative￨L￨JJ￨O￨- care￨L￨NN￨O￨A of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- missed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- campaign￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- palliative￨L￨NN￨O￨- care￨L￨NN￨O￨A are￨L￨VBP￨O￨- administered￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- by￨L￨IN￨O￨- choosing￨L￨VBG￨O￨- a￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- maximizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- lives￨L￨NNS￨O￨- saved￨L￨VBN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- unmanaged￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- objective￨L￨JJ￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- trajectories￨L￨NNS￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- balance￨L￨NN￨O￨- of￨L￨IN￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- limited￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- in￨L￨IN￨O￨- managing￨L￨VBG￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- budget￨L￨NN￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- allocated￨L￨VBN￨O￨- to￨L￨TO￨O￨- palliative￨L￨JJ￨O￨- care￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- to￨L￨TO￨O￨- immunizations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- start￨L￨VBP￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- unvaccinated￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- general￨L￨JJ￨TITLE￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- palliative￨L￨NN￨O￨- care￨L￨NN￨O￨A using￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- Exposed￨U￨VBN￨O￨- Infectious￨U￨JJ￨O￨- Removed￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- start￨L￨VBP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- Susceptible￨U￨NNP￨O￨- ,￨L￨,￨O￨- Exposed￨U￨VBN￨O￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨O￨- and￨L￨CC￨O￨- Removed￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- modify￨L￨VB￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- options￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- control￨L￨NN￨O￨- :￨L￨:￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- palliative￨L￨NN￨O￨- care￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Much￨U￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- using￨L￨VBG￨O￨- different￨L￨JJ￨O￨- underlying￨L￨VBG￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- but￨L￨CC￨O￨- relatively￨L￨RB￨O￨- little￨L￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fungicides￨L￨NNS￨O￨- themselves￨L￨PRP￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- invasion￨L￨NN￨O￨A and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- chemically￨L￨RB￨O￨- controlled￨L￨VBN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- fungicides￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- invasion￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- ask￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- questions￨L￨NNS￨O￨- :￨L￨:￨O￨- does￨L￨VBZ￨O￨- the￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- fungicide￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- criteria￨L￨NNS￨O￨- for￨L￨IN￨O￨- invasion￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- ?￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- host￨L￨NN￨TITLE￨A growth￨L￨NN￨O￨- and￨L￨CC￨O￨- explicitly￨L￨RB￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- purely￨L￨RB￨O￨- protectant￨L￨JJ￨O￨- fungicide￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- classes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- fungicides￨L￨NNS￨O￨- often￨L￨RB￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- fungicide￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- by￨L￨IN￨O￨- simply￨L￨RB￨O￨- modifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rates￨L￨NNS￨O￨A and/or￨L￨CC￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- recovery￨L￨NN￨O￨- rates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compare￨L￨VBP￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- implicitly￨L￨RB￨O￨- incorporates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- protectant￨L￨JJ￨O￨- fungicide￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- through￨L￨IN￨O￨- modification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rates￨L￨NNS￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +Pathogenicity￨U￨NN￨O￨- and￨L￨CC￨O￨- transmissibility￨L￨NN￨O￨A primarily￨L￨RB￨O￨- determine￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- population-level￨L￨JJ￨O￨- fitness￨L￨NN￨O￨- ,￨L￨,￨O￨- usually￨L￨RB￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- mutations￨L￨NNS￨O￨- in￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- genome￨L￨NN￨O￨- that￨L￨WDT￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- reduced￨L￨VBN￨O￨- tropism￨L￨NN￨O￨- for￨L￨IN￨O￨- upper￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- respiratory￨L￨JJ￨O￨A tract￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- URRT￨U￨NNP￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- nose￨L￨NN￨O￨- ,￨L￨,￨O￨- trachea￨L￨NN￨O￨- and￨L￨CC￨O￨- bronchi￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- impair￨L￨VBP￨O￨- or￨L￨CC￨O￨- abolish￨L￨VBP￨O￨- virus￨L￨NN￨O￨- transmissibility￨L￨NN￨O￨- in￨L￨IN￨O￨- animal￨L￨NN￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- mutations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- enhance￨L￨VBP￨O￨- URRT￨U￨NN￨ORGANIZATION￨- tropism￨L￨NN￨O￨- can￨L￨MD￨O￨- restore￨L￨VB￨O￨- transmissibility￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Influenza￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- tissue￨L￨NN￨O￨- tropism￨L￨NN￨O￨- defines￨L￨VBZ￨O￨- host￨L￨NN￨TITLE￨- cells￨L￨NNS￨O￨- and￨L￨CC￨O￨- tissues￨L￨NNS￨O￨- that￨L￨WDT￨O￨- support￨L￨VBP￨O￨- viral￨L￨JJ￨O￨- replication￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- governs￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- partly￨L￨RB￨O￨- which￨L￨WDT￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- respiratory￨L￨JJ￨O￨A tract￨L￨NN￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +Avian￨U￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- viruses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- predominantly￨L￨RB￨O￨- infect￨L￨VBP￨O￨- deeper￨L￨JJR￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- respiratory￨L￨JJ￨O￨A tract￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DRRT￨U￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- bronchioles￨L￨NNS￨O￨- and￨L￨CC￨O￨- alveoli￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- efficiently￨L￨RB￨O￨- transmit￨L￨VB￨O￨- among￨L￨IN￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- location￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨A tract￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- essential￨L￨JJ￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- pathogenicity￨L￨NN￨O￨- and￨L￨CC￨O￨- transmissibility￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- burdens￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- preventive￨L￨JJ￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- categorized￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- three￨L￨CD￨NUMBER￨- types3￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- change￨L￨VB￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- state￨L￨NN￨O￨- :￨L￨:￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- go￨L￨VBP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- ‘￨L￨``￨O￨- removed￨L￨VBN￨O￨- ’￨L￨''￨O￨- state￨L￨NN￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- receive￨L￨VBP￨O￨- vaccination23￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- change￨L￨VB￨O￨- in￨L￨IN￨O￨- system￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- :￨L￨:￨O￨- individuals￨L￨NNS￨O￨- might￨L￨MD￨O￨- choose￨L￨VB￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- masks￨L￨NNS￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- smaller￨L￨JJR￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- parameter18￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- change￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- topology24￨L￨NN￨O￨- :￨L￨:￨O￨- For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- neighbors￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- in24￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modified￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- base￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- compelling￨L￨JJ￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- incorporate￨L￨VBP￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- response￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- that￨L￨IN￨O￨- clearly￨L￨RB￨O￨- identifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- allow￨L￨VB￨O￨- analysis￨L￨NN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- contribute￨L￨VB￨O￨- toward￨L￨IN￨O￨- a￨L￨DT￨O￨- clarification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- spontaneous￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- results￨L￨VBZ￨O￨- in20￨L￨NN￨O￨- and15￨L￨NN￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ultimately￨L￨RB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- self-initiated￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- strengths￨L￨NNS￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A ,￨L￨,￨O￨- initial￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- quickly￨L￨RB￨O￨- die￨L￨VBP￨O￨- out￨L￨RP￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- strengths￨L￨NNS￨O￨- above￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- spread￨L￨VB￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Their￨U￨PRP$￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- incidence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- smoothing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- repeated￨L￨VBN￨O￨- age￨L￨NN￨O￨- structured￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- surveys￨L￨NNS￨O￨A and￨L￨CC￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- cumulative￨L￨JJ￨O￨- excess￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Brunet￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Struchiner￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- derived￨L￨VBD￨O￨- a￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- formula￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- also￨L￨RB￨O￨- forms￨L￨VBZ￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- expressing￨L￨VBG￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- excess￨L￨JJ￨O￨- mortality￨L￨NN￨O￨A rates￨L￨NNS￨O￨A and￨L￨CC￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- structured￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- entails￨L￨VBZ￨O￨- viewing￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- ageing￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- as￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- merely￨L￨RB￨O￨- using￨L￨VBG￨O￨- available￨L￨JJ￨O￨- serostatus￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- possible￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- prevalence￨L￨NN￨O￨A at￨L￨IN￨O￨- an￨L￨DT￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- circumvent￨L￨VBP￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- artefactual￨L￨JJ￨O￨- aggregated￨L￨JJ￨O￨- summary￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- are￨L￨VBP￨O￨- variations￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- theme￨L￨NN￨O￨- of￨L￨IN￨O￨- interpreting￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- successive￨L￨JJ￨O￨- age￨L￨NN￨O￨- structured￨L￨VBN￨O￨- prevalence￨L￨NN￨O￨- surveys￨L￨NNS￨O￨A into￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- aggregates￨L￨NNS￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- surveys￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- point￨L￨NN￨O￨- behind￨L￨IN￨O￨- the￨L￨DT￨O￨- simplification￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- map￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- onto￨L￨IN￨O￨- observable￨L￨JJ￨O￨A data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- observable￨L￨JJ￨O￨- –￨L￨:￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- were￨L￨VBD￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- simple￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- of￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- recent￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- times￨L￨NNS￨O￨- since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Unlike￨U￨IN￨O￨- classical￨L￨JJ￨O￨- agent￨L￨NN￨O￨- based￨L￨VBN￨O￨- approaches￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- tagging￨L￨VBG￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- attributes￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- detailed￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- contact￨L￨NN￨O￨- matrices￨L￨NNS￨O￨A by￨L￨IN￨O￨- age￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Empirical￨U￨JJ￨O￨- data￨L￨NNS￨O￨- collection￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- is￨L￨VBZ￨O￨- however￨L￨RB￨O￨- extremely￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- and￨L￨CC￨O￨- although￨L￨IN￨O￨- several￨L￨JJ￨O￨- models￨L￨NNS￨O￨- tackling￨L￨VBG￨O￨- both￨L￨CC￨O￨- new￨L￨JJ￨O￨- emerging￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- introduced￨L￨VBN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- clear￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- data-driven￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- support￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- calling￨L￨VBG￨O￨- for￨L￨IN￨O￨- novel￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨A patterns￨L￨NNS￨O￨A in￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virtual￨L￨JJ￨O￨- society￨L￨NN￨O￨- of￨L￨IN￨O￨- agents￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- matrices￨L￨NNS￨O￨A by￨L￨IN￨O￨- age￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- social￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- :￨L￨:￨O￨- household￨L￨NN￨O￨- ,￨L￨,￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- workplace￨L￨NN￨O￨- and￨L￨CC￨O￨- general￨L￨JJ￨TITLE￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- validate￨L￨VB￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- approach￨L￨NN￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- obtained￨L￨VBN￨O￨- contact￨L￨NN￨O￨- matrices￨L￨NNS￨O￨A by￨L￨IN￨O￨- age￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Polymod￨U￨NNP￨MISC￨- study￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- large-scale￨L￨JJ￨O￨- survey￨L￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- relevant￨L￨JJ￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- matrices￨L￨NNS￨O￨A by￨L￨IN￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- 26￨L￨CD￨NUMBER￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- position￨L￨NN￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- synthetic￨L￨JJ￨O￨- society￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- computer￨L￨NN￨O￨- by￨L￨IN￨O￨- integrating￨L￨VBG￨O￨- available￨L￨JJ￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- census￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- generating￨L￨VBG￨O￨- function￨L￨NN￨O￨- formalism￨L￨NN￨O￨- ,￨L￨,￨O￨- Newman￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- there￨L￨RB￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- threshold￨L￨NN￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- residual￨L￨JJ￨O￨- network￨L￨NN￨O￨- composed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- biggest￨L￨JJS￨O￨- giant￨L￨JJ￨O￨A susceptible￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- that￨L￨WDT￨O￨- remains￨L￨VBZ￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- propagation￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- destroyed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- percolation￨L￨NN￨O￨A framework￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- explained￨L￨VBD￨O￨- the￨L￨DT￨O￨- lost￨L￨VBN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- giant￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- not-random￨L￨JJ￨O￨- node￨L￨NN￨O￨- percolation￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- called￨L￨VBD￨O￨- node￨L￨NN￨O￨- void￨L￨NN￨O￨- percolation￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- void￨L￨NN￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- link￨L￨NN￨O￨- percolation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- its￨L￨PRP$￨O￨- discrete￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- susceptible￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- recover￨L￨VB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- time￨L￨NN￨O￨- since￨L￨IN￨O￨- they￨L￨PRP￨O￨- were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨A recovery￨L￨NN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- rules￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- until￨L￨IN￨O￨- it￨L￨PRP￨O￨- reaches￨L￨VBZ￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨A state￨L￨NN￨O￨A where￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- mode￨L￨NN￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- produces￨L￨VBZ￨O￨- temporal￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- fixations￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- linkage￨L￨NN￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- supply￨L￨NN￨O￨A of￨L￨IN￨O￨- beneficial￨L￨JJ￨O￨- mutations￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fitness￨L￨NN￨O￨- landscape￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- key￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- adaptation￨L￨NN￨O￨- under￨L￨IN￨O￨- linkage￨L￨NN￨O￨- produces￨L￨VBZ￨O￨- clonal￨L￨JJ￨O￨- interference￨L￨NN￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- mode￨L￨NN￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- by￨L￨IN￨O￨- recurrent￨L￨JJ￨O￨- selective￨L￨JJ￨O￨- sweeps￨L￨NNS￨O￨- ,￨L￨,￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- hemagglutinin￨L￨NN￨O￨- gene￨L￨NN￨O￨- .￨L￨.￨O￨- +Theoretical￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- asexual￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- clonal￨L￨JJ￨O￨- interference￨L￨NN￨O￨A emerges￨L￨VBZ￨O￨- whenever￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- sufficiently￨L￨RB￨O￨- high￨L￨JJ￨O￨- supply￨L￨NN￨O￨- of￨L￨IN￨O￨- beneficial￨L￨JJ￨O￨- mutations￨L￨NNS￨O￨- to￨L￨TO￨O￨- trigger￨L￨VB￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- mutant￨L￨JJ￨O￨- clones￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Schiffels￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- recent￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- argue￨L￨VBP￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- amino￨L￨NN￨O￨- acid￨L￨NN￨O￨- substitutions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- epitopes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- under￨L￨IN￨O￨- positive￨L￨JJ￨O￨- selection￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Shih￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- clusters￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- fixations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- caused￨L￨VBN￨O￨- primarily￨L￨RB￨O￨- by￨L￨IN￨O￨- fitness￨L￨NN￨O￨A interactions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- epistasis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- epitope￨L￨NN￨O￨- sites￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Shih￨U￨NN￨O￨- ;￨L￨:￨O￨- Kryazhimskiy￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- clonal￨L￨JJ￨O￨- interference￨L￨NN￨O￨A differs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- regime￨L￨NN￨O￨- of￨L￨IN￨O￨- episodic￨L￨JJ￨O￨- selective￨L￨JJ￨O￨- sweeps￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Koelle￨U￨NN￨PERSON￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- previous￨L￨JJ￨O￨- arguments￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- uptake￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- private￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- exchanged￨L￨VBD￨O￨- through￨L￨IN￨O￨- inter-personal￨L￨JJ￨O￨- communication￨L￨NN￨O￨- between￨L￨IN￨O￨- parents￨L￨NNS￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- eligible￨L￨JJ￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- during￨L￨IN￨O￨- their￨L￨PRP$￨O￨- social￨L￨JJ￨O￨A contacts￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- communicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- authorities￨L￨NNS￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- media￨L￨NNS￨O￨- and￨L￨CC￨O￨- related￨L￨JJ￨O￨- channels￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- aim￨L￨NN￨O￨- we￨L￨PRP￨O￨- amend￨L￨VBP￨O￨- the￨L￨DT￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- proportion￨L￨NN￨O￨- by￨L￨IN￨O￨- coupling￨L￨NN￨O￨- the￨L￨DT￨O￨- imitation￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- behaviour￨L￨NN￨O￨A change￨L￨NN￨O￨- spreads￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- private￨L￨JJ￨O￨- information￨L￨NN￨O￨- spontaneously￨L￨RB￨O￨- communicated￨L￨VBN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- not￨L￨RB￨O￨- considered￨L￨VBN￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- behavioural￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- behaviour￨L￨NN￨O￨- change￨L￨NN￨O￨- spreads￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- benefits￨L￨NNS￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Communicating￨U￨VBG￨O￨- that￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- net￨L￨JJ￨O￨- benefit￨L￨NN￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- actually￨L￨RB￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- systems￨L￨NNS￨O￨- can￨L￨MD￨O￨- adopt￨L￨VB￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- decline￨L￨NN￨O￨- that￨L￨WDT￨O￨- might￨L￨MD￨O￨- ensue￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- perceived￨L￨VBN￨O￨A risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- prevalence-dependent￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- unlike￨L￨IN￨O￨- private￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- conveyed￨L￨VBN￨O￨- by￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- systems￨L￨NNS￨O￨- suggests￨L￨VBZ￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- possibly￨L￨RB￨O￨- zero￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- perceived￨L￨VBN￨O￨A risk￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- side￨L￨NN￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- possibly￨L￨RB￨O￨- prevalence-independent￨L￨JJ￨O￨- ,￨L￨,￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨- game-theoretic￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- vaccinating￨L￨VBG￨O￨- behaviour￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- perceived￨L￨VBN￨O￨A as￨L￨IN￨O￨- “￨L￨``￨O￨- better￨L￨JJR￨O￨- ”￨L￨''￨O￨- spreads￨L￨VBZ￨O￨- only￨L￨RB￨O￨- through￨L￨IN￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- label￨L￨VBP￨O￨- “￨L￨``￨O￨- imitation￨L￨NN￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- parents￨L￨NNS￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- eligible￨L￨JJ￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- seldom￨L￨RB￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- reality￨L￨NN￨O￨- .￨L￨.￨O￨- +Current￨U￨JJ￨DATE￨- hypotheses￨L￨NNS￨O￨- explaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- EV71￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- include￨L￨VBP￨O￨- host￨L￨NN￨TITLE￨- immune￨L￨JJ￨O￨- competence￨L￨NN￨O￨- fluctuations￨L￨NNS￨O￨- mediated￨L￨VBN￨O￨- by￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- melatonin￨L￨NN￨O￨- or￨L￨CC￨O￨- vitamin￨L￨NN￨O￨- D￨U￨NN￨O￨- levels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- seasonal￨L￨JJ￨O￨- ,￨L￨,￨O￨- behavioral￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- unrelated￨L￨JJ￨O￨- to￨L￨TO￨O￨- weather￨L￨VB￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- school￨L￨NN￨O￨- attendance￨L￨NN￨O￨- and￨L￨CC￨O￨- indoor￨L￨JJ￨O￨- crowding￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- temperature￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- relative￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- alone￨L￨RB￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- appear￨L￨VB￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨A pattern￨L￨NN￨O￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- certain￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- EV71￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- occur￨L￨VB￨O￨- in￨L￨IN￨O￨- school-aged￨L￨JJ￨O￨- children￨L￨NNS￨O￨- or￨L￨CC￨O￨- in￨L￨IN￨O￨- association￨L￨NN￨O￨- with￨L￨IN￨O￨- household￨L￨NN￨O￨- crowding￨L￨VBG￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- humidity￨L￨NN￨O￨A have￨L￨VBP￨O￨- a￨L￨DT￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- EV71￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- could￨L￨MD￨O￨- increase￨L￨VB￨O￨- this￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ’s￨L￨POS￨O￨- burden￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- EV71￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- greatest￨L￨JJS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- summer￨L￨NN￨DATE￨- months￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- recur￨L￨VBP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨A pattern￨L￨NN￨O￨- .￨L￨.￨O￨- +Briefly￨U￨RB￨O￨- ,￨L￨,￨O￨- laboratory-confirmed￨L￨JJ￨O￨- cases￨L￨NNS￨O￨A of￨L￨IN￨O￨- EV71￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- reported￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Center￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Taiwan￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Taiwan￨U￨NNP￨ORGANIZATION￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- April￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 1998￨L￨CD￨DATE￨- and￨L￨CC￨O￨- December￨U￨NNP￨DATE￨- 31￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2008￨L￨CD￨DATE￨- were￨L￨VBD￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- following￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- interest￨L￨NN￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Differences￨U￨NNS￨O￨- in￨L￨IN￨O￨- ILI￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- in￨L￨IN￨O￨- Israel￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Synchrony￨U￨NN￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- Israeli￨U￨JJ￨NATIONALITY￨- cities￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- year￨L￨NN￨DURATION￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Comparing￨U￨VBG￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- local￨L￨JJ￨O￨- ”￨L￨''￨O￨- Israeli￨U￨JJ￨NATIONALITY￨- synchrony￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- intercontinental￨L￨JJ￨O￨- synchrony￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨- tested￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- Israel￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- France￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨JJR￨O￨- estimate￨L￨NN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- different￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Influenza-Like￨U￨JJ￨O￨- Illness￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- diagnoses￨L￨NNS￨O￨- ,￨L￨,￨O￨- virus￨L￨NN￨O￨- isolations￨L￨NNS￨O￨- ,￨L￨,￨O￨- death￨L￨NN￨O￨- records￨L￨NNS￨O￨- from￨L￨IN￨O￨- pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- physician￨L￨NN￨TITLE￨- visits￨L￨NNS￨O￨- and￨L￨CC￨O￨- web￨L￨NN￨O￨- search￨L￨NN￨O￨- queries￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- displays￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- over￨L￨IN￨O￨- eleven￨L￨NNS￨DURATION￨- years￨L￨NNS￨DURATION￨- when￨L￨WRB￨O￨- aggregated￨L￨JJ￨O￨- spatially￨L￨RB￨O￨- over￨L￨IN￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- Israel￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- classical￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- or￨L￨CC￨O￨- SIRS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incubation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- negligible￨L￨JJ￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- each￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- class￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- once￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- becomes￨L￨VBZ￨O￨- infectious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- move￨L￨VB￨O￨- to￨L￨TO￨O￨- I￨U￨PRP￨O￨- class￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- later￨L￨RB￨O￨- recovers￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- to￨L￨TO￨O￨- move￨L￨VB￨O￨- to￨L￨TO￨O￨- R￨U￨NN￨O￨- class￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- acquire￨L￨VBP￨O￨- permanent￨L￨JJ￨O￨- or￨L￨CC￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- quantity￨L￨NN￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- ℛ￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨A generated￨L￨VBN￨O￨A by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- other￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- establishing￨L￨VBG￨O￨- global￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨A include￨L￨VBP￨O￨A Dulac￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- criterion￨L￨NN￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- prove￨L￨VB￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Poincaré￨U￨NNP￨O￨- Bendixson￨U￨NNP￨O￨- theorem￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- Kamgang￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Sallet￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- Qiao￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- Lyapunov￨U￨NNP￨PERSON￨- function￨L￨NN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A with￨L￨IN￨O￨- standard￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- functions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- widely￨L￨RB￨O￨A used￨L￨VBN￨O￨A in￨L￨IN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- those￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- are￨L￨VBP￨O￨- that￨L￨IN￨O￨- small￨L￨JJ￨O￨- commuter￨L￨NN￨O￨- counts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- at￨L￨IN￨O￨- longer￨L￨JJR￨O￨- distances￨L￨NNS￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- fitting￨L￨JJ￨O￨A the￨L￨DT￨O￨- power-law￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- that￨L￨IN￨O￨- small￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- still￨L￨RB￨O￨- trigger￨L￨VB￨O￨- disproportionately￨L￨RB￨O￨- large￨L￨JJ￨O￨- local￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Most￨U￨RBS￨O￨- importantly￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- synthetic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- reconstructed￨L￨VBN￨O￨- from￨L￨IN￨O￨- fitted￨L￨JJ￨O￨- gravity￨L￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- ask￨L￨VB￨O￨- how￨L￨WRB￨O￨- epidemic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- aggregation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- fitting￨L￨JJ￨O￨A the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- gravity￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- commuting￨L￨VBG￨O￨- data￨L￨NNS￨O￨- successfully￨L￨RB￨O￨- captured￨L￨VBN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- synchrony￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- distance￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- look￨L￨VB￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- gravity￨L￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- commuter￨L￨NN￨O￨- movement￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- US￨U￨NNP￨COUNTRY￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fidelity￨L￨NN￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- expected￨L￨VBN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- models￨L￨NNS￨O￨- we￨L￨PRP￨O￨- fit￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- destination￨L￨NN￨O￨- work￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- we￨L￨PRP￨O￨- exclude￨L￨VBP￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨A fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- wards￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- no￨L￨DT￨O￨- commuter￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- study￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- conventional￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- variance￨L￨NN￨O￨- component￨L￨NN￨O￨- estimation￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- capture￨L￨VB￨O￨- genetic￨L￨JJ￨O￨A variation￨L￨NN￨O￨A in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- exposure￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- factor￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- indirect￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IGE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- associative￨L￨JJ￨O￨- or￨L￨CC￨O￨- social￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A variation￨L￨NN￨O￨A in￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- investigates￨L￨VBZ￨O￨- heritable￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- trait￨L￨NN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- another￨L￨DT￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2012a￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- that￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A variation￨L￨NN￨O￨A in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- infectivity￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- captured￨L￨VBN￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- extent￨L￨NN￨O￨- from￨L￨IN￨O￨- binary￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- IGE￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- standard￨L￨JJ￨O￨- models￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- lend￨L￨VB￨O￨- themselves￨L￨PRP￨O￨- to￨L￨TO￨O￨- estimating￨L￨VBG￨O￨- genetic￨L￨JJ￨O￨A variation￨L￨NN￨O￨A in￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- individual￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- expressing￨L￨VBG￨O￨- it￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- study￨L￨NN￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- severe￨L￨JJ￨O￨- shortcomings￨L￨NNS￨O￨- in￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- IGE￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- genetic￨L￨JJ￨O￨- variance￨L￨NN￨O￨- in￨L￨IN￨O￨- infectivity￨L￨NN￨O￨A .￨L￨.￨O￨- +Short￨U￨NNP￨MISC￨- Report￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Prevalence￨U￨NN￨MISC￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨O￨- E￨U￨NN￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- swine￨L￨NNS￨O￨A populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- European￨U￨JJ￨NATIONALITY￨- countriesAlessandra￨L￨NN￨O￨- Berto1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Jantien￨U￨NNP￨O￨- A￨U￨NNP￨O￨- Backer1￨U￨NN￨O￨- ,￨L￨,￨O￨- Joao￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- Mesquita3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Maria￨U￨NNP￨PERSON￨- SJ￨U￨NNP￨PERSON￨- Nascimento4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Malcolm￨U￨NNP￨PERSON￨- Banks2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Francesca￨U￨NNP￨PERSON￨- Martelli2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Fabio￨U￨NNP￨PERSON￨- Ostanello5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Giorgia￨U￨NNP￨PERSON￨- Angeloni6￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ilaria￨U￨NNP￨PERSON￨- Di￨U￨NNP￨PERSON￨- Bartolo6￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Franco￨U￨NNP￨PERSON￨- M￨U￨NNP￨O￨- Ruggeri6￨U￨NN￨O￨- ,￨L￨,￨O￨- Petra￨U￨NNP￨PERSON￨- Vasickova8￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marta￨U￨NNP￨PERSON￨- Diez-Valcarce7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marta￨U￨NNP￨PERSON￨- Hernandez7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- Rodriguez-Lazaro7￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wim￨U￨NNP￨PERSON￨- HM￨U￨NNS￨PERSON￨- van￨L￨NN￨PERSON￨- der￨L￨FW￨PERSON￨- Poel1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 5:190￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Berto￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Hepatitis￨U￨NNP￨O￨- E￨U￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HEV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- genotype￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 4￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- liver￨L￨NN￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- its￨L￨PRP$￨O￨- main￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- in￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- describes￨L￨VBZ￨O￨- HEV￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- within-herd￨L￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- European￨U￨JJ￨NATIONALITY￨- Countries￨U￨NNS￨MISC￨- (￨L￨-LRB-￨O￨- EU￨U￨NNP￨LOCATION￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Czech￨U￨NNP￨COUNTRY￨- Republic￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Portugal￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Spain￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- The￨U￨DT￨O￨- Netherlands￨U￨NNPS￨COUNTRY￨- and￨L￨CC￨O￨- United￨U￨NNP￨COUNTRY￨- Kingdom￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- confirming￨L￨VBG￨O￨- that￨L￨IN￨O￨- HEV￨U￨NN￨O￨- is￨L￨VBZ￨O￨- circulating￨L￨VBG￨O￨- in￨L￨IN￨O￨- pig￨L￨NN￨O￨- farms￨L￨NNS￨O￨A from￨L￨IN￨O￨- weaners￨L￨NNS￨O￨- to￨L￨TO￨O￨- fatteners￨L￨NNS￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- range￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- countries￨L￨NNS￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- collected￨L￨VBN￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- were￨L￨VBD￨O￨- analyzed￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HEV￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- confirming￨L￨VBG￨O￨- that￨L￨IN￨O￨- HEV￨U￨NN￨O￨- is￨L￨VBZ￨O￨- endemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- pig￨L￨NN￨O￨- farms￨L￨NNS￨O￨A .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- swine￨L￨NNS￨O￨- HEV￨U￨NN￨O￨- in￨L￨IN￨O￨- 274￨L￨CD￨NUMBER￨- pigs￨L￨NNS￨O￨- from￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- swine￨L￨NNS￨O￨- farms￨L￨NNS￨O￨A of￨L￨IN￨O￨- Northern￨U￨JJ￨LOCATION￨- Italy￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Findings￨U￨NNS￨O￨- The￨U￨DT￨O￨- HEV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- commercial￨L￨JJ￨O￨- pig￨L￨NN￨O￨- farms￨L￨NNS￨O￨A in￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- was￨L￨VBD￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +Whereas￨U￨IN￨O￨- social￨L￨JJ￨O￨A network￨L￨NN￨O￨A epidemiology￨L￨NN￨O￨- maps￨L￨VBZ￨O￨- risk￨L￨NN￨O￨- pathways￨L￨NNS￨O￨- between￨L￨IN￨O￨- PWID￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- thereby￨L￨RB￨O￨- identifying￨L￨VBG￨O￨- potential￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- of￨L￨IN￨O￨- HCV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- genetic￨L￨JJ￨O￨- make-up￨L￨NN￨O￨- of￨L￨IN￨O￨- HCV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- members￨L￨NNS￨O￨- using￨L￨VBG￨O￨- molecular￨L￨JJ￨O￨- phylogenetics￨L￨NNS￨O￨- can￨L￨MD￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- pathways￨L￨NNS￨O￨- though￨L￨IN￨O￨- which￨L￨WDT￨O￨- HCV￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- actually￨L￨RB￨O￨- been￨L￨VBN￨O￨- transmitted￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- investigators￨L￨NNS￨O￨- previously￨L￨RB￨DATE￨- conducted￨L￨VBN￨O￨- a￨L￨DT￨O￨- cross-sectional￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- study￨L￨NN￨O￨- but￨L￨CC￨O￨- observed￨L￨VBD￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- social￨L￨JJ￨O￨A distance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- links￨L￨NNS￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- recent￨L￨JJ￨O￨- injecting￨L￨VBG￨O￨- contacts￨L￨NNS￨O￨- connecting￨L￨VBG￨O￨- any￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- network￨L￨NN￨O￨- members￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- distance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- index￨L￨NN￨O￨- participants￨L￨NNS￨O￨A '￨L￨POS￨O￨- injecting￨L￨VBG￨O￨- partners￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- important￨L￨JJ￨O￨- determinants￨L￨NNS￨O￨- of￨L￨IN￨O￨- HCV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- HCV￨U￨NN￨O￨- status￨L￨NN￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- at￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- injecting￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- injecting￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- geographic￨L￨JJ￨O￨- injecting￨L￨VBG￨O￨- location￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- used￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- relationship￨L￨NN￨O￨- with￨L￨IN￨O￨- index￨L￨NN￨O￨- participants￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- whilst￨L￨IN￨O￨- social￨L￨JJ￨O￨A network￨L￨NN￨O￨A characteristics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- linked￨L￨VBN￨O￨- to￨L￨TO￨O￨- HCV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- association￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- confounding￨L￨VBG￨O￨- relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- injecting￨L￨VBG￨O￨- risk￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Networks￨U￨NNP￨MISC￨- 2￨L￨CD￨NUMBER￨- Study￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- -￨L￨:￨O￨- a￨L￨DT￨O￨- longitudinal￨L￨JJ￨O￨- study￨L￨NN￨O￨- that￨L￨WDT￨O￨- combined￨L￨VBD￨O￨- molecular￨L￨JJ￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨A network￨L￨NN￨O￨A epidemiological￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- HCV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- PWID￨U￨NN￨O￨- in￨L￨IN￨O￨- Melbourne￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨A and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- described￨L￨VBN￨O￨- using￨L￨VBG￨O￨- discrete￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- since￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- different￨L￨JJ￨O￨- incubation￨L￨NN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- durations￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- health￨L￨NN￨O￨- status￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- several￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨A analysis￨L￨NN￨O￨A of￨L￨IN￨O￨- individual-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- parameters￨L￨NNS￨O￨- on￨L￨IN￨O￨- public￨L￨JJ￨O￨- policy￨L￨NN￨O￨- related￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- Smallpox￨U￨NNP￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨A analysis￨L￨NN￨O￨A could￨L￨MD￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- assumptions￨L￨NNS￨O￨- relating￨L￨VBG￨O￨- to￨L￨TO￨O￨- how￨L￨WRB￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- individual￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- after￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- might￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- outcomes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- by￨L￨IN￨O￨- Burke￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- simplify￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- :￨L￨:￨O￨- transmissibility￨L￨NN￨O￨- ,￨L￨,￨O￨- incubation￨L￨NN￨O￨A period￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- minimum￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- a￨L￨DT￨O￨- CRS￨U￨NNP￨O￨- increase￨L￨NN￨O￨- after￨L￨IN￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- universal￨L￨JJ￨O￨- rubella￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- rooting￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ranging￨L￨VBG￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- plausible￨L￨JJ￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- contexts￨L￨NNS￨O￨- and￨L￨CC￨O￨- remaining￨L￨VBG￨O￨- uncertainties￨L￨NNS￨O￨- in￨L￨IN￨O￨- rubella￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- challenge￨L￨NN￨O￨- of￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- CRS￨U￨NNP￨O￨- by￨L￨IN￨O￨- rubella-containing￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RCV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- complex￨L￨JJ￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- feedbacks￨L￨NNS￨O￨- between￨L￨IN￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- mean￨L￨VBP￨O￨- that￨L￨IN￨O￨- routine￨L￨JJ￨O￨- infant￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ‘￨L￨``￨O￨- universal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ’￨L￨''￨O￨- )￨L￨-RRB-￨O￨- will￨L￨MD￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- if￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- enough￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- age-specific￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- rubella￨L￨NN￨O￨A decreases￨L￨VBZ￨O￨- at￨L￨IN￨O￨- all￨L￨DT￨O￨- ages￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- approach￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- or￨L￨CC￨O￨- eliminate￨L￨VB￨O￨- rubella￨L￨NN￨O￨A transmission￨L￨NN￨O￨- by￨L￨IN￨O￨- universal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- male￨L￨NN￨O￨- and￨L￨CC￨O￨- female￨L￨JJ￨O￨- infants￨L￨NNS￨O￨- and￨L￨CC￨O￨- young￨L￨JJ￨O￨- children￨L￨NNS￨O￨- ,￨L￨,￨O￨- sometimes￨L￨RB￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- supplementary￨L￨JJ￨O￨- catch-up￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- in￨L￨IN￨O￨- older￨L￨JJR￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- serious￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- modelling￨L￨NN￨O￨- rubella￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- high-income￨L￨JJ￨O￨- ,￨L￨,￨O￨- low￨L￨JJ￨O￨- birth-rate￨L￨JJ￨O￨- contexts￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- infants￨L￨NNS￨O￨A and￨L￨CC￨O￨- young￨L￨JJ￨O￨- children￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- sole￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- coverage￨L￨NN￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- around￨L￨IN￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- is￨L￨VBZ￨O￨- required￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recommendation￨L￨NN￨O￨- of￨L￨IN￨O￨- WHO￨U￨WP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vector-borne￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- over￨L￨IN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- covers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- vector-host￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- involvement￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- population￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- specific￨L￨JJ￨O￨- terminology￨L￨NN￨O￨- :￨L￨:￨O￨- Recruitment￨U￨NN￨O￨- rate￨L￨NN￨O￨- :￨L￨:￨O￨- Since￨U￨IN￨O￨- only￨L￨RB￨O￨- adult￨L￨JJ￨O￨- female￨L￨JJ￨O￨A mosquitoes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- models￨L￨NNS￨O￨- only￨L￨RB￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- adult￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- female￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- mosquitoes￨L￨NNS￨O￨- ,￨L￨,￨O￨- ignoring￨L￨VBG￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- aquatic￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- eggs￨L￨NNS￨O￨- ,￨L￨,￨O￨- larvae￨L￨NNS￨O￨- and￨L￨CC￨O￨- pupae￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- previously￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- ,￨L￨,￨O￨- subsequent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- another￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- serotype￨L￨NN￨O￨A leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clinical￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- serotype￨L￨NN￨O￨- combinations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- risk-factor￨L￨NN￨O￨- for￨L￨IN￨O￨- DHF/DSS￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +published￨L￨VBN￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- dengue￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- estimation￨L￨NN￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- consequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- we￨L￨PRP￨O￨- review￨L￨VBP￨O￨- was￨L￨VBD￨O￨- also￨L￨RB￨O￨- briefly￨L￨RB￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Johansson￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- more￨L￨JJR￨O￨- detailed￨L￨JJ￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- structures￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- link￨L￨NN￨O￨- this￨L￨DT￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- entomological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- schools￨L￨NNS￨O￨- closures￨L￨NNS￨O￨A were￨L￨VBD￨O￨- sporadic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- triggered￨L￨VBN￨O￨- by￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- decision-making￨L￨JJ￨O￨- entities￨L￨NNS￨O￨- under￨L￨IN￨O￨- variable￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- Mexico￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- implemented￨L￨VBD￨O￨- nationwide￨L￨JJ￨O￨- school￨L￨NN￨O￨- closures￨L￨NNS￨O￨- that￨L￨WDT￨O￨- lasted￨L￨VBD￨O￨- for￨L￨IN￨O￨- about￨L￨RB￨O￨- 2￨L￨CD￨NUMBER￨- weeks.In￨L￨JJ￨O￨- developing￨L￨VBG￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- policies￨L￨NNS￨O￨- for￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- pandemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- quantitative￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- their￨L￨PRP$￨O￨- efficacies￨L￨NNS￨O￨- and￨L￨CC￨O￨- costs￨L￨NNS￨O￨- under￨L￨IN￨O￨- possible￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- combine￨L￨VBP￨O￨- a￨L￨DT￨O￨- decision￨L￨NN￨O￨- analytic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- with￨L￨IN￨O￨- economic￨L￨JJ￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modeling￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closures￨L￨NNS￨O￨A in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- .￨L￨.￨O￨- +Software￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- EpiFire￨U￨NNP￨O￨- :￨L￨:￨O￨- An￨U￨DT￨O￨- open￨L￨JJ￨O￨- source￨L￨NN￨O￨- C++￨U￨NNP￨O￨- library￨L￨NN￨O￨- and￨L￨CC￨O￨- application￨L￨NN￨O￨- for￨L￨IN￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A epidemiologyThomas￨L￨NNS￨O￨- Hladish1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Eugene￨U￨NNP￨PERSON￨- Melamud2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Luis￨U￨NNP￨PERSON￨- Alberto￨U￨NNP￨PERSON￨- Barrera1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Alison￨U￨NNP￨PERSON￨- Galvani4￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Lauren￨U￨NNP￨PERSON￨- Ancel￨U￨NNP￨PERSON￨- Meyers1￨U￨NN￨O￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 13:76￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Hladish￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Contact￨U￨NN￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- increasingly￨L￨RB￨O￨- common￨L￨JJ￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- we￨L￨PRP￨O￨- lack￨L￨VBP￨O￨- a￨L￨DT￨O￨- flexible￨L￨JJ￨O￨- programming￨L￨NN￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- through￨L￨IN￨O￨- such￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- EpiFire￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- applications￨L￨NNS￨O￨- programming￨L￨VBG￨O￨- interface￨L￨NN￨O￨A and￨L￨CC￨O￨- graphical￨L￨JJ￨O￨- user￨L￨NN￨O￨- interface￨L￨NN￨O￨- implemented￨L￨VBD￨O￨- in￨L￨IN￨O￨- C++￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fast￨L￨JJ￨O￨- and￨L￨CC￨O￨- efficient￨L￨JJ￨O￨- library￨L￨NN￨O￨- for￨L￨IN￨O￨- generating￨L￨VBG￨O￨- ,￨L￨,￨O￨- analyzing￨L￨VBG￨O￨- and￨L￨CC￨O￨- manipulating￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Network-based￨U￨JJ￨O￨- percolation￨L￨NN￨O￨- and￨L￨CC￨O￨- chain-binomial￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨A of￨L￨IN￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- non-network￨L￨JJ￨O￨- mass-action￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- performed￨L￨VBN￨O￨- using￨L￨VBG￨O￨- EpiFire￨U￨NNP￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- EpiFire￨U￨NNP￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- open-source￨L￨JJ￨O￨- programming￨L￨NN￨O￨- interface￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- focus￨L￨NN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +EpiFire￨U￨NNP￨PERSON￨- also￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- point-and-click￨L￨JJ￨O￨- interface￨L￨NN￨O￨A for￨L￨IN￨O￨- generating￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- conducting￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- creating￨L￨VBG￨O￨- figures￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨- simulation￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- ,￨L￨,￨O￨- stratified￨L￨VBN￨O￨- worm￨L￨NN￨O￨A burden￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SWB￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- of￨L￨IN￨O￨- multi-village￨L￨JJ￨O￨- Schistosoma￨U￨NN￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- project￨L￨NN￨O￨- programmatic￨L￨JJ￨O￨- success￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- mass￨L￨NN￨O￨- treatment￨L￨NN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- Schistosoma-endemic￨U￨JJ￨MISC￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- advantage￨L￨NN￨O￨- where￨L￨WRB￨O￨- decision-making￨L￨JJ￨O￨- policy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- made￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- population￨L￨NN￨O￨- or￨L￨CC￨O￨- school￨L￨NN￨O￨- age￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- Schistosoma￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- After￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- calibrated￨L￨VBN￨O￨- with￨L￨IN￨O￨- available￨L￨JJ￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- pilot￨L￨NN￨TITLE￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- project￨L￨VB￨O￨A the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- targeted-or￨L￨JJ￨O￨- population-wide￨L￨JJ￨O￨- mass￨L￨NN￨O￨- treatment￨L￨NN￨O￨- programs￨L￨NNS￨O￨- now￨L￨RB￨DATE￨- being￨L￨VBG￨O￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- predicting￨L￨VBG￨O￨- schistosomiasis￨L￨NN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- community-level￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- burden￨L￨NN￨O￨A using￨L￨VBG￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Stratified￨U￨JJ￨MISC￨- Worm￨U￨NN￨MISC￨- Burden￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- SWB￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- formulation￨L￨NN￨O￨- ,￨L￨,￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- calibration￨L￨NN￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- completed￨L￨VBN￨O￨- multi-year￨L￨JJ￨O￨- pilot￨L￨NN￨TITLE￨- schistosomiasis￨L￨NN￨O￨- control￨L￨NN￨O￨- program￨L￨NN￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- control￨L￨NN￨O￨- initiatives￨L￨NNS￨O￨- have￨L￨VBP￨O￨- had￨L￨VBN￨O￨- success￨L￨NN￨O￨A in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- Schistosoma￨U￨NN￨LOCATION￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- although￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- other￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- mostly￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- is￨L￨VBZ￨O￨- typical￨L￨JJ￨O￨A for￨L￨IN￨O￨- schistosomiasis￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- pre-treatment￨L￨NN￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- Schistosoma￨U￨NN￨LOCATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- school￨L￨NN￨O￨- age￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- varied￨L￨VBD￨O￨- significantly￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- 23￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- to￨L￨TO￨O￨- 74￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- landscape￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- span￨L￨NN￨O￨- of￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- km￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- simulations￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- grid￨L￨NN￨O￨- cell￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- vectors￨L￨NNS￨O￨A locate￨L￨VBP￨O￨- host￨L￨NN￨TITLE￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- affected￨L￨VBN￨O￨- cattle￨L￨NNS￨O￨- increases￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- seen￨L￨VBN￨O￨- on￨L￨IN￨O￨- rows￨L￨NNS￨O￨- in￨L￨IN￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨A between￨L￨IN￨O￨- pasture￨L￨NN￨O￨- areas￨L￨NNS￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- that￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- parameters￨L￨NNS￨O￨- affecting￨L￨VBG￨O￨- vectors￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- should￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- so￨L￨RB￨O￨- fast￨L￨RB￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- several￨L￨JJ￨O￨- different￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- should￨L￨MD￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- vector-borne￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- enter￨L￨VBP￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨A of￨L￨IN￨O￨- interest￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- simulate￨L￨VB￨O￨- this￨L￨DT￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- CPU￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- vectors￨L￨NNS￨O￨A can￨L￨MD￨O￨- locate￨L￨VB￨O￨- hosts￨L￨NNS￨O￨- with￨L￨IN￨O￨- certainty￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- driving￨L￨NN￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Uptake￨U￨NN￨O￨- of￨L￨IN￨O￨- screening￨L￨NN￨O￨- ranged￨L￨VBD￨O￨- from￨L￨IN￨O￨- 64￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- all￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- trials￨L￨NNS￨O￨- found￨L￨VBD￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- PID￨U￨NN￨O￨- from￨L￨IN￨O￨- any￨L￨DT￨O￨- cause￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- group￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- group.It￨L￨NN￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- when￨L￨WRB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- PID￨U￨NN￨O￨- occurs￨L￨VBZ￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- screening￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- should￨L￨MD￨O￨- take￨L￨VB￨O￨- place￨L￨NN￨O￨- to￨L￨TO￨O￨- maximise￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨A screening￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- PID￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- currently￨L￨RB￨DATE￨- unknown￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objectives￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- were￨L￨VBD￨O￨- :￨L￨:￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- progression￨L￨NN￨O￨- from￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- PID￨U￨NNP￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- chlamydia￨L￨NN￨O￨- screening￨L￨NN￨O￨- intervention￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- progresses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- PID￨U￨NNP￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- published￨L￨VBN￨O￨- randomised￨L￨JJ￨O￨- controlled￨L￨JJ￨O￨- trial￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- predicted￨L￨VBN￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- PID￨U￨NN￨O￨- cases￨L￨NNS￨O￨- from￨L￨IN￨O￨- all￨L￨DT￨O￨- causes￨L￨NNS￨O￨- after￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨A infected￨L￨JJ￨O￨- women￨L￨NNS￨O￨- that￨L￨WDT￨O￨- progresses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- PID￨U￨NN￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- progression￨L￨NN￨O￨- .￨L￨.￨O￨- +Amongst￨U￨IN￨O￨- the￨L￨DT￨O￨- few￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- with￨L￨IN￨O￨- explicit￨L￨JJ￨O￨- descriptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- progression￨L￨NN￨O￨- from￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- PID￨U￨NNP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- that￨L￨IN￨O￨- PID￨U￨NN￨O￨- develops￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- half￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- chlamydia￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- half￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- chlamydia￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨A infected￨L￨JJ￨O￨- women￨L￨NNS￨O￨- who￨L￨WP￨O￨- progress￨L￨VBP￨O￨- to￨L￨TO￨O￨- PID￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- process￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- method￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- RCT￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- classic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- studied￨L￨VBN￨O￨- on￨L￨IN￨O￨- regular￨L￨JJ￨O￨- lattices￨L￨NNS￨O￨A and￨L￨CC￨O￨- on￨L￨IN￨O￨- specific￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- random￨L￨JJ￨O￨- ,￨L￨,￨O￨- small￨L￨JJ￨O￨- world￨L￨NN￨O￨- or￨L￨CC￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- review￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- or￨L￨CC￨O￨- social￨L￨JJ￨O￨- details￨L￨NNS￨O￨- quantitatively￨L￨RB￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨- and￨L￨CC￨O￨- universal￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- adaptive￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- impacts￨L￨NNS￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A by￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- voluntary￨L￨JJ￨O￨- vaccinations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- interpersonal￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- affected￨L￨VBN￨O￨- population￨L￨NN￨O￨- influence￨L￨NN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨A topology￨L￨NN￨O￨A .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- behavioral￨L￨JJ￨O￨- adaptations￨L￨NNS￨O￨- will￨L￨MD￨O￨- change￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨A topology￨L￨NN￨O￨A and￨L￨CC￨O￨- feed￨L￨VB￨O￨- back￨L￨RB￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- personal￨L￨JJ￨O￨- consideration￨L￨NN￨O￨- of￨L￨IN￨O￨- safe￨L￨JJ￨O￨A moves￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- profound￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- city￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- choice￨L￨NN￨O￨- of￨L￨IN￨O￨- mobility￨L￨NN￨O￨- destination￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- movement￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- city￨L￨NN￨O￨- further￨L￨RB￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- there￨L￨RB￨O￨- .￨L￨.￨O￨- +Resorting￨U￨VBG￨O￨- to￨L￨TO￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- possible￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- that￨L￨WDT￨O￨- encompass￨L￨VBP￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- safety￨L￨NN￨O￨- information￨L￨NN￨O￨- situations￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- safe￨L￨JJ￨O￨A moves￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- unsafe￨L￨JJ￨O￨- moves￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- explain￨L￨VB￨O￨- it￨L￨PRP￨O￨- later￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- quantified￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- few￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- reaction-diffusion￨L￨NN￨O￨- processes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- successfully￨L￨RB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- considerations￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- mobility￨L￨NN￨O￨A patterns123456789101112131415161718192021￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- relevance￨L￨NN￨O￨- of￨L￨IN￨O￨- safe￨L￨JJ￨O￨A moves￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- safety￨L￨NN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- often￨L￨RB￨O￨- collect￨L￨VBP￨O￨- information￨L￨NN￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- on-going￨L￨JJ￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- utilize￨L￨VB￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- guide￨L￨VB￨O￨- their￨L￨PRP$￨O￨- mobility￨L￨NN￨O￨A patterns343536￨L￨NN￨O￨- .￨L￨.￨O￨- +Unfortunately￨U￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- questionnaire￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- bias￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- purposes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- relevant￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- partners￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- year￨L￨NN￨DATE￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- lifetime￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- particularly￨L￨RB￨O￨- strong￨L￨JJ￨O￨- bias￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- allow￨L￨VB￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- build￨L￨VB￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- network￨L￨NN￨O￨- behind￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- subjects￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- larger￨L￨JJR￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- unknown￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- high￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- extreme￨L￨JJ￨O￨- topologies￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- important￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- infinite￨L￨JJ￨O￨A scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- we￨L￨PRP￨O￨- take￨L￨VBP￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- run￨L￨VB￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- subjects￨L￨NNS￨O￨A infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- formation￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Romantic￨U￨JJ￨MISC￨- network￨L￨NN￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- makes￨L￨VBZ￨O￨- this￨L￨DT￨O￨- particular￨L￨JJ￨O￨- example￨L￨NN￨O￨- even￨L￨RB￨O￨- more￨L￨RBR￨O￨- interesting￨L￨JJ￨O￨- .￨L￨.￨O￨- +General￨U￨NNP￨TITLE￨- results￨L￨VBZ￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- bursts￨L￨NNS￨O￨- were￨L￨VBD￨O￨- given￨L￨VBN￨O￨- for￨L￨IN￨O￨- small-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- dimensions￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Software￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Development￨U￨NNP￨MISC￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- resource￨L￨NN￨O￨A modelling￨L￨NN￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- decision￨L￨NN￨O￨- makers￨L￨NNS￨O￨- in￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- preparedness￨L￨NN￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- AsiaFluCap￨U￨NNP￨MISC￨- SimulatorMart￨U￨NNP￨MISC￨- Lambertus￨U￨NNP￨MISC￨- Stein1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- James￨U￨NNP￨PERSON￨- W￨U￨NNP￨PERSON￨- Rudge3￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Richard￨U￨NNP￨PERSON￨- Coker3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Charlie￨U￨NNP￨PERSON￨- van￨L￨NNP￨PERSON￨- der￨L￨FW￨PERSON￨- Weijden4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ralf￨U￨NNP￨PERSON￨- Krumkamp5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Piya￨U￨NNP￨PERSON￨- Hanvoravongchai7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Irwin￨U￨NNP￨PERSON￨- Chavez8￨U￨NNP￨O￨- ,￨L￨,￨O￨- Weerasak￨U￨NNP￨PERSON￨- Putthasri9￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Bounlay￨U￨NNP￨O￨- Phommasack10￨U￨NNP￨O￨- ,￨L￨,￨O￨- Wiku￨U￨NNP￨O￨- Adisasmito11￨U￨NNP￨O￨- ,￨L￨,￨O￨- Sok￨U￨NNP￨O￨- Touch12￨U￨NNP￨O￨- ,￨L￨,￨O￨- Le￨U￨NNP￨PERSON￨- Minh￨U￨NNP￨PERSON￨- Sat13￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Yu-Chen￨U￨NNP￨O￨- Hsu14￨U￨NN￨O￨- ,￨L￨,￨O￨- Mirjam￨U￨NNP￨PERSON￨- Kretzschmar1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Aura￨U￨NNP￨MISC￨- Timen1￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 12:870￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Stein￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- care￨L￨NN￨O￨- planning￨L￨NN￨O￨- for￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenging￨L￨JJ￨O￨- task￨L￨NN￨O￨- which￨L￨WDT￨O￨- requires￨L￨VBZ￨O￨- predictive￨L￨JJ￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- response￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- evaluated￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- tool￨L￨NN￨O￨- was￨L￨VBD￨O￨- built￨L￨VBN￨O￨- in￨L￨IN￨O￨- MS￨U￨NN￨STATE_OR_PROVINCE￨- Excel￨U￨NNP￨MISC￨- ©￨L￨SYM￨O￨- and￨L￨CC￨O￨- contains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- user-friendly￨L￨JJ￨O￨- interface￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- users￨L￨NNS￨O￨- to￨L￨TO￨O￨- select￨L￨JJ￨O￨- mild￨L￨JJ￨O￨- or￨L￨CC￨O￨- severe￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- change￨L￨NN￨O￨- resource￨L￨NN￨O￨A parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- run￨L￨VB￨O￨- simulations￨L￨NNS￨O￨- for￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- multiple￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- AsiaFluCap￨U￨NNP￨O￨- project￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- and￨L￨CC￨O￨- flexible￨L￨JJ￨O￨- resource￨L￨NN￨O￨A modelling￨L￨NN￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- in￨L￨IN￨O￨- understanding￨L￨NN￨O￨- and￨L￨CC￨O￨- preparing￨L￨VBG￨O￨- for￨L￨IN￨O￨- surges￨L￨VBZ￨O￨- in￨L￨IN￨O￨- resource￨L￨NN￨O￨- demand￨L￨NN￨O￨- during￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- pandemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- AsiaFluCap￨U￨NNP￨O￨- Simulator￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- resource￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- containing￨L￨VBG￨O￨- 28￨L￨CD￨NUMBER￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- resources￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- specific￨L￨JJ￨O￨- hypotheses￨L￨NNS￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- primates￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- demographics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- birth￨L￨NN￨O￨A rates￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- will￨L￨MD￨O￨- experience￨L￨VB￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- periodicities￨L￨NNS￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- observed￨L￨VBN￨O￨- as￨L￨IN￨O￨- isolated￨L￨VBN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- coupling￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- subsystems￨L￨NNS￨O￨- through￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- biting￨L￨VBG￨O￨- will￨L￨MD￨O￨- act￨L￨VB￨O￨- to￨L￨TO￨O￨- synchronize￨L￨VB￨O￨- incidence￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- eight-year￨L￨JJ￨DURATION￨- periodicity￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- observed￨L￨VBN￨O￨- across￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- primate￨L￨JJ￨O￨- species￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- cycling￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Surveillance￨U￨NN￨O￨- is￨L￨VBZ￨O￨- performed￨L￨VBN￨O￨- by￨L￨IN￨O￨- capturing￨L￨VBG￨O￨- mosquitoes￨L￨NNS￨O￨- via-human￨L￨JJ￨O￨- landing￨L￨NN￨O￨- collection￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- gallery￨L￨NN￨O￨- forest￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- and￨L￨CC￨O￨- opportunistic￨L￨JJ￨O￨- capture￨L￨NN￨O￨- of￨L￨IN￨O￨- primates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- note￨L￨NN￨O￨- :￨L￨:￨O￨- Yellow￨U￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- chikungunya￨L￨NN￨O￨- isolations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- included￨L￨VBN￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- inactivity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A time￨L￨NN￨O￨- series￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- collection￨L￨NN￨O￨- activities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- independent￨L￨JJ￨RELIGION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- would￨L￨MD￨O￨- expect￨L￨VB￨O￨- to￨L￨TO￨O￨- see￨L￨VB￨O￨- primates￨L￨NNS￨O￨- with￨L￨IN￨O￨- higher￨L￨JJR￨O￨- birth￨L￨NN￨O￨A rates￨L￨NNS￨O￨A having￨L￨VBG￨O￨- shorter￨L￨JJR￨O￨- inter-epidemic￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- than￨L￨IN￨O￨- primates￨L￨NNS￨O￨- with￨L￨IN￨O￨- lower￨L￨JJR￨O￨- birth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- driving￨L￨VBG￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- hosts￨L￨NNS￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- synchrony￨L￨NN￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- synchronized￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Dengue￨U￨JJ￨O￨- virus￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- :￨L￨:￨O￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- non-human￨L￨JJ￨O￨- primates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- occasionally￨L￨RB￨O￨- among￨L￨IN￨O￨- humans￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- Aedes￨U￨NNPS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- forest￨L￨NN￨O￨A canopy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- sylvatic￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- humans￨L￨NNS￨O￨- primarily￨L￨RB￨O￨- by￨L￨IN￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨- in￨L￨IN￨O￨- rural￨L￨JJ￨O￨- villages￨L￨NNS￨O￨- and￨L￨CC￨O￨- urban￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- hypothesized￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- long-period￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- sylvatic￨L￨JJ￨O￨- dengue￨L￨NN￨O￨A is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- population￨L￨NN￨O￨- turnover￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cycling￨L￨NN￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- non-human￨L￨JJ￨O￨- primates￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- dependence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨A level￨L￨NN￨O￨A is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- differ￨L￨VB￨O￨- from￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- is￨L￨VBZ￨O￨- influenced￨L￨VBN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- by￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- diagnostic￨L￨JJ￨O￨- performance￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- govern￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clarify￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- epidemiologically￨L￨RB￨O￨- observed￨L￨VBN￨O￨- risk￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- antigenic￨L￨JJ￨O￨- types￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- scaled￨L￨VBN￨O￨- by￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- make￨L￨VB￨O￨- a￨L￨DT￨O￨- clear￨L￨JJ￨O￨- distinction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- hereafter￨L￨RB￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- VE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- population￨L￨NN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- among￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨A level￨L￨NN￨O￨A ,￨L￨,￨O￨- reflecting￨L￨VBG￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- measure￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨A level￨L￨NN￨O￨A ,￨L￨,￨O￨- involves￨L￨VBZ￨O￨- an￨L￨DT￨O￨- observational￨L￨JJ￨O￨- problem￨L￨NN￨O￨- that￨L￨WDT￨O￨- stems￨L￨VBZ￨O￨- from￨L￨IN￨O￨- dependence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- have￨L￨VBP￨O￨- required￨L￨VBN￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- various￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- study￨L￨NN￨O￨- designs￨L￨NNS￨O￨- and￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- setting￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- strain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- either￨L￨CC￨O￨- VT￨U￨NN￨STATE_OR_PROVINCE￨- or￨L￨CC￨O￨- NVT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- elicits￨L￨VBZ￨O￨- life-long￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- by￨L￨IN￨O￨- employing￨L￨VBG￨O￨A the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infectious-Recovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- without￨L￨IN￨O￨- re-infection￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Every￨U￨DT￨SET￨- 2￨L￨CD￨SET￨- years￨L￨NNS￨SET￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Joint￨U￨NNP￨ORGANIZATION￨- United￨U￨NNP￨ORGANIZATION￨- Nations￨U￨NNPS￨ORGANIZATION￨- Programme￨U￨NNP￨ORGANIZATION￨- on￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- UNAIDS￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- produces￨L￨VBZ￨O￨- estimates￨L￨NNS￨O￨- and￨L￨CC￨O￨- projections￨L￨NNS￨O￨A of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- by￨L￨IN￨O￨- country￨L￨NN￨O￨- .1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- technical￨L￨JJ￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- effort￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- guided￨L￨VBN￨O￨- by￨L￨IN￨O￨- recommendations￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- UNAIDS￨U￨NNP￨ORGANIZATION￨- Reference￨U￨NNP￨ORGANIZATION￨- Group￨U￨NNP￨ORGANIZATION￨- on￨L￨IN￨ORGANIZATION￨- Estimates￨U￨NNS￨ORGANIZATION￨- ,￨L￨,￨O￨- Modelling￨U￨NN￨O￨- and￨L￨CC￨O￨- Projections￨U￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- suite￨L￨NN￨O￨- of￨L￨IN￨O￨- analytic￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- purpose￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- UNAIDS￨U￨NNP￨O￨- Estimation￨U￨NN￨O￨- and￨L￨CC￨O￨- Projection￨U￨NNP￨O￨- Package￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- EPP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Spectrum￨U￨NN￨O￨- .8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- EPP￨U￨NN￨O￨- fits￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- sentinel￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- national￨L￨JJ￨O￨- population-based￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- seroprevalence￨L￨NN￨O￨- surveys￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Spectrum￨U￨NN￨O￨- translates￨L￨VBZ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- corresponding￨L￨VBG￨O￨- population￨L￨NN￨O￨- health￨L￨NN￨O￨- consequences￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- obtain￨L￨VB￨O￨- probabilistic￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- and￨L￨CC￨O￨- projections￨L￨NNS￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- integrate￨L￨VB￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- modelled￨L￨VBN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .7￨L￨CD￨NUMBER￨- 16￨L￨CD￨NUMBER￨- Formally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- mapping￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- input￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- outputs￨L￨NNS￨O￨- on￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- by￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- ρ￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- national￨L￨JJ￨O￨- population-based￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- surveys￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- generalised￨L￨JJ￨O￨A epidemics￨L￨NNS￨O￨- to￨L￨TO￨O￨- calibrate￨L￨VB￨O￨- overall￨L￨JJ￨O￨- population￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- levels￨L￨NNS￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .16￨L￨CD￨NUMBER￨- 17￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- UNAIDS￨U￨NN￨O￨- EPP￨U￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- formulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- section￨L￨NN￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- specific￨L￨JJ￨O￨- formulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- were￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- :￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- parameterised￨L￨VBD￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- penalised￨L￨VBN￨O￨- B-splines￨U￨NNS￨O￨- ,13￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- another￨L￨DT￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risks￨L￨NNS￨O￨- follow￨L￨VBP￨O￨- a￨L￨DT￨O￨- Gaussian￨U￨JJ￨MISC￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- with￨L￨IN￨O￨- mean￨L￨JJ￨O￨- zero￨L￨CD￨NUMBER￨- .14￨L￨CD￨NUMBER￨- These￨U￨DT￨O￨- flexible￨L￨JJ￨O￨- models￨L￨NNS￨O￨- appeared￨L￨VBD￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- better￨L￨JJR￨O￨- fits￨L￨NNS￨O￨A to￨L￨TO￨O￨- recent￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- several￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- incorporated￨L￨VBD￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- four-parameter￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- patterned￨L￨VBN￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- closed￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .2￨L￨NN￨NUMBER￨- This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- provided￨L￨VBD￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- fit￨L￨NN￨O￨- to￨L￨TO￨O￨- most￨L￨RBS￨O￨- generalised￨L￨JJ￨O￨A epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- concentrated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- sometimes￨L￨RB￨O￨- failed￨L￨VBD￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- flat￨L￨JJ￨O￨- enough￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- for￨L￨IN￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- turnover￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- injecting￨L￨VBG￨O￨- drug￨L￨NN￨O￨- users￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IDU￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- contains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- flexible￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- option￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- parameter￨L￨NN￨O￨- r￨L￨NN￨O￨- to￨L￨TO￨O￨- change￨L￨VB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- currently￨L￨RB￨DATE￨- achieved￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- formulation￨L￨NN￨O￨- that￨L￨WDT￨O￨- draws￨L￨VBZ￨O￨- new￨L￨JJ￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- r￨L￨NN￨O￨- annually￨L￨RB￨SET￨- .1￨L￨CD￨NUMBER￨- 4￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- general￨L￨JJ￨TITLE￨- modelling￨L￨NN￨O￨- framework￨L￨NN￨O￨- here￨L￨RB￨O￨- but￨L￨CC￨O￨- employed￨L￨VBN￨O￨- splines￨L￨NNS￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- smooth￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- for￨L￨IN￨O￨- r.￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- 9￨L￨CD￨NUMBER￨- More￨U￨JJR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- analogue￨L￨NN￨O￨- to￨L￨TO￨O￨- B-splines￨U￨NNS￨MISC￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- penalised￨L￨VBD￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- slope￨L￨NN￨O￨- of￨L￨IN￨O￨- r￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- degree￨L￨NN￨O￨- difference￨L￨NN￨O￨- penalty￨L￨NN￨O￨- ,￨L￨,￨O￨- formulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- prior￨L￨JJ￨O￨A distributions￨L￨NNS￨O￨- around￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- adjacent￨L￨JJ￨O￨- spline￨L￨NN￨O￨- coefficients￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- βi￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- expressed￨L￨VBN￨O￨- as￨L￨IN￨O￨- :￨L￨:￨O￨- βi￨L￨NN￨O￨- =￨L￨JJ￨O￨- βi￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- βi￨L￨FW￨O￨- −￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- βi￨L￨NN￨O￨- −￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ui￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- 10￨L￨CD￨NUMBER￨- By￨U￨IN￨O￨- letting￨L￨VBG￨O￨- ui￨L￨NN￨O￨- ∼￨L￨NN￨O￨- normal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- τ2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- smoothness￨L￨NN￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- parameter￨L￨NN￨O￨- τ2￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- must￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- τ2￨L￨NN￨O￨- ∼￨L￨CD￨NUMBER￨- inverse-gamma￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0.001,0.001￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .6￨L￨CD￨NUMBER￨- 10￨L￨CD￨NUMBER￨- As￨U￨IN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- previous￨L￨JJ￨O￨- proposal￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spline￨L￨NN￨O￨- was￨L￨VBD￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- evenly￨L￨RB￨O￨- spaced￨L￨VBN￨O￨- basis￨L￨NN￨O￨- functions￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- nine￨L￨CD￨NUMBER￨- unknown￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- seven￨L￨CD￨NUMBER￨- spline￨L￨NN￨O￨- coefficients￨L￨NNS￨O￨- ,￨L￨,￨O￨- τ2￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- pulse￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- seed￨L￨NN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .6￨L￨CD￨NUMBER￨- Models￨U￨NNS￨O￨- were￨L￨VBD￨O￨- fit￨L￨JJ￨O￨- via￨L￨IN￨O￨- incremental￨L￨JJ￨O￨- mixture￨L￨NN￨O￨- importance￨L￨NN￨O￨- sampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IMIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .11￨L￨CD￨NUMBER￨- Results￨U￨NNS￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- calibrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- national￨L￨JJ￨O￨- population-based￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- visual￨L￨JJ￨O￨- inspection￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- fits￨L￨VBZ￨O￨- to￨L￨TO￨O￨- prevalence￨L￨NN￨O￨- trends￨L￨NNS￨O￨- implied￨L￨VBN￨O￨- by￨L￨IN￨O￨- sentinel￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +UNAIDS￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- working￨L￨VBG￨O￨- with￨L￨IN￨O￨- country￨L￨NN￨O￨- analysts￨L￨NNS￨O￨- ,￨L￨,￨O￨- currently￨L￨RB￨DATE￨- uses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Estimation￨U￨NN￨O￨- and￨L￨CC￨O￨- Projection￨U￨NNP￨O￨- Package￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- EPP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- and￨L￨CC￨O￨- predict￨L￨VB￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- .1￨L￨NN￨NUMBER￨- 2￨L￨CD￨NUMBER￨- EPP￨U￨NN￨ORGANIZATION￨- incorporates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- ,￨L￨,￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- sentinel￨L￨NN￨O￨A surveillance￨L￨NN￨O￨A and￨L￨CC￨O￨- national￨L￨JJ￨O￨- population-based￨L￨JJ￨O￨- survey￨L￨NN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- .3￨L￨NN￨NUMBER￨- Previous￨U￨JJ￨O￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- EPP￨U￨NN￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- produced￨L￨VBD￨O￨- highly￨L￨RB￨O￨- plausible￨L￨JJ￨O￨- fits￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- diverse￨L￨JJ￨O￨- array￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- but￨L￨CC￨O￨- have￨L￨VBP￨O￨- had￨L￨VBN￨O￨- difficulty￨L￨NN￨O￨- reproducing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Uganda￨U￨NNP￨COUNTRY￨- where￨L￨WRB￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- increasing￨L￨VBG￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- declining￨L￨VBG￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- that￨L￨WDT￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- r￨L￨NN￨O￨- has￨L￨VBZ￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- projections￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explored￨L￨VBD￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- making￨L￨VBG￨O￨- future￨L￨JJ￨DATE￨- predictions￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- spline-based￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- formulation￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- imposes￨L￨VBZ￨O￨- very￨L￨RB￨O￨- little￨L￨JJ￨O￨- prior￨L￨JJ￨O￨A information￨L￨NN￨O￨- on￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- trajectories￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .4￨L￨NN￨NUMBER￨- 5￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- implemented￨L￨VBD￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- by￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- spline-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- informative￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- prior￨L￨RB￨O￨- for￨L￨IN￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- projection￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- equilibrium￨L￨NN￨O￨- prior￨L￨RB￨O￨A uses￨L￨VBZ￨O￨- this￨L￨DT￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- r￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- normally￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- prior￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- r￨L￨NN￨O￨- when￨L￨WRB￨O￨- making￨L￨VBG￨O￨- future￨L￨JJ￨DATE￨- projections￨L￨NNS￨O￨- .6￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spline-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- employs￨L￨VBZ￨O￨- this￨L￨DT￨O￨- prior￨L￨JJ￨O￨- yields￨L￨NNS￨O￨- rapidly￨L￨RB￨O￨- changing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- incidence￨L￨NN￨O￨- when￨L￨WRB￨O￨- predicting￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- facilitate￨L￨VB￨O￨- these￨L￨DT￨O￨- projections￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spline-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- presented￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- ,6￨L￨RB￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- flexible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- EPP￨U￨NN￨O￨- ,4￨L￨CD￨NUMBER￨- incorporate￨L￨VB￨O￨- a￨L￨DT￨O￨- prior￨L￨JJ￨O￨A distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- r￨L￨NN￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- year￨L￨NN￨DATE￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- directs￨L￨VBZ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- towards￨L￨IN￨O￨- an￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- here￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- equilibrium￨L￨NN￨O￨- prior￨L￨RB￨O￨- ’￨L￨''￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spline￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- fits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- penalised￨L￨VBN￨O￨- B-splines.10￨U￨JJ￨O￨- The￨U￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- follow￨L￨VBP￨O￨- a￨L￨DT￨O￨- Gaussian￨U￨JJ￨MISC￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- with￨L￨IN￨O￨- mean￨L￨JJ￨O￨- zero￨L￨CD￨NUMBER￨- .11￨L￨CD￨NUMBER￨- They￨U￨PRP￨O￨- both￨L￨DT￨O￨- offer￨L￨VBP￨O￨- more￨L￨JJR￨O￨- flexible￨L￨JJ￨O￨A structures￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- better￨L￨RBR￨O￨- when￨L￨WRB￨O￨- EPP￨U￨NN￨O￨- encounters￨L￨VBZ￨O￨- challenges￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- incorporates￨L￨VBZ￨O￨- population￨L￨NN￨O￨- change￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- four￨L￨CD￨NUMBER￨- input￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- :￨L￨:￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- t0￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ;￨L￨:￨O￨- f0￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adult￨L￨JJ￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- φ￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- change￨L￨NN￨O￨- parameter￨L￨NN￨O￨- .3￨L￨NN￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- output￨L￨NN￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- yearly￨L￨JJ￨SET￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨A rates￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- national￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- survival￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- eligible￨L￨JJ￨O￨- for￨L￨IN￨O￨- ART￨U￨NN￨O￨- also￨L￨RB￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- they￨L￨PRP￨O￨- receive￨L￨VBP￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- .8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- implementation￨L￨NN￨O￨- experience￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- the￨L￨DT￨O￨- Gaussian￨U￨JJ￨MISC￨- random￨L￨JJ￨O￨A walk￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- provides￨L￨VBZ￨O￨- similar￨L￨JJ￨O￨- trends￨L￨NNS￨O￨- of￨L￨IN￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- across￨L￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- generalised￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- examples￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Unlike￨U￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- EPP￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spline￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- impose￨L￨VB￨O￨- any￨L￨DT￨O￨- common￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨A across￨L￨IN￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- fitted￨L￨JJ￨O￨- curve￨L￨NN￨O￨- is￨L￨VBZ￨O￨- completely￨L￨RB￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- EPP￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- hard￨L￨JJ￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- .6￨L￨CD￨NUMBER￨- 10￨L￨CD￨NUMBER￨- 11￨L￨CD￨NUMBER￨- A￨U￨DT￨O￨- flexible￨L￨JJ￨O￨A epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- fit￨L￨NN￨O￨- to￨L￨TO￨O￨- recently￨L￨RB￨DATE￨- observed￨L￨VBN￨O￨- prevalence￨L￨NN￨O￨- trends￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- correct￨L￨VB￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- adopt￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- procedure￨L￨NN￨O￨- :￨L￨:￨O￨- first￨L￨RB￨ORDINAL￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- randomly￨L￨RB￨O￨- sampling￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨A load￨L￨NN￨O￨A over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- generate￨L￨VBP￨O￨- different￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- profiles￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- by￨L￨IN￨O￨- fitting￨L￨NN￨O￨- a￨L￨DT￨O￨- gamma￨L￨NN￨O￨- distribution￨L￨NN￨O￨- with￨L￨IN￨O￨- offset￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- second￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- MARV￨U￨NNP￨O￨- infected￨L￨JJ￨O￨- survive￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- we￨L￨PRP￨O￨- weigh￨L￨VBP￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- decaying￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectiousness￨L￨NN￨O￨- profiles￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- factor￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- generation￨L￨NN￨O￨A time￨L￨NN￨O￨A distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨- measures￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- appropriate￨L￨JJ￨O￨- health￨L￨NN￨O￨- responses￨L￨NNS￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- MARV￨U￨NN￨ORGANIZATION￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- fitting￨L￨JJ￨O￨- a￨L￨DT￨O￨- gamma￨L￨NN￨O￨- distribution￨L￨NN￨O￨- with￨L￨IN￨O￨- offset￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- viral￨L￨JJ￨O￨A load￨L￨NN￨O￨A over￨L￨IN￨O￨- time￨L￨NN￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- 3￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- average￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- 13.9￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- :￨L￨:￨O￨- 12.7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- standard￨L￨JJ￨O￨- deviation￨L￨NN￨O￨- 7.5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- :￨L￨:￨O￨- 5.5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11.4￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- pointed￨L￨VBN￨O￨- out￨L￨RP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨A time￨L￨NN￨O￨A distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- individually￨L￨RB￨O￨- targeted￨L￨VBN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- case￨L￨NN￨O￨- isolation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- by￨L￨IN￨O￨- performing￨L￨VBG￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- viral￨L￨JJ￨O￨A load￨L￨NN￨O￨A data￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- non-human￨L￨JJ￨O￨- primates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- specifically￨L￨RB￨O￨- on￨L￨IN￨O￨- Cercopithecus￨U￨NN￨MISC￨- aethiops￨L￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- injected￨L￨VBN￨O￨- by￨L￨IN￨O￨- Marburg￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Notification￨U￨NN￨O￨- of￨L￨IN￨O￨- previous￨L￨JJ￨O￨- partners￨L￨NNS￨O￨- of￨L￨IN￨O￨- index￨L￨NN￨O￨- cases￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- recommended￨L￨VBN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- screening￨L￨NN￨O￨- programs￨L￨NNS￨O￨- that￨L￨WDT￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- limit￨L￨VB￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- C.￨U￨NNP￨O￨- Mathematical￨U￨NNP￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- examination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- PN￨U￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- index￨L￨NN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- onward￨L￨RB￨O￨- transmission￨L￨NN￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- partnerships￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- partnership￨L￨NN￨O￨A history￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- documented￨L￨VBN￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- partner￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- structure￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- partnerships￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- partnership￨L￨NN￨O￨A network￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- reconstructed￨L￨VBN￨O￨- over￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- partnership￨L￨NN￨O￨- history￨L￨NN￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- partner￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- kept￨L￨VBN￨O￨- on￨L￨IN￨O￨- record￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Complex￨U￨NN￨O￨- PN￨U￨NN￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- involve￨L￨VBP￨O￨- tracing￨L￨VBG￨O￨- both￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- and￨L￨CC￨O￨- previous￨L￨JJ￨O￨- partners￨L￨NNS￨O￨- of￨L￨IN￨O￨- index￨L￨NN￨O￨A cases￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- investigated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- individual-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- notifying￨L￨VBG￨O￨- current￨L￨JJ￨DATE￨- partners￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- index￨L￨NN￨O￨A cases￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- illustrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- reviews￨L￨NNS￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- modeling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- where￨L￨WRB￨O￨- PN￨U￨NNP￨ORGANIZATION￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- re-infection￨L￨NN￨O￨- of￨L￨IN￨O￨- index￨L￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +RNA-Seq￨U￨NN￨O￨- is￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- gene￨L￨NN￨O￨- expression￨L￨NN￨O￨A profiling￨L￨NN￨O￨- in￨L￨IN￨O￨- plants￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- provides￨L￨VBZ￨O￨- significant￨L￨JJ￨O￨- advantages￨L￨NNS￨O￨- over￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- microarray￨L￨NN￨O￨- analysis￨L￨NN￨O￨- :￨L￨:￨O￨- e.g.￨L￨FW￨O￨- accurate￨L￨JJ￨O￨- quantification￨L￨NN￨O￨- of￨L￨IN￨O￨- gene￨L￨NN￨O￨- expression￨L￨NN￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- background￨L￨NN￨O￨- ,￨L￨,￨O￨- high￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- expression￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- range￨L￨NN￨O￨- ,￨L￨,￨O￨- high￨L￨JJ￨O￨- reproducibility￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- technical￨L￨JJ￨O￨- and￨L￨CC￨O￨- biological￨L￨JJ￨O￨- replicates￨L￨VBZ￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- novel￨L￨JJ￨O￨- splicing￨L￨NN￨O￨- isoforms￨L￨NNS￨O￨- and￨L￨CC￨O￨- boundaries￨L￨NNS￨O￨- of￨L￨IN￨O￨- un-translated￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- at￨L￨IN￨O￨- single￨L￨JJ￨O￨- nucleotide￨L￨NN￨O￨- resolution￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +GV-specific￨U￨JJ￨O￨- response￨L￨NN￨O￨- was￨L￨VBD￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- prompt￨L￨JJ￨O￨- induction￨L￨NN￨O￨- and￨L￨CC￨O￨- fine￨L￨JJ￨O￨- regulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- battery￨L￨NN￨CRIMINAL_CHARGE￨- of￨L￨IN￨O￨- processes￨L￨NNS￨O￨- including￨L￨VBG￨O￨- up-regulation￨L￨NN￨O￨- of￨L￨IN￨O￨- diterpene￨L￨JJ￨O￨- phytoalexin￨L￨NN￨O￨- biosynthetic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- DPB￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- genes￨L￨NNS￨O￨A ,￨L￨,￨O￨- perception￨L￨NN￨O￨- and￨L￨CC￨O￨- signalling￨L￨NN￨O￨- through￨L￨IN￨O￨- wall￨L￨NN￨O￨- associated￨L￨VBN￨O￨- kinases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- WAKs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- chitin￨L￨NN￨O￨- sensors￨L￨NNS￨O￨- ,￨L￨,￨O￨- WRKY￨U￨NN￨O￨- and￨L￨CC￨O￨- MAP￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- KKK￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- genes￨L￨NNS￨O￨- families￨L￨NNS￨O￨- ,￨L￨,￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- defence￨L￨NN￨O￨- genes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- chitinase￨L￨NN￨O￨- ,￨L￨,￨O￨- glycosyl￨L￨NN￨O￨- hydrolase￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- regulated￨L￨VBN￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- gene￨L￨NN￨O￨- analogs￨L￨NNS￨O￨- .￨L￨.￨O￨- +Upon￨U￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- GV￨U￨NN￨LOCATION￨- typically￨L￨RB￨O￨- shows￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- pin-point￨L￨JJ￨O￨- lesions￨L￨NNS￨O￨- without￨L￨IN￨O￨- further￨L￨JJ￨O￨- progress￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- current￨L￨JJ￨DATE￨- genetic￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- major￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- gene￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- govern￨L￨VBP￨O￨- GV￨U￨NN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- blast￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- unpublished￨L￨JJ￨O￨- data￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- blast￨L￨NN￨O￨- R￨U￨NN￨O￨- genes￨L￨NNS￨O￨A ,￨L￨,￨O￨- all￨L￨DT￨O￨- located￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- rice￨L￨NN￨O￨- chromosome￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- confer￨L￨VBP￨O￨- broad-spectrum￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- blast￨L￨NN￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- Pi9￨U￨NN￨O￨- ,￨L￨,￨O￨- Pi2￨U￨NN￨O￨- and￨L￨CC￨O￨- Piz-t￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Differentially￨U￨RB￨O￨- expressed￨L￨VBN￨O￨- genes￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- DEGs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- called￨L￨VBN￨O￨- with￨L￨IN￨O￨- DESeq￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- voluntarily￨L￨RB￨O￨- choosing￨L￨VBG￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- rely￨L￨VB￨O￨- upon￨L￨IN￨O￨- how￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- weigh￨L￨VBP￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨A versus￨L￨CC￨O￨- the￨L￨DT￨O￨- risks￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- tension￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- game￨L￨NN￨O￨- theory￨L￨NN￨O￨- or￨L￨CC￨O￨- related￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- previous￨L￨JJ￨O￨- game￨L￨NN￨O￨- theoretical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨A behavior￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- identified￨L￨VBD￨O￨- one￨L￨CD￨NUMBER￨- possible￨L￨JJ￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- paradox￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- constraining￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- changes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- incentive￨L￨NN￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- and￨L￨CC￨O￨- makes￨L￨VBZ￨O￨- rapid￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- through￨L￨IN￨O￨- voluntary￨L￨JJ￨O￨- ring￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- possible￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- some￨L￨DT￨O￨- circumstances￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- prophylactic￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- need￨L￨VBP￨O￨- not￨L￨RB￨O￨- wait￨L￨VB￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨A until￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- being￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- our￨L￨PRP$￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- only￨L￨RB￨O￨- seek￨L￨VBP￨O￨- vaccination￨L￨NN￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- would￨L￨MD￨O￨- not￨L￨RB￨O￨- apply￨L￨VB￨O￨- .￨L￨.￨O￨- +Ring￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- strategy￨L￨NN￨O￨- of￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨A the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- simplicity￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- node￨L￨NN￨O￨- who￨L￨WP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- efficaciously￨L￨RB￨O￨- vaccinated￨L￨VBN￨O￨A is￨L￨VBZ￨O￨- immediately￨L￨RB￨O￨- protected￨L￨VBN￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- has￨L￨VBZ￨O￨- no￨L￨DT￨O￨- effect￨L￨NN￨O￨- in￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- already￨L￨RB￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +Concurrently￨U￨RB￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- response￨L￨NN￨O￨- cells￨L￨NNS￨O￨A are￨L￨VBP￨O￨- activated￨L￨VBN￨O￨- to￨L￨TO￨O￨- kill￨L￨VB￨O￨- K￨U￨NNP￨O￨- pathogens￨L￨NNS￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨JJ￨O￨- kill￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- cell￨L￨NN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- and￨L￨CC￨O￨- kill￨L￨VB￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ρ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- scaling￨L￨NN￨O￨- parameter￨L￨NN￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- theoretical￨L￨JJ￨O￨- limits￨L￨NNS￨O￨- at￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- one￨L￨CD￨NUMBER￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- within-host￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- follows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- response￨L￨NN￨O￨- cells￨L￨NNS￨O￨A and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- populations￨L￨NNS￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- B￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- concentration￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- C￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- concentration￨L￨NN￨O￨- of￨L￨IN￨O￨- response￨L￨NN￨O￨- cells￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t.￨L￨NN￨O￨- Within￨U￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- D￨U￨NN￨O￨- new￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- while￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- multiply￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- killed￨L￨VBN￨O￨- by￨L￨IN￨O￨- response￨L￨NN￨O￨- cells￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- P￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- B￨U￨NN￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- C￨U￨NN￨O￨- response￨L￨NN￨O￨- cells￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- obtained￨L￨VBD￨O￨- weekly￨L￨JJ￨SET￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- H3N2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2009￨L￨CD￨DATE￨- by￨L￨IN￨O￨- combining￨L￨VBG￨O￨- influenza-like-illness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- records￨L￨NNS￨O￨- of￨L￨IN￨O￨- associated￨L￨VBN￨O￨- ,￨L￨,￨O￨- laboratory-confirmed￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A by￨L￨IN￨O￨- type￨L￨NN￨O￨- and￨L￨CC￨O￨- subtype￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- similarly￨L￨RB￨O￨- for￨L￨IN￨O￨- France￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- USA￨U￨NN￨COUNTRY￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- supplementary￨L￨JJ￨O￨- online￨L￨NN￨O￨- material￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Text￨U￨VB￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- this￨L￨DT￨O￨- has￨L￨VBZ￨O￨- limited￨L￨VBN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- statistically￨L￨RB￨O￨- interfaced￨L￨VBN￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- simultaneously￨L￨RB￨O￨- estimated￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +ABC￨U￨NNP￨ORGANIZATION￨- allows￨L￨VBZ￨O￨- mechanistic￨L￨JJ￨O￨- phylodynamic￨L￨JJ￨O￨A models￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- simultaneously￨L￨RB￨O￨- fitted￨L￨VBN￨O￨- against￨L￨IN￨O￨- both￨L￨DT￨O￨- sequence￨L￨NN￨O￨- and￨L￨CC￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- fit￨L￨VBP￨O￨- and￨L￨CC￨O￨- assess￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- combined￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- sequence￨L￨NN￨O￨A and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- fitting￨L￨JJ￨O￨- and￨L￨CC￨O￨- assessing￨L￨VBG￨O￨- phylodynamic￨L￨JJ￨O￨A models￨L￨NNS￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- not￨L￨RB￨O￨- commonly￨L￨RB￨O￨- done￨L￨VBN￨O￨- .￨L￨.￨O￨- +Influenza￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- through￨L￨IN￨O￨- various￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- routes￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- aerosol￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- occurs￨L￨VBZ￨O￨- through￨L￨IN￨O￨- inhalation￨L￨NN￨O￨- of￨L￨IN￨O￨- droplet￨L￨NN￨O￨- nuclei￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- shrunk￨L￨VBN￨O￨- dried￨L￨VBD￨O￨- droplets￨L￨NNS￨O￨- with￨L￨IN￨O￨- diameters￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 10￨L￨CD￨NUMBER￨- µm￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- droplet￨L￨NN￨O￨- spray￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- particles￨L￨NNS￨O￨- with￨L￨IN￨O￨- diameters￨L￨NNS￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- µm￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- cough￨L￨NN￨O￨- or￨L￨CC￨O￨- sneeze￨L￨VBP￨O￨- directly￨L￨RB￨O￨- deposit￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mucous￨L￨JJ￨O￨- membranes￨L￨NNS￨O￨- of￨L￨IN￨O￨- others￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- pathogen￨L￨NN￨O￨- transfer￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- handshake￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨- contact￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- pathogens￨L￨NNS￨O￨- transfer￨L￨VB￨O￨- from￨L￨IN￨O￨- fomites￨L￨NNS￨O￨- to￨L￨TO￨O￨- hands￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- fomite￨L￨NN￨O￨- mediated￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- routes￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- :￨L￨:￨O￨- Droplet-contaminated-fomite￨U￨JJ￨O￨- route￨L￨NN￨O￨- :￨L￨:￨O￨- exposed￨L￨VBN￨O￨- surfaces￨L￨NNS￨O￨- near￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- person￨L￨NN￨O￨- become￨L￨VBN￨O￨- contaminated￨L￨VBN￨O￨A by￨L￨IN￨O￨- spray￨L￨NN￨O￨- or￨L￨CC￨O￨- settling￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- laden￨L￨JJ￨O￨- large￨L￨JJ￨O￨- droplets￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- separating￨L￨VBG￨O￨- fomite￨L￨JJ￨O￨- routes￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contamination￨L￨NN￨O￨- source￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- study￨L￨VB￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- covering￨L￨VBG￨O￨- coughs￨L￨NNS￨O￨- by￨L￨IN￨O￨- hands￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- fomite￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- on￨L￨IN￨O￨- fomite￨L￨NN￨O￨- mediated￨L￨VBD￨O￨- transmissions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Hand-contaminated-fomite￨U￨JJ￨O￨- route￨L￨NN￨O￨- :￨L￨:￨O￨- hands￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- contaminated￨L￨VBN￨O￨A with￨L￨IN￨O￨- virus￨L￨NN￨O￨- following￨L￨VBG￨O￨- excretion￨L￨NN￨O￨- ;￨L￨:￨O￨- virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- deposited￨L￨VBN￨O￨- to￨L￨TO￨O￨- surfaces￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- manuscript￨L￨NN￨O￨- we￨L￨PRP￨O￨- classify￨L￨VBP￨O￨- fomites￨L￨NNS￨O￨- by￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- surface￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- and￨L￨CC￨O￨- touching￨L￨VBG￨O￨- rates￨L￨NNS￨O￨- ;￨L￨:￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- fomite￨L￨JJ￨O￨- types￨L￨NNS￨O￨- separately￨L￨RB￨O￨A as￨L￨IN￨O￨- if￨L￨IN￨O￨- each￨L￨DT￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- independent￨L￨JJ￨RELIGION￨- contribution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Applying￨U￨VBG￨O￨- different￨L￨JJ￨O￨- forecasting￨L￨NN￨O￨A methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- exploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- predictive￨L￨JJ￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- non-environmental￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- reducing￨L￨VBG￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- necessary￨L￨JJ￨O￨- next￨L￨JJ￨O￨- steps￨L￨NNS￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- will￨L￨MD￨O￨- help￨L￨VB￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- approach￨L￨NN￨O￨- and￨L￨CC￨O￨- predictors￨L￨NNS￨O￨- for￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- forecasting￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- diversity￨L￨NN￨O￨- in￨L￨IN￨O￨- forecasting￨L￨NN￨O￨A accuracy￨L￨NN￨O￨- measures￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- scale-dependent￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- limits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- comparability￨L￨NN￨O￨- of￨L￨IN￨O￨- forecasting￨L￨NN￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- it￨L￨PRP￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- predictors￨L￨NNS￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- forecasting￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- objective￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- and￨L￨CC￨O￨- assess￨L￨VB￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- predictors￨L￨NNS￨O￨- ,￨L￨,￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- included￨L￨VBD￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- scoping￨L￨VBG￨O￨- review￨L￨NN￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- forecasted￨L￨VBD￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- prevalence￨L￨NN￨O￨- or￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Dynamic￨U￨NNP￨MISC￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- health￨L￨NN￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A during￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemicYiting￨L￨NN￨O￨- Xue1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Ivar￨U￨NNP￨PERSON￨- Sønbø￨U￨NNP￨PERSON￨- Kristiansen3￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Birgitte￨U￨NNP￨PERSON￨- Freiesleben￨U￨NNP￨PERSON￨- de￨L￨IN￨O￨- Blasio1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 12:962￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Xue￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- between￨L￨IN￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- health￨L￨NN￨O￨- benefits￨L￨NNS￨O￨- for￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- involving￨L￨VBG￨O￨- different￨L￨JJ￨O￨- target￨L￨NN￨O￨- groups￨L￨NNS￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- closure￨L￨NN￨O￨- durations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A by￨L￨IN￨O￨- varying￨L￨VBG￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- targets￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- kindergarten￨L￨NN￨O￨- ,￨L￨,￨O￨- primary￨L￨JJ￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- secondary￨L￨JJ￨O￨- school￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- closure￨L￨NN￨O￨- durations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- pandemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- 1.5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2.0￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- 2.5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- severe￨L￨JJ￨O￨- pandemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- 1-2￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Spanish￨U￨JJ￨CAUSE_OF_DEATH￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- indirect￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- disregarded￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- closing￨L￨VBG￨O￨- kindergarten￨L￨NN￨O￨- ,￨L￨,￨O￨- primary￨L￨JJ￨O￨- and￨L￨CC￨O￨- secondary￨L￨JJ￨O￨- school￨L￨NN￨O￨A for￨L￨IN￨O￨- extended￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- capturing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- economic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- capturing￨L￨VBG￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A varies￨L￨VBZ￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- indirect￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- very￨L￨RB￨O￨- informative￨L￨JJ￨O￨- for￨L￨IN￨O￨- revealing￨L￨VBG￨O￨- key￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- limitations￨L￨NNS￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨- from￨L￨IN￨O￨- densely￨L￨RB￨O￨- sampled￨L￨VBN￨O￨A outbreaks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- population￨L￨NN￨O￨- consensus￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- extreme￨L￨JJ￨O￨- similarity￨L￨NN￨O￨- and￨L￨CC￨O￨- where￨L￨WRB￨O￨- samples￨L￨NNS￨O￨- include￨L￨VBP￨O￨- both￨L￨CC￨O￨- ancestral￨L￨JJ￨O￨- and￨L￨CC￨O￨- descendent￨L￨JJ￨O￨- isolates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Vertical￨U￨JJ￨O￨- bars￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- copy￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- estimated￨L￨VBN￨O￨- by￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- PCR￨U￨NN￨O￨- from￨L￨IN￨O￨- all￨L￨DT￨O￨- horses￨L￨NNS￨O￨- sampled￨L￨VBN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨DATE￨- same￨L￨JJ￨DATE￨- day￨L￨NN￨DATE￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- log￨L￨NN￨O￨- scale￨L￨NN￨O￨- .￨L￨.￨O￨- +Nasal￨U￨JJ￨O￨- swabs￨L￨NNS￨O￨- from￨L￨IN￨O￨- horses￨L￨NNS￨O￨- were￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- 19￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 21￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- yards￨L￨NNS￨O￨- in￨L￨IN￨O￨- Newmarket￨U￨NNP￨CITY￨- infected￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- March￨U￨NNP￨DATE￨- 13th￨L￨NNP￨DATE￨- to￨L￨TO￨O￨- May￨U￨NNP￨DATE￨- 8￨L￨CD￨DATE￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- yards￨L￨NNS￨O￨- located￨L￨JJ￨O￨- outside￨L￨IN￨O￨A of￨L￨IN￨O￨- Newmarket￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- yards￨L￨NNS￨O￨- O￨U￨NN￨O￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- and￨L￨CC￨O￨- W￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Details￨U￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- horses￨L￨NNS￨O￨- in￨L￨IN￨O￨- training￨L￨NN￨O￨- per￨L￨IN￨O￨- yard￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- yard￨L￨NN￨O￨- location￨L￨NN￨O￨- and￨L￨CC￨O￨- date￨L￨NN￨O￨- of￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- diagnosis￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- its￨L￨PRP$￨O￨- original￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- antigenic￨L￨JJ￨O￨A types￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- low￨L￨JJ￨O￨- frequencies￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- idea￨L￨NN￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- mutation￨L￨NN￨O￨- from￨L￨IN￨O￨- preexisting￨L￨VBG￨O￨- strains￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- rate￨L￨NN￨O￨- as￨L￨IN￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- limit￨L￨VB￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- type￨L￨NN￨O￨- favored￨L￨VBN￨O￨- by￨L￨IN￨O￨- selection￨L￨NN￨O￨- .￨L￨.￨O￨- +Antigenic￨U￨JJ￨O￨- types￨L￨NNS￨O￨- replace￨L￨VBP￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- with￨L￨IN￨O￨- waves￨L￨NNS￨O￨- of￨L￨IN￨O￨- dominance￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- frequency-dependent￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- mediated￨L￨JJ￨O￨- selection￨L￨NN￨O￨- as￨L￨IN￨O￨- “￨L￨``￨O￨- niches￨L￨NNS￨O￨- ”￨L￨''￨O￨- in￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨A space￨L￨NN￨O￨- are￨L￨VBP￨O￨- dynamically￨L￨RB￨O￨- generated￨L￨VBN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- exploited￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨JJ￨O￨- virus￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- eschews￨L￨VBZ￨O￨- the￨L￨DT￨O￨- paradigm￨L￨NN￨O￨- of￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨A drift￨L￨NN￨O￨- ,￨L￨,￨O￨- instead￨L￨RB￨O￨- considering￨L￨VBG￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- functional￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- defining￨L￨VBG￨O￨- epitopes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- limited￨L￨JJ￨O￨- phenotypically￨L￨RB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- restricted￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- types￨L￨NNS￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- immune￨L￨JJ￨O￨- selection￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- manner￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- limited￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨A mutations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- of￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- tend￨L￨VBP￨O￨- to￨L￨TO￨O￨- polarize￨L￨VB￨O￨- between￨L￨IN￨O￨- those￨L￨DT￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- types￨L￨NNS￨O￨- dictate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- where￨L￨WRB￨O￨- host￨L￨NN￨TITLE￨- immune-mediated￨L￨JJ￨O￨- selection￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- driver￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- look￨L￨VBP￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- protective￨L￨JJ￨O￨A action￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- history￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- what￨L￨WP￨O￨- drives￨L￨VBZ￨O￨- people￨L￨NNS￨O￨- 's￨L￨POS￨O￨- decision￨L￨NN￨O￨- to￨L￨TO￨O￨- adopt￨L￨VB￨O￨- self-protective￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- multiplayer￨L￨JJ￨O￨- virtual￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- game￨L￨NN￨O￨A to￨L￨TO￨O￨- study￨L￨VB￨O￨- how￨L￨WRB￨O￨- people￨L￨NNS￨O￨- respond￨L￨VBP￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- offers￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- advantages￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- players￨L￨NNS￨O￨- '￨L￨POS￨O￨- decision￨L￨NN￨O￨- environments￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- its￨L￨PRP$￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- every￨L￨DT￨O￨- round￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- game￨L￨NN￨O￨- ,￨L￨,￨O￨- healthy￨L￨JJ￨O￨- players￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- option￨L￨NN￨O￨- to￨L￨TO￨O￨- choose￨L￨VB￨O￨- —￨L￨:￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- cost￨L￨NN￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- protective￨L￨JJ￨O￨A action￨L￨NN￨O￨- that￨L￨WDT￨O￨- reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- getting￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- any￨L￨DT￨O￨- round￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- player￨L￨NN￨O￨- can￨L￨MD￨O￨- choose￨L￨VB￨O￨- a￨L￨DT￨O￨- safe￨L￨JJ￨O￨- action￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- self-protect￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- risky￨L￨JJ￨O￨- action￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- not￨L￨RB￨O￨- self-protect￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- clicking￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- button￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- computer￨L￨NN￨O￨- screen￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨O￨- Access￨U￨NN￨O￨- Accounting￨U￨NN￨O￨- for￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨A in￨L￨IN￨O￨- model-based￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- estimation￨L￨NN￨O￨- :￨L￨:￨O￨- paratuberculosis￨L￨NN￨O￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- dairy￨L￨NN￨O￨- herdsRoss￨L￨NN￨O￨- S￨U￨NN￨O￨- Davidson1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Iain￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- McKendrick2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Joanna￨U￨NNP￨PERSON￨- C￨U￨NNP￨PERSON￨- Wood2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Glenn￨U￨NNP￨PERSON￨- Marion2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Alistair￨U￨NNP￨PERSON￨- Greig1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Karen￨U￨NNP￨PERSON￨- Stevenson3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Michael￨U￨NNP￨PERSON￨- Sharp4￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Michael￨U￨NNP￨PERSON￨- R￨U￨NNP￨O￨- Hutchings1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 8:159￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Davidson￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- A￨U￨NNP￨O￨- common￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- point￨L￨NN￨O￨- estimate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- parameterisation￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- A￨U￨DT￨O￨- technique￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Latin￨U￨JJ￨O￨- hypercube￨L￨NN￨O￨- sampling￨L￨NN￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- reweighting￨L￨NN￨O￨- method￨L￨NN￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- which￨L￨WDT￨O￨- enables￨L￨VBZ￨O￨- parameter￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A and￨L￨CC￨O￨- variability￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- model-based￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- was￨L￨VBD￨O￨- evaluated￨L￨VBN￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- paratuberculosis￨L￨NN￨O￨- in￨L￨IN￨O￨- dairy￨L￨NN￨O￨- herds￨L￨NNS￨O￨- which￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- stochastic￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- with￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- features￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- within￨L￨IN￨O￨- herd￨L￨NN￨O￨- variability￨L￨NN￨O￨A in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- shedding￨L￨VBG￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- explored￨L￨VBN￨O￨- in￨L￨IN￨O￨- paratuberculosis￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Paratuberculosis￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- many￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨A values￨L￨NNS￨O￨- are￨L￨VBP￨O￨- poorly￨L￨RB￨O￨- understood￨L￨VBN￨O￨- and￨L￨CC￨O￨- highly￨L￨RB￨O￨- variable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- and￨L￨CC￨O￨- apply￨L￨VB￨O￨- statistical￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- which￨L￨WDT￨O￨- make￨L￨VBP￨O￨- maximal￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Generated￨U￨VBN￨O￨- sample￨L￨NN￨O￨- parameter￨L￨NN￨O￨- combinations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- assigned￨L￨VBN￨O￨- a￨L￨DT￨O￨- weight￨L￨NN￨O￨- ,￨L￨,￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ’s￨L￨POS￨O￨- resultant￨L￨JJ￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- prevalence￨L￨NN￨O￨A data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- durability￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨A may￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- landscape￨L￨NN￨O￨- composition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- host￨L￨NN￨TITLE￨- variety￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- increased￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- spatially￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- mixtures￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- cultivars￨L￨NNS￨O￨- with￨L￨IN￨O￨- similar￨L￨JJ￨O￨- agronomic￨L￨JJ￨O￨- traits￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- differing￨L￨VBG￨O￨- in￨L￨IN￨O￨- resistance￨L￨NN￨O￨- genes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- issue￨L￨NN￨O￨- and￨L￨CC￨O￨- supports￨L￨VBZ￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- inherent￨L￨JJ￨O￨- quality￨L￨NN￨O￨- and￨L￨CC￨O￨- durability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- plant￨L￨NN￨O￨- resistance￨L￨NN￨O￨A gene￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- fitness￨L￨NN￨O￨- penalty￨L￨NN￨O￨- imposed￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- to￨L￨TO￨O￨- overcome￨L￨VB￨O￨- that￨L￨DT￨O￨- resistance￨L￨NN￨O￨- gene￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- definition￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- conceptually￨L￨RB￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- provide￨L￨VB￨O￨- an￨L￨DT￨O￨- objective￨L￨JJ￨O￨- procedure￨L￨NN￨O￨- for￨L￨IN￨O￨- measuring￨L￨VBG￨O￨- and￨L￨CC￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- durability￨L￨NN￨O￨- of￨L￨IN￨O￨- crop￨L￨NN￨O￨- resistance￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- discussion￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- goals￨L￨NNS￨O￨- of￨L￨IN￨O￨- virulence￨L￨NN￨O￨- management￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- durability￨L￨NN￨O￨- of￨L￨IN￨O￨- crop￨L￨NN￨O￨- resistance￨L￨NN￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- concept￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- and￨L￨CC￨O￨- predict￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Johnson￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- was￨L￨VBD￨O￨- perhaps￨L￨RB￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- durable￨L￨JJ￨O￨- resistance￨L￨NN￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- resistance￨L￨NN￨O￨- that￨L￨WDT￨O￨- remains￨L￨VBZ￨O￨- effective￨L￨JJ￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- prolonged￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- widespread￨L￨JJ￨O￨- use￨L￨NN￨O￨- under￨L￨IN￨O￨- conditions￨L￨NNS￨O￨- conducive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- parasite￨L￨NN￨O￨- was￨L￨VBD￨O￨- recently￨L￨RB￨DATE￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- flies￨L￨NNS￨O￨- on￨L￨IN￨O￨- Bioko￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- ongoing￨L￨JJ￨O￨- circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- wild￨L￨JJ￨O￨- animal￨L￨NN￨O￨- reservoir￨L￨NN￨O￨- appearing￨L￨VBG￨O￨- plausible￨L￨JJ￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- detected￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- or￨L￨CC￨O￨- domestic￨L￨JJ￨O￨A animals￨L￨NNS￨O￨- on￨L￨IN￨O￨- Bioko￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +b.￨L￨NN￨O￨- gambiense￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- numerous￨L￨JJ￨O￨- domestic￨L￨JJ￨O￨A and￨L￨CC￨O￨- wild￨L￨JJ￨O￨- species￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- species￨L￨NNS￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- both￨L￨CC￨O￨- experimentally￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- naturally￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- in￨L￨IN￨O￨- gambiense￨L￨NN￨O￨- HAT￨U￨NN￨O￨- epidemiology￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- an￨L￨DT￨O￨- unsolved￨L￨JJ￨O￨- puzzle￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +b.￨L￨NN￨O￨- gambiense￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- domestic￨L￨JJ￨O￨A NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- wild￨L￨JJ￨O￨- animal￨L￨NN￨O￨- species￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- tsetse￨L￨NN￨O￨- flies￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- biting￨L￨VBG￨O￨- preferences￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- habitat￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- rich￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- ecological￨L￨JJ￨O￨- dataset￨L￨NN￨O￨- .￨L￨.￨O￨- +b.￨L￨NN￨O￨- gambiense￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- animal￨L￨NN￨O￨- species￨L￨NNS￨O￨A to￨L￨TO￨O￨- human￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- survey￨L￨NN￨O￨- performed￨L￨VBN￨O￨- over￨L￨IN￨O￨- several￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- historical￨L￨JJ￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- Bipindi￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Cameroon￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- 44￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 99￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Human￨U￨JJ￨MISC￨- African￨U￨JJ￨NATIONALITY￨- Trypanosomiasis￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- HAT￨U￨NN￨O￨- ,￨L￨,￨O￨- sleeping￨L￨VBG￨O￨- sickness￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vector-borne￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- parasites￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- species￨L￨NNS￨O￨A Trypanosoma￨U￨NN￨O￨- brucei￨L￨NN￨O￨- and￨L￨CC￨O￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- flies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- genus￨L￨NN￨O￨- Glossina￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- tsetse￨L￨NN￨O￨- flies￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- pathogenesis￨L￨NN￨O￨- of￨L￨IN￨O￨- chronic￨L￨JJ￨O￨- rejection￨L￨NN￨O￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- depend￨L￨VB￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- partially￨L￨RB￨O￨- different￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- on￨L￨IN￨O￨- actual￨L￨JJ￨O￨- drug￨L￨NN￨O￨- toxicity￨L￨NN￨O￨- ,￨L￨,￨O￨- recommending￨L￨VBG￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- clinically￨L￨RB￨O￨- effective￨L￨JJ￨O￨- dose￨L￨NN￨O￨- of￨L￨IN￨O￨- medication.Rejection￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- described￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- medical￨L￨JJ￨O￨- and￨L￨CC￨O￨- biological￨L￨JJ￨O￨- viewpoint￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- there￨L￨EX￨O￨- have￨L￨VBP￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- been￨L￨VBN￨O￨- no￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨A describing￨L￨VBG￨O￨A this￨L￨DT￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Acute￨U￨JJ￨O￨- rejection￨L￨NN￨O￨- develops￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- few￨L￨JJ￨DURATION￨- weeks￨L￨NNS￨DURATION￨- or￨L￨CC￨O￨- months￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- transplantation￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- cellular￨L￨JJ￨O￨- and￨L￨CC￨O￨- molecular￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- partially￨L￨RB￨O￨- differ￨L￨VB￨O￨- from￨L￨IN￨O￨- those￨L￨DT￨O￨- leading￨L￨VBG￨O￨- ,￨L￨,￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- months￨L￨NNS￨DURATION￨- or￨L￨CC￨O￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- chronic￨L￨JJ￨O￨- rejection.After￨L￨NN￨O￨- many￨L￨JJ￨O￨- decades￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- experimentation￨L￨NN￨O￨- on￨L￨IN￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- pharmacological￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- ,￨L￨,￨O￨- organ￨L￨NN￨O￨- transplantation￨L￨NN￨O￨- has￨L￨VBZ￨O￨- evolved￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- therapeutic￨L￨JJ￨O￨- procedure￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨- which￨L￨WDT￨O￨- also￨L￨RB￨O￨- takes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- needed￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- general￨L￨JJ￨TITLE￨- enough￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- applicable￨L￨JJ￨O￨- in￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- contexts￨L￨NNS￨O￨- described￨L￨VBN￨O￨- above￨L￨IN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- existing￨L￨VBG￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- adequate￨L￨JJ￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- purpose￨L￨NN￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- changing￨L￨VBG￨O￨- percolation￨L￨NN￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- static￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨- ,￨L￨,￨O￨- percolation￨L￨NN￨O￨- centrality￨L￨NN￨O￨- ,￨L￨,￨O￨- capturing￨L￨VBG￨O￨- relative￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- during￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- possibly￨L￨RB￨O￨- partial￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- percolation￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- measure￨L￨NN￨O￨- subsumes￨L￨VBZ￨O￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨A by￨L￨IN￨O￨- explicitly￨L￨RB￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- percolated￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- on￨L￨IN￨O￨- relevant￨L￨JJ￨O￨- shortest￨L￨JJS￨O￨- paths￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- percolated￨L￨JJ￨O￨- state￨L￨NN￨O￨- this￨L￨DT￨O￨- measure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨A per￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- Z￨U￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- negative￨L￨JJ￨O￨- binomial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- mean￨L￨VB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- among￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- dispersion￨L￨NN￨O￨- parameter￨L￨NN￨O￨- k￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- superspreading￨L￨JJ￨O￨- events￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SSE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨A generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- superspreader￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- estimated￨L￨VBN￨O￨- for￨L￨IN￨O￨- directly-transmitted￨L￨JJ￨O￨- acute￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- never￨L￨RB￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- for￨L￨IN￨O￨- chronic￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- onward￨L￨RB￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- another￨L￨DT￨O￨- epidemiologically-important￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- and￨L￨CC￨O￨- secondary￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- typically￨L￨RB￨O￨- termed￨L￨VBN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- T￨U￨NN￨O￨- ;￨L￨:￨O￨- several￨L￨JJ￨O￨- other￨L￨JJ￨O￨- definitions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Central￨U￨NNP￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- endeavour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨A per￨L￨IN￨O￨- primary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- notations￨L￨NNS￨O￨- see￨L￨VBP￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- small￨L￨JJ￨O￨- k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- <￨L￨JJR￨O￨- 0.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A actively￨L￨RB￨O￨- transmit￨L￨VBP￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- whilst￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- >￨L￨JJR￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- contribute￨L￨VBP￨O￨- approximately￨L￨RB￨O￨- equally￨L￨RB￨O￨- to￨L￨TO￨O￨- onwards￨L￨NNS￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- aim￨L￨VBP￨O￨- here￨L￨RB￨O￨- at￨L￨IN￨O￨- developing￨L￨VBG￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- made￨L￨VBD￨O￨- up￨L￨RP￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- units￨L￨NNS￨O￨- ,￨L￨,￨O￨- applicable￨L￨JJ￨O￨- beyond￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- models￨L￨NNS￨O￨- or￨L￨CC￨O￨- Hamiltonian￨U￨JJ￨IDEOLOGY￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- interest￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- at￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- some￨L￨DT￨O￨- generic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- particle￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- macroscopic￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A .￨L￨.￨O￨- +While￨U￨IN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- naïve￨L￨JJ￨O￨- arguments￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- should￨L￨MD￨O￨- conclude￨L￨VB￨O￨- that￨L￨IN￨O￨- global￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A increase￨L￨VBP￨O￨- in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- interacting￨L￨VBG￨O￨- particles￨L￨NNS￨O￨- fluctuations￨L￨NNS￨O￨- actually￨L￨RB￨O￨- decrease￨L￨VBP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- issue￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- less￨L￨JJR￨O￨- studied￨L￨VBN￨O￨- ,￨L￨,￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- particle￨L￨NN￨O￨A heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- systems9101112￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- particles￨L￨NNS￨O￨- themselves￨L￨PRP￨O￨- in￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- exceptions￨L￨NNS￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- reference13￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- on￨L￨IN￨O￨- consensus￨L￨NN￨O￨- times￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- voter￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- works￨L￨VBZ￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- “￨L￨``￨O￨- committed￨L￨VBN￨O￨- ”￨L￨''￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- and￨L￨CC￨O￨- related￨L￨VBN￨O￨- models1415￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- see￨L￨VB￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- particle￨L￨NN￨O￨A heterogeneity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- diversity￨L￨NN￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- measuring￨L￨VBG￨O￨- only￨L￨RB￨O￨- global￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- regards￨L￨VBZ￨O￨- the￨L￨DT￨O￨- cytokine￨L￨NN￨O￨- profile￨L￨NN￨O￨- after￨L￨IN￨O￨- specific￨L￨JJ￨O￨- chemotherapy￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨- that￨L￨IN￨O￨- peripheral￨L￨JJ￨O￨- blood￨L￨NN￨O￨- mononuclear￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PBMC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- patients￨L￨NNS￨O￨- with￨L￨IN￨O￨- acute￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- responded￨L￨VBD￨O￨- to￨L￨TO￨O￨- SEA￨U￨NN￨O￨- and￨L￨CC￨O￨- soluble￨L￨JJ￨O￨- worm￨L￨NN￨O￨- antigen￨L￨NN￨O￨- preparation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SWAP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- producing￨L￨VBG￨O￨- significantly￨L￨RB￨O￨- higher￨L￨JJR￨O￨- amounts￨L￨NNS￨O￨- of￨L￨IN￨O￨- IFN-γ￨U￨NN￨O￨- and￨L￨CC￨O￨- IL-10￨U￨NN￨O￨- .￨L￨.￨O￨- +mansoni￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨A that￨L￨IN￨O￨- interleukin￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IL￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- -4￨L￨CD￨NUMBER￨- upregulates￨L￨VBZ￨O￨- fibroblast￨L￨NN￨O￨- chemokine￨L￨NN￨O￨- ,￨L￨,￨O￨- matrix￨L￨NN￨O￨- protein￨L￨NN￨O￨- expression￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- collagen￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- IL-4￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- cytokine￨L￨NN￨O￨- for￨L￨IN￨O￨- granuloma￨L￨NN￨O￨- formation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- cellular￨L￨JJ￨O￨- proliferative￨L￨JJ￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- soluble￨L￨JJ￨O￨- egg￨L￨NN￨O￨- antigens￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SEA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- evaluated￨L￨VBD￨O￨- the￨L￨DT￨O￨- cytokine￨L￨NN￨O￨- profile￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IFN-γ￨U￨NN￨O￨- ,￨L￨,￨O￨- TNF-α￨U￨NN￨O￨- ,￨L￨,￨O￨- IL-4￨U￨NN￨O￨- ,￨L￨,￨O￨- IL-5￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- IL-10￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- T￨U￨NN￨O￨- lymphocytes￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- subsets￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- ultrasonographic￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- with￨L￨IN￨O￨- acute￨L￨JJ￨O￨A schistosomiasis￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- before￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- praziquantel￨L￨NN￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- phase￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- mixed￨L￨JJ￨O￨- cytokine￨L￨NN￨O￨- profile￨L￨NN￨O￨A with￨L￨IN￨O￨- predominance￨L￨NN￨O￨- of￨L￨IN￨O￨- Th1￨U￨NN￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T-cell￨U￨NN￨O￨- differentiation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- making￨L￨VBG￨O￨- contacts￨L￨NNS￨O￨A versus￨L￨CC￨O￨- avoiding￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- extremes￨L￨NNS￨O￨- :￨L￨:￨O￨- either￨L￨RB￨O￨- to￨L￨TO￨O￨- adopt￨L￨VB￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- cautious￨L￨JJ￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- suppressing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- quickly￨L￨RB￨O￨- by￨L￨IN￨O￨- drastically￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- contacts￨L￨NNS￨O￨- as￨L￨RB￨O￨- soon￨L￨RB￨O￨- as￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- detected￨L￨VBN￨O￨- ;￨L￨:￨O￨- or￨L￨CC￨O￨- else￨L￨RB￨O￨- to￨L￨TO￨O￨- forego￨L￨VB￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- allow￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- run￨L￨VB￨O￨- its￨L￨PRP$￨O￨- course￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Controlling￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨A spread￨L￨NN￨O￨A by￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨- :￨L￨:￨O￨- Do￨U￨VB￨O￨- it￨L￨PRP￨O￨- well￨L￨RB￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- at￨L￨IN￨O￨- allSavi￨L￨NNP￨O￨- Maharaj1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Adam￨U￨NNP￨O￨- Kleczkowski1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 12:679￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Maharaj￨U￨NNP￨O￨- and￨L￨CC￨O￨- Kleczkowski￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Existing￨U￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- largely￨L￨RB￨O￨- tended￨L￨VBN￨O￨- to￨L￨TO￨O￨- neglect￨L￨NN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Disease￨U￨NNP￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- is￨L￨VBZ￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- temporarily￨L￨RB￨O￨- reduce￨L￨VB￨O￨- their￨L￨PRP$￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨A in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- their￨L￨PRP$￨O￨- local￨L￨JJ￨O￨- neighbourhood￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- robust￨L￨JJ￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- long-range￨L￨JJ￨O￨- ,￨L￨,￨O￨- small-world￨L￨JJ￨O￨- links￨L￨NNS￨O￨- which￨L￨WDT￨O￨- destroy￨L￨VBP￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- whether￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- or￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- control￨L￨VB￨O￨A them￨L￨PRP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- evaluate￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨A models￨L￨NNS￨O￨A that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- broadly￨L￨RB￨O￨- classified￨L￨VBN￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- increasing￨L￨VBG￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- looking￨L￨VBG￨O￨- specifically￨L￨RB￨O￨- at￨L￨IN￨O￨- whether￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- distinguish￨L￨VB￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- types￨L￨NNS￨O￨- using￨L￨VBG￨O￨- high-level￨L￨JJ￨O￨- and￨L￨CC￨O￨- common￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- summary￨L￨NN￨O￨- statistics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- take￨L￨VBP￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- step￨L￨NN￨O￨- towards￨L￨IN￨O￨- this￨L￨DT￨O￨- goal￨L￨NN￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- utility￨L￨NN￨O￨- of￨L￨IN￨O￨- commonly￨L￨RB￨O￨- gathered￨L￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- likelihood-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A framework￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- Alternatives￨U￨NNP￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- paradigm￨L￨NN￨O￨- do￨L￨VBP￨O￨- exist￨L￨VB￨O￨- ;￨L￨:￨O￨- notably￨L￨RB￨O￨- ,￨L￨,￨O￨- synthetic￨L￨JJ￨O￨- network￨L￨NN￨O￨A models￨L￨NNS￨O￨A that￨L￨WDT￨O￨- use￨L￨VBP￨O￨- census￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- socio-demographic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- possible￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- first-principles￨L￨JJ￨O￨- approach￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- )￨L￨-RRB-￨O￨- +We￨U￨PRP￨O￨- test￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- inferential￨L￨JJ￨O￨- framework￨L￨NN￨O￨- with￨L￨IN￨O￨- synthetic￨L￨JJ￨O￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- contact￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- comparing￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A results￨L￨VBZ￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- measure￨L￨NN￨O￨- with￨L￨IN￨O￨- ground￨L￨NN￨O￨- truth￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- class￨L￨NN￨O￨- that￨L￨WDT￨O￨- generated￨L￨VBD￨O￨- it￨L￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- alternative￨L￨NN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- data-hungry￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- inferred￨L￨VBN￨O￨- using￨L￨VBG￨O￨- available￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- likelihood￨L￨NN￨O￨A framework￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- age-specific￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- vaccine-induced￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨- in￨L￨IN￨O￨- circulation￨L￨NN￨O￨- ,￨L￨,￨O￨- operating￨L￨VBG￨O￨- either￨L￨CC￨O￨- via￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨- in￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- cover￨L￨NN￨O￨- or￨L￨CC￨O￨- via￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- cover￨L￨NN￨O￨- of￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- magnitude￨L￨NN￨O￨- to￨L￨TO￨O￨- break￨L￨VB￨O￨- the￨L￨DT￨O￨- chains￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- push￨L￨NN￨O￨- communities￨L￨NNS￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- community￨L￨NN￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- immunizing￨L￨JJ￨O￨A childhood￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- vulnerable￨L￨JJ￨O￨- to￨L￨TO￨O￨- stochastic￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- immunizing￨L￨VBG￨O￨A ,￨L￨,￨O￨- safe￨L￨JJ￨O￨- and￨L￨CC￨O￨- relatively￨L￨RB￨O￨- cheap￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- that￨L￨IN￨O￨- inadequate￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- may￨L￨MD￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- CRS￨U￨NNP￨O￨- burden￨L￨NN￨O￨- by￨L￨IN￨O￨- raising￨L￨VBG￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- without￨L￨IN￨O￨- sufficiently￨L￨RB￨O￨- decreasing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- pattern￨L￨NN￨O￨- suggested￨L￨VBD￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- occurred￨L￨VBN￨O￨- in￨L￨IN￨O￨- Greece￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- Costa￨U￨NNP￨COUNTRY￨- Rica￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- considerable￨L￨JJ￨O￨- caution￨L￨NN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- introduction￨L￨NN￨O￨- .￨L￨.￨O￨- +Forecasting￨U￨NN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- is￨L￨VBZ￨O￨- challenging￨L￨VBG￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- complex￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- is￨L￨VBZ￨O￨- particularly￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- for￨L￨IN￨O￨- AIVs￨U￨NNS￨O￨- in￨L￨IN￨O￨- live-bird￨L￨JJ￨O￨- markets￨L￨NNS￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- intricate￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ecology￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rarity￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- subtypes￨L￨NNS￨O￨A that￨L￨WDT￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- H5￨U￨NN￨O￨- and￨L￨CC￨O￨- H7￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- comprehensive￨L￨JJ￨O￨- longitudinal￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- subtypes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- identified￨L￨VBD￨O￨- strong￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- preferences￨L￨NNS￨O￨- between￨L￨IN￨O￨- subtypes￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- sample￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- prevalence￨L￨NN￨O￨- within￨L￨IN￨O￨- individual￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- reported￨L￨VBD￨O￨- 6￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- monthly￨L￨JJ￨SET￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- Hemagglutinin￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- subtypes￨L￨NNS￨O￨A 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- in￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- in￨L￨IN￨O￨- live-bird￨L￨JJ￨O￨- markets￨L￨NNS￨O￨- in￨L￨IN￨O￨- Shantou￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Lastly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- conducted￨L￨VBD￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- which￨L￨WDT￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- most￨L￨RBS￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- prevalence￨L￨NN￨O￨A of￨L￨IN￨O￨- H9￨U￨NN￨O￨- and￨L￨CC￨O￨- H5￨U￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- failure￨L￨NN￨O￨- of￨L￨IN￨O￨- chemotherapeutic￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- large￨L￨JJ￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- ,￨L￨,￨O￨- much￨L￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- biology￨L￨NN￨O￨- of￨L￨IN￨O￨- –￨L￨:￨O￨- and￨L￨CC￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- policy￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- –￨L￨:￨O￨- resistance￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- especially￨L￨RB￨O￨- important￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- highly￨L￨RB￨O￨- pathogenic￨L￨JJ￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- H5N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- combine￨L￨VB￨O￨- network￨L￨NN￨O￨- simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- resistance￨L￨NN￨O￨A under￨L￨IN￨O￨- chemotherapy￨L￨NN￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- regimes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- targeted￨L￨VBN￨O￨- versus￨L￨CC￨O￨- non-targeted￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- .￨L￨.￨O￨- +Though￨U￨IN￨O￨- fundamentally￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- bulk￨L￨NN￨O￨- of￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- studies￨L￨NNS￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- on￨L￨IN￨O￨- resistance￨L￨NN￨O￨A to￨L￨TO￨O￨- therapies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- ignored￨L￨VBN￨O￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- employ￨L￨VBP￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- extending￨L￨VBG￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- treatment￨L￨NN￨O￨A .￨L￨.￨O￨- +and￨L￨CC￨O￨- three￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- treatment￨L￨NN￨O￨- regime￨L￨NN￨O￨- ,￨L￨,￨O￨- targeted￨L￨VBN￨O￨- by￨L￨IN￨O￨- degree￨L￨NN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- ,￨L￨,￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- least￨L￨JJS￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨A ?￨L￨.￨O￨- +Published￨U￨VBN￨O￨- forecast￨L￨NN￨O￨- models￨L￨NNS￨O￨- integrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- outcome￨L￨NN￨O￨- variable￨L￨NN￨O￨- ,￨L￨,￨O￨- typically￨L￨RB￨O￨- previous￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- or￨L￨CC￨O￨- ILI￨U￨NN￨O￨- visits￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- several￨L￨JJ￨O￨- external￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- emergency￨L￨NN￨O￨- medical￨L￨JJ￨O￨- service￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- EMS￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- calls￨L￨VBZ￨O￨- ,￨L￨,￨O￨- sick￨L￨JJ￨O￨- leaves￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- counter￨L￨NN￨O￨- drug￨L￨NN￨O￨- sales￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- climate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- temperature￨L￨NN￨O￨- ,￨L￨,￨O￨- humidity￨L￨NN￨O￨- ,￨L￨,￨O￨- rainfall￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- atmospheric￨L￨JJ￨O￨- pressure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- forecasts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Primarily￨U￨RB￨O￨- ,￨L￨,￨O￨- forecast￨L￨NN￨O￨A models￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- point￨L￨NN￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- counts￨L￨NNS￨O￨- of￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨- influenza-related￨L￨JJ￨O￨- ED￨U￨NNP￨O￨- patient￨L￨NN￨O￨- visits￨L￨NNS￨O￨- were￨L￨VBD￨O￨- designed￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Negative￨U￨JJ￨MISC￨- Binomial￨U￨NNP￨MISC￨- Generalized￨U￨NNP￨MISC￨- Autoregressive￨U￨NNP￨MISC￨- Moving￨U￨VBG￨MISC￨- Average￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- GARMA￨U￨NN￨LOCATION￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- in￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- counts￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- non-stationarity￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- chose￨L￨VBD￨O￨- to￨L￨TO￨O￨- employ￨L￨VB￨O￨- the￨L￨DT￨O￨- Generalized￨U￨NNP￨MISC￨- Autoregressive￨U￨NNP￨MISC￨- Moving￨U￨VBG￨MISC￨- Average￨U￨JJ￨MISC￨- (￨L￨-LRB-￨O￨- GARMA￨U￨NN￨LOCATION￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- discrete-valued￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- integrated￨L￨VBN￨O￨- external￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- external￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- are￨L￨VBP￨O￨- lagged￨L￨VBN￨O￨- by￨L￨IN￨O￨- one-week￨L￨JJ￨DURATION￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- forecasted￨L￨VBN￨O￨- values￨L￨NNS￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- uses￨L￨VBZ￨O￨- only￨L￨RB￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- prediction￨L￨NN￨O￨- one￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨JJ￨DATE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- real-time￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- demonstrated￨L￨VBN￨O￨- strong￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- with￨L￨IN￨O￨- ED￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- go￨L￨VB￨O￨- beyond￨L￨IN￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- forecast￨L￨NN￨O￨A future￨L￨JJ￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Modeling￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- air￨L￨NN￨O￨A ,￨L￨,￨O￨- sea￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- land￨L￨NN￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨- supplemented￨L￨VBN￨O￨- by￨L￨IN￨O￨- other￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨JJ￨O￨- virusKa￨L￨NNP￨O￨- Chun￨U￨NNP￨O￨- Chong1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Benny￨U￨NNP￨PERSON￨- Chung￨U￨NNP￨PERSON￨- Ying￨U￨NNP￨O￨- Zee1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 12:309￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Chong￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Zee￨U￨NNP￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- During￨U￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- travel￨L￨NN￨O￨- restriction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- immediate￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-pharmaceutical￨L￨JJ￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- retarding￨L￨VBG￨O￨- incidence￨L￨NN￨O￨- growth￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Regarding￨U￨VBG￨O￨- air￨L￨NN￨O￨A travel￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- route￨L￨NN￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- source￨L￨NN￨O￨- area￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- targeted￨L￨VBN￨O￨- for￨L￨IN￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨- ;￨L￨:￨O￨- imposing￨L￨VBG￨O￨- a￨L￨DT￨O￨- 99￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- air￨L￨NN￨O￨- travel￨L￨NN￨O￨- restriction￨L￨NN￨O￨- delayed￨L￨VBD￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨- by￨L￨IN￨O￨- up￨L￨RB￨DURATION￨- to￨L￨TO￨DURATION￨- two￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Public￨U￨NNP￨O￨- health￨L￨NN￨O￨- measures￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- travel￨L￨NN￨O￨A restrictions￨L￨NNS￨O￨- then￨L￨RB￨O￨- become￨L￨VBP￨O￨- essential￨L￨JJ￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- pandemic￨L￨JJ￨O￨- spread.Novel￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- called￨L￨VBN￨O￨- swine￨L￨NNS￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- arrivals￨L￨NNS￨O￨- from￨L￨IN￨O￨- 44￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- via￨L￨IN￨O￨- air￨L￨NN￨O￨A ,￨L￨,￨O￨- sea￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- land￨L￨NN￨O￨- transports￨L￨NNS￨O￨- were￨L￨VBD￨O￨- imported￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- Susceptible￨U￨NNP￨O￨- ,￨L￨,￨O￨- Exposed￨U￨VBN￨O￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨O￨- and￨L￨CC￨O￨- Recovered￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- host-flow￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨DT￨O￨- pandemic￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- regulating￨L￨VBG￨O￨- air￨L￨NN￨O￨A ,￨L￨,￨O￨- sea￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- land￨L￨NN￨O￨- transport￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- studies￨L￨NNS￨O￨- demonstrated￨L￨VBD￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- network￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- styles￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- connection￨L￨NN￨O￨- density￨L￨NN￨O￨- and￨L￨CC￨O￨- weight￨L￨NN￨O￨A distributions￨L￨NNS￨O￨- among￨L￨IN￨O￨- communities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- in-community￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- density￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- modularity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- strongly￨L￨RB￨O￨- affect￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rational￨L￨JJ￨O￨A offender￨L￨NN￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- their￨L￨PRP$￨O￨- decisions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- merits￨L￨NNS￨O￨- of￨L￨IN￨O￨- actions￨L￨NNS￨O￨- -￨L￨:￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- rewards￨L￨NNS￨O￨- available￨L￨JJ￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- -￨L￨:￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- minimise￨L￨VB￨O￨- costs￨L￨NNS￨O￨- ,￨L￨,￨O￨- choosing￨L￨VBG￨O￨- nearby￨L￨JJ￨O￨- targets￨L￨NNS￨O￨- and￨L￨CC￨O￨- seeking￨L￨VBG￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- capture￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- appears￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- during￨L￨IN￨O￨- rioting22￨L￨NN￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- research￨L￨NN￨O￨- specific￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- London￨U￨NNP￨CITY￨- disorder￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- criminological￨L￨JJ￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- social￨L￨JJ￨O￨- disorganisation￨L￨NN￨O￨- theory19￨L￨NN￨O￨- and￨L￨CC￨O￨- rational￨L￨JJ￨O￨A choice￨L￨NN￨O￨- theory20￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- applicable￨L￨JJ￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- case21￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- its￨L￨PRP$￨O￨- implications￨L￨NNS￨O￨- are￨L￨VBP￨O￨- therefore￨L￨RB￨O￨- a￨L￨DT￨O￨- well-justified￨L￨JJ￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- trends￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- several￨L￨JJ￨O￨- phases￨L￨NNS￨O￨- of￨L￨IN￨O￨- riot￨L￨NN￨CRIMINAL_CHARGE￨- development￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- involvement￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- target￨L￨NN￨O￨- choice￨L￨NN￨O￨A stage￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- participants￨L￨NNS￨O￨- and￨L￨CC￨O￨- police￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- London￨U￨NNP￨CITY￨- riots￨L￨NNS￨O￨- are￨L￨VBP￨O￨- notable￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- being￨L￨VBG￨O￨- apparently￨L￨RB￨O￨- catalysed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- incident￨L￨NN￨O￨- -￨L￨:￨O￨- the￨L￨DT￨O￨- fatal￨L￨JJ￨O￨- shooting￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- police￨L￨NN￨TITLE￨- officer￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- suspect￨L￨NN￨O￨- in￨L￨IN￨O￨- Tottenham￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- North￨U￨NNP￨LOCATION￨- London￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- peaceful￨L￨JJ￨O￨- protest￨L￨NN￨O￨- -￨L￨:￨O￨- disorder￨L￨NN￨O￨A escalated￨L￨VBD￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- dramatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- unanticipated￨L￨JJ￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- widely￨L￨RB￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- with￨L￨IN￨O￨- much￨L￨JJ￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- considering￨L￨VBG￨O￨- previous￨L￨JJ￨O￨- episodes9￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- focussed￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- psycho-social￨L￨JJ￨O￨- motives￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- rioters￨L￨NNS￨O￨- ,￨L￨,￨O￨- ascribing￨L￨VBG￨O￨- willingness￨L￨NN￨O￨- to￨L￨TO￨O￨- participate￨L￨VB￨O￨- to￨L￨TO￨O￨- various￨L￨JJ￨O￨- social￨L￨JJ￨O￨A factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- unemployment￨L￨NN￨O￨- ,￨L￨,￨O￨- poor￨L￨JJ￨O￨- police￨L￨NNS￨O￨- relations￨L￨NNS￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- criminality￨L￨NN￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- main￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- canine￨L￨JJ￨O￨- rabies￨L￨NNP￨O￨A :￨L￨:￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Cleaveland￨U￨NN￨ORGANIZATION￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Schneider￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Cleaveland￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- measures￨L￨VBZ￨O￨- aiming￨L￨VBG￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- dog￨L￨NN￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- usually￨L￨RB￨O￨- by￨L￨IN￨O￨- culling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- widespread￨L￨JJ￨O￨- killing￨L￨NN￨O￨- of￨L￨IN￨O￨- dogs￨L￨NNS￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Windiyaningsih￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- by￨L￨IN￨O￨- sterilization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Culling￨U￨NN￨O￨- of￨L￨IN￨O￨- dogs￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- used￨L￨VBN￨O￨- ,￨L￨,￨O￨- alone￨L￨RB￨O￨- or￨L￨CC￨O￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Larghi￨U￨NNP￨LOCATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- physical￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dogs￨L￨NNS￨O￨- must￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A ,￨L￨,￨O￨- despite￨L￨IN￨O￨- evidence￨L￨NN￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- ineffective￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Windiyaningsih￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theoretical￨L￨JJ￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- culling￨L￨NN￨O￨- or￨L￨CC￨O￨- sterilization￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- density-dependent￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Anderson￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Wandeler￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Hampson￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Social￨U￨NNP￨O￨- ,￨L￨,￨O￨- economic￨L￨JJ￨O￨- and￨L￨CC￨O￨- political￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- contribute￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- inadequate￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A in￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- dog￨L￨NN￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- accentuated￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- incomplete￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- density-dependent￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- will￨L￨MD￨O￨- exist￨L￨VB￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- density￨L￨NN￨O￨A below￨L￨IN￨O￨- which￨L￨WDT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- invade￨L￨VB￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- guidance￨L￨NN￨O￨- document￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- detailing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- quickly￨L￨RB￨O￨- determine￨L￨VB￨O￨- after￨L￨IN￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- symptoms￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- serial￨L￨NN￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- onset￨L￨NN￨O￨- in￨L￨IN￨O￨- primary￨L￨JJ￨O￨- and￨L￨CC￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A ratio￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- primary￨L￨JJ￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +Software￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- R0￨U￨NN￨MISC￨- package￨L￨NN￨O￨A :￨L￨:￨O￨- a￨L￨DT￨O￨- toolbox￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreaksThomas￨L￨NN￨O￨- Obadia1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Romana￨U￨NNP￨O￨- Haneef4￨U￨NNP￨O￨- and￨L￨CC￨O￨- Pierre-Yves￨U￨NNP￨PERSON￨- Boëlle1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 12:147￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Obadia￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Several￨U￨JJ￨O￨- generic￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- This￨U￨DT￨O￨- software￨L￨NN￨O￨- package￨L￨NN￨O￨A allows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- standardized￨L￨JJ￨O￨- and￨L￨CC￨O￨- extensible￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- generation￨L￨NN￨O￨- interval￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- from￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- categories￨L￨NNS￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- were￨L￨VBD￨O￨- available￨L￨JJ￨O￨- :￨L￨:￨O￨- those￨L￨DT￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- estimating￨L￨VBG￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- methods￨L￨NNS￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨A time￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +Anderson￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Watson￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- 1980￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- analytic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- major￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Exposed-Infectious-Removed￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- gamma-distributed￨L￨JJ￨O￨- incubating￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- exposed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- various￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- incubating￨L￨VBG￨O￨- or￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- introduced￨L￨VBN￨O￨- pathogen￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- greatly￨L￨RB￨O￨- exceed￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- closed￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- may￨L￨MD￨O￨- either￨L￨RB￨O￨- be￨L￨VB￨O￨- minor￨L￨JJ￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- fadeout￨L￨NN￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- transmissions￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- major￨L￨JJ￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- case￨L￨NN￨O￨- fadeout￨L￨NN￨O￨- only￨L￨RB￨O￨- occurs￨L￨VBZ￨O￨- after￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- spread￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- factors￨L￨NNS￨O￨- influence￨L￨VBP￨O￨- whether￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- major￨L￨JJ￨O￨- or￨L￨CC￨O￨- minor￨L￨JJ￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- incubating￨L￨VBG￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- prediction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- x￨L￨NN￨O￨- th￨L￨DT￨O￨- death￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- θ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Intuitively￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- expect￨L￨VBP￨O￨- that￨L￨IN￨O￨- useful￨L￨JJ￨O￨- information￨L￨NN￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨A final￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- contained￨L￨VBN￨O￨- in￨L￨IN￨O￨- observable￨L￨JJ￨O￨- data￨L￨NNS￨O￨- :￨L￨:￨O￨- specifically￨L￨RB￨O￨- the￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- death￨L￨NN￨O￨- times￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- schematic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- exact￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- confirm￨L￨VBP￨O￨- that￨L￨IN￨O￨- p￨L￨NN￨O￨- reliably￨L￨RB￨O￨- predicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A network￨L￨NN￨O￨A approach￨L￨NN￨O￨- to￨L￨TO￨O￨- such￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- view￨L￨VBP￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- as￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- entity￨L￨NN￨O￨- and￨L￨CC￨O￨- assume￨L￨VB￨O￨- that￨L￨DT￨O￨- contagion￨L￨NN￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- only￨L￨RB￨O￨- inside￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- window￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- implicit￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- behind￨L￨IN￨O￨- most￨L￨JJS￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- studies￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- incessant￨L￨JJ￨O￨- pathway￨L￨NN￨O￨- for￨L￨IN￨O￨- contagion￨L￨NN￨O￨A .￨L￨.￨O￨- +Social￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- animals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- ,￨L￨,￨O￨- extent￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- speed￨L￨NN￨O￨A of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- also￨L￨RB￨O￨- need￨L￨VB￨O￨- a￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A network￨L￨NN￨O￨A approach￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- previous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- analyzed￨L￨VBN￨O￨- how￨L￨WRB￨O￨- behavioral￨L￨JJ￨O￨- feedbacks￨L￨NNS￨O￨- influence￨L￨VBP￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A that￨L￨WDT￨O￨- target￨L￨VBP￨O￨- superspreaders￨L￨NNS￨O￨- ,￨L￨,￨O￨- nor￨L￨CC￨O￨- have￨L￨VBP￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- explored￨L￨VBD￨O￨- how￨L￨WRB￨O￨- incentive￨L￨NN￨O￨- use￨L￨NN￨O￨- influences￨L￨VBZ￨O￨- vaccination￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- superspreader￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A usually￨L￨RB￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- will￨L￨MD￨O￨- always￨L￨RB￨O￨- agree￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- arbitrarily￨L￨RB￨O￨- specified￨L￨VBN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- uptake￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Network-based￨U￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨A show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- targeting￨L￨VBG￨O￨- superspreaders￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- effective￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- efficient￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Incorporating￨U￨VBG￨O￨- behavior￨L￨NN￨O￨- into￨L￨IN￨O￨- transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- important￨L￨JJ￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- exemption￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- suboptimal￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- selected￨L￨VBD￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- simple￨L￨JJ￨O￨- but￨L￨CC￨O￨- plausible￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- HPV-16￨U￨NN￨O￨- ,￨L￨,￨O￨- differing￨L￨VBG￨O￨- in￨L￨IN￨O￨- assumptions￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- seropositivity￨L￨NN￨O￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- attempted￨L￨VBN￨O￨- to￨L￨TO￨O￨- calibrate￨L￨VB￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- Australian￨U￨JJ￨NATIONALITY￨- HPV￨U￨NN￨O￨- seroprevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- females￨L￨NNS￨O￨A and￨L￨CC￨O￨- males￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- DNA￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- females￨L￨NNS￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- comparison￨L￨NN￨O￨- procedure￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- seroreversion￨L￨NN￨O￨- where￨L￨WRB￨O￨- seropositivity￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- partial￨L￨JJ￨O￨- or￨L￨CC￨O￨- very￨L￨RB￨O￨- short-term￨L￨JJ￨O￨- full￨L￨JJ￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- re-infection￨L￨NN￨O￨- generate￨L￨VBP￨O￨- age-specific￨L￨JJ￨O￨- HPV￨U￨NN￨O￨- DNA￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- most￨L￨RBS￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨A when￨L￨WRB￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨A related￨L￨VBN￨O￨- to￨L￨TO￨O￨- seroreactivity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- production￨L￨NN￨O￨- of￨L￨IN￨O￨- antibodies￨L￨NNS￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- seroconversion￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- decay￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- seroreversion￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- timely￨L￨JJ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- possibilities￨L￨NNS￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- them￨L￨PRP￨O￨- for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- calibration￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- exception￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- aware￨L￨JJ￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨A have￨L￨VBP￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- calibration￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- seropositivity￨L￨NN￨O￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- well￨L￨RB￨O￨- understood￨L￨VBN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Models￨U￨NNS￨O￨- supporting￨L￨VBG￨O￨- the￨L￨DT￨O￨- notion￨L￨NN￨O￨- that￨L￨IN￨O￨- seropositive￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- fully￨L￨RB￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- reinfection￨L￨NN￨O￨- demonstrated￨L￨VBD￨O￨- consistently￨L￨RB￨O￨- inferior￨L￨JJ￨O￨- fits￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨A than￨L￨IN￨O￨- other￨L￨JJ￨O￨- models￨L￨NNS￨O￨- making￨L￨VBG￨O￨- no￨L￨DT￨O￨- such￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- potentially￨L￨RB￨O￨- devastating￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- emerging￨L￨VBG￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- wildlife￨L￨NN￨O￨- conservation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- EBOV￨U￨NN￨O￨- and￨L￨CC￨O￨- gorillas￨L￨NNS￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- improve￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- bat￨L￨NN￨O￨- ecology￨L￨NN￨O￨- may￨L￨MD￨O￨- influence￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- propensity￨L￨NN￨O￨- to￨L￨TO￨O￨- serve￨L￨VB￨O￨- as￨L￨IN￨O￨- reservoirs￨L￨NNS￨O￨- for￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- field￨L￨NN￨O￨- and￨L￨CC￨O￨- laboratory￨L￨NN￨O￨- studies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨- data-driven￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- elucidate￨L￨VB￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- bat￨L￨NN￨O￨- ecology￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨A bat￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Understanding￨U￨VBG￨O￨- the￨L￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- anthropogenic￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- on￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- within￨L￨IN￨O￨- bat￨L￨NN￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- and￨L￨CC￨O￨- prevent￨L￨VB￨O￨- human￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨A of￨L￨IN￨O￨- bat￨L￨NN￨O￨- origin￨L￨NN￨O￨- .￨L￨.￨O￨- +Bats￨U￨NNS￨O￨- are￨L￨VBP￨O￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨A ,￨L￨,￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- and￨L￨CC￨O￨- cause￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- initially￨L￨RB￨O￨- requires￨L￨VBZ￨O￨- understanding￨L￨VBG￨O￨A both￨L￨DT￨O￨- bat￨L￨NN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- human￨L￨JJ￨O￨- contact￨L￨NN￨O￨- pattern￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- reflected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- constant14142￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- metapopulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- subpopulations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- identical￨L￨JJ￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- inside￨L￨IN￨O￨- each￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨A are￨L￨VBP￨O￨- uniform￨L￨JJ￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- inside￨L￨IN￨O￨- each￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨A may￨L￨MD￨O￨- possess￨L￨VB￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- reflecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- encounters￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- study￨L￨NN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- to￨L￨TO￨O￨- homogeneous￨L￨JJ￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A ,￨L￨,￨O￨- heterogeneous￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- speed￨L￨VB￨O￨- up￨L￨RP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- new￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- during￨L￨IN￨O￨- which￨L￨WDT￨O￨- vertices￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- are￨L￨VBP￨O￨- active￨L￨JJ￨O￨- are￨L￨VBP￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- precisely￨L￨RB￨O￨- map￨L￨VB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A into￨L￨IN￨O￨- an￨L￨DT￨O￨- evolving￨L￨VBG￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Numerical￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- using￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A between￨L￨IN￨O￨- conference￨L￨NN￨O￨- attendees￨L￨NNS￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- durations￨L￨NNS￨O￨- causes￨L￨VBZ￨O￨- lower￨L￨JJR￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- ladder-like￨L￨JJ￨O￨- trees￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 3A￨L￨NN￨O￨- could￨L￨MD￨O￨- reflect￨L￨VB￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- directional￨L￨JJ￨O￨- selection￨L￨NN￨O￨- ,￨L￨,￨O￨- ladder-like￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- could￨L￨MD￨O￨- also￨L￨RB￨O￨- reflect￨L￨VB￨O￨- sequential￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- bottlenecks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- might￨L￨MD￨O￨- occur￨L￨VB￨O￨- with￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨- virus￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Their￨U￨PRP$￨O￨- study￨L￨NN￨O￨- showcased￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- phylogenies￨L￨NNS￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- serve￨L￨VB￨O￨- as￨L￨IN￨O￨- rules￨L￨NNS￨O￨- of￨L￨IN￨O￨- thumb￨L￨NN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- important￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- ,￨L￨,￨O￨- immunological￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- evolutionary￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- coining￨L￨VBG￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- phylodynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- Grenfell￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- coauthors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- postulated￨L￨VBD￨O￨- that￨L￨IN￨O￨- viral￨L￨JJ￨O￨- phylogenies￨L￨NNS￨O￨A “￨L￨``￨O￨- …￨L￨:￨O￨- are￨L￨VBP￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- selection￨L￨NN￨O￨- ,￨L￨,￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- viral￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- ”￨L￨''￨O￨- +While￨U￨IN￨O￨- spatial￨L￨JJ￨O￨A structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- observed￨L￨VBN￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- phylodynamic￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- ,￨L￨,￨O￨- viruses￨L￨NNS￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- have￨L￨VB￨O￨- nonrandom￨L￨JJ￨O￨- admixture￨L￨NN￨O￨- by￨L￨IN￨O￨- attributes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- race￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- risk￨L￨NN￨O￨- behavior￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- directional￨L￨JJ￨O￨- selection￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨A phylogeny￨L￨NN￨O￨- is￨L￨VBZ￨O￨- exemplified￨L￨VBN￨O￨- by￨L￨IN￨O￨- contrasting￨L￨VBG￨O￨- the￨L￨DT￨O￨- trees￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- 's￨L￨POS￨O￨- surface￨L￨NN￨O￨- proteins￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Novel￨U￨JJ￨MISC￨- lipoprotein￨L￨NN￨O￨- density￨L￨NN￨O￨- profiling￨L￨NN￨O￨- in￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨A of￨L￨IN￨O￨- various￨L￨JJ￨O￨- breeds￨L￨NNS￨O￨- ,￨L￨,￨O￨- healthy￨L￨JJ￨O￨- miniature￨L￨NN￨O￨- schnauzers￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- miniature￨L￨NN￨O￨- schnauzers￨L￨NNS￨O￨- with￨L￨IN￨O￨- hyperlipidemiaPanagiotis￨L￨NN￨O￨- G￨U￨NN￨O￨- Xenoulis1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Paul￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Cammarata2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Rosemary￨U￨NNP￨PERSON￨- L￨U￨NNP￨PERSON￨- Walzem3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ronald￨U￨NNP￨PERSON￨- D￨U￨NNP￨PERSON￨- Macfarlane2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jan￨U￨NNP￨DATE￨- S￨U￨NNP￨O￨- Suchodolski1￨U￨NN￨O￨- and￨L￨CC￨O￨- Jörg￨U￨NN￨O￨- M￨U￨NN￨O￨- Steiner1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 9:47￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Xenoulis￨U￨NNPS￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- abnormalities￨L￨NNS￨O￨- in￨L￨IN￨O￨- lipoprotein￨L￨NN￨O￨- metabolism￨L￨NN￨O￨- in￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- canine￨L￨JJ￨O￨- medicine￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- previously￨L￨RB￨DATE￨- used￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- lipoprotein￨L￨NN￨O￨- profiling￨L￨NN￨O￨- are￨L￨VBP￨O￨- rather￨L￨RB￨O￨- laborious￨L￨JJ￨O￨- and￨L￨CC￨O￨- time-consuming￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- obstacle￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- wide￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- application￨L￨NN￨O￨- and￨L￨CC￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- lipoprotein￨L￨NN￨O￨- profiling￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- species￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- feasibility￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- lipoprotein￨L￨NN￨O￨- density￨L￨NN￨O￨- profile￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CLPDP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- generated￨L￨VBN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- bismuth￨L￨NN￨O￨- sodium￨L￨NN￨O￨- ethylenediaminetetraacetic￨L￨JJ￨O￨- acid￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NaBiEDTA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- density￨L￨NN￨O￨- gradient￨L￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- lipoprotein￨L￨NN￨O￨- profiles￨L￨NNS￨O￨- of￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨A of￨L￨IN￨O￨- various￨L￨JJ￨O￨- breeds￨L￨NNS￨O￨- ,￨L￨,￨O￨- healthy￨L￨JJ￨O￨- Miniature￨U￨NNP￨O￨- Schnauzers￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Miniature￨U￨NNP￨O￨- Schnauzers￨U￨NNPS￨O￨- with￨L￨IN￨O￨- primary￨L￨JJ￨O￨- hypertriacylglycerolemia￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 35￨L￨CD￨NUMBER￨- healthy￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨A of￨L￨IN￨O￨- various￨L￨JJ￨O￨- breeds￨L￨NNS￨O￨- with￨L￨IN￨O￨- serum￨L￨NN￨O￨- triacylglycerol￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TAG￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- cholesterol￨L￨NN￨O￨- concentrations￨L￨NNS￨O￨- within￨L￨IN￨O￨- their￨L￨PRP$￨O￨- respective￨L￨JJ￨O￨- reference￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- selected￨L￨VBN￨O￨- for￨L￨IN￨O￨- use￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- reference￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- results￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- CLPDP￨U￨NN￨O￨- using￨L￨VBG￨O￨- NaBiEDTA￨U￨NN￨O￨- provides￨L￨VBZ￨O￨- unique￨L￨JJ￨O￨- diagnostic￨L￨JJ￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- measurements￨L￨NNS￨O￨- of￨L￨IN￨O￨- serum￨L￨NN￨O￨- TAG￨U￨NN￨O￨- and￨L￨CC￨O￨- cholesterol￨L￨NN￨O￨- concentrations￨L￨NNS￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- useful￨L￨JJ￨O￨- screening￨L￨NN￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- dogs￨L￨NNS￨O￨A with￨L￨IN￨O￨- suspected￨L￨VBN￨O￨- lipoprotein￨L￨NN￨O￨- metabolism￨L￨NN￨O￨- disorders￨L￨NNS￨O￨- .￨L￨.￨O￨- +Thirty-one￨U￨CD￨NUMBER￨- Miniature￨U￨NNP￨O￨- Schnauzers￨U￨NNPS￨O￨- with￨L￨IN￨O￨- serum￨L￨NN￨O￨- TAG￨U￨NN￨O￨- and￨L￨CC￨O￨- cholesterol￨L￨NN￨O￨- concentrations￨L￨NNS￨O￨A within￨L￨IN￨O￨- their￨L￨PRP$￨O￨- respective￨L￨JJ￨O￨- reference￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- and￨L￨CC￨O￨- 31￨L￨CD￨NUMBER￨- Miniature￨U￨NNP￨O￨- Schnauzers￨U￨NNPS￨O￨- with￨L￨IN￨O￨- hypertriacylglyceridemia￨L￨NN￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨A require￨L￨VBP￨O￨- costly￨L￨JJ￨O￨- human￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- this￨L￨DT￨O￨- we￨L￨PRP￨O￨- need￨L￨VBP￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- will￨L￨MD￨O￨- help￨L￨VB￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- fora￨L￨NN￨O￨- react￨L￨VBP￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- under￨L￨IN￨O￨- stress￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- cybernetic￨L￨JJ￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- recorded￨L￨VBD￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- members￨L￨NNS￨O￨- registered￨L￨VBN￨O￨- from￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- fora￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- reported￨L￨VBN￨O￨- automatically￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- forum￨L￨NN￨O￨- platforms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Table￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- list￨L￨NN￨O￨- of￨L￨IN￨O￨- forums￨L￨NNS￨O￨- analyzed￨L￨VBN￨O￨- and￨L￨CC￨O￨- monitoring￨L￨VBG￨O￨- statistics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- turn￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- violent￨L￨JJ￨O￨- extremist￨L￨NN￨O￨- groups￨L￨NNS￨O￨- that￨L￨WDT￨O￨- make￨L￨VBP￨O￨- intensive￨L￨JJ￨O￨A use￨L￨NN￨O￨- of￨L￨IN￨O￨- Internet￨U￨NN￨MISC￨- fora￨L￨NN￨O￨- for￨L￨IN￨O￨- recruitment￨L￨NN￨O￨- ,￨L￨,￨O￨- illegal￨L￨JJ￨O￨- financing￨L￨NN￨O￨- ,￨L￨,￨O￨- internal￨L￨JJ￨O￨- communication￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- fully￨L￨RB￨O￨- radicalized￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- operative￨L￨JJ￨O￨- support￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- violent￨L￨JJ￨O￨- activity21222324￨L￨NN￨O￨- .￨L￨.￨O￨- +Case￨U￨NN￨O￨- studies￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- extremist￨L￨NN￨O￨- fora￨L￨NN￨O￨- control￨L￨NN￨O￨- growth￨L￨NN￨O￨- by￨L￨IN￨O￨- limiting￨L￨VBG￨O￨A the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- participants48￨L￨NN￨O￨- .￨L￨.￨O￨- +Agent￨U￨NNP￨O￨- based￨L￨VBN￨O￨A models￨L￨NNS￨O￨A are￨L￨VBP￨O￨- being￨L￨VBG￨O￨- increasingly￨L￨RB￨O￨- employed￨L￨VBN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- complex￨L￨JJ￨O￨- emergent￨L￨JJ￨O￨- behaviours￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- these￨L￨DT￨O￨- behaviours￨L￨NNS￨O￨- arise￨L￨VBP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- non-linearities￨L￨NNS￨O￨- of￨L￨IN￨O￨- human-human￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- -￨L￨:￨O￨- exposed￨L￨VBN￨O￨- -￨L￨:￨O￨- infected￨L￨JJ￨O￨- -￨L￨:￨O￨- recovered￨L￨VBN￨O￨- ,￨L￨,￨O￨- SEIR￨U￨NNP￨O￨- type￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- directly￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- ABM￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- resemble￨L￨VBP￨O￨- simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- based￨L￨VBN￨O￨A models￨L￨NNS￨O￨A mentioned￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Complex￨U￨NN￨O￨- networks￨L￨NNS￨O￨- underlie￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- agent￨L￨NN￨O￨- based￨L￨VBN￨O￨A models￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Network-based￨U￨JJ￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A use￨L￨VBP￨O￨- a￨L￨DT￨O￨- percolation-like￨L￨JJ￨O￨- principle￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- unique￨L￨JJ￨O￨- capability￨L￨NN￨O￨- will￨L￨MD￨O￨- enable￨L￨VB￨O￨- decision￨L￨NN￨O￨A makers￨L￨NNS￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- more￨L￨RBR￨O￨- effectively￨L￨RB￨O￨- when￨L￨WRB￨O￨- selecting￨L￨VBG￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Center￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Advanced￨U￨NNP￨ORGANIZATION￨- Study￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Informatics￨U￨NNPS￨ORGANIZATION￨- in￨L￨IN￨ORGANIZATION￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CASIPH￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- developing￨L￨VBG￨O￨- and￨L￨CC￨O￨- integrating￨L￨VBG￨O￨- software￨L￨NN￨O￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨- a￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- ,￨L￨,￨O￨- decision-theoretic￨L￨JJ￨O￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A surveillance￨L￨NN￨O￨A and￨L￨CC￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- translating￨L￨VBG￨O￨- this￨L￨DT￨O￨- system￨L￨NN￨O￨- into￨L￨IN￨O￨- practice￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- Allegheny￨U￨NNP￨ORGANIZATION￨- County￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- ACHD￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- CDS￨U￨NN￨O￨- computes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- diagnosis￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- monitored￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- every￨L￨DT￨O￨- patient￨L￨NN￨O￨- visit￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- monitored￨L￨JJ￨O￨- facility￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- work￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- paradigm￨L￨NN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A surveillance￨L￨NN￨O￨A ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- decision￨L￨NN￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- computes￨L￨VBZ￨O￨- both￨L￨CC￨O￨- a￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- patient￨L￨NN￨O￨A data￨L￨NNS￨O￨- |￨L￨SYM￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- visit￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- commuting￨L￨VBG￨O￨- behaviors￨L￨NNS￨O￨- in￨L￨IN￨O￨- meta-population￨L￨NN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- working-age￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- daily￨L￨JJ￨SET￨- return￨L￨NN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- home￨L￨NN￨O￨- census￨L￨NN￨O￨- district￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- significantly￨L￨RB￨O￨- reduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- propagation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- predicted￨L￨VBN￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- assuming￨L￨VBG￨O￨- irregular￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- probabilistic￨L￨JJ￨O￨- or￨L￨CC￨O￨- random￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- movements￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Routine￨U￨JJ￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- cities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- of￨L￨IN￨O￨- paramount￨L￨JJ￨O￨- importance￨L￨NN￨O￨- for￨L￨IN￨O￨- planning￨L￨VBG￨O￨- urban￨L￨JJ￨O￨- infrastructures￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- developing￨L￨VBG￨O￨- transport￨L￨NN￨O￨- and￨L￨CC￨O￨- commuting￨L￨VBG￨O￨- alternatives￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- improving￨L￨VBG￨O￨- wireless￨L￨JJ￨O￨A communication￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- promoting￨L￨VBG￨O￨- healthy￨L￨JJ￨O￨- lifestyles￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- preventing￨L￨VBG￨O￨- or￨L￨CC￨O￨- responding￨L￨VBG￨O￨- to￨L￨TO￨O￨- emergence￨L￨NN￨O￨- ,￨L￨,￨O￨- propagation￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- recent￨L￨JJ￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- location-aware￨L￨JJ￨O￨- technologies￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- phones￨L￨NNS￨O￨- ,￨L￨,￨O￨- GPS-enabled￨U￨JJ￨O￨- devices￨L￨NNS￨O￨- ,￨L￨,￨O￨- wireless￨L￨JJ￨O￨A local￨L￨JJ￨O￨- area￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- personal￨L￨JJ￨O￨- digital￨L￨JJ￨O￨- assistants￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- provided￨L￨VBN￨O￨- quantitative￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- human￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- recursive￨L￨JJ￨O￨- and￨L￨CC￨O￨- dominated￨L￨VBN￨O￨- by￨L￨IN￨O￨- highly￨L￨RB￨O￨- reproducible￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- laws￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- reality￨L￨NN￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨A and￨L￨CC￨O￨- potential￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- dynamic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- such￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- profound￨L￨JJ￨O￨- impacts￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- individual￨L￨JJ￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- movement￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- play￨L￨VBP￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- modulating￨L￨VBG￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- requirement￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- that￨L￨IN￨O￨- re-infection￨L￨NN￨O￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- cause￨L￨VB￨O￨- symptoms￨L￨NNS￨O￨A than￨L￨IN￨O￨- a￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- satisfied￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨- that￨L￨IN￨O￨- deer￨L￨NNS￨O￨- previously￨L￨RB￨DATE￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- virus￨L￨NN￨O￨- show￨L￨VBP￨O￨- no￨L￨DT￨O￨- or￨L￨CC￨O￨- minimal￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- on￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- reinfection￨L￨NN￨O￨- with￨L￨IN￨O￨- related￨L￨JJ￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- naïve￨L￨JJ￨O￨- deer￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- show￨L￨VBP￨O￨- severe￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- experimental￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- these￨L￨DT￨O￨- criteria￨L￨NNS￨O￨- are￨L￨VBP￨O￨- general￨L￨JJ￨TITLE￨- and￨L￨CC￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- specific￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨A ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- thought￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- satisfied￨L￨VBN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- systems￨L￨NNS￨O￨- spanning￨L￨VBG￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- animal￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ;￨L￨:￨O￨- viral￨L￨JJ￨O￨- ,￨L￨,￨O￨- bacterial￨L￨JJ￨O￨- and￨L￨CC￨O￨- protozoan￨L￨NN￨O￨- parasites￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- vector-borne￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- less￨L￨RBR￨O￨- likely￨L￨JJ￨O￨A compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- does￨L￨VBZ￨O￨- themselves￨L￨PRP￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- line￨L￨NN￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨- ,￨L￨,￨O￨- infection-induced￨L￨JJ￨O￨- antibodies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- wane￨L￨VB￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- year￨L￨NN￨DURATION￨- causing￨L￨VBG￨O￨- adults￨L￨NNS￨O￨- to￨L￨TO￨O￨- revert￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- status￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- deer￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- serotype￨L￨NN￨O￨- have￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- viral￨L￨JJ￨O￨A titer￨L￨NN￨O￨- profiles￨L￨NNS￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- observed￨L￨VBN￨O￨- during￨L￨IN￨O￨- primary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- capacity￨L￨NN￨O￨- for￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Enzootic￨U￨JJ￨O￨- or￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- refers￨L￨VBZ￨O￨A to￨L￨TO￨O￨- systems￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- maximized￨L￨VBN￨O￨- at￨L￨IN￨O￨- intermediate￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Existing￨U￨VBG￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- vaccination￨L￨NN￨O￨- decision￨L￨NN￨O￨A making￨L￨VBG￨O￨A have￨L￨VBP￨O￨- typically￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- several￨L￨JJ￨O￨- determinants￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- risks￨L￨NNS￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- perceived￨L￨VBN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- perceived￨L￨VBN￨O￨- safety￨L￨NN￨O￨- and￨L￨CC￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- side-effect￨L￨JJ￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- related￨L￨JJ￨O￨- adverse￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- financial￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- charge￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- administration￨L￨NN￨O￨- ,￨L￨,￨O￨- expenses￨L￨NNS￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- absence￨L￨NN￨O￨- from￨L￨IN￨O￨- work￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- current￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- describing￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- vaccination￨L￨NN￨O￨- decision￨L￨NN￨O￨A making￨L￨VBG￨O￨A by￨L￨IN￨O￨- integrating￨L￨VBG￨O￨- an￨L￨DT￨O￨- extended￨L￨JJ￨O￨- SIT-based￨U￨JJ￨MISC￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- game-theoretical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- cost￨L￨NN￨O￨- minimization￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- doing￨L￨VBG￨O￨- so￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- decision￨L￨NN￨O￨A making￨L￨NN￨O￨A and￨L￨CC￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- conformity￨L￨NN￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- decision￨L￨NN￨O￨A making￨L￨NN￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- tendency￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- idea￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- collecting￨L￨VBG￨O￨- samples￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- paths￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- sequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- adjacent￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- randomly￨L￨RB￨O￨- selected￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- these￨L￨DT￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- exploiting￨L￨VBG￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- matching￨L￨VBG￨O￨- each￨L￨DT￨O￨- description￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- probabilistically￨L￨RB￨O￨- coalesce￨L￨VB￨O￨- vertices￨L￨NNS￨O￨A to￨L￨TO￨O￨- build￨L￨VB￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- ensemble￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- estimate￨L￨VB￨O￨- some￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Having￨U￨VBG￨O￨- reconstructed￨L￨VBN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- then￨L￨RB￨O￨- attempt￨L￨VB￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- it￨L￨PRP￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- communities￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- vertices￨L￨NNS￨O￨A which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- sense￨L￨NN￨O￨- .￨L￨.￨O￨- +Now￨U￨RB￨DATE￨- a￨L￨DT￨O￨- vertex￨L￨NN￨ORGANIZATION￨- v￨L￨LS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- additional￨L￨JJ￨O￨- offspring￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tree￨L￨NN￨O￨- :￨L￨:￨O￨- these￨L￨DT￨O￨- are￨L￨VBP￨O￨- neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- v￨L￨LS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨A network￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- (￨L￨-LRB-￨O￨- but￨L￨CC￨O￨- need￨L￨MD￨O￨- not￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- include￨L￨VBP￨O￨- v￨L￨LS￨O￨- 's￨L￨POS￨O￨- predecessor￨L￨NN￨O￨- and￨L￨CC￨O￨- successor￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- task￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- possibly￨L￨RB￨O￨- duplicated￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨A and￨L￨CC￨O￨- attempt￨L￨NN￨O￨- to￨L￨TO￨O￨- coalesce￨L￨VB￨O￨- all￨L￨DT￨O￨- duplicates￨L￨VBZ￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- better￨L￨JJR￨O￨- adheres￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- observable￨L￨JJ￨O￨A information￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- study￨L￨NN￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- classifies￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- symptomatic￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- while￨L￨IN￨O￨- still￨L￨RB￨O￨- adopting￨L￨VBG￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- multistate￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- observable￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- including￨L￨VBG￨O￨- symptom￨L￨NN￨O￨- onset￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- from￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- observable￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- unobservable￨L￨JJ￨O￨- information￨L￨NN￨O￨- including￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- event￨L￨NN￨O￨- and￨L￨CC￨O￨- infectiousness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- unobservable￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- tended￨L￨VBD￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- employing￨L￨VBG￨O￨- the￨L￨DT￨O￨- widely￨L￨RB￨O￨- adopted￨L￨VBN￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- while￨L￨IN￨O￨- splitting￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- I-class￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- asymptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g￨L￨FW￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- specific￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- concerning￨L￨VBG￨O￨- this￨L￨DT￨O￨- delay￨L￨NN￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- general￨L￨JJ￨TITLE￨- form￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- allow￨L￨VBP￨O￨- for￨L￨IN￨O￨- random￨L￨JJ￨O￨- detection￨L￨NN￨O￨- delay￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- infected￨L￨JJ￨O￨- member￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- notification￨L￨NN￨O￨- of￨L￨IN￨O￨- authorities￨L￨NNS￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- subsequent￨L￨JJ￨O￨- random￨L￨JJ￨O￨- deployment￨L￨NN￨O￨- delay￨L￨NN￨O￨- until￨L￨IN￨O￨- intervention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- begun￨L￨VBN￨O￨- ;￨L￨:￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- delay￨L￨NN￨O￨- to￨L￨TO￨O￨- intervention￨L￨NN￨O￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- infectious￨L￨JJ￨O￨- case￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- modelling￨L￨NN￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- households￨L￨NNS￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- complex￨L￨JJ￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- focusing￨L￨VBG￨O￨- specifically￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- household￨L￨NN￨O￨A antiviral￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- population-level￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- treatment￨L￨NN￨O￨- regime￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨A basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- *￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- households￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- household￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- clear￨L￨JJ￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- households￨L￨NNS￨O￨- are￨L￨VBP￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- doubling￨L￨VBG￨O￨- time￨L￨NN￨O￨- early￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- Td￨U￨NN￨LOCATION￨- .￨L￨.￨O￨- +Detecting￨U￨VBG￨O￨- a￨L￨DT￨O￨- signature￨L￨NN￨O￨- of￨L￨IN￨O￨- climate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- seasons￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- weather￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- shorter-term￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- climatic￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- daily￨L￨JJ￨SET￨- maximum￨L￨NN￨O￨- temperature￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- chytridiomycosis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- complicated￨L￨VBN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- metric￨L￨JJ￨O￨- used￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- intensity￨L￨NN￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- mortality￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- decline/extirpation￨L￨NN￨O￨- ,￨L￨,￨O￨- extinction￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- by￨L￨IN￨O￨- species-specific￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- differential￨L￨JJ￨O￨- susceptibility/immunity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- invasion￨L￨NN￨O￨- history￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- numerous￨L￨JJ￨O￨- other￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- influence￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- breeding￨L￨VBG￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- predator￨L￨NN￨O￨- fluctuations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- tremendous￨L￨JJ￨O￨- attention￨L￨NN￨O￨- this￨L￨DT￨O￨- topic￨L￨NN￨O￨- has￨L￨VBZ￨O￨- received￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Bd￨U￨NN￨MISC￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- quantitative￨L￨JJ￨O￨- process-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- growth￨L￨NN￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- ultimately￨L￨RB￨O￨- population￨L￨NN￨O￨- decline￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- remain￨L￨VBP￨O￨- poorly￨L￨RB￨O￨- explored￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- but￨L￨CC￨O￨- see￨L￨VBP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- simulation￨L￨NN￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- address￨L￨NN￨O￨- of￨L￨IN￨O￨- historical￨L￨JJ￨O￨- amphibian￨L￨JJ￨O￨- declines￨L￨NNS￨O￨A ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ‘￨L￨``￨O￨- thermal-optimum￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- ’￨L￨''￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- declines￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- also￨L￨RB￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- explicitly￨L￨RB￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- climatic￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- nevertheless￨L￨RB￨O￨- co-vary￨L￨VB￨O￨- with￨L￨IN￨O￨- temperature￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- moisture￨L￨NN￨O￨- availability￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- Bd￨U￨NN￨O￨- occurrence￨L￨NN￨O￨- or￨L￨CC￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- field-based￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- investigations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- above￨L￨JJ￨O￨- growth￨L￨NN￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨FW￨O￨- vitro￨L￨FW￨O￨- thresholds￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- researchers￨L￨NNS￨O￨- to￨L￨TO￨O￨- retrospectively￨L￨RB￨O￨- interpret￨L￨VB￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- cases￨L￨NNS￨O￨- declines￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- range￨L￨NN￨O￨- over￨L￨IN￨O￨- which￨L￨WDT￨O￨- Bd￨U￨NN￨O￨- grows￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- laboratory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Seasonal￨U￨JJ￨O￨- and￨L￨CC￨O￨- elevational￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- and￨L￨CC￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- Bd￨U￨NN￨O￨- has￨L￨VBZ￨O￨- long￨L￨RB￨O￨- implicated￨L￨VBN￨O￨- temperature￨L￨NN￨O￨A as￨L￨IN￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- mechanistic￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- chytridiomycosis￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- mortalities￨L￨NNS￨O￨- more￨L￨RBR￨O￨- frequently￨L￨RB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- cooler￨L￨JJR￨O￨- climes￨L￨NNS￨O￨- and￨L￨CC￨O￨- periods￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- reasons￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- current￨L￨JJ￨DATE￨- policies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- doubts￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- chickenpox￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- shift￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- at￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- varicella￨L￨NN￨O￨- among￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- children￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- extent￨L￨NN￨O￨- ,￨L￨,￨O￨- about￨L￨IN￨O￨- a￨L￨DT￨O￨- possible￨L￨JJ￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- HZ￨U￨NN￨O￨- incidence￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- immunological￨L￨JJ￨O￨- boosting￨L￨VBG￨O￨A caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- varicella￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- debate￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- innovative￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- robustly￨L￨RB￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- VZV￨U￨NN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- HZ￨U￨NN￨O￨- epidemiology￨L￨NN￨O￨A ,￨L￨,￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- remarkable￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- varicella￨L￨NN￨O￨- and￨L￨CC￨O￨- HZ￨U￨NN￨O￨- :￨L￨:￨O￨- Italy￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Finland￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- safe￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- largely￨L￨RB￨O￨- effective￨L￨JJ￨O￨- against￨L￨IN￨O￨- varicella￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨A VZV￨U￨NN￨O￨- immunization￨L￨NN￨O￨- programs￨L￨NNS￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- is￨L￨VBZ￨O￨- stalled￨L￨VBN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Germany￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Greece￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Luxembourg￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- regions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Sicily￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Tuscany￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Veneto￨U￨NNP￨LOCATION￨- in￨L￨IN￨O￨- Italy￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Autonomous￨U￨NNP￨ORGANIZATION￨- Community￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Madrid￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- Spain￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- currently￨L￨RB￨DATE￨- vaccinating￨L￨VBG￨O￨- routinely￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- latter￨L￨JJ￨O￨- effect￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- CMI￨U￨NN￨ORGANIZATION￨- boosting￨L￨VBG￨O￨A effect￨L￨NN￨O￨- ,￨L￨,￨O￨- predicting￨L￨VBG￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- HZ￨U￨NN￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨DURATION￨- decades￨L￨NNS￨DURATION￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- prevailing￨L￨VBG￨O￨- view￨L￨NN￨O￨- ,￨L￨,￨O￨- dating￨L￨VBG￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- Hope-Simpson￨U￨NNP￨PERSON￨- seminal￨L￨JJ￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- after￨L￨IN￨O￨- temporary￨L￨JJ￨O￨A immunity￨L￨NN￨O￨- following￨L￨VBG￨O￨- varicella￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- VZV￨U￨NN￨O￨- reactivation￨L￨NN￨O￨- may￨L￨MD￨O￨- occur￨L￨VB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- decline￨L￨NN￨O￨- of￨L￨IN￨O￨- Cell￨U￨NN￨O￨- Mediated￨U￨VBN￨O￨- Immunity￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- CMI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- ageing￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- immune-suppressing￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- HZ￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- built￨L￨VBN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- yet￨L￨RB￨O￨- produced￨L￨VBN￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- net￨L￨JJ￨O￨- human￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- report￨L￨VBP￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- mechanistic￨L￨JJ￨O￨- ,￨L￨,￨O￨- within-host￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- simulates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- Plasmodium￨U￨NN￨LOCATION￨- falciparum￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- human-to-mosquito￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- mechanistic￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨- incorporate￨L￨VBP￨O￨- the￨L￨DT￨O￨- within-host￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- human￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- built￨L￨VBD￨O￨- upon￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- work￨L￨NN￨O￨- by￨L￨IN￨O￨- Molineaux￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Dietz￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- first￨L￨RB￨ORDINAL￨- developed￨L￨VBD￨O￨- the￨L￨DT￨O￨- asexual￨L￨JJ￨O￨- and￨L￨CC￨O￨- gametocyte￨L￨NN￨O￨- components￨L￨NNS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- from￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A therapy￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- tertiary￨L￨JJ￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- P.￨U￨NNP￨O￨- +Transitioning￨U￨VBG￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectivity￨L￨NN￨O￨A occurs￨L￨VBZ￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- clearance￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- densities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨A of￨L￨IN￨O￨- phocine￨L￨NN￨O￨- distemper￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PDV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- spread￨L￨NN￨O￨- rapidly￨L￨RB￨O￨- causing￨L￨VBG￨O￨- severe￨L￨JJ￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- among￨L￨IN￨O￨- mainly￨L￨RB￨O￨- harbour￨L￨VBP￨O￨- seals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Phoca￨U￨NN￨LOCATION￨- vitulina￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- signs￨L￨NNS￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- related￨L￨JJ￨O￨- morbillivirus￨L￨NN￨O￨- ,￨L￨,￨O￨- canine￨L￨JJ￨O￨- distemper￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CDV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- serum￨L￨NN￨O￨- samples￨L￨NNS￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- from￨L￨IN￨O￨- seals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- admitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- seal￨L￨NN￨O￨- research￨L￨NN￨O￨- and￨L￨CC￨O￨- rehabilitation￨L￨NN￨O￨- centre￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SRRC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- and￨L￨CC￨O￨- were￨L￨VBD￨O￨- tested￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨A of￨L￨IN￨O￨- antibodies￨L￨NNS￨O￨- against￨L￨IN￨O￨- PDV￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- CDV￨U￨NNP￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- pandemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- experienced￨L￨VBD￨O￨- multiple￨L￨JJ￨O￨- waves￨L￨NNS￨O￨A of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- exhibited￨L￨VBD￨O￨- well-separated￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- peaks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- separation￨L￨NN￨O￨- time-scale￨L￨NN￨O￨- of￨L￨IN￨O￨- months￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- five￨L￨CD￨NUMBER￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- formulated￨L￨VBN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- complementary￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- produce￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- waves￨L￨NNS￨O￨A of￨L￨IN￨O￨- acute￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- hypothesize￨L￨VBP￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- mutations￨L￨NNS￨O￨- increased￨L￨VBD￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- increased￨L￨VBN￨O￨- viral￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- caused￨L￨VBD￨O￨- some￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨A to￨L￨TO￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- five￨L￨CD￨NUMBER￨- mechanisms￨L￨NNS￨O￨A are￨L￨VBP￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- appropriate￨L￨JJ￨O￨- extensions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Exposed-Infected-Removed￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- changes￨L￨NNS￨O￨- manifest￨L￨VBP￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨A varying￨L￨VBG￨O￨A transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- varying￨L￨VBG￨O￨- PCV13￨U￨NN￨O￨- effectiveness￨L￨NN￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- patient￨L￨NN￨O￨- risk￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- base￨L￨NN￨O￨- case￨L￨NN￨O￨- scenario￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- vaccinating￨L￨VBG￨O￨- at￨L￨IN￨O￨- 65￨L￨CD￨DURATION￨A years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- younger￨L￨JJR￨O￨- high-risk￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- per￨L￨IN￨O￨- quality-adjusted￨L￨JJ￨O￨- life￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- (￨L￨-LRB-￨O￨- QALY￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- USD￨U￨NNP￨O￨- 28,900￨L￨CD￨NUMBER￨- versus￨L￨CC￨O￨- no￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- PCV13￨U￨NN￨O￨- was￨L￨VBD￨O￨- more￨L￨RBR￨O￨- efficient￨L￨JJ￨O￨- than￨L￨IN￨O￨- PPV23￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- targeting￨L￨VBG￨O￨- a￨L￨DT￨O￨- 65-year-old￨L￨JJ￨DURATION￨- cohort￨L￨NN￨O￨- versus￨L￨CC￨O￨- a￨L￨DT￨O￨- no-vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- transmission-dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Spain￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 23-valent￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨A polysaccharide￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PPV23￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- recommended￨L￨VBN￨O￨- for￨L￨IN￨O￨- adults￨L￨NNS￨O￨- with￨L￨IN￨O￨- certain￨L￨JJ￨O￨- underlying￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- 65￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- older￨L￨JJR￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- routine￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨A conjugate￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- induce￨L￨VBP￨O￨- a￨L￨DT￨O￨- T-cell￨U￨NN￨MISC￨- dependent￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccine-preventable￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- IPD￨U￨NN￨O￨- and￨L￨CC￨O￨- non-IPD￨L￨JJ￨O￨- in￨L￨IN￨O￨- young￨L￨JJ￨O￨- children￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- cost-effectiveness￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- published￨L￨VBN￨O￨- analysing￨L￨VBG￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- implementing￨L￨VBG￨O￨- an￨L￨DT￨O￨- adult￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨A immunization￨L￨NN￨O￨- programme￨L￨NN￨O￨- with￨L￨IN￨O￨- PCV13￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Effects￨U￨NNS￨MISC￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- ageing￨L￨JJ￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- replacement￨L￨NN￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- birth￨L￨NN￨O￨- cohorts￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨A of￨L￨IN￨O￨- hepatitis￨L￨NN￨O￨- A￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- NetherlandsScott￨U￨NNP￨O￨- A￨U￨NNP￨O￨- McDonald1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Marie-Josée￨U￨JJ￨O￨- J￨U￨NN￨O￨- Mangen2￨U￨NN￨O￨- ,￨L￨,￨O￨- Anita￨U￨NNP￨PERSON￨- Suijkerbuijk3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Edoardo￨U￨NNP￨PERSON￨- Colzani4￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Mirjam￨U￨NNP￨PERSON￨- EE￨U￨NNP￨PERSON￨- Kretzschmar1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 13:120￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- McDonald￨U￨NNP￨ORGANIZATION￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- In￨U￨IN￨MISC￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨O￨- A￨U￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HAV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- declined￨L￨VBN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- socio-economic￨L￨JJ￨O￨- improvements￨L￨NNS￨O￨- ,￨L￨,￨O￨- better￨L￨JJR￨O￨- sanitation￨L￨NN￨O￨- and￨L￨CC￨O￨- hygiene￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- birth￨L￨NN￨O￨- cohorts￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- long-term￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- through￨L￨IN￨O￨- exposure￨L￨NN￨O￨- early￨L￨RB￨O￨- in￨L￨IN￨O￨- life￨L￨NN￨O￨- are￨L￨VBP￨O￨- now￨L￨RB￨DATE￨- being￨L￨VBG￨O￨- replaced￨L￨VBN￨O￨- by￨L￨IN￨O￨- non-immune￨L￨JJ￨O￨- cohorts￨L￨NNS￨O￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- that￨L￨IN￨O￨- more￨L￨JJR￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- elderly￨L￨JJ￨O￨- may￨L￨MD￨O￨- occur￨L￨VB￨O￨- in￨L￨IN￨O￨- future￨L￨NN￨DATE￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- further￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- and￨L￨CC￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- continued￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- decline￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- HAV￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A burden￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- decrease￨L￨VB￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DATE￨- coming￨L￨VBG￨DATE￨- decades￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- with￨L￨IN￨O￨- proportionally￨L￨RB￨O￨- more￨L￨JJR￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- occurring￨L￨VBG￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- increasingly￨L￨RB￨O￨- larger￨L￨JJR￨O￨- segment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- elderly￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- no￨L￨RB￨O￨- longer￨L￨RB￨O￨- naturally￨L￨RB￨O￨- immune￨L￨JJ￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- dynamic￨L￨JJ￨O￨- MSIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- maternal￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- –￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infectious￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2030￨L￨CD￨DATE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- estimated￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A burden￨L￨NN￨O￨A using￨L￨VBG￨O￨- the￨L￨DT￨O￨- disability-adjusted￨L￨JJ￨O￨- life￨L￨NN￨O￨- years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- DALY￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- measure￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- pre-defined￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- goal￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- qualitatively￨L￨RB￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- cohort￨L￨NN￨O￨- effect￨L￨NN￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- change￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- population￨L￨NN￨O￨- ageing￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A burden￨L￨NN￨O￨A of￨L￨IN￨O￨- HAV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- decreasing￨L￨VBG￨O￨- trend￨L￨NN￨O￨- was￨L￨VBD￨O￨- absent￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- 55￨L￨CD￨NUMBER￨A +￨L￨CC￨O￨- years￨L￨NNS￨DURATION￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- ;￨L￨:￨O￨- 23.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 55￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- 5.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 55￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- simulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- community￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- representations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- explains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- periods￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- movement￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- local￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- farm￨L￨NN￨O￨A density￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- areas￨L￨NNS￨O￨- affected￨L￨VBN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- function￨L￨NN￨O￨- obtained￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- farm￨L￨NN￨O￨A location￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- between-farm￨L￨NN￨O￨- transmission￨L￨NN￨O￨- risks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- areas￨L￨NNS￨O￨- and￨L￨CC￨O￨- periods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- without￨L￨IN￨O￨- new￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- about￨L￨IN￨DURATION￨- three￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- reappeared￨L￨VBD￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- farm￨L￨NN￨O￨A in￨L￨IN￨O￨- Cremona￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- province￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- Lombardy￨U￨NNP￨LOCATION￨- that￨L￨WDT￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- affected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- population￨L￨NN￨O￨A genetics￨L￨NNS￨O￨A simulator￨L￨NN￨O￨- ,￨L￨,￨O￨- TreesimJ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- O￨U￨NN￨O￨- ’￨L￨''￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- joint￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- history￨L￨NN￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- sequences￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- genealogy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- discrete￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- generation￨L￨NN￨O￨- ,￨L￨,￨O￨- discarding￨L￨VBG￨O￨- extinct￨L￨JJ￨O￨- lineages￨L￨NNS￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨A genetics￨L￨NNS￨O￨A ,￨L￨,￨O￨- recent￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- include￨L￨VBP￨O￨- Nemo￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- FFPopSim￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- perform￨L￨VBP￨O￨- simulations￨L￨NNS￨O￨- under￨L￨IN￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- assume￨L￨VBP￨O￨- discrete￨L￨JJ￨O￨- generation￨L￨NN￨O￨- times￨L￨NNS￨O￨- and￨L￨CC￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- direct￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- sequence￨L￨NN￨O￨- evolution￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨A genetics￨L￨NNS￨O￨A simulators￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- chemical￨L￨NN￨O￨- kinetics￨L￨NNS￨O￨- software￨L￨NN￨O￨- above￨L￨IN￨O￨- deals￨L￨NNS￨O￨- with￨L￨IN￨O￨- continuous-time￨L￨JJ￨O￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- individual￨L￨JJ￨O￨- “￨L￨``￨O￨- demographic￨L￨JJ￨O￨- ”￨L￨''￨O￨- events￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- at￨L￨IN￨O￨- times￨L￨NNS￨O￨- separated￨L￨VBN￨O￨- by￨L￨IN￨O￨- exponentially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- intervals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- traditional￨L￨JJ￨O￨- population￨L￨NN￨O￨A genetics￨L￨NNS￨O￨A models￨L￨NNS￨O￨- ,￨L￨,￨O￨- neither￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- programs￨L￨NNS￨O￨- allow￨L￨VBP￨O￨- for￨L￨IN￨O￨- genealogy￨L￨NN￨O￨- simulation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- prairie￨L￨NN￨O￨- dogs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Cynomys￨U￨NNS￨O￨- spp.￨L￨VBP￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- between￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- plague￨L￨VB￨O￨A persistence￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- empirically￨L￨RB￨O￨- observed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- theoretically￨L￨RB￨O￨- confirmed￨L￨VBD￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- on￨L￨IN￨O￨- short￨L￨JJ￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Salkeld￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- plague￨L￨VB￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- adjacent￨L￨JJ￨O￨- coteries￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- structured￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- enzootic￨L￨JJ￨O￨- phases￨L￨NNS￨O￨- which￨L￨WDT￨O￨- last￨L￨RB￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- 1￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- in￨L￨IN￨O￨- about￨L￨RB￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- runs￨L￨VBZ￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- developed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Keeling￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Gilligan￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- metapopulation￨L￨NN￨O￨- structure￨L￨NN￨O￨- can￨L￨MD￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- plague￨L￨VB￨O￨A via￨L￨IN￨O￨- extinction-recolonization￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- population￨L￨NN￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- modelled￨L￨VBD￨O￨- included￨L￨VBD￨O￨- some￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- roles￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- factors￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- disentangled￨L￨VBN￨O￨- .￨L￨.￨O￨- +Susceptible￨U￨JJ￨O￨- hosts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- plague￨L￨VB￨O￨A transmission￨L￨NN￨O￨- by￨L￨IN￨O￨- developing￨L￨VBG￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- septicemia￨L￨NN￨CAUSE_OF_DEATH￨- needed￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- would￨L￨MD￨O￨- help￨L￨VB￨O￨- maintain￨L￨VB￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- flea￨L￨NN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- would￨L￨MD￨O￨- lower￨L￨VB￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- encounter￨L￨NN￨O￨- between￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- fleas￨L￨NNS￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- factor￨L￨NN￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- explain￨L￨VB￨O￨- plague￨L￨VB￨O￨A endemism￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- metapopulation￨L￨NN￨O￨- structure￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- extinction-recolonization￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- plague￨L￨VBP￨O￨- in￨L￨IN￨O￨- local￨L￨JJ￨O￨- foci￨L￨NNS￨O￨- ,￨L￨,￨O￨- between￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- slowly￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- values￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- of￨L￨IN￨O￨- :￨L￨:￨O￨- intrinsic￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- immunity￨L￨NN￨O￨- or￨L￨CC￨O￨- predisposition￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- modifications￨L￨NNS￨O￨- in￨L￨IN￨O￨- behavior￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- increased￨L￨VBN￨O￨- or￨L￨CC￨O￨- decreased￨L￨VBN￨O￨- hand￨L￨NN￨O￨- hygiene￨L￨NN￨O￨- ;￨L￨:￨O￨- seasonal￨L￨JJ￨O￨- climatic￨L￨JJ￨O￨- variability￨L￨NN￨O￨A ;￨L￨:￨O￨- methodological￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- ;￨L￨:￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- pathogen-specific￨L￨JJ￨O￨- virulence￨L￨NN￨O￨- across￨L￨IN￨O￨- regions￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- time￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- data-gathering￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- rapidly￨L￨RB￨O￨- and￨L￨CC￨O￨- reliably￨L￨RB￨O￨- characterize￨L￨VBP￨O￨- novel￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- transmissibility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- health￨L￨NN￨O￨- planners￨L￨NNS￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- civilian￨L￨JJ￨O￨- and￨L￨CC￨O￨- military￨L￨JJ￨O￨- domains￨L￨NNS￨O￨- :￨L￨:￨O￨- without￨L￨IN￨O￨- good￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- nor￨L￨CC￨O￨- is￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- variability￨L￨NN￨O￨A in￨L￨IN￨O￨- transmissibility￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Possible￨U￨JJ￨O￨- strengths￨L￨NNS￨O￨- of￨L￨IN￨O￨- analyses￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- DMSS￨U￨NNP￨O￨- data￨L￨NNS￨O￨A compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- for￨L￨IN￨O￨- civilian￨L￨JJ￨O￨- population￨L￨NN￨O￨- are￨L￨VBP￨O￨- :￨L￨:￨O￨- localization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- to￨L￨TO￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- zip￨L￨NN￨O￨- code￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- consistent￨L￨JJ￨O￨- reporting￨L￨NN￨O￨- over￨L￨IN￨O￨- many￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- potentially￨L￨RB￨O￨- ,￨L￨,￨O￨- near-realtime￨L￨JJ￨O￨- availability￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Defense￨U￨NNP￨O￨- Medical￨U￨NNP￨O￨- Surveillance￨U￨NNP￨O￨- System￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- DMSS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A profiles￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- at￨L￨IN￨O￨- military￨L￨JJ￨O￨- installations￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- compare￨L￨VB￨O￨- them￨L￨PRP￨O￨- with￨L￨IN￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- surrounding￨L￨VBG￨O￨- civilian￨L￨JJ￨O￨- population￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- how￨L￨WRB￨O￨- much￨L￨JJ￨O￨- civilian￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- drive￨L￨VBP￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- military￨L￨JJ￨O￨- installations￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- parsimonious￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- installation-specific￨L￨JJ￨O￨- values￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- pandemic￨L￨JJ￨O￨A ranged￨L￨VBD￨O￨- from￨L￨IN￨O￨- 1.1￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 3.3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- were￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- influenza-like-illness￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- ad￨L￨NN￨O￨- hoc￨L￨FW￨O￨- data￨L￨NNS￨O￨- gathering￨L￨VBG￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- age￨L￨NN￨O￨- distributed￨L￨VBN￨O￨- in￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- age￨L￨NN￨O￨- classes￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 64￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- over￨L￨IN￨O￨- 65￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- age-classes￨L￨NNS￨O￨- typically￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- data￨L￨NNS￨O￨- report￨L￨VBP￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- regular￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- site￨L￨NN￨O￨- is￨L￨VBZ￨O￨- occupied￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- fixed￨L￨VBN￨O￨A identity￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨A number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- identities￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- change￨L￨VBP￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- authors￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- declared￨L￨VBN￨O￨- that￨L￨IN￨O￨- exogenous￨L￨JJ￨O￨- reinfection￨L￨NN￨O￨A plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- inhalation￨L￨NN￨O￨- of￨L￨IN￨O￨- tubercle￨L￨JJ￨O￨- bacilli￨L￨NNS￨O￨- by￨L￨IN￨O￨- persons￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- previously￨L￨RB￨DATE￨- for￨L￨IN￨O￨- more￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- five￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- represents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- risk￨L￨NN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- active￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- soon￨L￨RB￨O￨- after￨L￨IN￨O￨- reinfection￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨A concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- immunodeficient￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- improper￨L￨JJ￨O￨- precautions￨L￨NNS￨O￨- taken￨L￨VBN￨O￨- for￨L￨IN￨O￨- protection￨L￨NN￨O￨- ,￨L￨,￨O￨- delay￨L￨NN￨O￨- in￨L￨IN￨O￨- diagnosis￨L￨NN￨O￨- ,￨L￨,￨O￨- sustained￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- inadequate￨L￨JJ￨O￨- ventilation￨L￨NN￨O￨- and/or￨L￨CC￨O￨- overcrowding￨L￨NN￨O￨- make￨L￨VBP￨O￨- them￨L￨PRP￨O￨- well￨L￨RB￨O￨- suited￨L￨VBD￨O￨- for￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- creating￨L￨VBG￨O￨- this￨L￨DT￨O￨- way￨L￨NN￨O￨- genuine￨L￨JJ￨O￨- high￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- pockets￨L￨NNS￨O￨- of￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- inserted￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relative￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- pathways￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- significant￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- treatment￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- most￨L￨RBS￨O￨- notably￨L￨RB￨O￨- in￨L￨IN￨O￨- deciding￨L￨VBG￨O￨- whether￨L￨IN￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- treated￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- reinfection￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Unreliable￨U￨JJ￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- metrics￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- peak￨L￨JJ￨O￨- week￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- intensity￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- have￨L￨VBP￨O￨- far-reaching￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- society￨L￨NN￨O￨- including￨L￨VBG￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- economic￨L￨JJ￨O￨- and￨L￨CC￨O￨- health-care￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- if￨L￨IN￨O￨- models￨L￨NNS￨O￨- underestimate￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- intensity￨L￨NN￨O￨- and￨L￨CC￨O￨- insufficient￨L￨JJ￨O￨- mobilization￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- lasts￨L￨VBZ￨O￨- longer￨L￨JJR￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Model￨U￨NNP￨TITLE￨- predictions￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- how￨L￨WRB￨O￨- epidemics￨L￨NNS￨O￨- will￨L￨MD￨O￨- spread￨L￨VB￨O￨- under￨L￨IN￨O￨- each￨L￨DT￨O￨- mitigation￨L￨NN￨O￨- strategy￨L￨NN￨O￨- are￨L￨VBP￨O￨- captured￨L￨VBN￨O￨- by￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- metrics￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- absolute￨L￨JJ￨O￨- intensity￨L￨NN￨O￨- ,￨L￨,￨O￨- peak￨L￨NN￨O￨- week￨L￨NN￨DURATION￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- duration￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- policy￨L￨NN￨O￨A makers￨L￨NNS￨O￨A use￨L￨VBP￨O￨- model￨L￨NN￨TITLE￨- predictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- consider￨L￨VB￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- plan￨L￨VBP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +Optimisation￨U￨NN￨O￨- of￨L￨IN￨O￨- total￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- costs￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- palliative￨L￨JJ￨O￨- cost￨L￨NN￨O￨A associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- appropriate￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- appearance￨L￨NN￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- basic￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- Global￨U￨JJ￨O￨- Strategy￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- GS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- whereby￨L￨WRB￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- status￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- contrasted￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- Null￨U￨NNP￨O￨- Strategy￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- NS￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- authorities￨L￨NNS￨O￨- completely￨L￨RB￨O￨- refrain￨L￨VBP￨O￨- from￨L￨IN￨O￨- preventive￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- and￨L￨CC￨O￨- concentrate￨L￨NN￨O￨- on￨L￨IN￨O￨- palliative￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- these￨L￨DT￨O￨- uncertainties￨L￨NNS￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- modelling￨L￨NN￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨A effective￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- lowest￨L￨JJS￨O￨- overall￨L￨JJ￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- this￨L￨DT￨O￨- issue￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- such￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- treating￨L￨VBG￨O￨- them￨L￨PRP￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- side￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +Modelling￨U￨VBG￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- :￨L￨:￨O￨- It￨U￨PRP￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- how￨L￨WRB￨O￨- far￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- spread￨L￨VB￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨A effective￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extend￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- to￨L￨TO￨O￨- two￨L￨CD￨NUMBER￨- contrasting￨L￨VBG￨O￨- and￨L￨CC￨O￨- yet￨L￨RB￨O￨- complementary￨L￨JJ￨O￨A models￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- either￨L￨DT￨O￨- treat￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- activity￨L￨NN￨O￨- as￨L￨IN￨O￨- proxy￨L￨NN￨O￨- for￨L￨IN￨O￨- tie￨L￨NN￨O￨- presence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- communication￨L￨NN￨O￨- channels￨L￨NNS￨O￨- like￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨- calls￨L￨NNS￨O￨- ,￨L￨,￨O￨- emails￨L￨NNS￨O￨- ,￨L￨,￨O￨- electronic￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- etc.￨L￨FW￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- tie￨L￨NN￨O￨- activity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- bursty21￨L￨JJ￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- clear￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- discriminate￨L￨VB￨O￨- those￨L￨DT￨O￨- social￨L￨JJ￨O￨- ties￨L￨NNS￨O￨A that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- already￨L￨RB￨O￨- inactive￨L￨JJ￨O￨- from￨L￨IN￨O￨- large-inter￨L￨JJ￨O￨- even￨L￨RB￨O￨- times￨L￨NNS￨O￨- within￨L￨IN￨O￨- active￨L￨JJ￨O￨- relationships42￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- what￨L￨WP￨O￨- mechanisms￨L￨NNS￨O￨- control￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- activating￨L￨VBG￨O￨- or￨L￨CC￨O￨- deactivating￨L￨VBG￨O￨- social￨L￨JJ￨O￨- ties￨L￨NNS￨O￨A have￨L￨VBP￨O￨- uncovered￨L￨VBN￨O￨- forces￨L￨NNS￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- geography￨L￨NN￨O￨- to￨L￨TO￨O￨- structural￨L￨JJ￨O￨- positions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- preferential￨L￨JJ￨O￨- attachment￨L￨NN￨O￨- ,￨L￨,￨O￨- triadic￨L￨JJ￨O￨- closure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- homophily1￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- most￨L￨JJS￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- communication￨L￨NN￨O￨- networks￨L￨NNS￨O￨- a￨L￨DT￨O￨- tie￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- present￨L￨JJ￨DATE￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- shows￨L￨VBZ￨O￨- any￨L￨DT￨O￨- activity￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨- window22￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- differs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- previous￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extreme￨L￨JJ￨O￨- case￨L￨NN￨O￨A fatality￨L￨NN￨O￨A in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- currently￨L￨RB￨DATE￨- estimated￨L￨VBN￨O￨- at￨L￨IN￨O￨- 60￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- cent￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- high￨L￨JJ￨O￨- case￨L￨NN￨O￨A fatality￨L￨NN￨O￨A makes￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- likely￨L￨JJ￨O￨- that￨L￨IN￨O￨- virulence￨L￨NN￨O￨- will￨L￨MD￨O￨- attenuate￨L￨VB￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- immediate￨L￨JJ￨O￨- question￨L￨NN￨O￨- is￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- with￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- could￨L￨MD￨O￨- successfully￨L￨RB￨O￨- invade￨L￨VB￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- cause￨L￨VB￨O￨- a￨L￨DT￨O￨- sustainable￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- immediate￨L￨JJ￨O￨A risk￨L￨NN￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- viruses￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- will￨L￨MD￨O￨- evolve￨L￨VB￨O￨- the￨L￨DT￨O￨- capacity￨L￨NN￨O￨- for￨L￨IN￨O￨- sustainable￨L￨JJ￨O￨- human-to-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- pathways￨L￨NNS￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- ferret￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- recently￨L￨RB￨DATE￨- debated￨L￨VBN￨O￨- whether￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- missing￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- denominator￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- calculation￨L￨NN￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- case￨L￨NN￨O￨A fatality￨L￨NN￨O￨A of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- that￨L￨DT￨O￨- observed￨L￨VBN￨O￨- from￨L￨IN￨O￨- severe￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- alone￨L￨RB￨O￨- [￨L￨-LRB-￨O￨- 33￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 38￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- nevertheless￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- prevailing￨L￨VBG￨O￨- opinion￨L￨NN￨O￨- leans￨L￨VBZ￨O￨- towards￨L￨IN￨O￨- this￨L￨DT￨O￨- high￨L￨JJ￨O￨- 60￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- cent￨L￨NN￨O￨- estimate￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Jacobian￨U￨JJ￨MISC￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- point￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- e￨L￨SYM￨O￨- ,￨L￨,￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- takes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- If￨U￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- P￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨A stable￨L￨JJ￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Let￨U￨VB￨O￨- We￨U￨PRP￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- J￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- P￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- eigenvalues￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- being￨L￨VBG￨O￨- with￨L￨IN￨O￨- negative￨L￨JJ￨O￨- real￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- guaranteed￨L￨VBN￨O￨- by￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- R￨U￨NN￨O￨- 01￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- P￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨A stable￨L￨JJ￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Consider￨U￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- function￨L￨NN￨O￨- :￨L￨:￨O￨- Its￨U￨PRP$￨O￨- derivative￨L￨NN￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- L￨U￨NN￨O￨- ′￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- e￨L￨SYM￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- these￨L￨DT￨O￨- considerations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- reference￨L￨NN￨O￨- to￨L￨TO￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- derivative￨L￨JJ￨O￨A d/dt￨L￨NN￨O￨- is￨L￨VBZ￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- ′￨L￨NN￨O￨- and￨L￨CC￨O￨- F￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- qE￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- N￨U￨NN￨O￨- +￨L￨CC￨O￨- βaS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- qE￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- N￨U￨NN￨O￨- .￨L￨.￨O￨- +Li￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Fang￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- in￨L￨IN￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- homogeneous￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- advent￨L￨NN￨O￨- of￨L￨IN￨O￨- population-level￨L￨JJ￨O￨- whole￨L￨JJ￨O￨- genome￨L￨NN￨O￨- sequencing￨L￨NN￨O￨- has￨L￨VBZ￨O￨- revealed￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- unfathomed￨L￨JJ￨O￨- diversity￨L￨NN￨O￨A in￨L￨IN￨O￨- pathogenic￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- wider￨L￨JJR￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- integrated￨L￨VBN￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- genetics￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemiology￨L￨NN￨O￨- beyond￨L￨IN￨O￨- rapidly￨L￨RB￨O￨- evolving￨L￨VBG￨O￨- viruses￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- HCV￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- implement￨L￨VBP￨O￨- SI￨U￨NNP￨O￨- ,￨L￨,￨O￨- SIS￨U￨NNP￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- BEAST￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- conduct￨L￨VB￨O￨- a￨L￨DT￨O￨- meta-analysis￨L￨NN￨O￨- investigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- underlie￨L￨VBP￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨A between￨L￨IN￨O￨- HCV￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- modelling￨L￨VBG￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infectious￨L￨JJ￨O￨- –￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- estimated￨L￨VBN￨O￨- directly￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- population￨L￨NN￨O￨- genetic￨L￨JJ￨O￨A inference￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Changes￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- proportions￨L￨NNS￨O￨A of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- hosts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modelled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- results￨L￨NNS￨O￨- have￨L￨VBP￨O￨- generated￨L￨VBN￨O￨- considerable￨L￨JJ￨O￨- interest￨L￨NN￨O￨- because￨L￨IN￨O￨- a￨L￨DT￨O￨- brain￨L￨NN￨O￨- at￨L￨IN￨O￨- or￨L￨CC￨O￨- near￨L￨IN￨O￨- criticality￨L￨NN￨O￨A would￨L￨MD￨O￨- have￨L￨VB￨O￨- maximum￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- range￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- enabling￨L￨VBG￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- optimally￨L￨RB￨O￨- react￨L￨VB￨O￨- and￨L￨CC￨O￨- adapt￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- surrounding￨L￨JJ￨O￨- environment￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- whilst￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- balanced￨L￨JJ￨O￨- neuronal￨L￨JJ￨O￨- activity￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- power￨L￨NN￨O￨A laws￨L￨NNS￨O￨- may￨L￨MD￨O￨- underlie￨L￨VB￨O￨- other￨L￨JJ￨O￨- observables￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- amenable￨L￨JJ￨O￨- to￨L￨TO￨O￨- robust￨L￨JJ￨O￨- experimental￨L￨JJ￨O￨- assessment.KeywordsActive￨L￨JJ￨O￨- NeuroneCritical￨U￨JJ￨MISC￨- RegimeTranscritical￨U￨JJ￨MISC￨- BifurcationAvalanche￨U￨NNP￨O￨- SizeModel￨U￨NNP￨O￨- Selection￨U￨NN￨O￨- Approach￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionA￨U￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- in￨L￨FW￨O￨- vitro￨L￨FW￨O￨- and￨L￨CC￨O￨- in￨L￨FW￨O￨- vivo￨L￨FW￨O￨- studies￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- neuronal￨L￨JJ￨O￨- avalanches￨L￨NNS￨O￨- —￨L￨:￨O￨- cascades￨L￨NNS￨O￨- of￨L￨IN￨O￨- neuronal￨L￨JJ￨O￨- firing￨L￨NN￨O￨- —￨L￨:￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- exhibit￨L￨VB￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- statistics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- avalanche￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- occurrence￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- calculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- avalanche￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- avalanche￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- precisely￨L￨RB￨O￨- identify￨L￨VBP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- has￨L￨VBZ￨O￨- scale￨L￨NN￨O￨- free￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- but￨L￨CC￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨A law￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- Theoretical￨U￨JJ￨O￨- Investigation￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Non-driven￨U￨JJ￨MISC￨- CaseTimothy￨U￨NNP￨O￨- J￨U￨NNP￨O￨- Taylor1￨U￨NN￨O￨- ,￨L￨,￨O￨- Caroline￨U￨NNP￨PERSON￨- Hartley2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Péter￨U￨NN￨O￨- L￨U￨NN￨O￨- Simon4￨U￨NN￨O￨- ,￨L￨,￨O￨- Istvan￨U￨NNP￨PERSON￨- Z￨U￨NNP￨PERSON￨- Kiss5￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Luc￨U￨NN￨PERSON￨- Berthouze1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 3:5￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- T.J.￨U￨NNP￨PERSON￨- Taylor￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- purely￨L￨RB￨O￨- excitatory￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- network￨L￨NN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- construction￨L￨NN￨O￨- ,￨L￨,￨O￨- operates￨L￨VBZ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +Existing￨U￨VBG￨O￨- studies￨L￨NNS￨O￨- usually￨L￨RB￨O￨- consider￨L￨VBP￨O￨- random￨L￨JJ￨O￨- drift￨L￨NN￨O￨- affecting￨L￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- how￨L￨WRB￨O￨- large￨L￨JJ￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- to￨L￨TO￨O￨- sustain￨L￨VB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- “￨L￨``￨MISC￨- Critical￨U￨JJ￨MISC￨- Community￨U￨NN￨MISC￨- Size￨U￨NN￨MISC￨- ”￨L￨''￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- calculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨A probability￨L￨NN￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- ascertaining￨L￨VBG￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- sustained￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- cases￨L￨NNS￨O￨- over￨L￨IN￨O￨- an￨L￨DT￨O￨- area￨L￨NN￨O￨- has￨L￨VBZ￨O￨- occurred￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- this￨L￨DT￨O￨- importance￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- seldom￨L￨RB￨O￨- been￨L￨VBN￨O￨- addressed￨L￨VBN￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- needed￨L￨VBN￨O￨A to￨L￨TO￨O￨- declare￨L￨VB￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- occurring￨L￨VBG￨O￨- :￨L￨:￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- can￨L￨MD￨O￨- go￨L￨VB￨O￨- extinct￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- stochastic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- infects￨L￨VBZ￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- enough￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- manner￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- needed￨L￨VBN￨O￨A to￨L￨TO￨O￨- almost￨L￨RB￨O￨- guarantee￨L￨VB￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- will￨L￨MD￨O￨- cause￨L￨VB￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- maintain￨L￨VB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- once￨L￨IN￨DATE￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- appeared￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Critical￨U￨JJ￨O￨- Community￨U￨NN￨O￨- Size￨U￨NN￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- also￨L￨RB￨O￨- Box￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- classic￨L￨JJ￨O￨- prediction￨L￨NN￨O￨- for￨L￨IN￨O￨- pathogen￨L￨NN￨O￨A outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- 's￨L￨POS￨O￨- reproductive￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- to￨L￨TO￨O￨- exceed￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- lies￨L￨VBZ￨O￨- below￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- around￨L￨IN￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- needed￨L￨VBN￨O￨A to￨L￨TO￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- measures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- vaccine￨L￨NN￨O￨- allocation￨L￨NN￨O￨- that￨L￨WDT￨O￨- immunizes￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨- that￨L￨WDT￨O￨- reduces￨L￨VBZ￨O￨- individuals￨L￨NNS￨O￨- effective￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmissions￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- prophylactic￨L￨NN￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- prompt￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- change￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- uninfected￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Existing￨U￨VBG￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- allocation￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- population￨L￨NN￨O￨- have￨L￨VBP￨O￨- suggested￨L￨VBN￨O￨- different￨L￨JJ￨O￨- criteria￨L￨NNS￨O￨- for￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- priority￨L￨NN￨O￨- subpopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- school-age￨L￨JJ￨O￨- children￨L￨NNS￨O￨- for￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmissions￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- elderly￨L￨JJ￨O￨- for￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- influenza-attributable￨L￨JJ￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- cross-age￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨A exhibit￨L￨VBP￨O￨- specific￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- that￨L￨WDT￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- likelihoods￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- mixing￨L￨VBG￨O￨- together￨L￨RB￨O￨- within￨L￨IN￨O￨- certain￨L￨JJ￨O￨- social￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- households￨L￨NNS￨O￨- ,￨L￨,￨O￨- workplaces￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- general￨L￨JJ￨TITLE￨- communities￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- socio-demographical￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- school￨L￨NN￨O￨- attendance￨L￨NN￨O￨- ,￨L￨,￨O￨- household￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- working￨L￨VBG￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +That￨U￨DT￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- say￨L￨VB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- priority￨L￨NN￨O￨- subpopulations￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- measures￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- cutting￨L￨VBG￨O￨- down￨L￨RP￨O￨- individuals￨L￨NNS￨O￨- effective￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- for￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmissions￨L￨NNS￨O￨A .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- intervention￨L￨NN￨O￨- by￨L￨IN￨O￨- contact￨L￨NN￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- refers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- adjustment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ratios￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- contacts￨L￨NNS￨O￨A in￨L￨IN￨O￨- such￨L￨JJ￨O￨- social￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- LF￨U￨NN￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- concurrently￨L￨RB￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- consistent￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- effects￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- parasites￨L￨NNS￨O￨- within￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +High￨U￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- L3￨U￨NN￨O￨- larvae￨L￨NNS￨O￨- in￨L￨IN￨O￨- co-infected￨L￨JJ￨O￨- vectors￨L￨NNS￨O￨- increases￨L￨VBZ￨O￨- mortality￨L￨NN￨O￨- ,￨L￨,￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- vectors￨L￨NNS￨O￨- survive￨L￨VBP￨O￨- long￨L￨RB￨O￨- enough￨L￨RB￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- transmit￨L￨VB￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨DATE￨- may￨L￨MD￨DATE￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- regulatory￨L￨JJ￨O￨- mechanism￨L￨NN￨O￨- underlying￨L￨VBG￨O￨- co-transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- filariasis￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨- that￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- only￨L￨RB￨O￨- LF￨U￨NN￨O￨- may￨L￨MD￨O￨- actually￨L￨RB￨O￨- increase￨L￨VB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- –￨L￨:￨O￨- LF￨U￨NN￨O￨- infected￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- mortality￨L￨NN￨O￨- than￨L￨IN￨O￨- uninfected￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- larval￨L￨JJ￨O￨- burden￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- eliminating￨L￨VBG￨O￨- LF￨U￨NN￨O￨- increases￨L￨NNS￨O￨- vector￨L￨NN￨O￨- lifespan￨L￨NN￨O￨- ,￨L￨,￨O￨- enabling￨L￨VBG￨O￨- greater￨L￨JJR￨O￨- malarial￨L￨JJ￨O￨- parasite￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Explicitly￨U￨RB￨O￨- modelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- LF￨U￨NN￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- how￨L￨WRB￨O￨- co-infection￨L￨NN￨O￨- may￨L￨MD￨O￨- impact￨L￨VB￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- elimination￨L￨NN￨O￨- thresholds￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- clearly￨L￨RB￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- of￨L￨IN￨O￨- import￨L￨NN￨O￨- to￨L￨TO￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- integrated￨L￨VBN￨O￨- control￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- .￨L￨.￨O￨- +Interactions￨U￨NNS￨O￨- between￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- LF￨U￨NN￨O￨- parasites￨L￨NNS￨O￨- are￨L￨VBP￨O￨- thought￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- an￨L￨DT￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- through￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- vector￨L￨NN￨O￨- mortality￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- single￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- co-infection￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- theoretical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- and￨L￨CC￨O￨- practical￨L￨JJ￨O￨- value￨L￨NN￨O￨- to￨L￨TO￨O￨- know￨L￨VB￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- influential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨A effectively￨L￨RB￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- rumor￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- NumericCitation￨U￨NN￨MISC￨- ,￨L￨,￨O￨- electric￨L￨JJ￨O￨- power￨L￨NN￨O￨- supply￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- cooperation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- game￨L￨NN￨O￨- theory￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- link￨L￨NN￨O￨- prediction￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- robust￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- of￨L￨IN￨O￨- organisms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Concretely￨U￨RB￨O￨- ,￨L￨,￨O￨- Physarum￨U￨NNP￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- flux￨L￨NN￨O￨- through￨L￨IN￨O￨- its￨L￨PRP$￨O￨- body￨L￨NN￨O￨- tube￨L￨NN￨O￨- dynamically￨L￨RB￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- adapt￨L￨VB￨O￨- itself￨L￨PRP￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- connecting￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- specified￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- conveniently￨L￨RB￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- physarum￨L￨NN￨O￨- centrality￨L￨NN￨O￨A is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- in￨L￨IN￨O￨- dynamically￨L￨RB￨O￨- changed￨L￨VBN￨O￨- large￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- suitably￨L￨RB￨O￨- .￨L￨.￨O￨- +Three￨U￨CD￨NUMBER￨- best￨L￨RB￨O￨- known￨L￨VBN￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- were￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- distinguish￨L￨VB￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- central￨L￨JJ￨O￨- than￨L￨IN￨O￨- others￨L￨NNS￨O￨- in￨L￨IN￨O￨- binary￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- closeness￨L￨NN￨O￨- and￨L￨CC￨O￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Various￨U￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- years￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- network￨L￨NN￨O￨- entities￨L￨NNS￨O￨- meanings￨L￨NNS￨O￨- influence￨L￨VBP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- importance￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- popularity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- controllability￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- efficiency￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- whether￨L￨IN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- comparable￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- stage￨L￨NN￨O￨- and￨L￨CC￨O￨- history￨L￨NN￨O￨- ,￨L￨,￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- otherwise￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨A contact￨L￨NN￨O￨A network￨L￨NN￨O￨- over￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- is￨L￨VBZ￨O￨- spreading￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- host￨L￨NN￨TITLE￨A contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- significant￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- indeed￨L￨RB￨O￨- ,￨L￨,￨O￨- phylogenetic￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- now￨L￨RB￨DATE￨- being￨L￨VBG￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- for￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- host￨L￨NN￨TITLE￨A contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- phylogenies￨L￨NNS￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- not￨L￨RB￨O￨- fixed￨L￨VBN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Pathogens￨U￨NNS￨O￨- with￨L￨IN￨O￨- identical￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- very￨L￨RB￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨A contact￨L￨NN￨O￨A network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- schematically￨L￨RB￨O￨- illustrated￨L￨VBN￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨A contact￨L￨NN￨O￨A network￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- shape￨L￨VBP￨O￨- pathogen￨L￨NN￨O￨- phylogenies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- medicine￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- growing￨L￨VBG￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- reporting￨L￨VBG￨O￨- simultaneous￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- microorganisms￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- pathogenic￨L￨JJ￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- different￨L￨JJ￨O￨- mammal￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- wild￨L￨JJ￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- well-known￨L￨JJ￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- deterministic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- SIR￨U￨NN￨O￨- or￨L￨CC￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Infected￨U￨JJ￨O￨- and￨L￨CC￨O￨- Recovered￨U￨VBN￨O￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- several￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- demography￨L￨NN￨O￨A ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- immunity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- studied￨L￨VBN￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- explored￨L￨VBN￨O￨- .￨L￨.￨O￨- +Longitudinal￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- host￨L￨NN￨TITLE￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- recaptured￨L￨VBN￨O￨- several￨L￨JJ￨O￨- times￨L￨NNS￨O￨- ,￨L￨,￨O￨- allow￨L￨VBP￨O￨- the￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- investigated￨L￨VBN￨O￨- to￨L￨TO￨O￨- test￨L￨VB￨O￨A whether￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- microparasite￨L￨NN￨O￨- taxon￨L￨NN￨O￨- modifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- discriminate￨L￨VB￨O￨- real￨L￨JJ￨O￨- biologic￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- from￨L￨IN￨O￨- statistic￨L￨NN￨O￨- associations￨L￨NNS￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- improved￨L￨JJ￨O￨- Chi-square￨U￨JJ￨MISC￨- test￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- further￨L￨RB￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- confounding￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- Generalised￨U￨JJ￨O￨- Linear￨U￨NNP￨O￨- Mixed￨U￨NNP￨O￨- Models￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- GLMM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- 12￨L￨CD￨NUMBER￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- microorganisms￨L￨NNS￨O￨- in￨L￨IN￨O￨- field￨L￨NN￨O￨- vole￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- large￨L￨JJ￨O￨- stockpile￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- very￨L￨RB￨O￨- costly￨L￨JJ￨O￨- but￨L￨CC￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- stockpile￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- insufficient￨L￨JJ￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- pandemic￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- severe￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A and/or￨L￨CC￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- reliable￨L￨JJ￨O￨- ,￨L￨,￨O￨- timely￨L￨JJ￨O￨- and￨L￨CC￨O￨- cost￨L￨NN￨O￨- effective￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- care￨L￨NN￨O￨- test￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- strain￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- decision￨L￨NN￨O￨- to￨L￨TO￨O￨- stockpile￨L￨VB￨O￨- enough￨L￨JJ￨O￨- antivirals￨L￨NNS￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- 17.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Canadian￨U￨JJ￨NATIONALITY￨- population￨L￨NN￨O￨- was￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- expert￨L￨JJ￨O￨- opinion￨L￨NN￨O￨- after￨L￨IN￨O￨- consideration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- clinical￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A planning￨L￨VBG￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- care￨L￨NN￨O￨- test￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A/H1N1￨U￨NN￨O￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- Canada￨U￨NNP￨COUNTRY￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- static￨L￨JJ￨O￨- planning￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- plans￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- anticipated￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A of￨L￨IN￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- empirical￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- quickly￨L￨RB￨O￨- deplete￨L￨VB￨O￨- antiviral￨L￨JJ￨O￨- stockpiles￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A strain￨L￨NN￨O￨- emerges￨L￨VBZ￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- spring￨L￨NN￨DATE￨- and￨L￨CC￨O￨- activity￨L￨NN￨O￨- continues￨L￨VBZ￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- fall￨L￨NN￨DATE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Canadian￨U￨JJ￨NATIONALITY￨- government￨L￨NN￨O￨- maintains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- National￨U￨NNP￨O￨- Antiviral￨U￨NNP￨O￨- Stockpile￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- NAS￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨A .￨L￨.￨O￨- +Reference￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- presented￨L￨VBD￨O￨- the￨L￨DT￨O￨- vector-host￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- they￨L￨PRP￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- presented￨L￨VBD￨O￨- their￨L￨PRP$￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- numerical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- vector￨L￨NN￨O￨A host￨L￨NN￨TITLE￨A dengue￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Reference￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- presented￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- vector￨L￨NN￨O￨A host￨L￨NN￨TITLE￨A in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- vector￨L￨NN￨O￨- transmitted￨L￨VBD￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- pathogen￨L￨NN￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨A population￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Slaving￨U￨VBG￨MISC￨- and￨L￨CC￨O￨- release￨L￨NN￨O￨- in￨L￨IN￨O￨- co-infection￨L￨NN￨O￨- controlLaith￨L￨NN￨O￨- Yakob1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Gail￨U￨NN￨PERSON￨- M￨U￨NN￨O￨- Williams1￨U￨NN￨O￨- ,￨L￨,￨O￨- Darren￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Gray1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kate￨U￨NNP￨PERSON￨- Halton3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Juan￨U￨NNP￨PERSON￨- Antonio￨U￨NNP￨PERSON￨- Solon4￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Archie￨U￨NNP￨PERSON￨- CA￨U￨NNP￨STATE_OR_PROVINCE￨- Clements1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 6:157￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Yakob￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Animal￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- parasite￨L￨NN￨O￨- species￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- norm￨L￨NN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- exception￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- animal￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- diverse￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- synergisms￨L￨NNS￨O￨- between￨L￨IN￨O￨- species￨L￨NNS￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- becoming￨L￨VBG￨O￨- epidemiologically￨L￨RB￨O￨- slaved￨L￨VBD￨O￨- within￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- presenting￨L￨VBG￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- opportunity￨L￨NN￨O￨- for￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- drug￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- parasites￨L￨NNS￨O￨A by￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- co-circulating￨L￨JJ￨O￨- species￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- gastro-intestinal￨L￨JJ￨O￨- nematode￨L￨NN￨O￨- parasites￨L￨NNS￨O￨A as￨L￨IN￨O￨- an￨L￨DT￨O￨- illustrative￨L￨JJ￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- different￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- multiple￨L￨JJ￨O￨- ,￨L￨,￨O￨- interacting￨L￨VBG￨O￨- parasites.Gastro-intestinal￨L￨JJ￨O￨- nematodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- direct￨L￨JJ￨O￨- lifecycle￨L￨NN￨O￨- parasites￨L￨NNS￨O￨- of￨L￨IN￨O￨- veterinary￨L￨JJ￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- health￨L￨NN￨O￨- significance￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Scenarios￨U￨NNS￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- whereby￨L￨WRB￨O￨- control￨L￨NN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- releases￨L￨VBZ￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- resistant￨L￨JJ￨O￨- parasite￨L￨NN￨O￨A from￨L￨IN￨O￨- antagonistic￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- risks￨L￨NNS￨O￨- increasing￨L￨VBG￨O￨- co-infection￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- exacerbating￨L￨VBG￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Various￨U￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- households￨L￨NNS￨O￨A models￨L￨NNS￨O￨- appeared￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- differing￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- govern￨L￨VBP￨O￨- the￨L￨DT￨O￨- person-to-person￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- facts￨L￨NNS￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- household￨L￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- data￨L￨NNS￨O￨- about￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- directly￨L￨RB￨O￨- transmissible￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- appear￨L￨VBP￨O￨- clustered￨L￨VBN￨O￨- in￨L￨IN￨O￨- households￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- suggest￨L￨VBP￨O￨- the￨L￨DT￨O￨- choice￨L￨NN￨O￨- of￨L￨IN￨O￨- interpreting￨L￨VBG￨O￨- groups￨L￨NNS￨O￨- as￨L￨IN￨O￨- households￨L￨NNS￨O￨- –￨L￨:￨O￨- hence￨L￨RB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- name￨L￨NN￨O￨- –￨L￨:￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- there￨L￨EX￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studies￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨- size￨L￨NN￨O￨- was￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- large￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- households￨L￨NNS￨O￨A have￨L￨VBP￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- households￨L￨NNS￨O￨- grows￨L￨VBZ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- grows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- possible￨L￨JJ￨O￨- generalisation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- households￨L￨NNS￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- when￨L￨WRB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- being￨L￨VBG￨O￨- member￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- household￨L￨NN￨O￨- and￨L￨CC￨O￨- making￨L￨VBG￨O￨- global￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- also￨L￨RB￨O￨- belongs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- mixing￨L￨VBG￨O￨- group￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- define￨L￨VB￨O￨- R0￨U￨NN￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- take￨L￨VBP￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- approach￨L￨NN￨O￨- of￨L￨IN￨O￨- approximating￨L￨VBG￨O￨A the￨L￨DT￨O￨- early￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- suitably￨L￨RB￨O￨- defined￨L￨VBN￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Real-time￨U￨JJ￨O￨- forecast￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨A requires￨L￨VBZ￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- good￨L￨JJ￨O￨- monitoring￨L￨NN￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- adequate￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- extends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- forecasting￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- curve￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨A the￨L￨DT￨O￨- time￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- counts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Their￨U￨PRP$￨O￨- method￨L￨NN￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- power-law￨L￨NN￨O￨- logistic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- parameters￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨A .￨L￨.￨O￨- +Third￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- aware￨L￨JJ￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- degrees￨L￨NNS￨O￨A and￨L￨CC￨O￨- make￨L￨VB￨O￨- decisions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- partly￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- willing￨L￨JJ￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- could￨L￨MD￨O￨- either￨L￨RB￨O￨- come￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- realize￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- getting￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- are￨L￨VBP￨O￨- relatively￨L￨RB￨O￨- high￨L￨JJ￨O￨- or￨L￨CC￨O￨- result￨L￨VBP￨O￨- from￨L￨IN￨O￨- communications￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- with￨L￨IN￨O￨- others￨L￨NNS￨O￨- through￨L￨IN￨O￨- their￨L￨PRP$￨O￨- social￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- proving￨L￨VBG￨O￨- efficient￨L￨JJ￨O￨- theoretically￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- policy￨L￨NN￨O￨- mentioned￨L￨VBN￨O￨- above￨L￨IN￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- unlikely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- reality￨L￨NN￨O￨- because￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- government￨L￨NN￨O￨A can￨L￨MD￨O￨- not￨L￨RB￨O￨- discover￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- provide￨L￨VB￨O￨- preferential￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- to￨L￨TO￨O￨- individuals￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- connectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- sufficiently￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- any￨L￨DT￨O￨- non-degree-oriented￨L￨JJ￨O￨- policy￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- inefficient￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- government￨L￨NN￨O￨A should￨L￨MD￨O￨- intervene￨L￨VB￨O￨- by￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- degrees￨L￨NNS￨O￨- first￨L￨RB￨ORDINAL￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Voluntary￨U￨JJ￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- ineffective￨L￨JJ￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- supply￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- available￨L￨JJ￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- priority￨L￨NN￨O￨- given￨L￨VBN￨O￨- to￨L￨TO￨O￨- sub-populations￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- hospital-related￨L￨JJ￨O￨- employees￨L￨NNS￨O￨- ,￨L￨,￨O￨- students￨L￨NNS￨O￨- ,￨L￨,￨O￨- grocery￨L￨NN￨O￨- workers￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- socially￨L￨RB￨O￨- active￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- contract￨L￨NN￨O￨- and￨L￨CC￨O￨- transmit￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- positions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨A network￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- government￨L￨NN￨O￨A does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- the￨L￨DT￨O￨- authority￨L￨NN￨O￨- to￨L￨TO￨O￨- decide￨L￨VB￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- get￨L￨VBP￨O￨- vaccinated￨L￨VBN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- rather￨L￨RB￨O￨- choose￨L￨VB￨O￨- a￨L￨DT￨O￨- subsidization￨L￨NN￨O￨- policy￨L￨NN￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- incentivize￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- some￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- so￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- categorised￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- area￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- now￨L￨RB￨DATE￨- re-attracting￨L￨VBG￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- attention￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- estimation￨L￨NN￨O￨A of￨L￨IN￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- address￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- combining￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨A data￨L￨NNS￨O￨A .￨L￨.￨O￨- +These￨U￨DT￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- observed￨L￨VBN￨O￨A data￨L￨NNS￨O￨A that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨A loss￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- summary￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- four￨L￨CD￨NUMBER￨- individual￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- among￨L￨IN￨O￨- which￨L￨WDT￨O￨- two￨L￨CD￨NUMBER￨- act￨L￨VBP￨O￨- as￨L￨IN￨O￨- protective￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- single￨L￨JJ￨O￨- primary￨L￨JJ￨O￨A case￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- αm￨L￨NN￨O￨- and￨L￨CC￨O￨- αd￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- partially￨L￨RB￨O￨- immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- split￨L￨VBD￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- sub-groups￨L￨NNS￨O￨- by￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- history￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- sub-group￨L￨JJ￨O￨- i￨L￨FW￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- primary￨L￨JJ￨O￨A case￨L￨NN￨O￨A of￨L￨IN￨O￨- sub-group￨L￨JJ￨O￨- j￨L￨NN￨O￨- is￨L￨VBZ￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- Rij￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- subscripts￨L￨NNS￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- j￨L￨FW￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- history￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- otherwise￨L￨RB￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- practice￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- accompanied￨L￨VBN￨O￨- by￨L￨IN￨O￨- case￨L￨NN￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- takes￨L￨VBZ￨O￨- place￨L￨NN￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- traced￨L￨VBN￨O￨- exposed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- q￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- primary￨L￨JJ￨O￨A case￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- traced￨L￨VBN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- effectively￨L￨RB￨O￨- prevented￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- aimed￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- involves￨L￨VBZ￨O￨- contact￨L￨NN￨O￨A tracing￨L￨VBG￨O￨A and￨L￨CC￨O￨- case￨L￨NN￨O￨- isolation￨L￨NN￨O￨- under￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- feasibility￨L￨NN￨O￨- and￨L￨CC￨O￨- identifying￨L￨VBG￨O￨- associated￨L￨VBN￨O￨- data￨L￨NNS￨O￨- gaps￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- survey￨L￨VBP￨O￨- the￨L￨DT￨O￨- related￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- network￨L￨NN￨O￨- inference￨L￨NN￨O￨- ,￨L￨,￨O￨- discuss￨L￨VB￨O￨- how￨L￨WRB￨O￨- such￨L￨JJ￨O￨- an￨L￨DT￨O￨- approach￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- utilized￨L￨VBN￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- means￨L￨NNS￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- partial￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- what￨L￨WP￨O￨- methodological￨L￨JJ￨O￨- steps￨L￨NNS￨O￨- and￨L￨CC￨O￨- issues￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- formulation￨L￨NN￨O￨- and￨L￨CC￨O￨- validation.KeywordsMalariaMalaria￨L￨NN￨MISC￨- TransmissionSurveillance￨U￨NN￨MISC￨- DataTransmission￨U￨NN￨MISC￨- NetworkHuman￨U￨NNP￨MISC￨- Mobility￨U￨NN￨MISC￨- Multilingual￨U￨JJ￨MISC￨- abstractsPlease￨L￨NN￨O￨- see￨L￨VB￨O￨- Additional￨U￨JJ￨O￨- file1￨L￨NN￨O￨- for￨L￨IN￨O￨- translations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- abstract￨L￨JJ￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- six￨L￨CD￨NUMBER￨- official￨L￨JJ￨O￨- working￨L￨VBG￨O￨- languages￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨ORGANIZATION￨- Nations￨U￨NNPS￨ORGANIZATION￨- .￨L￨.￨O￨- +Scoping￨U￨VBG￨MISC￨- Review￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Malaria￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- modelling￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- perspectiveJiming￨L￨VBG￨O￨- Liu1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Bo￨U￨NNP￨PERSON￨- Yang2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- William￨U￨NNP￨PERSON￨- K￨U￨NNP￨PERSON￨- Cheung1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Guojing￨U￨NN￨O￨- Yang3￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 1:11￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Liu￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨A Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractMalaria￨U￨NNP￨O￨- transmission￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- hidden￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- it￨L￨PRP￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- timely￨L￨JJ￨O￨- and￨L￨CC￨O￨- accurately￨L￨RB￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- elimination￨L￨NN￨O￨- and￨L￨CC￨O￨- eradication￨L￨NN￨O￨- programs￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- undertaken￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- resurgence￨L￨NN￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- continue￨L￨VB￨O￨- to￨L￨TO￨O￨- emerge￨L￨VB￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- an￨L￨DT￨O￨- interdisciplinary￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- interesting￨L￨JJ￨O￨- to￨L￨TO￨O￨- ask￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- important￨L￨JJ￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- challenging￨L￨JJ￨O￨- question￨L￨NN￨O￨- :￨L￨:￨O￨- Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- can￨L￨MD￨O￨- we￨L￨PRP￨O￨- build￨L￨VB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- for￨L￨IN￨O￨- monitoring￨L￨NN￨O￨- and￨L￨CC￨O￨- early￨L￨JJ￨O￨- detecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A ?￨L￨.￨O￨- +What￨U￨WP￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- note￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- clustering-based￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- software￨L￨NN￨O￨- systems￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- network￨L￨NN￨O￨- perspective￨L￨NN￨O￨- further￨L￨RB￨O￨- extends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- modelling￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- chosen￨L￨VBN￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- up￨L￨RP￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Ross￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- published￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- seminal￨L￨JJ￨O￨- papers￨L￨NNS￨O￨A which￨L￨WDT￨O￨- founded￨L￨VBD￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- modeling.-In￨L￨NN￨O￨- these￨L￨DT￨O￨- papers￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- addressed￨L￨VBD￨O￨- the￨L￨DT￨O￨- mass￨L￨NN￨O￨- –￨L￨:￨O￨- action￨L￨NN￨O￨- incident￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- cycle￨L￨NN￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- virgin￨L￨JJ￨O￨- from￨L￨IN￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- analogous￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- Ross￨U￨NNP￨PERSON￨- addressed￨L￨VBD￨O￨A the￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito-borne￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- discussion￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- see￨L￨VB￨O￨- also￨L￨RB￨O￨- Smith￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Forty￨U￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- of￨L￨IN￨O￨- Ross￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- MacDonald￨U￨NNP￨PERSON￨- extended￨L￨VBD￨O￨- Ross￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- in￨L￨IN￨O￨- depth￨L￨NN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- propose￨L￨VBP￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- eradicating￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- operational￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- through￨L￨IN￨O￨- discrete￨L￨JJ￨O￨A time￨L￨NN￨O￨A Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- events￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Enko￨U￨NN￨PERSON￨- evaluated￨L￨VBD￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨A between￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- and￨L￨CC￨O￨- susceptibles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- promising￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- forecast￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal-geographic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- forecast￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- consisted￨L￨VBD￨O￨- of￨L￨IN￨O￨- 425￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- include￨L￨VBP￨O￨- limitations￨L￨NNS￨O￨- inherent￨L￨JJ￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- challenges￨L￨NNS￨O￨- incurred￨L￨VBN￨O￨- in￨L￨IN￨O￨- data￨L￨NNS￨O￨- availability￨L￨NN￨O￨- and￨L￨CC￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- approaches￨L￨NNS￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨A different￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨A epidemiology￨L￨NN￨O￨A has￨L￨VBZ￨O￨- produced￨L￨VBN￨O￨- many￨L￨JJ￨O￨- new￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- contact￨L￨NN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- discovering￨L￨VBG￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- detecting￨L￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +Assuming￨U￨VBG￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- by￨L￨IN￨O￨- individual￨L￨JJ￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- ∑￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- sequence￨L￨NN￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- static-network￨L￨JJ￨O￨- predictors￨L￨NNS￨O￨- of￨L￨IN￨O￨- importance￨L￨NN￨O￨- :￨L￨:￨O￨- i￨L￨FW￨O￨- 's￨L￨POS￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- since￨L￨IN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- our￨L￨PRP$￨O￨- main￨L￨JJ￨O￨- focus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- scan￨L￨VB￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- representations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- to￨L￨TO￨O￨- limit￨L￨VB￨O￨- ourselves￨L￨PRP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spreading￨L￨NN￨O￨A simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- we￨L￨PRP￨O￨- want￨L￨VBP￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- network￨L￨NN￨O￨A epidemiology￨L￨NN￨O￨A to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨DATE￨- future￨L￨JJ￨DATE￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- just￨L￨RB￨O￨- map￨L￨VB￨O￨- out￨L￨RP￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- good￨L￨JJ￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- sequence￨L￨NN￨O￨A should￨L￨MD￨O￨- give￨L￨VB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- sequence￨L￨NN￨O￨- itself￨L￨PRP￨O￨- .￨L￨.￨O￨- +Karsai￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- colleagues￨L￨NNS￨O￨- simulated￨L￨JJ￨O￨- the￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- bursty￨L￨JJ￨O￨- activity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- slow￨L￨VB￨O￨- down￨L￨RP￨O￨- contagions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Bursty￨U￨JJ￨O￨- activity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- long-tailed￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interevent￨L￨JJ￨O￨- times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IETs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- simulate￨L￨VB￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- read￨L￨VBD￨O￨- the￨L￨DT￨O￨- events￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- event￨L￨NN￨O￨- sequence￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- chronological￨L￨JJ￨O￨- order￨L￨NN￨O￨- and￨L￨CC￨O￨- possibly￨L￨RB￨O￨- update￨L￨VB￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- traditional￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- them￨L￨PRP￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- aggregated￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- are￨L￨VBP￨O￨- drawn￨L￨VBN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- communicate￨L￨VBP￨O￨- in￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- event￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- investigate￨L￨VBP￨O￨- structural￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- aggregated￨L￨JJ￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- consider￨L￨VB￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- generalize￨L￨VBP￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- history￨L￨NN￨O￨- dependence￨L￨NN￨O￨- and￨L￨CC￨O￨- memory￨L￨NN￨O￨- decay￨L￨NN￨O￨- and￨L￨CC￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A network￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- and￨L￨CC￨O￨- richer￨L￨JJR￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- them￨L￨PRP￨O￨- as￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- only￨L￨RB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- event￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- theoretical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- predict￨L￨VBP￨O￨- shifts￨L￨NNS￨O￨- in￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A epidemiology￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- :￨L￨:￨O￨- epidemic￨L￨JJ￨O￨- duration￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- shift￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- fadeout￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- vaccination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- continued￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- probably￨L￨RB￨O￨- reflects￨L￨VBZ￨O￨- local￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- progress￨L￨NN￨O￨- towards￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- target￨L￨NN￨O￨- goals￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- reflect￨L￨VB￨O￨- local￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- replenishment￨L￨NN￨O￨- through￨L￨IN￨O￨- births￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- local￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- take￨L￨VBP￨O￨- a￨L￨DT￨O￨- comparative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- response￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- vaccination￨L￨NN￨O￨- using￨L￨VBG￨O￨- contemporary￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- age-specific￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- national￨L￨JJ￨O￨- scale￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- effective￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- shifts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- cyclical￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- mortality￨L￨NN￨O￨- risk￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- in￨L￨IN￨O￨- infants￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- thus￨L￨RB￨O￨- increasing￨L￨VBG￨O￨- mean￨L￨JJ￨O￨- age￨L￨NN￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- childhood￨L￨NN￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Can￨U￨MD￨MISC￨- informal￨L￨JJ￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A interventions￨L￨NNS￨O￨- minimize￨L￨VBP￨O￨- demand￨L￨NN￨O￨- for￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- severe￨L￨JJ￨O￨- pandemic?Amy￨L￨NN￨O￨- L￨U￨NN￨O￨- Greer1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 13:669￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Greer￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- alter￨L￨VB￨O￨- their￨L￨PRP$￨O￨- behaviour￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- examined￨L￨VBN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨A measures￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- demand￨L￨NN￨O￨- for￨L￨IN￨O￨- limited￨L￨JJ￨O￨- healthcare￨L￨NN￨O￨- resources￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- central￨L￨JJ￨O￨- stockpile￨L￨NN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- severe￨L￨JJ￨O￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +Encouraging￨U￨VBG￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- adopt￨L￨VB￨O￨- behaviours￨L￨NNS￨O￨- that￨L￨WDT￨O￨- decrease￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- daily￨L￨JJ￨SET￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- until￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- however￨L￨RB￨O￨- ;￨L￨:￨O￨- relying￨L￨VBG￨O￨- on￨L￨IN￨O￨- these￨L￨DT￨O￨- measures￨L￨NNS￨O￨- to￨L￨TO￨O￨- justify￨L￨VB￨O￨- stockpiling￨L￨NN￨O￨- fewer￨L￨JJR￨O￨- courses￨L￨NNS￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- will￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- severe￨L￨JJ￨O￨A pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨A behaviours￨L￨NNS￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- severe￨L￨JJ￨O￨- pandemic￨L￨NN￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- existing￨L￨VBG￨O￨- age-structured￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Canada￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- biologically￨L￨RB￨O￨- plausible￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- for￨L￨IN￨O￨- severe￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- vaccine-induced￨L￨JJ￨O￨- strain￨L￨NN￨O￨- replacement￨L￨NN￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- relates￨L￨VBZ￨O￨- to￨L￨TO￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- pneumococcus￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- recently￨L￨RB￨DATE￨- in￨L￨IN￨O￨- S.￨U￨NNP￨O￨- Previous￨U￨JJ￨O￨- models￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- clearly￨L￨RB￨O￨- support￨L￨VB￨O￨- a￨L￨DT￨O￨- role￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- against￨L￨IN￨O￨- drug-resistant￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- in￨L￨IN￨O￨- achieving￨L￨VBG￨O￨- sustainable￨L￨JJ￨O￨- population-wide￨L￨JJ￨O￨- reductions￨L￨NNS￨O￨- in￨L￨IN￨O￨- drug-resistance￨L￨NN￨O￨- .￨L￨.￨O￨- +Intermediate￨U￨NNP￨O￨- models￨L￨NNS￨O￨- between￨L￨IN￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- include￨L￨VBP￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- reinfection￨L￨NN￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- reinfection￨L￨NN￨O￨- state￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- reduced￨L￨VBD￨O￨- infectiousness￨L￨NN￨O￨- ;￨L￨:￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- susceptible-infected￨L￨JJ￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- partially￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- re￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SISI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- homotopy￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- σ￨L￨NN￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- and￨L￨CC￨O￨- ρ￨L￨NN￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- primary￨L￨JJ￨O￨- and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- infectiousness￨L￨NN￨O￨A and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- SEIRS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨A forcing￨L￨VBG￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- specific￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- acquisition￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- compartmentalisation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨A based￨L￨VBN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- status￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- four￨L￨CD￨NUMBER￨- homotopy￨L￨NN￨O￨- parameters￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- σ￨L￨NN￨O￨- ,￨L￨,￨O￨- ρ￨L￨NN￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- take￨L￨VBP￨O￨- values￨L￨NNS￨O￨- between￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- setting￨L￨VBG￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- extremes￨L￨NNS￨O￨- and￨L￨CC￨O￨- estimating￨L￨VBG￨O￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- different￨L￨JJ￨O￨- sub-models￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- susceptible-infectious-recovered/removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- an￨L￨DT￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨- whereby￨L￨WRB￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- combined￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- make￨L￨VBP￨O￨- infection-causing￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- recover￨L￨VB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- infecteds￨L￨NNS￨O￨- will￨L￨MD￨O￨- either￨L￨CC￨O￨- cause￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- ’￨L￨''￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rapidly￨L￨RB￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- finite￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- do￨L￨VBP￨O￨- pose￨L￨VB￨O￨- conceptual￨L￨JJ￨O￨- difficulties￨L￨NNS￨O￨- ;￨L￨:￨O￨- indeed￨L￨RB￨O￨- ,￨L￨,￨O￨- endemic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- non-trivial￨L￨JJ￨O￨- stationary￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- which￨L￨WDT￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- finite￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- exist￨L￨VB￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- invasion￨L￨NN￨O￨A probability￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- which￨L￨WDT￨O￨- posits￨L￨VBZ￨O￨- an￨L￨DT￨O￨- infinite￨L￨JJ￨O￨- population￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- invasion￨L￨NN￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- indefinite￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infinite￨L￨JJ￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbours￨L￨NNS￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- contact￨L￨NN￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- sometimes￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨A probability￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- fractional￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- utilising￨L￨VBG￨O￨- percolation￨L￨NN￨O￨- theory￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +‘￨L￨``￨O￨- Compartmental￨U￨NN￨O￨- ’￨L￨''￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- interacting￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- exist￨L￨VBP￨O￨A in￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- ,￨L￨,￨O￨- capture￨L￨VBP￨O￨- the￨L￨DT￨O￨- essence￨L￨NN￨O￨- of￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- host-to-host￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- ‘￨L￨``￨O￨- Theoretical￨U￨JJ￨O￨- Results￨U￨NNS￨O￨- ’￨L￨POS￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- define￨L￨VB￨O￨- and￨L￨CC￨O￨- justify￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- strongly￨L￨RB￨O￨- connected￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- exact￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- quantifiers￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- invasion￨L￨NN￨O￨A probability￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- exceptions91011￨L￨NN￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- attention￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- initiator￨L￨NN￨O￨- fraction￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- opinion￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- regime￨L￨NN￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- active￨L￨JJ￨O￨- node￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- clique￨L￨NN￨O￨- is￨L￨VBZ￨O￨- insufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- trigger￨L￨VB￨O￨- global￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- long￨L￨RB￨O￨- been￨L￨VBN￨O￨- known￨L￨VBN￨O￨- through￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- socially￨L￨RB￨O￨- interacting￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- node￨L￨NN￨O￨- holds￨L￨VBZ￨O￨- an￨L￨DT￨O￨- opinion￨L￨NN￨O￨A from￨L￨IN￨O￨- a￨L￨DT￨O￨- binary￨L￨JJ￨O￨- set￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- initiators￨L￨NNS￨O￨- holding￨L￨VBG￨O￨- opinion￨L￨NN￨O￨- opposite￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- held￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- can￨L￨MD￨O￨- trigger￨L￨VB￨O￨- large￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨- and￨L￨CC￨O￨- eventually￨L￨RB￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- majority￨L￨NN￨O￨- holding￨L￨VBG￨O￨- the￨L￨DT￨O￨- initiators￨L￨NNS￨O￨- '￨L￨POS￨O￨- opinion￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- its￨L￨PRP$￨O￨- introduction3￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- vanishingly￨L￨RB￨O￨- small￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- initiators￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- triggering￨L￨VBG￨O￨- a￨L￨DT￨O￨- cascade￨L￨NN￨O￨- of￨L￨IN￨O￨- opinion￨L￨NN￨O￨A change468￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- global￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨A in￨L￨IN￨O￨- connected￨L￨JJ￨O￨- sparse￨L￨JJ￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- ϕ￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 〈￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- 〉￨L￨NN￨O￨- 468￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- 〈￨L￨SYM￨O￨- k￨L￨NN￨O￨- 〉￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- initiators￨L￨NNS￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- select￨L￨VB￨O￨- these￨L￨DT￨O￨- initiators￨L￨NNS￨O￨- from￨L￨IN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- cascade￨L￨NN￨O￨A size￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- remains￨L￨VBZ￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- question￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- important￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- gained￨L￨VBN￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- ecological￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- environment￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- parasites￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- initially￨L￨RB￨O￨- shaped￨L￨VBN￨O￨- selection￨L￨NN￨O￨- for￨L￨IN￨O￨- immune￨L￨JJ￨O￨- memory￨L￨NN￨O￨A ,￨L￨,￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- apparent￨L￨JJ￨O￨- discrepancy￨L￨NN￨O￨- in￨L￨IN￨O￨- investment￨L￨NN￨O￨- in￨L￨IN￨O￨- immunity￨L￨NN￨O￨- with￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- lifespan￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- SIR-type￨U￨JJ￨O￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- [￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- -￨L￨:￨O￨- type￨L￨NN￨O￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- immune￨L￨JJ￨O￨- memory￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- shall￨L￨MD￨O￨- also￨L￨RB￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- single￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- focus￨L￨VB￨O￨- more￨L￨RBR￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- feedbacks￨L￨NNS￨O￨- to￨L￨TO￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- implicitly￨L￨RB￨O￨- removing￨L￨VBG￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- specificity￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- further￨L￨JJ￨O￨- key￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- immune￨L￨JJ￨O￨A system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Discussion￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- could￨L￨MD￨O￨- evolve￨L￨VB￨O￨- the￨L￨DT￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- period￨L￨NN￨O￨- then￨L￨RB￨O￨- investment￨L￨NN￨O￨- was￨L￨VBD￨O￨- indeed￨L￨RB￨O￨- greatest￨L￨JJS￨O￨A for￨L￨IN￨O￨- long-lived￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- if￨L￨IN￨O￨- permanent￨L￨JJ￨O￨- acquired￨L￨VBN￨O￨- immunity￨L￨NN￨O￨- was￨L￨VBD￨O￨- evolved￨L￨VBN￨O￨- then￨L￨RB￨O￨- investment￨L￨NN￨O￨- was￨L￨VBD￨O￨- instead￨L￨RB￨O￨- greatest￨L￨JJS￨O￨- at￨L￨IN￨O￨- intermediate￨L￨JJ￨O￨- lifespans￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- mechanism￨L￨NN￨O￨- is￨L￨VBZ￨O￨- incorporated￨L￨VBN￨O￨- in￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- upon￨L￨IN￨O￨- recovery￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- hosts￨L￨NNS￨O￨A gain￨L￨VB￨O￨- long-lasting￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- re-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- focus￨L￨NN￨O￨- here￨L￨RB￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- ecological￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- promote￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- acquired￨L￨VBN￨O￨- immune￨L￨JJ￨O￨- memory￨L￨NN￨O￨A in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- novel￨L￨JJ￨O￨- mechanistic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- dengue￨L￨JJ￨O￨A incidence￨L￨NN￨O￨- using￨L￨VBG￨O￨- past￨L￨JJ￨DATE￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- 38-year￨L￨JJ￨DURATION￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- serotype-specific￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- exposed￨L￨VBN￨O￨- –￨L￨:￨O￨- infectious￨L￨JJ￨O￨- –￨L￨:￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- modelling￨L￨NN￨O￨- structure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- continuous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- at￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- reporting￨L￨NN￨O￨A rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- human￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- confering￨L￨VBG￨O￨- lifelong￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- little￨L￨JJ￨O￨- effort￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- directed￨L￨VBN￨O￨- at￨L￨IN￨O￨- elucidating￨L￨VBG￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- reporting￨L￨VBG￨O￨- data￨L￨NNS￨O￨- into￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- ecological￨L￨JJ￨O￨- viewpoint￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Variation￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- and￨L￨CC￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- can￨L￨MD￨O￨- themselves￨L￨PRP￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- reporting￨L￨VBG￨O￨A rate￨L￨NN￨O￨- variation￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- mapping￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- reporting￨L￨VBG￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- surveillance￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- across￨L￨IN￨O￨- space￨L￨NN￨O￨- or￨L￨CC￨O￨- time￨L￨NN￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- identify￨L￨VB￨O￨- specific￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- need￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- .￨L￨.￨O￨- +Resources￨U￨NNPS￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨A are￨L￨VBP￨O￨- always￨L￨RB￨O￨- in￨L￨IN￨O￨- limited￨L￨JJ￨O￨- supply￨L￨NN￨O￨- and￨L￨CC￨O￨- any￨L￨DT￨O￨- strategy￨L￨NN￨O￨- that￨L￨WDT￨O￨- provides￨L￨VBZ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- guidance￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- valued￨L￨VBN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- infrastructure￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- reporting￨L￨VBG￨O￨A data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- both￨L￨CC￨O￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- negative￨L￨JJ￨O￨- occurrences￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- geographical￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- where￨L￨WRB￨O￨- surveillance￨L￨NN￨O￨- levels￨L￨NNS￨O￨- are￨L￨VBP￨O￨- potentially￨L￨RB￨O￨- insufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- constant￨L￨JJ￨O￨- reporting￨L￨NN￨O￨A rate￨L￨NN￨O￨- ,￨L￨,￨O￨- intended￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- documented￨L￨VBN￨O￨- significant￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- behavior￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- possibly￨L￨RB￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- perceived￨L￨VBN￨O￨- protection￨L￨NN￨O￨- offered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- treated￨L￨VBN￨O￨- individual￨L￨NN￨O￨- ;￨L￨:￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- change￨L￨NN￨O￨A following￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- could￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- response￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- risky￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- on￨L￨IN￨O￨- prophylactic￨L￨NN￨O￨- treatments￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- perversity￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- dependence￨L￨NN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- precise￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- change￨L￨NN￨O￨A has￨L￨VBZ￨O￨- remained￨L￨VBN￨O￨- largely￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- risk￨L￨NN￨O￨- behavior￨L￨NN￨O￨- change￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- observe￨L￨VBP￨O￨- a￨L￨DT￨O￨- rich￨L￨JJ￨O￨- and￨L￨CC￨O￨- complex￨L￨JJ￨O￨- structure￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- both￨L￨DT￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- network￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- important￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- Blower￨U￨NNP￨O￨- and￨L￨CC￨O￨- her￨L￨PRP$￨O￨- collaborators￨L￨NNS￨O￨- demonstrated￨L￨VBD￨O￨- that￨L￨IN￨O￨- risk￨L￨NN￨O￨- behavior￨L￨NN￨O￨- change￨L￨NN￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- vaccinations￨L￨NNS￨O￨- ,￨L￨,￨O￨- could￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- unintended￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- both￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- random￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- vaccinated￨L￨VBN￨O￨- independently￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- probability￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- vaccinations￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- vaccinated￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- connectedness￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- position￨L￨NN￨O￨- sensitive￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- on￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- 20-year￨L￨JJ￨DURATION￨- period￨L￨NN￨O￨- using￨L￨VBG￨O￨- sex￨L￨NN￨O￨A role￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- South￨U￨NNP￨LOCATION￨- India￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- individual￨L￨JJ￨O￨- sex￨L￨NN￨O￨A role￨L￨NN￨O￨- preference￨L￨NN￨O￨- and￨L￨CC￨O￨- mixing￨L￨VBG￨O￨- by￨L￨IN￨O￨- sex￨L￨NN￨O￨- role￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- to￨L￨TO￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- role￨L￨NN￨O￨- segregation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- insertive￨L￨JJ￨O￨- and￨L￨CC￨O￨- receptive￨L￨JJ￨O￨- anal￨L￨JJ￨O￨- sex￨L￨NN￨O￨A and￨L￨CC￨O￨- because￨L￨IN￨O￨- biomedical￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- target￨L￨VB￨O￨- specific￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- sex￨L￨NN￨O￨- role￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- insertive￨L￨JJ￨O￨- or￨L￨CC￨O￨- receptive￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Unique￨U￨JJ￨O￨- to￨L￨TO￨O￨- men￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨A with￨L￨IN￨O￨- men￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MSM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- internationally￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- India￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Peru￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- adoption￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- sexual￨L￨JJ￨O￨- role￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- insertive￨L￨JJ￨O￨- or￨L￨CC￨O￨- receptive￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- versatile￨L￨JJ￨O￨- role￨L￨NN￨O￨- during￨L￨IN￨O￨- intercourse￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- candidate￨L￨NN￨TITLE￨- prevention￨L￨NN￨O￨- interventions￨L￨NNS￨O￨A for￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- currently￨L￨RB￨DATE￨- under￨L￨IN￨O￨- study￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- circumcision￨L￨NN￨O￨- and￨L￨CC￨O￨- anal￨L￨JJ￨O￨- microbicides￨L￨NNS￨O￨- would￨L￨MD￨O￨- likely￨L￨RB￨O￨- only￨L￨RB￨O￨- protect￨L￨VB￨O￨- insertive￨L￨JJ￨O￨- and￨L￨CC￨O￨- receptive￨L￨JJ￨O￨- partners￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- experimental￨L￨JJ￨O￨A systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨PDT￨O￨- an￨L￨DT￨O￨- integrative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- would￨L￨MD￨O￨- allow￨L￨VB￨O￨- quantitative￨L￨JJ￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- ecological￨L￨JJ￨O￨- or￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- would￨L￨MD￨O￨- provide￨L￨VB￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- developing￨L￨VBG￨O￨- system-specific￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- choice￨L￨NN￨O￨- for￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- several￨L￨JJ￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- explored￨L￨VBN￨O￨- its￨L￨PRP$￨O￨- use￨L￨NN￨O￨- for￨L￨IN￨O￨- inference￨L￨NN￨O￨- for￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- experimental￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- study￨L￨NN￨O￨- associates￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- elements￨L￨NNS￨O￨- :￨L￨:￨O￨- experimental￨L￨JJ￨O￨A time￨L￨NN￨O￨- series￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- statistical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- fits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- characterises￨L￨VBZ￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- variability￨L￨NN￨O￨- .￨L￨.￨O￨- +Host-pathogen￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- systems￨L￨NNS￨O￨- maintained￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- laboratory￨L￨NN￨O￨- have￨L￨VBP￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- played￨L￨VBD￨O￨A an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- driving￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- hierarchical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- supplement￨L￨VBP￨O￨A information￨L￨NN￨O￨- on￨L￨IN￨O￨- each￨L￨DT￨O￨- replicate￨L￨VBP￨O￨- with￨L￨IN￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- other￨L￨JJ￨O￨- replicates￨L￨VBZ￨O￨- via￨L￨IN￨O￨- their￨L￨PRP$￨O￨- joint￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- population￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- Rift￨U￨NNP￨O￨- Valley￨U￨NNP￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨- among￨L￨IN￨O￨- livestock￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNPS￨COUNTRY￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- modelling￨L￨NN￨O￨- studyEgil￨L￨NNP￨O￨- AJ￨U￨NNP￨O￨- Fischer1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Gert-Jan￨U￨NNP￨PERSON￨- Boender1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Gonnie￨U￨NNP￨O￨- Nodelijk1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Aline￨U￨NNP￨PERSON￨- A￨U￨NNP￨PERSON￨- de￨L￨IN￨PERSON￨- Koeijer1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Herman￨U￨NNP￨PERSON￨- JW￨U￨NNP￨O￨- van￨L￨NNP￨O￨- Roermund1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 44:58￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Fischer￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractsRift￨U￨NNP￨O￨- Valley￨U￨NNP￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RVFV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- zoonotic￨L￨JJ￨O￨- vector-borne￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- causes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- potentially￨L￨RB￨O￨- severe￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A potential￨L￨NN￨O￨A of￨L￨IN￨O￨- RVFV￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- growth￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Floquet￨U￨NNP￨MISC￨- ratio￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- indicators￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- changing￨L￨VBG￨O￨- environment￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- seasonality￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- what￨L￨WP￨O￨- extent￨L￨NN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- classical￨L￨JJ￨O￨- vector￨L￨NN￨O￨- life-history￨L￨JJ￨O￨- traits￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- developmental￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- fecundity￨L￨NN￨O￨- or￨L￨CC￨O￨- survival￨L￨NN￨O￨- could￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- parasite￨L￨NN￨O￨- virulence￨L￨NN￨O￨- to￨L￨TO￨O￨- hosts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- not￨L￨RB￨O￨- completely￨L￨RB￨O￨- clear￨L￨JJ￨O￨- .￨L￨.￨O￨- +Vector￨U￨NNP￨O￨- life-history￨L￨JJ￨O￨- traits￨L￨NNS￨O￨A do￨L￨VBP￨O￨- not￨L￨RB￨O￨- seem￨L￨VB￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- parasite￨L￨NN￨O￨- virulence￨L￨NN￨O￨- to￨L￨TO￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- setting￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +MCC￨U￨NN￨ORGANIZATION￨- vaccination￨L￨NN￨O￨- achieved￨L￨VBD￨O￨- high￨L￨JJ￨O￨- uptake￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- considerable￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- group￨L￨NN￨O￨- C￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- due￨L￨JJ￨O￨- both￨L￨CC￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- and￨L￨CC￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- carriage￨L￨NN￨O￨A ,￨L￨,￨O￨- interrupting￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- generating￨L￨VBG￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- using￨L￨VBG￨O￨- Berkley￨U￨NNP￨PERSON￨- Madonna￨U￨NNP￨PERSON￨- software￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- vaccines￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- cohort￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- assumes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- prevents￨L￨VBZ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- only￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- also￨L￨RB￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- carriage￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- key￨L￨JJ￨O￨- to￨L￨TO￨O￨- reducing￨L￨VBG￨O￨- incidence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- prevention￨L￨NN￨O￨- through￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨RB￨O￨- early￨L￨JJ￨O￨A signs￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- non-distinct￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- progress￨L￨VB￨O￨- rapidly￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- fatal￨L￨JJ￨O￨- in￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- treatment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- initiated￨L￨VBN￨O￨- early￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Until￨U￨IN￨O￨- recently￨L￨RB￨DATE￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- no￨L￨DT￨O￨- broadly￨L￨RB￨O￨- effective￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- against￨L￨IN￨O￨- capsular￨L￨JJ￨O￨- group￨L￨NN￨O￨A B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- MenB￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Europe￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- MenB￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- accounted￨L￨VBD￨O￨- for￨L￨IN￨O￨- 89￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Incidence￨U￨NN￨O￨- rates￨L￨NNS￨O￨- include￨L￨VBP￨O￨- all￨L￨DT￨O￨- capsular￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- group￨L￨NN￨O￨A specific￨L￨JJ￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- certain￨L￨JJ￨O￨- outcome￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- considerations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨A allocation￨L￨NN￨O￨A of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- accordingly￨L￨RB￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- optimization￨L￨NN￨O￨- procedure￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨A of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- relative￨L￨JJ￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- varies￨L￨VBZ￨O￨- between￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- often￨L￨RB￨O￨- provide￨L￨VBP￨O￨- important￨L￨JJ￨O￨- guidelines￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- determination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨A allocation￨L￨NN￨O￨A of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Multistrain￨U￨JJ￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- assuming￨L￨VBG￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- or￨L￨CC￨O￨- lattices￨L￨NNS￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- considering￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- mobility￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- often￨L￨RB￨O￨- providing￨L￨VBG￨O￨- detailed￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- biological￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- they￨L￨PRP￨O￨- properly￨L￨RB￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- mutation￨L￨NN￨O￨- ,￨L￨,￨O￨- physiological￨L￨JJ￨O￨- trade-off￨L￨NN￨O￨- ,￨L￨,￨O￨- cross-immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- relevant￨L￨JJ￨O￨- immunological￨L￨JJ￨O￨- and￨L￨CC￨O￨- biological￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- but￨L￨CC￨O￨- lacking￨L￨VBG￨O￨- explicit￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- behavioral￨L￨JJ￨O￨- ecology￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- mobility￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- introducing￨L￨VBG￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- mobility￨L￨NN￨O￨A rate￨L￨NN￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- ecological￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host-multipathogen￨L￨NN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- changes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- competitive￨L￨JJ￨O￨- balance￨L￨NN￨O￨- between￨L￨IN￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- shift￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- abundance￨L￨NN￨O￨- and/or￨L￨CC￨O￨- dominance￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- available￨L￨JJ￨O￨- massive￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- enabled￨L￨VBN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- quantity￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- that￨L￨WDT￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- relevance￨L￨NN￨O￨- and￨L￨CC￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- '￨L￨POS￨O￨- mobility￨L￨NN￨O￨- features￨L￨NNS￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- competition￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- mobility￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- structured￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- strains￨L￨NNS￨O￨- with￨L￨IN￨O￨- full￨L￨JJ￨O￨- cross-immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- an￨L￨DT￨O￨- exploration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- partial￨L￨JJ￨O￨- cross-immunity￨L￨NN￨O￨- case￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Text￨U￨VBP￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- generation￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- value￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨A in￨L￨IN￨O￨- each￨L￨DT￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- divide￨L￨VBP￨O￨- the￨L￨DT￨O￨- vertices￨L￨NNS￨O￨A into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- removed￨L￨VBN￨O￨- refers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- vertices￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- once￨L￨RB￨DATE￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- no￨L￨DT￨O￨- longer￨L￨JJR￨O￨- transmit￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- average￨L￨JJ￨O￨- excess￨L￨JJ￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- Z￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- stubs￨L￨NNS￨O￨- emanating￨L￨VBG￨O￨- from￨L￨IN￨O￨- vertices￨L￨NNS￨O￨A selected￨L￨VBN￨O￨- by￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- stub￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨- as￨L￨IN￨O￨- Z￨U￨NN￨O￨- =￨L￨JJ￨O￨- Σk￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- q￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- N￨U￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- vertices￨L￨NNS￨O￨A in￨L￨IN￨O￨- class￨L￨NN￨O￨- α￨L￨NN￨O￨- in￨L￨IN￨O￨- generation￨L￨NN￨O￨- g￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- z￨L￨SYM￨O￨- as￨L￨IN￨O￨- their￨L￨PRP$￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- calculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- generation￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- two￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- interact￨L￨VBP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- previous￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨A .￨L￨.￨O￨- +Mechanistic￨U￨JJ￨O￨- infection-spread￨L￨JJ￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- explicitly￨L￨RB￨O￨- incorporate￨L￨VB￨O￨- interactions￨L￨NNS￨O￨A between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- typically￨L￨RB￨O￨- fall￨L￨VBP￨O￨- into￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- real￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- expect￨L￨VBP￨O￨A that￨L￨IN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- tend￨L￨VBP￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- those￨L￨DT￨O￨- surrounding￨L￨VBG￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- local￨L￨JJ￨O￨- depletion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- social￨L￨JJ￨O￨A contact￨L￨NN￨O￨A network￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- directly￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- identified￨L￨VBD￨O￨- experimental￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- studies￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- host-pathogen￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- bird-virus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- systems￨L￨NNS￨O￨- that￨L￨WDT￨O￨- satisfied￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- criteria￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- experiment￨L￨NN￨O￨- were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- known￨L￨VBN￨O￨- dose￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- exposure￨L￨NN￨O￨- was￨L￨VBD￨O￨- controlled￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- were￨L￨VBD￨O￨- wild-type￨L￨JJ￨O￨- or￨L￨CC￨O￨- wild-caught￨L￨JJ￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- natural￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- pathogen￨L￨NN￨O￨- load￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- avian￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- monitored￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- host￨L￨NN￨TITLE￨- pathogen￨L￨NN￨O￨- load￨L￨NN￨O￨- was￨L￨VBD￨O￨- measured￨L￨VBN￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- anatomic￨L￨JJ￨O￨- site￨L￨NN￨O￨- most￨L￨RBS￨O￨- relevant￨L￨JJ￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- host-pathogen￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- specific￨L￨JJ￨O￨- goals￨L￨NNS￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- were￨L￨VBD￨O￨- to￨L￨TO￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- test￨L￨NN￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- that￨L￨IN￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨A in￨L￨IN￨O￨- birds￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- consistently￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- by￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- determining￨L￨VBG￨O￨- which￨L￨WDT￨O￨- data￨L￨NNS￨O￨- distribution￨L￨NN￨O￨- function￨L￨NN￨O￨- best￨L￨RB￨O￨- fit￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Weibull￨U￨NNP￨PERSON￨- or￨L￨CC￨O￨- Pareto￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- measuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- inequality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- via￨L￨IN￨O￨- Gini￨U￨NNP￨PERSON￨- coefficients￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- across￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- study￨L￨NN￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- II￨U￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- evaluate￨L￨VBP￨O￨- factors￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- shedding￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- supershedding￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- III￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- indicate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- our￨L￨PRP$￨O￨- observations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- further￨L￨RBR￨O￨- understand￨L￨VB￨O￨- and￨L￨CC￨O￨- control￨L￨VB￨O￨- avian-borne￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- zoonotic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- comprehensively￨L￨RB￨O￨- evaluated￨L￨VBD￨O￨- the￨L￨DT￨O￨- inequality￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨A and￨L￨CC￨O￨- present￨L￨VB￨DATE￨- a￨L￨DT￨O￨- meta-analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- 24￨L￨CD￨NUMBER￨- avian-virus￨L￨NN￨O￨- experimental￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- included￨L￨VBD￨O￨- 17￨L￨CD￨NUMBER￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- birds￨L￨NNS￨O￨- and￨L￨CC￨O￨- five￨L￨CD￨NUMBER￨- RNA￨U￨NN￨MISC￨- viruses￨L￨NNS￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- families￨L￨NNS￨O￨- ,￨L￨,￨O￨- Orthomyxoviridae￨U￨NNP￨O￨- ,￨L￨,￨O￨- low￨L￨JJ￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- pathogenic￨L￨JJ￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LPand￨U￨NN￨O￨- HPAIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Flaviviridae￨U￨NNP￨O￨- ,￨L￨,￨O￨- West￨U￨NNP￨LOCATION￨- Nile￨U￨NNP￨LOCATION￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- WNV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- St.￨U￨NNP￨LOCATION￨- Louis￨U￨NNP￨LOCATION￨- encephalitis￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SLEV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- Togaviridae￨U￨NNP￨O￨- ,￨L￨,￨O￨- eastern￨L￨JJ￨O￨- equine￨L￨JJ￨O￨- encephalitis￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EEEV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- western￨L￨JJ￨O￨- equine￨L￨JJ￨O￨- encephalitis￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- WEEV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- individual￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- load￨L￨NN￨O￨A as￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- particles￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- plaque￨L￨NN￨O￨- forming￨L￨VBG￨O￨- unit￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PFU￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- ml￨L￨NN￨O￨- for￨L￨IN￨O￨- live￨L￨JJ￨O￨- virus￨L￨NN￨O￨- or￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- copy￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- RNA￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- subject￨L￨NN￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- group￨L￨NN￨O￨- ’s￨L￨POS￨O￨- pathogen￨L￨NN￨O￨- load￨L￨NN￨O￨- is￨L￨VBZ￨O￨- simply￨L￨RB￨O￨- a￨L￨DT￨O￨- summation￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- loads￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- anatomic￨L￨JJ￨O￨- site￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- virus￨L￨NN￨O￨- was￨L￨VBD￨O￨- measured￨L￨VBN￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- virus￨L￨NN￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- experimental￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- study￨L￨NN￨O￨- were￨L￨VBD￨O￨- evaluated￨L￨VBN￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- Gini￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- Wilcoxon￨U￨NNP￨PERSON￨- or￨L￨CC￨O￨- Kruskal-Wallis￨U￨NN￨O￨- for￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- multiple￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- factor￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- SAS￨U￨NNP￨O￨- JMP￨U￨NNP￨O￨- 8.0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Cary￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- NC￨U￨NNP￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- Brigham￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- parameterize￨L￨JJ￨O￨- simple￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- ;￨L￨:￨O￨- our￨L￨PRP$￨O￨- objectives￨L￨NNS￨O￨- were￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- R0￨U￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- Richards￨U￨NNP￨O￨- generalized￨L￨VBN￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- projected￨L￨JJ￨O￨- ratios￨L￨NNS￨O￨- of￨L￨IN￨O￨- recognized￨L￨VBN￨O￨- :￨L￨:￨O￨- unrecognized￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- using￨L￨VBG￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- formula￨L￨NN￨O￨- for￨L￨IN￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- utility￨L￨NN￨O￨- of￨L￨IN￨O￨- historical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- parameterization￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Cholera￨U￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- treatable￨L￨JJ￨O￨- with￨L￨IN￨O￨- oral￨L￨JJ￨O￨- rehydration￨L￨NN￨O￨- therapy￨L￨NN￨O￨- and￨L￨CC￨O￨- preventable￨L￨JJ￨O￨- with￨L￨IN￨O￨- adequate￨L￨JJ￨O￨- sanitation￨L￨NN￨O￨- and￨L￨CC￨O￨- water￨L￨NN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A epidemics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- high￨L￨JJ￨O￨- income￨L￨NN￨O￨- countries￨L￨NNS￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨DATE￨- early￨L￨JJ￨DATE￨- 20th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- remains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- global￨L￨JJ￨O￨- threat￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- 100000￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 120000￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- annually￨L￨RB￨SET￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Brigham￨U￨NNP￨ORGANIZATION￨- published￨L￨VBD￨O￨- the￨L￨DT￨O￨- book￨L￨NN￨O￨- in￨L￨IN￨O￨- 1832￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- the￨L￨DT￨DATE￨- year￨L￨NN￨DATE￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A first￨L￨RB￨ORDINAL￨- appeared￨L￨VBD￨O￨- in￨L￨IN￨O￨- North￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- although￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- disheartening￨L￨VBG￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨- Brigham￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- encyclopedic￨L￨JJ￨O￨- list￨L￨NN￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- remedies￨L￨NNS￨O￨- ”￨L￨''￨O￨- for￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- included￨L￨VBD￨O￨- everything￨L￨NN￨O￨- from￨L￨IN￨O￨- bloodletting￨L￨VBG￨O￨- and￨L￨CC￨O￨- blisters￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- cautery￨L￨NN￨O￨- ,￨L￨,￨O￨- heated￨L￨JJ￨O￨- sand￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- electricity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- book￨L￨NN￨O￨- also￨L￨RB￨O￨- includes￨L￨VBZ￨O￨- quantitative￨L￨JJ￨O￨- appendices￨L￨NNS￨O￨- containing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- for￨L￨IN￨O￨- numerous￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- North￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- quantitative￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A epidemics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- occurred￨L￨VBD￨O￨- without￨L￨IN￨O￨- intervention￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- previously￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- explored￨L￨VBN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- A￨U￨DT￨O￨- Treatise￨U￨NN￨MISC￨- on￨L￨IN￨MISC￨- Epidemic￨U￨JJ￨MISC￨- Cholera￨U￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- American￨U￨JJ￨NATIONALITY￨- psychiatrist￨L￨NN￨TITLE￨- Amariah￨U￨NNP￨PERSON￨- Brigham￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- estimated￨L￨VBD￨O￨A the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- immunologically￨L￨RB￨O￨- naïve￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- approximately￨L￨RB￨O￨- 1.6￨L￨CD￨NUMBER￨- ±￨L￨CD￨NUMBER￨- 0.3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- Hartley￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Behavioural￨U￨JJ￨MISC￨- manipulation￨L￨NN￨O￨- of￨L￨IN￨O￨- insect￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- by￨L￨IN￨O￨- Baculoviridaeas￨U￨NNP￨PERSON￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- niche￨L￨NN￨O￨- constructionSteven￨L￨NN￨O￨- Hamblin1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Mark￨U￨NNP￨O￨- M￨U￨NNP￨O￨- Tanaka1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 13:170￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Hamblin￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Tanaka￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Niche￨U￨NNP￨O￨- construction￨L￨NN￨O￨A has￨L￨VBZ￨O￨- received￨L￨VBN￨O￨- increasing￨L￨VBG￨O￨- attention￨L￨NN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- vital￨L￨JJ￨O￨- force￨L￨NN￨O￨- in￨L￨IN￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- niche￨L￨NN￨O￨- construction￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- identified￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- taxa￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- viruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- conspicuously￨L￨RB￨O￨- absent￨L￨JJ￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- these￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- modify￨L￨VBP￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- lasting￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- viral￨L￨JJ￨O￨- selection￨L￨NN￨O￨- pressure￨L￨NN￨O￨- ,￨L￨,￨O￨- niche￨L￨NN￨O￨- construction￨L￨NN￨O￨A will￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- operation.In￨L￨NNP￨O￨- a￨L￨DT￨O￨- fashion￨L￨NN￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- parasites￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- manipulations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- create￨L￨VBP￨O￨- niche￨L￨NN￨O￨- construction￨L￨NN￨O￨- effects￨L￨NNS￨O￨- for￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- may￨L￨MD￨O￨- occur￨L￨VB￨O￨- at￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- organisms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- demonstrates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- niche￨L￨NN￨O￨- construction￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- potent￨L￨JJ￨O￨- force￨L￨NN￨O￨- in￨L￨IN￨O￨- viral￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- acquisition￨L￨NN￨O￨- and￨L￨CC￨O￨- maintenance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- behavioural￨L￨JJ￨O￨- manipulation￨L￨NN￨O￨- and￨L￨CC￨O￨- liquefaction￨L￨NN￨O￨- traits￨L￨NNS￨O￨- in￨L￨IN￨O￨- Baculoviridae￨U￨NNP￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- niche￨L￨NN￨O￨- constructing￨L￨VBG￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- how￨L￨WRB￨O￨- niche￨L￨NN￨O￨- construction￨L￨NN￨O￨A can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- viruses￨L￨NNS￨O￨- engineering￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- behavioural￨L￨JJ￨O￨- manipulation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- feedback￨L￨NN￨O￨- on￨L￨IN￨O￨- selective￨L￨JJ￨O￨- pressures￨L￨NNS￨O￨- for￨L￨IN￨O￨- viral￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- virulence￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- showing￨L￨VBG￨O￨- how￨L￨WRB￨O￨- niche￨L￨NN￨O￨- construction￨L￨NN￨O￨A leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- feedback￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- behavioural￨L￨JJ￨O￨- manipulation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- liquefaction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- linking￨L￨VBG￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- traits￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- show￨L￨VB￨O￨- how￨L￨WRB￨O￨- this￨L￨DT￨O￨- association￨L￨NN￨O￨- arises￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- action￨L￨NN￨O￨- of￨L￨IN￨O￨- niche￨L￨NN￨O￨- construction￨L￨NN￨O￨- .￨L￨.￨O￨- +Methodology￨U￨NN￨O￨- Open￨U￨VB￨O￨- Access￨U￨NN￨O￨- Application￨U￨NN￨O￨- of￨L￨IN￨O￨- loop￨L￨NN￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- veterinary￨L￨JJ￨O￨- epidemiologyLucie￨L￨NN￨O￨- Collineau1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Raphaël￨U￨NN￨O￨- Duboz1￨U￨NN￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mathilde￨U￨NNP￨PERSON￨- Paul2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marisa￨U￨NNP￨PERSON￨- Peyre1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Flavie￨U￨NNP￨O￨- Goutard1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Sinel￨U￨NNP￨O￨- Holl3￨U￨NNP￨O￨- and￨L￨CC￨O￨- François￨U￨NNP￨PERSON￨- Roger1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 10:7￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Collineau￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Systems￨U￨NNPS￨O￨- for￨L￨IN￨O￨- animal￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- mitigation￨L￨NN￨O￨A involve￨L￨VBP￨O￨- both￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- activities￨L￨NNS￨O￨- and￨L￨CC￨O￨- interventions￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- chose￨L￨VBD￨O￨- the￨L￨DT￨O￨- mitigation￨L￨NN￨O￨A system￨L￨NN￨O￨- of￨L￨IN￨O￨- highly￨L￨RB￨O￨- pathogenic￨L￨JJ￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- HPAI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- H5N1￨U￨NN￨O￨- in￨L￨IN￨O￨- Cambodia￨U￨NNP￨COUNTRY￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- loop￨L￨NN￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- mitigation￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- loop￨L￨NN￨O￨A analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- qualitatively￨L￨RB￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ;￨L￨:￨O￨- it￨L￨PRP￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sign￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- components￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- restricted￨L￨VBD￨O￨- the￨L￨DT￨O￨- applicability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- event-based￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- excluding￨L￨VBG￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- eradication￨L￨NN￨O￨- phases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Breaking￨U￨VBG￨O￨- down￨L￨RP￨O￨- the￨L￨DT￨O￨- generic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- 6-variables￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- H5N1￨U￨NN￨O￨- mitigation￨L￨NN￨O￨A system￨L￨NN￨O￨- in￨L￨IN￨O￨- Cambodia￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- environmental￨L￨JJ￨O￨- opportunist￨L￨NN￨O￨- pathogen￨L￨NN￨O￨- we￨L￨PRP￨O￨- mean￨L￨VBP￨O￨- an￨L￨DT￨O￨- organism￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- both￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- grow￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- infect￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Worldwide￨U￨NNP￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨- battle￨L￨NN￨O￨- against￨L￨IN￨O￨- opportunistic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- persistent￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogens￨L￨NNS￨O￨- ’￨L￨POS￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- grow￨L￨VB￨O￨- outside￨L￨JJ￨O￨A hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- models￨L￨NNS￨O￨- definitively￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- agencies￨L￨NNS￨O￨- working￨L￨VBG￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- media￨L￨NNS￨O￨A can￨L￨MD￨O￨- significantly￨L￨RB￨O￨- decrease￨L￨VB￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- by￨L￨IN￨O￨- providing￨L￨VBG￨O￨- timely￨L￨JJ￨O￨- accounts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- media￨L￨NNS￨O￨A reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- take￨L￨VBP￨O￨- steps￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- social￨L￨JJ￨O￨- distance￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- themselves￨L￨PRP￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- immediate￨L￨JJ￨O￨- families￨L￨NNS￨O￨- from￨L￨IN￨O￨- severe￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- significant￨L￨JJ￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- death￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- models￨L￨NNS￨O￨- elucidate￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- media￨L￨NNS￨O￨A on￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- 's￨L￨POS￨O￨- decision￨L￨NN￨O￨- to￨L￨TO￨O￨- employ￨L￨VB￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨- measures￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- media￨L￨NNS￨O￨A influence￨L￨NN￨O￨- and￨L￨CC￨O￨- resulting￨L￨VBG￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- add￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- crucial￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- implement￨L￨VBP￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- fourth￨L￨JJ￨ORDINAL￨- compartment￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- carefully￨L￨RB￨O￨- examine￨L￨VBP￨O￨- and￨L￨CC￨O￨- illustrate￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- media￨L￨NNS￨O￨A influence￨L￨NN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- emerging￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- city￨L￨NN￨O￨- .￨L￨.￨O￨- +Changes￨U￨NNS￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- can￨L￨MD￨O￨- often￨L￨RB￨O￨- be￨L￨VB￨O￨- attributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- secular￨L￨JJ￨RELIGION￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- key￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- or￨L￨CC￨O￨- climatic￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- :￨L￨:￨O￨- though￨L￨IN￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- cause￨L￨VB￨O￨- shifts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A ’￨L￨''￨O￨- interepidemic￨L￨JJ￨O￨- period￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- such￨L￨JJ￨O￨- trends￨L￨NNS￨O￨- are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- regime-switching￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- age-specified￨L￨JJ￨O￨- ,￨L￨,￨O￨- weekly￨L￨JJ￨SET￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A reports￨L￨NNS￨O￨- from￨L￨IN￨O￨- Copenhagen￨U￨NNP￨CITY￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- early￨L￨JJ￨DATE￨- 20th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- excellent￨L￨JJ￨O￨- illustration￨L￨NN￨O￨- of￨L￨IN￨O￨- regime-switching￨L￨NN￨O￨- ,￨L￨,￨O￨- displaying￨L￨VBG￨O￨- distinct￨L￨JJ￨O￨- shifts￨L￨NNS￨O￨- between￨L￨IN￨O￨- low-amplitude￨L￨NN￨O￨- ,￨L￨,￨O￨- noisy￨L￨JJ￨O￨- multiannual￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- and￨L￨CC￨O￨- high-amplitude￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- marked￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- signal-to-noise￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Historically￨U￨NNP￨O￨- ,￨L￨,￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A was￨L￨VBD￨O￨- thought￨L￨VBN￨O￨- of￨L￨IN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- classic￨L￨JJ￨O￨- ,￨L￨,￨O￨- permanently￨L￨RB￨O￨- immunizing￨L￨VBG￨O￨- ,￨L￨,￨O￨- childhood￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- around￨L￨IN￨O￨- five￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- few￨L￨JJ￨O￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- re-infection￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- high-risk￨L￨JJ￨O￨- human￨L￨JJ￨O￨- papillomavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- hrHPV￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complicated￨L￨JJ￨O￨- process￨L￨NN￨O￨- including￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- clearance￨L￨NN￨O￨A of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- HPV￨U￨NN￨O￨- types￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- progression￨L￨NN￨O￨- and￨L￨CC￨O￨- regression￨L￨NN￨O￨- of￨L￨IN￨O￨- associated￨L￨VBN￨O￨- lesions￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- separate￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- facilitates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- hrHPV￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- natural￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- differences￨L￨NNS￨O￨- across￨L￨IN￨O￨- hrHPV￨L￨NN￨O￨- types￨L￨NNS￨O￨- in￨L￨IN￨O￨- clearance￨L￨NN￨O￨A and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- HPV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- hrHPV￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- beneficial￨L￨JJ￨O￨- to￨L￨TO￨O￨- disentangle￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- processes￨L￨NNS￨O￨- thus￨L￨RB￨O￨- avoiding￨L￨VBG￨O￨- the￨L￨DT￨O￨- confounding￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- screening￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- policies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- against￨L￨IN￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A by￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- hrHPV￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- then￨L￨RB￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨O￨- have￨L￨VBP￨O￨- typically￨L￨RB￨O￨- included￨L￨VBN￨O￨- both￨L￨CC￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- although￨L￨IN￨O￨- some￨L￨DT￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- hrHPV￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Earlier￨U￨JJR￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- EBOV￨U￨NN￨O￨- mostly￨L￨RB￨O￨- indicated￨L￨VBD￨O￨- shorter￨L￨JJR￨O￨- incubation￨L￨NN￨O￨- periods￨L￨NNS￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- 6￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨A to￨L￨TO￨O￨- 10￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- range￨L￨VB￨O￨- from￨L￨IN￨O￨- 2￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- 21￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨A [￨L￨-LRB-￨O￨- 10,23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- EBOV￨U￨NN￨O￨- most￨L￨RBS￨O￨- calculations￨L￨NNS￨O￨- put￨L￨VBD￨O￨- it￨L￨PRP￨O￨- at￨L￨IN￨O￨- 6￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- 10￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- for￨L￨IN￨O￨- EBOV￨U￨NN￨O￨- hemorrhagic￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 12.7￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨A (￨L￨-LRB-￨O￨- SD￨U￨NN￨STATE_OR_PROVINCE￨- 4.31￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- known￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨A period￨L￨NN￨O￨- could￨L￨MD￨O￨- only￨L￨RB￨O￨- be￨L￨VB￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- and￨L￨CC￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- forced￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- contacts￨L￨NNS￨O￨- were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- periods￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Statistical￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- was￨L￨VBD￨O￨- adopted￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- patients￨L￨NNS￨O￨- in￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- using￨L￨VBG￨O￨- sentinel￨L￨NN￨O￨A surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- can￨L￨MD￨O￨- consider￨L￨VB￨O￨- Susceptible-Infectious-Removed-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- temporary￨L￨JJ￨O￨A immunity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Actually￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨A case￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infectious-Removed￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- authors￨L￨NNS￨O￨- took￨L￨VBD￨O￨- obesity￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨A based￨L￨VBN￨O￨A on￨L￨IN￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- applied￨L￨VBD￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- difference￨L￨NN￨O￨A equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- obesity￨L￨NN￨O￨- in￨L￨IN￨O￨- Korean￨U￨JJ￨NATIONALITY￨- adults￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- 19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 59￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- projected￨L￨VBD￨O￨- the￨L￨DT￨O￨- findings￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- two-compartmental￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- difference￨L￨NN￨O￨A equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- obesity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Korean￨U￨JJ￨NATIONALITY￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- propose￨L￨VB￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- its￨L￨PRP$￨O￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +S0￨U￨NN￨O￨- and￨L￨CC￨O￨- O0￨U￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- proportions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- normal￨L￨JJ￨O￨- weight￨L￨NN￨O￨- and￨L￨CC￨O￨- obese￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- 18￨L￨CD￨DURATION￨A years￨L￨NNS￨DURATION￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- many￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- viruses￨L￨NNS￨O￨- and￨L￨CC￨O￨- intervention￨L￨NN￨O￨- effects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- uncertain￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- performed￨L￨VBD￨O￨- sensitivity￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- by￨L￨IN￨O￨- randomly￨L￨RB￨O￨- choosing￨L￨VBG￨O￨- values￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- listed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- given￨L￨VBN￨O￨- ranges￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- simulation￨L￨NN￨O￨- produces￨L￨VBZ￨O￨- daily￨L￨JJ￨SET￨- time￨L￨NN￨O￨- courses￨L￨NNS￨O￨- and￨L￨CC￨O￨- cumulative￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- outpatients￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Parameter￨U￨NN￨O￨- values￨L￨NNS￨O￨A hospitalizations￨L￨NNS￨O￨- using￨L￨VBG￨O￨- demographic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- Appendix￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- patients￨L￨NNS￨O￨- seek￨L￨VBP￨O￨- medical￨L￨JJ￨O￨- care￨L￨NN￨O￨- within￨L￨IN￨O￨- 48￨L￨CD￨DURATION￨- hours￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- antiviral￨L￨JJ￨O￨A treatment￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- and￨L￨CC￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- hospitalization￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- sampled￨L￨VBN￨O￨- parameter￨L￨NN￨O￨A values￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulated￨L￨JJ￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- wave￨L￨NN￨O￨- using￨L￨VBG￨O￨- InfluSim￨U￨NNP￨O￨- software￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- were￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- both￨L￨CC￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- were￨L￨VBD￨O￨- then￨L￨RB￨O￨- estimated￨L￨VBN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨A values￨L￨NNS￨O￨A .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- more￨L￨RBR￨O￨- importantly￨L￨RB￨O￨- all￨L￨DT￨O￨- local￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- communities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- embedded￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨A in￨L￨IN￨O￨- which￨L￨WDT￨O￨- rescue￨L￨NN￨O￨- effects￨L￨NNS￨O￨- will￨L￨MD￨O￨- take￨L￨VB￨O￨- place￨L￨NN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- extent￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- scaling￨L￨NN￨O￨- of￨L￨IN￨O￨- import￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- change￨L￨VBP￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- zero-incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- further￨L￨RB￨O￨- isolate￨L￨VB￨O￨- this￨L￨DT￨O￨- rescue￨L￨NN￨O￨- effect￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- control￨L￨VBP￨O￨- for￨L￨IN￨O￨- covariates￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- of￨L￨IN￨O￨- critical￨L￨JJ￨O￨- importance￨L￨NN￨O￨- in￨L￨IN￨O￨- sustaining￨L￨VBG￨O￨- a￨L￨DT￨O￨- chain￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- development￨L￨NN￨O￨- index￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- indicative￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- migrants￨L￨NNS￨O￨- living￨L￨VBG￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- overall￨L￨JJ￨O￨- connectedness￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- comparison￨L￨NN￨O￨- between￨L￨IN￨O￨- island￨L￨NN￨O￨- and￨L￨CC￨O￨- mainland￨L￨NN￨O￨- countries￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- means￨L￨NN￨O￨- to￨L￨TO￨O￨- elucidate￨L￨VB￨O￨- rescue￨L￨NN￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- greater￨L￨JJR￨O￨- requirements￨L￨NNS￨O￨- for￨L￨IN￨O￨- reaching￨L￨VBG￨O￨- islands￨L￨NNS￨O￨- mean￨L￨VB￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- less￨L￨RBR￨O￨- well￨L￨RB￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨A .￨L￨.￨O￨- +Low￨U￨JJ￨O￨- birth￨L￨NN￨O￨A rates￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- analogous￨L￨JJ￨O￨- effect￨L￨NN￨O￨- NumericCitation￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- increase￨L￨VBP￨O￨- the￨L￨DT￨O￨- CCS￨U￨NN￨ORGANIZATION￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- comparing￨L￨VBG￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- does￨L￨VBZ￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Critical￨U￨JJ￨O￨- Community￨U￨NN￨O￨- Size￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- CCS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- population￨L￨NN￨O￨A size￨L￨NN￨O￨A below￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- liable￨L￨JJ￨O￨- to￨L￨TO￨O￨- stochastic￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- during￨L￨IN￨O￨- post-epidemic￨L￨JJ￨O￨- troughs￨L￨NNS￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- pool￨L￨NN￨O￨- is￨L￨VBZ￨O￨- exhausted￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- important￨L￨JJ￨O￨- aspect￨L￨NN￨O￨- of￨L￨IN￨O￨- metabolic￨L￨JJ￨O￨- pathway￨L￨NN￨O￨A analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- metabolic￨L￨JJ￨O￨- pathways￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- major￨L￨JJ￨O￨- problem￨L￨NN￨O￨- lies￨L￨VBZ￨O￨A in￨L￨IN￨O￨- tracking￨L￨VBG￨O￨- the￨L￨DT￨O￨- progress￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- non-infected￨L￨JJ￨O￨- neighboring￨L￨VBG￨O￨- metabolites￨L￨NNS￨O￨- and￨L￨CC￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- spread￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- us￨L￨PRP￨O￨- consider￨L￨VB￨O￨- a￨L￨DT￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- wherein￨L￨WRB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- metabolite￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- healthy￨L￨JJ￨O￨A metabolic￨L￨JJ￨O￨- network￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- mutation￨L￨NN￨O￨- or￨L￨CC￨O￨- external￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨- .￨L￨.￨O￨- +Tackling￨U￨VBG￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- metabolic￨L￨JJ￨O￨- pathway￨L￨NN￨O￨A as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- curing￨L￨VBG￨O￨- it￨L￨PRP￨O￨- simultaneously￨L￨RB￨O￨- is￨L￨VBZ￨O￨- rather￨L￨RB￨O￨- complex￨L￨JJ￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- metabolite￨L￨NN￨O￨- is￨L￨VBZ￨O￨- said￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- if￨L￨IN￨O￨- its￨L￨PRP$￨O￨- formation￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- metabolic￨L￨JJ￨O￨- pathway￨L￨NN￨O￨A ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- somehow￨L￨RB￨O￨- impaired￨L￨JJ￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- assume￨L￨VB￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- discovery￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- strain￨L￨NN￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- arrival￨L￨NN￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- particular￨L￨JJ￨O￨- region￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- pandemic￨L￨JJ￨O￨- strain￨L￨NN￨O￨- arrived￨L￨VBD￨O￨- in￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- two￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- discovery￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- since￨L￨IN￨O￨- border￨L￨NN￨O￨- quarantine￨L￨NN￨O￨- inspections￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- fully￨L￨RB￨O￨- detect￨L￨VB￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- administration￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- residents￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- simultaneous￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- large-scale￨L￨JJ￨O￨- multi-agent￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨A to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinations￨L￨NNS￨O￨- in￨L￨IN￨O￨- suppressing￨L￨VBG￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- urban￨L￨JJ￨O￨- area￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- were￨L￨VBD￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- collective￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- enhanced￨L￨VBN￨O￨- if￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- were￨L￨VBD￨O￨- distributed￨L￨VBN￨O￨- preferentially￨L￨RB￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- selected￨L￨VBN￨O￨- groups￨L￨NNS￨O￨A rather￨L￨RB￨O￨- than￨L￨IN￨O￨- equally￨L￨RB￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- full-scale￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- places￨L￨NNS￨O￨- and￨L￨CC￨O￨- residents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- as￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- agents￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- 1,246,732￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- Fig￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- investigate￨L￨VB￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- simulations￨L￨NNS￨O￨A in￨L￨IN￨O￨- which￨L￨WDT￨O￨- different￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- received￨L￨VBD￨O￨- priority￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +pylori￨L￨NN￨PERSON￨- with￨L￨IN￨O￨- them￨L￨PRP￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- left￨L￨VBD￨O￨- Africa￨U￨NNP￨LOCATION￨- about￨L￨IN￨DATE￨- 60,000￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- ago￨L￨RB￨DATE￨- (￨L￨-LRB-￨O￨- 60￨L￨CD￨NUMBER￨A kya￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- diverse￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- selective￨L￨JJ￨O￨- pressures￨L￨NNS￨O￨- subsequently￨L￨RB￨O￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- additional￨L￨JJ￨O￨- ,￨L￨,￨O￨- geographically-associated￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Eurasia￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Sahul￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +pylori￨L￨NN￨O￨- alike￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- three￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- African￨U￨JJ￨NATIONALITY￨- populations￨L￨NNS￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- identified￨L￨VBN￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨- species￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +pylori￨L￨NN￨O￨- populations￨L￨NNS￨O￨A that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- indigenous￨L￨JJ￨O￨- to￨L￨TO￨O￨- Africa￨U￨NNP￨LOCATION￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- designated￨L￨VBN￨O￨- hpNEAfrica￨L￨NN￨O￨- ,￨L￨,￨O￨- hpAfrica1￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hpAfrica2￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Helicobacter￨U￨NNP￨PERSON￨- pylori￨L￨NNP￨PERSON￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- gastric￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- that￨L￨WDT￨O￨- infects￨L￨VBZ￨O￨A more￨L￨JJR￨O￨- than￨L￨IN￨O￨- half￨L￨PDT￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- 's￨L￨POS￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +pylori￨L￨NN￨O￨- populations￨L￨NNS￨O￨A ,￨L￨,￨O￨- was￨L￨VBD￨O￨- isolated￨L￨VBN￨O￨- only￨L￨RB￨O￨- from￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- South￨U￨NNP￨COUNTRY￨- Africa￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Namibia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- southern￨L￨JJ￨O￨- Angola￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +‘￨L￨``￨O￨- Herald￨U￨NNP￨ORGANIZATION￨- ’￨L￨''￨O￨- waves￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- strains￨L￨NNS￨O￨- which￨L￨WDT￨O￨- begin￨L￨VBP￨O￨- to￨L￨TO￨O￨- dominate￨L￨VB￨O￨- very￨L￨RB￨O￨- late￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- season￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- successfully￨L￨RB￨O￨- used￨L￨VBN￨O￨- many￨L￨JJ￨O￨- times￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- the￨L￨DT￨DATE￨- following￨L￨JJ￨DATE￨- year￨L￨NN￨DATE￨- 's￨L￨POS￨O￨- vaccines￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Such￨U￨PDT￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- would￨L￨MD￨O￨- ideally￨L￨RB￨O￨- take￨L￨VB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- several￨L￨JJ￨O￨- key￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- drift￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- strains￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- co-circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- related￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- pre-existing￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- useful￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- strains￨L￨NNS￨O￨- from￨L￨IN￨O￨- season￨L￨NN￨O￨A to￨L￨TO￨O￨- season￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- helpful￨L￨JJ￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- once￨L￨RB￨DATE￨- a￨L￨DT￨DURATION￨- few￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- have￨L￨VBP￨O￨- passed￨L￨VBN￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- subtype￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- become￨L￨VB￨O￨- almost￨L￨RB￨O￨- completely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- currently￨L￨RB￨DATE￨- circulating￨L￨VBG￨O￨- grand-daughter￨L￨NN￨O￨- strain￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- large￨L￨JJ￨O￨- body￨L￨NN￨O￨- of￨L￨IN￨O￨- works￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- numerous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- variants￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- fractures￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- fibers12￨L￨NN￨O￨- ;￨L￨:￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- load￨L￨NN￨O￨- at￨L￨IN￨O￨- every￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- shortest￨L￨JJS￨O￨- paths￨L￨NNS￨O￨- passing￨L￨VBG￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- node1314￨L￨NN￨O￨- ;￨L￨:￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- links￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- topple15￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- d￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- cascades￨L￨NNS￨O￨A of￨L￨IN￨O￨- rewiring￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- self-organized￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks16￨L￨NN￨O￨- ;￨L￨:￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- sandpile￨L￨NN￨O￨- model17￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- its￨L￨PRP$￨O￨- variant￨L￨NN￨O￨- on￨L￨IN￨O￨- several￨L￨JJ￨O￨- interdependent￨L￨JJ￨O￨- networks18￨L￨NN￨O￨- ;￨L￨:￨O￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- interdependent￨L￨JJ￨O￨- networks3￨L￨NN￨O￨- .￨L￨.￨O￨- +Unlike￨U￨IN￨O￨- previous￨L￨JJ￨O￨- works￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- deliver￨L￨VBP￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- of￨L￨IN￨O￨- systemic￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨A :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- individual￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- robustness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- banks￨L￨NNS￨O￨- '￨L￨POS￨O￨- capital￨L￨NN￨O￨- ratios￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- relative￨L￨JJ￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- contagion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- market￨L￨NN￨O￨- illiquidity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- random￨L￨JJ￨O￨- vs￨L￨CC￨O￨- targeted￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- shocks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- quantifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- protection￨L￨NN￨O￨- of￨L￨IN￨O￨- women￨L￨NNS￨O￨A with￨L￨IN￨O￨- prior￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- HPV16/18￨U￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- protection￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- extending￨L￨VBG￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- catch-up￨L￨NN￨O￨- programme￨L￨NN￨O￨- to￨L￨TO￨O￨- older￨L￨JJR￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- from￨L￨IN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- include￨L￨VB￨O￨- vaccine￨L￨NN￨O￨- protection￨L￨NN￨O￨- in￨L￨IN￨O￨- non-naive￨L￨JJ￨O￨- women￨L￨NNS￨O￨A may￨L￨MD￨O￨- underestimate￨L￨VB￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- including￨L￨VBG￨O￨- older￨L￨JJR￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- in￨L￨IN￨O￨- catch-up￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- since￨L￨IN￨O￨- included￨L￨VBN￨O￨- this￨L￨DT￨O￨- protection￨L￨NN￨O￨- to￨L￨TO￨O￨- non-naive￨L￨JJ￨O￨- women￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- no￨L￨DT￨O￨- other￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- devised￨L￨VBN￨O￨- to￨L￨TO￨O￨- explicitly￨L￨RB￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- protection￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- adults￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- older￨L￨JJR￨O￨- HPV￨U￨NN￨O￨- models￨L￨NNS￨O￨- made￨L￨VBD￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- trial￨L￨NN￨O￨- results￨L￨VBZ￨O￨- at￨L￨IN￨O￨- that￨L￨DT￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- only￨L￨RB￨O￨- offers￨L￨VBZ￨O￨- protection￨L￨NN￨O￨- to￨L￨TO￨O￨- women￨L￨NNS￨O￨A who￨L￨WP￨O￨- had￨L￨VBD￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- infected￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- are￨L￨VBP￨O￨- naive￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- three￨L￨CD￨NUMBER￨- bivalent￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- trial￨L￨NN￨O￨- was￨L￨VBD￨O￨- expanded￨L￨VBN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- women￨L￨NNS￨O￨A that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- currently￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- but￨L￨CC￨O￨- who￨L￨WP￨O￨- had￨L￨VBD￨O￨- previous￨L￨JJ￨O￨- serological￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- HPV￨U￨NN￨O￨- 16/18￨L￨CD￨NUMBER￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- women￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- non-naïve￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- comparably￨L￨RB￨O￨- high￨L￨JJ￨O￨- efficacy￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- women￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- HPV￨U￨NN￨O￨- naive￨L￨JJ￨O￨- women￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Stochastic￨U￨JJ￨O￨- “￨L￨``￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- ”￨L￨''￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- implemented￨L￨VBN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨A .￨L￨.￨O￨- +Bauch￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Earn￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- term-time￨L￨JJ￨O￨- forced￨L￨JJ￨O￨A susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- exposed￨L￨VBN￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBD￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- frequencies￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- good￨L￨JJ￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- positions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- peaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- spectra￨L￨NNS￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- records￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- childhood￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- ingredients￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- rubella￨L￨NN￨O￨A and￨L￨CC￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- seasonality￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- owing￨L￨NN￨O￨- to￨L￨TO￨O￨- schooling￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- demographic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- stochasticity￨L￨NN￨O￨- was￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- multiplicative￨L￨JJ￨O￨- noise￨L￨NN￨O￨- of￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- amplitude￨L￨NN￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- using￨L￨VBG￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- standard￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- unforced￨L￨JJ￨O￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- extensions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- seasonally￨L￨RB￨O￨- forced￨L￨VBN￨O￨A models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- rubella￨L￨NN￨O￨A may￨L￨MD￨O￨- result￨L￨VB￨O￨- from￨L￨IN￨O￨- switching￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- cyclic￨L￨JJ￨O￨- attractors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- annual￨L￨JJ￨SET￨- and￨L￨CC￨O￨- multi-annual￨L￨JJ￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- a￨L￨DT￨O￨- term-time￨L￨JJ￨O￨- forced￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- its￨L￨PRP$￨O￨- dynamics￨L￨NNS￨O￨- with￨L￨IN￨O￨- rubella￨L￨NN￨O￨A data￨L￨NNS￨O￨- in￨L￨IN￨O￨- Copenhagen￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- survey￨L￨NN￨O￨- comprised￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- information￨L￨NN￨O￨- :￨L￨:￨O￨- colony￨L￨NN￨O￨- reference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- identifier￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- apiary￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- island￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- repeat￨L￨NN￨O￨- visits￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- identified￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- owner￨L￨NN￨TITLE￨- reference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- label￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- owner￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- may￨L￨MD￨O￨- own￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- multiple￨L￨JJ￨O￨- apiaries￨L￨NNS￨O￨- on￨L￨IN￨O￨- Jersey￨U￨NNP￨LOCATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- honeybee￨L￨NN￨O￨- colonies￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- apiary￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- this￨L￨DT￨O￨- occasionally￨L￨RB￨O￨- changed￨L￨VBN￨O￨- between￨L￨IN￨O￨- inspections￨L￨NNS￨O￨- ,￨L￨,￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- hive￨L￨VB￨O￨- addition￨L￨NN￨O￨- or￨L￨CC￨O￨- removal￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- x-and￨L￨JJ￨O￨- y-coordinates￨L￨NNS￨O￨- ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- AFB-positive￨U￨JJ￨O￨- hives￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- apiary￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- date￨L￨NN￨O￨- of￨L￨IN￨O￨- inspection￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- are￨L￨VBP￨O￨- tested￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- parameter￨L￨NN￨O￨A values￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- MCMC￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- predicted￨L￨VBN￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- June￨U￨NNP￨DATE￨- and￨L￨CC￨O￨- August￨U￨NNP￨DATE￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Whenever￨U￨NNP￨O￨- an￨L￨DT￨O￨- inspection￨L￨NN￨O￨- was￨L￨VBD￨O￨- carried￨L￨VBN￨O￨A out￨L￨RP￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- AFB￨U￨NN￨O￨- was￨L￨VBD￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- hive￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- hive￨L￨NN￨O￨- was￨L￨VBD￨O￨- destroyed￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- parts￨L￨NNS￨O￨- scorched￨L￨VBD￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- guarantee￨L￨VB￨O￨- removal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Follow-up￨U￨JJ￨O￨- inspections￨L￨NNS￨O￨- were￨L￨VBD￨O￨- carried￨L￨VBN￨O￨A out￨L￨IN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- apiaries￨L￨NNS￨O￨- between￨L￨IN￨O￨- 8￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 16￨L￨CD￨DATE￨- August￨U￨NNP￨DATE￨- ;￨L￨:￨O￨- some￨L￨DT￨O￨- follow-up￨L￨JJ￨O￨- inspections￨L￨NNS￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- apiary￨L￨NN￨O￨- was￨L￨VBD￨O￨- AFB-negative￨U￨JJ￨O￨- .￨L￨.￨O￨- +Pooled￨U￨VBN￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- reanalyzed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- pre-pandemic￨L￨JJ￨O￨- age￨L￨NN￨O￨A specific￨L￨JJ￨O￨A seroprotective￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- and￨L￨CC￨O￨- age￨L￨NN￨O￨- specific￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Early￨U￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A ,￨L￨,￨O￨- age-specific￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- suspected￨L￨VBN￨O￨- to￨L￨TO￨O￨- play￨L￨VB￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Epidemiological￨U￨JJ￨O￨- surveillance￨L￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- season￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A the￨L￨DT￨O￨- A/H1N1pdm￨U￨NN￨O￨- infected￨L￨JJ￨O￨- many￨L￨JJ￨O￨- more￨L￨JJR￨O￨- school￨L￨NN￨O￨- age￨L￨NN￨O￨- children￨L￨NNS￨O￨- than￨L￨IN￨O￨- adults￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- background￨L￨NN￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- partly￨L￨RB￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- previously￨L￨RB￨DATE￨- circulating￨L￨VBG￨O￨A cross-reactive￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- and￨L￨CC￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- pathogenicity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- circulating￨L￨VBG￨O￨- viruses￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- is￨L￨VBZ￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- match￨L￨NN￨O￨- between￨L￨IN￨O￨- wild￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- quantitative￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- test￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- programmes￨L￨NNS￨O￨A have￨L￨VBP￨O￨- thus￨L￨RB￨O￨- made￨L￨VBN￨O￨- substantial￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- background￨L￨NN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- most￨L￨JJS￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- programmes￨L￨NNS￨O￨A have￨L￨VBP￨O￨- traditionally￨L￨RB￨O￨- targeted￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- 65￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- and￨L￨CC￨O￨- older￨L￨JJR￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- in￨L￨IN￨O￨- high-risk￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- line￨L￨NN￨O￨- with￨L￨IN￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- recommendations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Children￨U￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- target￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A ,￨L￨,￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- protection￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- indirect￨L￨JJ￨O￨- protection￨L￨NN￨O￨- of￨L￨IN￨O￨- others￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- the￨L￨DT￨O￨- experience￨L￨NN￨O￨- with￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- H1N1/2009￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- priority￨L￨NN￨O￨- groups￨L￨NNS￨O￨A for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- are￨L￨VBP￨O￨- now￨L￨RB￨DATE￨- being￨L￨VBG￨O￨- reconsidered￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- can￨L￨MD￨O￨- summarize￨L￨VB￨O￨- the￨L￨DT￨O￨- events￨L￨NNS￨O￨- before￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- discovery￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- boson￨L￨NN￨O￨- ,￨L￨,￨O￨- dividing￨L￨VBG￨O￨- them￨L￨PRP￨O￨- into￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- :￨L￨:￨O￨- Period￨U￨NN￨O￨- I￨U￨NN￨O￨- :￨L￨:￨O￨- Before￨U￨IN￨O￨- the￨L￨DT￨O￨- announcement￨L￨NN￨O￨- on￨L￨IN￨O￨- 2nd￨L￨JJ￨DATE￨- July￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- some￨L￨DT￨O￨- rumors￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- discovery￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Higgs-like￨U￨JJ￨MISC￨- boson￨L￨NN￨O￨- at￨L￨IN￨O￨- Tevatron￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- Period￨U￨NN￨O￨- II￨U￨CD￨NUMBER￨- :￨L￨:￨O￨- On￨U￨IN￨O￨- 2nd￨L￨JJ￨DATE￨- July￨U￨NNP￨DATE￨- at￨L￨IN￨TIME￨- 1￨L￨CD￨TIME￨- PM￨U￨NNP￨TIME￨- GMT￨U￨NNP￨TIME￨- ,￨L￨,￨O￨- scientists￨L￨NNS￨O￨- from￨L￨IN￨O￨- CDF￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- D0￨U￨NN￨O￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- at￨L￨IN￨O￨- Tevatron￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- presented￨L￨VBD￨O￨- results￨L￨NNS￨O￨- indicating￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Higgs￨U￨NNP￨O￨- particle￨L￨NN￨O￨- should￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- mass￨L￨NN￨O￨- between￨L￨IN￨O￨- 115￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 135￨L￨CD￨NUMBER￨- GeV/c2￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- about￨L￨IN￨O￨- 123￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 144￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- the￨L￨DT￨O￨- mass￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proton￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 7￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- Period￨U￨NN￨O￨- III￨U￨CD￨NUMBER￨- :￨L￨:￨O￨- After￨U￨IN￨O￨- 2nd￨L￨JJ￨DATE￨- July￨U￨NNP￨DATE￨- and￨L￨CC￨O￨- before￨L￨IN￨O￨- 4th￨L￨JJ￨DATE￨- of￨L￨IN￨DATE￨- July￨U￨NNP￨DATE￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- many￨L￨JJ￨O￨- rumors￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- Higgs￨U￨NNP￨PERSON￨- boson￨L￨NN￨O￨- discovery￨L￨NN￨O￨- at￨L￨IN￨O￨- LHC8￨U￨NN￨O￨- ;￨L￨:￨O￨- Period￨U￨NN￨O￨- IV￨U￨CD￨NUMBER￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- main￨L￨JJ￨O￨- event￨L￨NN￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- announcement￨L￨NN￨O￨- on￨L￨IN￨O￨- 4th￨L￨JJ￨DATE￨- July￨U￨NNP￨DATE￨- at￨L￨IN￨TIME￨- 8￨L￨CD￨TIME￨- AM￨U￨NNP￨TIME￨- GMT￨U￨NNP￨TIME￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- scientists￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- ATLAS￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- CMS￨U￨NNP￨ORGANIZATION￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- at￨L￨IN￨O￨- CERN￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- presenting￨L￨VBG￨O￨- results￨L￨NNS￨O￨- indicating￨L￨VBG￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- particle￨L￨NN￨O￨- ,￨L￨,￨O￨- compatible￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- Higgs￨U￨NNP￨PERSON￨- boson￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- mass￨L￨NN￨O￨- around￨L￨IN￨O￨- 125￨L￨CD￨NUMBER￨- GeV/c2910￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- report￨L￨VBP￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- non-trivial￨L￨JJ￨O￨- spatio-temporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- user￨L￨NN￨O￨A activities￨L￨NNS￨O￨- at￨L￨IN￨O￨- individual￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- tweeting￨L￨NN￨O￨- ,￨L￨,￨O￨- re-tweeting￨L￨NN￨O￨- or￨L￨CC￨O￨- replying￨L￨VBG￨O￨- to￨L￨TO￨O￨- existing￨L￨VBG￨O￨- tweets￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- section￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- both￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- user￨L￨NN￨O￨A activity￨L￨NN￨O￨- on￨L￨IN￨O￨- Twitter￨U￨NNP￨O￨- before￨L￨IN￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- event￨L￨NN￨O￨- on￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- memoryless￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- activation￨L￨NN￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- social￨L￨JJ￨O￨- reinforcement￨L￨NN￨O￨- at￨L￨IN￨O￨- neighborhood￨L￨NN￨O￨A level￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- the￨L￨DT￨O￨- anatomy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- scientific￨L￨JJ￨O￨- rumor￨L￨NN￨O￨- by￨L￨IN￨O￨- following￨L￨VBG￨O￨- and￨L￨CC￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- related￨L￨JJ￨O￨- Twitter￨U￨NNP￨MISC￨- user￨L￨NN￨O￨A activity￨L￨NN￨O￨- during￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- announcement￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- their￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- birth￨L￨NN￨O￨- seasonality￨L￨NN￨O￨- on￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- He￨U￨PRP￨O￨- and￨L￨CC￨O￨- Earn￨U￨VB￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- whether￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- birth￨L￨NN￨O￨- amplitude￨L￨NN￨O￨A could￨L￨MD￨O￨- create￨L￨VB￨O￨- resonance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- amplitude￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- birth￨L￨NN￨O￨- amplitude￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- which￨L￨WDT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- ranges￨L￨NNS￨O￨- of￨L￨IN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- result￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- childhood￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- realistic￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- birth￨L￨NN￨O￨- seasonality￨L￨NN￨O￨- for￨L￨IN￨O￨- developed￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- induce￨L￨VB￨O￨- resonance￨L￨NN￨O￨- ;￨L￨:￨O￨- furthermore￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- birth￨L￨NN￨O￨- amplitude￨L￨NN￨O￨A increases￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- wider￨L￨JJR￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- complex￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Researchers￨U￨NNS￨O￨- have￨L￨VBP￨O￨- clearly￨L￨RB￨O￨- illustrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- birth￨L￨NN￨O￨A and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- rates￨L￨NNS￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- dynamical￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- in￨L￨IN￨O￨- periodicity￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- multiannual￨L￨JJ￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- seasonality￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- ubiquitous￨L￨JJ￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- birth￨L￨NN￨O￨A rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- slow￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- birth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- birth￨L￨NN￨O￨A rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- birth￨L￨NN￨O￨- seasonality￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- confound￨L￨VBP￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- well-mixed￨L￨JJ￨O￨- population￨L￨NN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- establishment￨L￨NN￨O￨- and￨L￨CC￨O￨- initial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- until￨L￨IN￨O￨- now￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- systematically￨L￨RB￨O￨- explored￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- comparative￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- system￨L￨NN￨O￨- between￨L￨IN￨O￨- similar￨L￨JJ￨O￨- species￨L￨NNS￨O￨A modify￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- potential￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- primate￨L￨JJ￨O￨- species￨L￨NNS￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- social￨L￨JJ￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- demography￨L￨NN￨O￨A predisposes￨L￨VBZ￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- invasion￨L￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- potentially￨L￨RB￨O￨- lethal￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- that￨L￨WDT￨O￨- produces￨L￨VBZ￨O￨- no￨L￨DT￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- pathogen￨L￨NN￨O￨- like￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- circulating￨L￨VBG￨O￨- human￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Primate￨U￨JJ￨TITLE￨- species￨L￨NNS￨O￨A exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- group￨L￨NN￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- structures￨L￨NNS￨O￨- ;￨L￨:￨O￨- their￨L￨PRP$￨O￨- life-history￨L￨JJ￨O￨- traits￨L￨NNS￨O￨- broadly￨L￨RB￨O￨- correlate￨L￨VBP￨O￨- with￨L￨IN￨O￨- social￨L￨JJ￨O￨- system￨L￨NN￨O￨- type￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- small-bodied￨L￨JJ￨O￨- primates￨L￨NNS￨O￨- typifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- monogamous￨L￨JJ￨O￨- and￨L￨CC￨O￨- solitary￨L￨JJ￨O￨- social￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- larger￨L￨JJR￨O￨- species￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- chimpanzees￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Pan￨U￨NN￨O￨- troglodytes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- having￨L￨VBG￨O￨- complex￨L￨NN￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- in￨L￨IN￨O￨- larger￨L￨JJR￨O￨- groups￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- catastrophic￨L￨JJ￨O￨- declines￨L￨NNS￨O￨- in￨L￨IN￨O￨- African￨U￨JJ￨NATIONALITY￨- gorilla￨L￨NN￨O￨- and￨L￨CC￨O￨- chimpanzee￨L￨NN￨O￨- populations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- illustrated￨L￨VBN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- that￨L￨WDT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- on￨L￨IN￨O￨- wild￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- we￨L￨PRP￨O￨- rarely￨L￨RB￨O￨- hear￨L￨VBP￨O￨- of￨L￨IN￨O￨- similar￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- impacts￨L￨NNS￨O￨- to￨L￨TO￨O￨- Asian￨U￨JJ￨NATIONALITY￨- great￨L￨JJ￨O￨- apes￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- smaller￨L￨JJR￨O￨- primates￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- hypothesize￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- demography￨L￨NN￨O￨A predispose￨L￨VBP￨O￨- some￨L￨DT￨O￨- primates￨L￨NNS￨O￨- to￨L￨TO￨O￨- greater￨L￨JJR￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- impact￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- mode￨L￨NN￨O￨- is￨L￨VBZ￨O￨- central￨L￨JJ￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- classic￨L￨JJ￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- compartment￨L￨NN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- fewer￨L￨JJR￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- or￨L￨CC￨O￨- discrete-time￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- efficient￨L￨JJ￨O￨- ,￨L￨,￨O￨- derivative-based￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- from￨L￨IN￨O￨- historical￨L￨JJ￨O￨- case￨L￨NN￨O￨A data￨L￨NNS￨O￨A .￨L￨.￨O￨- +Childhood￨U￨NN￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- chickenpox￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- long-term￨L￨JJ￨O￨- case￨L￨NN￨O￨- count￨L￨NN￨TITLE￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- test￨L￨NN￨O￨- bed￨L￨NN￨O￨- for￨L￨IN￨O￨- developing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- estimation￨L￨NN￨O￨A procedures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Advanced￨U￨NNP￨O￨- NLP￨U￨NNP￨O￨- packages￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- excellent￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- efficient￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- from￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- case￨L￨NN￨O￨A data￨L￨NNS￨O￨A .￨L￨.￨O￨- +Both￨U￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- goals￨L￨NNS￨O￨- require￨L￨VBP￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A from￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- high-risk￨L￨JJ￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- whether￨L￨IN￨O￨- immediate￨L￨JJ￨O￨- antiviral￨L￨JJ￨O￨- therapy￨L￨NN￨O￨A once￨L￨IN￨DATE￨- people￨L￨NNS￨O￨- are￨L￨VBP￨O￨- diagnosed￨L￨VBN￨O￨- with￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- beneficial￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- is￨L￨VBZ￨O￨- controversial￨L￨JJ￨O￨- since￨L￨IN￨O￨- early￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- will￨L￨MD￨O￨- inevitably￨L￨RB￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- early￨L￨JJ￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- bad￨L￨JJ￨O￨- adherence￨L￨NN￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- additional￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- antiviral￨L￨JJ￨O￨- therapy￨L￨NN￨O￨A has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- since￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- studies￨L￨NNS￨O￨- demonstrating￨L￨VBG￨O￨- that￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- therapy￨L￨NN￨O￨- can￨L￨MD￨O￨- extend￨L￨VB￨O￨- the￨L￨DT￨O￨- life￨L￨NN￨O￨- expectancy￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- reduce￨L￨VB￨O￨- their￨L￨PRP$￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- put￨L￨VBD￨O￨- forward￨L￨RP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- therapy￨L￨NN￨O￨A ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- antiviral￨L￨JJ￨O￨- therapy￨L￨NN￨O￨- as￨L￨RB￨O￨- soon￨L￨RB￨O￨- as￨L￨IN￨O￨- people￨L￨NNS￨O￨- are￨L￨VBP￨O￨- diagnosed￨L￨VBN￨O￨- with￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- such￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- HIV/AIDS￨U￨NN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- 13￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- stage￨L￨NN￨O￨- people￨L￨NNS￨O￨A have￨L￨VBP￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A rate￨L￨NN￨O￨A via￨L￨IN￨O￨- homosexual￨L￨JJ￨O￨- contact￨L￨NN￨O￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- heterosexual￨L￨JJ￨O￨- contact￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- modeling￨L￨NN￨O￨- H5N1￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- with￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- wild￨L￨JJ￨O￨- birds￨L￨NNS￨O￨A and￨L￨CC￨O￨- poultry￨L￨NN￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- studies￨L￨NNS￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- wild￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- are￨L￨VBP￨O￨- lacking￨L￨VBG￨O￨- .￨L￨.￨O￨- +Fewer￨U￨JJR￨O￨- large-scale￨L￨JJ￨O￨- monitoring￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- conducted￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- birds￨L￨NNS￨O￨A in￨L￨IN￨O￨- India1314￨U￨NN￨O￨- .￨L￨.￨O￨- +Few￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- included￨L￨VBD￨O￨- both￨L￨CC￨O￨- wild￨L￨JJ￨O￨- birds￨L￨NNS￨O￨A as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- poultry￨L￨NN￨O￨- with￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other1617￨L￨NN￨O￨- .￨L￨.￨O￨- +HPAI￨U￨NNP￨ORGANIZATION￨- models￨L￨NNS￨O￨- created￨L￨VBD￨O￨- until￨L￨IN￨O￨- now￨L￨RB￨DATE￨- have￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- from￨L￨IN￨O￨- wild￨L￨JJ￨O￨- birds￨L￨NNS￨O￨A to￨L￨TO￨O￨- poultry￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- consideration￨L￨NN￨O￨- of￨L￨IN￨O￨- spatio-temporal￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- importance￨L￨NN￨O￨- for￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- drivers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- epidemiologies￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- confounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- substantial￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨A in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- densities￨L￨NNS￨O￨- through￨L￨IN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DENV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- immunological￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- antibody-dependent￨L￨JJ￨O￨- enhancement￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- ADE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- temporary￨L￨JJ￨O￨- and/or￨L￨CC￨O￨- partial￨L￨JJ￨O￨- cross-immunity￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- independently￨L￨RB￨O￨- proposed￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- driving￨L￨VBG￨O￨- forces￨L￨NNS￨O￨- behind￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- '￨L￨''￨O￨- complex￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- that￨L￨WDT￨O￨- comprises￨L￨VBZ￨O￨- multi-annual￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- sequential￨L￨JJ￨O￨- replacement￨L￨NN￨O￨- of￨L￨IN￨O￨- dominant￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- these￨L￨DT￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- models￨L￨NNS￨O￨- qualitatively￨L￨RB￨O￨- capture￨L￨VBP￨O￨- dengue￨L￨NN￨O￨A 's￨L￨POS￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- across￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- observed￨L￨VBN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- serotype￨L￨NN￨O￨- distribution￨L￨NN￨O￨- within￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- host-population￨L￨NN￨O￨- structure￨L￨NN￨O￨- or￨L￨CC￨O￨- local￨L￨JJ￨O￨- ecological￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- can￨L￨MD￨O￨- create￨L￨VB￨O￨- short-lived￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- refuges￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- significantly￨L￨RB￨O￨- affect￨L￨VB￨O￨- pathogen￨L￨NN￨O￨- persistence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- derivatives￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- framework￨L￨NN￨O￨- have￨L￨VBP￨O￨- greatly￨L￨RB￨O￨- improved￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- important￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Arrival￨U￨NN￨O￨- times￨L￨NNS￨O￨- *￨L￨SYM￨O￨- discard￨L￨VB￨O￨- by￨L￨IN￨O￨- definition￨L￨NN￨O￨- many￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- usually￨L￨RB￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- well-defined￨L￨JJ￨O￨- distribution26￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- robust￨L￨JJ￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- starting￨L￨VBG￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- across￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A of￨L￨IN￨O￨- human￨L￨JJ￨O￨- contact￨L￨NN￨O￨- measured￨L￨VBN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- contexts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- work26￨L￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- non-stationarity￨L￨JJ￨O￨- and￨L￨CC￨O￨- burstiness￨L￨NN￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- noisy￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- arrival￨L￨NN￨O￨A times￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- shifting￨L￨VBG￨O￨- the￨L￨DT￨O￨- perspective￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- notion￨L￨NN￨O￨- of￨L￨IN￨O￨- wall-clock￨L￨JJ￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- node-specific￨L￨JJ￨O￨- “￨L￨``￨O￨- time￨L￨NN￨O￨- ”￨L￨''￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- node￨L￨NN￨O￨- activity￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- to￨L￨TO￨O￨- expose￨L￨VB￨O￨- a￨L￨DT￨O￨- clear￨L￨JJ￨O￨- and￨L￨CC￨O￨- robust￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- in￨L￨IN￨O￨- arrival￨L￨NN￨O￨- “￨L￨``￨O￨- times￨L￨NNS￨O￨- ”￨L￨''￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- durations￨L￨NNS￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- link￨L￨NN￨O￨- are￨L￨VBP￨O￨- conserved￨L￨VBN￨O￨- by￨L￨IN￨O￨- construction￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A correlations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- destroyed￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- inter-contact￨L￨JJ￨O￨- times￨L￨NNS￨O￨- differs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- aim￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A of￨L￨IN￨O￨- human￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- hierarchies￨L￨NNS￨O￨- of￨L￨IN￨O￨- null￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- generative￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- selectively￨L￨RB￨O￨- retain￨L￨VBP￨O￨- or￨L￨CC￨O￨- discard￨L￨VBP￨O￨- specific￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- arrival￨L￨NN￨O￨A times￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SI￨U￨NNP￨O￨- process￨L￨NN￨O￨- unfolding￨L￨VBG￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Keeping￨U￨VBG￨O￨- this￨L￨DT￨O￨- in￨L￨IN￨O￨- mind￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- ranking￨L￨NN￨O￨A method￨L￨NN￨O￨- ,￨L￨,￨O￨- named￨L￨VBN￨O￨- ClusterRank￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- influential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- directed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- on￨L￨IN￨O￨- information￨L￨NN￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +Besides￨U￨IN￨O￨- the￨L￨DT￨O￨- localization￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- another￨L￨DT￨O￨- distinguishable￨L￨JJ￨O￨- difference￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- above-mentioned￨L￨JJ￨O￨- diffusion-based￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨A coefficient￨L￨NN￨O￨- is￨L￨VBZ￨O￨- directly￨L￨RB￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- influence￨L￨NN￨O￨- in￨L￨IN￨O￨- ClusterRank￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- path￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- path￨L￨NN￨O￨- diversity￨L￨NN￨O￨- while￨L￨IN￨O￨- ranking￨L￨VBG￨O￨A the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- introduced￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- correction￨L￨NN￨O￨- factors￨L￨NNS￨O￨- correspondingly￨L￨RB￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- researches￨L￨VBZ￨O￨- show￨L￨NN￨O￨- that￨L￨IN￨O￨- top-degree￨L￨JJ￨O￨- ranking￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- cooperative￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- may￨L￨MD￨O￨- play￨L￨VB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- than￨L￨IN￨O￨- its￨L￨PRP$￨O￨- degree￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- FMD￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- prophylactic￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- outside￨L￨IN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- permitted￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- EU￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- reactive￨L￨JJ￨O￨- ring￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- alongside￨L￨IN￨O￨- animal￨L￨NN￨O￨- movement￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨- and￨L￨CC￨O￨- “￨L￨``￨O￨- stamping￨L￨VBG￨O￨- out￨L￨RP￨O￨- ”￨L￨''￨O￨- measures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- culling￨L￨NN￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- premises￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- farms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- had￨L￨VBD￨O￨- epidemiological￨L￨JJ￨O￨- contact￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- silent￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- potentially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- dangerous￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- DCs￨U￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- required￨L￨VBN￨O￨- under￨L￨IN￨O￨- EU￨U￨NNP￨ORGANIZATION￨- legislation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Commission￨U￨NN￨MISC￨- Regulation￨U￨NN￨MISC￨- No.￨U￨NN￨MISC￨- 2003/85/EC￨L￨NN￨MISC￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- parameter￨L￨NN￨O￨- set￨L￨VBN￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination-to-live￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- ’￨L￨''￨O￨- (￨L￨-LRB-￨O￨- VB￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- computed￨L￨VBN￨O￨- in￨L￨IN￨O￨- relative￨L￨JJ￨O￨- terms￨L￨NNS￨O￨- by￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- when￨L￨WRB￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- complement￨L￨NN￨O￨- to￨L￨TO￨O￨- routine￨L￨JJ￨O￨- mitigation￨L￨NN￨O￨- procedures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- NMB￨U￨NN￨O￨- +￨L￨CC￨O￨- IP/DC￨U￨NN￨O￨- culling￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- geometric￨L￨JJ￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- when￨L￨WRB￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- complement￨L￨NN￨O￨- to￨L￨TO￨O￨- routine￨L￨JJ￨O￨- mitigation￨L￨NN￨O￨- procedures￨L￨NNS￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- routine￨L￨JJ￨O￨- mitigation￨L￨NN￨O￨- procedures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- implemented￨L￨VBN￨O￨- alone￨L￨RB￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- facing￨L￨VBG￨O￨- a￨L￨DT￨O￨- FMD￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- following￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- :￨L￨:￨O￨- firstly￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- to￨L￨TO￨O￨- restrict￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- as￨L￨RB￨O￨- quickly￨L￨RB￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- ,￨L￨,￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- culling￨L￨NN￨O￨A of￨L￨IN￨O￨- all￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- animals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incursion￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- field￨L￨NN￨O￨- implementation￨L￨NN￨O￨- alter￨L￨VBP￨O￨- the￨L￨DT￨O￨- benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨A policy￨L￨NN￨O￨- against￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- FMD￨U￨NN￨O￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- transient￨L￨JJ￨O￨A population￨L￨NN￨O￨- allow￨L￨VBP￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨DATE￨- day￨L￨NN￨DATE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transients￨L￨NNS￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- the￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨- among￨L￨IN￨O￨- subpopulations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- heterogeneous￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- residents￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- transient￨L￨JJ￨O￨A subpopulation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- residents￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- synthetic￨L￨JJ￨O￨- population-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- resident￨L￨JJ￨O￨- and￨L￨CC￨O￨- transient￨L￨JJ￨O￨A activities￨L￨NNS￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- their￨L￨PRP$￨O￨- interactions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- probable￨L￨JJ￨O￨- vector￨L￨NN￨O￨A density￨L￨NN￨O￨- that￨L￨WDT￨O￨- caused￨L￨VBD￨O￨- the￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- quantified￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- vector￨L￨NN￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- on￨L￨IN￨O￨- vector￨L￨NN￨O￨- competence￨L￨NN￨O￨- .￨L￨.￨O￨- +Outbreaks￨U￨NNS￨O￨- occur￨L￨VBP￨O￨- when￨L￨WRB￨O￨- vector￨L￨NN￨O￨A density￨L￨NN￨O￨- exceeds￨L￨VBZ￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- ambient￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- level￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Density￨U￨NN￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- quantity￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- measure￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- differently￨L￨RB￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- vector￨L￨NN￨O￨A density￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- female￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- per￨L￨IN￨O￨- person￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MPP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- dengue￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- concern￨L￨NN￨O￨- in￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- at￨L￨IN￨O￨- present￨L￨JJ￨DATE￨- ,￨L￨,￨O￨- annual￨L￨JJ￨SET￨- mean￨L￨NN￨O￨- temperature￨L￨NN￨O￨- has￨L￨VBZ￨O￨- gradually￨L￨RB￨O￨- been￨L￨VBN￨O￨- increasing￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- Aedes￨U￨NNP￨O￨- albopictus￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨A ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- expanded￨L￨VBN￨O￨- its￨L￨PRP$￨O￨- infestation￨L￨NN￨O￨- range￨L￨NN￨O￨- northwards￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- decades￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- imported￨L￨VBN￨O￨- dengue￨L￨JJ￨O￨A cases￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- rise￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- re-emergence￨L￨NN￨O￨- in￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨A ,￨L￨,￨O￨- different￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- faced￨L￨VBD￨O￨- different￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- pandemic￨L￨NN￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- massively￨L￨RB￨O￨- produced￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- pandemic￨L￨NN￨O￨A was￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- mild￨L￨JJ￨O￨- to￨L￨TO￨O￨- moderate￨L￨JJ￨O￨- in￨L￨IN￨O￨- seriousness￨L￨NN￨O￨- ;￨L￨:￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- quarantines￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- recommended￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- began￨L￨VBD￨O￨- in￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- subtype￨L￨NN￨O￨- of￨L￨IN￨O￨- H1N1￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- pandemic￨L￨JJ￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- of￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 214￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- pandemic￨L￨NN￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- over￨L￨IN￨O￨- 18,449￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- include￨L￨VBP￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Number￨U￨NN￨O￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- and￨L￨CC￨O￨- sheep￨L￨NN￨O￨- farms￨L￨NNS￨O￨A ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Land￨U￨NN￨O￨- area￨L￨NN￨O￨- per￨L￨IN￨O￨- municipality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- square￨L￨JJ￨O￨- km￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Land￨U￨NN￨O￨- composition￨L￨NN￨O￨- variables￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- crop￨L￨NN￨O￨- land￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- quantifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- farms￨L￨NNS￨O￨A within￨L￨IN￨O￨- a￨L￨DT￨O￨- municipality￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- farms￨L￨NNS￨O￨- across￨L￨IN￨O￨- neighbouring￨L￨JJ￨O￨- municipalities￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- movement/transport￨L￨NN￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- restriction￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- movement￨L￨NN￨O￨- between￨L￨IN￨O￨- farms￨L￨NNS￨O￨A and/or￨L￨CC￨O￨- countries￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- BTV￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- farms￨L￨NNS￨O￨A in￨L￨IN￨O￨- Belgium￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- two￨L￨CD￨NUMBER￨- model-derived￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- metrics￨L￨NNS￨O￨A that￨L￨WDT￨O￨- quantify￨L￨VBP￨O￨- expectations￨L￨NNS￨O￨- for￨L￨IN￨O￨- typical￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- maximal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- disease-free￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- map￨L￨VBP￨O￨- these￨L￨DT￨O￨- metrics￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- vector￨L￨NN￨O￨- abundance￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- various￨L￨JJ￨O￨- land￨L￨NN￨O￨- uses￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- southern￨L￨JJ￨O￨- half￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Central￨U￨NNP￨ORGANIZATION￨- Valley￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- contains￨L￨VBZ￨O￨- very￨L￨RB￨O￨- high￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- livestock￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- primarily￨L￨RB￨O￨- dairy￨L￨NN￨O￨- cows￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- cattle￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- area￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- interspersed￨L￨VBN￨O￨- with￨L￨IN￨O￨- managed￨L￨VBN￨O￨- wetlands￨L￨NNS￨O￨- and￨L￨CC￨O￨- multicrop￨L￨JJ￨O￨- agriculture￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- produce￨L￨VB￨O￨- large￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- competent￨L￨JJ￨O￨- vectors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Culex￨U￨JJ￨MISC￨- tarsalis￨L￨NN￨MISC￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- 's￨L￨POS￨O￨- structure￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- extended￨L￨VBN￨O￨- in￨L￨IN￨O￨- several￨L￨JJ￨O￨- important￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- to￨L￨TO￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- accommodate￨L￨VB￨O￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- through￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- or￨L￨CC￨O￨- vector￨L￨NN￨O￨- movements￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- assess￨L￨VB￨O￨- potential￨L￨JJ￨O￨- control￨L￨NN￨O￨- methods￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- include￨L￨VBP￨O￨- humans￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- asymptomatic￨L￨JJ￨O￨- livestock￨L￨NN￨O￨A hosts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Mosquito￨U￨NN￨O￨- species￨L￨NNS￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- vectors￨L￨NNS￨O￨A of￨L￨IN￨O￨- RVFV￨U￨NN￨O￨- with￨L￨IN￨O￨- varying￨L￨VBG￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- efficiency￨L￨NN￨O￨- in￨L￨IN￨O￨- laboratory￨L￨NN￨O￨- settings￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- present￨L￨JJ￨DATE￨- throughout￨L￨IN￨O￨- much￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- U.S.￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- other￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- inadequately￨L￨RB￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- RVFV￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- that￨L￨WDT￨O￨- included￨L￨VBD￨O￨- livestock￨L￨NN￨O￨A hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- genera￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- ,￨L￨,￨O￨- Aedes￨U￨NNP￨O￨- and￨L￨CC￨O￨- Culex￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- respectively￨L￨RB￨O￨- were￨L￨VBD￨O￨- or￨L￨CC￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- capable￨L￨JJ￨O￨- vertically￨L￨RB￨O￨- transmitting￨L￨VBG￨O￨- RVFV￨U￨NN￨O￨- .￨L￨.￨O￨- +Compared￨U￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- homogeneously￨L￨RB￨O￨- mixing￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- increasing￨L￨VBG￨O￨A the￨L￨DT￨O￨- neighborhood￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- eliminate￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- if￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- decide￨L￨VBP￨O￨- whether￨L￨IN￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- by￨L￨IN￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risks￨L￨NNS￨O￨- from￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- driving￨L￨VBG￨O￨- force￨L￨NN￨O￨- increasingly￨L￨RB￨O￨- favors￨L￨VBZ￨O￨- organized￨L￨JJ￨O￨A states￨L￨NNS￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- negligible￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- occupation￨L￨NN￨O￨- in￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- common￨L￨JJ￨O￨- mechanism￨L￨NN￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- behind￨L￨IN￨O￨- the￨L￨DT￨O￨- dilution￨L￨NN￨O￨- effect￨L￨NN￨O￨- is￨L￨VBZ￨O￨- rather￨L￨RB￨O￨- simple￨L￨JJ￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- diversity￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- or￨L￨CC￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨A will￨L￨MD￨O￨- come￨L￨VB￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- competent￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- the￨L￨DT￨O￨- respective￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- dilution￨L￨NN￨O￨- or￨L￨CC￨O￨- amplification￨L￨NN￨O￨- will￨L￨MD￨O￨- occur￨L￨VB￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- very￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- vector￨L￨NN￨O￨- borne￨L￨VBD￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- incorporate￨L￨VB￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- preference￨L￨NN￨O￨A ,￨L￨,￨O￨- although￨L￨IN￨O￨- many￨L￨JJ￨O￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- significant￨L￨JJ￨O￨- preference￨L￨NN￨O￨- toward￨L￨IN￨O￨- certain￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- for￨L￨IN￨O￨- certain￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- explores￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- diversity￨L￨NN￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- transmission￨L￨NN￨O￨- ability￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- preference￨L￨NN￨O￨A ,￨L￨,￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- vector￨L￨NN￨O￨- preference￨L￨NN￨O￨A induces￨L￨VBZ￨O￨- heterogeneous￨L￨JJ￨O￨- biting￨L￨VBG￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- individuals￨L￨NNS￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- significantly￨L￨RB￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- ,￨L￨,￨O￨- field￨L￨NN￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Existing￨U￨VBG￨O￨- models￨L￨NNS￨O￨- also￨L￨RB￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- extreme￨L￨JJ￨O￨- obesity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- include￨L￨VB￨O￨- important￨L￨JJ￨O￨- moderators￨L￨NNS￨O￨- of￨L￨IN￨O￨- obesity￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨O￨- obesity￨L￨NN￨O￨- ,￨L￨,￨O￨- differential￨L￨JJ￨O￨- population￨L￨NN￨O￨- birth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- weight￨L￨NN￨O￨A regain￨L￨VB￨O￨- in￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- lost￨L￨VBN￨O￨- weight￨L￨NN￨O￨- .￨L￨.￨O￨- +Existing￨U￨VBG￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- obesity￨L￨NN￨O￨- trends￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- fully￨L￨RB￨O￨- answer￨L￨VB￨O￨- these￨L￨DT￨O￨- questions￨L￨NNS￨O￨- because￨L￨IN￨O￨- their￨L￨PRP$￨O￨- underlying￨L￨VBG￨O￨- models￨L￨NNS￨O￨- assume￨L￨VB￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- that￨L￨WDT￨O￨- obesity￨L￨NN￨O￨- prevalence￨L￨NN￨O￨A will￨L￨MD￨O￨- either￨L￨CC￨O￨- increase￨L￨VB￨O￨- without￨L￨IN￨O￨- bound￨L￨VBN￨O￨- or￨L￨CC￨O￨- will￨L￨MD￨O￨- continue￨L￨VB￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- and￨L￨CC￨O￨- eventually￨L￨RB￨O￨- plateau￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- existing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨- from￨L￨IN￨O￨- normal￨L￨JJ￨O￨- weight￨L￨NN￨O￨A to￨L￨TO￨O￨- overweight￨L￨JJ￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- obese￨L￨JJ￨O￨- classification￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- obesity￨L￨NN￨O￨- prevalence￨L￨NN￨O￨A after￨L￨IN￨O￨- input￨L￨NN￨O￨- of￨L￨IN￨O￨- country￨L￨NN￨O￨- specific￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- flexible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- developed￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- or￨L￨CC￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- predicted￨L￨VBD￨O￨- obesity￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- by￨L￨IN￨O￨- segregating￨L￨VBG￨O￨- normal￨L￨JJ￨O￨- weight￨L￨NN￨O￨A and￨L￨CC￨O￨- obese￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- compartments￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- usefulness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- exploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- recrudescence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- Hendra￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- confirmed￨L￨VBD￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- adequately￨L￨RB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- life￨L￨NN￨O￨- cycle￨L￨NN￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- breeding￨L￨NN￨O￨- ,￨L￨,￨O￨- pregnancy￨L￨NN￨O￨- ,￨L￨,￨O￨- birth￨L￨NN￨O￨- ,￨L￨,￨O￨- lactation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- pup￨L￨NN￨O￨- dependency￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- seasonal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- stage-class￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- pups￨L￨NNS￨O￨- ,￨L￨,￨O￨- juveniles￨L￨NNS￨O￨- ,￨L￨,￨O￨- sub-adults￨L￨NNS￨O￨- ,￨L￨,￨O￨- adults￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- stable￨L￨JJ￨O￨- age-class￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- implicitly￨L￨RB￨O￨- under￨L￨IN￨O￨- constant￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- which￨L￨WDT￨O￨- would￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- stability￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- regard￨L￨NN￨O￨- to￨L￨TO￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- Hendra￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- 0.0000476￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- latency￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- incubation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- period￨L￨NN￨O￨- lasting￨L￨JJ￨O￨A 6￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- lasting￨L￨VBG￨O￨- 7￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- for￨L￨IN￨O￨- pups￨L￨NNS￨O￨- birthed￨L￨VBN￨O￨- by￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨JJ￨O￨- mothers￨L￨NNS￨O￨- lasting￨L￨VBG￨O￨- from￨L￨IN￨O￨- 4￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- 6￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- most￨L￨JJS￨O￨- pups￨L￨NNS￨O￨- losing￨L￨VBG￨O￨- maternal￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- by￨L￨IN￨O￨- 5￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- recent￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- indicated￨L￨VBN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- Hendra￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- flying-fox￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- novel￨L￨JJ￨O￨- paramyxovirus￨L￨NN￨O￨- may￨L￨MD￨O￨- differ￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- acute￨L￨JJ￨O￨- ,￨L￨,￨O￨- self-limiting￨L￨JJ￨O￨- ,￨L￨,￨O￨- episodic￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- observed￨L￨VBN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- paramyxoviruses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- measles￨L￨FW￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- phocine￨L￨NN￨O￨- distemper￨L￨NN￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- rinderpest￨L￨NN￨O￨- virus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- recrudescence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- Hendra￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨A in￨L￨IN￨O￨- flying-fox￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- via￨L￨IN￨O￨- computer￨L￨NN￨O￨- simulation￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- integrates￨L￨VBZ￨O￨- published￨L￨VBN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- ecology￨L￨NN￨O￨- of￨L￨IN￨O￨- flying-foxes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ecology￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- Hendra￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- seroprevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- Hendra￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- spectacled￨L￨JJ￨O￨- flying-fox￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Pteropus￨U￨NN￨O￨- conspicillatus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- northern￨L￨JJ￨O￨- Australia￨U￨NNP￨COUNTRY￨- gradually￨L￨RB￨O￨- increased￨L￨VBD￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- two-year￨L￨JJ￨DURATION￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- endemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- logistic￨L￨JJ￨O￨A growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- besides￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- R￨U￨NN￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- meaning￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- mainly￨L￨RB￨O￨- study￨L￨VB￨O￨- their￨L￨PRP$￨O￨- threshold￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A which￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- invade￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- successfully￨L￨RB￨O￨- .￨L￨.￨O￨- +Noticing￨U￨VBG￨O￨- the￨L￨DT￨O￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- When￨U￨WRB￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- no￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- Let￨U￨VB￨O￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- r/m￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- →￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- m/r￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- k￨L￨NN￨O￨- for￨L￨IN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- t￨L￨NN￨O￨- →￨L￨NN￨O￨- +￨L￨CC￨O￨- ∞￨L￨NN￨O￨- ;￨L￨:￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- will￨L￨MD￨O￨- grow￨L￨VB￨O￨A and￨L￨CC￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- N￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- business-cycle￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- logistic￨L￨JJ￨O￨A population￨L￨NN￨O￨- growth￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨A A/H5N1￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- remain￨L￨VBP￨O￨- high￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- do￨L￨VBP￨O￨- the￨L￨DT￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- chickens￨L￨NNS￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- breeds￨L￨NNS￨O￨- of￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- ducks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- difficult￨L￨JJ￨O￨- and￨L￨CC￨O￨- urgent￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- dense￨L￨JJ￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- extensive￨L￨JJ￨O￨- backyard￨L￨NN￨O￨- poultry￨L￨NN￨O￨A rearing￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- repeated￨L￨VBN￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- A/H5N1￨U￨NN￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- no￨L￨DT￨O￨- or￨L￨CC￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- human￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Bangladesh￨U￨FW￨LOCATION￨- ,￨L￨,￨O￨- India￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- a￨L￨DT￨O￨- patch￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- uses￨L￨VBZ￨O￨- standard￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- addition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Twelve￨U￨CD￨NUMBER￨- other￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- have￨L￨VBP￨O￨- reported￨L￨VBN￨O￨A sporadic￨L￨JJ￨O￨- and￨L￨CC￨O￨- occasional￨L￨JJ￨O￨- human￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- 48￨L￨CD￨NUMBER￨- additional￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- have￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- reported￨L￨VBN￨O￨- spillover￨L￨NN￨O￨- to￨L￨TO￨O￨- people￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- backyard￨L￨NN￨O￨- poultry￨L￨NN￨O￨A rearing￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- ,￨L￨,￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- by￨L￨IN￨O￨- far￨L￨RB￨O￨- most￨L￨RBS￨O￨- costly￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- US$￨U￨$￨MONEY￨- 1,658￨L￨CD￨MONEY￨- to￨L￨TO￨O￨- US$￨U￨$￨MONEY￨- 8,274￨L￨CD￨MONEY￨- yields￨L￨NNS￨O￨- one￨L￨CD￨NUMBER￨- DALY￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Disability-adjusted￨U￨JJ￨MISC￨- life￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- gaining￨L￨VBG￨O￨- that￨L￨DT￨O￨- same￨L￨JJ￨O￨- year￨L￨NN￨DURATION￨- through￨L￨IN￨O￨- promoting￨L￨VBG￨O￨- hand-hygiene￨L￨JJ￨O￨- need￨L￨NN￨O￨- US$￨U￨$￨MONEY￨- 3.35￨L￨CD￨MONEY￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- hand-hygiene￨L￨JJ￨O￨- the￨L￨DT￨O￨- cheapest￨L￨JJS￨O￨- among￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- interventions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +So￨U￨IN￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- balance￨L￨NN￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- may￨L￨MD￨O￨- significantly￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- cost￨L￨NN￨O￨- .￨L￨.￨O￨- +Well￨U￨RB￨O￨- strategic￨L￨JJ￨O￨- deployment￨L￨NN￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A intervention/interventions￨L￨NNS￨O￨- in￨L￨IN￨O￨- Zimbabwe￨U￨NNP￨COUNTRY￨- may￨L￨MD￨O￨- reduce￨L￨VB￨O￨- future￨L￨JJ￨DATE￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- projected￨L￨VBN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- interventions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- debatable￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- substantial￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- provinces￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- Manicaland￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Mashonaland￨U￨NNP￨LOCATION￨- West￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Masvingo￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Midlands￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 09￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- indicate￨L￨VBP￨O￨- a￨L￨DT￨O￨- plausible￨L￨JJ￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- in￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- provinces￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- provinces￨L￨NNS￨O￨- of￨L￨IN￨O￨- Zimbabwe￨U￨NNP￨COUNTRY￨- experienced￨L￨VBD￨O￨- a￨L￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 2101￨L￨CD￨DATE￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A cases￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- to￨L￨TO￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- confidence￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- broad￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- transmission￨L￨NN￨O￨A potential￨L￨NN￨O￨A of￨L￨IN￨O￨- A/H7N9￨U￨NN￨O￨- appears￨L￨VBZ￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- zoonotic￨L￨JJ￨O￨- threats￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A/H5N1￨U￨NN￨O￨- ,￨L￨,￨O￨- swine￨L￨NNS￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- H3N2sw￨U￨NN￨O￨- and￨L￨CC￨O￨- Nipah￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Estimates￨U￨NNS￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- A/H7N9￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- were￨L￨VBD￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- sustained￨L￨JJ￨O￨- human-to-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- remained￨L￨VBD￨O￨- near￨L￨IN￨O￨- 0.1￨L￨CD￨NUMBER￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- broad￨L￨JJ￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- credible￨L￨JJ￨O￨- intervals￨L￨NNS￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0.01￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 0.49￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- approach￨L￨NN￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Exposed-Infectious-Removed￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- fitted￨L￨VBD￨O￨- to￨L￨TO￨O￨- daily￨L￨JJ￨SET￨- case￨L￨NN￨O￨A data￨L￨NNS￨O￨A to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- A/H7N9￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Transmission￨U￨NNP￨MISC￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A A/H7N9￨U￨NN￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- ChinaGerardo￨U￨NNP￨O￨- Chowell1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Lone￨U￨NNP￨O￨- Simonsen1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Sherry￨U￨NNP￨PERSON￨- Towers2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Mark￨U￨NNP￨O￨- A￨U￨NNP￨O￨- Miller1￨U￨NN￨O￨- and￨L￨CC￨O￨- Cécile￨U￨NNP￨O￨- Viboud1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 11:214￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Chowell￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- On￨U￨IN￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- human￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- novel￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A/H7N9￨U￨NN￨O￨- virus￨L￨NN￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- Eastern￨U￨NNP￨LOCATION￨- China￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- used￨L￨VBD￨O￨- alternative￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- R￨U￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- individual-level￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- prior￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A potential￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A/H7N9￨U￨NN￨O￨- with￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- recent￨L￨JJ￨O￨- zoonoses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- evaluate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- certain￨L￨JJ￨O￨- farm￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- –￨L￨:￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- turnover￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- effort￨L￨NN￨O￨- –￨L￨:￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- shaped￨L￨VBN￨O￨- by￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- incentives￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- how￨L￨WRB￨O￨- culling￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- market￨L￨NN￨O￨- price￨L￨NN￨O￨- can￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- HPAI￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- combine￨L￨VBP￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- profit￨L￨NN￨O￨- maximization￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- farmer￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- farmer￨L￨NN￨TITLE￨- ’s￨L￨POS￨O￨- optimal￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- subsequently￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- government￨L￨NN￨O￨- ’s￨L￨POS￨O￨- poultry￨L￨NN￨O￨A procurement￨L￨NN￨O￨- policy￨L￨NN￨O￨- on￨L￨IN￨O￨- poultry￨L￨NN￨O￨- production￨L￨NN￨O￨- and￨L￨CC￨O￨- HPAI￨U￨NN￨ORGANIZATION￨- risks￨L￨NNS￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemiological￨L￨JJ￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Susceptible￨U￨NNP￨O￨- –￨L￨:￨O￨- Infected￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- poultry￨L￨NN￨O￨A on￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- farm￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- uninfected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- healthy￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- poultry￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- sick￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- poultry￨L￨NN￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- price￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- fundamental￨L￨JJ￨O￨- to￨L￨TO￨O￨- policy￨L￨NN￨O￨- optimization￨L￨NN￨O￨- –￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- government￨L￨NN￨O￨- should￨L￨MD￨O￨- compensate￨L￨VB￨O￨- farmers￨L￨NNS￨O￨- for￨L￨IN￨O￨- culled￨L￨JJ￨O￨- poultry￨L￨NN￨O￨A and/or￨L￨CC￨O￨- the￨L￨DT￨O￨- effort￨L￨NN￨O￨- to￨L￨TO￨O￨- expend￨L￨VB￨O￨- on￨L￨IN￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- parameter￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- farmers￨L￨NNS￨O￨- procure￨L￨VBP￨O￨- chicks/eggs￨L￨NNS￨O￨- to￨L￨TO￨O￨- re-stock￨L￨VB￨O￨- their￨L￨PRP$￨O￨- farms￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- non-infected￨L￨JJ￨O￨- poultry￨L￨NN￨O￨A are￨L￨VBP￨O￨- born￨L￨VBN￨O￨- ;￨L￨:￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- farm￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- poultry￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- farm￨L￨NN￨O￨- .￨L￨.￨O￨- +1e1￨L￨SYM￨O￨- -￨L￨:￨O￨- e4￨L￨NN￨O￨- and￨L￨CC￨O￨- S5e1￨U￨NN￨O￨- -￨L￨:￨O￨- e3￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- for￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- hence￨L￨RB￨O￨- these￨L￨DT￨O￨- systems￨L￨NNS￨O￨- develop￨L￨VBP￨O￨- heterogeneous￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- fat-tailed￨L￨JJ￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨- but￨L￨CC￨O￨- a￨L￨DT￨O￨- bounded￨L￨VBN￨O￨A P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +1b1￨L￨SYM￨O￨- -￨L￨:￨O￨- c4￨L￨NN￨O￨- and￨L￨CC￨O￨- S5b1￨U￨NN￨O￨- -￨L￨:￨O￨- c3￨L￨NN￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- impact￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- a￨L￨DT￨O￨- seemingly￨L￨RB￨O￨- inconsistent￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- :￨L￨:￨O￨- for￨L￨IN￨O￨- ε￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- bounded￨L￨VBN￨O￨A when￨L￨WRB￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- bounded￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Erdős-Rényi￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- fat-tailed￨L￨NN￨O￨- when￨L￨WRB￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- fat-tailed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- scale-free￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- always￨L￨RB￨O￨- bounded￨L￨VBN￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- and￨L￨CC￨O￨- both￨L￨DT￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- always￨L￨RB￨O￨- bounded￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- G￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- scale-free￨L￨NN￨O￨- ,￨L￨,￨O￨- Erdős-Rényi￨U￨NNP￨O￨- or￨L￨CC￨O￨- networks￨L￨NNS￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- data￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- ν￨L￨NN￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- only￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨A laws￨L￨NNS￨O￨- that￨L￨WDT￨O￨- govern￨L￨VBP￨O￨- these￨L￨DT￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Protein￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- uniform￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨- ,￨L￨,￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- bounded￨L￨VBN￨O￨A P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- measurements￨L￨NNS￨O￨- support￨L￨VBP￨O￨- this￨L￨DT￨O￨- :￨L￨:￨O￨- we￨L￨PRP￨O￨- obtained￨L￨VBD￨O￨- G￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- Table￨U￨NNP￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- case￨L￨NN￨O￨- finding￨L￨NN￨O￨A that￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- G￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ∼￨L￨CD￨NUMBER￨- G￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figs￨U￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- function￨L￨NN￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- =￨L￨JJ￨O￨- βSI￨L￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- +￨L￨CC￨O￨- αI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- to￨L￨TO￨O￨- certain￨L￨JJ￨O￨- communicable￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- βSI￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- +￨L￨CC￨O￨- αI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- inhibition￨L￨NN￨O￨- effect￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A increases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- works￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- formulate￨L￨VB￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- constant￨L￨JJ￨O￨- immigration￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- classical￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨A is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Wang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ruan￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- considered￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- capacity￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨A .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- Cannon￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- reviewed￨L￨VBN￨O￨- different￨L￨JJ￨O￨- metrics￨L￨NNS￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- resource￨L￨NN￨O￨- optimization￨L￨NN￨O￨- problems￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- objectives￨L￨NNS￨O￨A by￨L￨IN￨O￨- decision-makers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- maximizing￨L￨VBG￨O￨- detection￨L￨NN￨O￨- ,￨L￨,￨O￨- minimizing￨L￨VBG￨O￨- detection￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- maximizing￨L￨VBG￨O￨- benefits￨L￨NNS￨O￨- from￨L￨IN￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- generic￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- for￨L￨IN￨O￨- setting￨L￨VBG￨O￨- up￨L￨RP￨O￨- each￨L￨DT￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Put￨U￨VB￨O￨- differently￨L￨RB￨O￨- ,￨L￨,￨O￨- decisions￨L￨NNS￨O￨- by￨L￨IN￨O￨- policymakers￨L￨NNS￨O￨- in￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- programs￨L￨NNS￨O￨A will￨L￨MD￨O￨- have￨L￨VB￨O￨- an￨L￨DT￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- producers￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- actors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- agri-food￨L￨JJ￨O￨- chain￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- can￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- consequently￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- Hadorn￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Stärk￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- recently￨L￨RB￨DATE￨- contrasted￨L￨VBD￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- and￨L￨CC￨O￨- passive￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- decision-tree￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- capture￨L￨VB￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- objectives￨L￨NNS￨O￨A could￨L￨MD￨O￨- change￨L￨VB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- failing￨L￨VBG￨O￨- to￨L￨TO￨O￨- control￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- changes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Rather￨U￨RB￨O￨- ,￨L￨,￨O￨- surveillance￨L￨NN￨O￨- programs￨L￨NNS￨O￨A are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- analyzed￨L￨VBN￨O￨- in￨L￨IN￨O￨- more￨L￨JJR￨O￨- broad￨L￨JJ￨O￨- terms￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- mitigation￨L￨NN￨O￨- options￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10-15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- in￨L￨IN￨O￨- benefit-cost￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- using￨L￨VBG￨O￨- economic￨L￨JJ￨O￨- welfare￨L￨NN￨O￨- indicators￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- producer￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- consumer￨L￨NN￨O￨- surplus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Surveillance￨U￨NN￨O￨- programs￨L￨NNS￨O￨- will￨L￨MD￨O￨- differ￨L￨VB￨O￨- in￨L￨IN￨O￨- nature￨L￨NN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- objectives￨L￨NNS￨O￨A and￨L￨CC￨O￨- goals￨L￨NNS￨O￨- of￨L￨IN￨O￨- decision￨L￨NN￨O￨- makers￨L￨NNS￨O￨- themselves￨L￨PRP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- address￨L￨VB￨O￨- these￨L￨DT￨O￨- gaps￨L￨NNS￨O￨- about￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- scales￨L￨NNS￨O￨A for￨L￨IN￨O￨- measuring￨L￨VBG￨O￨- and￨L￨CC￨O￨- modeling￨L￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- took￨L￨VBD￨O￨- a￨L￨DT￨O￨- reductionist￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- and￨L￨CC￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- ecological￨L￨JJ￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- encounters￨L￨NNS￨O￨- between￨L￨IN￨O￨- adult￨L￨JJ￨O￨- female￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- vertebrate￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- relatively￨L￨RB￨O￨- coarse￨L￨JJ￨O￨- scales￨L￨NNS￨O￨A ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- “￨L￨``￨O￨- hotspots￨L￨NNS￨O￨- ”￨L￨''￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- at￨L￨IN￨O￨- finer￨L￨JJR￨TITLE￨- scales￨L￨NNS￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- biting￨L￨VBG￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- highly￨L￨RB￨O￨- skewed￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- biting￨L￨VBG￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- gets￨L￨VBZ￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- bites￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Theory￨U￨NNP￨O￨- and￨L￨CC￨O￨- practice￨L￨NN￨O￨- for￨L￨IN￨O￨- mosquito-borne￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- thus￨L￨RB￨O￨- requires￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- scales￨L￨NNS￨O￨A that￨L￨WDT￨O￨- characterize￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- ubiquitous￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- mosquito-borne￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨A transmission￨L￨NN￨O￨A rarely￨L￨RB￨O￨- consider￨L￨VB￨O￨- these￨L￨DT￨O￨- complexities￨L￨NNS￨O￨- and￨L￨CC￨O￨- usually￨L￨RB￨O￨- assume￨L￨VBP￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Ross-Macdonald￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- well-mixed￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨A population￨L￨NN￨O￨A of￨L￨IN￨O￨- indeterminate￨L￨JJ￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- scales￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- moment￨L￨NN￨O￨A and￨L￨CC￨O￨- first￨L￨JJ￨ORDINAL￨- moment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- mean￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- k.￨L￨VBP￨O￨- On￨U￨IN￨O￨- both￨L￨DT￨O￨- static￨L￨JJ￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- diverging￨L￨VBG￨O￨- variance￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemics￨L￨NNS￨O￨- die￨L￨VBP￨O￨- out￨L￨RP￨O￨- only￨L￨RB￨O￨- for￨L￨IN￨O￨- very￨L￨RB￨O￨- small￨L￨JJ￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- vanishing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- β￨L￨VBP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- framework￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- with￨L￨IN￨O￨- explicit￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- early￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- expansion￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproductive￨L￨JJ￨O￨A ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- without￨L￨IN￨O￨- requiring￨L￨VBG￨O￨- strong￨L￨JJ￨O￨- simplifying￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- weights￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- also￨L￨RB￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- time￨L￨NN￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A prevalence￨L￨NN￨O￨A and￨L￨CC￨O￨- contact￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- generating￨L￨VBG￨O￨- functions￨L￨NNS￨O￨- –￨L￨:￨O￨- PGFs￨U￨NNS￨O￨- –￨L￨:￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- striking￨L￨JJ￨O￨- result￨L￨NN￨O￨- is￨L￨VBZ￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- heterogeneous￨L￨JJ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- rapid￨L￨JJ￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- further￨L￨JJ￨O￨- limitation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- all￨L￨DT￨O￨- variables￨L￨NNS￨O￨- are￨L￨VBP￨O￨- dealt￨L￨VBN￨O￨- with￨L￨IN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- additively￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- explanatory￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- right￨L￨JJ￨O￨- side￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- equation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whether￨L￨IN￨O￨- endogenous￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- genes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- individual-level￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- education￨L￨NN￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- neighborhood-level￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- suitability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- school-level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- education￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- policy-level￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- forth￨L￨RB￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- integrate￨L￨VB￨O￨- the￨L￨DT￨O￨- growing￨L￨VBG￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- multilevel￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- feedback￨L￨NN￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- how￨L￨WRB￨O￨- specific￨L￨JJ￨O￨- policy￨L￨NN￨O￨A interventions￨L￨NNS￨O￨- could￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- and￨L￨CC￨O￨- maintenance￨L￨NN￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- inequalities￨L￨NNS￨O￨- ,￨L￨,￨O￨- simulation￨L￨NN￨O￨A models￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- new￨L￨JJ￨O￨- options￨L￨NNS￨O￨- for￨L￨IN￨O￨- policy￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- simulation￨L￨NN￨O￨A models￨L￨NNS￨O￨A developed￨L￨VBD￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- or￨L￨CC￨O￨- modify￨L￨VB￨O￨- socioeconomic￨L￨JJ￨O￨- inequalities￨L￨NNS￨O￨- in￨L￨IN￨O￨- health￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- simulation￨L￨NN￨O￨A models￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- developed￨L￨VBN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- socioeconomic￨L￨JJ￨O￨- inequalities￨L￨NNS￨O￨- in￨L￨IN￨O￨- health￨L￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- extensively￨L￨RB￨O￨- used￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- susceptible-exposed-infectious-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- after￨L￨IN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pass￨L￨VBP￨O￨- through￨L￨IN￨O￨- an￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- latent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- become￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- finally￨L￨RB￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- pool￨L￨NN￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- simultaneously￨L￨RB￨O￨- recover￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- die￨L￨VB￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- acquire￨L￨VB￨O￨- permanent￨L￨JJ￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- infecting￨L￨VBG￨O￨- strain￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2011￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- biologically￨L￨RB￨O￨- realistic￨L￨JJ￨O￨- reinfection￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- two￨L￨CD￨NUMBER￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- retained￨L￨VBN￨O￨- :￨L￨:￨O￨- some￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- with￨L￨IN￨O￨- either￨L￨CC￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- or￨L￨CC￨O￨- deficient￨L￨JJ￨O￨- humoral￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A were￨L￨VBD￨O￨- reinfected￨L￨VBN￨O￨- following￨L￨VBG￨O￨- rapid￨L￨JJ￨O￨- re-exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- strain￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- humoral￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- antibody-mediated￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- immune￨L￨JJ￨O￨A response￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- provides￨L￨VBZ￨O￨- long-term￨L￨JJ￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- infecting￨L￨VBG￨O￨- strain￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- takes￨L￨VBZ￨O￨- several￨L￨JJ￨DURATION￨- weeks￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- efficient￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- host￨L￨NN￨TITLE￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- protective￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- as￨L￨IN￨O￨- some￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- show￨L￨VBP￨O￨- high￨L￨JJ￨O￨- antibody￨L￨NN￨O￨A titres￨L￨NNS￨O￨- shortly￨L￨RB￨O￨- after￨L￨IN￨O￨- recovery￨L￨NN￨O￨- whereas￨L￨IN￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- fail￨L￨VBP￨O￨- to￨L￨TO￨O￨- reach￨L￨VB￨O￨- a￨L￨DT￨O￨- protective￨L￨JJ￨O￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- phylogeny￨L￨NN￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- sequences￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- putative￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- pair￨L￨NN￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- sequences￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- background￨L￨NN￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- matching￨L￨JJ￨O￨- geographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- risk-behavior￨L￨JJ￨O￨- profile￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- putative￨L￨JJ￨O￨- donor￨L￨NN￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- distant￨L￨JJ￨O￨- in￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨- terms￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- recipient￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- problems￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- ,￨L￨,￨O￨- relatively￨L￨RB￨O￨- little￨L￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- performed￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- potential￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- -￨L￨:￨O￨- i.e.￨L￨FW￨O￨- understanding￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- -￨L￨:￨O￨- using￨L￨VBG￨O￨- population-level￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- collected￨L￨VBN￨O￨A for￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- or￨L￨CC￨O￨- surveillance￨L￨NN￨O￨- purposes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- similarity￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- pair￨L￨NN￨O￨A depends￨L￨VBZ￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- other￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- since￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- immunological￨L￨JJ￨O￨- pressure￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- substitution￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- within￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- substitution￨L￨NN￨O￨- rate￨L￨NN￨O￨- changes￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- within￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- rapid￨L￨JJ￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- transmission￨L￨NN￨O￨- sources￨L￨NNS￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- complete￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- every￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- phylogeny￨L￨NN￨O￨A .￨L￨.￨O￨- +Provided￨U￨VBN￨O￨- a￨L￨DT￨O￨- realistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- pathogen￨L￨NN￨O￨- sequences￨L￨NNS￨O￨A diverge￨L￨VBP￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- consensus￨L￨NN￨O￨- sequence￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- recipient￨L￨JJ￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- diverged￨L￨VBD￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- span￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- putative￨L￨JJ￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- latifundia￨L￨NN￨O￨- formation￨L￨NN￨O￨- that￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- land￨L￨NN￨O￨A use￨L￨NN￨O￨- change￨L￨NN￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- land-use￨L￨NN￨O￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- forest￨L￨NN￨O￨- ,￨L￨,￨O￨- agricultural￨L￨JJ￨O￨- land￨L￨NN￨O￨- and￨L￨CC￨O￨- land￨L￨NN￨O￨- in￨L￨IN￨O￨- recovery￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- pre-capitalist￨L￨JJ￨O￨- trade￨L￨NN￨O￨- of￨L￨IN￨O￨- land￨L￨NN￨O￨- in￨L￨IN￨O￨- recovery￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- additional￨L￨JJ￨O￨- insight￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- deforestation￨L￨NN￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- endemicity￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- formation￨L￨NN￨O￨- of￨L￨IN￨O￨- latifundia￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- accumulation￨L￨NN￨O￨- of￨L￨IN￨O￨- land￨L￨NN￨O￨A tenure￨L￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- landowners￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- pattern￨L￨NN￨O￨- observed￨L￨VBD￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Agro-Pontino￨U￨NNP￨MISC￨- Romano￨U￨NNP￨MISC￨- for￨L￨IN￨O￨- centuries￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- land￨L￨NN￨O￨A cover￨L￨NN￨O￨- is￨L￨VBZ￨O￨- primarily￨L￨RB￨O￨- forested￨L￨VBN￨O￨- ,￨L￨,￨O￨- land￨L￨NN￨O￨- tenure￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- redistributed￨L￨VBN￨O￨- for￨L￨IN￨O￨- agricultural￨L￨JJ￨O￨- exploitation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- repeated￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- agricultural￨L￨JJ￨O￨- exploitation￨L￨NN￨O￨- ,￨L￨,￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- latifundia￨L￨NN￨O￨- formation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- debilitating￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- farmers￨L￨NNS￨O￨- reduce￨L￨VB￨O￨- their￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- harvest￨L￨VB￨O￨- crops￨L￨NNS￨O￨- and￨L￨CC￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- sale￨L￨NN￨O￨- or￨L￨CC￨O￨- abandonment￨L￨NN￨CRIMINAL_CHARGE￨- and￨L￨CC￨O￨- adjudication￨L￨NN￨O￨- of￨L￨IN￨O￨- land￨L￨NN￨O￨A by￨L￨IN￨O￨- healthier￨L￨JJR￨O￨- and/or￨L￨CC￨O￨- wealthier￨L￨JJR￨O￨- landowners￨L￨NNS￨O￨- that￨L￨WDT￨O￨- will￨L￨MD￨O￨- underutilize￨L￨VB￨O￨- land￨L￨NN￨O￨- as￨L￨IN￨O￨- latifundia￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- large￨L￨JJ￨O￨- states￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- exploitation￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- landmass￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- require￨L￨VBP￨O￨- the￨L￨DT￨O￨- labor￨L￨NN￨O￨- of￨L￨IN￨O￨- workers￨L￨NNS￨O￨- who￨L￨WP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- own￨L￨VB￨O￨- the￨L￨DT￨O￨- land￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- and￨L￨CC￨O￨- equal￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- land￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- land￨L￨NN￨O￨- use￨L￨NN￨O￨- “￨L￨``￨O￨- states￨L￨NNS￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- among￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- landowners￨L￨NNS￨O￨- which￨L￨WDT￨O￨- get￨L￨VBP￨O￨- different￨L￨JJ￨O￨- utilities￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- land￨L￨NN￨O￨- they￨L￨PRP￨O￨- own￨L￨VBP￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +Salathe￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Jones￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- bridge￨L￨NN￨O￨A finder￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CBF￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- to￨L￨TO￨O￨- search￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- bridge￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- based￨L￨VBN￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- local￨L￨JJ￨O￨- structural￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- efficient￨L￨JJ￨O￨- than￨L￨IN￨O￨- immunization￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- targeting￨L￨VBG￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- hubs￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- acquaintance￨L￨NN￨O￨- immunization￨L￨NN￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- henceforth￨L￨NN￨O￨- labeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- ACQ￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- random￨L￨JJ￨O￨- acquaintances￨L￨NNS￨O￨- of￨L￨IN￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- immunized￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- search￨L￨NN￨O￨A algorithms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- bridge￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- community￨L￨NN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- crucial￨L￨JJ￨O￨- in￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Community￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- typically￨L￨RB￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- weak￨L￨JJ￨O￨- ties￨L￨NNS￨O￨- originating￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- bridge￨L￨NN￨O￨A node￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- bridge￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- were￨L￨VBD￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- important￨L￨JJ￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- hubs￨L￨NNS￨O￨- in￨L￨IN￨O￨- diffusing￨L￨VBG￨O￨- information￨L￨NN￨O￨- through￨L￨IN￨O￨- community￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- self-initiated￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- classified￨L￨VBN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- that￨L￨WDT￨O￨- induces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- either￨L￨CC￨O￨- local￨L￨JJ￨O￨- or￨L￨CC￨O￨- global￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- prevalence￨L￨NN￨O￨- based￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- belief￨L￨NN￨O￨- based￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- include￨L￨VB￨O￨- modifications￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- modifications￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- prophylaxis￨L￨FW￨O￨- procedures￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- modifications￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- increased￨L￨VBN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨A hypothesis￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- it￨L￨PRP￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- regulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- age-dependent￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- designed￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- those￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- ,￨L￨,￨O￨- indeed￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨- and￨L￨CC￨O￨- fear￨L￨NN￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- media￨L￨NNS￨O￨- campaign￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- published￨L￨VBN￨O￨- by￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- individual￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨A changes￨L￨NNS￨O￨A ,￨L￨,￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Ref.s￨U￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- lattice￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Ref.s￨U￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- adaptive￨L￨JJ￨O￨- restrictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- alter￨L￨VBP￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- already￨L￨RB￨O￨- included￨L￨VBN￨O￨- .￨L￨.￨O￨- +Previously￨U￨RB￨DATE￨- ,￨L￨,￨O￨- model-based￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- averted￨L￨VBN￨O￨- through￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- response￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- setting￨L￨NN￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- use￨L￨VBP￨O￨- simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- nonselective￨L￨JJ￨O￨- campaign￨L￨NN￨O￨A versus￨L￨CC￨O￨- targeted￨L￨VBN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- before￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- CR￨U￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- age￨L￨NN￨O￨- classes￨L￨NNS￨O￨- A￨U￨DT￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- is￨L￨VBZ￨O￨- Consider￨U￨VB￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨A targeting￨L￨VBG￨O￨- only￨L￨RB￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- age￨L￨NN￨O￨- class￨L￨NN￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- immunizes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- immune￨L￨JJ￨O￨- and￨L￨CC￨O￨- nonimmune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- vaccinated￨L￨VBN￨O￨- in￨L￨IN￨O￨- proportion￨L￨NN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- representations￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- of￨L￨IN￨O￨- nonimmune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- should￨L￨MD￨O￨- equal￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- coverage￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- nonselective￨L￨JJ￨O￨- campaign￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- accurate￨L￨JJ￨O￨- and￨L￨CC￨O￨- reliable￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- representing￨L￨VBG￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- recursively￨L￨RB￨O￨- optimized￨L￨VBN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- ensemble￨L￨NN￨O￨A data￨L￨NNS￨O￨- assimilation￨L￨NN￨O￨- technique￨L￨NN￨O￨- and￨L￨CC￨O￨- real-time￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +Those￨U￨DT￨O￨- previous￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨A for￨L￨IN￨O￨- New￨U￨NNP￨CITY￨- York￨U￨NNP￨CITY￨- City￨U￨NNP￨CITY￨- were￨L￨VBD￨O￨- generated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- humidity-forced￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Flu￨U￨NNP￨CAUSE_OF_DEATH￨- Trends￨U￨NNPS￨O￨- (￨L￨-LRB-￨O￨- GFT￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- EAKF￨U￨NN￨MISC￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- perform￨L￨VB￨O￨- a￨L￨DT￨O￨- forecast￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 200-member￨L￨JJ￨O￨- ensemble￨L￨NN￨O￨A of￨L￨IN￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- simulations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- numerically￨L￨RB￨O￨- integrated￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- location￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- New￨U￨NNP￨CITY￨- York￨U￨NNP￨CITY￨- City￨U￨NNP￨CITY￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- assimilation￨L￨NN￨O￨- of￨L￨IN￨O￨- observations￨L￨NNS￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- forecast￨L￨NN￨O￨- essentially￨L￨RB￨O￨- optimizes￨L￨VBZ￨O￨- the￨L￨DT￨DATE￨- future￨L￨JJ￨DATE￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ensemble￨L￨NN￨O￨A to￨L￨TO￨O￨- better￨L￨JJR￨O￨- match￨L￨NN￨O￨- the￨L￨DT￨O￨- evolving￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- retrospective￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- for￨L￨IN￨O￨- New￨U￨NNP￨CITY￨- York￨U￨NNP￨CITY￨- City￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- a￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- ensemble￨L￨NN￨O￨A predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- metric￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relatively￨L￨RB￨O￨- slow￨L￨JJ￨O￨- early￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- clustering￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- many￨L￨JJ￨O￨- short￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- super￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- people￨L￨NNS￨O￨- infecting￨L￨VBG￨O￨- many￨L￨JJ￨O￨- more￨L￨RBR￨O￨- others￨L￨NNS￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- person￨L￨NN￨O￨- do￨L￨VBP￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- attributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- broad￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- degree￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- basic￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- :￨L￨:￨O￨- Networks￨U￨NNP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- power-law￨L￨NN￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- Methods￨U￨NNS￨O￨- section￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- most￨L￨JJS￨O￨- (￨L￨-LRB-￨O￨- perhaps￨L￨RB￨O￨- all￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨A time￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- per-contact-transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- λ￨L￨NN￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- λ-value￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- study￨L￨VB￨O￨- extinction￨L￨NN￨O￨A times￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- various￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- use￨L￨VBP￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Erdős-Rényi￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- much￨L￨JJ￨O￨- narrower￨L￨JJR￨O￨- Poisson￨U￨NNP￨PERSON￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- Methods￨U￨NNS￨O￨- section￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Contact￨U￨NN￨O￨- network￨L￨NN￨O￨A epidemiology￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- overcome￨L￨VB￨O￨- these￨L￨DT￨O￨- limitations￨L￨NNS￨O￨- by￨L￨IN￨O￨- explicitly￨L￨RB￨O￨- modeling￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- graph￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- intrinsic￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- and￨L￨CC￨O￨- structural￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Earlier￨U￨JJR￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨- setting￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- start￨L￨NN￨O￨- with￨L￨IN￨O￨- limited￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- validate￨L￨VBP￨O￨- the￨L￨DT￨O￨- HCW￨U￨NN￨O￨- networks￨L￨NNS￨O￨- constructed￨L￨VBN￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- EMR￨U￨NN￨ORGANIZATION￨- data￨L￨NNS￨O￨A using￨L￨VBG￨O￨A a￨L￨DT￨O￨- 10-day￨L￨JJ￨DURATION￨- long￨L￨JJ￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨- network￨L￨NN￨O￨- deployment￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Medical￨U￨NNP￨O￨- Intensive￨U￨NNP￨O￨- Care￨U￨NNP￨O￨- Unit￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- MICU￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- UIHC￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- vertical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- impulsive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- newborns￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- removed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- newborns￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- which￨L￨WDT￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- vertical￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- delayed￨L￨VBN￨O￨- SEIR￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨A ,￨L￨,￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +τ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- βe￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- +￨L￨CC￨O￨- αI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- surviving￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- τ￨L￨NN￨O￨- and￨L￨CC￨O￨- becoming￨L￨VBG￨O￨- infective￨L￨JJ￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- available￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- when￨L￨WRB￨O￨- case￨L￨NN￨O￨- counts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- aggregated￨L￨VBN￨O￨- to￨L￨TO￨O￨- reflect￨L￨VB￨O￨- likely￨L￨JJ￨O￨- generation￨L￨NN￨O￨A times￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- readily￨L￨RB￨O￨- calculated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- importance￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- estimated￨L￨VBN￨O￨- empirically￨L￨RB￨O￨- for￨L￨IN￨O￨- novel￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- this￨L￨DT￨O￨- simple￨L￨JJ￨O￨- difference￨L￨NN￨O￨- equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- fit￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- IDEA￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- varying￨L￨VBG￨O￨- orders￨L￨NNS￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- under-reporting￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- multiple￨L￨JJ￨O￨- waves￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- generating￨L￨VBG￨O￨- empirical￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- and￨L￨CC￨O￨- d￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- via￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- manipulated￨L￨VBN￨O￨- algebraically￨L￨RB￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- tmax￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨A where￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- effectively￨L￨RB￨O￨- over￨L￨RB￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- extends￨L￨VBZ￨O￨- previous￨L￨JJ￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- analyzed￨L￨VBN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- decision￨L￨NN￨O￨A makers￨L￨NNS￨O￨- influences￨L￨VBZ￨O￨- optimal￨L￨JJ￨O￨- decision￨L￨NN￨O￨- making￨L￨VBG￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- settings￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- variable￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- decision￨L￨NN￨O￨- makers￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- patient￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- between￨L￨IN￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- institutions￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- .￨L￨.￨O￨- +Disease￨U￨NN￨CAUSE_OF_DEATH￨- screening￨L￨NN￨O￨A can￨L￨MD￨O￨- facilitate￨L￨VB￨O￨- efforts￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- or￨L￨CC￨O￨- reducing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- healthcare￨L￨NN￨O￨- setting￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- screening￨L￨NN￨O￨A decisions￨L￨NNS￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- institution￨L￨NN￨O￨- can￨L￨MD￨O￨- impact￨L￨VB￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- consequently￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- screening￨L￨NN￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- institutions￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- shared￨L￨JJ￨O￨- patient￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- screening￨L￨NN￨O￨A and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- are￨L￨VBP￨O￨- expensive￨L￨JJ￨O￨- ,￨L￨,￨O￨- institutions￨L￨NNS￨O￨- must￨L￨MD￨O￨- choose￨L￨VB￨O￨- a￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- screening￨L￨VBG￨O￨- to￨L￨TO￨O￨- balance￨L￨VB￨O￨- the￨L￨DT￨O￨- associated￨L￨VBN￨O￨- costs￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- lower￨L￨JJR￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- screening￨L￨NN￨O￨A and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- are￨L￨VBP￨O￨- costly￨L￨JJ￨O￨- ,￨L￨,￨O￨- institutions￨L￨NNS￨O￨- must￨L￨MD￨O￨- consider￨L￨VB￨O￨- a￨L￨DT￨O￨- tradeoff￨L￨NN￨O￨- when￨L￨WRB￨O￨- choosing￨L￨VBG￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- screening￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- saturation￨L￨NN￨O￨A effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- allowed￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- much￨L￨JJ￨O￨- better￨L￨JJR￨O￨- fit￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- lineages￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- small￨L￨JJ￨O￨- species￨L￨NNS￨O￨- trees￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- infer￨L￨VBP￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- original￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- strong￨L￨JJ￨O￨- limiting￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Birth￨U￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- models￨L￨NNS￨O￨- naturally￨L￨RB￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- stochasticity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨NN￨O￨A are￨L￨VBP￨O￨- not￨L￨RB￨O￨- justified￨L￨JJ￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- saturation￨L￨NN￨O￨A effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- that￨L￨IN￨O￨- transmission￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- pool￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- depleted￨L￨VBN￨O￨- .￨L￨.￨O￨- +Phylogenetic￨U￨JJ￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- therefore￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- misspecification￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- incorrect￨L￨JJ￨O￨- parameter￨L￨NN￨O￨A estimates￨L￨NNS￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A diffusion￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- friend￨L￨NN￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- ISS￨U￨NNP￨ORGANIZATION￨- diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- construct￨L￨VBP￨O￨- an￨L￨DT￨O￨- artificial￨L￨JJ￨O￨- society￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- zombie-city￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- rumor￨L￨NN￨O￨A diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- roles￨L￨NNS￨O￨- :￨L￨:￨O￨- ignorant￨L￨JJ￨O￨- ,￨L￨,￨O￨- spreader￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stifler￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- spreader￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- lose￨L￨VB￨O￨- the￨L￨DT￨O￨- interest￨L￨NN￨O￨- for￨L￨IN￨O￨- defusing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A with￨L￨IN￨O￨- time￨L￨NN￨O￨- ;￨L￨:￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- interests￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spreader￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- diffuse￨L￨VB￨O￨- rumor￨L￨NN￨O￨- decay￨L￨NN￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- a￨L￨DT￨O￨- spreader￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- automatically￨L￨RB￨O￨- become￨L￨VB￨O￨- a￨L￨DT￨O￨- stifler￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A diffusion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- various￨L￨JJ￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Social￨U￨NNP￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- tunnel￨L￨NN￨O￨- for￨L￨IN￨O￨- rumor￨L￨NN￨O￨A or￨L￨CC￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- govern￨L￨VBP￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- hrHPV￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- per￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- partnership￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- clearance￨L￨NN￨O￨A of￨L￨IN￨O￨- incident￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- following￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- clearance￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- currently￨L￨RB￨DATE￨- ill-defined￨L￨JJ￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- inferred￨L￨VBN￨O￨- from￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- based￨L￨VBD￨O￨- validation￨L￨NN￨O￨A on￨L￨IN￨O￨- both￨L￨DT￨O￨- cross-validation￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- consistency￨L￨NN￨O￨- of￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- different￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- out-of-sample￨L￨JJ￨O￨- validation￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- consistency￨L￨NN￨O￨- between￨L￨IN￨O￨- model-based￨L￨JJ￨O￨- projections￨L￨NNS￨O￨- and￨L￨CC￨O￨- independent￨L￨JJ￨RELIGION￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- population￨L￨NN￨O￨- not￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- accounted￨L￨VBD￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- sexual￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- categorized￨L￨VBN￨O￨- in￨L￨IN￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- activity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CSA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- time￨L￨NN￨O￨- since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- clearance￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- re-infection￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- separately￨L￨RB￨O￨- estimated￨L￨VBN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- mentioned￨L￨VBN￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- 13￨L￨CD￨NUMBER￨- hrHPV￨L￨NN￨O￨- types￨L￨NNS￨O￨- by￨L￨IN￨O￨- independently￨L￨RB￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- two￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- recruited￨L￨VBN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- studies￨L￨NNS￨O￨- in￨L￨IN￨O￨- Italy￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- Sweden￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨A results￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- compared￨L￨VBN￨O￨A the￨L￨DT￨O￨- HPV16￨U￨NN￨O￨- age-specific￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- observed￨L￨VBD￨O￨- three￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- later￨L￨RB￨DATE￨- among￨L￨IN￨O￨- initially￨L￨RB￨O￨- negative￨L￨JJ￨O￨- women￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Italian￨U￨JJ￨NATIONALITY￨- study￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- model-based￨L￨JJ￨O￨- projection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- curve￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- freezing￨L￨JJ￨O￨- period￨L￨NN￨O￨- H￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- switching￨L￨NN￨O￨A capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- voter￨L￨NN￨O￨- 's￨L￨POS￨O￨- opinion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Methods￨U￨NNS￨O￨- for￨L￨IN￨O￨- further￨L￨JJ￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- freezing￨L￨JJ￨O￨- period￨L￨NN￨O￨A gradually￨L￨RB￨O￨- increases￨L￨VBZ￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- emerges￨L￨VBZ￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- H￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- produces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fastest￨L￨JJS￨O￨- consensus￨L￨NN￨O￨- formation￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- freezing￨L￨JJ￨O￨- period￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- voter￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- frozen￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- transition￨L￨NN￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- switching￨L￨VBG￨O￨A opinions￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- we￨L￨PRP￨O￨- further￨L￨RB￨O￨- increase￨L￨VBP￨O￨- the￨L￨DT￨O￨- freezing￨L￨JJ￨O￨- period￨L￨NN￨O￨A H￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- reaching￨L￨VBG￨O￨- a￨L￨DT￨O￨- consensus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- exacerbated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- illustrates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dependence￨L￨NN￨O￨A of￨L￨IN￨O￨- consensus￨L￨NN￨O￨- time￨L￨NN￨O￨- T￨U￨NN￨O￨- on￨L￨IN￨O￨- H￨U￨NN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- dynamic￨L￨JJ￨O￨- representations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- explicitly￨L￨RB￨O￨- account￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- shape￨L￨VB￨O￨- infection-related￨L￨JJ￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- a￨L￨DT￨DURATION￨- century￨L￨NN￨DURATION￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨A history￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨- and￨L￨CC￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- prevention￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Garnett￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A has￨L￨VBZ￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- entered￨L￨VBD￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- infection-related￨L￨JJ￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- notably￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HBV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- papillomavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HPV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- related￨L￨JJ￨O￨- cancers￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- concepts￨L￨NNS￨O￨- ,￨L￨,￨O￨- terminology￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- domain￨L￨NN￨O￨- of￨L￨IN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +Infection￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨A and￨L￨CC￨O￨- chronic-disease￨L￨NN￨O￨- modelling￨L￨NN￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- increasingly￨L￨RB￨O￨- combined￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Kim￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Garnett￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Arm￨U￨NN￨O￨- C￨U￨NN￨O￨- will￨L￨MD￨O￨- serve￨L￨VB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- control￨L￨NN￨O￨- arm￨L￨NN￨O￨- with￨L￨IN￨O￨- health￨L￨NN￨O￨- system￨L￨NN￨O￨- strengthening￨L￨VBG￨O￨- activities￨L￨NNS￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- that￨L￨IN￨O￨- standard￨L￨NN￨O￨- of￨L￨IN￨O￨- care￨L￨NN￨O￨- services￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- voluntary￨L￨JJ￨O￨- testing￨L￨NN￨O￨A and￨L￨CC￨O￨- counseling￨L￨NN￨O￨- ,￨L￨,￨O￨- male￨L￨JJ￨O￨- circumcision￨L￨NN￨O￨- ,￨L￨,￨O￨- PMTCT￨U￨NN￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- STIs￨U￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ART￨U￨NN￨O￨- for￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- positive￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- delivered￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- national￨L￨JJ￨O￨- guidelines￨L￨NNS￨O￨- .￨L￨.￨O￨- +Interventions￨U￨NNS￨O￨- in￨L￨IN￨O￨- arms￨L￨NNS￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- will￨L￨MD￨O￨- include￨L￨VB￨O￨- home-based￨L￨JJ￨O￨- voluntary￨L￨JJ￨O￨- testing￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- HBT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- counseling￨L￨NN￨O￨- ,￨L￨,￨O￨- male￨L￨JJ￨O￨- circumcision￨L￨NN￨O￨- ,￨L￨,￨O￨- prevention￨L￨NN￨O￨- of￨L￨IN￨O￨- mother￨L￨NN￨O￨- to￨L￨TO￨O￨- child￨L￨NN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PMTCT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- services￨L￨NNS￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- STIs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- condom￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ART￨U￨NN￨O￨- for￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- positive￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- finding￨L￨NN￨O￨- ,￨L￨,￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- closely￨L￨RB￨O￨- monitored￨L￨JJ￨O￨- individually-randomized￨L￨JJ￨O￨- trial￨L￨NN￨O￨- ,￨L￨,￨O￨- corroborated￨L￨VBD￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- opened￨L￨VBD￨O￨- new￨L￨JJ￨O￨- and￨L￨CC￨O￨- exciting￨L￨JJ￨O￨- perspectives￨L￨NNS￨O￨- for￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- :￨L￨:￨O￨- expanding￨L￨VBG￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- testing￨L￨NN￨O￨A and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- could￨L￨MD￨O￨- reduce￨L￨VB￨O￨- sexual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- close￨L￨NN￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- trials￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- designed￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- test￨L￨VB￨O￨- the￨L￨DT￨O￨- feasibility￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- combination￨L￨NN￨O￨- prevention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- including￨L￨VBG￨O￨- universal￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- testing￨L￨NN￨O￨A with￨L￨IN￨O￨- immediate￨L￨JJ￨O￨- antiretroviral￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- for￨L￨IN￨O￨- HIV-positive￨U￨JJ￨O￨- persons￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- their￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- recent￨L￨JJ￨O￨- observational￨L￨JJ￨O￨A study￨L￨NN￨O￨- in￨L￨IN￨O￨- South￨U￨NNP￨COUNTRY￨- Africa￨U￨NNP￨COUNTRY￨- demonstrated￨L￨VBD￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ART￨U￨NN￨O￨- coverage￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- immediately￨L￨RB￨O￨- surrounding￨L￨VBG￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- was￨L￨VBD￨O￨- highly￨L￨RB￨O￨- predictive￨L￨JJ￨O￨- of￨L￨IN￨O￨- his/her￨L￨NN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- acquisition￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- raises￨L￨VBZ￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- producing￨L￨VBG￨O￨- a￨L￨DT￨O￨- biological￨L￨JJ￨O￨- agent￨L￨NN￨O￨- which￨L￨WDT￨O￨- targets￨L￨VBZ￨O￨- the￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasite￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- disrupt￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- cycle￨L￨NN￨O￨- and￨L￨CC￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans.Interestingly￨L￨NNP￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- fungal￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Metarhizium￨U￨NNP￨O￨- do￨L￨VBP￨O￨- n’t￨L￨RB￨O￨- kill￨L￨VB￨O￨- infected￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- until￨L￨IN￨O￨- their￨L￨PRP$￨O￨- later￨L￨JJ￨O￨- life‐stages￨L￨NNS￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- reproduction￨L￨NN￨O￨- has￨L￨VBZ￨O￨- occurred￨L￨VBN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- believed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- selection￨L￨NN￨O￨- pressure￨L￨NN￨O￨- for￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- resistance￨L￨NN￨O￨- is￨L￨VBZ￨O￨- quite￨L￨RB￨O￨- low￨L￨JJ￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- resistance￨L￨NN￨O￨- should￨L￨MD￨O￨- develop￨L￨VB￨O￨- slowly￨L￨RB￨O￨- even￨L￨RB￨O￨- under￨L￨IN￨O￨- widespread￨L￨JJ￨O￨- deployment￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- other￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- high‐virulence￨L￨JJ￨O￨- fungus￨L￨NN￨O￨- that￨L￨WDT￨O￨- more￨L￨RBR￨O￨- effectively￨L￨RB￨O￨- reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨A population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- preferable.Mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- possible￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- century￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +MethodsTwo￨U￨NNP￨O￨- prototype￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- that￨L￨IN￨O￨- take￨L￨VBP￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- fundamental￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasite￨L￨NN￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- mosquito￨L￨NN￨O￨A vector￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- fungal￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +Aside￨U￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- obvious￨L￨JJ￨O￨- annual￨L￨JJ￨SET￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- mortality￨L￨NN￨O￨- records￨L￨NNS￨O￨A reveal￨L￨VBP￨O￨- longer-term￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- are￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- common￨L￨JJ￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Cost-effective￨U￨JJ￨MISC￨- length￨L￨NN￨O￨- and￨L￨CC￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A during￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨JJ￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- severityHiroshi￨L￨NN￨MISC￨- Nishiura1Email￨U￨NN￨MISC￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Keisuke￨U￨NNP￨PERSON￨- Ejima1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kenji￨U￨NNP￨PERSON￨- Mizumoto1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Shinji￨U￨NNP￨PERSON￨- Nakaoka4￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Hisashi￨U￨NNP￨PERSON￨- Inaba5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Seiya￨U￨NNP￨PERSON￨- Imoto6￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Rui￨U￨NNP￨PERSON￨- Yamaguchi6￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Masaya￨U￨NNP￨PERSON￨- M￨U￨NNP￨O￨- Saito7￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 11:5￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Nishiura￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- There￨U￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- published￨L￨VBN￨O￨- opinions￨L￨NNS￨O￨- toward￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- reactively￨L￨RB￨O￨- when￨L￨WRB￨O￨- substantial￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmissions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- seen￨L￨VBN￨O￨- at￨L￨IN￨O￨- schools￨L￨NNS￨O￨- .￨L￨.￨O￨- +Parameterizing￨U￨VBG￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- using￨L￨VBG￨O￨- published￨L￨VBN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- H1N1-2009￨U￨NN￨O￨- and￨L￨CC￨O￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examined￨L￨VBD￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A could￨L￨MD￨O￨- be￨L￨VB￨O￨- optimized￨L￨VBN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- death￨L￨NN￨O￨- is￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- or￨L￨CC￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- H1N1-2009￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A could￨L￨MD￨O￨- be￨L￨VB￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- cost￨L￨NN￨O￨- effective￨L￨JJ￨O￨- .￨L￨.￨O￨- +School￨U￨NNP￨O￨- closure￨L￨NN￨O￨A was￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- place￨L￨NN￨O￨- only￨L￨RB￨O￨- once￨L￨RB￨DATE￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- abruptly￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- child-to-child￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- children￨L￨NNS￨O￨- and￨L￨CC￨O￨- adults￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- School￨U￨NNP￨O￨- closure￨L￨NN￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨- appeared￨L￨VBD￨O￨- to￨L￨TO￨O￨- yield￨L￨VB￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- was￨L￨VBD￨O￨- validated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- simulated￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- was￨L￨VBD￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- tree-based￨L￨JJ￨O￨- classification￨L￨NN￨O￨- technique￨L￨NN￨O￨- ,￨L￨,￨O￨- Random￨U￨NNP￨ORGANIZATION￨- Forest￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- RF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- high￨L￨JJ￨O￨- accuracy￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A curves￨L￨NNS￨O￨A using￨L￨VBG￨O￨- a￨L￨DT￨O￨- classification￨L￨NN￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- The￨U￨DT￨O￨- DP￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nonparametric￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- enables￨L￨VBZ￨O￨- the￨L￨DT￨O￨- matching￨L￨NN￨O￨- of￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- to￨L￨TO￨O￨- simulated￨L￨JJ￨O￨- and￨L￨CC￨O￨- historical￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- identifies￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨A curves￨L￨NNS￨O￨A different￨L￨JJ￨O￨- from￨L￨IN￨O￨- those￨L￨DT￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- and￨L￨CC￨O￨- enables￨L￨VBZ￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- Dirichlet￨U￨NNP￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- classifying￨L￨VBG￨O￨- and￨L￨CC￨O￨- forecasting￨L￨VBG￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨A curves￨L￨NNS￨O￨A .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- DP￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- performed￨L￨VBN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- RF￨U￨NN￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- several￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨A epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- nested￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- follow￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- find￨L￨VB￨O￨- equilibrium￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- explicitly￨L￨RB￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- within-host￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨A of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- competing￨L￨VBG￨O￨- strains￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +SPVL￨U￨NN￨O￨- is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- partly￨L￨RB￨O￨- heritable￨L￨JJ￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- seems￨L￨VBZ￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- evolved￨L￨VBN￨O￨- an￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- virulence￨L￨NN￨O￨- that￨L￨WDT￨O￨- maximizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- its￨L￨PRP$￨O￨- transmission￨L￨NN￨O￨A potential￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- maximizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- between-host￨L￨JJ￨O￨- fitness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- we￨L￨PRP￨O￨- should￨L￨MD￨O￨- expect￨L￨VB￨O￨- strains￨L￨NNS￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- competitive￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- to￨L￨TO￨O￨- sweep￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- within-host￨L￨JJ￨O￨- population￨L￨NN￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- arise￨L￨VBP￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- whether￨L￨IN￨O￨- this￨L￨DT￨O￨- reduces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- or￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- conflicting￨L￨VBG￨O￨- evolutionary￨L￨JJ￨O￨- pressures￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- virulence￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- constructed￨L￨VBN￨O￨- a￨L￨DT￨O￨- nested￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- integrates￨L￨VBZ￨O￨- within-host￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨A and￨L￨CC￨O￨- between-host￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- allows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- strains￨L￨NNS￨O￨- to￨L￨TO￨O￨- coexist￨L￨VB￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +HIV￨U￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- evolve￨L￨VB￨O￨- extremely￨L￨RB￨O￨- quickly￨L￨RB￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- face￨L￨NN￨O￨- of￨L￨IN￨O￨- it￨L￨PRP￨O￨- giving￨L￨VBG￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- ample￨L￨JJ￨O￨- opportunity￨L￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- strains￨L￨NNS￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- replicative￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- to￨L￨TO￨O￨- sweep￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- within-host￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- long-distance￨L￨JJ￨O￨- travellers￨L￨NNS￨O￨- ,￨L￨,￨O￨- present￨L￨JJ￨DATE￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- arbitrarily￨L￨RB￨O￨- neglected￨L￨VBN￨O￨- the￨L￨DT￨O￨- travel￨L￨NN￨O￨A types￨L￨NNS￨O￨- and￨L￨CC￨O￨- assumed￨L￨VBD￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- population￨L￨NN￨O￨- will￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- equivalent￨L￨JJ￨O￨- risk￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- travellers￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- underestimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- incorporated￨L￨VBN￨O￨- demogeographic￨L￨JJ￨O￨- information￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- integrated￨L￨VBN￨O￨- it￨L￨PRP￨O￨- with￨L￨IN￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨A mobility￨L￨NN￨O￨A data￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- pursue￨L￨VB￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- binary￨L￨JJ￨O￨- presence/absence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- notified￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- districts￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- swash￨L￨NN￨O￨- –￨L￨:￨O￨- backwash￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- leading￨L￨VBG￨O￨- and￨L￨CC￨O￨- trailing￨L￨VBG￨O￨- edges￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- advance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ‘￨L￨``￨O￨- swash￨L￨NN￨O￨- ’￨L￨''￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- retreat￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ‘￨L￨``￨O￨- backwash￨L￨NN￨O￨- ’￨L￨''￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- wave￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- means￨L￨NN￨O￨- of￨L￨IN￨O￨- measuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- geographical￨L￨JJ￨O￨- units￨L￨NNS￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- infective￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- status￨L￨NN￨O￨- as￨L￨IN￨O￨- dimensionless￨L￨JJ￨O￨- integrals￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- yields￨L￨NNS￨O￨- robust￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- velocity￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- waves￨L￨NNS￨O￨- from￨L￨IN￨O￨- space￨L￨NN￨O￨- –￨L￨:￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 1305￨L￨CD￨DATE￨- registration￨L￨NN￨O￨- weeks￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- ending￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Saturday￨U￨NNP￨DATE￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 25-year￨L￨JJ￨DURATION￨- observation￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- notified￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- poliomyelitis￨L￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 1479￨L￨CD￨DATE￨- standard￨L￨JJ￨O￨- local￨L￨JJ￨O￨- government￨L￨NN￨O￨- districts￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- 28￨L￨CD￨NUMBER￨- metropolitan￨L￨JJ￨O￨- boroughs￨L￨NNS￨O￨- ,￨L￨,￨O￨- 83￨L￨CD￨NUMBER￨- county￨L￨NN￨O￨- boroughs￨L￨NNS￨O￨- ,￨L￨,￨O￨- 310￨L￨CD￨NUMBER￨- municipal￨L￨JJ￨O￨- boroughs￨L￨NNS￨O￨- ,￨L￨,￨O￨- 576￨L￨CD￨NUMBER￨- urban￨L￨JJ￨O￨- districts￨L￨NNS￨O￨- and￨L￨CC￨O￨- 482￨L￨CD￨NUMBER￨- rural￨L￨JJ￨O￨- districts￨L￨NNS￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Wales￨U￨NNP￨LOCATION￨- was￨L￨VBD￨O￨- abstracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Weekly￨U￨NNP￨SET￨- Return￨U￨NN￨O￨- to￨L￨TO￨O￨- form￨L￨VB￨O￨- a￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- 1305￨L￨CD￨DATE￨- weeks￨L￨NNS￨DURATION￨- ×￨L￨VBP￨O￨- 1479￨L￨CD￨DATE￨- districts￨L￨NNS￨O￨- =)￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- 93￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- cell￨L￨NN￨O￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- poliomyelitis￨L￨NNP￨O￨- notifications￨L￨NNS￨O￨- .￨L￨.￨O￨- +Between￨U￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- wars￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- monthly￨L￨JJ￨SET￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- poliomyelitis￨L￨NNP￨O￨- notifications￨L￨NNS￨O￨- in￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Wales￨U￨NNP￨LOCATION￨- rarely￨L￨RB￨O￨- rose￨L￨VBD￨O￨- above￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- 5￨L￨CD￨NUMBER￨- cases/100￨L￨NN￨O￨- 000￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- 1926￨L￨CD￨DATE￨- Citation￨U￨NNP￨O￨- were￨L￨VBD￨O￨- the￨L￨DT￨DURATION￨- only￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨A of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- note￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- purposes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- drew￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨A notifications￨L￨NNS￨O￨- of￨L￨IN￨O￨- poliomyelitis￨L￨NNP￨O￨- (￨L￨-LRB-￨O￨- acute￨L￨JJ￨O￨- poliomyelitis￨L￨NNP￨O￨- and￨L￨CC￨O￨- acute￨L￨JJ￨O￨- polioencephalitis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- included￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Registrar￨U￨NNP￨ORGANIZATION￨- General￨U￨NNP￨ORGANIZATION￨- 's￨L￨POS￨ORGANIZATION￨- Weekly￨U￨NNP￨ORGANIZATION￨- Return￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Births￨U￨NNS￨ORGANIZATION￨- and￨L￨CC￨O￨- Deaths￨U￨NNS￨O￨- …￨L￨:￨O￨- and￨L￨CC￨O￨- Cases￨U￨NNS￨MISC￨- of￨L￨IN￨MISC￨- Certain￨U￨JJ￨MISC￨- Specified￨U￨VBN￨MISC￨- Infectious￨U￨JJ￨MISC￨- Diseases￨U￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- London￨U￨NNP￨CITY￨- :￨L￨:￨O￨- HMSO￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 1964￨L￨CD￨DATE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- P.￨U￨NNP￨O￨- By￨U￨IN￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- Yunnan￨U￨NNP￨STATE_OR_PROVINCE￨- province￨L￨NN￨LOCATION￨- ,￨L￨,￨O￨- People￨U￨NNS￨LOCATION￨- 's￨L￨POS￨LOCATION￨- Republic￨U￨NN￨COUNTRY￨- of￨L￨IN￨COUNTRY￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- pay￨L￨VBP￨O￨- special￨L￨JJ￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨A the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- P.￨U￨NNP￨O￨- vivax￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- tempo-spatial￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- observed/reported￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨A the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- P.￨U￨NNP￨O￨- vivax￨L￨NN￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- geographical￨L￨JJ￨O￨- location￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- tempo-spatial￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- sparse￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- ?￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- 30￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- population￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- demographic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- four￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- a￨L￨DT￨O￨- one-child￨L￨JJ￨O￨- policy￨L￨NN￨O￨A was￨L￨VBD￨O￨- fully￨L￨RB￨O￨- launched￨L￨VBN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- calibrated￨L￨VBD￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- projections￨L￨NNS￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- one-child￨L￨JJ￨O￨- policy￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- census￨L￨NN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- population￨L￨NN￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- one-child￨L￨JJ￨O￨- policy￨L￨NN￨O￨- with￨L￨IN￨O￨- projections￨L￨NNS￨O￨- from￨L￨IN￨O￨- previous￨L￨JJ￨O￨- literature￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- was￨L￨VBD￨O￨- predicted￨L￨VBN￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- control￨L￨NN￨O￨- policies￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- calibrated￨L￨VBD￨O￨- the￨L￨DT￨O￨- influenza-specific￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- secondary￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- literature￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- compared￨L￨VBD￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- annual￨L￨JJ￨SET￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- secondary￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- one-child￨L￨JJ￨O￨- policy￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- strict￨L￨JJ￨O￨- one-child￨L￨JJ￨O￨- policy￨L￨NN￨O￨A was￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- one-child￨L￨JJ￨O￨- policy￨L￨NN￨O￨- to￨L￨TO￨O￨- rates￨L￨NNS￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- actual￨L￨JJ￨O￨- one-child￨L￨JJ￨O￨- policy￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- children￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- allowed￨L￨VBN￨O￨- in￨L￨IN￨O￨- rural￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- ethnic￨L￨JJ￨O￨- minorities￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- census￨L￨NN￨O￨- data￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- reflect￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- truly￨L￨RB￨O￨- restricting￨L￨VBG￨O￨- families￨L￨NNS￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- child￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- transmission￨L￨NN￨O￨- while￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- different￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- control￨L￨NN￨O￨- policies￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- one-child￨L￨JJ￨O￨- policy￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- control￨L￨NN￨O￨- policy￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- strict￨L￨JJ￨O￨- one-child￨L￨JJ￨O￨- policy￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- ,￨L￨,￨O￨- event-driven￨L￨JJ￨O￨- ,￨L￨,￨O￨- individual-based￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Subsequently￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- policy￨L￨NN￨O￨A reduced￨L￨VBD￨O￨- fertility￨L￨NN￨O￨- rates￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- household￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- dependent￨L￨JJ￨O￨- child￨L￨NN￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- households￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- relate￨L￨VB￨O￨- transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- serological￨L￨JJ￨O￨A markers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- acquisition￨L￨NN￨O￨- of￨L￨IN￨O￨- PfEMP1￨U￨NN￨O￨- variants￨L￨NNS￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- life￨L￨NN￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- evolutionary￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- acting￨L￨VBG￨O￨- on￨L￨IN￨O￨- var￨L￨NN￨O￨- genes￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +falciparum￨L￨NN￨O￨- elimination￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- insecticide￨L￨NN￨O￨- and￨L￨CC￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- high￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- and￨L￨CC￨O￨- breakdown￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- might￨L￨MD￨O￨- re-emerge￨L￨VB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- causing￨L￨VBG￨O￨- more￨L￨RBR￨O￨- severe￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- declining￨L￨VBG￨O￨- immunity￨L￨NN￨O￨- levels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- serological￨L￨JJ￨O￨A data￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- intraclonal￨L￨JJ￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- PfEMP1￨U￨NN￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- polymerase￨L￨NN￨O￨- chain￨L￨NN￨O￨- reaction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PCR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- technique￨L￨NN￨O￨- that￨L￨WDT￨O￨- detects￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- efficiently￨L￨RB￨O￨- the￨L￨DT￨O￨- asymptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- constitute￨L￨VBP￨O￨- a￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Upon￨U￨IN￨O￨- reducing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- concern￨L￨NN￨O￨- that￨L￨IN￨O￨- waning￨L￨VBG￨O￨- serological￨L￨JJ￨O￨A immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- PfEMP1￨U￨NN￨O￨- antigenic￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- may￨L￨MD￨O￨- render￨L￨VB￨O￨- individuals￨L￨NNS￨O￨- more￨L￨RBR￨O￨- vulnerable￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- sample￨L￨NN￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- 9￨L￨CD￨NUMBER￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- initially￨L￨RB￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- were￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- clearance￨L￨NN￨O￨A rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Analytic￨U￨NNP￨O￨- perspective￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Cholera￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- practitionersIsaac￨L￨NN￨MISC￨- Chun-Hai￨U￨NNP￨MISC￨- Fung1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 11:1￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Fung￨U￨VBN￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractGreat￨U￨NNP￨O￨- progress￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- made￨L￨VBN￨O￨- in￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- collaboration￨L￨NN￨O￨- is￨L￨VBZ￨O￨- needed￨L￨VBN￨O￨- between￨L￨IN￨O￨- policy-makers￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemiologists￨L￨NNS￨O￨- and￨L￨CC￨O￨- modelers￨L￨NNS￨O￨- in￨L￨IN￨O￨- public￨L￨JJ￨O￨- health.KeywordsCholeraSusceptible￨L￨JJ￨MISC￨- PopulationBasic￨U￨NNP￨MISC￨- Reproduction￨U￨NNP￨MISC￨- NumberModel￨U￨NNP￨MISC￨- MisspecificationPublic￨U￨NNP￨MISC￨- Health￨U￨NNP￨MISC￨- Practitioner￨U￨NNP￨MISC￨- IntroductionSince￨U￨NNP￨MISC￨- the￨L￨DT￨DATE￨- 19th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- ,￨L￨,￨O￨- humans￨L￨NNS￨O￨- have￨L￨VBP￨O￨- experienced￨L￨VBN￨O￨- seven￨L￨CD￨NUMBER￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A pandemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- highlight￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- misspecification￨L￨NN￨O￨- and￨L￨CC￨O￨- parameter￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- water￨L￨NN￨O￨- ,￨L￨,￨O￨- sanitation￨L￨NN￨O￨- and￨L￨CC￨O￨- hygiene￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- brief￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- basics￨L￨NNS￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- discuss￨L￨VBP￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- adapted￨L￨VBN￨O￨- from￨L￨IN￨O￨- Codeço￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2001￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modified￨L￨VBN￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- different￨L￨JJ￨O￨- hypotheses￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- or￨L￨CC￨O￨- inapparent￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hyperinfectious￨L￨JJ￨O￨- V￨U￨NN￨O￨- .￨L￨.￨O￨- +Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- that￨L￨WDT￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- global￨L￨JJ￨O￨- air￨L￨NN￨O￨A transportation￨L￨NN￨O￨- ,￨L￨,￨O￨- provides￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- support￨L￨NN￨O￨- for￨L￨IN￨O￨- air￨L￨NN￨O￨- travel￨L￨NN￨O￨- governing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- H3N2￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Current￨U￨JJ￨DATE￨- attempts￨L￨NNS￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨- viral￨L￨JJ￨O￨- spread￨L￨NN￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨- from￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- typically￨L￨RB￨O￨- fit￨L￨VBP￨O￨- parameter-rich￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- sparse￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨A data￨L￨NNS￨O￨- and￨L￨CC￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- phylogeographic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- relate￨L￨VB￨O￨- directly￨L￨RB￨O￨- to￨L￨TO￨O￨- underlying￨L￨VBG￨O￨- ecological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Air￨U￨NNP￨O￨- travel￨L￨NN￨O￨A likely￨L￨JJ￨O￨- drives￨L￨NNS￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H3N2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- viruses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- explain￨L￨VB￨O￨- seasonal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- locally-persistent￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- between￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- seasons￨L￨NNS￨O￨- .￨L￨.￨O￨- +Retrospective￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- Hong￨U￨NNP￨CAUSE_OF_DEATH￨- Kong￨U￨NNP￨CAUSE_OF_DEATH￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- ’￨L￨''￨O￨- H3N2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- spread￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- cities￨L￨NNS￨O￨- interconnected￨L￨VBN￨O￨- by￨L￨IN￨O￨- air￨L￨NN￨O￨A travel￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- model-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- explicitly￨L￨RB￨O￨- tests￨L￨VBZ￨O￨- spatial￨L￨JJ￨O￨A epidemiological￨L￨JJ￨O￨- hypotheses￨L￨NNS￨O￨- by￨L￨IN￨O￨- integrating￨L￨VBG￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- with￨L￨IN￨O￨- viral￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- publicly￨L￨RB￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- independent￨L￨JJ￨RELIGION￨- introductions￨L￨NNS￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- resulted￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- clusters￨L￨NNS￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- considered￨L￨VBD￨O￨- four￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- conservative￨L￨JJ￨IDEOLOGY￨- estimate￨L￨NN￨O￨- for￨L￨IN￨O￨- R￨U￨NN￨O￨- that￨L￨WDT￨O￨- assumes￨L￨VBZ￨O￨- as￨L￨IN￨O￨- many￨L￨JJ￨O￨- separate￨L￨JJ￨O￨- introductions￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- chains￨L￨NNS￨O￨- as￨L￨IN￨O￨- is￨L￨VBZ￨O￨- reasonable￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- maximum￨L￨JJ￨O￨- introductions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2-3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- two￨L￨CD￨NUMBER￨- likely￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- interval￨L￨NN￨O￨- for￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- likely￨L￨JJ￨O￨- introductions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- scenario￨L￨NN￨O￨- that￨L￨WDT￨O￨- assumes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fewest￨L￨JJS￨O￨- introductions￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- chains￨L￨NNS￨O￨- possible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- minimum￨L￨JJ￨O￨- introductions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Shortly￨U￨RB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Mexican￨U￨JJ￨NATIONALITY￨- government￨L￨NN￨O￨- began￨L￨VBD￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- a￨L￨DT￨O￨- national￨L￨JJ￨O￨- prevention￨L￨NN￨O￨- campaign￨L￨NN￨O￨- including￨L￨VBG￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- follow-up￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- potential￨L￨JJ￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- oral￨L￨JJ￨O￨- rehydration￨L￨NN￨O￨- salt￨L￨NN￨O￨- packages￨L￨NNS￨O￨- and￨L￨CC￨O￨- chlorine￨L￨NN￨O￨- tablets￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- liming￨L￨NN￨O￨- of￨L￨IN￨O￨- latrines￨L￨NNS￨O￨- ,￨L￨,￨O￨- septic￨L￨JJ￨O￨- tanks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- banks￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Tecoluco￨U￨NNP￨LOCATION￨- River￨U￨NNP￨TITLE￨- in￨L￨IN￨O￨- Huejutla￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Hidalgo￨U￨NNP￨CITY￨- .9￨L￨CD￨NUMBER￨- Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- published￨L￨VBN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- as￨L￨IN￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- additional￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- each￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Identifying￨U￨VBG￨O￨- Likely￨U￨JJ￨O￨- Introductions￨U￨NNS￨O￨- We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- R￨U￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- suspected￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- chains￨L￨NNS￨O￨- stemming￨L￨VBG￨O￨- from￨L￨IN￨O￨- likely￨L￨JJ￨O￨- independent￨L￨JJ￨RELIGION￨- introductions￨L￨NNS￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- into￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 12￨L￨CD￨NUMBER￨- Through￨U￨IN￨O￨- January￨U￨NNP￨DATE￨- 25￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2014￨L￨CD￨DATE￨- there￨L￨EX￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- 185￨L￨CD￨NUMBER￨- confirmed￨L￨VBD￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- excluding￨L￨VBG￨O￨- 2￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- from￨L￨IN￨O￨- Federal￨U￨NNP￨LOCATION￨- District￨U￨NNP￨LOCATION￨- in￨L￨IN￨O￨- week￨L￨NN￨DURATION￨A 36￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- strain￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Confirmed￨U￨VBN￨O￨- cases￨L￨NNS￨O￨- following￨L￨VBG￨DATE￨- a￨L￨DT￨DATE￨- week￨L￨NN￨DATE￨A without￨L￨IN￨O￨- any￨L￨DT￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- new￨L￨JJ￨O￨- primary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- introduction￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- interval￨L￨NN￨O￨- for￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Starting￨U￨VBG￨O￨- the￨L￨DT￨DATE￨- following￨L￨VBG￨DATE￨- week￨L￨NN￨DATE￨A almost￨L￨RB￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Hidalgo￨U￨NNP￨CITY￨- State￨U￨NNP￨LOCATION￨- were￨L￨VBD￨O￨- in￨L￨IN￨O￨- Huejutla￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- chain￨L￨NN￨O￨- in￨L￨IN￨O￨- Huejutla￨U￨NNP￨O￨- from￨L￨IN￨O￨- week￨L￨NN￨DURATION￨- 38￨L￨CD￨NUMBER￨- until￨L￨IN￨O￨- no￨L￨DT￨O￨- cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- week￨L￨NN￨DURATION￨- 42￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- discussed￨L￨VBN￨O￨- here￨L￨RB￨O￨- build￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- pioneering￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- conducted￨L￨VBN￨O￨- using￨L￨VBG￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- 3,5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- North￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- 6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- demonstrated￨L￨VBD￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- humoural￨L￨JJ￨O￨- immune￨L￨JJ￨O￨A responses￨L￨NNS￨O￨A to￨L￨TO￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- providing￨L￨VBG￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- challenge￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- output￨L￨NN￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- earliest￨L￨JJS￨O￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- naturally￨L￨RB￨O￨- occurring￨L￨VBG￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- equine￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- horses￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- and￨L￨CC￨O￨- was￨L￨VBD￨O￨- validated￨L￨VBN￨O￨- as￨L￨IN￨O￨- being￨L￨VBG￨O￨- accurate￨L￨JJ￨O￨- against￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- 10￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- neither￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- against￨L￨IN￨O￨- nor￨L￨CC￨O￨- previously￨L￨RB￨DATE￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- equine￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- all￨L￨DT￨O￨- 100￨L￨CD￨NUMBER￨- horses￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- compartmentalised￨L￨VBN￨O￨- as￨L￨IN￨O￨- being￨L￨VBG￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- allows￨L￨VBZ￨O￨- individual￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- horse￨L￨NN￨O￨- coming￨L￨VBG￨O￨A into￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- animal￨L￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- will￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- equine￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- captured￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Agent-based￨U￨JJ￨MISC￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- simulation￨L￨NN￨O￨A are￨L￨VBP￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- high￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- artificial￨L￨JJ￨O￨- society￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- base￨L￨NN￨O￨- conception￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finite￨L￨JJ￨O￨- state￨L￨NN￨O￨- automata￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FSA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- agent￨L￨NN￨O￨A models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Agent￨U￨NNP￨O￨- ,￨L￨,￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- illustrated￨L￨VBN￨O￨A in￨L￨IN￨O￨- detail￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- section￨L￨NN￨O￨- .￨L￨.￨O￨- +Vectorial￨U￨JJ￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- v￨L￨LS￨O￨- also￨L￨RB￨O￨- called￨L￨VBN￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- daily￨L￨JJ￨SET￨- reproductive￨L￨JJ￨O￨- rate￨L￨NN￨O￨- ’￨L￨''￨O￨- ,￨L￨,￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- by￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- bites￨L￨VBZ￨O￨- that￨L￨DT￨O￨- would￨L￨MD￨O￨- eventually￨L￨RB￨O￨- arise￨L￨VB￨O￨- from￨L￨IN￨O￨- all￨L￨DT￨O￨- the￨L￨DT￨O￨- mosquitoes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- bite￨L￨VBP￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- human￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- day￨L￨NN￨DURATION￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- simplifying￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- both￨L￨DT￨O￨- parsimonious￨L￨JJ￨O￨- and￨L￨CC￨O￨- mathematically￨L￨RB￨O￨- convenient￨L￨JJ￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- to￨L￨TO￨O￨- vertebrate￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- constant￨L￨JJ￨O￨- ;￨L￨:￨O￨- mosquitoes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- feed￨L￨VB￨O￨- and￨L￨CC￨O￨- die￨L￨VB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- per-capita￨L￨JJ￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- f￨L￨FW￨O￨- and￨L￨CC￨O￨- g￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- portion￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- bloodmeals￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- 's￨L￨POS￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Q￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Macdonald￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- formula￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- superficially￨L￨RB￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- criterion￨L￨NN￨O￨- developed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Ross￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- yet￨L￨RB￨O￨- compelling￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- entomological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- most￨L￨RBS￨O￨- notably￨L￨RB￨O￨- daily￨L￨JJ￨SET￨- mosquito￨L￨NN￨O￨A survival￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- MBPT￨U￨NNP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- productively￨L￨RB￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- and￨L￨CC￨O￨- identify￨L￨VB￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- guide￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- few￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- evaluated￨L￨VBD￨O￨- independent￨L￨JJ￨RELIGION￨- or￨L￨CC￨O￨- joint￨L￨JJ￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- testing￨L￨NN￨O￨A ,￨L￨,￨O￨- risk￨L￨NN￨O￨- reduction￨L￨NN￨O￨- intervention￨L￨NN￨O￨- and￨L￨CC￨O￨- ART￨U￨NN￨O￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- were￨L￨VBD￨O￨- mainly￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- ,￨L￨,￨O￨- Western￨U￨NNP￨LOCATION￨- Europe￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Australia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- long￨L￨RB￨O￨- established￨L￨VBN￨O￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- none￨L￨NN￨O￨- from￨L￨IN￨O￨- regions￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- rapidly￨L￨RB￨O￨- rising￨L￨VBG￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨O￨- .￨L￨.￨O￨- +China￨U￨NNP￨COUNTRY￨- has￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- several￨L￨JJ￨O￨- aggressive￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- programs￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- routine￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- testing￨L￨NN￨O￨A and￨L￨CC￨O￨- risk￨L￨NN￨O￨- reduction￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- for￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- free￨L￨JJ￨O￨- ART￨U￨NN￨O￨- for￨L￨IN￨O￨- HIV-infected￨U￨JJ￨O￨- treatment-eligible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- programs￨L￨NNS￨O￨A curtailed￨L￨VBD￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- through￨L￨IN￨O￨- unhygienic￨L￨JJ￨O￨- plasma￨L￨NN￨O￨- collection￨L￨NN￨O￨- and￨L￨CC￨O￨- injecting￨L￨VBG￨O￨- drug￨L￨NN￨O￨- use￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reduced￨L￨VBD￨O￨- mortality￨L￨NN￨O￨- among￨L￨IN￨O￨- HIV-infected￨U￨JJ￨MISC￨- patients￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- programs￨L￨NNS￨O￨- have￨L￨VBP￨O￨- reversed￨L￨VBN￨O￨- the￨L￨DT￨O￨- rising￨L￨VBG￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- among￨L￨IN￨O￨- Chinese￨U￨JJ￨NATIONALITY￨- MSM￨U￨NN￨ORGANIZATION￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- recently￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- mathematic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- estimated￨L￨VBD￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- four-fold￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- testing￨L￨NN￨O￨A rates￨L￨NNS￨O￨- may￨L￨MD￨O￨- prevent￨L￨VB￨O￨- 42,000￨L￨CD￨NUMBER￨- new￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- all￨L￨DT￨O￨- at-risk￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- over￨L￨IN￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- modeled￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HIV/AIDS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- 's￨L￨POS￨O￨- capital￨L￨NN￨O￨- city￨L￨NN￨O￨- ,￨L￨,￨O￨- Beijing￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- representative￨L￨NN￨TITLE￨A of￨L￨IN￨O￨- most￨L￨JJS￨O￨- Chinese￨U￨JJ￨NATIONALITY￨- urban￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨A network￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- contact-contagion￨L￨NN￨O￨- formulation￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- layer￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- layers￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨A network￨L￨NN￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- information￨L￨NN￨O￨- layers￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- virtual￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- physical￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- speeds￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- point￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- isolated￨L￨VBN￨O￨- layer￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- reinfected￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- through￨L￨IN￨O￨- branches￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- tree-like￨L￨JJ￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- generating￨L￨VBG￨O￨- function￨L￨NN￨O￨- formalism￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- that￨L￨IN￨O￨- holds￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨A limit￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- significant￨L￨JJ￨O￨- constraint￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- partially￨L￨RB￨O￨- overlapped￨L￨VBD￨O￨- multiplex￨L￨JJ￨O￨A network￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- layers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- finite￨L￨JJ￨O￨- elements￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- age-structured￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- numerical￨L￨JJ￨O￨- tests￨L￨NNS￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- simple￨L￨JJ￨O￨- geometries￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- rectangles￨L￨NNS￨O￨- or￨L￨CC￨O￨- one-dimensional￨L￨JJ￨O￨- intervals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Though￨U￨IN￨O￨- some￨L￨DT￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- compartmentalized￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- extremely￨L￨RB￨O￨- well￨L￨RB￨O￨- developed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- simple￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- region￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- denote￨L￨VBP￨O￨- by￨L￨IN￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- e￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨A (￨L￨-LRB-￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- but￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- evident￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- yet￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- location￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- t.￨L￨IN￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- movement￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- process￨L￨NN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- geographical￨L￨JJ￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- time-dependent￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨A process￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- illustration￨L￨NN￨O￨- purposes￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- throughout￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨- among￨L￨IN￨O￨- raccoons￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- USA￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +So￨U￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨A coverage￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modified￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- the￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- functional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨A solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- satisfying￨L￨VBG￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- From￨U￨IN￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- τ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A E￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- b/d￨L￨JJ￨O￨- ,￨L￨,￨O￨- 0,0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- exists￨L￨VBZ￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨A endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- *￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- *￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- *￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Denoting￨U￨VBG￨O￨- Γ￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨CD￨NUMBER￨- ℛ￨U￨NN￨O￨- +￨L￨CC￨O￨- 3￨L￨CD￨NUMBER￨- |￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- ⩽￨L￨CD￨NUMBER￨- b/d￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- results￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- are￨L￨VBP￨O￨- here￨L￨RB￨O￨- just￨L￨RB￨O￨- recalled￨L￨VBN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- τ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- animal-to-animal￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- at￨L￨IN￨O￨- higher￨L￨JJR￨O￨- temporal￨L￨JJ￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- within￨L￨IN￨O￨- farm￨L￨NN￨O￨- animal￨L￨NN￨O￨A groups￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- rarely￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- unknown￨L￨JJ￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨- change￨L￨VBP￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- structure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- degree￨L￨NN￨O￨- order￨L￨NN￨O￨- ,￨L￨,￨O￨- individual￨L￨JJ￨O￨- rank￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- objectives￨L￨NNS￨O￨- were￨L￨VBD￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- individual￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- within-day￨L￨JJ￨O￨- and￨L￨CC￨O￨- between-day￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- animal￨L￨NN￨O￨A contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- pen￨L￨NN￨O￨- level￨L￨NN￨O￨- and￨L￨CC￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Toward￨U￨IN￨O￨- that￨L￨DT￨O￨- purpose￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- incorporated￨L￨VBD￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- identified￨L￨VBN￨O￨- heterogeneity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- temporal￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨A and￨L￨CC￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- order￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- contact-based￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- constructed￨L￨VBD￨O￨- animal￨L￨JJ￨O￨A contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- real-time￨L￨JJ￨O￨- animal￨L￨NN￨O￨- position￨L￨NN￨O￨- data￨L￨NNS￨O￨- at￨L￨IN￨O￨- high￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- resolutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- calves￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- validity￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- assumptions￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- constant￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- among￨L￨IN￨O￨- individual￨L￨JJ￨O￨- and￨L￨CC￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- and￨L￨CC￨O￨- discussed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- principle￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- may￨L￨MD￨O￨- harbor￨L￨VB￨O￨- a￨L￨DT￨O￨- diverse￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- population￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- diverse￨L￨JJ￨O￨- inoculum￨L￨NN￨O￨- ,￨L￨,￨O￨- diversification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- mutation￨L￨NN￨O￨A or￨L￨CC￨O￨- other￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- change￨L￨NN￨O￨- during￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- multiple￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- different￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- until￨L￨IN￨O￨- now￨L￨RB￨DATE￨- ,￨L￨,￨O￨- attempts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- transmission￨L￨NN￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- relied￨L￨VBN￨O￨- on￨L￨IN￨O￨- sparse￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- simplifying￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- genetically￨L￨RB￨O￨- homogeneous￨L￨JJ￨O￨A carriage￨L￨NN￨O￨- and/or￨L￨CC￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +number￨L￨NN￨O￨- of￨L￨IN￨O￨- single￨L￨JJ￨O￨- nucleotide￨L￨NN￨O￨- polymorphisms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SNPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- observed￨L￨VBN￨O￨- when￨L￨WRB￨O￨- sampling￨L￨NN￨O￨- two￨L￨CD￨NUMBER￨- random￨L￨JJ￨O￨- isolates￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- genetic￨L￨JJ￨O￨- distance￨L￨NN￨O￨A between￨L￨IN￨O￨- variants￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- respective￨L￨JJ￨O￨- frequencies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- neutral￨L￨JJ￨IDEOLOGY￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- pairwise￨L￨JJ￨O￨- SNP￨U￨NN￨ORGANIZATION￨- distance￨L￨NN￨O￨- at￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mutation￨L￨NN￨O￨A rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- actually￨L￨RB￨O￨- provided￨L￨VBD￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- molecular￨L￨JJ￨O￨- signature￨L￨NN￨O￨- of￨L￨IN￨O￨- negative￨L￨JJ￨O￨- selection￨L￨NN￨O￨A in￨L￨IN￨O￨- wild-type￨L￨JJ￨O￨- Murinae-associated￨U￨JJ￨MISC￨- hantaviruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- reversed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- treatment￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- mutagen-increasing￨L￨JJ￨O￨- molecule￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- ribavirin￨L￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- induces￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- mutational￨L￨JJ￨O￨- load￨L￨NN￨O￨- and￨L￨CC￨O￨- positive￨L￨JJ￨O￨- selection￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Hantaviruses￨U￨NNS￨O￨- exist￨L￨VBP￨O￨- within￨L￨IN￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- complex￨L￨NN￨O￨- and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- genetic￨L￨JJ￨O￨A drift￨L￨NN￨O￨- ,￨L￨,￨O￨- neutral￨L￨JJ￨IDEOLOGY￨- mutation￨L￨NN￨O￨- accumulation￨L￨NN￨O￨- and￨L￨CC￨O￨- small￨L￨JJ￨O￨- deletion/insertion￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- non-coding￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- RNA￨U￨NN￨O￨- segments￨L￨NNS￨O￨- seem￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- promoting￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- other￨L￨JJ￨O￨- RNA￨U￨NN￨O￨- viruses￨L￨NNS￨O￨A ,￨L￨,￨O￨- hantaviruses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- replication￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- poor￨L￨JJ￨O￨- proof-reading￨L￨JJ￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- RNA-dependent￨U￨JJ￨O￨- RNA￨U￨NN￨O￨- polymerase￨L￨NN￨O￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- now￨L￨RB￨DATE￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- different￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- biology￨L￨NN￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- by￨L￨IN￨O￨- polymerase￨L￨NN￨O￨- fidelity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Reassortments￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- exchange￨L￨NN￨O￨- of￨L￨IN￨O￨- genome￨L￨NN￨O￨- segments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- species￨L￨NNS￨O￨A when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- infect￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- cell￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- resolution￨L￨NN￨O￨A imagery￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- successes￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- detection￨L￨NN￨O￨- at￨L￨IN￨O￨- some￨L￨DT￨O￨- specific￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- experimental￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- cost￨L￨NN￨O￨- and￨L￨CC￨O￨- limited￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- airborne￨L￨JJ￨O￨- and￨L￨CC￨O￨- spaceborne￨L￨JJ￨O￨- data￨L￨NNS￨O￨- restrict￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- implementation￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- regional￨L￨JJ￨O￨- scale￨L￨NN￨O￨- .￨L￨.￨O￨- +Traditionally￨U￨RB￨O￨- ,￨L￨,￨O￨- manual￨L￨JJ￨O￨- inspection￨L￨NN￨O￨- and￨L￨CC￨O￨- field￨L￨NN￨O￨A survey￨L￨NN￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- collect￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- distribution￨L￨NN￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨JJ￨O￨- time￨L￨NN￨O￨- consuming￨L￨NN￨O￨- and￨L￨CC￨O￨- labor￨L￨NN￨O￨- intensive￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- impossible￨L￨JJ￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- continuous￨L￨JJ￨O￨- manner￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- area￨L￨NN￨O￨- .￨L￨.￨O￨- +Instead￨U￨RB￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- moderate￨L￨JJ￨O￨- resolution￨L￨NN￨O￨A remote￨L￨JJ￨O￨- sensing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Advanced￨U￨NNP￨O￨- Spaceborne￨U￨NNP￨O￨- Thermal￨U￨JJ￨O￨- Emission￨U￨NN￨O￨- and￨L￨CC￨O￨- Reflection￨U￨NN￨O￨- Radiometer￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ASTER￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Landsat￨U￨NNP￨O￨- Thematic￨U￨NNP￨O￨- Mapper￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- TM￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- potential￨L￨NN￨O￨- in￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- or￨L￨CC￨O￨- mapping￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- vast￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- given￨L￨VBN￨O￨- their￨L￨PRP$￨O￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- cost￨L￨NN￨O￨- and￨L￨CC￨O￨- wide￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- we￨L￨PRP￨O￨- think￨L￨VBP￨O￨- that￨L￨IN￨O￨- spatial/spectral￨L￨JJ￨O￨- resolutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- remote￨L￨JJ￨O￨- sensing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- resolution￨L￨NN￨O￨A is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- a￨L￨DT￨O￨- vital￨L￨JJ￨O￨- factor￨L￨NN￨O￨- in￨L￨IN￨O￨- monitoring￨L￨NN￨O￨- plant￨L￨NN￨O￨- disease/insect￨L￨NN￨O￨- damage￨L￨NN￨O￨- .￨L￨.￨O￨- +Its￨U￨PRP$￨O￨- successes￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- monitoring￨L￨NN￨O￨A were￨L￨VBD￨O￨- demonstrated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- great￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- at￨L￨IN￨O￨- leaf￨L￨NN￨O￨- ,￨L￨,￨O￨- canopy￨L￨NN￨O￨- and￨L￨CC￨O￨- field￨L￨NN￨O￨- levels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- BDSIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- gene￨L￨NN￨O￨- genealogy￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- phylogeny￨L￨NN￨O￨- connecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- sampled￨L￨VBN￨O￨A sequences￨L￨NNS￨O￨- ,￨L￨,￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- transmission￨L￨NN￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- note￨L￨NN￨O￨- that￨L￨IN￨O￨- of￨L￨IN￨O￨- course￨L￨NN￨O￨- this￨L￨DT￨O￨- transmission￨L￨NN￨O￨- history￨L￨NN￨O￨- is￨L￨VBZ￨O￨- incomplete￨L￨JJ￨O￨- as￨L￨IN￨O￨- many￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- sampled￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- here￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- BDSKY￨U￨NNP￨O￨- plot￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- parametrized￨L￨VBN￨O￨- to￨L￨TO￨O￨- enable￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- modelled￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- classic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- changing￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- composition￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- Stadler￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- –￨L￨:￨O￨- sampling￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- skyline￨L￨NN￨O￨- plot￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- BDSKY￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- serially￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- rate￨L￨NN￨O￨- changes￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- phylodynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- simultaneously￨L￨RB￨O￨- estimates￨L￨VBZ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- reconstructs￨L￨VBZ￨O￨- phylogenetic￨L￨JJ￨O￨- history￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- BDSIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨A ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- vaccination￨L￨NN￨O￨- decision-making￨L￨NN￨O￨- have￨L￨VBP￨O￨- typically￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- several￨L￨JJ￨O￨- determinants￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- perceived￨L￨VBN￨O￨A benefits￨L￨NNS￨O￨- and￨L￨CC￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- vaccine-induced￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- adverse￨L￨JJ￨O￨- events￨L￨NNS￨O￨- following￨L￨VBG￨O￨- immunization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- AEFI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- financial￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- expenses￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- indirect￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- absence￨L￨NN￨O￨- from￨L￨IN￨O￨- workplaces￨L￨NNS￨O￨- or￨L￨CC￨O￨- schools￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- others￨L￨NNS￨O￨- have￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- issues￨L￨NNS￨O￨- of￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- information￨L￨NN￨O￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- discrepancy￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- perceptions￨L￨NNS￨O￨- and￨L￨CC￨O￨- real￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- perceived￨L￨VBN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- adverse￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- different￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- previous￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- or￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Empirical￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- vaccination￨L￨NN￨O￨- decisions￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- subjected￨L￨VBN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- perceptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- continuously￨L￨RB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- environment￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- interact￨L￨VBP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- regard￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- awareness￨L￨NN￨O￨- about￨L￨IN￨O￨- severe￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- vaccine-related￨L￨JJ￨O￨- AEFI￨U￨NNP￨O￨- will￨L￨MD￨O￨- affect￨L￨VB￨O￨- their￨L￨PRP$￨O￨- perceptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- safety￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- ,￨L￨,￨O￨- influence￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- vaccination￨L￨NN￨O￨- decisions￨L￨NNS￨O￨A .￨L￨.￨O￨- +That￨U￨DT￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- say￨L￨VB￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- perceptions￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- prompted￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- alter￨L￨VB￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- vaccination￨L￨NN￨O￨- decisions￨L￨NNS￨O￨A and￨L￨CC￨O￨- ,￨L￨,￨O￨- hence￨L￨RB￨O￨- ,￨L￨,￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Only￨U￨RB￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- van￨L￨NN￨O￨- Hoek￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- evaluated￨L￨VBD￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- PCV13￨U￨NN￨O￨- in￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Wales￨U￨NNP￨LOCATION￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- epidemiological￨L￨JJ￨O￨- projections￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨A impacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- quantity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- and￨L￨CC￨O￨- next-nearest￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- formally￨L￨RB￨O￨A as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- the￨L￨DT￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- specified￨L￨VBN￨O￨- by￨L￨IN￨O￨- Chen￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- set￨L￨NN￨O￨A of￨L￨IN￨O￨- spreaders￨L￨NNS￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨JJR￨O￨- generalized￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- NP-hard￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- ,￨L￨,￨O￨- formally￨L￨RB￨O￨A .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- seroprevalence￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- conducted￨L￨VBN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- consensus￨L￨NN￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- select￨L￨VB￨O￨- seropositivity￨L￨NN￨O￨- thresholds￨L￨NNS￨O￨A and￨L￨CC￨O￨- adjust￨L￨VBP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- became￨L￨VBD￨O￨- seropositive￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- infection-seropositivity￨L￨JJ￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- ISP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- surveillance￨L￨NN￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- borders￨L￨NNS￨O￨- was￨L￨VBD￨O￨- quite￨L￨RB￨O￨- thorough￨L￨JJ￨O￨- for￨L￨IN￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- even￨L￨RB￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- H1N1￨U￨NN￨O￨- virus￨L￨NN￨O￨- had￨L￨VBD￨O￨- spread￨L￨VBN￨O￨- globally￨L￨RB￨O￨- ,￨L￨,￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- early￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- import￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- country￨L￨NN￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- more￨L￨RBR￨O￨- complete￨L￨JJ￨O￨- and￨L￨CC￨O￨- timely￨L￨JJ￨O￨- than￨L￨IN￨O￨- other￨L￨JJ￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- reporting￨L￨NN￨O￨- rate￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- routine￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨- with￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- refined￨L￨VBN￨O￨- from￨L￨IN￨O￨- statistics￨L￨NNS￨O￨- of￨L￨IN￨O￨- travellers￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- country￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- previous￨L￨JJ￨O￨- study￨L￨NN￨O￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- official￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨A only￨L￨RB￨O￨- reveals￨L￨VBZ￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- actual￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- during￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- instances￨L￨NNS￨O￨- the￨L￨DT￨O￨- consultation￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- case-patients￨L￨NNS￨O￨- was￨L￨VBD￨O￨- no￨L￨RB￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- reliable￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- reporting￨L￨NN￨O￨- rate￨L￨NN￨O￨- during￨L￨IN￨O￨- early￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- good￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- response￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- this￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- H1N1￨U￨NN￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Ministry￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- was￨L￨VBD￨O￨- measured￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- as￨L￨RB￨O￨- low￨L￨JJ￨O￨- as￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- 003￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- 's￨L￨POS￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- v￨L￨LS￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- uninfected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- free￨L￨JJ￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- biological￨L￨JJ￨O￨- grounds￨L￨NNS￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- primary￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- approximately￨L￨RB￨O￨- proportionate￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- load￨L￨NN￨O￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨A .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨A in￨L￨FW￨O￨- vivo￨L￨FW￨O￨- is￨L￨VBZ￨O￨- limited￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- approach￨L￨VB￨O￨- saturation￨L￨NN￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- virus￨L￨NN￨O￨- produced￨L￨VBD￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- reasonable￨L￨JJ￨O￨- to￨L￨TO￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- approximately￨L￨RB￨O￨- proportionate￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨A k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- x.￨L￨NN￨O￨- +Srivastava￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Chandra￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- have￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- :￨L￨:￨O￨- uninfected￨L￨JJ￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- advantages￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- capture￨L￨VB￨O￨- complicated￨L￨JJ￨O￨- mobility￨L￨NN￨O￨A and￨L￨CC￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- pixels￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- mobility￨L￨NN￨O￨A models￨L￨NNS￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- travel￨L￨VB￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- censuses￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- was￨L￨VBD￨O￨- seeded￨L￨VBN￨O￨- with￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- central￨L￨JJ￨O￨- region￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1G￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- simulations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- repeated￨L￨VBN￨O￨- 25￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- resolution￨L￨NN￨O￨A .￨L￨.￨O￨- +Both￨U￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- resolution￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- representation￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- resolution￨L￨NN￨O￨- defines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pixels￨L￨NNS￨O￨- making￨L￨VBG￨O￨- up￨L￨RP￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- image￨L￨NN￨O￨- ”￨L￨''￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- generation￨L￨NN￨O￨- Bayesian￨U￨NNP￨O￨- Evolutionary￨U￨NNP￨O￨- Analysis￨U￨NN￨O￨- by￨L￨IN￨O￨- Sampling￨U￨VBG￨O￨- Trees￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- BEAST￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- package￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- popular￨L￨JJ￨O￨- platform￨L￨NN￨O￨A for￨L￨IN￨O￨- solving￨L￨VBG￨O￨- such￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- and￨L￨CC￨O￨- takes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- modeling￨L￨NN￨O￨- philosophy￨L￨NN￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- problems￨L￨NNS￨O￨- share￨L￨VBP￨O￨- at￨L￨IN￨O￨- their￨L￨PRP$￨O￨- core￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- phylogenetic￨L￨JJ￨O￨- time-trees￨L￨NNS￨O￨- .￨L￨.￨O￨- +All￨U￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- design￨L￨NN￨O￨- goals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- made￨L￨VBN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- scope￨L￨NN￨O￨- that￨L￨WDT￨O￨- encompasses￨L￨VBZ￨O￨- efficient￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- and￨L￨CC￨O￨- model-based￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- testing￨L￨NN￨O￨- for￨L￨IN￨O￨- sequence￨L￨NN￨O￨- data￨L￨NN￨O￨- analysis￨L￨NN￨O￨- involving￨L￨VBG￨O￨- phylogenetic￨L￨JJ￨O￨A time-tree￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- BEAST￨U￨NN￨O￨- 1.x￨L￨NN￨O￨- design￨L￨NN￨O￨A resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- separately￨L￨RB￨O￨- maintained￨L￨VBD￨O￨- parts￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- BEAST￨U￨NN￨O￨- model/likelihood/operator￨L￨NN￨O￨- class￨L￨NN￨O￨- hierarchies￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- BEAST￨U￨NN￨O￨- XML￨U￨NN￨O￨- parsing￨L￨NN￨O￨- class￨L￨NN￨O￨- hierarchy￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- BEAUti￨U￨NN￨O￨- 1.x￨L￨NN￨O￨- class￨L￨NN￨O￨- hierarchy￨L￨NN￨O￨- and￨L￨CC￨O￨- user￨L￨NN￨O￨- interface￨L￨NN￨O￨- code￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- Bayesian￨U￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- encompass￨L￨VB￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- analysis￨L￨NN￨O￨- types￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- at￨L￨IN￨O￨- their￨L￨PRP$￨O￨- core￨L￨NN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- including￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- phylogenetic￨L￨JJ￨O￨A or￨L￨CC￨O￨- genealogical￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- overarching￨L￨JJ￨O￨- design￨L￨NN￨O￨- and￨L￨CC￨O￨- implementation￨L￨NN￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- re-write￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- BEAST￨U￨NN￨O￨- platform￨L￨NN￨O￨A that￨L￨IN￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- designated￨L￨VBN￨O￨- BEAST￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- presenting￨L￨VBG￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- significant￨L￨JJ￨O￨- new￨L￨JJ￨O￨- models￨L￨NNS￨O￨- developed￨L￨VBD￨O￨- especially￨L￨RB￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- new￨L￨JJ￨O￨- platform￨L￨NN￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- RVFV￨U￨NN￨O￨- is￨L￨VBZ￨O￨- spread￨L￨VBN￨O￨- primarily￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- bite￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- ,￨L￨,￨O￨- mainly￨L￨RB￨O￨- Aedes￨U￨NNP￨O￨- and￨L￨CC￨O￨- Culex￨U￨NNP￨MISC￨- spp.￨L￨NNP￨O￨- mosquito￨L￨NN￨O￨A is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- transmitting￨L￨VBG￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- directly￨L￨RB￨O￨- to￨L￨TO￨O￨- her￨L￨PRP$￨O￨- offspring￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- vertical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- via￨L￨IN￨O￨- eggs￨L￨NNS￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- new￨L￨JJ￨O￨- generations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- hatching￨L￨VBG￨O￨- from￨L￨IN￨O￨- eggs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- heavy￨L￨JJ￨O￨- rainfall￨L￨NNS￨O￨- ,￨L￨,￨O￨- larval￨L￨JJ￨O￨- habitats￨L￨NNS￨O￨- frequently￨L￨RB￨O￨- become￨L￨VBP￨O￨- flooded￨L￨VBN￨O￨- ,￨L￨,￨O￨- enabling￨L￨VBG￨O￨- the￨L￨DT￨O￨- eggs￨L￨NNS￨O￨- to￨L￨TO￨O￨- hatch￨L￨VB￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨A population￨L￨NN￨O￨- to￨L￨TO￨O￨- rapidly￨L￨RB￨O￨- increase￨L￨VB￨O￨- ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- animals￨L￨NNS￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- feed￨L￨VBP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +RVFV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- severe￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- animals￨L￨NNS￨O￨A and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- induced￨L￨VBD￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- livestock￨L￨NN￨O￨- ,￨L￨,￨O￨- long-term￨L￨JJ￨O￨- health￨L￨NN￨O￨- effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- destruction￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- system￨L￨NN￨O￨- which￨L￨WDT￨O￨- included￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- mosquito￨L￨NN￨O￨A populations￨L￨NNS￨O￨- Aedes￨U￨NNS￨O￨- and￨L￨CC￨O￨- Culex￨U￨JJ￨MISC￨- spp￨L￨NN￨MISC￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- occurred￨L￨VBD￨O￨- in￨L￨IN￨O￨- Taipei￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- government￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- 129,106￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨A who￨L￨WP￨O￨- were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- virus￨L￨NN￨O￨- or￨L￨CC￨O￨- herpangina￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 405￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- got￨L￨VBD￨O￨- even￨L￨RB￨O￨- worse￨L￨JJR￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- neurological￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- pulmonary￨L￨JJ￨CAUSE_OF_DEATH￨- edema￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- 78￨L￨CD￨NUMBER￨- children￨L￨NNS￨O￨- died￨L￨VBD￨O￨- during￨L￨IN￨O￨- this￨L￨DT￨O￨- HFMD￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- 25,000￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨A infected￨L￨VBN￨O￨A with￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- among￨L￨IN￨O￨- these￨L￨DT￨O￨- ,￨L￨,￨O￨- 42￨L￨CD￨NUMBER￨- children￨L￨NNS￨O￨- lost￨L￨VBD￨O￨- their￨L￨PRP$￨O￨- lives￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- appeared￨L￨VBD￨O￨- in￨L￨IN￨O￨- Bulgaria￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- 750￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨A were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- 149￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- had￨L￨VBD￨O￨- paralyses￨L￨NNS￨O￨- and￨L￨CC￨O￨- 44￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- died￨L￨VBD￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- serious￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- that￨L￨DT￨O￨- by￨L￨IN￨O￨- other￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- enterovirus￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- HFMD￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- attacked￨L￨VBN￨O￨- Sarawak￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Malaysia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- causing￨L￨VBG￨O￨- 34￨L￨CD￨NUMBER￨- children￨L￨NNS￨O￨A deaths￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- one￨L￨CD￨NUMBER￨- could￨L￨MD￨O￨- seek￨L￨VB￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- time-dependent￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- signalling￨L￨NN￨O￨- and￨L￨CC￨O￨- metabolic￨L￨JJ￨O￨- substances￨L￨NNS￨O￨- within￨L￨IN￨O￨- individual￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- while￨L￨IN￨O￨- spatially￨L￨RB￨O￨- discriminating￨L￨VBG￨O￨- analytical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Raman￨U￨NN￨O￨- spectroscopy￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- mass￨L￨NN￨O￨- spectrometry￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 109￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 113￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- do￨L￨VBP￨O￨- exist￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- in￨L￨FW￨O￨- situ￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- commonest￨L￨JJS￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- substances￨L￨NNS￨O￨- in￨L￨IN￨O￨- ecosystems￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- assumes￨L￨VBZ￨O￨- ‘￨L￨``￨O￨- fully￨L￨RB￨O￨- mixed￨L￨JJ￨O￨- ’￨L￨''￨O￨- compartments￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- ‘￨L￨``￨O￨- pools￨L￨NNS￨O￨- ’￨L￨''￨O￨- of￨L￨IN￨O￨- metabolites￨L￨NNS￨O￨- ,￨L￨,￨O￨- cf.￨L￨VBP￨O￨- The￨U￨DT￨O￨- gut￨L￨NN￨O￨- microflora￨L￨NN￨O￨- contain￨L￨VBP￨O￨- some￨L￨DT￨O￨- 1013￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1014￨L￨CD￨NUMBER￨- bacteria￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- over￨L￨IN￨O￨- 1000￨L￨CD￨NUMBER￨- bacterial￨L￨JJ￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- unique￨L￨JJ￨O￨- metabolic￨L￨JJ￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- metabolite￨L￨NN￨O￨- transformation￨L￨NN￨O￨A and￨L￨CC￨O￨- cross-feeding￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- prokaryotic￨L￨JJ￨O￨- group￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- gut￨L￨NN￨O￨- epithelia￨L￨NN￨O￨- ;￨L￨:￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- noteworthy￨L￨JJ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- antibiotics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- obvious￨L￨JJ￨O￨- effect￨L￨NN￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- other￨L￨JJ￨O￨- human-targeted￨L￨JJ￨O￨- pharmaceuticals￨L￨NNS￨O￨- will￨L￨MD￨O￨- also￨L￨RB￨O￨- undergo￨L￨VB￨O￨- microbial￨L￨JJ￨O￨- drug￨L￨NN￨O￨- transformation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- cause￨L￨VB￨O￨- shifts￨L￨NNS￨O￨- in￨L￨IN￨O￨- gut￨L￨NN￨O￨- flora￨L￨NN￨O￨- metabolism￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- clearly￨L￨RB￨O￨- not￨L￨RB￨O￨- news￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- productivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pharmaceutical￨L￨JJ￨O￨- industry￨L￨NN￨O￨- has￨L￨VBZ￨O￨- declined￨L￨VBN￨O￨- significantly￨L￨RB￨O￨- during￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- following￨L￨VBG￨O￨- an￨L￨DT￨O￨- ‘￨L￨``￨O￨- inverse￨L￨JJ￨O￨- Moore￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- Law￨U￨NNP￨O￨- ’￨L￨POS￨O￨- ,￨L￨,￨O￨- Eroom￨U￨NNP￨ORGANIZATION￨- 's￨L￨POS￨O￨- Law￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- that￨L￨DT￨O￨- many￨L￨JJ￨O￨- commentators￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- [￨L￨-LRB-￨O￨- 7,8,14￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 47￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- consider￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- cause￨L￨NN￨O￨A of￨L￨IN￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- excessive￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- individual￨L￨JJ￨O￨- molecular￨L￨JJ￨O￨- target￨L￨NN￨O￨- discovery￨L￨NN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- sensible￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- systems-level￨L￨JJ￨O￨- approach￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Why￨U￨WRB￨O￨- we￨L￨PRP￨O￨- choose￨L￨VBP￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- metabolic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- more￨L￨RBR￨O￨- than￨L￨IN￨O￨- transcriptomic￨L￨JJ￨O￨- or￨L￨CC￨O￨- proteomic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- comes￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- recognition￨L￨NN￨O￨- –￨L￨:￨O￨- made￨L￨VBN￨O￨- particularly￨L￨RB￨O￨- clear￨L￨JJ￨O￨- by￨L￨IN￨O￨- workers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- metabolic￨L￨JJ￨O￨- control￨L￨NN￨O￨- analysis￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 69￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 77￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- –￨L￨:￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- activities￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- enzymes￨L￨NNS￨O￨- tend￨L￨VBP￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- rather￨L￨RB￨O￨- small￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- metabolic￨L￨JJ￨O￨- fluxes￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- and￨L￨CC￨O￨- do￨L￨VB￨O￨- have￨L￨VB￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- metabolite￨L￨NN￨O￨- concentrations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- metabolome￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 78￨L￨CD￨NUMBER￨A –￨L￨:￨O￨- 81￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Overall￨U￨RB￨O￨- ,￨L￨,￨O￨- metabolites￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- mathematical￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- graphs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- familiar￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- biochemical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- laboratory￨L￨NN￨O￨- posters￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- now￨L￨RB￨DATE￨- available￨L￨JJ￨O￨- digitally￨L￨RB￨O￨- –￨L￨:￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- reflect￨L￨VBP￨O￨A enzymes￨L￨NNS￨O￨- catalysing￨L￨VBG￨O￨- interconversions￨L￨NNS￨O￨- of￨L￨IN￨O￨- biochemical￨L￨JJ￨O￨- substances￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- transporters￨L￨NNS￨O￨- ,￨L￨,￨O￨- see￨L￨VBP￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Dividing￨U￨VBG￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- health￨L￨NN￨O￨- certification￨L￨NN￨O￨- method￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- being￨L￨VBG￨O￨- exported￨L￨VBN￨O￨- provided￨L￨VBN￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- cost-effectiveness￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- $￨L￨$￨O￨- )￨L￨-RRB-￨O￨- per￨L￨IN￨O￨- infected￨L￨JJ￨O￨- animal￨L￨NN￨O￨- prevented￨L￨VBD￨O￨A from￨L￨IN￨O￨- being￨L￨VBG￨O￨- exported￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- smaller￨L￨JJR￨O￨- the￨L￨DT￨O￨- Figure￨U￨NNP￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- cost-effective￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- note￨L￨NN￨O￨- :￨L￨:￨O￨- $￨L￨$￨MONEY￨- refers￨L￨VBZ￨MONEY￨- to￨L￨TO￨O￨- US$￨U￨$￨MISC￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- manuscript￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- evaluate￨L￨VBP￨O￨- current￨L￨JJ￨DATE￨- export￨L￨NN￨O￨- health￨L￨NN￨O￨- certification￨L￨NN￨O￨- methods￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- port￨L￨NN￨O￨- quarantine￨L￨NN￨O￨A inspection￨L￨NN￨O￨- and￨L￨CC￨O￨- alternatives￨L￨NNS￨O￨- using￨L￨VBG￨O￨- upstream￨L￨JJ￨O￨- health￨L￨NN￨O￨- certification￨L￨NN￨O￨- at￨L￨IN￨O￨- regional￨L￨JJ￨O￨- markets￨L￨NNS￨O￨- ;￨L￨:￨O￨- minor￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- quarantine￨L￨NN￨O￨- and￨L￨CC￨O￨- laboratory￨L￨NN￨O￨- testing￨L￨NN￨O￨- protocols￨L￨NNS￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- assessed￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- effectiveness￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- certification￨L￨NN￨O￨- methods￨L￨NNS￨O￨- was￨L￨VBD￨O￨- taken￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- exported￨L￨VBN￨O￨- animals￨L￨NNS￨O￨A that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- any￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- benefits￨L￨NNS￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- provided￨L￨VBD￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- prevented￨L￨VBD￨O￨A from￨L￨IN￨O￨- being￨L￨VBG￨O￨- exported￨L￨VBN￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- certification￨L￨NN￨O￨- methods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- exporting￨L￨VBG￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- some￨L￨DT￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- Somalia￨U￨NNP￨COUNTRY￨- animals￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- clinically￨L￨RB￨O￨- inspected￨L￨VBN￨O￨- at￨L￨IN￨O￨- regional￨L￨JJ￨O￨- markets￨L￨NNS￨O￨- before￨L￨IN￨O￨- reaching￨L￨VBG￨O￨- the￨L￨DT￨O￨- quarantine￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- possums￨L￨NNS￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- predicted￨L￨VBD￨O￨- that￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- would￨L￨MD￨O￨- spread￨L￨VB￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- population￨L￨NN￨O￨- if￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 8￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- killer￨L￨NN￨O￨- whales￨L￨NNS￨O￨- were￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- highly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- relationships￨L￨NNS￨O￨- within￨L￨IN￨O￨- it￨L￨PRP￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- African￨U￨JJ￨NATIONALITY￨- buffaloes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- predicted￨L￨VBD￨O￨A that￨L￨IN￨O￨- slowly￨L￨RB￨O￨- spreading￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- would￨L￨MD￨O￨- affect￨L￨VB￨O￨- more￨L￨RBR￨O￨- individuals￨L￨NNS￨O￨- than￨L￨IN￨O￨- rapidly￨L￨RB￨O￨- spreading￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- between￨L￨IN￨O￨- groups￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Patterns￨U￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A are￨L￨VBP￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- most￨L￨RBS￨O￨- importantly￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- organisation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- species￨L￨NNS￨O￨- and￨L￨CC￨O￨- disease-specific￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- transmission￨L￨NN￨O￨- mode￨L￨NN￨O￨- ,￨L￨,￨O￨- infectiousness￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- recovery￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- African￨U￨JJ￨NATIONALITY￨- buffalo￨L￨NN￨O￨- indicated￨L￨VBD￨O￨- a￨L￨DT￨O￨- much￨L￨JJ￨O￨- faster￨L￨JJR￨O￨- spread￨L￨NN￨O￨A of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- network￨L￨NN￨O￨- than￨L￨IN￨O￨- on￨L￨IN￨O￨- actual￨L￨JJ￨O￨- association￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A in￨L￨IN￨O￨- chimpanzees￨L￨NNS￨O￨- and￨L￨CC￨O￨- orang-utans￨L￨NNS￨O￨- .￨L￨.￨O￨- +Statistical￨U￨JJ￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- fitting￨L￨NN￨O￨- of￨L￨IN￨O￨- structured￨L￨JJ￨O￨- coalescent￨L￨JJ￨O￨A models￨L￨NNS￨O￨- to￨L￨TO￨O￨- genealogies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- parameters￨L￨NNS￨O￨- relating￨L￨VBG￨O￨- to￨L￨TO￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- migration￨L￨NN￨O￨- rates￨L￨NNS￨O￨- between￨L￨IN￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- great￨L￨JJ￨O￨- appeal￨L￨NN￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- generalizes￨L￨VBZ￨O￨- coalescent￨L￨JJ￨O￨A models￨L￨NNS￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- both￨L￨DT￨O￨- birth￨L￨NN￨O￨- and￨L￨CC￨O￨- migration￨L￨NN￨O￨- rates￨L￨NNS￨O￨- to￨L￨TO￨O￨- change￨L￨VB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- nonlinear￨L￨JJ￨O￨- and￨L￨CC￨O￨- far￨L￨RB￨O￨- from￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- also￨L￨RB￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- coalescent￨L￨JJ￨O￨A process￨L￨NN￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- change￨L￨VBP￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- manner￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- coalescent￨L￨JJ￨O￨A models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- populations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- birth￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rates￨L￨NNS￨O￨- vary￨L￨VBP￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨A parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- genealogy￨L￨NN￨O￨- using￨L￨VBG￨O￨- likelihood-based￨L￨JJ￨O￨- inference￨L￨NN￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- comparing￨L￨VBG￨O￨- results￨L￨NNS￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- spiking￨L￨VBG￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- an￨L￨DT￨O￨- implicit￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- collective￨L￨JJ￨O￨- activity￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- avalanches￨L￨NNS￨O￨- ,￨L￨,￨O￨- LFPs￨U￨NNS￨O￨- and￨L￨CC￨O￨- spikes￨L￨NNS￨O￨- behave￨L￨VBP￨O￨- similarly￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- exception￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- authors￨L￨NNS￨O￨- which￨L￨WDT￨O￨- carefully￨L￨RB￨O￨- state￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- activity￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- units￨L￨NNS￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- LFP￨U￨NNP￨ORGANIZATION￨- measured￨L￨VBN￨O￨A at￨L￨IN￨O￨- an￨L￨DT￨O￨- electrode￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Networks￨U￨NNP￨O￨- of￨L￨IN￨O￨- excitable￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- automata￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- well-established￨L￨JJ￨O￨- models￨L￨NNS￨O￨- allowing￨L￨VBG￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- system￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- directed￨L￨VBN￨O￨- percolation￨L￨NN￨O￨- universality￨L￨NN￨O￨- class￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- direct￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- experimental￨L￨JJ￨O￨A results￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- tuned￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- point￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- self-organizes￨L￨JJ￨O￨- itself￨L￨PRP￨O￨- around￨L￨IN￨O￨- it￨L￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- avalanches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- measured￨L￨VBN￨O￨A by￨L￨IN￨O￨- counting￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- spikes￨L￨NNS￨O￨- ”￨L￨''￨O￨- in￨L￨IN￨O￨- those￨L￨DT￨O￨- neurons￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- a￨L￨DT￨O￨- genetic-epidemiological￨L￨JJ￨O￨- function￨L￨NN￨O￨- for￨L￨IN￨O￨- quantitative￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- binary￨L￨JJ￨O￨A infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- unlike￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- takes￨L￨VBZ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- and￨L￨CC￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectiousness￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- some￨L￨DT￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- reported￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- could￨L￨MD￨O￨- confer￨L￨VB￨O￨- cross-protective￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- related￨L￨JJ￨O￨- genotypes￨L￨NNS￨O￨A which￨L￨WDT￨O￨- would￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- hr￨L￨NN￨DURATION￨- nonvaccine￨L￨NN￨O￨- HPVs￨U￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- HPVs￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- HPVs￨U￨NNS￨O￨- 16￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 18￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- HPVs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- may￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- selection￨L￨NN￨O￨- pressure￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- hr￨L￨NN￨DURATION￨- HPVs￨U￨NNS￨O￨- or￨L￨CC￨O￨- hr￨L￨NN￨DURATION￨- nonvaccine￨L￨NN￨O￨- HPV￨U￨NN￨O￨- types￨L￨NNS￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- vaccines￨L￨NNS￨O￨- could￨L￨MD￨O￨- modulate￨L￨VB￨O￨- positively￨L￨RB￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- genotypes￨L￨NNS￨O￨A through￨L￨IN￨O￨- a￨L￨DT￨O￨- replacement￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- genotype￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- hr￨L￨NN￨DURATION￨- nonvaccine￨L￨NN￨O￨- HPVs￨U￨NNS￨O￨- after￨L￨IN￨O￨- actual￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- scheme￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- clinically￨L￨RB￨O￨- healthy￨L￨JJ￨O￨- Mexican￨U￨JJ￨NATIONALITY￨- women￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- 15￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- percentage￨L￨NN￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- HPVs￨U￨NNS￨O￨- 16￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 18￨L￨CD￨NUMBER￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- CC￨U￨NN￨O￨- is￨L￨VBZ￨O￨- 71￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- (￨L￨-LRB-￨O￨- 63￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- HPV￨U￨NN￨O￨- 16￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 8￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- HPV￨U￨NN￨O￨- 18￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- genotypes￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- highlighting￨L￨VBG￨O￨- the￨L￨DT￨DATE￨- hr￨L￨NN￨DATE￨- HPVs￨U￨NNS￨O￨- 31￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 58￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- frequent￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- type￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- previous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- studied￨L￨VBN￨O￨- HPV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- ,￨L￨,￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- CC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- screening￨L￨NN￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨O￨- quadrivalent￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- human￨L￨JJ￨O￨- papillomavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HPV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- helped￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- against￨L￨IN￨O￨- oncogenic￨L￨JJ￨O￨- HPVs￨U￨NNS￨O￨- 16￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 18￨L￨CD￨NUMBER￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- warts￨L￨NNS￨O￨- causing￨L￨VBG￨O￨- genital￨L￨JJ￨O￨- HPVs￨U￨NNS￨O￨- 6￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 11￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- filtering￨L￨VBG￨O￨A procedure￨L￨NN￨O￨- includes￨L￨VBZ￨O￨- repeated￨L￨VBN￨O￨- short-term￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- prediction-update￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- propagates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- particles/ensemble￨L￨NN￨O￨- forward￨L￨RB￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- update￨L￨VBP￨O￨- ,￨L￨,￨O￨- triggered￨L￨VBN￨O￨- by￨L￨IN￨O￨- arrival￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- observation￨L￨NN￨O￨- record￨L￨NN￨O￨- ,￨L￨,￨O￨- assimilates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- observation￨L￨NN￨O￨- to￨L￨TO￨O￨- refine￨L￨VB￨O￨- the￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- state￨L￨NN￨O￨- variables￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- document￨L￨VBP￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- conditions￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- represent￨L￨VBP￨O￨- biological￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- inherent￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A strain￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- which￨L￨WDT￨O￨- also￨L￨RB￨O￨- can￨L￨MD￨O￨- vary￨L￨VB￨O￨- from￨L￨IN￨O￨- region￨L￨NN￨O￨- to￨L￨TO￨O￨- region￨L￨NN￨O￨- and￨L￨CC￨O￨- season￨L￨NN￨O￨- to￨L￨TO￨O￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- accurate￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- fidelity￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- represents￨L￨VBZ￨O￨- real-world￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- specification￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- state￨L￨NN￨O￨- variable￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- forecast￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- accurately￨L￨RB￨O￨- predicted￨L￨VBN￨O￨- with￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- recursively￨L￨RB￨O￨- optimized￨L￨VBN￨O￨- using￨L￨VBG￨O￨- real-time￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- assimilation￨L￨NN￨O￨- methods￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- assimilation￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- filtering￨L￨VBG￨O￨A ,￨L￨,￨O￨- methods￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- conjunction￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- variable￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- and￨L￨CC￨O￨- infer￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- works￨L￨NNS￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- revealed￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- indeed￨L￨RB￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- propagation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A spreading￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- small-world￨L￨JJ￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- much￨L￨JJ￨O￨- faster￨L￨JJR￨O￨- and￨L￨CC￨O￨- broader￨L￨JJR￨O￨- than￨L￨IN￨O￨- that￨L￨DT￨O￨- on￨L￨IN￨O￨- regular￨L￨JJ￨O￨- network￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- long-range￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- summarized￨L￨VBD￨O￨- the￨L￨DT￨O￨- significant￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- enhancement￨L￨NN￨O￨- ,￨L￨,￨O￨- would￨L￨MD￨O￨- spread￨L￨VB￨O￨- more￨L￨RBR￨O￨- effectively￨L￨RB￨O￨- in￨L￨IN￨O￨- regular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- than￨L￨IN￨O￨- that￨L￨DT￨O￨- in￨L￨IN￨O￨- random￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- of￨L￨IN￨O￨- informed￨L￨VBN￨O￨- proportion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- approximate￨L￨JJ￨O￨- to￨L￨TO￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- random￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A when￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infinite￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨A spreading￨L￨VBG￨O￨A process￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- would￨L￨MD￨O￨- lose￨L￨VB￨O￨- interest￨L￨NN￨O￨- of￨L￨IN￨O￨- further￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- less￨L￨JJR￨O￨- predictable￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨A on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- hub￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- can￨L￨MD￨O￨- enhance￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- speed￨L￨NN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- influenced￨L￨VBN￨O￨- scope￨L￨NN￨O￨- .￨L￨.￨O￨- +Generalizations￨U￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- have￨L￨VBP￨O￨- revealed￨L￨VBN￨O￨- an￨L￨DT￨O￨- intimate￨L￨JJ￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- 's￨L￨POS￨O￨- adjacency￨L￨NN￨O￨- matrix13￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- solve￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- and￨L￨CC￨O￨- differential￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- its￨L￨PRP$￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨A number￨L￨NN￨O￨A R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- topology-infection￨L￨JJ￨O￨- matrix￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- mean-field￨L￨JJ￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- look￨L￨VBP￨O￨- at￨L￨IN￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- correlations￨L￨NNS￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- or￨L￨CC￨O￨- connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- positive￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- degree￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- more￨L￨RBR￨O￨- vulnerable￨L￨JJ￨O￨- to￨L￨TO￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- increasing￨L￨VBG￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- negative￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- make￨L￨VBP￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- less￨L￨RBR￨O￨- vulnerable￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- decrease￨L￨NN￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- degree￨L￨NN￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- degree-degree￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨A number￨L￨NN￨O￨A R0￨U￨NN￨O￨- generalizes￨L￨VBZ￨O￨- to34￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- superscript￨L￨JJ￨O￨- unc￨L￨NN￨O￨- stands￨L￨VBZ￨O￨- for￨L￨IN￨O￨- uncorrelated￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- 〈￨L￨SYM￨O￨- k￨L￨NN￨O￨- 〉￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- 〈￨L￨CD￨NUMBER￨- k2￨L￨NN￨O￨- 〉￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degrees￨L￨NNS￨O￨- squared￨L￨VBD￨O￨- and￨L￨CC￨O￨- σ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- deviation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- shows￨L￨VBZ￨O￨- then￨L￨RB￨O￨- even￨L￨RB￨O￨- a￨L￨DT￨O￨- mild￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- segregation￨L￨NN￨O￨- can￨L￨MD￨O￨- drastically￨L￨RB￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨A number￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- Different￨U￨JJ￨O￨- functions￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨A during￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- will￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- key￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- measurements￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- agent-based￨L￨JJ￨O￨- Monte￨U￨NNP￨LOCATION￨- Carlo￨U￨NNP￨LOCATION￨- simulation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- created￨L￨VBN￨O￨- to￨L￨TO￨O￨- access￨L￨NN￨O￨- variability￨L￨NN￨O￨- around￨L￨IN￨O￨- key￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- measurements￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- completed￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- which￨L￨WDT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- media￨L￨NNS￨O￨A during￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- including￨L￨VBG￨O￨- ‘￨L￨``￨O￨- media￨L￨NNS￨O￨- functions￨L￨NNS￨O￨- ’￨L￨POS￨O￨- that￨L￨WDT￨O￨- affect￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Parameters￨U￨NNS￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- influence￨L￨VBP￨O￨- key￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- different￨L￨JJ￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- media￨L￨NNS￨O￨A function￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Epidemic￨U￨JJ￨O￨- outcome￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- media￨L￨NNS￨O￨A function￨L￨NN￨O￨- chosen￨L￨VBN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨A interaction￨L￨NN￨O￨- data￨L￨NNS￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- demonstrating￨L￨VBG￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- promising￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨- communication￨L￨NN￨O￨- logs￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- concrete￨L￨JJ￨O￨- source￨L￨NN￨O￨- for￨L￨IN￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- takes￨L￨VBZ￨O￨- place￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- close-proximity￨L￨JJ￨O￨- physical￨L￨JJ￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- never￨L￨RB￨O￨- be￨L￨VB￨O￨- fully￨L￨RB￨O￨- recovered￨L￨VBN￨O￨- in￨L￨IN￨O￨- reality￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- assume￨L￨VB￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- occurs￨L￨VBZ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- differing￨L￨VBG￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- a￨L￨DT￨O￨- communication￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- phone￨L￨NN￨O￨A ,￨L￨,￨O￨- sms￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- inferred￨L￨VBD￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨A model￨L￨NN￨TITLE￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- tracing￨L￨VBG￨O￨- efforts￨L￨NNS￨O￨- on￨L￨IN￨O￨- noisy￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- a￨L￨DT￨O￨- perturbed￨L￨VBN￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- present￨L￨JJ￨DATE￨- effort￨L￨NN￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- exploiting￨L￨VBG￨O￨- these￨L￨DT￨O￨- phone￨L￨NN￨O￨A communication￨L￨NN￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨- traces￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- immunization￨L￨NN￨O￨A ratio￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- acquaintance￨L￨NN￨O￨- immunization￨L￨NN￨O￨- and￨L￨CC￨O￨- community-bridge￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- was￨L￨VBD￨O￨- determined￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- influences￨L￨NNS￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- primary￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- ring￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- detection￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- trace￨L￨NN￨O￨- escape￨L￨NN￨CRIMINAL_CHARGE￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- trace￨L￨NN￨O￨- lag￨L￨NN￨O￨- were￨L￨VBD￨O￨- analyzed￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- realistic￨L￨JJ￨O￨- urban￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- Portland￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- many￨L￨JJ￨O￨- directly￨L￨RB￨O￨- person-to-person￨L￨JJ￨O￨- transmitted￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- ,￨L￨,￨O￨- SARS￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- network￨L￨NN￨O￨A models￨L￨NNS￨O￨A could￨L￨MD￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- possibly￨L￨RB￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- successful￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- immunization￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A regularly￨L￨RB￨O￨- outperform￨L￨VBP￨O￨- stochastic￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- realistic￨L￨JJ￨O￨- global￨L￨JJ￨O￨- network￨L￨NN￨O￨- information￨L￨NN￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- constantly￨L￨RB￨O￨- unavailable￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- control￨L￨VBP￨O￨- practice￨L￨NN￨O￨- .￨L￨.￨O￨- +Network￨U￨NNP￨O￨- models￨L￨NNS￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- conducive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- widely￨L￨RB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- immunization￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- immunization￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- compared￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- growing￨L￨VBG￨O￨- body￨L￨NN￨O￨- of￨L￨IN￨O￨- literature￨L￨NN￨O￨- on￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- crowd￨L￨NN￨O￨- behaviour￨L￨NN￨O￨A in￨L￨IN￨O￨- crowded￨L￨JJ￨O￨- places￨L￨NNS￨O￨- have￨L￨VBP￨O￨- revealed￨L￨VBN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- non-linear￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- ,￨L￨,￨O￨- adaptive￨L￨JJ￨O￨- and￨L￨CC￨O￨- self-organised￨L￨JJ￨O￨- crowd￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- that￨L￨WDT￨O￨- seriously￨L￨RB￨O￨- question￨L￨VBP￨O￨- the￨L￨DT￨O￨- validity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- well-mixed￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- network￨L￨NN￨O￨- effects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- some￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- contemporary￨L￨JJ￨O￨- network￨L￨NN￨O￨- science￨L￨NN￨O￨- approaches91015￨L￨NN￨O￨- to￨L￨TO￨O￨- modelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- greatly￨L￨RB￨O￨- improved￨L￨VBN￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨- accuracy￨L￨NN￨O￨- at￨L￨IN￨O￨- large￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- limited￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- crowd￨L￨NN￨O￨- behaviour￨L￨NN￨O￨A that￨L￨WDT￨O￨- come￨L￨VBP￨O￨- into￨L￨IN￨O￨- play￨L￨NN￨O￨- in￨L￨IN￨O￨- densely￨L￨RB￨O￨- crowded￨L￨VBN￨O￨- and￨L￨CC￨O￨- confined￨L￨VBN￨O￨- spaces￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- transport￨L￨NN￨O￨- hubs￨L￨NNS￨O￨- ,￨L￨,￨O￨- mass￨L￨NN￨O￨- gatherings￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- city￨L￨NN￨O￨- centres￨L￨NNS￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- we￨L￨PRP￨O￨- want￨L￨VBP￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- crowd￨L￨NN￨O￨- behaviour￨L￨NN￨O￨A explicitly￨L￨RB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- now￨L￨RB￨DATE￨- propose￨L￨VB￨O￨- an￨L￨DT￨O￨- improved￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- λ￨L￨NN￨O￨- will￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- crowd￨L￨NN￨O￨- density￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- will￨L￨MD￨O￨- study￨L￨VB￨O￨- how￨L￨WRB￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- crowd￨L￨NN￨O￨- behaviour￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- importantly￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- crowd￨L￨NN￨O￨- density￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- data￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- release￨L￨NN￨O￨- of￨L￨IN￨O￨- TgHSP70￨U￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- bloodstream￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasites￨L￨NNS￨O￨- mediated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- DXM-treated￨U￨JJ￨O￨- mice￨L￨NNS￨O￨A presented￨L￨VBD￨O￨- lower￨L￨JJR￨O￨- inflammatory￨L￨JJ￨O￨- alterations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- protein￨L￨NN￨O￨- expression￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- brain￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- multiplication￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- T.￨U￨FW￨MISC￨- gondii￨L￨FW￨O￨- soluble￨L￨JJ￨O￨- antigen￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- STAg￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- preparation￨L￨NN￨O￨- ,￨L￨,￨O￨- tachyzoites￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- RH￨U￨NN￨O￨- strain￨L￨NN￨O￨- were￨L￨VBD￨O￨- maintained￨L￨VBN￨O￨- in￨L￨IN￨O￨- BALB/c￨U￨NN￨O￨- mice￨L￨NNS￨O￨- by￨L￨IN￨O￨- intraperitoneal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.p.￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- serial￨L￨JJ￨O￨- passages￨L￨NNS￨O￨- at￨L￨IN￨O￨- 48-h￨L￨JJ￨O￨- intervals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- report￨L￨VBP￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- TgHSP70-specific￨U￨JJ￨O￨- IgY￨U￨NN￨O￨- antibodies￨L￨NNS￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- immunological￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- the￨L￨DT￨O￨- protein￨L￨NN￨O￨- in￨L￨IN￨O￨- serum￨L￨NN￨O￨- samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- BALB/c￨U￨NN￨O￨- and￨L￨CC￨O￨- C57BL/6￨U￨NN￨O￨- mice￨L￨NNS￨O￨A under￨L￨IN￨O￨- immunosuppressive￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- with￨L￨IN￨O￨- DXM￨U￨NN￨O￨- .￨L￨.￨O￨- +gondii￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- Fukaya￨U￨NNP￨PERSON￨- strain￨L￨NN￨O￨- induced￨L￨VBD￨O￨- transient￨L￨JJ￨O￨- TgHSP70-specific￨U￨JJ￨O￨- antibodies￨L￨NNS￨O￨- in￨L￨IN￨O￨- BALB/c￨U￨NN￨O￨- and￨L￨CC￨O￨- C57BL/6￨U￨NN￨O￨- mice￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- antibody￨L￨NN￨O￨- titers￨L￨NNS￨O￨- were￨L￨VBD￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- C57BL/6￨U￨NN￨O￨- mice￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +BALB/c￨U￨NN￨O￨- and￨L￨CC￨O￨- C57BL/6￨U￨NN￨O￨- mice￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- mice￨L￨NNS￨O￨- per￨L￨IN￨O￨- group￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- infected￨L￨JJ￨O￨- i.p.￨L￨RB￨O￨- with￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- cysts￨L￨NNS￨O￨- of￨L￨IN￨O￨- ME49￨U￨NN￨O￨- T.￨U￨FW￨O￨- +More￨U￨RBR￨O￨- precisely￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- life￨L￨NN￨O￨- lengths￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- exponentially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- with￨L￨IN￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- life￨L￨NN￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- gives￨L￨VBZ￨O￨- birth￨L￨NN￨O￨A to￨L￨TO￨O￨- new￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- Poisson￨U￨NNP￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- intensity￨L￨NN￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- random￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- mentioned￨L￨VBD￨O￨- being￨L￨VBG￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- upon￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- become￨L￨VBN￨O￨- latent￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Exposed￨U￨VBN￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- time￨L￨NN￨O￨- before￨L￨IN￨O￨- they￨L￨PRP￨O￨- enter￨L￨VBP￨O￨- the￨L￨DT￨O￨- Infectious￨U￨JJ￨O￨- state.We￨L￨NN￨O￨- study￨L￨NN￨O￨- the￨L￨DT￨O￨- simplified￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- mix￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- also￨L￨RB￨O￨- infect￨L￨VB￨O￨- )￨L￨-RRB-￨O￨- uniformly￨L￨RB￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- starting￨L￨VBG￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- n￨L￨NN￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- strictly￨L￨RB￨O￨- positive￨L￨JJ￨O￨- integer￨L￨NN￨O￨- n.It￨L￨NN￨O￨- is￨L￨VBZ￨O￨- well-known￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- positive￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- growing￨L￨VBG￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- does￨L￨VBZ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- grows￨L￨VBZ￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ∼￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨JJ￨O￨- −￨L￨NN￨O￨- μ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- developed￨L￨VBD￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- that￨L￨WDT￨O￨- conjugation￨L￨NN￨O￨- has￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- fitness￨L￨NN￨O￨A of￨L￨IN￨O￨- unicellular￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- static￨L￨JJ￨O￨- environments￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- conjugation-mediated￨L￨JJ￨O￨- HGT￨U￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- confer￨L￨VB￨O￨- a￨L￨DT￨O￨- selective￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- indeed￨L￨RB￨O￨- conjugation-mediated￨L￨JJ￨O￨- HGT￨U￨NN￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- slightly￨L￨RB￨O￨- deleterious￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- fitness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Yet￨U￨RB￨O￨- even￨L￨RB￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- exhibit￨L￨VB￨O￨- fairly￨L￨RB￨O￨- non-trivial￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- additional￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- point-mutation￨L￨NN￨O￨- framework￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- conservative￨L￨JJ￨IDEOLOGY￨- versus￨L￨CC￨O￨- semiconservative￨L￨JJ￨O￨- replication￨L￨NN￨O￨- ,￨L￨,￨O￨- fitness￨L￨NN￨O￨A landscapes￨L￨NNS￨O￨- ,￨L￨,￨O￨- polysomic￨L￨JJ￨O￨- genomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- instability￨L￨NN￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- repair￨L￨NN￨O￨- and￨L￨CC￨O￨- mutators￨L￨NNS￨O￨- ,￨L￨,￨O￨- finite-size￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- repression/derepression￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- into￨L￨IN￨O￨- our￨L￨PRP$￨O￨- original￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨A population￨L￨NN￨O￨- that￨L￨WDT￨O￨- transfers￨L￨VBZ￨O￨- genetic￨L￨JJ￨O￨- information￨L￨NN￨O￨- among￨L￨IN￨O￨- its￨L￨PRP$￨O￨- members￨L￨NNS￨O￨- both￨L￨CC￨O￨- vertically￨L￨RB￨O￨- and￨L￨CC￨O￨- horizontally￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- these￨L￨DT￨O￨- plasmids￨L￨NNS￨O￨- contain￨L￨VBP￨O￨- genes￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- trait￨L￨NN￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- antibiotic￨L￨JJ￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- conjugation￨L￨NN￨O￨- can￨L￨MD￨O￨- significantly￨L￨RB￨O￨- speed￨L￨VB￨O￨- up￨L￨RP￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- such￨L￨PDT￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- trait￨L￨NN￨O￨- spreads￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- F￨U￨NN￨O￨- +￨L￨CC￨O￨- /￨L￨:￨O￨- F￨U￨NN￨O￨- −￨L￨NN￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- ways￨L￨NNS￨O￨- atypical￨L￨JJ￨O￨- for￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨A conjugation￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- conjugative￨L￨JJ￨O￨- machinery￨L￨NN￨O￨- being￨L￨VBG￨O￨- chronically￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- de-repressed￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- in￨L￨IN￨O￨- nature￨L￨NN￨O￨- most￨L￨RBS￨O￨- conjugative￨L￨JJ￨O￨- plasmid￨L￨NN￨O￨- systems￨L￨NNS￨O￨- are￨L￨VBP￨O￨- repressed￨L￨VBN￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- T4SS￨U￨NN￨O￨- modules￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- VP35￨U￨NN￨O￨- protein￨L￨NN￨O￨A is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- block￨L￨VB￨O￨- interferon￨L￨NN￨O￨- induction￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- Marburg￨U￨NNP￨O￨- and￨L￨CC￨O￨- Ebola￨U￨NNP￨MISC￨- viruses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- discovery￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- open￨L￨JJ￨O￨- reading￨L￨NN￨O￨- frame￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- protein￨L￨NN￨O￨- integrated￨L￨VBN￨O￨- into￨L￨IN￨O￨- bat￨L￨NN￨O￨- genomes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- area￨L￨NN￨O￨- for￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- research￨L￨NN￨O￨- exploration￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- host-virus￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- individual￨L￨JJ￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- suggested￨L￨VBN￨O￨- Zaire￨U￨NNP￨COUNTRY￨- ebolavirus￨L￨NN￨O￨- viruses￨L￨NNS￨O￨A diverged￨L￨VBD￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- ancestor￨L￨NN￨O￨- very￨L￨RB￨O￨- recently￨L￨RB￨DATE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- Kitaka￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Python￨U￨NNP￨O￨- cave￨L￨NN￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨A to￨L￨TO￨O￨- harbor￨L￨VB￨O￨- large￨L￨JJ￨O￨- bat￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- sites￨L￨NNS￨O￨- for￨L￨IN￨O￨- follow￨L￨VBP￨O￨- up￨L￨RP￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- Marburg￨U￨NNP￨O￨- ecology￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Subsequently￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- small￨L￨JJ￨O￨- human￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- Marburgvirus￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- both￨L￨DT￨O￨- Marburg￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A and￨L￨CC￨O￨- Ravn￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 1997￨L￨CD￨DATE￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- had￨L￨VBD￨O￨- some￨L￨DT￨O￨- link￨L￨NN￨O￨- to￨L￨TO￨O￨- bat￨L￨NN￨O￨- caves￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- obtain￨L￨VBP￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- from￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- different￨L￨JJ￨O￨- methodologies￨L￨NNS￨O￨A applied￨L￨VBD￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- robustness￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- estimate￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- estimate￨L￨VBP￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- by￨L￨IN￨O￨- fitting￨L￨NN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- ODE￨U￨NN￨O￨- vector-host￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- single-strain￨L￨JJ￨O￨- dengue￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- both￨L￨CC￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- ordinary￨L￨JJ￨O￨- least￨L￨JJS￨O￨- squares￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- OLS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- least￨L￨JJS￨O￨- squares￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- GLS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- scheme￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- strong￨L￨JJ￨O￨- agreement￨L￨NN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- pre-control￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- across￨L￨IN￨O￨- different￨L￨JJ￨O￨- methodologies￨L￨NNS￨O￨A as￨L￨RB￨O￨- well￨L￨RB￨O￨- across￨L￨IN￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- a￨L￨DT￨O￨- direct-transmission￨L￨NN￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- using￨L￨VBG￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- MCMC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- significant￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- our￨L￨PRP$￨O￨- estimates￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- post-control￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- assumptions￨L￨NNS￨O￨- made￨L￨VBN￨O￨- to￨L￨TO￨O￨- built￨L￨VBN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- were￨L￨VBD￨O￨- evaluated￨L￨VBN￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- following￨L￨VBG￨O￨- results￨L￨NNS￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- low￨L￨JJ￨O￨- contact￨L￨NN￨O￨A rate￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- like￨L￨IN￨O￨- in￨L￨IN￨O￨- quarantine￨L￨NN￨O￨- process￨L￨NN￨O￨- or￨L￨CC￨O￨- low￨L￨JJ￨O￨- density￨L￨NN￨O￨- population￨L￨NN￨O￨- areas￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- other￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- higher￨L￨JJR￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- spacial￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- different￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- A￨U￨DT￨O￨- cellular￨L￨JJ￨O￨- automata￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- the￨L￨DT￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- geographical￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- desease￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Addressing￨U￨VBG￨MISC￨- population￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- models￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- cellular￨L￨JJ￨O￨- automata￨L￨NN￨O￨A approachLeonardo￨L￨NN￨O￨- López1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Germán￨U￨NNP￨O￨- Burguerner1￨U￨NN￨O￨- and￨L￨CC￨O￨- Leonardo￨U￨NNP￨PERSON￨- Giovanini1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 7:234￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- López￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- biological￨L￨JJ￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- way￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- situation￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- to￨L￨TO￨O￨- individually￨L￨RB￨O￨- define￨L￨VB￨O￨- the￨L￨DT￨O￨- characteristic￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- establish￨L￨VB￨O￨- different￨L￨JJ￨O￨A scenarios￨L￨NNS￨O￨A and￨L￨CC￨O￨- implement￨L￨VB￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- cell￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- automata￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- following￨L￨VBG￨O￨- information￨L￨NN￨O￨- was￨L￨VBD￨O￨- extracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- text￨L￨NN￨O￨- ,￨L￨,￨O￨- tables￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- figures￨L￨NNS￨O￨- provided￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- available￨L￨JJ￨O￨- :￨L￨:￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ;￨L￨:￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- closing￨L￨VBG￨O￨- schools￨L￨NNS￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- closure￨L￨NN￨O￨- ;￨L￨:￨O￨- assumed￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A on￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ;￨L￨:￨O￨- predicted￨L￨VBN￨O￨- percentage￨L￨NN￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- 100￨L￨CD￨NUMBER￨- ×￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- peak￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- –￨L￨:￨O￨- peak￨L￨NN￨O￨- with￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- peak￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- predicted￨L￨VBN￨O￨- percentage￨L￨NN￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- 100￨L￨CD￨NUMBER￨- ×￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- cumulative￨L￨JJ￨O￨- AR￨U￨NN￨STATE_OR_PROVINCE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- –￨L￨:￨O￨- cumulative￨L￨JJ￨O￨- AR￨U￨NNS￨STATE_OR_PROVINCE￨- with￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- cumulative￨L￨JJ￨O￨- AR￨U￨NNS￨STATE_OR_PROVINCE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- predicted￨L￨VBN￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ;￨L￨:￨O￨- predicted￨L￨VBN￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- identified￨L￨VBN￨O￨- studies￨L￨NNS￨O￨- presented￨L￨VBD￨O￨- several￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- predicted￨L￨VBN￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A on￨L￨IN￨O￨- measures￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- assumptions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closures￨L￨NNS￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- article￨L￨NN￨O￨- discusses￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- revealed￨L￨VBD￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- physical￨L￨JJ￨O￨- process￨L￨NN￨O￨- –￨L￨:￨O￨- the￨L￨DT￨O￨- resonance￨L￨NN￨O￨- phenomenon￨L￨NN￨O￨A in￨L￨IN￨O￨- population￨L￨NN￨O￨- persistence￨L￨NN￨O￨- –￨L￨:￨O￨- underlying￨L￨VBG￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- seemed￨L￨VBD￨O￨- entirely￨L￨RB￨O￨- unrelated￨L￨JJ￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- ,￨L￨,￨O￨- aside￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- were￨L￨VBD￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- external￨L￨JJ￨O￨- forces￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- studies￨L￨NNS￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- dosing￨L￨NN￨O￨- schedule￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- patient￨L￨NN￨O￨A is￨L￨VBZ￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- specific￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- 's￨L￨POS￨O￨- internal￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- drug￨L￨NN￨O￨- regimens￨L￨NNS￨O￨- ought￨L￨MD￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- patient￨L￨NN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Agur￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Webb￨U￨NNP￨PERSON￨- later￨L￨RB￨O￨- expanded￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- theory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4-6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- further￨L￨RB￨O￨- ,￨L￨,￨O￨- asserted￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- resonance￨L￨NN￨O￨- phenomenon￨L￨NN￨O￨A characterized￨L￨VBD￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- under￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- under￨L￨IN￨O￨- therapy￨L￨NN￨O￨- .￨L￨.￨O￨- +Agur￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Deneubourg￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- first￨L￨JJ￨ORDINAL￨- discovered￨L￨VBN￨O￨- this￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨A when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- mollusk￨L￨NN￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Red￨U￨NNP￨LOCATION￨- Sea￨U￨NNP￨LOCATION￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- despite￨L￨IN￨O￨- periodically￨L￨RB￨O￨- being￨L￨VBG￨O￨- decimated￨L￨VBN￨O￨- by￨L￨IN￨O￨- severe￨L￨JJ￨O￨- storms￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- National￨U￨NNP￨O￨- Hepatitis￨U￨NNP￨O￨- Survey￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2005￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2009￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- conducted￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- representative￨L￨JJ￨TITLE￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- aged￨L￨JJ￨O￨A 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- revealed￨L￨VBD￨O￨- the￨L￨DT￨O￨- seroprevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- HA￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- approximately￨L￨RB￨O￨- 40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- Northeast￨U￨NNP￨O￨- and￨L￨CC￨O￨- Midwest￨U￨NNP￨LOCATION￨- macro-regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- HA￨U￨NN￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨A group￨L￨NN￨O￨A over￨L￨IN￨O￨- time￨L￨NN￨O￨- are￨L￨VBP￨O￨- essential￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- sanitation￨L￨NN￨O￨- improvement￨L￨NN￨O￨- and/or￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- implementation￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Impact￨U￨NN￨MISC￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- drift￨L￨NN￨O￨- on￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenzaYanyu￨L￨NN￨O￨- Xiao1￨U￨NN￨O￨- and￨L￨CC￨O￨- Seyed￨U￨NNP￨O￨- M￨U￨NN￨O￨- Moghadas1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 13:589￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Xiao￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Moghadas￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Much￨U￨JJ￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- devoted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- determination￨L￨NN￨O￨- of￨L￨IN￨O￨- optimal￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- antigenically￨L￨RB￨O￨- drifted￨L￨VBD￨O￨- variants￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- findings￨L￨NNS￨O￨- highlight￨L￨VBP￨O￨- the￨L￨DT￨O￨- difficulty￨L￨NN￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- optimal￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- links￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- intra-seasonal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- drift￨L￨NN￨O￨- on￨L￨IN￨O￨- optimal￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨A for￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- study￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- short-and￨L￨JJ￨O￨- long-term￨L￨JJ￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨A epidemics￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- evaluated￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- population-pathogen￨L￨JJ￨O￨- landscape￨L￨NN￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- evolution￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Simulation￨U￨NN￨O￨- results￨L￨VBZ￨O￨- show￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨A epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- strongly￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- specific￨L￨JJ￨O￨- cross-protection￨L￨NN￨O￨- immunity￨L￨NN￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Saturating￨U￨VBG￨O￨- host￨L￨NN￨TITLE￨- abundance￨L￨NN￨O￨A could￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- result￨L￨NN￨O￨- between￨L￨IN￨O￨- completely￨L￨RB￨O￨- additive￨L￨JJ￨O￨- and￨L￨CC￨O￨- completely￨L￨RB￨O￨- compensatory￨L￨JJ￨O￨- richness-abundance￨L￨NN￨O￨- relationships￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- being￨L￨VBG￨O￨- a￨L￨DT￨O￨- non-monotonic￨L￨JJ￨O￨- trend￨L￨NN￨O￨- between￨L￨IN￨O￨- richness￨L￨NN￨O￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- dilution￨L￨NN￨O￨- effect￨L￨NN￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- abundance￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- strongly￨L￨RB￨O￨- contributes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- pathogen￨L￨NN￨O￨- reproduction￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- competent￨L￨JJ￨O￨- focal￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- negatively￨L￨RB￨O￨- correlates￨L￨VBZ￨O￨- with￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- richness￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- richness￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- abundance￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- density￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- diversity-disease￨L￨NN￨O￨- trends￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- richness￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- abundance￨L￨NN￨O￨A affect￨L￨VBP￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- richness￨L￨NN￨O￨- and￨L￨CC￨O￨- total￨L￨JJ￨O￨- community￨L￨NN￨O￨- abundance￨L￨NN￨O￨- should￨L￨MD￨O￨- affect￨L￨VB￨O￨- how￨L￨WRB￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- scales￨L￨NNS￨O￨- with￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- richness￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- dilution￨L￨NN￨O￨- effect￨L￨NN￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- if￨L￨IN￨O￨- species￨L￨NNS￨O￨- rich￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- have￨L￨VBP￨O￨- more￨L￨RBR￨O￨- host￨L￨NN￨TITLE￨A species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- resistant￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- demonstrating￨L￨VBG￨O￨- a￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- richness￨L￨NN￨O￨- per￨L￨FW￨O￨- se￨L￨FW￨O￨- in￨L￨IN￨O￨- limiting￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Transmission￨U￨NNP￨MISC￨- parameters￨L￨NNS￨O￨A estimated￨L￨VBN￨O￨A for￨L￨IN￨O￨- Salmonella￨U￨FW￨O￨- typhimurium￨L￨FW￨O￨- in￨L￨IN￨O￨- swine￨L￨NNS￨O￨- using￨L￨VBG￨O￨- susceptible-infectious-resistant￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- approachCarla￨L￨NN￨MISC￨- Correia-Gomes1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- 7Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Theodoros￨U￨NNP￨O￨- Economou2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Trevor￨U￨NNP￨PERSON￨- Bailey2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Pavel￨U￨NNP￨PERSON￨- Brazdil3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Lis￨U￨NNP￨O￨- Alban5￨U￨NNP￨O￨- and￨L￨CC￨O￨- João￨U￨NNP￨O￨- Niza-Ribeiro1￨U￨NN￨O￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 10:101￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Correia-Gomes￨U￨NNPS￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Transmission￨U￨NNP￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- aid￨L￨VB￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- testing￨L￨VBG￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Cohort￨U￨NN￨O￨- random￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- were￨L￨VBD￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- unobserved￨L￨JJ￨O￨- cohort-specific￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- unobserved￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- enabling￨L￨VBG￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A parameters￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- formulate￨L￨VB￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- Susceptible-Infectious-Resistant/Carrier￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- Salmonella￨U￨FW￨O￨- Typhimurium￨U￨FW￨O￨- in￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- estimate￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A parameters￨L￨NNS￨O￨A between￨L￨IN￨O￨- states￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- transmission￨L￨NN￨O￨A parameters￨L￨NNS￨O￨A were￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- longitudinal￨L￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- Danish￨U￨JJ￨NATIONALITY￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨- herds￨L￨NNS￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cohort￨L￨NN￨O￨A random￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- time￨L￨NN￨O￨- varying￨L￨VBG￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- further￨L￨JJ￨O￨- motivating￨L￨VBG￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- by￨L￨IN￨O￨- investigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- statistics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interevent￨L￨NN￨O￨- -￨L￨:￨O￨- ,￨L￨,￨O￨- beginning￨L￨VBG￨O￨A and￨L￨CC￨O￨- end￨L￨VB￨O￨- intervals￨L￨NNS￨O￨- for￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- on￨L￨IN￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- note￨L￨VBP￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- studies1426￨L￨NN￨O￨- try￨L￨VB￨O￨- to￨L￨TO￨O￨- paint￨L￨VB￨O￨- an￨L￨DT￨O￨- even￨L￨RB￨O￨- fuller￨L￨JJR￨O￨- picture￨L￨NN￨O￨- and￨L￨CC￨O￨- include￨L￨VBP￨O￨- statistics￨L￨NNS￨O￨- about￨L￨IN￨O￨- both￨L￨DT￨O￨- interevent￨L￨JJ￨O￨- intervals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- interval￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- contact￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- interval￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- starting￨L￨VBG￨O￨- point￨L￨NN￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- twelve￨L￨CD￨NUMBER￨- temporal￨L￨JJ￨O￨- network￨L￨NN￨O￨- data￨L￨NNS￨O￨A sets￨L￨NNS￨O￨A of￨L￨IN￨O￨- different￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- —￨L￨:￨O￨- some￨L￨DT￨O￨- arguably￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- others￨L￨NNS￨O￨- probably￨L￨RB￨O￨- not￨L￨RB￨O￨- .￨L￨.￨O￨- +Heterogeneous￨U￨JJ￨O￨- interevent￨L￨JJ￨O￨- intervals￨L￨NNS￨O￨A are￨L￨VBP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- possible￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- contact￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- take￨L￨VB￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- modeling￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨- link￨L￨NN￨O￨- picture￨L￨NN￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- two-layer￨L￨JJ￨O￨- overlay￨L￨NN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- completely￨L￨RB￨O￨- overlapping￨L￨VBG￨O￨- links￨L￨NNS￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- locally￨L￨RB￨O￨- spreading￨L￨VBG￨O￨- awareness￨L￨NN￨O￨- triggered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- can￨L￨MD￨O￨- raise￨L￨VB￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A remain￨L￨VBP￨O￨- unchanged1617￨L￨JJ￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- reasonable￨L￨JJ￨O￨- setting￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- complicated￨L￨JJ￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- assume￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- interacting￨L￨VBG￨O￨- network￨L￨NN￨O￨- layers￨L￨NNS￨O￨- of￨L￨IN￨O￨- of￨L￨IN￨O￨- identical￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨A dynamics￨L￨NNS￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- can￨L￨MD￨O￨- mitigate￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- broadly￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨A dynamics￨L￨NNS￨O￨A has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- science15￨L￨NN￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- layers￨L￨NNS￨O￨A can￨L￨MD￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- be￨L￨VB￨O￨- quite￨L￨RB￨O￨- distinct￨L￨JJ￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- progress￨L￨VBP￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- initially￨L￨RB￨O￨- ‘￨L￨``￨O￨- susceptible￨L￨JJ￨O￨- ’￨L￨''￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- before￨L￨IN￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- started￨L￨VBN￨O￨- clapping￨L￨VBG￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- ‘￨L￨``￨O￨- infected￨L￨JJ￨O￨- ’￨L￨''￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- clapping￨L￨VBG￨O￨- and￨L￨CC￨O￨- eventually￨L￨RB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- ‘￨L￨``￨O￨- recovered￨L￨VBN￨O￨- ’￨L￨''￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- once￨L￨IN￨DATE￨- they￨L￨PRP￨O￨- stop￨L￨VBP￨O￨A clapping￨L￨VBG￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- started￨L￨VBN￨O￨- clapping￨L￨VBG￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- either￨L￨RB￨O￨- stop￨L￨VB￨O￨A or￨L￨CC￨O￨- continue￨L￨VB￨O￨- after￨L￨IN￨O￨- each￨L￨DT￨O￨- successive￨L￨JJ￨O￨- clap￨L￨NN￨O￨- ,￨L￨,￨O￨- stopping￨L￨VBG￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- Pstop￨U￨NN￨PERSON￨- or￨L￨CC￨O￨- continuing￨L￨VBG￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- Pstart￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- construct￨L￨VBP￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- specify￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- will￨L￨MD￨O￨- start￨L￨VB￨O￨- or￨L￨CC￨O￨- stop￨L￨VB￨O￨A clapping￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- figure￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- ask￨L￨VBP￨O￨- how￨L￨WRB￨O￨- host￨L￨NN￨TITLE￨- life-history￨L￨JJ￨O￨- traits￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- lifespan￨L￨NN￨O￨- and￨L￨CC￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- birth￨L￨NN￨O￨A pulse￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- interact￨L￨VBP￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- following￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- introduction￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Substantial￨U￨JJ￨O￨- seasonal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- birth￨L￨NN￨O￨A rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- recently￨L￨RB￨DATE￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- significant￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- periodicity￨L￨NN￨O￨- ,￨L￨,￨O￨- magnitude￨L￨NN￨O￨- and￨L￨CC￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- CCS￨U￨NN￨ORGANIZATION￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- explored￨L￨VBN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- wild￨L￨JJ￨O￨- mammalian￨L￨JJ￨O￨- species￨L￨NNS￨O￨- give￨L￨VBP￨O￨- birth￨L￨NN￨O￨A only￨L￨RB￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- step￨L￨NN￨O￨- function￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- zero￨L￨VB￨NUMBER￨- for￨L￨IN￨O￨- several￨L￨JJ￨DURATION￨- months￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- seasonal￨L￨JJ￨O￨- birth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- birth￨L￨NN￨O￨A pulses￨L￨NNS￨O￨- in￨L￨IN￨O￨- shaping￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- cycles￨L￨NNS￨O￨- in￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- hypothesize￨L￨VBP￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- cycles￨L￨NNS￨O￨- could￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- extinction￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- CCS￨U￨NN￨ORGANIZATION￨- .￨L￨.￨O￨- +Herein￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- seasonal￨L￨JJ￨O￨- birth￨L￨NN￨O￨A pulse￨L￨NN￨O￨- on￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- persistence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- weighted￨L￨JJ￨O￨- physical￨L￨JJ￨O￨- encounter￨L￨NN￨O￨A network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- contact￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- duration￨L￨NN￨O￨- as￨L￨IN￨O￨- weight￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- i￨L￨FW￨O￨- will￨L￨MD￨O￨- transmit￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- neighbor￨L￨NN￨O￨- j￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- βd￨L￨NN￨O￨- per￨L￨IN￨O￨- 20￨L￨CD￨DURATION￨- seconds￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- contagion￨L￨NN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- universal￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- d￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- encounter￨L￨NN￨O￨- duration￨L￨NN￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NNP￨O￨- 1A￨L￨NN￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- full￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- enables￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨DATE￨- whole￨L￨JJ￨DATE￨- week￨L￨NN￨DATE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- contagious￨L￨JJ￨O￨A outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- registering￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- pathway￨L￨NN￨O￨- on￨L￨IN￨O￨- individual￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- obtaining￨L￨VBG￨O￨- results￨L￨NNS￨O￨- from￨L￨IN￨O￨- 20￨L￨CD￨NUMBER￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- measured￨L￨VBD￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- 〈￨L￨NN￨O￨- I/N￨U￨NN￨O￨- 〉￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sensor￨L￨NN￨O￨A groups￨L￨NNS￨O￨- and￨L￨CC￨O￨- 〈￨L￨NN￨O￨- I/N￨U￨NN￨O￨- 〉￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- temporally￨L￨RB￨O￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- that￨L￨IN￨O￨- friend￨L￨NN￨O￨- sensors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- large￨L￨JJ￨O￨- lead-times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- cellular￨L￨JJ￨O￨- automata￨L￨NN￨O￨- supplemented￨L￨VBN￨O￨- with￨L￨IN￨O￨- wavelet￨L￨NN￨O￨- transforms￨L￨VBZ￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- a￨L￨DT￨O￨- SEIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- attempts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- locally￨L￨RB￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- space￨L￨NN￨O￨- refers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨A from￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨A modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- changes￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- or￨L￨CC￨O￨- fixed￨L￨JJ￨O￨- delay￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- delay￨L￨NN￨O￨A in￨L￨IN￨O￨- many￨L￨JJ￨O￨- population￨L￨NN￨O￨- models￨L￨NNS￨O￨- considers￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- can￨L￨MD￨O￨- destabilize￨L￨VB￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- individual￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- populations￨L￨NNS￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- investigations￨L￨NNS￨O￨- among￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- apply￨L￨VB￨O￨- game￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- conflicts￨L￨NNS￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- arise￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- perceived￨L￨VBN￨O￨A costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- disclosure￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- disclosure￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- benefit￨L￨NN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- perceive￨L￨VBP￨O￨- a￨L￨DT￨O￨- cost￨L￨NN￨O￨- for￨L￨IN￨O￨- disclosing￨L￨VBG￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- there￨L￨EX￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- conflict￨L￨NN￨O￨- between￨L￨IN￨O￨- real￨L￨JJ￨O￨- or￨L￨CC￨O￨- perceived￨L￨VBN￨O￨A individual￨L￨JJ￨O￨- interests￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- good￨L￨JJ￨O￨- .￨L￨.￨O￨- +Contact￨U￨NN￨O￨- investigation￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- come￨L￨VBN￨O￨- into￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- investigation￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- 43￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 64￨L￨CD￨NUMBER￨- possible￨L￨JJ￨O￨- states￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨- group￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- let￨L￨VB￨O￨- q￨L￨VB￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- individual￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- state￨L￨NN￨O￨- X￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- individual￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- state￨L￨NN￨O￨- X￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨A N￨U￨NN￨O￨- =￨L￨JJ￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- q￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- person￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- persons￨L￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 3￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- unifying￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- analyses￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- of￨L￨IN￨O￨- coupling￨L￨NN￨O￨- between￨L￨IN￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- often￨L￨RB￨O￨- expressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- ‘￨L￨``￨O￨- gravity￨L￨NN￨O￨- ’￨L￨''￨O￨- or￨L￨CC￨O￨- ‘￨L￨``￨O￨- radiation￨L￨NN￨O￨- ’￨L￨''￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- hierarchical￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨A spread￨L￨NN￨O￨A ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- or￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- modulating￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- aggregation￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- in￨L￨IN￨O￨- schools￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- humidity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- Previous￨U￨JJ￨O￨- efforts￨L￨NNS￨O￨- have￨L￨VBP￨O￨- sought￨L￨VBN￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- simulations￨L￨NNS￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- intricate￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- demography￨L￨NN￨O￨- and￨L￨CC￨O￨- mixing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Dynamic￨U￨NNP￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- key￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- acute￨L￨JJ￨O￨- ,￨L￨,￨O￨- directly￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- rotavirus￨L￨NN￨O￨- ,￨L￨,￨O￨- dengue￨L￨NN￨O￨- ,￨L￨,￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- and￨L￨CC￨O￨- pandemic￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- A/H1N1pdm09￨U￨NN￨O￨- pandemic￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- opportunity￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨A spread￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- more￨L￨JJR￨O￨- detail￨L￨NN￨O￨- ,￨L￨,￨O￨- identify￨L￨VBP￨O￨- further￨L￨JJ￨O￨- data￨L￨NNS￨O￨- gaps￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- validate￨L￨VB￨O￨- existing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- suggested￨L￨VBN￨O￨- that￨L￨IN￨O￨- school￨L￨NN￨O￨- fall￨L￨NN￨DATE￨- terms￨L￨NNS￨O￨- starts￨L￨VBZ￨O￨- were￨L￨VBD￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fall￨L￨NN￨DATE￨- pandemic￨L￨JJ￨O￨A onsets￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- US￨U￨NNP￨COUNTRY￨- states￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- reactive￨L￨JJ￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spring￨L￨NN￨DATE￨- reduced￨L￨VBD￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- Hong-Kong￨U￨NNP￨O￨- and￨L￨CC￨O￨- Mexico￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- candidate￨L￨NN￨TITLE￨- driver￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- is￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- absolute￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- experimental￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- may￨L￨MD￨O￨- favour￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Regarding￨U￨VBG￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- with￨L￨IN￨O￨- infinitesimally￨L￨RB￨O￨- small￨L￨JJ￨O￨- time￨L￨NN￨O￨- steps￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- naturally￨L￨RB￨O￨- become￨L￨VBN￨O￨- simplified￨L￨VBN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- strong￨L￨JJ￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- contagions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- node￨L￨NN￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- generalization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A 's￨L￨POS￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- classified￨L￨VBN￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- categories￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- vigilant/vaccinated￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- node￨L￨NN￨O￨A can￨L￨MD￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- with￨L￨IN￨O￨- or￨L￨CC￨O￨- recover￨L￨VB￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- is￨L￨VBZ￨O￨- later￨L￨RBR￨O￨- made￨L￨VBN￨O￨- where￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- possesses￨L￨VBZ￨O￨- both￨L￨CC￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- partial￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- R0p￨U￨NN￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- sheep￨L￨NN￨O￨A introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- cattle￨L￨NNS￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- either￨L￨CC￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- chain￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- transient￨L￨JJ￨O￨- state￨L￨NN￨O￨- method￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- method￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Estimation￨U￨NN￨MISC￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- foot-and-mouth￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- sheep￨L￨NN￨O￨A to￨L￨TO￨O￨- cattleCarla￨L￨NN￨O￨- Bravo￨U￨NNP￨O￨- de￨L￨IN￨O￨- Rueda1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mart￨U￨NNP￨O￨- CM￨U￨NN￨O￨- de￨L￨IN￨O￨- Jong2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Phaedra￨U￨NNP￨PERSON￨- L￨U￨NNP￨O￨- Eblé1￨U￨NN￨O￨- and￨L￨CC￨O￨- Aldo￨U￨NNP￨O￨- Dekker1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 45:58￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Bravo￨U￨NNP￨O￨- de￨L￨IN￨O￨- Rueda￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- quantitative￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- sheep￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- foot-and-mouth￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FMDV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- sheep￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- FMDV￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- transmission￨L￨NN￨O￨- experiment￨L￨NN￨O￨- with￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- each￨L￨DT￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- lambs￨L￨NNS￨O￨- and￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- contact￨L￨NN￨O￨- calf￨L￨NN￨O￨- was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- estimate￨L￨VB￨O￨A FMDV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- VI￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- RT-PCR￨U￨NN￨O￨- and￨L￨CC￨O￨- serology￨L￨NN￨O￨- results￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- .￨L￨.￨O￨- +Dedicated￨U￨VBN￨O￨- methodological￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- traditionally￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- separately￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- exploit￨L￨VB￨O￨- information￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- symptom￨L￨NN￨O￨- onsets￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- amongst￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- geographic￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- genetic￨L￨JJ￨O￨A sequences￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Besides￨U￨IN￨O￨- dedicated￨L￨JJ￨O￨- packages￨L￨NNS￨O￨- for￨L￨IN￨O￨- e.g.￨L￨FW￨O￨- advanced￨L￨VBD￨O￨- linear￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- multivariate￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨A data￨L￨NN￨O￨- analysis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- graphics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- offers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- flexibility￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- interpreted￨L￨VBN￨O￨- computer￨L￨NN￨O￨- language￨L￨NN￨O￨- ,￨L￨,￨O￨- allied￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- calling￨L￨VBG￨O￨- upon￨L￨IN￨O￨- precompiled￨L￨JJ￨O￨- routines￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- in￨L￨IN￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- C++￨U￨NNP￨O￨- or￨L￨CC￨O￨- Fortran￨U￨NNP￨O￨- ,￨L￨,￨O￨- whenever￨L￨WRB￨O￨- computationally￨L￨RB￨O￨- intensive￨L￨JJ￨O￨- tasks￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- undertaken￨L￨VBN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- software￨L￨NN￨O￨- ,￨L￨,￨O￨- initiated￨L￨VBN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- hackathon￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- provides￨L￨VBZ￨O￨- object￨L￨NN￨O￨- classes￨L￨NNS￨O￨- implementing￨L￨VBG￨O￨- a￨L￨DT￨O￨- flexible￨L￨JJ￨O￨- and￨L￨CC￨O￨- coherent￨L￨JJ￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨A data￨L￨NNS￨O￨A ,￨L￨,￨O￨- alongside￨L￨IN￨O￨- procedures￨L￨NNS￨O￨- to￨L￨TO￨O￨- manipulate￨L￨VB￨O￨- ,￨L￨,￨O￨- summarize￨L￨VB￨O￨- and￨L￨CC￨O￨- visualize￨L￨VB￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- overview￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- OutbreakTools￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- platform￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨A data￨L￨NNS￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- ensure￨L￨VB￨O￨- coherence￨L￨NN￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- different￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- and￨L￨CC￨O￨- promote￨L￨VB￨O￨- further￨L￨JJ￨O￨- developments￨L￨NNS￨O￨- ,￨L￨,￨O￨- basic￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- storing￨L￨VBG￨O￨- and￨L￨CC￨O￨- handling￨L￨VBG￨O￨- outbreak￨L￨NN￨O￨A data￨L￨NNS￨O￨A are￨L￨VBP￨O￨- needed￨L￨VBN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- chickenpox￨L￨NN￨O￨- consultations￨L￨NNS￨O￨- changed￨L￨VBD￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- symptom￨L￨NN￨O￨- severity￨L￨NN￨O￨- varies￨L￨VBZ￨O￨- with￨L￨IN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- allowed￨L￨VBD￨O￨- the￨L￨DT￨O￨- reporting￨L￨NN￨O￨A fraction￨L￨NN￨O￨- to￨L￨TO￨O￨- differ￨L￨VB￨O￨- between￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- periods￨L￨NNS￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- consultations￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- we￨L￨PRP￨O￨- fitted￨L￨VBD￨O￨- separate￨L￨JJ￨O￨- lines￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- plot￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- births￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- periods￨L￨NNS￨O￨- :￨L￨:￨O￨- 1967￨L￨CD￨DATE￨- –￨L￨:￨O￨- 76￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- most￨L￨RBS￨O￨- consultations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- for￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- year-olds￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 1977￨L￨CD￨DATE￨- –￨L￨:￨O￨- 97￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- consultations￨L￨NNS￨O￨- in￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- year-olds￨L￨NNS￨O￨- declined￨L￨VBD￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- year-olds￨L￨NNS￨O￨- increased￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2008￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- most￨L￨RBS￨O￨- consultations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- for￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- year-olds￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- TSIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- Equation￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- rearranged￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- reporting￨L￨NN￨O￨A fraction￨L￨NN￨O￨- as￨L￨IN￨O￨- above￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- expression￨L￨NN￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- Equation￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- fortnightly￨L￨RB￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +Equation￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- rearranged￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- fortnightly￨L￨RB￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- parameter￨L￨NN￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- I￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- were￨L￨VBD￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- RCGP￨U￨NN￨ORGANIZATION￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- corrected￨L￨VBN￨O￨- for￨L￨IN￨O￨- under-reporting￨L￨VBG￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- reporting￨L￨NN￨O￨A fractions￨L￨NNS￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- TSIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- modelling￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- long-term￨L￨JJ￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Wales￨U￨NNP￨LOCATION￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- VZV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- changes￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨DATE￨- year￨L￨NN￨DATE￨A and￨L￨CC￨O￨- whether￨L￨IN￨O￨- its￨L￨PRP$￨O￨- relationship￨L￨NN￨O￨- to￨L￨TO￨O￨- school￨L￨NN￨O￨- holidays￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- changed￨L￨VBN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- modification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- Fine￨U￨NNP￨O￨- and￨L￨CC￨O￨- Clarkson￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- fortnightly￨L￨RB￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨A using￨L￨VBG￨O￨- Equations￨U￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Briefly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- idea￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- sexual￨L￨JJ￨O￨- revolution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- activity￨L￨NN￨O￨- and￨L￨CC￨O￨- HPV-16￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- pre-sexual￨L￨JJ￨O￨- revolution￨L￨NN￨O￨- times￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- cross-sectional￨L￨JJ￨O￨- study￨L￨NN￨O￨- collecting￨L￨VBG￨O￨- HPV-16￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- would￨L￨MD￨O￨- cover￨L￨VB￨O￨- younger￨L￨JJR￨O￨- women￨L￨NNS￨O￨A with￨L￨IN￨O￨- post-sexual￨L￨JJ￨O￨- revolution￨L￨NN￨O￨- sexual￨L￨JJ￨O￨- experiences￨L￨NNS￨O￨- and￨L￨CC￨O￨- older￨L￨JJR￨O￨- women￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- sexual￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- pre-sexual￨L￨JJ￨O￨- revolution￨L￨NN￨O￨- norms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- HPV-16￨U￨NN￨MISC￨- reactivation￨L￨NN￨O￨- on￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- older￨L￨JJR￨O￨- AustraliansIgor￨U￨NNP￨MISC￨- A￨U￨NNP￨MISC￨- Korostil1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- David￨U￨NNP￨PERSON￨- G￨U￨NNP￨O￨- Regan1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 14:312￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Korostil￨U￨NNP￨O￨- and￨L￨CC￨O￨- Regan￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Some￨U￨DT￨O￨- regional￨L￨JJ￨O￨- cross-sectional￨L￨JJ￨O￨- human￨L￨JJ￨O￨- papillomavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HPV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- DNA￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- show￨L￨VBP￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- older￨L￨JJR￨O￨- women￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- reasons￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- as￨L￨RB￨O￨- yet￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- hypothesised￨L￨VBN￨O￨- that￨L￨IN￨O￨- reactivation￨L￨NN￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- partly￨L￨RB￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- HPV￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- older￨L￨JJR￨O￨- women￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- another￨L￨DT￨O￨- possibility￨L￨NN￨O￨- worth￨L￨IN￨O￨- consideration￨L￨NN￨O￨- is￨L￨VBZ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- men￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- women￨L￨NNS￨O￨- in￨L￨IN￨O￨- middle-age￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- reconstructions￨L￨NNS￨O￨- published￨L￨VBN￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- rely￨L￨VBP￨O￨- heavily￨L￨RB￨O￨- upon￨L￨IN￨O￨- fieldwork￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- utility￨L￨NN￨O￨- of￨L￨IN￨O￨- genome￨L￨NN￨O￨- sequencing￨L￨NN￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- transmission￨L￨NN￨O￨A events￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- —￨L￨:￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- incomplete￨L￨JJ￨O￨- or￨L￨CC￨O￨- unavailable￨L￨JJ￨O￨- —￨L￨:￨O￨- remains￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- for￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- latency￨L￨NN￨O￨- or￨L￨CC￨O￨- chronic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- which￨L￨WDT￨O￨- substantial￨L￨JJ￨O￨- within-host￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- may￨L￨MD￨O￨- arise￨L￨VB￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- branch￨L￨NN￨O￨- length￨L￨NN￨O￨- in￨L￨IN￨O￨- inferring￨L￨VBG￨O￨A the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- phylogeny￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- inference￨L￨NN￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- sampling￨L￨NN￨O￨- times￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- molecular￨L￨JJ￨O￨- clock￨L￨NN￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- preferable￨L￨JJ￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- using￨L￨VBG￨O￨- neighbor-joining￨L￨JJ￨O￨- ,￨L￨,￨O￨- maximum￨L￨JJ￨O￨- parsimony￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- simplified￨L￨VBN￨O￨- tree-building￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- genomic￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- transmission￨L￨NN￨O￨A events￨L￨NNS￨O￨A from￨L￨IN￨O￨- genomic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- alone￨L￨RB￨O￨- while￨L￨IN￨O￨- also￨L￨RB￨O￨- considering￨L￨VBG￨O￨- within-host￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- offers￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- reconstruction￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- most￨L￨JJS￨O￨- investigations￨L￨NNS￨O￨- include￨L￨VBP￨O￨- a￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- isolates￨L￨NNS￨O￨- ,￨L￨,￨O￨- phylogenetic￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- directly￨L￨RB￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- identify￨L￨VB￨O￨- specific￨L￨JJ￨O￨- person-to-person￨L￨NN￨O￨- transmission￨L￨NN￨O￨A events￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- methods￨L￨NNS￨O￨- typically￨L￨RB￨O￨- identify￨L￨VBP￨O￨- transmission￨L￨NN￨O￨A events￨L￨NNS￨O￨A as￨L￨IN￨O￨- branching￨L￨VBG￨O￨- events￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- phylogeny￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- consider￨L￨VB￨O￨- within-host￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- vaccines￨L￨NNS￨O￨- which￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- immediate￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- move￨L￨VBP￨O￨- directly￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- removed￨L￨VBN￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ρ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- VE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NNP￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- For￨U￨IN￨O￨- vaccines￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- lag￨L￨NN￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- protection￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- hepatitis￨L￨NN￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- requiring￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- doses￨L￨NNS￨O￨- at￨L￨IN￨O￨- specific￨L￨JJ￨O￨- time￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- additional￨L￨JJ￨O￨- holding￨L￨NN￨O￨- classes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- required￨L￨VBN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- classes￨L￨NNS￨O￨- with￨L￨IN￨O￨- rates￨L￨NNS￨O￨- reflecting￨L￨VBG￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ρ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- efficacy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- VE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- lag￨L￨NN￨O￨- or￨L￨CC￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- doses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- serology￨L￨NN￨O￨- implies￨L￨VBZ￨O￨- complete￨L￨JJ￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- assign￨L￨VB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- protect￨L￨VB￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- inward￨L￨JJ￨O￨- rotating￨L￨VBG￨O￨- troops￨L￨NNS￨O￨- with￨L￨IN￨O￨- preexisting￨L￨VBG￨O￨- immunity￨L￨NN￨O￨- “￨L￨``￨O￨- protected￨L￨VBD￨O￨- ”￨L￨''￨O￨- status￨L￨NN￨O￨- —￨L￨:￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- now￨L￨RB￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- removed￨L￨VBN￨O￨- class￨L￨NN￨O￨- —￨L￨:￨O￨- and￨L￨CC￨O￨- separate￨L￨VB￨O￨- them￨L￨PRP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- segment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deployed￨L￨VBN￨O￨A population￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- participate￨L￨VB￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- situation￨L￨NN￨O￨- ,￨L￨,￨O￨- soldiers￨L￨NNS￨O￨- enter￨L￨VBP￨O￨- unit￨L￨NN￨O￨- i￨L￨FW￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deployed￨L￨VBN￨O￨A population￨L￨NN￨O￨- via￨L￨IN￨O￨- inbound￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- IN￨U￨IN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- exit￨L￨NN￨O￨- through￨L￨IN￨O￨- outbound￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- OUT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- casualty￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- upon￨L￨IN￨O￨- deployment￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- enter￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- class￨L￨NN￨O￨- and￨L￨CC￨O￨- proceed￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- class￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- soldiers￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- different￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- units￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- with￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- inclocal￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Deployed￨U￨VBN￨O￨- troops￨L￨NNS￨O￨- function￨L￨VBP￨O￨- in￨L￨IN￨O￨- environments￨L￨NNS￨O￨- favorable￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- and￨L￨CC￨O￨- efficient￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- —￨L￨:￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- disease-carrying￨L￨JJ￨O￨- forces￨L￨NNS￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- high-risk￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- inadequate￨L￨JJ￨O￨- medical￨L￨JJ￨O￨- care￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- —￨L￨:￨O￨- particularly￨L￨RB￨O￨- when￨L￨WRB￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨A are￨L￨VBP￨O￨- suboptimal￨L￨JJ￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- computational￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- preexisting￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- compares￨L￨VBZ￨O￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- deployment￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- means￨L￨NN￨O￨- of￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- protecting￨L￨VBG￨O￨- troops￨L￨NNS￨O￨- and￨L￨CC￨O￨- mission￨L￨NN￨O￨- objectives￨L￨NNS￨O￨- during￨L￨IN￨O￨- extended￨L￨VBN￨O￨- military￨L￨JJ￨O￨- deployment￨L￨NN￨O￨- actions￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- still￨L￨RB￨O￨- have￨L￨VBP￨O￨- little￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- to￨L￨TO￨O￨- guide￨L￨VB￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Lyme￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Rift￨U￨NNP￨LOCATION￨- Valley￨U￨NNP￨CITY￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- West￨U￨NNP￨LOCATION￨- Nile￨U￨NNP￨LOCATION￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- dengue￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- sampling￨L￨NN￨O￨A could￨L￨MD￨O￨- occur￨L￨VB￨O￨- in￨L￨IN￨O￨- vector￨L￨NN￨O￨- populations￨L￨NNS￨O￨- or￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Past￨U￨JJ￨DATE￨- analytical￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- active￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- detection￨L￨NN￨O￨- examined￨L￨VBD￨O￨- how￨L￨WRB￨O￨- sampling￨L￨NN￨O￨A for￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- detected￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- discovery￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- may￨L￨MD￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- sentinel￨L￨NN￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- longitudinal￨L￨JJ￨O￨- sampling￨L￨NN￨O￨A of￨L￨IN￨O￨- vector￨L￨NN￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- combined￨L￨VBD￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- host-vector￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- sampling￨L￨NN￨O￨A procedure￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- constrained￨L￨VBN￨O￨- by￨L￨IN￨O￨- economic￨L￨JJ￨O￨- limitations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- sampling￨L￨NN￨O￨A design￨L￨NN￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- detection￨L￨NN￨O￨- using￨L￨VBG￨O￨- formulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- vector￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- randomness￨L￨NN￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- needed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- reaction￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- states￨L￨NNS￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamical￨L￨JJ￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- proved￨L￨VBN￨O￨- by￨L￨IN￨O￨- Kurtz￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- under￨L￨IN￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- scaling￨L￨VBG￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- reaction￨L￨NN￨O￨A rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- reaction￨L￨NN￨O￨- network￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- is￨L￨VBZ￨O￨- infinite￨L￨NN￨O￨- or￨L￨CC￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- in￨L￨IN￨O￨- size￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- approximating￨L￨VBG￨O￨- the￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- CME￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- trajectories￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- stochastic￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- pure-jump￨L￨JJ￨O￨- process￨L￨NN￨O￨- whose￨L￨WP$￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- contains￨L￨VBZ￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- vectors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- reachable￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Traditionally￨U￨RB￨O￨- ,￨L￨,￨O￨- reaction￨L￨NN￨O￨A networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- mathematically￨L￨RB￨O￨- analyzed￨L￨VBN￨O￨- by￨L￨IN￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- formulation￨L￨NN￨O￨- generalised￨L￨VBD￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- by￨L￨IN￨O￨- varying￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨A groups￨L￨NNS￨O￨A and￨L￨CC￨O￨- contact￨L￨NN￨O￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- could￨L￨MD￨O￨- implement￨L￨VB￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mass-action￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- structured￨L￨VBN￨O￨- only￨L￨RB￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- 2009/10￨L￨CD￨NUMBER￨- survey￨L￨NN￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- NumericCitation￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- included￨L￨VBD￨O￨- both￨L￨DT￨O￨- reported￨L￨VBN￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- biologically￨L￨RB￨O￨- confirmed￨L￨VBD￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- explored￨L￨VBD￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- structures￨L￨NNS￨O￨A influenced￨L￨VBD￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- age￨L￨NN￨O￨A groups￨L￨NNS￨O￨A and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- contact￨L￨NN￨O￨- classes￨L￨NNS￨O￨- were￨L￨VBD￨O￨- included￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- framework￨L￨NN￨O￨- produced￨L￨VBD￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mass-action￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- had￨L￨VBD￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- dividing￨L￨VBG￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- different￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨A groups￨L￨NNS￨O￨A and￨L￨CC￨O￨- contact￨L￨NN￨O￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- recreate￨L￨VB￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- structures￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- structured￨L￨VBN￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- reported￨L￨VBN￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- ages￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Computational￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- has￨L￨VBZ￨O￨- long￨L￨RB￨O￨- been￨L￨VBN￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- spread￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- predicting￨L￨VBG￨O￨- outbreak￨L￨NN￨O￨- severity￨L￨NN￨O￨- ,￨L￨,￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- optimizing￨L￨VBG￨O￨A the￨L￨DT￨O￨- deployment￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- control￨L￨NN￨O￨- policies￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨A network￨L￨NN￨O￨A consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- that￨L￨WDT￨O￨- connect￨L￨VBP￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- spatial￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- with￨L￨IN￨O￨- reported￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- observed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidences￨L￨VBZ￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- directional￨L￨JJ￨O￨- links￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- likelihood￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- stressed￨L￨VBN￨O￨- the￨L￨DT￨O￨- urgency￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A over￨L￨IN￨O￨- geographical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- rely￨L￨VBP￨O￨- strongly￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A network￨L￨NN￨O￨A topology￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨A in￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨O￨- The￨U￨DT￨O￨- pathogenesis-related￨L￨JJ￨O￨- protein￨L￨NN￨O￨A PR-4b￨U￨NN￨O￨- from￨L￨IN￨O￨- Theobroma￨U￨NN￨O￨- cacao￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- RNase￨U￨NN￨MISC￨- activity￨L￨NN￨O￨- ,￨L￨,￨O￨- Ca2￨U￨NN￨O￨- +￨L￨CC￨O￨- and￨L￨CC￨O￨- Mg2￨U￨NN￨O￨- +￨L￨CC￨O￨- dependent-DNase￨L￨NN￨MISC￨- activity￨L￨NN￨O￨- and￨L￨CC￨O￨- antifungal￨L￨JJ￨O￨- action￨L￨NN￨O￨- on￨L￨IN￨O￨- Moniliophthora￨U￨NNP￨O￨- perniciosaSara￨L￨NNP￨O￨- Pereira￨U￨NNP￨O￨- Menezes1￨U￨NN￨O￨- ,￨L￨,￨O￨- Edson￨U￨NNP￨PERSON￨- Mario￨U￨NNP￨PERSON￨- de￨L￨IN￨PERSON￨- Andrade￨U￨NNP￨PERSON￨- Silva1￨U￨NN￨O￨- ,￨L￨,￨O￨- Eline￨U￨NNP￨PERSON￨- Matos￨U￨NNP￨PERSON￨- Lima1￨U￨NN￨O￨- ,￨L￨,￨O￨- Aurizângela￨U￨NNP￨PERSON￨- Oliveira￨U￨NNP￨PERSON￨- de￨L￨IN￨O￨- Sousa1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Bruno￨U￨NNP￨PERSON￨- Silva￨U￨NNP￨PERSON￨- Andrade2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Livia￨U￨NNP￨PERSON￨- Santos￨U￨NNP￨PERSON￨- Lima￨U￨NNP￨PERSON￨- Lemos3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Karina￨U￨NNP￨PERSON￨- Peres￨U￨NNP￨PERSON￨- Gramacho3￨U￨NN￨O￨- ,￨L￨,￨O￨- Abelmon￨U￨NNP￨PERSON￨- da￨L￨NNP￨PERSON￨- Silva￨U￨NNP￨PERSON￨- Gesteira4￨U￨NN￨O￨- ,￨L￨,￨O￨- Carlos￨U￨NNP￨PERSON￨- Priminho￨U￨NNP￨PERSON￨- Pirovani1￨U￨NN￨O￨- and￨L￨CC￨O￨- Fabienne￨U￨NN￨PERSON￨- Micheli1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 14:161￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Pereira￨U￨NNP￨PERSON￨- Menezes￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨DT￨O￨- production￨L￨NN￨O￨- and￨L￨CC￨O￨- accumulation￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogenesis-related￨L￨JJ￨O￨- proteins￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PR￨U￨NN￨STATE_OR_PROVINCE￨- proteins￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- plants￨L￨NNS￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- biotic￨L￨JJ￨O￨- or￨L￨CC￨O￨- abiotic￨L￨JJ￨O￨- stresses￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- mechanism￨L￨NN￨O￨- for￨L￨IN￨O￨- plant￨L￨NN￨O￨- defense￨L￨NN￨O￨- .￨L￨.￨O￨- +Molecular￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- TcPR-4b￨U￨NN￨O￨- confirmed￨L￨VBD￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cysteine￨L￨NN￨O￨- residues￨L￨NNS￨O￨- to￨L￨TO￨O￨- maintain￨L￨VB￨O￨- the￨L￨DT￨O￨- protein￨L￨NN￨O￨A structure￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- conserved￨L￨VBN￨O￨- amino￨L￨NN￨O￨- acids￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- catalytic￨L￨JJ￨O￨- activity￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- pathogenesis-related￨L￨JJ￨O￨- protein￨L￨NN￨O￨A 4￨L￨CD￨NUMBER￨- cDNA￨L￨NN￨O￨- was￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- cacao-Moniliophthora￨L￨NN￨MISC￨- perniciosa￨L￨NN￨O￨- interaction￨L￨NN￨O￨- cDNA￨L￨NN￨O￨- library￨L￨NN￨O￨- and￨L￨CC￨O￨- named￨L￨VBN￨O￨- TcPR-4b￨U￨NN￨O￨- .￨L￨.￨O￨- +TcPR-4b￨U￨JJ￨O￨- RT-qPCR￨U￨NN￨O￨- analysis￨L￨NN￨O￨- in￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- cacao￨L￨NN￨O￨- plants￨L￨NNS￨O￨A infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- M￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- recombinant￨L￨JJ￨O￨- TcPR-4b￨U￨NN￨O￨- protein￨L￨NN￨O￨A showed￨L￨VBD￨O￨- RNase￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- bivalent￨L￨JJ￨O￨- ions￨L￨NNS￨O￨- dependent-DNase￨L￨JJ￨MISC￨- activity￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- no￨L￨DT￨O￨- chitinase￨L￨NN￨O￨- activity￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- pandemic￨L￨JJ￨O￨A disproportionally￨L￨RB￨O￨- killed￨L￨VBN￨O￨- young￨L￨JJ￨O￨- adults￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- school-aged￨L￨JJ￨O￨- children￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- elderly￨L￨JJ￨O￨- were￨L￨VBD￨O￨- relatively￨L￨RB￨O￨- unaffected￨L￨JJ￨O￨- .4￨L￨NN￨NUMBER￨- Other￨U￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- produced￨L￨VBN￨O￨- shifts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- patterns￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- diminution￨L￨NN￨O￨- of￨L￨IN￨O￨- elderly￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- apparent￨L￨JJ￨O￨- higher￨L￨JJR￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- young￨L￨JJ￨O￨- adults￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 20-to￨L￨NN￨O￨- 40-year-olds￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- pandemic￨L￨NN￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- recorded￨L￨VBN￨O￨- since￨L￨IN￨O￨- this￨L￨DT￨O￨- event￨L￨NN￨O￨- .3￨L￨NN￨NUMBER￨- Whether￨U￨IN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmissibility￨L￨NN￨O￨- among￨L￨IN￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- contributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- examined￨L￨VBN￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- pandemic￨L￨JJ￨O￨A were￨L￨VBD￨O￨- unusual￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- observed￨L￨VBN￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- not￨L￨RB￨O￨- well￨L￨RB￨O￨- understood￨L￨VBN￨O￨- .2,3￨L￨CD￨NUMBER￨- Many￨U￨JJ￨O￨- regions￨L￨NNS￨O￨- experienced￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- waves￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨DATE￨- same￨L￨JJ￨DATE￨- year￨L￨NN￨DATE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- brief￨L￨JJ￨O￨- quiescent￨L￨JJ￨O￨- interval￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- waves￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- well￨L￨RB￨O￨- explained￨L￨VBN￨O￨- .2,3￨L￨CD￨NUMBER￨- Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- potential￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmissibility￨L￨NN￨O￨- among￨L￨IN￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- calculated￨L￨VBD￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Re￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1-year￨L￨JJ￨DURATION￨- interval￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A waves￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mills￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- pandemic￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 2nd￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- 3￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- with￨L￨IN￨O￨- excess￨L￨JJ￨O￨- pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- P&I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- mortality￨L￨NN￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- 100￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Unfortunately￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- proportion￨L￨NN￨O￨A infected￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- infinitesimally￨L￨RB￨O￨- small￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- absolute￨L￨JJ￨O￨- number￨L￨NN￨O￨- infected￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- large￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- deterministic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- assumption￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- break￨L￨VBP￨O￨- down￨L￨RP￨O￨- if￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- early￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- proportion￨L￨NN￨O￨A infected￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- negligible￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- remainder￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- generalize￨L￨VBP￨O￨- the￨L￨DT￨O￨- EBCM￨U￨NN￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- proportion￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- treated￨L￨VBN￨O￨- as￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- we￨L￨PRP￨O￨- assume￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨A number￨L￨NN￨O￨- infected￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- enough￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- behave￨L￨VB￨O￨- deterministically￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- modify￨L￨VBP￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- which￨L￨WDT￨O￨- assumed￨L￨VBD￨O￨- an￨L￨DT￨O￨- infinitesimal￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- proportion￨L￨NN￨O￨A infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- polymorphic￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- Plasmodium￨U￨NN￨O￨- falciparum￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- one-strain￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- misleading￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- further￨L￨RB￨O￨- ,￨L￨,￨O￨- coinfections￨L￨NNS￨O￨- may￨L￨MD￨O￨- imply￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- survivorship￨L￨NN￨O￨- of￨L￨IN￨O￨- strains￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- maximized￨L￨VBN￨O￨- by￨L￨IN￨O￨- maximizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Cross-immunity￨U￨NN￨O￨- was￨L￨VBD￨O￨- also￨L￨RB￨O￨- found￨L￨VBN￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- strains￨L￨NNS￨O￨A of￨L￨IN￨O￨- other￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- once￨L￨RB￨DATE￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- strains￨L￨NNS￨O￨A infect￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- will￨L￨MD￨O￨- interact￨L￨VB￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- imitation￨L￨NN￨O￨- rule￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- previously￨L￨RB￨DATE￨- studied￨L￨VBN￨O￨- subsidy￨L￨NN￨O￨- policies￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- partial-subsidy￨L￨JJ￨O￨- policy￨L￨NN￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- subsidy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- distributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- free-subsidy￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- subsidy￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- randomly￨L￨RB￨O￨- vaccinated￨L￨VBN￨O￨- without￨L￨IN￨O￨- any￨L￨DT￨O￨- personal￨L￨JJ￨O￨- cost￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- contrary￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- large￨L￨JJ￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- β￨L￨NN￨O￨- gives￨L￨VBZ￨O￨- rise￨L￨NN￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- subsidy￨L￨NN￨O￨- policies￨L￨NNS￨O￨- :￨L￨:￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- partial￨L￨JJ￨O￨- policy￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- β￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- subsidy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- opposite￨L￨JJ￨O￨- case￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- subsidy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considerable￨L￨JJ￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- small￨L￨JJ￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverages￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- policies￨L￨NNS￨O￨A increase￨L￨VBP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- selection￨L￨NN￨O￨- strength￨L￨NN￨O￨- β￨L￨NN￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rational/cautious￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- imitation￨L￨NN￨O￨- rule￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- finding￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- ”￨L￨''￨O￨- effect￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- free-subsidy￨L￨JJ￨O￨- policy￨L￨NN￨O￨A on￨L￨IN￨O￨- promoting￨L￨VBG￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- as￨L￨RB￨O￨- effective￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- partial-subsidy￨L￨JJ￨O￨- policy￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- free-subsidy￨L￨JJ￨O￨- policy￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- non-monotonically￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- factors￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A of￨L￨IN￨O￨- these￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- including￨L￨VBG￨O￨- HIV/AIDS￨U￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- guidelines￨L￨NNS￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- controlled￨L￨VBN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- who￨L￨WP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- screening￨L￨NN￨O￨- of￨L￨IN￨O￨- unaware￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- .￨L￨.￨O￨- +Not￨U￨RB￨O￨- much￨L￨JJ￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨A of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- on￨L￨IN￨O￨- productivity￨L￨NN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- workplace￨L￨NN￨O￨- can￨L￨MD￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fight￨L￨NN￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- who￨L￨WP￨O￨- presented￨L￨VBD￨O￨- a￨L￨DT￨O￨- preliminary￨L￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- proposing￨L￨VBG￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Stilianakis￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- other￨L￨JJ￨O￨- models￨L￨NNS￨O￨A proposed￨L￨VBN￨O￨A to￨L￨TO￨O￨- study￨L￨VB￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- [￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- references￨L￨NNS￨O￨- therein￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- appraisal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- compartmentalization￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- refine￨L￨VB￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- industry￨L￨NN￨O￨A and￨L￨CC￨O￨- country-specific￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- modelling￨L￨NN￨O￨- framework￨L￨NN￨O￨- developed￨L￨VBD￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- leakage￨L￨NN￨O￨- from￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- British￨U￨JJ￨NATIONALITY￨- commercial￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- industry￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- better￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- through￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- proximity￨L￨NN￨O￨- and￨L￨CC￨O￨- through￨L￨IN￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- vehicles￨L￨NNS￨O￨- and￨L￨CC￨O￨- equipment￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- could￨L￨MD￨O￨- help￨L￨VB￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- specific￨L￨JJ￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- compartmentalization￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- British￨U￨JJ￨NATIONALITY￨- commercial￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- industry￨L￨NN￨O￨A .￨L￨.￨O￨- +As￨U￨IN￨O￨- single-site￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- premises￨L￨NNS￨O￨A tended￨L￨VBD￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- spatially￨L￨RB￨O￨- clustered￨L￨VBN￨O￨- around￨L￨IN￨O￨- MS￨U￨NN￨STATE_OR_PROVINCE￨- premises￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 80￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- premises￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- proximity￨L￨NN￨O￨- of￨L￨IN￨O￨- MS￨U￨NN￨STATE_OR_PROVINCE￨- were￨L￨VBD￨O￨- SS￨U￨JJ￨O￨- premises￨L￨NNS￨O￨- across￨L￨IN￨O￨- distances￨L￨NNS￨O￨- of￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- km￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- captured￨L￨VBD￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- MS￨U￨NN￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- SS￨U￨NN￨O￨- premises￨L￨NNS￨O￨- both￨L￨CC￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- compartment￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- network￨L￨NN￨O￨- characterization￨L￨NN￨O￨- was￨L￨VBD￨O￨- then￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- an￨L￨DT￨O￨- unweighted￨L￨JJ￨O￨- and￨L￨CC￨O￨- undirected￨L￨JJ￨O￨- unipartite￨L￨JJ￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- represented￨L￨VBN￨O￨- poultry￨L￨NN￨O￨A companies￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- represented￨L￨VBD￨O￨- shared￨L￨VBN￨O￨- SH￨U￨NN￨O￨- or￨L￨CC￨O￨- CC￨U￨NN￨O￨- associations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- theoretical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨- complex￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- compressed￨L￨VBN￨O￨- sensing￨L￨VBG￨O￨- theory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CST￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 353637383940￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- paradigm￨L￨NN￨O￨- for￨L￨IN￨O￨- sparse-signal￨L￨JJ￨O￨- reconstruction￨L￨NN￨O￨- with￨L￨IN￨O￨- broad￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- in￨L￨IN￨O￨- signal￨L￨NN￨O￨- and￨L￨CC￨O￨- image￨L￨NN￨O￨- processing￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- no￨L￨DT￨O￨- immediate￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- tree-structure-based￨L￨JJ￨O￨- inference￨L￨NN￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- inapplicable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- reconstruction￨L￨NN￨O￨A and￨L￨CC￨O￨- locating￨L￨VBG￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- extremely￨L￨RB￨O￨- challenging￨L￨JJ￨O￨- ,￨L￨,￨O￨- hindering￨L￨VBG￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- and￨L￨CC￨O￨- delivery￨L￨NN￨O￨- of￨L￨IN￨O￨- immunization￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- CST￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- uncover￨L￨VB￨O￨- the￨L￨DT￨O￨- nodal￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- for￨L￨IN￨O￨- coupled￨L￨VBN￨O￨- oscillator￨L￨NN￨O￨- networks￨L￨NNS￨O￨- or￨L￨CC￨O￨- evolutionary￨L￨JJ￨O￨- games￨L￨NNS￨O￨- from￨L￨IN￨O￨- time￨L￨NN￨O￨- series414243￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- highly￨L￨RB￨O￨- stochastic￨L￨JJ￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- binary￨L￨JJ￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A ,￨L￨,￨O￨- rendering￨L￨VBG￨O￨- inapplicable￨L￨JJ￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- CST-based￨U￨JJ￨MISC￨- formulation￨L￨NN￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- significant￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- in￨L￨IN￨O￨- reconstructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- spreading￨L￨NN￨O￨- network￨L￨NN￨O￨- lies￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A :￨L￨:￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- polarized￨L￨VBN￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- among￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- great￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- nodal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- but￨L￨CC￨O￨- only￨L￨RB￨O￨- limited￨L￨JJ￨O￨- measured￨L￨VBN￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- study￨L￨NN￨O￨- objective￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIDA1/2/3￨U￨NN￨O￨- intervention￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- heterosexual￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Cotonou￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- categorised￨L￨VBN￨O￨- as￨L￨IN￨O￨- generalised￨L￨JJ￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organisation￨U￨NNP￨ORGANIZATION￨- classification￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- because￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨A population￨L￨NN￨O￨A HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- exceeded￨L￨VBD￨O￨- 1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- positive￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- targeted￨L￨VBN￨O￨- to￨L￨TO￨O￨- sex￨L￨NN￨O￨- workers￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- clients￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨A population￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- declines￨L￨VBZ￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- representative￨L￨JJ￨TITLE￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨A population￨L￨NN￨O￨A were￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- among￨L￨IN￨O￨- FSW￨U￨NNP￨O￨- clients￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2002￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- males￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- females￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Also￨U￨RB￨O￨- shown￨L￨VBN￨O￨- are￨L￨VBP￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- counterfactuals￨L￨NNS￨O￨- CF-1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- red￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- CF-2￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- blue￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- FSW￨U￨NNP￨ORGANIZATION￨- condom￨L￨NN￨O￨- use￨L￨NN￨O￨- mirrors￨L￨VBZ￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- moderate￨L￨JJ￨O￨- risk￨L￨NN￨O￨- females￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨A population￨L￨NN￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- there￨L￨RB￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- threefold￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- condom￨L￨NN￨O￨- use￨L￨NN￨O￨- among￨L￨IN￨O￨- FSWs￨U￨NNS￨O￨- ,￨L￨,￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- substantial￨L￨JJ￨O￨- decline￨L￨NN￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨A among￨L￨IN￨O￨- FSWs￨U￨NNS￨O￨- in￨L￨IN￨O￨- Cotonou￨U￨NNP￨CITY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- 53￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- to￨L￨TO￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- in￨L￨IN￨O￨- gonorrhoea￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- influence￨L￨NN￨O￨- maximization￨L￨NN￨O￨A in￨L￨IN￨O￨- signed￨L￨VBN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- ignoring￨L￨VBG￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- polarity￨L￨NN￨O￨- between￨L￨IN￨O￨- users￨L￨NNS￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- the￨L￨DT￨O￨- signed￨L￨VBN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- as￨L￨IN￨O￨- unsigned￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- and￨L￨CC￨O￨- applying￨L￨VBG￨O￨- traditional￨L￨JJ￨O￨- influence￨L￨NN￨O￨- maximization￨L￨NN￨O￨- methods￨L￨NNS￨O￨- may￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- over-estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- influence￨L￨NN￨O￨- in￨L￨IN￨O￨- practical￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- viral￨L￨JJ￨O￨- marketing￨L￨NN￨O￨- ,￨L￨,￨O￨- influence￨L￨NN￨O￨- maximization￨L￨NN￨O￨A emerges￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- problem￨L￨NN￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- products￨L￨NNS￨O￨- ,￨L￨,￨O￨- opinions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- innovations￨L￨NNS￨O￨- through￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- these￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- extensions￨L￨NNS￨O￨- ,￨L￨,￨O￨- influence￨L￨VBP￨O￨- maximization￨L￨NN￨O￨A problem￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- improved￨L￨VBN￨O￨- greedy￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- and￨L￨CC￨O￨- scalable￨L￨JJ￨O￨- heuristics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +All￨U￨PDT￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- works￨L￨NNS￨O￨- consider￨L￨VBP￨O￨- influence￨L￨NN￨O￨- maximization￨L￨NN￨O￨A in￨L￨IN￨O￨- unsigned￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- which￨L￨WDT￨O￨- only￨L￨RB￨O￨- have￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- users￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- friend￨L￨NN￨O￨- or￨L￨CC￨O￨- trust￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- modeled￨L￨VBD￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- find￨L￨VB￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- activating￨L￨VBG￨O￨- them￨L￨PRP￨O￨- initially￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- activated￨L￨VBN￨O￨- by￨L￨IN￨O￨- these￨L￨DT￨O￨- seed￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- maximized￨L￨VBN￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rapid￨L￨JJ￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- platform￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dissemination￨L￨NN￨O￨A and￨L￨CC￨O￨- sharing￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- users￨L￨NNS￨O￨- of￨L￨IN￨O￨- self-worth￨L￨NN￨O￨- ,￨L￨,￨O￨- expressing￨L￨VBG￨O￨- interest￨L￨NN￨O￨- demands￨L￨NNS￨O￨- and￨L￨CC￨O￨- maintain￨L￨VB￨O￨- interpersonal￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- user￨L￨NN￨O￨- 's￨L￨POS￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A mechanisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- potential￨L￨JJ￨O￨- dissemination￨L￨NN￨O￨- law￨L￨NN￨O￨- is￨L￨VBZ￨O￨- having￨L￨VBG￨O￨- important￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- and￨L￨CC￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- commercial￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- media￨L￨NNS￨O￨- which￨L￨WDT￨O￨- rely￨L￨VBP￨O￨- on￨L￨IN￨O￨- content￨L￨NN￨O￨- as￨L￨IN￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- communication￨L￨NN￨O￨- theme￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spreader￨L￨NN￨TITLE￨- 's￨L￨POS￨O￨- influence￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- relations￨L￨NNS￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- interest￨L￨NN￨O￨- ,￨L￨,￨O￨- relationship￨L￨NN￨O￨- circles￨L￨NNS￨O￨- of￨L￨IN￨O￨- friends￨L￨NNS￨O￨- or￨L￨CC￨O￨- fans￨L￨NNS￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- user￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- SNS￨U￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- friend￨L￨NN￨O￨- 's￨L￨POS￨O￨- relationships￨L￨NNS￨O￨A between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- abstractly￨L￨RB￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dissemination￨L￨NN￨O￨A mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- summarized￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- users￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- wide￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- communication￨L￨NN￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- create￨L￨VB￨O￨- a￨L￨DT￨O￨- breeding￨L￨NN￨O￨- ground￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨A virus￨L￨NN￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- characteristic￨L￨NN￨O￨- of￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- exhibited￨L￨VBD￨O￨- by￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨A virus￨L￨NN￨O￨- through￨L￨IN￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- challenging￨L￨VBG￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- user-tricking￨L￨JJ￨O￨- and￨L￨CC￨O￨- vulnerability-exploiting￨L￨JJ￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨A virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- than￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- Internet￨U￨NN￨MISC￨- worms￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- only￨L￨RB￨O￨- reproduces￨L￨VBZ￨O￨- and￨L￨CC￨O￨- propagates￨L￨VBZ￨O￨- by￨L￨IN￨O￨- tricking￨L￨VBG￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨A users￨L￨NNS￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- user-tricking￨L￨JJ￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- spread￨L￨VBN￨O￨- automatically￨L￨RB￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- noteworthy￨L￨JJ￨O￨- example￨L￨NN￨O￨- is￨L￨VBZ￨O￨- Commwarrior￨U￨JJ￨MISC￨- NumericCitation￨U￨NN￨MISC￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨A virus￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- propagate￨L￨VB￨O￨- via￨L￨IN￨O￨- MMS￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- identify￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- survey￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- among￨L￨IN￨O￨- students￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- school￨L￨NN￨O￨A involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pdm09￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Compared￨U￨VBN￨O￨- to￨L￨TO￨O￨- Western￨U￨JJ￨MISC￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- few￨L￨JJ￨O￨- descriptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pdm09￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- school￨L￨NN￨O￨A outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- mainland￨L￨NN￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- campus￨L￨NN￨O￨- quarantines￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- fengxiao￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- school￨L￨NN￨O￨- closures￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- intervention45101116182031￨L￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- whether￨L￨IN￨O￨- freshmen￨L￨NNS￨O￨- affected￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pdm09￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- school￨L￨NN￨O￨A was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- by￨L￨IN￨O￨- calculating￨L￨VBG￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- grades￨L￨NNS￨O￨- .￨L￨.￨O￨- +Understanding￨U￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- within￨L￨IN￨O￨- school￨L￨NN￨O￨A settings￨L￨NNS￨O￨- would￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- helpful￨L￨JJ￨O￨- in￨L￨IN￨O￨- defining￨L￨VBG￨O￨- effective￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pdm09￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A dynamic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 2,035￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- resulted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 20th￨L￨JJ￨DATE￨- day￨L￨NN￨DATE￨- if￨L￨IN￨O￨- no￨L￨DT￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- were￨L￨VBD￨O￨- implemented￨L￨VBN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- initiated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- freshman￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- plants￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- ethical￨L￨JJ￨O￨- concerns￨L￨NNS￨O￨- that￨L￨IN￨O￨- hamper￨L￨VBP￨O￨- experimentation￨L￨NN￨O￨- targeting￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- or￨L￨CC￨O￨- human￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- nevertheless￨L￨RB￨O￨- becomes￨L￨VBZ￨O￨- particularly￨L￨RB￨O￨- compelling￨L￨JJ￨O￨- for￨L￨IN￨O￨- plant￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- when￨L￨WRB￨O￨- logistic￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- mean￨L￨VBP￨O￨- that￨L￨IN￨O￨- experimentation￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- costly￨L￨JJ￨O￨- or￨L￨CC￨O￨- difficult￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- go￨L￨VBP￨O￨- on￨L￨IN￨O￨- to￨L￨TO￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- topology￨L￨NN￨O￨- and￨L￨CC￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨A the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- and￨L￨CC￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- grove￨L￨NN￨O￨- as￨L￨IN￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- citrus￨L￨NN￨O￨- production￨L￨NN￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- therefore￨L￨RB￨O￨- concentrate￨L￨VBP￨O￨- on￨L￨IN￨O￨- cultural￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- planting￨L￨VBG￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- roguing￨L￨VBG￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- searching￨L￨VBG￨O￨- for￨L￨IN￨O￨- and￨L￨CC￨O￨- removing￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- plants￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- plant￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- screen￨L￨NN￨O￨- and￨L￨CC￨O￨- assess￨L￨VB￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Surveillance￨U￨NNP￨MISC￨- of￨L￨IN￨O￨- low￨L￨JJ￨O￨- pathogenic￨L￨JJ￨O￨- novel￨L￨JJ￨O￨- H7N9￨U￨NN￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- commercial￨L￨JJ￨O￨A poultry￨L￨NN￨O￨- barns￨L￨NNS￨O￨- :￨L￨:￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- introduction￨L￨NN￨O￨- timeAmy￨L￨NN￨O￨- Pinsent1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Isobel￨U￨NNP￨PERSON￨- M￨U￨NNP￨PERSON￨- Blake1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Michael￨U￨NNP￨PERSON￨- T￨U￨NN￨PERSON￨- White1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Steven￨U￨NNP￨PERSON￨- Riley1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 14:427￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Pinsent￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Both￨U￨CC￨MISC￨- high￨L￨JJ￨O￨- and￨L￨CC￨O￨- low￨L￨JJ￨O￨- pathogenic￨L￨JJ￨O￨- subtype￨L￨NN￨O￨- A￨U￨DT￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- remain￨L￨VBP￨O￨- ongoing￨L￨JJ￨O￨- threats￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- commercial￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- industry￨L￨NN￨O￨- globally￨L￨RB￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- If￨U￨IN￨O￨- birds￨L￨NNS￨O￨A were￨L￨VBD￨O￨- tested￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- slaughter￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- HI￨U￨NN￨STATE_OR_PROVINCE￨- assay￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- rt-PCR￨L￨NN￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- was￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- <￨L￨JJR￨O￨- 2￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- slaughter￨L￨NN￨O￨- .￨L￨.￨O￨- +Prior￨U￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- N￨U￨NN￨O￨- s￨L￨VBZ￨O￨- a￨L￨DT￨O￨- m￨L￨NN￨O￨- p￨L￨NN￨O￨- l￨L￨NN￨O￨- e￨L￨SYM￨O￨- =￨L￨JJ￨O￨- 50￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- birds￨L￨NNS￨O￨A were￨L￨VBD￨O￨- sampled￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- basis￨L￨NN￨O￨- once￨L￨RB￨DATE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- after￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- detected￨L￨VBN￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- s￨L￨VBZ￨O￨- a￨L￨DT￨O￨- m￨L￨NN￨O￨- p￨L￨NN￨O￨- l￨L￨NN￨O￨- e￨L￨SYM￨O￨- =￨L￨JJ￨O￨- 2000￨L￨CD￨NUMBER￨- birds￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- sampled￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- both￨L￨CC￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- scenarios￨L￨NNS￨O￨- where￨L￨WRB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- was￨L￨VBD￨O￨- known￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨DATE￨- day￨L￨NN￨DATE￨A of￨L￨IN￨O￨- virus￨L￨NN￨O￨- introduction￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- barn￨L￨NN￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨DATE￨- day￨L￨NN￨DATE￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- introduction￨L￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- were￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- jointly￨L￨RB￨O￨- from￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨A flock￨L￨NN￨O￨- sampling￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- vaccine￨L￨NN￨O￨A efficacy￨L￨NN￨O￨A under￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- action￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- stratified￨L￨VBN￨O￨- into￨L￨IN￨O￨- households￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- acute￨L￨JJ￨O￨- ,￨L￨,￨O￨- directly￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- stratified￨L￨JJ￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- discussed￨L￨VBD￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- under￨L￨IN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- action￨L￨NN￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- estimated￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨A efficacy￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- nonrandomly￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- ignored￨L￨VBN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- action￨L￨NN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- strata￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- issues￨L￨NNS￨O￨- one￨L￨CD￨NUMBER￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- when￨L￨WRB￨O￨- estimating￨L￨VBG￨O￨- vaccine￨L￨NN￨O￨A efficacy￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- small-group-mixing￨L￨JJ￨O￨- population￨L￨NN￨O￨- are￨L￨VBP￨O￨- heterogeneous￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- action￨L￨NN￨O￨- and￨L￨CC￨O￨- nonrandom￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 1992￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- discussed￨L￨VBD￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨A efficacy￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨- mixing￨L￨VBG￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- AIVs￨U￨NNS￨O￨- typically￨L￨RB￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- scaled￨L￨VBN￨O￨- effective￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- order￨L￨NN￨O￨- of￨L￨IN￨O￨- magnitude￨L￨NN￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- human￨L￨JJ￨O￨- counterparts￨L￨NNS￨O￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 7.0￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- and￨L￨CC￨O￨- 1.5￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- H1￨U￨NN￨O￨- and￨L￨CC￨O￨- H3￨U￨NN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- 38.7￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- and￨L￨CC￨O￨- 77.5￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- in￨L￨IN￨O￨- birds￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1E￨L￨NN￨O￨- and￨L￨CC￨O￨- 1F￨L￨NN￨O￨- ;￨L￨:￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- below￨L￨IN￨O￨- ,￨L￨,￨O￨- other￨L￨JJ￨O￨- avian￨L￨JJ￨O￨- subtypes￨L￨NNS￨O￨A also￨L￨RB￨O￨- exhibit￨L￨VBP￨O￨- higher￨L￨JJR￨O￨- diversity￨L￨NN￨O￨- than￨L￨IN￨O￨- commonly￨L￨RB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- H1￨U￨NN￨O￨- and￨L￨CC￨O￨- H3￨U￨NN￨O￨- human￨L￨JJ￨O￨- subtypes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- avian￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- rich￨L￨JJ￨O￨- array￨L￨NN￨O￨- of￨L￨IN￨O￨- subtypes￨L￨NNS￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- fully￨L￨RB￨O￨- 13￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- known￨L￨VBN￨O￨- 18￨L￨CD￨NUMBER￨- HA￨U￨NN￨O￨- subtypes￨L￨NNS￨O￨- isolated￨L￨VBN￨O￨- from￨L￨IN￨O￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- birds￨L￨NNS￨O￨- over￨L￨IN￨O￨- this￨L￨DT￨O￨- time￨L￨NN￨O￨- span￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1D￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- –￨L￨:￨O￨- H￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Scaled￨U￨VBN￨O￨- effective￨L￨JJ￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- scaled￨L￨VBN￨O￨A by￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- surrogate￨L￨NN￨O￨- for￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- H1￨U￨NN￨O￨- and￨L￨CC￨O￨- H3￨U￨NN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- birds￨L￨NNS￨O￨- estimated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- nonparametric￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- estimator￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Materials￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Methods￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Human￨U￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- viruses￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- very￨L￨RB￨O￨- limited￨L￨JJ￨O￨- subtype￨L￨NN￨O￨- diversity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- serologically￨L￨RB￨O￨- distinct￨L￨JJ￨O￨- hemagglutinin￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- H￨U￨NN￨O￨- or￨L￨CC￨O￨- HA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- glycoprotein￨L￨NN￨O￨- types￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- only￨L￨RB￨O￨- H1￨U￨NN￨O￨- and￨L￨CC￨O￨- H3￨U￨NN￨O￨- subtypes￨L￨NNS￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- above￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIQRS￨U￨JJ￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- delays￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- computer￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clean￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- by￨L￨IN￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- above￨L￨RB￨O￨- ,￨L￨,￨O￨- Liu￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- incorporated￨L￨VBD￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- period￨L￨NN￨O￨- into￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIQRS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +proposed￨L￨VBN￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- SEIR￨U￨NNP￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- bifurcating￨L￨VBG￨O￨- parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- H￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- holds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨A P￨U￨NN￨O￨- *￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- *￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- *￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- without￨L￨IN￨O￨- delay￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- H￨U￨NN￨O￨- 21￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- H￨U￨NN￨O￨- 22￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- hold￨L￨VBP￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨A P￨U￨NN￨O￨- *￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- *￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- *￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- for￨L￨IN￨O￨- τ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ∈￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- undergoes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcation￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- P￨U￨NN￨O￨- *￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- *￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- *￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- τ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- τ￨L￨NN￨O￨- 10￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +One￨U￨PRP￨NUMBER￨- can￨L￨MD￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- straightforward￨L￨JJ￨O￨- method￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- each￨L￨DT￨O￨- infected￨L￨JJ￨O￨A node￨L￨NN￨O￨A i￨L￨FW￨O￨- as￨L￨IN￨O￨- μ￨L￨NN￨O￨- =￨L￨JJ￨O￨- m/M￨L￨NN￨O￨- where￨L￨WRB￨O￨- m￨L￨NN￨O￨- and￨L￨CC￨O￨- M￨U￨NN￨O￨- are￨L￨VBP￨O￨- respectively￨L￨RB￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- i￨L￨FW￨O￨- 's￨L￨POS￨O￨- neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- essential￨L￨JJ￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A probability￨L￨NN￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- snapshot￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- does￨L￨VBZ￨O￨- n't￨L￨RB￨O￨- distinguish￨L￨VB￨O￨- which￨L￨WDT￨O￨- node￨L￨NN￨O￨- spreads￨L￨VBZ￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨A node￨L￨NN￨O￨A ,￨L￨,￨O￨- each￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- once￨L￨RB￨DATE￨- in￨L￨IN￨O￨- μ￨L￨NN￨O￨- =￨L￨JJ￨O￨- m/M￨L￨NN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- illustration￨L￨NN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ongoing￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- mosquito-borne￨L￨JJ￨O￨- flavivirus￨L￨NN￨O￨- affecting￨L￨VBG￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- predominantly￨L￨RB￨O￨- tropical￨L￨JJ￨O￨- and￨L￨CC￨O￨- sub-tropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- into￨L￨IN￨O￨- higher￨L￨JJR￨O￨- latitudes￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- of￨L￨IN￨COUNTRY￨- America￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Europe￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- concern￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue-naive￨L￨JJ￨O￨- population￨L￨NN￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- frequent￨L￨JJ￨O￨- travels￨L￨NNS￨O￨- to￨L￨TO￨O￨- endemic￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- impose￨L￨VBP￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- regions￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A becoming￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- re￨L￨SYM￨O￨- -￨L￨:￨O￨- )￨L￨-RRB-￨O￨- established￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨DATE￨- following￨L￨VBG￨DATE￨- weeks￨L￨NNS￨DATE￨- the￨L￨DT￨O￨- island￨L￨NN￨O￨- witnessed￨L￨VBD￨O￨- its￨L￨PRP$￨O￨- first￨L￨JJ￨ORDINAL￨- dengue￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 2187￨L￨CD￨DATE￨- reported￨L￨VBD￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- approximately￨L￨RB￨O￨- were￨L￨VBD￨O￨- confirmed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Mean￨U￨NN￨O￨- of￨L￨IN￨O￨- minimum￨L￨JJ￨O￨- temperatures￨L￨NNS￨O￨- per￨L￨IN￨O￨- week￨L￨NN￨DURATION￨- (￨L￨-LRB-￨O￨- solid￨L￨JJ￨O￨- ,￨L￨,￨O￨- green￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- precipitation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- solid￨L￨JJ￨O￨- ,￨L￨,￨O￨- cyan￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- dengue￨L￨NN￨O￨A reported￨L￨VBD￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- week￨L￨NN￨DURATION￨- (￨L￨-LRB-￨O￨- dotted￨L￨VBN￨O￨- ,￨L￨,￨O￨- black￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- dengue￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Direcção￨U￨NNP￨ORGANIZATION￨- Geral￨U￨NNP￨ORGANIZATION￨- de￨L￨IN￨ORGANIZATION￨- Saúde￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Portuguese￨U￨NNP￨NATIONALITY￨- health￨L￨NN￨O￨- ministry￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- island￨L￨NN￨O￨- of￨L￨IN￨O￨- Madeira￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- extensive￨L￨JJ￨O￨- communication￨L￨NN￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- branches￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- cell￨L￨NN￨O￨- types￨L￨NNS￨O￨- and￨L￨CC￨O￨- factors￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- innate￨L￨JJ￨O￨- and￨L￨CC￨O￨- adaptive￨L￨JJ￨O￨- components￨L￨NNS￨O￨- .57￨L￨CD￨NUMBER￨- Direct￨U￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- components￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- pathogens￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- neutral￨L￨JJ￨IDEOLOGY￨- to￨L￨TO￨O￨- antagonistic￨L￨JJ￨O￨- ,145,146￨L￨CD￨NUMBER￨- but￨L￨CC￨O￨- some￨L￨DT￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- Epstein￨U￨NN￨PERSON￨- –￨L￨:￨O￨- Barr￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- directly￨L￨RB￨O￨- benefit￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- proliferation￨L￨NN￨O￨- of￨L￨IN￨O￨- certain￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A .147￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 150￨L￨CD￨NUMBER￨- Mechanisms￨U￨NNS￨O￨- to￨L￨TO￨O￨- evade￨L￨VB￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- are￨L￨VBP￨O￨- diverse￨L￨JJ￨O￨- .5￨L￨NN￨NUMBER￨- For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Streptococcus￨U￨NN￨O￨- pneumoniae￨L￨FW￨O￨- ,￨L￨,￨O￨- Klebsiella￨U￨NN￨O￨- pneumoniae￨L￨FW￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- possess￨L￨VBP￨O￨- polysaccharide￨L￨NN￨O￨- capsules￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reduce￨L￨VBP￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- phagocytosis￨L￨NN￨O￨- .6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Staphylococcus￨U￨FW￨O￨- aureus￨L￨FW￨O￨- and￨L￨CC￨O￨- Treponema￨U￨FW￨MISC￨- pallidum￨L￨FW￨O￨- use￨L￨NN￨O￨- surface￨L￨NN￨O￨- proteins￨L￨NNS￨O￨- to￨L￨TO￨O￨- aggregate￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- antigens￨L￨NNS￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- surface￨L￨NN￨O￨- .9,10￨L￨CD￨NUMBER￨- Many￨U￨JJ￨O￨- pathogens￨L￨NNS￨O￨- replicate￨L￨VBP￨O￨- in￨L￨IN￨O￨- ways￨L￨NNS￨O￨- that￨L￨WDT￨O￨- minimize￨L￨VBP￨O￨- interaction￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- .11￨L￨CD￨NUMBER￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- quickly￨L￨RB￨O￨- infects￨L￨VBZ￨O￨- and￨L￨CC￨O￨- replicates￨L￨VBZ￨O￨- in￨L￨IN￨O￨- respiratory￨L￨JJ￨O￨- epithelial￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- limiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- window￨L￨NN￨O￨- of￨L￨IN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- CD8￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨- and￨L￨CC￨O￨- antibodies￨L￨NNS￨O￨- .12￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- infecting￨L￨VBG￨O￨- keratinocytes￨L￨NNS￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- papillomaviruses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- exceedingly￨L￨RB￨O￨- low￨L￨JJ￨O￨- expression￨L￨NN￨O￨- levels￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- avoid￨L￨VB￨O￨- detection￨L￨NN￨O￨- until￨L￨IN￨O￨- they￨L￨PRP￨O￨- begin￨L￨VBP￨O￨- replicating￨L￨VBG￨O￨- inside￨L￨IN￨O￨- cells￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- about￨L￨IN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- shed￨L￨VBN￨O￨- .13,14￨L￨CD￨NUMBER￨- Replication￨U￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- macrophages￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- several￨L￨JJ￨O￨- proteins￨L￨NNS￨O￨- to￨L￨TO￨O￨- mask￨L￨NN￨O￨- its￨L￨PRP$￨O￨- activities￨L￨NNS￨O￨- .15￨L￨CD￨NUMBER￨- Avoidance￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- frequently￨L￨RB￨O￨- accompanied￨L￨VBN￨O￨- by￨L￨IN￨O￨- suppression￨L￨NN￨O￨- .￨L￨.￨O￨- +Immune￨U￨JJ￨O￨- systems￨L￨NNS￨O￨- have￨L￨VBP￨O￨- evolved￨L￨VBN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- great￨L￨JJ￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- partly￨L￨RB￨O￨- to￨L￨TO￨O￨- attenuate￨L￨VB￨O￨- the￨L￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- fitness￨L￨NN￨O￨- .142,143￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- vertebrates￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- accomplish￨L￨VBP￨O￨- this￨L￨DT￨O￨- goal￨L￨NN￨O￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- populations￨L￨NNS￨O￨- through￨L￨IN￨O￨- innate￨L￨JJ￨O￨- and￨L￨CC￨O￨- adaptive￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- .57￨L￨CD￨NUMBER￨- This￨U￨DT￨O￨- description￨L￨NN￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- analogues￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- prokaryotic￨L￨JJ￨O￨- level￨L￨NN￨O￨- .144￨L￨CD￨NUMBER￨- Innate￨U￨JJ￨O￨- immunity￨L￨NN￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- activities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complement￨L￨NN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- phagocytes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- natural￨L￨JJ￨O￨- killer￨L￨NN￨O￨- cells￨L￨NNS￨O￨A .￨L￨.￨O￨- +Expanding￨U￨VBG￨O￨- classic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- competition￨L￨NN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- more￨L￨JJR￨O￨- realistic￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- pathogen￨L￨NN￨O￨- interactions￨L￨NNS￨O￨A ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- simultaneous￨L￨JJ￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- specific￨L￨JJ￨O￨- and￨L￨CC￨O￨- nonspecific￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- strengths￨L￨NNS￨O￨- and￨L￨CC￨O￨- durations￨L￨NNS￨O￨- ,￨L￨,￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- breadth￨L￨NN￨O￨- of￨L￨IN￨O￨- phenomena￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- and￨L￨CC￨O￨- demonstrates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- for￨L￨IN￨O￨- anticipating￨L￨VBG￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- antigenic￨L￨JJ￨O￨- phenotype￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- with￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- sites￨L￨NNS￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- with￨L￨IN￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨A and￨L￨CC￨O￨- antibodies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- epitopes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨A reflects￨L￨VBZ￨O￨- strong￨L￨JJ￨O￨- and￨L￨CC￨O￨- enduring￨L￨JJ￨O￨- selection￨L￨NN￨O￨- to￨L￨TO￨O￨- escape￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- give￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- needed￨L￨VBN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨A drugs￨L￨NNS￨CRIMINAL_CHARGE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- isolated￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- practical￨L￨JJ￨O￨- reference￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- stockpiles￨L￨NNS￨O￨- and￨L￨CC￨O￨- healthcare￨L￨NN￨O￨- resources￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- beds￨L￨NNS￨O￨- and￨L￨CC￨O￨- personnel￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- advance￨L￨NN￨O￨- .￨L￨.￨O￨- +Before￨U￨IN￨O￨- effective￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- become￨L￨VBP￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- antiviral￨L￨JJ￨O￨A drugs￨L￨NNS￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Tamiflu￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- measures￨L￨VBZ￨O￨- that￨L￨IN￨O￨- reduce￨L￨VB￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- write￨L￨VBP￨O￨- S￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- L￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- latent￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- —￨L￨:￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- who￨L￨WP￨O￨- is￨L￨VBZ￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- isolated￨L￨VBN￨O￨A ,￨L￨,￨O￨- I￨U￨PRP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- who￨L￨WP￨O￨- is￨L￨VBZ￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- isolated￨L￨VBN￨O￨- ,￨L￨,￨O￨- A￨U￨DT￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- asymptomatic￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- who￨L￨WP￨O￨- has￨L￨VBZ￨O￨- recovered￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- using￨L￨VBG￨O￨- antiviral￨L￨JJ￨O￨A drugs￨L￨NNS￨CRIMINAL_CHARGE￨- for￨L￨IN￨O￨- prophylaxis￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- isolation￨L￨NN￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- importing￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- from￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- and￨L￨CC￨O￨- interventions￨L￨NNS￨O￨- with￨L￨IN￨O￨- isolation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨A drugs￨L￨NNS￨CRIMINAL_CHARGE￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- classical￨L￨JJ￨O￨- generalism￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- strategy￨L￨NN￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- bacteria￨L￨NNS￨O￨A to￨L￨TO￨O￨- extend￨L￨VB￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- range￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- multiple￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- positively￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- genome￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- predict￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- bacteria￨L￨NNS￨O￨A use￨L￨VBP￨O￨- this￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- modification￨L￨NN￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- multiple￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- positively￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secretions￨L￨NNS￨O￨- coded￨L￨VBN￨O￨- in￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- genomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- logic￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- prediction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- greater￨L￨JJR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secretions￨L￨NNS￨O￨- coded￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- genome￨L￨NN￨O￨- will￨L￨MD￨O￨- allow￨L￨VB￨O￨- bacteria￨L￨NNS￨O￨A to￨L￨TO￨O￨- modify￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- environments￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- greater￨L￨JJR￨O￨- extent￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- digestively￨L￨RB￨O￨- simplifying￨L￨VBG￨O￨- nutrient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- or￨L￨CC￨O￨- toxifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- for￨L￨IN￨O￨- resident￨L￨JJ￨O￨- competitors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- secretions￨L￨NNS￨O￨- allow￨L￨VBP￨O￨- pathogenic￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A to￨L￨TO￨O￨- modify￨L￨VB￨O￨- and￨L￨CC￨O￨- standardize￨L￨VB￨O￨- diverse￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- environments￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- allowing￨L￨VBG￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- expand￨L￨VB￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- range￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- bacteria￨L￨NNS￨O￨A use￨L￨VBP￨O￨- a￨L￨DT￨O￨- strategy￨L￨NN￨O￨- of￨L￨IN￨O￨- modifying￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- environments￨L￨NNS￨O￨- via￨L￨IN￨O￨- secretions￨L￨NNS￨O￨- we￨L￨PRP￨O￨- expect￨L￨VBP￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- genomic￨L￨JJ￨O￨- signature￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- controlling￨L￨VBG￨O￨- PRRS￨U￨NNP￨O￨- in￨L￨IN￨O￨- Vietnam￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- available1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- stamping￨L￨VBG￨O￨- out￨L￨RP￨O￨- (￨L￨-LRB-￨O￨- SO￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- culling￨L￨VBG￨O￨- all￨L￨DT￨O￨- infected￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A ;￨L￨:￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- strategic￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- implies￨L￨VBZ￨O￨- culling￨L￨VBG￨O￨- all￨L￨DT￨O￨- infected￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- vaccinating￨L￨VBG￨O￨- susceptible￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccination2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- preventive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- refers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- vaccinating￨L￨VBG￨O￨- all￨L￨DT￨O￨- pigs￨L￨NNS￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- policy￨L￨NN￨O￨- making￨L￨NN￨O￨- for￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- PRRS￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- purposes￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- are￨L￨VBP￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- field￨L￨NN￨O￨- research￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- pig￨L￨NN￨O￨A farmers￨L￨NNS￨O￨- ’￨L￨POS￨O￨- preference￨L￨NN￨O￨- for￨L￨IN￨O￨- PRRS￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- and￨L￨CC￨O￨- benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- PRRS￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- significance￨L￨NN￨O￨- of￨L￨IN￨O￨- PRRS￨U￨NN￨O￨- vaccination￨L￨NN￨O￨A ,￨L￨,￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- effectiveness￨L￨NN￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- PRRS￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- necessary￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SO￨U￨NN￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- was￨L￨VBD￨O￨- applied￨L￨VBN￨O￨- in￨L￨IN￨O￨- Vietnam￨U￨NNP￨COUNTRY￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- government￨L￨NN￨O￨- provided￨L￨VBD￨O￨- a￨L￨DT￨O￨- subsidy￨L￨NN￨O￨- to￨L￨TO￨O￨- encourage￨L￨VB￨O￨- pig￨L￨NN￨O￨- farmers￨L￨NNS￨O￨- to￨L￨TO￨O￨- cull￨L￨VB￨O￨- infected￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- PRRS￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- percentage￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- pig￨L￨NN￨O￨A farmers￨L￨NNS￨O￨- ’￨L￨POS￨O￨- preference￨L￨NN￨O￨- for￨L￨IN￨O￨- PRRS￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- needed￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- saturation￨L￨NN￨O￨A factor￨L￨NN￨O￨- that￨L￨WDT￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- inhibitory￨L￨JJ￨O￨- effect￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- or￨L￨CC￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- transformation￨L￨NN￨O￨- from￨L￨IN￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-related￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- ,￨L￨,￨O￨- υ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- medical￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- supplied￨L￨VBD￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- saturation￨L￨NN￨O￨- factor￨L￨NN￨O￨- that￨L￨WDT￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- being￨L￨VBG￨O￨- delayed￨L￨VBN￨O￨- for￨L￨IN￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- example￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- limited￨L￨JJ￨O￨- medical￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- which￨L￨WDT￨O￨- carefully￨L￨RB￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- another￨L￨DT￨O￨- simple￨L￨JJ￨O￨- example￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- bilinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- studied￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- motivations￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- further￨L￨RB￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- βSI￨L￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- +￨L￨CC￨O￨- αI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- continually￨L￨RB￨O￨- differentiable￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- function￨L￨NN￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- rI￨L￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- +￨L￨CC￨O￨- kI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- saturation￨L￨NN￨O￨A phenomenon￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- medical￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Zhang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Liu￨U￨NNP￨PERSON￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- and￨L￨CC￨O￨- differentiable￨L￨JJ￨O￨- saturated￨L￨JJ￨O￨A treatment￨L￨NN￨O￨- function￨L￨NN￨O￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- rI￨L￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- +￨L￨CC￨O￨- kI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- r￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- stands￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- cure￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- k￨L￨NN￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- being￨L￨VBG￨O￨- delayed￨L￨VBN￨O￨- for￨L￨IN￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +β￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- υ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- r￨L￨NN￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- and￨L￨CC￨O￨- k￨L￨NN￨O￨- are￨L￨VBP￨O￨- nonnegative￨L￨JJ￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- BU￨U￨NNP￨ORGANIZATION￨- involve￨L￨VB￨O￨- three￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- :￨L￨:￨O￨- that￨L￨IN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- water￨L￨NN￨O￨A bugs￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- M￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- submodel￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨A population￨L￨NN￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- type￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- S￨U￨NN￨O￨- denoting￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- those￨L￨DT￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- BU￨U￨NNP￨O￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- those￨L￨DT￨O￨- in￨L￨IN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- thus￨L￨RB￨O￨- plausible￨L￨JJ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- saturated￨L￨JJ￨O￨- treatment￨L￨NN￨O￨A function￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- limited￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- BU￨U￨NNP￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- also￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +ulcerans￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- secondly￨L￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- occurs￨L￨VBZ￨O￨- through￨L￨IN￨O￨- biting￨L￨VBG￨O￨- by￨L￨IN￨O￨- water￨L￨NN￨O￨A bugs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- total￨L￨JJ￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- The￨U￨DT￨O￨- submodel￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- water￨L￨NN￨O￨A bugs￨L￨NNS￨O￨- and￨L￨CC￨O￨- M.￨U￨NN￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- studies34567811￨L￨NN￨O￨- mentioned￨L￨VBN￨O￨- above￨L￨IN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- offering￨L￨VBG￨O￨- an￨L￨DT￨O￨- opportunity￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- reinforcement￨L￨NN￨O￨- and￨L￨CC￨O￨- decaying￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- quantified￨L￨VBN￨O￨- by￨L￨IN￨O￨- stickiness￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- information￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- diffusion￨L￨NN￨O￨- on￨L￨IN￨O￨- various￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Third￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- unlike￨L￨IN￨O￨- the￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- hearing￨L￨NN￨O￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- more￨L￨RBR￨O￨- opportunities￨L￨NNS￨O￨- to￨L￨TO￨O￨- add￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- remain￨L￨VBP￨O￨- )￨L￨-RRB-￨O￨- one￨L￨CD￨NUMBER￨- word￨L￨NN￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- more￨L￨JJR￨O￨- selected￨L￨VBN￨O￨- speakers￨L￨NNS￨O￨- try￨L￨VBP￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- it16171819￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- reinforcement￨L￨NN￨O￨- effect￨L￨NN￨O￨- in￨L￨IN￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- simple￨L￨JJ￨O￨- situation￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- neighbors￨L￨NNS￨O￨- adopting￨L￨VBG￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- likelihood￨L￨NN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- following￨L￨VBG￨O￨- them35￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- social￨L￨JJ￨O￨- reinforcement￨L￨NN￨O￨- and￨L￨CC￨O￨- decay￨L￨NN￨O￨- effects￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- emphasized￨L￨VBN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- guideline￨L￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- that￨L￨WDT￨O￨- attention￨L￨NN￨O￨- fades￨L￨VBZ￨O￨- away11￨L￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- best￨L￨JJS￨O￨- knowledge￨L￨NN￨O￨- few￨L￨JJ￨O￨- works￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- attempted￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- explicitly￨L￨RB￨O￨- the￨L￨DT￨O￨- competition￨L￨NN￨O￨- and￨L￨CC￨O￨- memory￨L￨NN￨O￨A effect￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- study￨L￨NN￨O￨- deeply￨L￨RB￨O￨- how￨L￨WRB￨O￨- it￨L￨PRP￨O￨- shapes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- researches6￨L￨NN￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ways￨L￨NNS￨O￨- that￨L￨WDT￨O￨- different￨L￨JJ￨O￨- information￨L￨NN￨O￨- spread￨L￨NN￨O￨- is￨L￨VBZ￨O￨- attributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- stickiness￨L￨NN￨O￨- –￨L￨:￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- adoption￨L￨NN￨O￨- is￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- dominated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- few￨L￨JJ￨O￨- exposures67￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- –￨L￨:￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- extent￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- more￨L￨RBR￨O￨- repeated￨L￨JJ￨O￨- exposures￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A continue￨L￨VBP￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- durative￨L￨JJ￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +Next￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- big￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- confronted￨L￨VBN￨O￨- with￨L￨IN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A spreading￨L￨VBG￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- both￨L￨DT￨O￨- social￨L￨JJ￨O￨- reinforcement￨L￨NN￨O￨- and￨L￨CC￨O￨- decay￨L￨NN￨O￨- effects￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- memory￨L￨NN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- vastly￨L￨RB￨O￨- different￨L￨JJ￨O￨- approach￨L￨NN￨O￨- was￨L￨VBD￨O￨- adopted￨L￨VBN￨O￨- by￨L￨IN￨O￨- Boëlle￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- constructed￨L￨VBD￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- interval￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- gonotrophic￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- causative￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- ,￨L￨,￨O￨- obtaining￨L￨VBG￨O￨- a￨L￨DT￨O￨- best￨L￨JJS￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- 3.7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨- region￨L￨NN￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 64￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- that￨L￨IN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- of￨L￨IN￨O￨- 1.22￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- primary￨L￨JJ￨O￨- focus￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- on￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨A host￨L￨NN￨TITLE￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- documented￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- over￨L￨IN￨O￨- 266,000￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- estimated￨L￨VBN￨O￨A to￨L￨TO￨O￨- have￨L￨VB￨O￨- occurred￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- also￨L￨RB￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- mosquito￨L￨NN￨O￨A mortality￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- yielding￨L￨VBG￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- moreover￨L￨RB￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- widely￨L￨RB￨O￨- distinct￨L￨JJ￨O￨- different￨L￨JJ￨O￨- timescales￨L￨NNS￨O￨- :￨L￨:￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- students￨L￨NNS￨O￨A from￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- ;￨L￨:￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- take￨L￨VBP￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- environment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- students￨L￨NNS￨O￨- changed￨L￨VBD￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- term￨L￨NN￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- school￨L￨NN￨O￨- .￨L￨.￨O￨- +Overall￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- thus￨L￨RB￨O￨- obtain￨L￨VB￨O￨- data￨L￨NNS￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- students￨L￨NNS￨O￨A for￨L￨IN￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- contain￨L￨VB￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- not￨L￨RB￨O￨- taking￨L￨VBG￨O￨- part￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- repartition￨L￨NN￨O￨- of￨L￨IN￨O￨- students￨L￨NNS￨O￨A into￨L￨IN￨O￨- classes￨L￨NNS￨O￨- and￨L￨CC￨O￨- investigate￨L￨VB￨O￨- if￨L￨IN￨O￨- gender￨L￨NN￨O￨- differences￨L￨NNS￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- primary￨L￨JJ￨O￨- school￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Fitting￨U￨JJ￨O￨- to￨L￨TO￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- thus￨L￨RB￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- dramatically￨L￨RB￨O￨- under-estimated￨L￨JJ￨O￨- confidence￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- potential￨L￨JJ￨O￨- biases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- fit￨L￨JJ￨O￨A central￨L￨JJ￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- points￨L￨NNS￨O￨- further￨L￨RB￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- nearly￨L￨RB￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- correlated￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- too￨L￨RB￨O￨- much￨L￨JJ￨O￨- weight￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- fit￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- Negative￨U￨JJ￨MISC￨- Binomial￨U￨JJ￨MISC￨- likelihood￨L￨NN￨O￨- fit￨L￨NN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- over-dispersion￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- we￨L￨PRP￨O￨- fit￨L￨VBP￨O￨- piecewise￨L￨JJ￨O￨- exponential￨L￨JJ￨O￨A curves￨L￨NNS￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- ten￨L￨CD￨NUMBER￨- contiguous￨L￨JJ￨O￨- points￨L￨NNS￨O￨- are￨L￨VBP￨O￨- fit￨L￨VBN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- exponential￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- rise￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- novel￨L￨JJ￨O￨- methodology￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- response￨L￨NN￨O￨- measures￨L￨NNS￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- piecewise￨L￨NN￨O￨- exponential￨L￨JJ￨O￨A curves￨L￨NNS￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- evolving￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- rise￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- decline￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Estimation￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- exponential￨L￨JJ￨O￨A rise￨L￨NN￨O￨- The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- generates￨L￨VBZ￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- current￨L￨JJ￨DATE￨- outbreak￨L￨NN￨O￨- incidence￨L￨NN￨O￨A data￨L￨NNS￨O￨A for￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Liberia￨U￨NNP￨COUNTRY￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- September￨U￨NNP￨DATE￨- 8￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2014￨L￨CD￨DATE￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- estimated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- importation￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- should￨L￨MD￨O￨- not￨L￨RB￨O￨- generate￨L￨VB￨O￨- large￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- countries￨L￨NNS￨O￨A where￨L￨WRB￨O￨- prompt￨L￨JJ￨O￨- isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- appropriate￨L￨JJ￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- facilities￨L￨NNS￨O￨- occurs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- clear￨L￨JJ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- importation￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- likelihood￨L￨NN￨O￨- ,￨L￨,￨O￨- timeline￨L￨NN￨O￨- ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- WA￨U￨NNP￨STATE_OR_PROVINCE￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- WA￨U￨NNP￨STATE_OR_PROVINCE￨- outbreak￨L￨NN￨O￨- that￨L￨WDT￨O￨- generate￨L￨VBP￨O￨- stochastic￨L￨JJ￨O￨A simulations￨L￨NNS￨O￨A of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- ,￨L￨,￨O￨- yielding￨L￨VBG￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- other￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- importation￨L￨NN￨O￨- events￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- resolution￨L￨NN￨O￨- for￨L￨IN￨O￨- 3,362￨L￨CD￨NUMBER￨- subpopulations￨L￨NNS￨O￨- in￨L￨IN￨O￨- 220￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- approach￨L￨NN￨O￨- selects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- numerical￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨A simulations￨L￨NNS￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ’s￨L￨POS￨O￨- local￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- within￨L￨IN￨O￨- West￨U￨JJ￨MISC￨- African￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- progression￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- analyses￨L￨NNS￨O￨- however￨L￨RB￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- affected￨L￨JJ￨O￨- countries￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨- etiology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- incubation￨L￨NN￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨MISC￨- West￨U￨NNP￨MISC￨- African￨U￨NNP￨NATIONALITY￨- (￨L￨-LRB-￨O￨- 2014WA￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- outbreak￨L￨NN￨O￨- has￨L￨VBZ￨O￨- demonstrated￨L￨VBN￨O￨- 98￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- homology￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- Zaire￨U￨NNP￨COUNTRY￨- Ebola￨U￨NNP￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- 55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CFR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- affected￨L￨JJ￨O￨- countries￨L￨NNS￨O￨A 3￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Comparing￨U￨VBG￨O￨- these￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- excess￨L￨JJ￨O￨- preventative￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- measures￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- signals￨L￨NNS￨O￨A provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- SAS￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- practice￨L￨NN￨O￨- of￨L￨IN￨O￨- syndromic￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- rapidly￨L￨RB￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- September￨U￨NNP￨DATE￨- 11￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2001￨L￨CD￨DATE￨- ,￨L￨,￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- Washington￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- D.C.￨U￨NNP￨LOCATION￨- Researchers￨U￨NNP￨O￨- have￨L￨VBP￨O￨- since￨L￨IN￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- patients￨L￨NNS￨O￨- '￨L￨POS￨O￨- chief￨L￨JJ￨O￨- complaints￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- OTC￨U￨NNP￨O￨- medication￨L￨NN￨O￨- sales￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- absenteeism￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- can￨L￨MD￨O￨- warn￨L￨VB￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- or￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨A in￨L￨IN￨O￨- advance￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- corresponding￨L￨JJ￨O￨- potential￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- occur￨L￨VB￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- but￨L￨CC￨O￨- from￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- signals￨L￨NNS￨O￨A defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- National￨U￨NNP￨ORGANIZATION￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Emergency￨U￨NNP￨ORGANIZATION￨- Information￨U￨NNP￨ORGANIZATION￨- Reporting￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- Management￨U￨NNP￨O￨- Specification￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- NPHEIRMS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ”￨L￨''￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- fit￨L￨VBP￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- occurred￨L￨VBD￨O￨- under￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- early￨L￨JJ￨O￨- SAS￨U￨NNP￨ORGANIZATION￨- signals￨L￨NNS￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- assesses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- SAS￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- varicella￨L￨NN￨O￨- ,￨L￨,￨O￨- mumps￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- well-established￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- mosquito￨L￨NN￨O￨- populations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- as￨L￨IN￨O￨- where￨L￨WRB￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- and￨L￨CC￨O￨- μ￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- from￨L￨IN￨O￨- vector￨L￨NN￨O￨- to￨L￨TO￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- vector￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- biting￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- A￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨A host￨L￨NN￨TITLE￨A ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- proportional￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquitoes￨L￨NNS￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- death￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨DURATION￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- scholars￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- and￨L￨CC￨O￨- partial￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- paid￨L￨VBN￨O￨- their￨L￨PRP$￨O￨- attentions￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- which￨L￨WDT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- derivative￨L￨NN￨O￨A is￨L￨VBZ￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- problems￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Assuming￨U￨VBG￨O￨- that￨L￨DT￨O￨- f￨L￨FW￨O￨- is￨L￨VBZ￨O￨- differential￨L￨JJ￨O￨- and￨L￨CC￨O￨- β-differentiable￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- opened￨L￨VBN￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- Let￨U￨VB￨O￨- f￨L￨FW￨O￨- :￨L￨:￨O￨- [￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- ∞￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- →￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- function￨L￨NN￨O￨- ;￨L￨:￨O￨- then￨L￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- integral￨L￨JJ￨O￨A of￨L￨IN￨O￨- order￨L￨NN￨O￨- β-integral￨L￨NN￨O￨- of￨L￨IN￨O￨- f￨L￨FW￨O￨- is￨L￨VBZ￨O￨- The￨U￨DT￨O￨- above￨L￨IN￨O￨- operator￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- inverse￨L￨JJ￨O￨- operator￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- beta-derivative￨L￨JJ￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- the￨L￨DT￨O￨- Atangana￨U￨NNP￨O￨- ‘￨L￨``￨O￨- beta￨L￨NN￨O￨- integral￨L￨JJ￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- our￨L￨PRP$￨O￨- main￨L￨JJ￨O￨- interest￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- extend￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- derivative￨L￨NN￨O￨A ;￨L￨:￨O￨- a￨L￨DT￨O￨- stability￨L￨NN￨O￨- analysis￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- presented￨L￨VBN￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- solution￨L￨NN￨O￨- using￨L￨VBG￨O￨- some￨L￨DT￨O￨- interesting￨L￨JJ￨O￨- iterations￨L￨NNS￨O￨- methods￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- presented￨L￨VBN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- assess￨L￨VB￨O￨- spatial￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- seropositive￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- constructed￨L￨VBD￨O￨- intensity￨L￨NN￨O￨- maps￨L￨NNS￨O￨- by￨L￨IN￨O￨- placing￨L￨VBG￨O￨- a￨L￨DT￨O￨- fine￨L￨JJ￨O￨- grid￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- area￨L￨NN￨O￨- and￨L￨CC￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- grid￨L￨NN￨O￨- segment￨L￨NN￨O￨- being￨L￨VBG￨O￨- seropositive￨L￨JJ￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Gaussian￨U￨JJ￨MISC￨- kernel￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- bandwidth￨L￨NN￨O￨- that￨L￨WDT￨O￨- minimized￨L￨VBD￨O￨- the￨L￨DT￨O￨- cross-validated￨L￨JJ￨O￨- error￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- assuming￨L￨VBG￨O￨- life-long￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- following￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- JE￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- in￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- calculated￨L￨VBD￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- was￨L￨VBD￨O￨- most￨L￨RBS￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Exposed￨U￨VBN￨O￨- pigs￨L￨NNS￨O￨A moved￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- compartment￨L￨NN￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- mean￨L￨JJ￨O￨- delay￨L￨NN￨O￨- of￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- extrinsic￨L￨JJ￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- viremia￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pig￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objectives￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- were￨L￨VBD￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- JEV￨U￨NN￨O￨- among￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- northwestern￨L￨JJ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- human￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- pigs￨L￨NNS￨O￨- on￨L￨IN￨O￨- JE￨U￨NN￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pig￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- fully￨L￨RB￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- removal￨L￨NN￨O￨- times￨L￨NNS￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- provided￨L￨VBD￨O￨- martingale￨L￨NN￨O￨- estimating￨L￨NN￨O￨- equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- propose￨L￨VB￨O￨- an￨L￨DT￨O￨- estimator￨L￨NN￨O￨A called￨L￨VBD￨O￨- the￨L￨DT￨O￨- M-estimator￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- approximate￨L￨JJ￨O￨- variance￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- derived￨L￨VBD￨O￨- a￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- counting￨L￨VBG￨O￨- process￨L￨NN￨O￨- theory￨L￨NN￨O￨- after￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- yield￨L￨VB￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- estimator￨L￨NN￨O￨A called￨L￨VBD￨O￨- the￨L￨DT￨O￨- k-MLE￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- approximate￨L￨JJ￨O￨- variance￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- improving￨L￨VBG￨O￨- the￨L￨DT￨O￨- estimator￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- employ￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- main￨L￨JJ￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- public￨L￨JJ￨O￨A policy￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- selection￨L￨NN￨O￨- and￨L￨CC￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- and￨L￨CC￨O￨- resources￨L￨NNS￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- .1￨L￨NN￨NUMBER￨- Reliable￨U￨JJ￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- measures￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- peak￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- peak￨L￨NN￨O￨- height￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- magnitude￨L￨NN￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- would￨L￨MD￨O￨- inform￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- practitioners￨L￨NNS￨O￨- and￨L￨CC￨O￨- healthcare￨L￨NN￨O￨- workers￨L￨NNS￨O￨- on￨L￨IN￨O￨- when￨L￨WRB￨O￨- to￨L￨TO￨O￨- expect￨L￨VB￨O￨- a￨L￨DT￨O￨- surge￨L￨NN￨O￨- in￨L￨IN￨O￨- demand￨L￨NN￨O￨- for￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- resources￨L￨NNS￨O￨- and￨L￨CC￨O￨- infrastructure￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- expected￨L￨VBN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- aims￨L￨NNS￨O￨- are￨L￨VBP￨O￨- to￨L￨TO￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- summarize￨L￨VB￨O￨- existing￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecasting￨L￨NN￨O￨A ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- present￨L￨JJ￨DATE￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- accuracy￨L￨NN￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- various￨L￨JJ￨O￨- performance￨L￨NN￨O￨- measures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- met￨L￨VBN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- discuss￨L￨VB￨O￨- limitations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- that￨L￨WDT￨O￨- impede￨L￨VBP￨O￨- forecasting￨L￨NN￨O￨- during￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- applied￨L￨VBD￨O￨- to￨L￨TO￨O￨- modeling￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- forecasting￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- brief￨L￨JJ￨O￨- descriptions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .2￨L￨NN￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- These￨U￨DT￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- reviewed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- preparedness￨L￨NN￨O￨- ,￨L￨,￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- mitigation￨L￨NN￨O￨- .1,6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- reviews￨L￨NNS￨O￨- discussing￨L￨VBG￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- forecasting￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- timely￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- measures￨L￨NNS￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- beneficial￨L￨JJ￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- reliable￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨A health￨L￨NN￨O￨- challenge￨L￨NN￨O￨- .￨L￨.￨O￨- +Eleven￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sixteen￨L￨NN￨NUMBER￨- studies￨L￨NNS￨O￨- forecasted￨L￨VBD￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- magnitude￨L￨NN￨O￨- ,￨L￨,￨O￨- daily￨L￨JJ￨SET￨- or￨L￨CC￨O￨- weekly￨L￨JJ￨SET￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A activity￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨- laboratory￨L￨NN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- and/or￨L￨CC￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Regarding￨U￨VBG￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- LTB4￨U￨NN￨O￨- displays￨L￨NNS￨O￨- leishmanicidal￨L￨JJ￨O￨- activity￨L￨NN￨O￨- on￨L￨IN￨O￨- macrophages￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- neutrophils￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- during￨L￨IN￨O￨- in￨L￨FW￨O￨- vitro￨L￨FW￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- L.￨U￨NNP￨O￨- infantum￨L￨NNP￨O￨- in￨L￨FW￨O￨- vitro￨L￨FW￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- inhibits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- LTB4￨U￨NN￨O￨- signaling￨L￨NN￨O￨- pathway￨L￨NN￨O￨A dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- homologous￨L￨JJ￨O￨- DCSIGN￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SIGNR3￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- during￨L￨IN￨O￨- parasite￨L￨NN￨O￨- recognition￨L￨NN￨O￨- by￨L￨IN￨O￨- macrophages￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- a￨L￨DT￨O￨- protective￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- LTB4￨U￨NN￨O￨- during￨L￨IN￨O￨- VL￨U￨NN￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- L.￨U￨NNP￨O￨- To￨U￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- Leishmania￨U￨NNP￨O￨- infantum￨L￨NN￨O￨- drives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- 5-LO￨L￨NN￨O￨- pathway￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- performed￨L￨VBD￨O￨- a￨L￨DT￨O￨- kinetic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- release￨L￨NN￨O￨- of￨L￨IN￨O￨- LTB4￨U￨NN￨O￨- by￨L￨IN￨O￨- bone￨L￨NN￨O￨- marrow-derived￨L￨JJ￨O￨- dendritic￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- after￨L￨IN￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 24￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 36￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- 48￨L￨CD￨DURATION￨- hours￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- parasite￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Initially￨U￨RB￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- activated￨L￨VBN￨O￨- dendritic￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- DCs￨U￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- modulate￨L￨VBP￨O￨- inflammatory￨L￨JJ￨O￨- leucocyte￨L￨NN￨O￨- recruitment￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- foci￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- T￨U￨NN￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- lymphocyte￨L￨NN￨O￨- response￨L￨NN￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- robust￨L￨JJ￨O￨- IFN-γ￨U￨NN￨O￨- and￨L￨CC￨O￨- IL-17￨U￨NN￨O￨- production￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- LTB4￨U￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- 5-LO￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- −￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- littermate￨L￨NN￨O￨- control￨L￨NN￨O￨- mice￨L￨NNS￨O￨A were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- L.￨U￨NN￨O￨- +was￨L￨VBD￨O￨- criticised￨L￨VBN￨O￨- as￨L￨IN￨O￨- being￨L￨VBG￨O￨- opaque￨L￨JJ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- previous￨L￨JJ￨O￨- published￨L￨VBN￨O￨- analyses￨L￨NNS￨O￨- had￨L￨VBD￨O￨- indicated￨L￨VBN￨O￨- that￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- cost￨L￨VBN￨O￨- effective￨L￨JJ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- price￨L￨NN￨O￨- .8￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- assessed￨L￨VBD￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- Bexsero￨U￨NNP￨LOCATION￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- substantially￨L￨RB￨O￨- revising￨L￨VBG￨O￨- a￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- mathematical￨L￨JJ￨O￨- model8￨L￨NN￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- new￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- and￨L￨CC￨O￨- deal￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- concerns￨L￨NNS￨O￨- raised￨L￨VBN￨O￨- by￨L￨IN￨O￨- stakeholders￨L￨NNS￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- consultation￨L￨NN￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- interim￨L￨JJ￨O￨- statement￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Joint￨U￨NNP￨ORGANIZATION￨- Committee￨U￨NNP￨ORGANIZATION￨- on￨L￨IN￨ORGANIZATION￨- Vaccination￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Immunisation￨U￨NN￨ORGANIZATION￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- and￨L￨CC￨O￨- care￨L￨NN￨O￨- ,￨L￨,￨O￨- losses￨L￨NNS￨O￨- of￨L￨IN￨O￨- quality￨L￨NN￨O￨A of￨L￨IN￨O￨- life￨L￨NN￨O￨- in￨L￨IN￨O￨- affected￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- litigation￨L￨NN￨O￨- costs￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- choice￨L￨NN￨O￨- of￨L￨IN￨O￨- discount￨L￨NN￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- compartments￨L￨NNS￨O￨- were￨L￨VBD￨O￨- further￨L￨JJ￨O￨- stratified￨L￨VBN￨O￨- into￨L￨IN￨O￨- routine￨L￨JJ￨O￨- infant￨L￨NN￨O￨- ,￨L￨,￨O￨- routine￨L￨JJ￨O￨- adolescent￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- catch￨L￨VB￨O￨- up￨L￨RP￨O￨- programmes￨L￨NNS￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨- from￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- elements￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- programme￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- was￨L￨VBD￨O￨- seen￨L￨VBN￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- meningococcal￨L￨JJ￨O￨- group￨L￨NN￨O￨- C￨U￨NN￨O￨- conjugate￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- campaign￨L￨NN￨O￨- .10￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- parameterised￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- carriage￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- systematic￨L￨JJ￨O￨- review11￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- assortative￨L￨JJ￨O￨- population￨L￨NN￨O￨- mixing￨L￨VBG￨O￨- pattern￨L￨NN￨O￨- ,￨L￨,￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- perform￨L￨VB￨O￨- well￨L￨RB￨O￨- in￨L￨IN￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- group￨L￨NN￨O￨- C￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- .12￨L￨CD￨NUMBER￨- After￨U￨IN￨O￨- meningococcal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- survive￨L￨VB￨O￨- without￨L￨IN￨O￨- sequelae￨L￨NNS￨O￨- ,￨L￨,￨O￨- survive￨L￨VBP￨O￨- with￨L￨IN￨O￨- sequelae￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- quality￨L￨NN￨O￨A of￨L￨IN￨O￨- life￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- die￨L￨VB￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- A￨U￨NNP￨O￨- large-scale￨L￨JJ￨O￨- immuno-epidemiological￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- epidemicsSarah￨L￨NN￨O￨- Lukens1￨U￨NN￨O￨- ,￨L￨,￨O￨- 9Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Jay￨U￨NNP￨PERSON￨- DePasse2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Roni￨U￨NNP￨PERSON￨- Rosenfeld3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Elodie￨U￨NNP￨PERSON￨- Ghedin4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ericka￨U￨NNP￨PERSON￨- Mochan7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Shawn￨U￨NNP￨PERSON￨- T￨U￨NN￨PERSON￨- Brown2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- John￨U￨NNP￨PERSON￨- Grefenstette6￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Donald￨U￨NNP￨PERSON￨- S￨U￨NNP￨O￨- Burke8￨U￨NN￨O￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- Swigon1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Gilles￨U￨NNP￨PERSON￨- Clermont5￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 14:1019￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Lukens￨U￨NNP￨ORGANIZATION￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Agent￨U￨NNP￨O￨- based￨L￨VBN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨MISC￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- useful￨L￨JJ￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- population-level￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- containment￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- typically￨L￨RB￨O￨- characterize￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- using￨L￨VBG￨O￨- simplified￨L￨VBN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- symptoms￨L￨NNS￨O￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Using￨U￨VBG￨O￨- an￨L￨DT￨O￨- equation-based￨L￨JJ￨O￨- ,￨L￨,￨O￨- host-level￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- that￨L￨WDT￨O￨- expresses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- symptoms￨L￨NNS￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- on￨L￨IN￨O￨- initial￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- viral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- phenotype￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- incorporate￨L￨VBP￨O￨- this￨L￨DT￨O￨- response￨L￨NN￨O￨- function￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population-scale￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨A a￨L￨DT￨O￨- hybrid￨L￨NN￨O￨- multiscale￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- reflects￨L￨VBZ￨O￨- both￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- individualized￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Adding￨U￨VBG￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- symptoms￨L￨NNS￨O￨A may￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨- more￨L￨JJR￨O￨- realistic￨L￨JJ￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- At￨U￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- parameter￨L￨NN￨O￨- ranges￨L￨NNS￨O￨- using￨L￨VBG￨O￨- experimental￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- H1N1￨U￨NN￨O￨- viral￨L￨JJ￨O￨- titers￨L￨NNS￨O￨- and￨L￨CC￨O￨- symptoms￨L￨NNS￨O￨A measured￨L￨VBN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- incorporated￨L￨VBN￨O￨- horizontal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- HDV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- include￨L￨VB￨O￨- vertical￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- specifically￨L￨RB￨O￨- include￨L￨VBP￨O￨- vertical￨L￨JJ￨O￨A HBV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- vaccination￨L￨NN￨O￨- for￨L￨IN￨O￨- children￨L￨NNS￨O￨- immediately￨L￨RB￨O￨- after￨L￨IN￨O￨- birth￨L￨NN￨O￨- on￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- HDV￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- higher￨L￨JJR￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- will￨L￨MD￨O￨- eradicate￨L￨VB￨O￨- both￨L￨DT￨O￨- HBV￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- HDV￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- term￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- vital￨L￨JJ￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨A through￨L￨IN￨O￨- HBV￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- HDV￨U￨NN￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ten￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- higher￨L￨JJR￨O￨A than￨L￨IN￨O￨- for￨L￨IN￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- monoinfection￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HDV￨U￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨A population￨L￨NN￨O￨A infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- HBV￨U￨NN￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- variant￨L￨NN￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- DivRank￨U￨NNP￨O￨- ,￨L￨,￨O￨- makes￨L￨VBZ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- reinforced￨L￨VBN￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- citation￨L￨NN￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- diversify￨L￨VB￨O￨- the￨L￨DT￨O￨- papers￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- obtained￨L￨VBN￨O￨- ranking￨L￨JJ￨O￨- list25￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- citing￨L￨VBG￨O￨- papers￨L￨NNS￨O￨A are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- not￨L￨RB￨O￨- extremely￨L￨RB￨O￨- outstanding￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- still￨L￨RB￨O￨- substantially￨L￨RB￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- citation￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- PageRank￨U￨NN￨O￨- score￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- papers￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- algorithm￨L￨NN￨O￨- takes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- citing￨L￨VBG￨O￨- papers￨L￨NNS￨O￨A and￨L￨CC￨O￨- assigns￨L￨VBZ￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- score￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- cited￨L￨VBN￨O￨- by￨L￨IN￨O￨- important￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- methodology￨L￨NN￨O￨- combining￨L￨VBG￨O￨- temporo-geospatial￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- phylogeographic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- critical￨L￨JJ￨O￨- epicenters￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- pathways￨L￨NNS￨O￨A along￨L￨IN￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- candidate￨L￨NN￨TITLE￨- regions￨L￨NNS￨O￨- for￨L￨IN￨O￨- increased￨L￨VBN￨O￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +Volume￨U￨NN￨O￨- 8￨L￨CD￨NUMBER￨- Supplement￨U￨NN￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Enhancing￨U￨NN￨MISC￨- epidemiological￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- intercontinental￨L￨JJ￨O￨- dispersion￨L￨NN￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- viral￨L￨JJ￨O￨- strains￨L￨NNS￨O￨A by￨L￨IN￨O￨- migratory￨L￨JJ￨O￨- waterfowl￨L￨NN￨O￨- using￨L￨VBG￨O￨- phylogeographyDhananjai￨L￨NN￨O￨- M￨U￨NN￨O￨- Rao1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Suppl￨U￨NN￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- S1￨U￨NN￨O￨- ©￨L￨SYM￨O￨- Rao￨U￨NNP￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Published￨L￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Intercontinental￨U￨NNP￨O￨- migratory￨L￨JJ￨O￨- waterfowl￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- vectors￨L￨NNS￨O￨- for￨L￨IN￨O￨- dispersion￨L￨NN￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- implicated￨L￨VBN￨O￨- in￨L￨IN￨O￨- several￨L￨JJ￨O￨- zoonotic￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- pandemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Dominant￨U￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pathways￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- 25,625￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 54,500￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- summering￨L￨VBG￨O￨- and￨L￨CC￨O￨- wintering￨L￨VBG￨O￨- zones￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- through￨L￨IN￨O￨- annotation￨L￨NN￨O￨- using￨L￨VBG￨O￨- phylogeographical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- computed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- phylogram￨L￨NN￨O￨- of￨L￨IN￨O￨- 2417￨L￨CD￨DATE￨- H5N1￨U￨NN￨O￨- HA￨U￨NN￨O￨- isolates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- from￨L￨IN￨O￨- GISAID￨U￨NN￨MISC￨- EpiFlu￨U￨NN￨MISC￨- database￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Epidemiological￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- 91,245￨L￨CD￨NUMBER￨- candidate￨L￨NN￨TITLE￨- global￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- pathways￨L￨NNS￨O￨A between￨L￨IN￨O￨- 22￨L￨CD￨NUMBER￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- waterfowl￨L￨NN￨O￨- species￨L￨NNS￨O￨- .￨L￨.￨O￨- +Annotation￨U￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pathways￨L￨NNS￨O￨A in￨L￨IN￨O￨- turn￨L￨NN￨O￨- delineated￨L￨VBN￨O￨- 23￨L￨CD￨NUMBER￨- influential￨L￨JJ￨O￨- clades￨L￨NNS￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- 130￨L￨CD￨NUMBER￨- clades￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- phylogram￨L￨NN￨O￨- .￨L￨.￨O￨- +Evolutionary￨U￨JJ￨O￨- Medicine￨U￨NN￨O￨- is￨L￨VBZ￨O￨- emerging￨L￨VBG￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- vibrant￨L￨JJ￨O￨- research￨L￨NN￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- international￨L￨JJ￨O￨- meetings￨L￨NNS￨O￨- devoted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- topic￨L￨NN￨O￨A ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- journal￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- steady￨L￨JJ￨O￨- stream￨L￨NN￨O￨- of￨L￨IN￨O￨- book-length￨L￨JJ￨O￨- treatments￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- topic￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- my￨L￨PRP$￨O￨- generous￨L￨JJ￨O￨- and￨L￨CC￨O￨- unscientific￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- would￨L￨MD￨O￨- say￨L￨VB￨O￨- that￨L￨IN￨O￨- physicians￨L￨NNS￨O￨- outnumber￨L￨VBP￨O￨- researchers￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨- medicine￨L￨NN￨O￨A by￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 1000￨L￨CD￨DATE￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- field￨L￨NN￨O￨- needs￨L￨VBZ￨O￨- books￨L￨NNS￨O￨- written￨L￨VBN￨O￨A for￨L￨IN￨O￨- this￨L￨DT￨O￨- purpose￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Perlman￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- book￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- move￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- right￨L￨JJ￨O￨- direction￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- back￨L￨JJ￨O￨- flap￨L￨NN￨O￨- of￨L￨IN￨O￨- my￨L￨PRP$￨O￨- copy￨L￨NN￨O￨- of￨L￨IN￨O￨- Evolution￨U￨NNP￨O￨- &￨L￨CC￨O￨- Medicine￨U￨NNP￨O￨- promises￨L￨VBZ￨O￨- a￨L￨DT￨O￨- text￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ‘￨L￨``￨O￨- written￨L￨VBN￨O￨A for￨L￨IN￨O￨- physicians￨L￨NNS￨O￨- ,￨L￨,￨O￨- biomedical￨L￨JJ￨O￨- scientists￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- both￨L￨DT￨O￨- premedical￨L￨JJ￨O￨- and￨L￨CC￨O￨- medical￨L￨JJ￨O￨- students￨L￨NNS￨O￨- ’￨L￨POS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- his￨L￨PRP$￨O￨- new￨L￨JJ￨O￨- book￨L￨NN￨O￨- Evolution￨U￨NN￨O￨- &￨L￨CC￨O￨- Medicine￨U￨NNP￨O￨- ,￨L￨,￨O￨- Robert￨U￨NNP￨PERSON￨- Perlman￨U￨NNP￨PERSON￨- sets￨L￨VBZ￨O￨A out￨L￨RP￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- this￨L￨DT￨O￨- important￨L￨JJ￨O￨- audience￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- transmitted￨L￨VBN￨O￨- also￨L￨RB￨O￨- after￨L￨IN￨O￨- sampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- transmission￨L￨NN￨O￨- at￨L￨IN￨O￨- funerals￨L￨NNS￨O￨- constitutes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- infection2￨L￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 20￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- further￨L￨RB￨O￨- run￨L￨VBP￨O￨- the￨L￨DT￨O￨- birth-death￨L￨JJ￨O￨- sampled-ancestors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- BDsa￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model21￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- extends￨L￨VBZ￨O￨- BD￨U￨NN￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- sampled￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- noninfectious￨L￨JJ￨O￨- upon￨L￨IN￨O￨- sampling￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- r￨L￨NN￨O￨- and￨L￨CC￨O￨- remain￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- 1-r￨L￨NN￨O￨- .￨L￨.￨O￨- +Birth-death￨U￨JJ￨O￨- models￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- transmit￨L￨VBP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- becoming-noninfectious￨L￨JJ￨O￨- rate￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- recover￨L￨VBP￨O￨- or￨L￨CC￨O￨- die￨L￨VBP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- sampling￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- person￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sampled￨L￨VBN￨O￨A and￨L￨CC￨O￨- sequenced￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- birth-death￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- BD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model17￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- becoming-noninfectious￨L￨JJ￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sampling￨L￨NN￨O￨A probability￨L￨NN￨O￨- to￨L￨TO￨O￨- change￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- piecewise￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- fashion￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- coalescent￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- coalSEIR￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- BEAST2￨U￨NN￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- were￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- genealogy￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨A hosts￨L￨NNS￨O￨A set￨L￨VBN￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- following￨L￨VBG￨O￨- Althaus￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 23￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- includes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨A hosts￨L￨NNS￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- LogNormal￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 8,4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- prior￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +Nishiura6￨U￨NN￨O￨- pointed￨L￨VBD￨O￨- out￨L￨RP￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- upper￨L￨JJ￨O￨- tail￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨A time￨L￨NN￨O￨- distribution￨L￨NN￨O￨- when￨L￨WRB￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- quarantine￨L￨NN￨O￨- period￨L￨NN￨O￨- following￨L￨VBG￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- contribution￨L￨NN￨O￨- will￨L￨MD￨O￨- outline￨L￨VB￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨A time￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- Zaire￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- what￨L￨WP￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- upper￨L￨JJ￨O￨- tail￨L￨NN￨O￨- percentiles￨L￨NNS￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- very￨L￨RB￨O￨- frequently￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- implied￨L￨VBN￨O￨- incubation￨L￨NN￨O￨A time￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- mean￨L￨JJ￨O￨- incubation￨L￨NN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- 1/k￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Zaire￨U￨NNP￨COUNTRY￨- outbreak11￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- Uganda￨U￨NNP￨COUNTRY￨- outbreak12￨L￨NN￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- reported￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- without￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- observed￨L￨VBN￨O￨- incubation￨L￨NN￨O￨A time￨L￨NN￨O￨- of￨L￨IN￨O￨- 21￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- none￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- often￨L￨RB￨O￨- used￨L￨VBN￨O￨- incubation￨L￨NN￨O￨A time￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- upper￨L￨JJ￨O￨- limit￨L￨NN￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Transmission￨U￨NNP￨MISC￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- EVD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- reviewGerardo￨L￨JJ￨O￨- Chowell1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Hiroshi￨U￨NNP￨O￨- Nishiura3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 12:196￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Chowell￨U￨NNP￨O￨- and￨L￨CC￨O￨- Nishiura￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- AbstractThe￨U￨NNP￨O￨- complex￨L￨NN￨O￨- and￨L￨CC￨O￨- unprecedented￨L￨JJ￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- ongoing￨L￨JJ￨O￨A in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- has￨L￨VBZ￨O￨- highlighted￨L￨VBN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- review￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- Virus￨U￨NN￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- EVD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- our￨L￨PRP$￨O￨- current￨L￨JJ￨DATE￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- against￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- review￨L￨VBP￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- Ebola￨U￨NNP￨MISC￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- carry￨L￨VBP￨O￨- out￨L￨RP￨O￨- a￨L￨DT￨O￨- comparative￨L￨JJ￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- causative￨L￨JJ￨O￨- Ebola￨U￨NNP￨MISC￨- strain￨L￨NN￨O￨- is￨L￨VBZ￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- strain￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- past￨L￨JJ￨DATE￨A EBOV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- Central￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- circulating￨L￨VBG￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- for￨L￨IN￨O￨- about￨L￨IN￨DURATION￨- a￨L￨DT￨DURATION￨- decade￨L￨NN￨DURATION￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- declared￨L￨VBD￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- a￨L￨DT￨O￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Emergency￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- International￨U￨NNP￨ORGANIZATION￨- Concern￨U￨NN￨ORGANIZATION￨- on￨L￨IN￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨A cases￨L￨NNS￨O￨A in￨L￨IN￨O￨- some￨L￨DT￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- -￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Brazilian￨U￨JJ￨NATIONALITY￨- cities￨L￨NNS￨O￨- were￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- Brazilian￨U￨JJ￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Geography￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Statistics￨U￨NNPS￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- IBGE￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- federal￨L￨JJ￨O￨- government￨L￨NN￨O￨- 's￨L￨POS￨O￨- institution￨L￨NN￨O￨- which￨L￨WDT￨O￨- performs￨L￨VBZ￨O￨- a￨L￨DT￨O￨- national￨L￨JJ￨O￨- census￨L￨NN￨O￨- about￨L￨IN￨O￨- every￨L￨DT￨SET￨- ten￨L￨CD￨SET￨- years￨L￨NNS￨SET￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- section￨L￨NN￨O￨- we￨L￨PRP￨O￨- report￨L￨VBP￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨A the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- which￨L￨WDT￨O￨- cover￨L￨VBP￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- 33￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- AIDS￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨A virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- —￨L￨:￨O￨- which￨L￨WDT￨O￨- causes￨L￨VBZ￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- —￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- started￨L￨VBD￨O￨- spreading￨L￨VBG￨O￨- quickly￨L￨RB￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- globe￨L￨NN￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- worldwide￨L￨JJ￨O￨- concern￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨A from￨L￨IN￨O￨- DATASUS￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- database￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- national￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- system￨L￨NN￨O￨- freely￨L￨RB￨O￨- available￨L￨JJ￨O￨- online￨L￨NN￨O￨- and￨L￨CC￨O￨- maintained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Informatics￨U￨NNPS￨ORGANIZATION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Brazilian￨U￨JJ￨NATIONALITY￨- Health￨U￨NNP￨O￨- System￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- current￨L￨JJ￨DATE￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- by￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨A its￨L￨PRP$￨O￨- annual￨L￨JJ￨SET￨- absolute￨L￨JJ￨O￨- frequency￨L￨NN￨O￨- per￨L￨IN￨O￨- city￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- combine￨L￨VBP￨O￨- individual-level￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- intake￨L￨NN￨O￨- ,￨L￨,￨O￨- output￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transfer￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- dogs￨L￨NNS￨O￨- among￨L￨IN￨O￨- US￨U￨NNP￨COUNTRY￨- animal￨L￨NN￨O￨A shelters￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- CIV￨U￨NN￨O￨- gene￨L￨NN￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- available￨L￨JJ￨O￨- seroprevalence￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- processes￨L￨NNS￨O￨- controlling￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- zoonoses￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- human-animal￨L￨JJ￨O￨- interface￨L￨NN￨O￨- .￨L￨.￨O￨- +CIV￨U￨NN￨LOCATION￨- enzootic￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- animal￨L￨NN￨O￨A shelters￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- transport￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- shelter￨L￨NN￨O￨- dogs￨L￨NNS￨O￨- to￨L￨TO￨O￨- facilities￨L￨NNS￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- readily￨L￨RB￨O￨- adopted￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Effectively￨U￨RB￨O￨- controlling￨L￨VBG￨O￨- CIV￨U￨NNP￨LOCATION￨- would￨L￨MD￨O￨- improve￨L￨VB￨O￨- conditions￨L￨NNS￨O￨- in￨L￨IN￨O￨- metropolitan￨L￨JJ￨O￨- animal￨L￨NN￨O￨A shelters￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨- human￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- posed￨L￨VBN￨O￨- by￨L￨IN￨O￨- CIV￨U￨NN￨LOCATION￨- ,￨L￨,￨O￨- before￨L￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- opportunity￨L￨NN￨O￨- to￨L￨TO￨O￨- evolve￨L￨VB￨O￨- higher￨L￨JJR￨O￨- transmissibility￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- companion￨L￨NN￨TITLE￨- dog￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- will￨L￨MD￨O￨- establish￨L￨VB￨O￨- itself￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- homogeneously￨L￨RB￨O￨- mixed￨L￨JJ￨O￨A population￨L￨NN￨O￨A of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1/R0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- estimating￨L￨VBG￨O￨- R0￨U￨NN￨O￨- from￨L￨IN￨O￨- all￨L￨DT￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- we￨L￨PRP￨O￨- ask￨L￨VBP￨O￨- :￨L￨:￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨A of￨L￨IN￨O￨- small￨L￨JJ￨O￨- shelters￨L￨NNS￨O￨- small￨L￨JJ￨O￨- enough￨L￨RB￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- fadeout￨L￨NN￨O￨- significantly￨L￨RB￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- shelters￨L￨NNS￨O￨- ?￨L￨.￨O￨- +As￨U￨IN￨O￨- an￨L￨DT￨O￨- alternative￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- inspired￨L￨VBN￨O￨- by￨L￨IN￨O￨- importance￨L￨NN￨O￨- sampling￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- considering￨L￨VBG￨O￨- arbitrarily￨L￨RB￨O￨- complex￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- requirement￨L￨NN￨O￨- being￨L￨VBG￨O￨- that￨L￨IN￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨A are￨L￨VBP￨O￨- easy￨L￨JJ￨O￨- to￨L￨TO￨O￨- sample￨L￨NN￨O￨- under￨L￨IN￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨- frameworks￨L￨NNS￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- joint￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- symptom￨L￨NN￨O￨- times￨L￨NNS￨O￨- and￨L￨CC￨O￨- genotypic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogenic￨L￨JJ￨O￨- isolates￨L￨NNS￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- refugee￨L￨NN￨O￨- camp￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- predict￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- direct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- highly￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 0.3￨L￨CD￨NUMBER￨- even￨L￨RB￨O￨- for￨L￨IN￨O￨- genetically￨L￨RB￨O￨- and￨L￨CC￨O￨- temporally￨L￨RB￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- isolates￨L￨NNS￨O￨A .￨L￨.￨O￨- +Sequence￨U￨NN￨O￨- data￨L￨NNS￨O￨- allow￨L￨VBP￨O￨- for￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨A to￨L￨TO￨O￨- time-series￨L￨JJ￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- ratios￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- importance￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- conditioning￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- genotypes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- isolates￨L￨NNS￨O￨A .￨L￨.￨O￨- +They￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- structured￨L￨VBN￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- similar￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- seen￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- hospitalization￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- large￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- ecological￨L￨JJ￨O￨- complexity￨L￨NN￨O￨- into￨L￨IN￨O￨- coalescent￨L￨JJ￨O￨A models￨L￨NNS￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- inferences￨L￨NNS￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- demography￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- parasites￨L￨NNS￨O￨- from￨L￨IN￨O￨- spatially￨L￨RB￨O￨- structured￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- less￨L￨RBR￨O￨- constrained￨L￨VBN￨O￨- by￨L￨IN￨O￨- costs￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- ‘￨L￨``￨O￨- generalism￨L￨NN￨O￨- ’￨L￨''￨O￨- than￨L￨IN￨O￨- those￨L￨DT￨O￨- from￨L￨IN￨O￨- well-mixed￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- spatial￨L￨JJ￨O￨A structure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- breadth￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- resistance/parasite￨L￨NN￨O￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- when￨L￨WRB￨O￨- this￨L￨DT￨O￨- increased￨L￨VBN￨O￨- breadth￨L￨NN￨O￨- carries￨L￨VBZ￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- fitness￨L￨NN￨O￨- cost￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Overall￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- recent￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- demonstrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- added￨L￨VBN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- spatial￨L￨JJ￨O￨A structure￨L￨NN￨O￨A into￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- ,￨L￨,￨O￨- phylodynamic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- evolutionary/ecological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- work￨L￨NN￨O￨- by￨L￨IN￨O￨- David￨U￨NNP￨PERSON￨- Rasmussen￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- colleagues￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- demonstrated￨L￨VBN￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- spatial￨L￨JJ￨O￨A structure￨L￨NN￨O￨A into￨L￨IN￨O￨- phylodynamic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- coalescent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- approaches￨L￨VBZ￨O￨- to￨L￨TO￨O￨- inferring￨L￨VBG￨O￨- past￨L￨JJ￨DATE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- from￨L￨IN￨O￨- genealogies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- advance￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- has￨L￨VBZ￨O￨- come￨L￨VBN￨O￨- from￨L￨IN￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨A structure￨L￨NN￨O￨A into￨L￨IN￨O￨- both￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ecology￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Feline￨U￨JJ￨O￨- CDV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- recorded￨L￨VBN￨O￨- in￨L￨IN￨O￨- captive￨L￨JJ￨O￨- large￨L￨JJ￨O￨- felids￨L￨NNS￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- threat￨L￨NN￨O￨A to￨L￨TO￨O￨- wild￨L￨JJ￨O￨- felines￨L￨NNS￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- recognized￨L￨VBN￨O￨- until￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- affecting￨L￨VBG￨O￨- lions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Panthera￨U￨NN￨PERSON￨- leo￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- 1,000￨L￨CD￨NUMBER￨- animals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- approximately￨L￨RB￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- disappeared￨L￨VBD￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- viability￨L￨NN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- African￨U￨JJ￨NATIONALITY￨- wild￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- causing￨L￨VBG￨O￨- high￨L￨JJ￨O￨- adult￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- can￨L￨MD￨O￨- pose￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- threat￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Together￨U￨RB￨O￨- these￨L￨DT￨O￨- represent￨L￨VBP￨O￨- a￨L￨DT￨O￨- diverse￨L￨JJ￨O￨- community￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- competent￨L￨JJ￨O￨- CDV￨U￨NN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- which￨L￨WDT￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨A could￨L￨MD￨O￨- act￨L￨VB￨O￨- as￨L￨IN￨O￨- source￨L￨NN￨O￨- populations￨L￨NNS￨O￨- for￨L￨IN￨O￨- tigers￨L￨NNS￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- contact￨L￨NN￨O￨- through￨L￨IN￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- predatory￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Worldwide￨U￨NNP￨O￨- tiger￨L￨NN￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- all-time￨L￨JJ￨O￨- low￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- estimated￨L￨VBN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- breeding￨L￨VBG￨O￨- females￨L￨NNS￨O￨- reduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- approximately￨L￨RB￨O￨A 1,000￨L￨CD￨NUMBER￨- animals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- assesses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- threat￨L￨NN￨O￨A and￨L￨CC￨O￨- impact￨L￨NN￨O￨- that￨L￨WDT￨O￨- CDV￨U￨NN￨O￨- poses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- Amur￨U￨NNP￨CITY￨- tigers￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- sub-population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Russian￨U￨NNP￨NATIONALITY￨- Far￨U￨NNP￨O￨- East￨U￨NNP￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- modelling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- using￨L￨VBG￨O￨- various￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- see￨L￨VB￨O￨- that￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- path￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- may￨L￨MD￨O￨- arise￨L￨VB￨O￨- from￨L￨IN￨O￨- random￨L￨JJ￨O￨- walks￨L￨VBZ￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- networks￨L￨NNS￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 1a￨L￨NN￨O￨- –￨L￨:￨O￨- c.￨L￨NN￨O￨- For￨U￨IN￨O￨- walk￨L￨NN￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- is￨L￨VBZ￨O￨- approximately￨L￨RB￨O￨- linear￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- log￨L￨NN￨O￨A –￨L￨:￨O￨- log￨L￨NN￨O￨- plot￨L￨NN￨O￨- ,￨L￨,￨O￨- implying￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- approximately￨L￨RB￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- :￨L￨:￨O￨- log￨L￨NN￨O￨- P￨U￨NN￨O￨- ≈￨L￨VBD￨O￨- a￨L￨DT￨O￨- +￨L￨CC￨O￨- b￨L￨NN￨O￨- log￨L￨NN￨O￨- r￨L￨NN￨O￨- or￨L￨CC￨O￨- P￨U￨NN￨O￨- ≈￨L￨CD￨NUMBER￨- cr￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- walk￨L￨NN￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- is￨L￨VBZ￨O￨- clearly￨L￨RB￨O￨- curvilinear￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- log￨L￨NN￨O￨A –￨L￨:￨O￨- log￨L￨NN￨O￨- plot￨L￨NN￨O￨- ,￨L￨,￨O￨- inconsistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- path￨L￨NN￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- general￨L￨JJ￨TITLE￨- parameter￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- oft￨L￨NN￨O￨- cited￨L￨VBD￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- more￨L￨RBR￨O￨- specifically￨L￨RB￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨A caused￨L￨VBN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- infected￨L￨JJ￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- analysis￨L￨NN￨O￨- builds￨L￨VBZ￨O￨- upon￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimating￨L￨VBG￨O￨- transmission￨L￨NN￨O￨A parameters￨L￨NNS￨O￨A from￨L￨IN￨O￨- chain￨L￨NN￨O￨- size￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- addressing￨L￨VBG￨O￨- issues￨L￨NNS￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- bias￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- specific￨L￨JJ￨O￨- hypotheses￨L￨NNS￨O￨A regarding￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- by￨L￨IN￨O￨- testing￨L￨NN￨O￨- whether￨L￨IN￨O￨- and￨L￨CC￨O￨- differ￨L￨VBP￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- Sun￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Shi￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- shall￨L￨MD￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- multi-group￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- relapse￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +So￨U￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- relapse￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- subject￨L￨NN￨O￨- of￨L￨IN￨O￨- intense￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- simulated￨L￨JJ￨O￨- both￨L￨CC￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- birth-death￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- trees￨L￨NNS￨O￨- with￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- from￨L￨IN￨O￨- now￨L￨RB￨DATE￨- on￨L￨IN￨O￨- simply￨L￨RB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- birth-death￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- unless￨L￨IN￨O￨- specified￨L￨VBN￨O￨- otherwise￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- coalescent￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- trees￨L￨NNS￨O￨- with￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- exponential￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- from￨L￨IN￨O￨- now￨L￨RB￨DATE￨- on￨L￨IN￨O￨- simply￨L￨RB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- unless￨L￨IN￨O￨- specified￨L￨VBN￨O￨- otherwise￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- see￨L￨VBP￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- birth-death￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- coalescent￨L￨NN￨O￨A in￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- birth-death￨L￨JJ￨O￨- process￨L￨NN￨O￨- produces￨L￨VBZ￨O￨- trees￨L￨NNS￨O￨- and￨L￨CC￨O￨- analyzes￨L￨VBZ￨O￨- phylogenies￨L￨NNS￨O￨- assuming￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- relaxing￨L￨VBG￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- assumption￨L￨NN￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- coalescent￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- note￨L￨NN￨O￨- that￨L￨IN￨O￨- extensions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨JJ￨O￨- accommodating￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- sizes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- published￨L￨VBN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- we￨L￨PRP￨O￨- only￨L￨RB￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- phylogenies￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- early￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- birth-death￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- birth-death￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- coalescent￨L￨NN￨O￨- with￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- exponential￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- comparative￨L￨JJ￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- birth-death￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- coalescent￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- phylodynamic￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- by￨L￨IN￨O￨- doing￨L￨VBG￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- separate￨L￨JJ￨O￨- body￨L￨NN￨O￨- of￨L￨IN￨O￨- theory￨L￨NN￨O￨- has￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- for￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- sequencing￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- classical￨L￨JJ￨O￨- population￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨JJ￨O￨A NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- classical￨L￨JJ￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- models￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- sampling￨L￨NN￨O￨A processes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- thus￨L￨RB￨O￨- far￨L￨RB￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death-sampling￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- BDMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- sampling￨L￨NN￨O￨- of￨L￨IN￨O￨- lineages￨L￨NNS￨O￨- may￨L￨MD￨O￨- take￨L￨VB￨O￨- place￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- or￨L￨CC￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- lineages￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- sampled￨L￨VBN￨O￨- uniformly￨L￨RB￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- potential￨L￨JJ￨O￨- disadvantage￨L￨NN￨O￨- of￨L￨IN￨O￨- BDMs￨U￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- require￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨A process￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- no￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- lineages￨L￨NNS￨O￨- are￨L￨VBP￨O￨- sampled￨L￨VBN￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- sampling￨L￨NN￨O￨A processes￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- combined￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recently￨L￨RB￨DATE￨- developed￨L￨VBD￨O￨- methods￨L￨NNS￨O￨- allow￨L￨VB￨O￨- sampling￨L￨NN￨O￨- rates￨L￨NNS￨O￨- to￨L￨TO￨O￨- vary￨L￨VB￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- step￨L￨NN￨O￨- function￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Estimates￨U￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- CoMs￨U￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- biased￨L￨VBN￨O￨- by￨L￨IN￨O￨- noisy￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- estimates￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- BDM￨U￨NNP￨ORGANIZATION￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- biased￨L￨VBN￨O￨- by￨L￨IN￨O￨- misspecification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨A process￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- scenarios￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- horizontal￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- symbionts￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- positively￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Analogous￨U￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- create￨L￨VBP￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- covariance￨L￨NN￨O￨- between￨L￨IN￨O￨- horizontal￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A and￨L￨CC￨O￨- symbiont-provided￨L￨JJ￨O￨- benefits￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- underexplored￨L￨JJ￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- partner￨L￨NN￨O￨- choice￨L￨NN￨O￨- also￨L￨RB￨O￨- creates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- covariance￨L￨NN￨O￨- between￨L￨IN￨O￨- transmission￨L￨NN￨O￨- success￨L￨NN￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨A when￨L￨WRB￨O￨- hosts￨L￨NNS￨O￨- favor￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- more￨L￨JJR￨O￨- beneficial￨L￨JJ￨O￨- symbionts￨L￨NNS￨O￨- .￨L￨.￨O￨- +How￨U￨WRB￨O￨- horizontal￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- symbiont-provided￨L￨JJ￨O￨- benefits￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- remained￨L￨VBN￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- question￨L￨NN￨O￨- .￨L￨.￨O￨- +Third￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- symbionts￨L￨NNS￨O￨- utilize￨L￨VBP￨O￨- toxic￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- by-products￨L￨NNS￨O￨- ,￨L￨,￨O￨- greater￨L￨JJR￨O￨- exploitation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- increased￨L￨VBN￨O￨- symbiont￨L￨NN￨O￨- fecundity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- enhancing￨L￨VBG￨O￨- horizontal￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- greater￨L￨JJR￨O￨- host￨L￨NN￨TITLE￨- fitness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- by￨L￨IN￨O￨- removing￨L￨VBG￨O￨- the￨L￨DT￨O￨- toxic￨L￨JJ￨O￨- waste￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- aggregation￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- from￨L￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- to￨L￨TO￨O￨- coincident￨L￨JJ￨O￨- aggregated￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Harrison￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- collaborators￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- increase￨L￨NN￨O￨- with￨L￨IN￨O￨- progressive￨L￨JJ￨IDEOLOGY￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- aggregation￨L￨NN￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- it￨L￨PRP￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- for￨L￨IN￨O￨- tick-borne￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- established￨L￨JJ￨O￨- and￨L￨CC￨O￨- persist￨L￨VBP￨O￨- .￨L￨.￨O￨- +Tick￨U￨VB￨O￨- aggregation￨L￨NN￨O￨A on￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- tick￨L￨NN￨O￨- stages￨L￨NNS￨O￨- facilitate￨L￨VBP￨O￨- co-feeding￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- significantly￨L￨RB￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- direct￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- its￨L￨PRP$￨O￨- persistence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- ecological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- highly￨L￨RB￨O￨- aggregated￨L￨JJ￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- harbouring￨L￨VBG￨O￨- few￨L￨JJ￨O￨- parasites￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- harbouring￨L￨VBG￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- other￨L￨JJ￨O￨- interesting￨L￨JJ￨O￨- references￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- about￨L￨IN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- hosts￨L￨NNS￨O￨A feed￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- larvae￨L￨NNS￨O￨- and￨L￨CC￨O￨- nymphs￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- larvae￨L￨NNS￨O￨- feeding￨L￨VBG￨O￨- alongside￨L￨IN￨O￨- nymphs￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- twice￨L￨RB￨O￨- as￨L￨RB￨O￨- many￨L￨JJ￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- were￨L￨VBD￨O￨- independent￨L￨JJ￨RELIGION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- E-NTPDases￨U￨NNS￨O￨- in￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- virulence￨L￨NN￨O￨- or￨L￨CC￨O￨- purine￨L￨NN￨O￨- acquisition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogenic￨L￨JJ￨O￨- protozoan￨L￨NN￨O￨- parasites￨L￨NNS￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- Trypanosoma￨U￨NNP￨O￨- cruzi￨L￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Toxoplasma￨U￨NNP￨ORGANIZATION￨- gondii￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- Leishmania￨U￨NNP￨LOCATION￨- that￨L￨WDT￨O￨- causes￨L￨VBZ￨O￨- tegumental￨L￨JJ￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- previous￨L￨JJ￨O￨- study￨L￨NN￨O￨- from￨L￨IN￨O￨- our￨L￨PRP$￨O￨- group￨L￨NN￨O￨- and￨L￨CC￨O￨- sequences￨L￨NNS￨O￨- deposited￨L￨VBN￨O￨- in￨L￨IN￨O￨- GenBank￨U￨NN￨ORGANIZATION￨- demonstrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- protein￨L￨NN￨O￨- family￨L￨NN￨O￨A in￨L￨IN￨O￨- trypanosomatids￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- T.￨U￨NNP￨O￨- +In￨U￨IN￨O￨- mammals￨L￨NNS￨O￨- ,￨L￨,￨O￨- E-NTPDases￨U￨NNS￨O￨- participate￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- purinergic￨L￨JJ￨O￨- signaling￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- parasites￨L￨NNS￨O￨A seem￨L￨VBP￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- responses￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- purinergic￨L￨JJ￨O￨- signaling￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- parasites￨L￨NNS￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- Leishmania￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- purine￨L￨NN￨O￨- salvage￨L￨NN￨O￨- pathway￨L￨NN￨O￨- to￨L￨TO￨O￨- synthesize￨L￨VB￨O￨- purine￨L￨NN￨O￨- nucleotides￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- synthesis￨L￨NN￨O￨- of￨L￨IN￨O￨- nucleic￨L￨JJ￨O￨- acid￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- important￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- molecules￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- such￨L￨JJ￨O￨- example￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- suspectible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- transition￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- states￨L￨NNS￨O￨- —￨L￨:￨O￨- near￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- positive￨L￨JJ￨O￨- feedbacks￨L￨NNS￨O￨- amplify￨L￨VBP￨O￨- small￨L￨JJ￨O￨- differences￨L￨NNS￨O￨A in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨- large￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- an￨L￨DT￨O￨- extremely￨L￨RB￨O￨- parsimonious￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- that￨L￨IN￨O￨- small￨L￨JJ￨O￨- but￨L￨CC￨O￨- significant￨L￨JJ￨O￨- differences￨L￨NNS￨O￨A in￨L￨IN￨O￨- prison￨L￨NN￨O￨- sentences￨L￨NNS￨O￨- can￨L￨MD￨O￨- induce￨L￨VB￨O￨- large￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- incarceration￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Racial￨U￨JJ￨O￨- disparities￨L￨NNS￨O￨- in￨L￨IN￨O￨- incarceration￨L￨NN￨O￨- rates￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- while￨L￨IN￨O￨- these￨L￨DT￨O￨- disparities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- partially￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- differences￨L￨NNS￨O￨A in￨L￨IN￨O￨- criminal￨L￨JJ￨O￨- involvement￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- matched￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- Black-male￨U￨JJ￨MISC￨- criminality￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Scholars￨U￨NNS￨O￨- offer￨L￨VBP￨O￨- several￨L￨JJ￨O￨- explanations￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- police￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- prosecutorial￨L￨JJ￨O￨- discrimination￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- incarceration￨L￨NN￨O￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- ‘￨L￨``￨O￨- racial￨L￨JJ￨O￨- threat￨L￨NN￨O￨A ’￨L￨''￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- sentencing￨L￨NN￨O￨- disparities￨L￨NNS￨O￨- between￨L￨IN￨O￨- Blacks￨U￨NNPS￨O￨- and￨L￨CC￨O￨- Whites￨U￨NNPS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Black￨U￨NNP￨O￨- incarceration￨L￨NN￨O￨- rates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- over￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- White￨U￨NNP￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 3023￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- 100￨L￨CD￨NUMBER￨A 000￨L￨CD￨NUMBER￨A for￨L￨IN￨O￨- Blacks￨U￨NNPS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 478￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- 100￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- Whites￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- advances￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- systems￨L￨NNS￨O￨- combining￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- Bayesian￨U￨JJ￨MISC￨- inference￨L￨NN￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- enabled￨L￨VBN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨A epidemiological￨L￨JJ￨O￨A characteristics￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- historical￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks3￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- partially￨L￨RB￨O￨- observed￨L￨VBN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- accurate￨L￨JJ￨O￨- real-time￨L￨JJ￨O￨- forecast￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- influenza4￨L￨NN￨O￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- observations￨L￨NNS￨O￨- ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- and￨L￨CC￨O￨- forecast￨L￨NN￨O￨- future￨L￨JJ￨DATE￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨A levels￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- West￨U￨JJ￨MISC￨- African￨U￨JJ￨NATIONALITY￨- Ebola￨U￨NN￨MISC￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Forecasts￨U￨NNS￨O￨- made￨L￨VBN￨O￨- in￨L￨IN￨O￨- prior￨L￨JJ￨O￨- weeks￨L￨NNS￨DURATION￨- are￨L￨VBP￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- subsequently￨L￨RB￨O￨- observed￨L￨VBN￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨A levels￨L￨NNS￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- performance￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- outlook￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨ORGANIZATION￨- reports￨L￨NNS￨O￨- were￨L￨VBD￨O￨- issued￨L￨VBN￨O￨- irregularly￨L￨RB￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨A data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- interpolated￨L￨VBN￨O￨- to￨L￨TO￨O￨- weekly￨L￨JJ￨SET￨- intervals￨L￨NNS￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- generation￨L￨NN￨O￨- of￨L￨IN￨O￨- regular￨L￨JJ￨O￨- ,￨L￨,￨O￨- weekly￨L￨JJ￨SET￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- and￨L￨CC￨O￨- forecasts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Incidence￨U￨NN￨O￨- and￨L￨CC￨O￨- Mortality￨U￨NNP￨O￨- Data￨U￨NNP￨O￨- Cumulative￨U￨NNP￨O￨- Ebola￨U￨NNP￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨A data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- WHO￨U￨WP￨O￨- ’s￨L￨VBZ￨O￨- Disease￨U￨NNP￨CAUSE_OF_DEATH￨- Outbreak￨U￨NNP￨MISC￨- News￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- situation￨L￨NN￨O￨- reports￨L￨NNS￨O￨- for￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨ORGANIZATION￨- Leone6￨U￨NNP￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- exhibited￨L￨VBD￨O￨- cycles￨L￨NNS￨O￨- in￨L￨IN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- sterilizing￨L￨VBG￨O￨- immunity￨L￨NN￨O￨- after￨L￨IN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- weak￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- purposefully￨L￨RB￨O￨- ignores￨L￨VBZ￨O￨- human￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨A ,￨L￨,￨O￨- vast￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A of￨L￨IN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- gonorrhea￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Neisseria￨U￨NNP￨ORGANIZATION￨- gonorrhoeae￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- ,￨L￨,￨O￨- network-based￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- adaptive￨L￨JJ￨O￨- disconnection/reconnection￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- 's￨L￨POS￨O￨- neighbours￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- identified￨L￨VBD￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- cycles￨L￨NNS￨O￨A in￨L￨IN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- proposed￨L￨VBN￨O￨- deterministic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- changing￨L￨VBG￨O￨- behaviour￨L￨NN￨O￨A on￨L￨IN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- STI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- explicitly￨L￨RB￨O￨- consider￨L￨VB￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- antibiotics￨L￨NNS￨O￨- and￨L￨CC￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- behaviour￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Multi-stream￨U￨JJ￨O￨- surveillance￨L￨NN￨O￨A ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- seldom￨L￨RB￨O￨- been￨L￨VBN￨O￨- evaluated￨L￨VBN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- superimposed￨L￨VBN￨O￨- directly￨L￨RB￨O￨- onto￨L￨IN￨O￨- different￨L￨JJ￨O￨- syndromic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- baselines￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- represent￨L￨VBP￨O￨- different￨L￨JJ￨O￨- health-related￨L￨JJ￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- visiting￨L￨VBG￨O￨- clinics￨L￨NNS￨O￨- ,￨L￨,￨O￨- OTC￨U￨NNP￨O￨- drug￨L￨NN￨O￨- purchasing￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- absence￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- syndromic￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨A studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- detection￨L￨NN￨O￨- performance￨L￨NN￨O￨- by￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- surveillance￨L￨NN￨O￨- signals￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- gold￨L￨JJ￨O￨- standard￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- laboratory￨L￨NN￨O￨- pathogen￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- or￨L￨CC￨O￨- conventional￨L￨JJ￨O￨- confirmed￨L￨VBD￨O￨- case￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Various￨U￨JJ￨O￨- data￨L￨NNS￨O￨- streams￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- clinic￨L￨NN￨O￨- visit￨L￨NN￨O￨- ,￨L￨,￨O￨- sales￨L￨NNS￨O￨- of￨L￨IN￨O￨- over-the-counter￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- OTC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- school/work￨L￨NN￨O￨- absence￨L￨NN￨O￨A ,￨L￨,￨O￨- calls￨L￨VBZ￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- lines￨L￨NNS￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- ambulance￨L￨NN￨O￨- dispatch￨L￨VBP￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- others￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Syndromic￨U￨JJ￨O￨- surveillance￨L￨NN￨O￨A collects￨L￨VBZ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- health-related￨L￨JJ￨O￨- events￨L￨NNS￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- official￨L￨JJ￨O￨- diagnosis￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- promotes￨L￨VBZ￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- single-stream￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨A through￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- disregard￨L￨VBP￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- use￨L￨NN￨O￨- on￨L￨IN￨O￨- treated￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- in￨L￨IN￨O￨- those￨L￨DT￨O￨- models￨L￨NNS￨O￨- comes￨L￨VBZ￨O￨- from￨L￨IN￨O￨- keeping￨L￨VBG￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- low￨L￨JJ￨O￨- once￨L￨RB￨DATE￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- generated￨L￨VBN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- do￨L￨VBP￨O￨- acknowledge￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- having￨L￨VBG￨O￨- low￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- antiviral￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- explicitly￨L￨RB￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- evolves￨L￨VBZ￨O￨- and￨L￨CC￨O￨- spreads￨L￨VBZ￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- further￨L￨JJ￨O￨- drug￨L￨NN￨O￨- use￨L￨NN￨O￨- can￨L￨MD￨O￨- fail￨L￨VB￨O￨- to￨L￨TO￨O￨- confer￨L￨VB￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨A benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- successful￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- doing￨L￨VBG￨O￨- so￨L￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- indirect￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- use￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- ‘￨L￨``￨O￨- direct￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- ’￨L￨POS￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- use￨L￨NN￨O￨- accrue￨L￨VBP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- morbidity￨L￨NN￨O￨- in￨L￨IN￨O￨- treated￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- contributions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- national￨L￨JJ￨O￨A population￨L￨NN￨O￨- surveys￨L￨NNS￨O￨- and￨L￨CC￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- surveillance￨L￨NN￨O￨- can￨L￨MD￨O￨- make￨L￨VB￨O￨- in￨L￨IN￨O￨- informing￨L￨VBG￨O￨- national￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- estimates￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- currently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- whether￨L￨IN￨O￨- these￨L￨DT￨O￨- differences￨L￨NNS￨O￨- have￨L￨VBP￨O￨- changed￨L￨VBN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- Spectrum￨U￨NNP￨O￨- can￨L￨MD￨O￨- best￨L￨JJS￨O￨- incorporate￨L￨VB￨O￨- both￨L￨DT￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- accurate￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- and￨L￨CC￨O￨- projections￨L￨NNS￨O￨- of￨L￨IN￨O￨- national￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- generalized￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- rely￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- national￨L￨JJ￨O￨A population￨L￨NN￨O￨- survey￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- national￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- using￨L￨VBG￨O￨- Spectrum￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- modelling￨L￨NN￨O￨- tool￨L￨NN￨O￨- supported￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Joint￨U￨NNP￨ORGANIZATION￨- United￨U￨NNP￨ORGANIZATION￨- Nations￨U￨NNPS￨ORGANIZATION￨- Programme￨U￨NNP￨ORGANIZATION￨- on￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- UNAIDS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- generalized￨L￨VBN￨O￨A HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- where￨L￨WRB￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- firmly￨L￨RB￨O￨- established￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- heterosexual￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- sentinel￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- among￨L￨IN￨O￨- pregnant￨L￨JJ￨O￨- women￨L￨NNS￨O￨- attending￨L￨VBG￨O￨- antenatal￨L￨JJ￨O￨- care￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- clinics￨L￨NNS￨O￨- in￨L￨IN￨O￨- urban￨L￨JJ￨O￨- and￨L￨CC￨O￨- rural￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- conducted￨L￨VBN￨O￨- every￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- 2￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- site￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- predominant￨L￨JJ￨O￨- data￨L￨NNS￨O￨- source￨L￨NN￨O￨- for￨L￨IN￨O￨- monitoring￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Spectrum￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- implemented￨L￨VBN￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- two-stage￨L￨JJ￨O￨- fitting￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- first￨L￨RB￨ORDINAL￨- estimates￨L￨VBZ￨O￨- prevalence￨L￨NN￨O￨- trends￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- applies￨L￨VBZ￨O￨- a￨L￨DT￨O￨- post-fitting￨L￨JJ￨O￨- calibration￨L￨NN￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- adjusts￨L￨VBZ￨O￨- these￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- trend￨L￨NN￨O￨- estimates￨L￨VBZ￨O￨- to￨L￨TO￨O￨- match￨L￨VB￨O￨- prevalence￨L￨NN￨O￨- levels￨L￨NNS￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- national￨L￨JJ￨O￨A population￨L￨NN￨O￨- surveys￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- generalized￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- no￨L￨DT￨O￨- national￨L￨JJ￨O￨A population￨L￨NN￨O￨- survey￨L￨NN￨O￨- ,￨L￨,￨O￨- UNAIDS￨U￨NNP￨ORGANIZATION￨- has￨L￨VBZ￨O￨- recommended￨L￨VBN￨O￨- a￨L￨DT￨O￨- default￨L￨NN￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- downward￨L￨JJ￨O￨- adjustment￨L￨NN￨O￨- to￨L￨TO￨O￨- ANC-based￨U￨JJ￨MISC￨- estimates￨L￨NNS￨O￨- in￨L￨IN￨O￨- urban￨L￨JJ￨O￨- and￨L￨CC￨O￨- rural￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- by￨L￨IN￨O￨- Gouws￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Dengue￨U￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨A epidemiology￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- show￨L￨VBP￨O￨- large￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ultimately￨L￨RB￨O￨- aim￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- predictive￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- hard￨L￨JJ￨O￨- copy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- book￨L￨NN￨O￨- format￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- hospital￨L￨NN￨O￨- admissions￨L￨NNS￨O￨- for￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- DF￨U￨NN￨O￨- ,￨L￨,￨O￨- DHF￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- DSS￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- reported￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- national￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- haemorrhagic￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- total￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DHF-total￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- that￨L￨IN￨O￨- every￨L￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- 70￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- 500￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- dengue￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- 36￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- DF￨U￨NN￨O￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- haemorrhagic￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- DHF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- dengue￨L￨JJ￨O￨- shock￨L￨NN￨O￨- syndrome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DSS￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 20￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Up￨U￨IN￨O￨- to￨L￨TO￨O￨- now￨L￨RB￨DATE￨- ,￨L￨,￨O￨- 33￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A illness￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- Thailand￨U￨NNP￨COUNTRY￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- continually￨L￨RB￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- modellers￨L￨NNS￨O￨- to￨L￨TO￨O￨- parametrize￨L￨VB￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g￨L￨FW￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- available￨L￨JJ￨O￨A as￨L￨IN￨O￨- electronic￨L￨JJ￨O￨- files￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- EF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- clinical￨L￨JJ￨O￨- classifications￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- DF￨U￨NN￨O￨- ,￨L￨,￨O￨- DHF￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- DSS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- notified￨L￨VBN￨O￨- separately￨L￨RB￨O￨- ,￨L￨,￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- WHO￨U￨WP￨ORGANIZATION￨- guidelines￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- line￨L￨NN￨O￨- list￨L￨NN￨O￨- to￨L￨TO￨O￨- compile￨L￨VB￨O￨- four￨L￨CD￨NUMBER￨- daily￨L￨JJ￨SET￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- :￨L￨:￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- following￨L￨VBG￨O￨- hospital￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- via￨L￨IN￨O￨- syringe￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 87￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- total￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- following￨L￨VBG￨O￨- person-to-person￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 140￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- total￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- reported￨L￨VBN￨O￨- deaths￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 248￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- total￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- reported￨L￨VBD￨O￨- recoveries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- total￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- assessed￨L￨VBD￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- hospital￨L￨NN￨O￨A and￨L￨CC￨O￨- community￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- only￨L￨RB￨O￨- five￨L￨CD￨NUMBER￨- syringes￨L￨NNS￨O￨- issued￨L￨VBN￨O￨- each￨L￨DT￨SET￨- day￨L￨NN￨SET￨- ,￨L￨,￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- contaminated￨L￨VBN￨O￨- syringes￨L￨NNS￨O￨- and￨L￨CC￨O￨- needles￨L￨NNS￨O￨- during￨L￨IN￨O￨- routine￨L￨JJ￨O￨- outpatient￨L￨NN￨O￨- visits￨L￨NNS￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- route￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ;￨L￨:￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- then￨L￨RB￨O￨- returned￨L￨VBD￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- villages￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- cases￨L￨NNS￨O￨- infected￨L￨JJ￨O￨- others￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VB￨O￨- the￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- actually￨L￨RB￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- ”￨L￨''￨O￨- susceptibles￨L￨NNS￨O￨- for￨L￨IN￨O￨- birds￨L￨NNS￨O￨A that￨L￨WDT￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- under￨L￨IN￨O￨- consideration￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- at￨L￨IN￨O￨- “￨L￨``￨O￨- actual￨L￨JJ￨O￨- ”￨L￨''￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- idea￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Richards￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- utilize￨L￨VBP￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- modeling￨L￨NN￨O￨- construction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Mathematical￨U￨JJ￨O￨- Details￨U￨NNS￨O￨- section￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- by￨L￨IN￨O￨- definition￨L￨NN￨O￨- only￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- eventually￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- modified￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- adopted￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- birds￨L￨NNS￨O￨A ;￨L￨:￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- single-equation￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- infected￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- make￨L￨VBP￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨A H7N9￨U￨NN￨O￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- by￨L￨IN￨O￨- onset￨L￨NN￨O￨- date￨L￨NN￨O￨- from￨L￨IN￨O￨- February￨U￨NNP￨DATE￨- 19￨L￨CD￨DATE￨- to￨L￨TO￨O￨- May￨U￨NNP￨DATE￨- 30￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2013￨L￨CD￨DATE￨- and￨L￨CC￨O￨- made￨L￨VBD￨O￨- public￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bird￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- final￨L￨JJ￨O￨- bird￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- H7N9￨U￨NNP￨O￨- have￨L￨VBP￨O￨- included￨L￨VBN￨O￨- both￨L￨CC￨O￨- birds￨L￨NNS￨O￨A and￨L￨CC￨O￨- human￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- purpose￨L￨NN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- only￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- coevolution￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- and￨L￨CC￨O￨- phage￨L￨NN￨O￨- in￨L￨IN￨O￨- soil￨L￨NN￨O￨- microcosms￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- characterised￨L￨VBN￨O￨- by￨L￨IN￨O￨- FSD￨U￨NN￨ORGANIZATION￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- ARD￨U￨NNP￨O￨- even￨L￨RB￨O￨- at￨L￨IN￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- costs￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- increased￨L￨VBN￨O￨- resistance￨L￨NN￨O￨A range￨L￨NN￨O￨- are￨L￨VBP￨O￨- greatly￨L￨RB￨O￨- elevated￨L￨JJ￨O￨- in￨L￨IN￨O￨- soil￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- nutrient-rich￨L￨JJ￨O￨- laboratory￨L￨NN￨O￨- media￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- host￨L￨NN￨TITLE￨- resistance￨L￨NN￨O￨A with￨L￨IN￨O￨- increased￨L￨VBN￨O￨- nutrient￨L￨NN￨O￨- availability￨L￨NN￨O￨- ,￨L￨,￨O￨- selection￨L￨NN￨O￨- for￨L￨IN￨O￨- elevated￨L￨JJ￨O￨- parasite￨L￨NN￨O￨- infectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- costs￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- generalism￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- selection￨L￨NN￨O￨- for￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- resistance￨L￨NN￨O￨A and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- ranges￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- arms￨L￨NNS￨O￨- race￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ARD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- nutrient￨L￨JJ￨O￨- availability￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- affect￨L￨VB￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- ARD￨U￨NNP￨ORGANIZATION￨- versus￨L￨CC￨O￨- FSD￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- coevolving￨L￨VBG￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- bacteria￨L￨NNS￨O￨- and￨L￨CC￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- frequencies￨L￨NNS￨O￨- of￨L￨IN￨O￨- genotypes￨L￨NNS￨O￨A with￨L￨IN￨O￨- similar￨L￨JJ￨O￨- ranges￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- infect/resist￨L￨VB￨O￨- different￨L￨JJ￨O￨- enemy￨L￨NN￨O￨- genotypes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- specialism￨L￨NN￨O￨- FSD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- analogous￨L￨JJ￨O￨- to￨L￨TO￨O￨- FSD￨U￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- MAM￨U￨NNP￨ORGANIZATION￨- specificity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- cross￨L￨JJ￨O￨A sectional￨L￨JJ￨O￨A serological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- blood￨L￨NN￨O￨- sample￨L￨NN￨O￨- is￨L￨VBZ￨O￨- drawn￨L￨VBN￨O￨- from￨L￨IN￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- tested￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- antibodies￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- constructed￨L￨VBD￨O￨- four￨L￨CD￨NUMBER￨- illustrative￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- for￨L￨IN￨O￨- baseline￨L￨NN￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- antibodies￨L￨NNS￨O￨- prior￨L￨RB￨O￨- and￨L￨CC￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- boosting￨L￨VBG￨O￨A following￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- investigates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- measuring￨L￨VBG￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- using￨L￨VBG￨O￨- different￨L￨JJ￨O￨- serological￨L￨JJ￨O￨A survey￨L￨NN￨O￨- designs￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- There￨U￨EX￨O￨- were￨L￨VBD￨O￨- substantial￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- background￨L￨NN￨O￨- antibody￨L￨NN￨O￨- titres￨L￨NNS￨O￨- and￨L￨CC￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- boosting￨L￨VBG￨O￨A within￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- illustrative￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- which￨L￨WDT￨O￨- were￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- evidence￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- directed￨L￨VBN￨O￨- against￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A vectors￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- at￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- LF￨U￨NNP￨O￨- if￨L￨IN￨O￨- their￨L￨PRP$￨O￨- use￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sustained￨L￨VBN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- as￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- lifespan￨L￨NN￨O￨- of￨L￨IN￨O￨- adult￨L￨JJ￨O￨- worms￨L￨NNS￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Whilst￨U￨IN￨O￨- one￨L￨CD￨NUMBER￨- study￨L￨NN￨O￨- estimated￨L￨VBD￨O￨- that￨L￨IN￨O￨- between￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 100￨L￨CD￨NUMBER￨- infective￨L￨JJ￨O￨- bites￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- will￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- thousands￨L￨NNS￨O￨- are￨L￨VBP￨O￨- required￨L￨VBN￨O￨- before￨L￨IN￨O￨- a￨L￨DT￨O￨- patent￨L￨NN￨O￨- filarial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- produced￨L￨VBN￨O￨- .￨L￨.￨O￨- +Interactions￨U￨NNS￨O￨- between￨L￨IN￨O￨- parasites￨L￨NNS￨O￨- and￨L￨CC￨O￨- mosquitoes￨L￨NNS￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- co-endemic￨L￨JJ￨O￨- for￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- LF￨U￨NN￨O￨- ,￨L￨,￨O￨- could￨L￨MD￨O￨- ,￨L￨,￨O￨- potentially￨L￨RB￨O￨- ,￨L￨,￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- perverse￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Vector￨U￨NNP￨O￨- control￨L￨NN￨O￨- continues￨L￨VBZ￨O￨- to￨L￨TO￨O￨- play￨L￨VB￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- ameliorating￨L￨VBG￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- long￨L￨JJ￨O￨- lasting￨L￨JJ￨O￨- insecticidal￨L￨JJ￨O￨- nets￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- LLINs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Central￨U￨NNP￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- LF￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- far￨L￨RB￨O￨- less￨L￨RBR￨O￨- efficient￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- than￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A NumericCitation￨U￨NN￨O￨- requiring￨L￨VBG￨O￨- a￨L￨DT￨O￨- far￨L￨RB￨O￨- greater￨L￨JJR￨O￨- critical￨L￨JJ￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- per￨L￨IN￨O￨- human￨L￨JJ￨O￨- for￨L￨IN￨O￨- LF￨U￨NN￨O￨- than￨L￨IN￨O￨- for￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Incomplete￨U￨JJ￨O￨- sampling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- explicitly￨L￨RB￨O￨- accounted￨L￨VBN￨O￨- for￨L￨IN￨O￨- by￨L￨IN￨O￨- birth-death-sampling￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- density￨L￨NN￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- trees￨L￨NNS￨O￨A are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- closed￨L￨JJ￨O￨- form￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- making￨L￨VBG￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- tractable￨L￨JJ￨O￨- for￨L￨IN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- Bayesian￨U￨JJ￨MISC￨- inference￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- both￨L￨DT￨O￨- cases￨L￨NNS￨O￨- the￨L￨DT￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨A assumes￨L￨VBZ￨O￨- complete￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- sampling￨L￨NN￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- explicitly￨L￨RB￨O￨- modelled￨L￨VBN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- serially￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- data￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- analysed￨L￨VBN￨O￨- using￨L￨VBG￨O￨- phylogenetic￨L￨JJ￨O￨A methods￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- sampled￨L￨VBN￨O￨- taxa￨L￨NN￨O￨- are￨L￨VBP￨O￨- leaf￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- appropriate￨L￨JJ￨O￨- .￨L￨.￨O￨- +Standard￨U￨NNP￨O￨- phylogenetic￨L￨JJ￨O￨A models￨L￨NNS￨O￨- developed￨L￨VBD￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- past￨L￨NN￨DATE￨- of￨L￨IN￨O￨- present￨L￨JJ￨DATE￨- day￨L￨NN￨DURATION￨- species￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- samples￨L￨NNS￨O￨- are￨L￨VBP￨O￨- terminal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- leaf￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- phylogenetic￨L￨JJ￨O￨- tree￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- tackle￨L￨VBP￨O￨- phylogenetic￨L￨JJ￨O￨A inference￨L￨NN￨O￨- with￨L￨IN￨O￨- trees￨L￨NNS￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- contain￨L￨VB￨O￨- sampled￨L￨VBN￨O￨- ancestors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- revealed￨L￨VBD￨O￨- limited￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- restrictions￨L￨NNS￨O￨A in￨L￨IN￨O￨- air￨L￨NN￨O￨- travel￨L￨NN￨O￨- –￨L￨:￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- countries￨L￨NNS￨O￨- –￨L￨:￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- containment￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- would￨L￨MD￨O￨- hamper￨L￨VB￨O￨- global￨L￨JJ￨O￨- travel￨L￨NN￨O￨- and￨L￨CC￨O￨- trade￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- restrictions￨L￨NNS￨O￨A are￨L￨VBP￨O￨- not￨L￨RB￨O￨- recommended￨L￨VBN￨O￨- by￨L￨IN￨O￨- WHO￨U￨WP￨ORGANIZATION￨- once￨L￨RB￨DATE￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- established.￨L￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- countries￨L￨NNS￨O￨- applied￨L￨VBD￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨- as￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pdm09￨L￨NN￨O￨- into￨L￨IN￨O￨- their￨L￨PRP$￨O￨- territories￨L￨NNS￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- subsequently￨L￨RB￨O￨- been￨L￨VBN￨O￨- questioned￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- any￨L￨DT￨O￨- meta-analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨A because￨L￨IN￨O￨- such￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- frequently￨L￨RB￨O￨- implemented￨L￨VBN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- countermeasures￨L￨NNS￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- following￨L￨VBG￨O￨- standardized￨L￨JJ￨O￨- protocols￨L￨NNS￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- no￨L￨RB￨O￨- more￨L￨RBR￨O￨- recent￨L￨JJ￨O￨- systematic￨L￨JJ￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- restrictions￨L￨NNS￨O￨A in￨L￨IN￨O￨- land￨L￨NN￨O￨- ,￨L￨,￨O￨- sea￨L￨NN￨O￨- or￨L￨CC￨O￨- air￨L￨NN￨O￨- travel￨L￨NN￨O￨- as￨L￨IN￨O￨- isolated￨L￨VBN￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- therefore￨L￨RB￨O￨- decided￨L￨VBD￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- containment￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- with￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- potential￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- A￨U￨NNP￨MISC￨- Bayesian￨U￨JJ￨MISC￨- spatio￨L￨NN￨O￨A –￨L￨:￨O￨- temporal￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- real￨L￨JJ￨O￨- –￨L￨:￨O￨- time￨L￨NN￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- studyJian￨L￨JJ￨O￨- Zou1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Alan￨U￨NNP￨PERSON￨- F￨U￨NN￨PERSON￨- Karr2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Gauri￨U￨NNP￨PERSON￨- Datta3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- James￨U￨NNP￨PERSON￨- Lynch4￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Shaun￨U￨NNP￨PERSON￨- Grannis5￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 14:108￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Zou￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- For￨U￨IN￨O￨- researchers￨L￨NNS￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- agencies￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- –￨L￨:￨O￨- dimensional￨L￨JJ￨O￨- spatio￨L￨NN￨O￨- –￨L￨:￨O￨- temporal￨L￨JJ￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- large￨L￨JJ￨O￨- reporting￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- presents￨L￨VBZ￨O￨- numerous￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- include￨L￨VBP￨O￨- low￨L￨JJ￨O￨- signal￨L￨NN￨O￨- –￨L￨:￨O￨- to￨L￨TO￨O￨- –￨L￨:￨O￨- noise￨L￨NN￨O￨- ratios￨L￨NNS￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- dependencies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- uncertainties￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- captures￨L￨VBZ￨O￨- salient￨L￨JJ￨O￨- spatio￨L￨NN￨O￨A –￨L￨:￨O￨- temporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- appears￨L￨VBZ￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- both￨L￨CC￨O￨- “￨L￨``￨O￨- annual￨L￨JJ￨SET￨- ”￨L￨''￨O￨- and￨L￨CC￨O￨- “￨L￨``￨O￨- atypical￨L￨JJ￨O￨- ”￨L￨''￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- timely￨L￨JJ￨O￨- ,￨L￨,￨O￨- accurate￨L￨JJ￨O￨- manner￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- a￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- Bayesian￨U￨JJ￨O￨- hierarchical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- data￨L￨NN￨O￨- set￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Indiana￨U￨NNP￨ORGANIZATION￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Emergency￨U￨NNP￨ORGANIZATION￨- Surveillance￨U￨NNP￨ORGANIZATION￨- System￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- PHESS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- containing￨L￨VBG￨O￨- three￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- emergency￨L￨NN￨O￨A department￨L￨NN￨O￨- visits￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- –￨L￨:￨O￨- like￨L￨IN￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- respiratory￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Combining￨U￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- U.S.￨U￨NNP￨COUNTRY￨- sex￨L￨NN￨O￨A surveys￨L￨NNS￨O￨- and￨L￨CC￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- commercial￨L￨JJ￨O￨- sex￨L￨NN￨O￨- ,￨L￨,￨O￨- Brewer￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 15￨L￨CD￨NUMBER￨- find￨L￨VBP￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- sex￨L￨NN￨O￨- workers￨L￨NNS￨O￨- and￨L￨CC￨O￨- sexual￨L￨JJ￨O￨- encounters￨L￨NNS￨O￨- with￨L￨IN￨O￨- them￨L￨PRP￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- underrepresented￨L￨JJ￨O￨- in￨L￨IN￨O￨- general-population￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- market￨L￨NN￨O￨- for￨L￨IN￨O￨- commercial￨L￨JJ￨O￨- sex￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- vertices￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- sex￨L￨NN￨O￨- buyers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- clients￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- sex￨L￨NN￨O￨- sellers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- sex￨L￨NN￨O￨- workers￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- map￨L￨VBP￨O￨- the￨L￨DT￨O￨- sexual￨L￨JJ￨O￨- encounters￨L￨NNS￨O￨- among￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- client-prostitute￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- naturally￨L￨RB￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- sexual￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- population￨L￨NN￨O￨- through￨L￨IN￨O￨- noncommercial￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- encounters￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- sex￨L￨NN￨O￨A workers￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- clients￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- throughout￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- highly￨L￨RB￨O￨- promiscuous￨L￨JJ￨O￨- individuals245￨L￨NN￨O￨- and￨L￨CC￨O￨- sex￨L￨NN￨O￨A workers￨L￨NNS￨O￨- typically￨L￨RB￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- partners￨L￨NNS￨O￨- .￨L￨.￨O￨- +How￨U￨WRB￨O￨- central￨L￨JJ￨O￨- are￨L￨VBP￨O￨- clients￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sexual￨L￨JJ￨O￨- network￨L￨NN￨O￨- created￨L￨VBN￨O￨- by￨L￨IN￨O￨- commercial￨L￨JJ￨O￨- sex￨L￨NN￨O￨A ?￨L￨.￨O￨- +Because￨U￨IN￨O￨- variability￨L￨NN￨O￨- typically￨L￨RB￨O￨- occurs￨L￨VBZ￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- any￨L￨DT￨O￨- simple￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- must￨L￨MD￨O￨- either￨L￨RB￨O￨- choose￨L￨VB￨O￨- to￨L￨TO￨O￨- ignore￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- unrepresented￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- or￨L￨CC￨O￨- incorporate￨L￨VB￨O￨- these￨L￨DT￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- phenomenological￨L￨JJ￨O￨- way.At￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- extreme￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spectrum￨L￨NN￨O￨- ,￨L￨,￨O￨- mean-field￨L￨JJ￨O￨- models￨L￨NNS￨O￨- aggregate￨L￨NN￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- variable￨L￨NN￨O￨- and￨L￨CC￨O￨- ignore￨L￨VB￨O￨- space￨L￨NN￨O￨- completely￨L￨RB￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- only￨L￨RB￨O￨- global￨L￨JJ￨O￨- densities￨L￨NNS￨O￨A under￨L￨IN￨O￨- the￨L￨DT￨O￨- simplifying￨L￨VBG￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- mixed￨L￨JJ￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- sample￨L￨NN￨O￨- space￨L￨NN￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- interactions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 211￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 222￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asSimple￨L￨NN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- :￨L￨:￨O￨- exploiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- densitiesAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsMercedes￨L￨NNS￨O￨- PascualManojit￨U￨NN￨MISC￨- RoyKarina￨U￨NNP￨MISC￨- LaneriOpen￨U￨NNP￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- paperFirst￨L￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 895￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨O￨- 12￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractSimple￨U￨NNP￨O￨- temporal￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- ignore￨L￨VBP￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- track￨L￨NN￨O￨- only￨L￨RB￨O￨- changes￨L￨VBZ￨O￨- in￨L￨IN￨O￨- mean￨L￨NN￨O￨- quantities￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- global￨L￨JJ￨O￨- densities￨L￨NNS￨O￨A ,￨L￨,￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- used￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- unrealistic￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- mixed￨L￨JJ￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- corrects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean-field￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- deviations￨L￨NNS￨O￨- from￨L￨IN￨O￨- random￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- associated￨L￨VBN￨O￨- influences￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- densities￨L￨NNS￨O￨A ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- relied￨L￨VBN￨O￨- on￨L￨IN￨O￨- modifications￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- functional￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- predator￨L￨NN￨O￨- –￨L￨:￨O￨- prey￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- whose￨L￨WP$￨O￨- mean-field￨L￨JJ￨O￨- counterpart￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- Lotka￨U￨NNP￨O￨- –￨L￨:￨O￨- Volterra￨U￨NNP￨CITY￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- densities￨L￨NNS￨O￨A and￨L￨CC￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- covariances￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- establish￨L￨VBP￨O￨- a￨L￨DT￨O￨- bi-power￨L￨JJ￨O￨- law￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- transient￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- clinical￨L￨JJ￨O￨- presentation￨L￨NN￨O￨- and￨L￨CC￨O￨- pathology￨L￨NN￨O￨- were￨L￨VBD￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- CDV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- antigenic￨L￨JJ￨O￨- characterization￨L￨NN￨O￨- and￨L￨CC￨O￨- gene￨L￨NN￨O￨- sequencing￨L￨NN￨O￨- demonstrated￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A was￨L￨VBD￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- and￨L￨CC￨O￨- distinct￨L￨JJ￨O￨- member￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Morbillivirus￨U￨NNP￨MISC￨- genus￨L￨NN￨O￨- ,￨L￨,￨O￨- phocine￨L￨NN￨O￨- distemper￨L￨NN￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- PDV￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- event￨L￨NN￨O￨A followed￨L￨VBD￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- canine￨L￨JJ￨O￨- distemper￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CDV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- terrestrial￨L￨JJ￨O￨- mammals￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- diagnostic￨L￨JJ￨O￨- tests￨L￨NNS￨O￨- later￨L￨RB￨O￨- confirmed￨L￨VBD￨O￨- that￨L￨IN￨O￨- CDV￨U￨NN￨O￨- was￨L￨VBD￨O￨- implicated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- seal￨L￨NN￨O￨- deaths￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- early￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- that￨L￨IN￨O￨- harp￨L￨NN￨O￨- seals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Pagophilus￨U￨NN￨O￨- groenlandicus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- eastern￨L￨JJ￨O￨A Arctic￨U￨NNP￨MISC￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- supported￨L￨VBN￨O￨- by￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- serological￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- in￨L￨IN￨O￨- Norway￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Greenland￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Canada￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- PDV￨U￨NNP￨ORGANIZATION￨- epidemic￨L￨JJ￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- virgin￨L￨JJ￨O￨- soil￨L￨NN￨O￨- ”￨L￨''￨O￨- event￨L￨NN￨O￨A in￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- naïve￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- raised￨L￨VBD￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- had￨L￨VBD￨O￨- originated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- swept￨L￨VBN￨O￨- through￨L￨IN￨O￨- breeding￨L￨VBG￨O￨- colonies￨L￨NNS￨O￨- of￨L￨IN￨O￨- European￨U￨JJ￨NATIONALITY￨- harbor￨L￨NN￨O￨- seals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Phoca￨U￨NN￨LOCATION￨- vitulina￨L￨NN￨O￨- vitulina￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- coasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- North￨U￨NNP￨O￨- ,￨L￨,￨O￨- Baltic￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- Irish￨U￨NNP￨NATIONALITY￨- seas￨L￨NNS￨O￨- killing￨L￨VBG￨O￨A up￨L￨RP￨O￨- to￨L￨TO￨O￨- 18,000￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- species￨L￨NNS￨O￨- and￨L￨CC￨O￨- possibly￨L￨RB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- hundred￨L￨CD￨NUMBER￨- sympatric￨L￨JJ￨O￨- grey￨L￨JJ￨O￨- seals￨L￨NNS￨O￨- ,￨L￨,￨O￨- Halichoerus￨U￨NNP￨O￨- grypus￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Nonetheless￨U￨RB￨O￨- ,￨L￨,￨O￨- scaling￨L￨NN￨O￨- analysis￨L￨NN￨O￨- in￨L￨IN￨O￨- small￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- revealed￨L￨VBN￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- predictability￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- statistics￨L￨NNS￨O￨A of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- recorded￨L￨VBN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Annual￨U￨JJ￨SET￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- live￨L￨JJ￨O￨- births￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- country￨L￨NN￨O￨- were￨L￨VBD￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- Iceland￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Statistics￨U￨NNP￨O￨- Iceland￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- Births￨U￨NNS￨O￨- by￨L￨IN￨O￨- months￨L￨NNS￨DATE￨- 1853￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2012￨L￨CD￨DATE￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- 262￨L￨CD￨NUMBER￨- municipalities￨L￨NNS￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- Iceland￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Statistics￨U￨NNP￨O￨- Iceland￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 1990￨L￨CD￨DATE￨- Municipal￨U￨JJ￨O￨- borders￨L￨NNS￨O￨- changed￨L￨VBD￨O￨- from￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- five￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- municipality￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- relevance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- breakpoint￨L￨NN￨O￨- phenomenon￨L￨NN￨O￨- in￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- compares￨L￨VBZ￨O￨- the￨L￨DT￨O￨- projections￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- established￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- Schistosoma￨U￨NNP￨LOCATION￨- transmission￨L￨NN￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- modified￨L￨VBN￨O￨- MacDonald-type￨U￨NNP￨MISC￨- Mean￨U￨NN￨MISC￨- Worm￨U￨NN￨MISC￨- Burden￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- MWB￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- May￨U￨NNP￨DATE￨- and￨L￨CC￨O￨- colleagues￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- Nåsell￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- colleagues￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- utilizing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- assumed￨L￨VBN￨O￨- negative￨L￨JJ￨O￨- binomial￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- NB￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- Poisson￨U￨NNP￨PERSON￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- worm￨L￨NN￨O￨A burden￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- distribution-free￨L￨JJ￨MISC￨- Stratified￨U￨NNP￨MISC￨- Worm￨U￨NNP￨MISC￨- Burden￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- SWB￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- now￨L￨RB￨DATE￨- modify￨L￨VB￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- parasite￨L￨NN￨O￨- mating￨L￨NN￨O￨- probability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- list￨L￨NN￨O￨- of￨L￨IN￨O￨- abbreviations￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- Schistosoma￨U￨NNP￨O￨- worm￨L￨NN￨O￨A distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- nearly￨L￨RB￨O￨- uniform￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- burden￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- whereby￨L￨WRB￨O￨- each￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- carries￨L￨VBZ￨O￨- approximately￨L￨RB￨O￨- worms-the￨L￨JJ￨O￨- total￨L￨JJ￨O￨- parasite￨L￨NN￨O￨- load￨L￨NN￨O￨- W￨U￨NN￨O￨- distributed￨L￨VBN￨O￨- evenly￨L￨RB￨O￨- over￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- –￨L￨:￨O￨- H￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- over-dispersed￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- negative￨L￨JJ￨O￨- binomial￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- NB￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- distribution￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- Poisson￨U￨NNP￨PERSON￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- greater￨L￨JJR￨O￨- aggregation￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- male￨L￨NN￨O￨- and￨L￨CC￨O￨- female￨L￨JJ￨O￨- worms￨L￨NNS￨O￨- are￨L￨VBP￨O￨- transmitted￨L￨VBN￨O￨- in￨L￨IN￨O￨- roughly￨L￨RB￨O￨- equal￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- if￨L￨IN￨O￨- worm￨L￨NN￨O￨A mating￨L￨NN￨O￨- is￨L￨VBZ￨O￨- promiscuous￨L￨JJ￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- monogamous￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- projected￨L￨VBN￨O￨- breakpoint￨L￨NN￨O￨- phenomenon￨L￨NN￨O￨- might￨L￨MD￨O￨- not￨L￨RB￨O￨- prove￨L￨VB￨O￨- relevant￨L￨JJ￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- females￨L￨NNS￨O￨- are￨L￨VBP￨O￨- increasingly￨L￨RB￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- successfully￨L￨RB￨O￨- mated￨L￨VBN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +Effectively￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- breakpoints￨L￨NNS￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- MacDonald￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- points￨L￨NNS￨O￨- or￨L￨CC￨O￨- regions￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- below￨L￨IN￨O￨- which￨L￨WDT￨O￨- existing￨L￨VBG￨O￨- worm￨L￨NN￨O￨A burden￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unsuccessful￨L￨JJ￨O￨- in￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- parasite￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- ultimately￨L￨RB￨O￨- go￨L￨VBP￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- without￨L￨IN￨O￨- further￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- practice￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- prolonged￨L￨JJ￨O￨- and￨L￨CC￨O￨- extensive￨L￨JJ￨O￨- reductions￨L￨NNS￨O￨- of￨L￨IN￨O￨- snail￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- were￨L￨VBD￨O￨- achieved￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Schistosoma￨U￨NNP￨PERSON￨- prevalence￨L￨NN￨O￨- often￨L￨RB￨O￨- dropped￨L￨VBD￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- interrupted￨L￨JJ￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- flaws￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- MacDonald￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- additional￨L￨JJ￨O￨- complicating￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- with￨L￨IN￨O￨- regard￨L￨NN￨O￨- to￨L￨TO￨O￨- parasite￨L￨NN￨O￨A mating￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- considering￨L￨VBG￨O￨- current￨L￨JJ￨DATE￨- limitations￨L￨NNS￨O￨- of￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- challenges￨L￨NNS￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- interpreting￨L￨VBG￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- outline￨L￨VB￨O￨- a￨L￨DT￨O￨- research￨L￨NN￨O￨- agenda￨L￨NN￨O￨- to￨L￨TO￨O￨- accelerate￨L￨VB￨O￨- the￨L￨DT￨O￨- genomics-driven￨L￨JJ￨O￨- transformation￨L￨NN￨O￨- in￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- microbiology.KeywordsInfluenzaSevere￨L￨NNP￨O￨- Acute￨U￨JJ￨MISC￨- Respiratory￨U￨JJ￨MISC￨- SyndromeReproduction￨U￨NN￨MISC￨- NumberSevere￨U￨NNP￨MISC￨- Acute￨U￨JJ￨MISC￨- Respiratory￨U￨JJ￨MISC￨- SyndromeMultilocus￨U￨NN￨MISC￨- Sequence￨U￨NN￨MISC￨- Typing￨U￨VBG￨MISC￨- IntroductionInfectious￨U￨JJ￨MISC￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiologists￨L￨NNS￨O￨A study￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- seek￨L￨VB￨O￨- ways￨L￨NNS￨O￨- to￨L￨TO￨O￨- turn￨L￨VB￨O￨- observations￨L￨NNS￨O￨- about￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- populations￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- into￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- decrease￨L￨VB￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- advent￨L￨NN￨O￨- of￨L￨IN￨O￨- cheap￨L￨JJ￨O￨- ,￨L￨,￨O￨- rapid￨L￨JJ￨O￨- whole-genome￨L￨JJ￨O￨- sequencing￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- latest￨L￨JJS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- historic￨L￨JJ￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ways￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- epidemiologists￨L￨NNS￨O￨- classify￨L￨VBP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- classification￨L￨NN￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- progressed￨L￨VBN￨O￨- from￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- definitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- syndromes￨L￨NNS￨O￨- to￨L￨TO￨O￨- microbiologic￨L￨JJ￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- now￨L￨RB￨DATE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- genotype￨L￨NN￨O￨- and￨L￨CC￨O￨- genome￨L￨NN￨O￨A sequence￨L￨NN￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Epidemiologic￨U￨JJ￨MISC￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- genome￨L￨NN￨O￨A sequences￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- powerful￨L￨JJ￨O￨- synergy￨L￨NN￨O￨- for￨L￨IN￨O￨- public￨L￨JJ￨O￨- healthYonatan￨L￨NN￨O￨- H￨U￨NN￨O￨- Grad1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Marc￨U￨NNP￨PERSON￨- Lipsitch1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 15:538￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Grad￨U￨NNP￨O￨- and￨L￨CC￨O￨- Lipsitch￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Published￨L￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractEpidemiologists￨U￨NNP￨O￨- aim￨L￨NN￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- with￨L￨IN￨O￨- evidence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- review￨L￨NN￨O￨- highlights￨L￨VBZ￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- addressed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- genome￨L￨NN￨O￨A sequence￨L￨NN￨O￨- and￨L￨CC￨O￨- traditional￨L￨JJ￨O￨- `￨L￨``￨O￨- line￨L￨NN￨O￨- lists￨L￨NNS￨O￨- ’￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- tables￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- line￨L￨NN￨O￨- includes￨L￨VBZ￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- clinical￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- evaluate￨L￨VBP￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- exploit￨L￨VBP￨O￨- pathogen￨L￨NN￨O￨- sequences￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- genomic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- recently￨L￨RB￨DATE￨- emerged￨L￨VBD￨O￨- infectious￨L￨JJ￨O￨- diseases.KeywordsDromedary￨L￨JJ￨O￨- CamelOffspring￨U￨NN￨MISC￨- DistributionInfectious￨U￨NNP￨MISC￨- Disease￨U￨NNP￨CAUSE_OF_DEATH￨- ResearchPathogen￨U￨NNP￨MISC￨- SequenceMolecular￨U￨NNP￨MISC￨- Clock￨U￨NN￨MISC￨- Model￨U￨NNP￨TITLE￨- IntroductionWhen￨U￨NNP￨MISC￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- crosses￨L￨VBZ￨O￨- over￨L￨IN￨O￨- from￨L￨IN￨O￨- animals￨L￨NNS￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- an￨L￨DT￨O￨- existing￨L￨VBG￨O￨- human￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- suddenly￨L￨RB￨O￨- increases￨L￨VBZ￨O￨- in￨L￨IN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- said￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- `￨L￨``￨O￨- emerging￨L￨VBG￨O￨- ’￨L￨''￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Genomic￨U￨JJ￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨A pathogens￨L￨NNS￨O￨- :￨L￨:￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- application￨L￨NN￨O￨- and￨L￨CC￨O￨- future￨L￨JJ￨DATE￨- trendsLucy￨L￨NN￨O￨- M￨U￨NN￨O￨- Li1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Nicholas￨U￨NNP￨PERSON￨- C￨U￨NNP￨PERSON￨- Grassly1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Christophe￨U￨NNP￨PERSON￨- Fraser1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 15:541￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Li￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Published￨L￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- increasing￨L￨VBG￨O￨- .￨L￨.￨O￨- +Modeling￨U￨NN￨O￨- plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- especially￨L￨RB￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A ,￨L￨,￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- directly￨L￨RB￨O￨- observable￨L￨JJ￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- 1867￨L￨CD￨DATE￨- and￨L￨CC￨O￨- 1879￨L￨NNS￨DATE￨- papers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- reaction￨L￨NN￨O￨A between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- substances￨L￨NNS￨O￨- with￨L￨IN￨O￨- M￨U￨NN￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- molecules￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- occurring￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- volume￨L￨NN￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- formulated￨L￨VBN￨O￨- asConsidering￨L￨NN￨O￨- concentrations￨L￨NNS￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- molecules￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- reaction￨L￨NN￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- substrates￨L￨NNS￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- and￨L￨CC￨O￨- q￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- products￨L￨NNS￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- ′￨L￨NN￨O￨- and￨L￨CC￨O￨- q￨L￨VB￨O￨- ′￨L￨NN￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- therefore￨L￨RB￨O￨- formulated￨L￨VBN￨O￨- asAccording￨L￨NN￨O￨- to￨L￨TO￨O￨- Equation￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- forces￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- reversible￨L￨JJ￨O￨- reaction￨L￨NN￨O￨- are￨L￨VBP￨O￨- k￨L￨NN￨O￨- p￨L￨NN￨O￨- q￨L￨NN￨O￨- and￨L￨CC￨O￨- k￨L￨NN￨O￨- ′￨L￨NN￨O￨- p￨L￨NN￨O￨- ′￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- ′￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- unrelated￨L￨JJ￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- retrospect￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- was￨L￨VBD￨O￨- ripe￨L￨JJ￨O￨- for￨L￨IN￨O￨- new￨L￨JJ￨O￨- ,￨L￨,￨O￨- formal￨L￨JJ￨O￨- ideas￨L￨NNS￨O￨- and￨L￨CC￨O￨- concepts￨L￨NNS￨O￨- about￨L￨IN￨O￨- affinity￨L￨NN￨O￨- ,￨L￨,￨O￨- Ludwig￨U￨NNP￨PERSON￨- Wilhelmy￨U￨NNP￨PERSON￨- derived￨L￨VBD￨O￨- a￨L￨DT￨O￨- differential￨L￨JJ￨O￨- mass￨L￨NN￨O￨A action￨L￨NN￨O￨A equation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- inversion￨L￨NN￨O￨- of￨L￨IN￨O￨- cane￨L￨NN￨O￨- sugar￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- Guldberg￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Waage￨U￨NNP￨PERSON￨- were￨L￨VBD￨O￨- apparently￨L￨RB￨O￨- not￨L￨RB￨O￨- aware￨L￨JJ￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +Berthelot￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Saint-Gilles￨U￨NNP￨PERSON￨- formulated￨L￨VBD￨O￨- the￨L￨DT￨O￨- forward￨L￨JJ￨O￨- process￨L￨NN￨O￨- mathematically￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- never￨L￨RB￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- reverse￨L￨JJ￨O￨- reaction￨L￨NN￨O￨A between￨L￨IN￨O￨- ester￨L￨NN￨O￨- and￨L￨CC￨O￨- water￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- started￨L￨VBD￨O￨- to￨L￨TO￨O￨- collaborate￨L￨VB￨O￨- in￨L￨IN￨O￨- 1862￨L￨CD￨DATE￨- and￨L￨CC￨O￨- documented￨L￨VBD￨O￨- the￨L￨DT￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨A action￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- articles￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- –￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- this￨L￨DT￨O￨- simplified￨L￨VBN￨O￨- equilibrium￨L￨NN￨O￨- view￨L￨NN￨O￨- is￨L￨VBZ￨O￨- true￨L￨JJ￨O￨- ,￨L￨,￨O￨- planning￨L￨VBG￨O￨- eradication￨L￨NN￨O￨A efforts￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- timelines￨L￨NNS￨O￨- as￨L￨IN￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- Macdonald￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- others￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- just￨L￨RB￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- conditions.This￨L￨NN￨O￨- R0￨U￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- simple￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- or￨L￨CC￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- durations￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- excessively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- structure￨L￨NN￨O￨- can￨L￨MD￨O￨- miss￨L￨VB￨O￨- key￨L￨JJ￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- simple￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- can￨L￨MD￨O￨- still￨L￨RB￨O￨- achieve￨L￨VB￨O￨- key￨L￨JJ￨O￨- results￨L￨NNS￨O￨- for￨L￨IN￨O￨- eradication￨L￨NN￨O￨A strategy￨L￨NN￨O￨- and￨L￨CC￨O￨- define￨L￨VB￨O￨- areas￨L￨NNS￨O￨- for￨L￨IN￨O￨- investigation￨L￨NN￨O￨- by￨L￨IN￨O￨- more￨L￨JJR￨O￨- complex￨L￨NN￨O￨- models.KeywordsMalariaIndoor￨L￨NNP￨O￨- Residual￨U￨NNP￨O￨- SprayVaccine￨U￨NNP￨O￨- EfficacyPrimaquineMalaria￨U￨NNP￨O￨- Eradication￨U￨NNP￨O￨- BackgroundMathematical￨U￨NNP￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- helpful￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- testing￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- and￨L￨CC￨O￨- elucidating￨L￨VBG￨O￨- the￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- features￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- examples￨L￨NNS￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- eradication￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- and￨L￨CC￨O￨- coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- drug￨L￨NN￨O￨- programs￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- delays￨L￨NNS￨O￨- to￨L￨TO￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonality￨L￨NN￨O￨- and￨L￨CC￨O￨- migration￨L￨NN￨O￨- coupling￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- fadeout￨L￨NN￨O￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- decay￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- infectious￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- for￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- Rc￨U￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- duration￨L￨NN￨O￨A averaging￨L￨VBG￨O￨- 180￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Existing￨U￨VBG￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨A coverage￨L￨NN￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- this￨L￨DT￨O￨- coverage￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals11121314￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- prototype￨L￨NN￨O￨- decreasing￨L￨VBG￨O￨- functions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- H￨U￨NN￨O￨- denoting￨L￨VBG￨O￨- hospitalized￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- infectives￨L￨NNS￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- exposed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- nonnegative￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- c1￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- c2f￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- constants￨L￨NNS￨O￨- c1￨L￨NN￨O￨- ,￨L￨,￨O￨- c2￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- embedded￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- incorporate￨L￨VB￨O￨- these￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- into￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- including￨L￨VBG￨O￨- media￨L￨NNS￨O￨A impacted-behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- here￨L￨RB￨O￨- differs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨A coverage11121314￨L￨NN￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- our￨L￨PRP$￨O￨- formulated￨L￨VBN￨O￨- media-impact￨L￨JJ￨O￨- function￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- change￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- media￨L￨NNS￨O￨A has￨L￨VBZ￨O￨- impacts￨L￨NNS￨O￨- on￨L￨IN￨O￨- individual￨L￨JJ￨O￨- behavioural￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- via￨L￨IN￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- number￨L￨NN￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- both181920￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- media￨L￨NNS￨O￨A impact￨L￨NN￨O￨- involves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- ′￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- implicit￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- class￨L￨NN￨O￨- closure￨L￨NN￨O￨- affords￨L￨VBZ￨O￨- strong￨L￨JJ￨O￨- mitigation￨L￨NN￨O￨A effects￨L￨NNS￨O￨- :￨L￨:￨O￨- closing￨L￨VBG￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- –￨L￨:￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- –￨L￨:￨O￨- whenever￨L￨WRB￨O￨- two￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- class￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- by￨L￨IN￨O￨- almost￨L￨RB￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- significantly￨L￨RB￨O￨- decreases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- severe￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- and￨L￨CC￨O￨- results￨L￨NNS￨O￨- We￨U￨PRP￨O￨- model￨L￨VBP￨O￨- mitigation￨L￨NN￨O￨A measures￨L￨NNS￨O￨- that￨L￨WDT￨O￨- involve￨L￨VBP￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- closure￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- classes￨L￨NNS￨O￨- or￨L￨CC￨O￨- grades￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- readily￨L￨RB￨O￨- available￨L￨JJ￨O￨- information￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- children￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- recent￨L￨JJ￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- high-resolution￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- school￨L￨NN￨O￨- environments￨L￨NNS￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- opportunity￨L￨NN￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- micro-interventions￨L￨NNS￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- mitigation￨L￨NN￨O￨A measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Mitigation￨U￨NNP￨MISC￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- school￨L￨NN￨O￨- :￨L￨:￨O￨- targeted￨L￨VBN￨O￨- class￨L￨NN￨O￨- closure￨L￨NN￨O￨A vs￨L￨CC￨O￨- school￨L￨NN￨O￨- closureValerio￨L￨NN￨O￨- Gemmetto1￨U￨NN￨O￨- ,￨L￨,￨O￨- Alain￨U￨NNP￨PERSON￨- Barrat2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 1Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Ciro￨U￨NNP￨O￨- Cattuto1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 14:695￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Barrat￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Cattuto￨U￨NNP￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨O￨- Central￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- closure￨L￨NN￨O￨A of￨L￨IN￨O￨- all￨L￨DT￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- grade￨L￨NN￨O￨- mitigates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- almost￨L￨RB￨O￨- as￨L￨RB￨O￨- much￨L￨JJ￨O￨- as￨L￨IN￨O￨- closing￨L￨VBG￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- school￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- functional￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- brain￨L￨NN￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- relationships￨L￨NNS￨O￨- among￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- inferred￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- condensed￨L￨JJ￨O￨- way￨L￨NN￨O￨- of￨L￨IN￨O￨- exploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- organization￨L￨NN￨O￨- of￨L￨IN￨O￨- excitable￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- neural￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- implemented￨L￨VBD￨O￨- stochastic￨L￨JJ￨O￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- well-established￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- brain￨L￨NN￨O￨A activity￨L￨NN￨O￨- ,￨L￨,￨O￨- SER￨U￨NN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- FHN￨U￨NN￨O￨- oscillators￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- reproducing￨L￨VBG￨O￨- different￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- functional￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- as￨L￨IN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- resting-state￨L￨JJ￨O￨- fMRI￨L￨NN￨O￨- data1415￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- ,￨L￨,￨O￨- initially￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- appeared￨L￨VBD￨O￨- to￨L￨TO￨O￨- yield￨L￨VB￨O￨- different￨L￨JJ￨O￨- findings￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SC-FC￨U￨NN￨O￨- relationship￨L￨NN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- randomization￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- adjustment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- window￨L￨NN￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- FC￨U￨NNP￨O￨- was￨L￨VBD￨O￨- derived￨L￨VBN￨O￨- demonstrated￨L￨VBD￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- similarity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SC-FC￨U￨NN￨O￨- relations￨L￨NNS￨O￨A .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- investigations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relations￨L￨NNS￨O￨A between￨L￨IN￨O￨- SC￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- FC￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- excitable￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- discrete￨L￨JJ￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- strongly￨L￨RB￨O￨- depended￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- network￨L￨NN￨O￨- topology9￨L￨NN￨O￨- .￨L￨.￨O￨- +Employing￨U￨VBG￨O￨- such￨L￨JJ￨O￨- requirements￨L￨NNS￨O￨- and￨L￨CC￨O￨- assumptions￨L￨NNS￨O￨- restrict￨L￨VBP￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- geographical￨L￨JJ￨O￨- routing￨L￨VBG￨O￨- protocols￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- a￨L￨DT￨O￨- huge￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- resource-constrained￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- characteristics￨L￨NNS￨O￨- consist￨L￨VBP￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- Traditional￨U￨JJ￨O￨- IP-based￨U￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- WSNs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- inapplicable￨L￨JJ￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deployment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sensor￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- and￨L￨CC￨O￨- static￨L￨JJ￨O￨- wormhole￨L￨NN￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- geographic￨L￨JJ￨O￨- routing￨L￨VBG￨O￨- protocols￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- DWGRP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- causative￨L￨JJ￨O￨- strain￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- this￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- past￨L￨JJ￨DATE￨A outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- Central￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- contributed￨L￨VBN￨O￨- disproportionately￨L￨RB￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- unprecedented￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- substantial￨L￨JJ￨O￨- delays￨L￨NNS￨O￨- in￨L￨IN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- region￨L￨NN￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- porous￨L￨JJ￨O￨- borders￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- limited￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- infrastructure￨L￨NN￨O￨- including￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- diagnostic￨L￨JJ￨O￨- testing￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- timely￨L￨JJ￨O￨- diagnosis￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- effective￨L￨JJ￨O￨- isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- to￨L￨TO￨O￨- rapidly￨L￨RB￨O￨- identify￨L￨VB￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- providing￨L￨VBG￨O￨- supportive￨L￨JJ￨O￨- care￨L￨NN￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- chances￨L￨NNS￨O￨- of￨L￨IN￨O￨- survival￨L￨NN￨O￨- to￨L￨TO￨O￨- EVD￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- cultural￨L￨JJ￨O￨- practices￨L￨NNS￨O￨- that￨L￨WDT￨O￨- involve￨L￨VBP￨O￨- touching￨L￨VBG￨O￨- the￨L￨DT￨O￨- body￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deceased￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- association￨L￨NN￨O￨- of￨L￨IN￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- witchcraft￨L￨NN￨RELIGION￨- or￨L￨CC￨O￨- conspiracy￨L￨NN￨CRIMINAL_CHARGE￨- theories￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- risk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CFR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- calculated￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- deaths￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- cases￨L￨NNS￨O￨- with￨L￨IN￨O￨- known￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- 9￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- at￨L￨IN￨O￨- 70.8￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- 68.6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 72.8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- broad￨L￨JJ￨O￨- agreement￨L￨NN￨O￨A with￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- from￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- quantifies￨L￨VBZ￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨A generated￨L￨VBN￨O￨A by￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- before￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- put￨L￨VBN￨O￨- in￨L￨IN￨O￨- place￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Estimates￨U￨NNS￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- have￨L￨VBP￨O￨- fluctuated￨L￨VBN￨O￨- around￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- good￨L￨JJ￨O￨- agreement￨L￨NN￨O￨A with￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- from￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- EVD￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- efforts￨L￨NNS￨O￨A are￨L￨VBP￨O￨- underway￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- way￨L￨NN￨O￨- of￨L￨IN￨O￨- relating￨L￨VBG￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- sampled￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨- involves￨L￨VBZ￨O￨- drawing￨L￨VBG￨O￨- a￨L￨DT￨O￨- realization￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- coalescent￨L￨JJ￨O￨A distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- Volz￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- a￨L￨DT￨O￨- tree￨L￨NN￨O￨- conditional￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- particular￨L￨JJ￨O￨- piecewise￨L￨NN￨O￨- constant￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- size￨L￨NN￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- realization￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- Dearlove￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wilson￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2013￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- paved￨L￨VBD￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- by￨L￨IN￨O￨- implementing￨L￨VBG￨O￨- a￨L￨DT￨O￨- coalescent￨L￨JJ￨O￨A approach￨L￨NN￨O￨- for￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- Bayesian￨U￨JJ￨MISC￨- inference￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- implement￨L￨VBP￨O￨- and￨L￨CC￨O￨- rigorously￨L￨RB￨O￨- test￨L￨NN￨O￨- both￨L￨CC￨O￨- deterministic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- coalescent￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- extended￨L￨VBN￨O￨- for￨L￨IN￨O￨- heterochronously￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- extension￨L￨NN￨O￨- and￨L￨CC￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- and￨L￨CC￨O￨- deterministic￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- trees￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- trajectories￨L￨NNS￨O￨- for￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- inference￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- are￨L￨VBP￨O￨- therefore￨L￨RB￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨A processes￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- significance￨L￨NN￨O￨- of￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- rate￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Kühnert￨U￨NN￨LOCATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Unlike￨U￨IN￨O￨- BDSIR￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- coalescent￨L￨JJ￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- require￨L￨VB￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- specified￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- organize￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- households￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- broadly￨L￨RB￨O￨- defined￨L￨VBN￨O￨- term￨L￨NN￨O￨- meant￨L￨VBD￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- “￨L￨``￨O￨- close￨L￨JJ￨O￨- ”￨L￨''￨O￨- contacts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- households￨L￨NNS￨O￨- are￨L￨VBP￨O￨- organized￨L￨VBN￨O￨- within￨L￨IN￨O￨- local￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- larger￨L￨JJR￨O￨- ,￨L￨,￨O￨- modularly￨L￨RB￨O￨- structured￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- less￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- and￨L￨CC￨O￨- less￨L￨RBR￨O￨- infectious￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- would￨L￨MD￨O￨- like￨L￨VB￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨MISC￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- network￨L￨NN￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- affected￨L￨VBN￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- daily￨L￨JJ￨SET￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨A rates￨L￨NNS￨O￨A and￨L￨CC￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- each￨L￨DT￨O￨- person￨L￨NN￨O￨- R￨U￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- naïve￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- 8￨L￨CD￨NUMBER￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- hospital￨L￨NN￨O￨- and￨L￨CC￨O￨- funereal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A rates￨L￨NNS￨O￨A ,￨L￨,￨O￨- predicts￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- transmissions￨L￨NNS￨O￨- from￨L￨IN￨O￨- funerals￨L￨NNS￨O￨- in￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- could￨L￨MD￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- faster￨L￨RBR￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- decreases￨L￨NNS￨O￨- quickly￨L￨RB￨O￨- to￨L￨TO￨O￨- values￨L￨NNS￨O￨- close￨L￨RB￨O￨A to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- significant￨L￨JJ￨O￨- saturation￨L￨NN￨O￨- effects￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- households￨L￨NNS￨O￨A and￨L￨CC￨O￨- communities￨L￨NNS￨O￨- of￨L￨IN￨O￨- households￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- country￨L￨NN￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- SEIR￨U￨NNP￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- to￨L￨TO￨O￨- end￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- by￨L￨IN￨O￨- pushing￨L￨VBG￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- below￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- patients￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- placed￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- Ebola￨U￨NNP￨O￨- Treatment￨U￨NN￨O￨- Centre￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- ETC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- 35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- isolated￨L￨VBN￨O￨- in￨L￨IN￨O￨- community￨L￨NN￨O￨- settings￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- and￨L￨CC￨O￨- safe￨L￨JJ￨O￨A burials￨L￨NNS￨O￨- are￨L￨VBP￨O￨- provided9￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- until￨L￨IN￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- aimed￨L￨VBN￨O￨- to￨L￨TO￨O￨- galvanize￨L￨VB￨O￨- support￨L￨NN￨O￨- for￨L￨IN￨O￨- multinational￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- by￨L￨IN￨O￨- demonstrating￨L￨VBG￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- long-term￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- delay￨L￨NN￨O￨A and￨L￨CC￨O￨- giving￨L￨VBG￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- needed9￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- interrupt￨L￨VB￨O￨- the￨L￨DT￨O￨- chains￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- prevent￨L￨VB￨O￨- further￨L￨JJ￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- initiated￨L￨VBN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- establishing￨L￨VBG￨O￨- Ebola￨U￨NNP￨ORGANIZATION￨- Treatment￨U￨NN￨ORGANIZATION￨- Centres￨U￨NNS￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- ETCs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- case￨L￨NN￨O￨- ascertainment￨L￨NN￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- promoting￨L￨VBG￨O￨- safe￨L￨JJ￨O￨A burial￨L￨NN￨O￨- practices2￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- reinforced￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- delay￨L￨NN￨O￨- is￨L￨VBZ￨O￨- devastating￨L￨VBG￨O￨- -￨L￨:￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- doubles￨L￨VBZ￨O￨- every￨L￨DT￨SET￨- 20￨L￨CD￨SET￨- days￨L￨NNS￨SET￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- the￨L￨DT￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- target￨L￨NN￨O￨A even￨L￨RB￨O￨- harder￨L￨RBR￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- semi-logarithmic￨L￨JJ￨O￨- scale￨L￨NN￨O￨- ,￨L￨,￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- is￨L￨VBZ￨O￨- evident￨L￨JJ￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- straight￨L￨JJ￨O￨- line￨L￨NN￨O￨- fits￨L￨VBZ￨O￨- well￨L￨RB￨O￨- several￨L￨JJ￨O￨- consecutive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- generations￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- curvature￨L￨NN￨O￨- in￨L￨IN￨O￨- semi-logarithmic￨L￨JJ￨O￨- scale￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- indicative￨L￨JJ￨O￨- of￨L￨IN￨O￨- sub-exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- as￨L￨IN￨O￨- illustrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- semi-logarithmic￨L￨JJ￨O￨- scale￨L￨NN￨O￨- ,￨L￨,￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- is￨L￨VBZ￨O￨- evident￨L￨JJ￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- straight￨L￨JJ￨O￨- line￨L￨NN￨O￨- fits￨L￨VBZ￨O￨- well￨L￨RB￨O￨- several￨L￨JJ￨O￨- consecutive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- generations￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- whereas￨L￨IN￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- curvature￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- indicative￨L￨JJ￨O￨- of￨L￨IN￨O￨- sub-exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- administrative￨L￨JJ￨O￨- division￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assessed￨L￨VBD￨O￨- whether￨L￨IN￨O￨- cumulative￨L￨JJ￨O￨- EVD￨U￨NN￨O￨- case￨L￨NN￨O￨- counts￨L￨VBZ￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- or￨L￨CC￨O￨- polynomial￨L￨JJ￨O￨- growth￨L￨NN￨O￨- during￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- 3￨L￨CD￨NUMBER￨- consecutive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- generations￨L￨NNS￨O￨A of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- about￨L￨IN￨DURATION￨- 6￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- is￨L￨VBZ￨O￨- ~￨L￨SYM￨O￨- 15￨L￨CD￨NUMBER￨- days12￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- fit￨L￨VB￨O￨- polynomial￨L￨JJ￨O￨- growth￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- borrowed￨L￨VBD￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- approach￨L￨NN￨O￨- used￨L￨VBD￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HIV/AIDS￨U￨NN￨O￨- epidemic17￨L￨NN￨O￨- and￨L￨CC￨O￨- fit￨L￨NN￨O￨- m-th￨L￨JJ￨O￨- degree￨L￨NN￨O￨- polynomials￨L￨NNS￨O￨- through￨L￨IN￨O￨- least-squares￨L￨NNS￨O￨- regression￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- over￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- generations￨L￨NNS￨O￨A ,￨L￨,￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- External￨U￨JJ￨O￨- flow￨L￨NN￨O￨A and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- three￨L￨CD￨NUMBER￨- typical￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- obvious￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- self-spreading￨L￨NN￨O￨- flow￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- spatial￨L￨JJ￨O￨- displacement￨L￨NN￨O￨- of￨L￨IN￨O￨- SARS￨U￨NN￨O￨- cases￨L￨NNS￨O￨- only￨L￨RB￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- province￨L￨NN￨O￨- or￨L￨CC￨O￨- municipality￨L￨NN￨O￨- of￨L￨IN￨O￨- onset￨L￨NN￨O￨- and￨L￨CC￨O￨- medical￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- hospitalized￨L￨VBN￨O￨- flow￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- spatial￨L￨JJ￨O￨- displacement￨L￨NN￨O￨- of￨L￨IN￨O￨- SARS￨U￨NN￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- seen￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- hospital￨L￨NN￨O￨- doctor￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- migrant￨L￨JJ￨O￨- flow￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- spatial￨L￨JJ￨O￨- displacement￨L￨NN￨O￨- of￨L￨IN￨O￨- SARS￨U￨NN￨O￨- cases￨L￨NNS￨O￨- among￨L￨IN￨O￨- migrant￨L￨JJ￨O￨- workers￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- studies￨L￨NNS￨O￨- were￨L￨VBD￨O￨- good￨L￨JJ￨O￨- at￨L￨IN￨O￨- reflecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- SARS￨U￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- area￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- interprovincial￨L￨JJ￨O￨- level.Information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SARS￨U￨NNP￨O￨- in-out￨L￨JJ￨O￨- flow￨L￨NN￨O￨A transmission￨L￨NN￨O￨- at￨L￨IN￨O￨- provincial￨L￨JJ￨O￨- level￨L￨NN￨O￨- in￨L￨IN￨O￨- Mainland￨U￨NNP￨LOCATION￨- China￨U￨NNP￨COUNTRY￨- helps￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- temporospatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- SARS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- reflect￨L￨VB￨O￨- the￨L￨DT￨O￨- interprovincial￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- paths￨L￨NNS￨O￨- and￨L￨CC￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SARS￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- used￨L￨VBD￨O￨- in-out￨L￨JJ￨O￨- flow￨L￨NN￨O￨A data￨L￨NNS￨O￨- at￨L￨IN￨O￨- provincial￨L￨JJ￨O￨- and￨L￨CC￨O￨- municipal￨L￨JJ￨O￨- level￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SARS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Mainland￨U￨NNP￨LOCATION￨- China￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- This￨U￨DT￨O￨- study￨L￨NN￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- in-out￨L￨JJ￨O￨- flow￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- flow￨L￨NN￨O￨- mapping￨L￨NN￨O￨- to￨L￨TO￨O￨- visualize￨L￨VB￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- SARS￨U￨NNP￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2003￨L￨CD￨DATE￨- ,￨L￨,￨O￨- SARS￨U￨NNP￨O￨- in-out￨L￨JJ￨O￨- flow￨L￨NN￨O￨A played￨L￨VBD￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- countrywide￨L￨NN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Mainland￨U￨NNP￨LOCATION￨- China￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- report￨L￨VBP￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- baseline￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- historical￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- transport￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- uniform￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- scenario￨L￨NN￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- countries￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- experienced￨L￨VBN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- 100￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- then￨L￨RB￨O￨- have￨L￨VBP￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- reduced￨L￨VBD￨O￨- outgoing￨L￨JJ￨O￨- traffic￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- scenario￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- higher￨L￨JJR￨O￨- economic￨L￨JJ￨O￨- status￨L￨NN￨O￨- countries￨L￨NNS￨O￨- have￨L￨VBP￨O￨- reduced￨L￨VBN￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- day￨L￨NN￨DURATION￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- an￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- individual￨L￨NN￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- travel￨L￨VB￨O￨- to￨L￨TO￨O￨- Australia￨U￨NNP￨COUNTRY￨- that￨L￨DT￨O￨- day￨L￨NN￨DURATION￨- was￨L￨VBD￨O￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- eligible￨L￨JJ￨O￨- to￨L￨TO￨O￨- fly￨L￨VB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- passengers￨L￨NNS￨O￨- arriving￨L￨VBG￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- exposed￨L￨VBN￨O￨- individual￨L￨JJ￨O￨- travelled￨L￨VBN￨O￨- to￨L￨TO￨O￨- Australia￨U￨NNP￨COUNTRY￨- on￨L￨IN￨O￨- or￨L￨CC￨O￨- before￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- T￨U￨NN￨O￨- is￨L￨VBZ￨O￨- :￨L￨:￨O￨- As￨U￨IN￨O￨- a￨L￨DT￨O￨- baseline￨L￨NN￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mean￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- 5.3￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- σ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/5￨L￨CD￨NUMBER￨- .3￨L￨NN￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- mean￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- 5.61￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/5￨L￨CD￨NUMBER￨- .61￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- reported￨L￨VBN￨O￨- by￨L￨IN￨O￨- Althaus￨U￨NNP￨PERSON￨- 12￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Guinea￨U￨NNP￨COUNTRY￨- were￨L￨VBD￨O￨- evolved￨L￨VBN￨O￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- Susceptible-Exposed-Infectious-Removed￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10￨L￨CD￨NUMBER￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- timesteps￨L￨NNS￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨A ;￨L￨:￨O￨- details￨L￨NNS￨O￨- in￨L￨IN￨O￨- Appendix￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- entry￨L￨NN￨O￨- into￨L￨IN￨O￨- Australia￨U￨NNP￨COUNTRY￨- was￨L￨VBD￨O￨- calculated￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- flying￨L￨VBG￨O￨- into￨L￨IN￨O￨- Australia￨U￨NNP￨COUNTRY￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- irrespective￨L￨RB￨O￨- of￨L￨IN￨O￨- stopovers￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- case￨L￨NN￨O￨- entering￨L￨VBG￨O￨- Australia￨U￨NNP￨COUNTRY￨- via￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- source￨L￨NN￨O￨- location￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- country￨L￨NN￨O￨A that￨L￨WDT￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- currently￨L￨RB￨DATE￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- network￨L￨NN￨O￨- secondary￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- constructed￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- outbreak￨L￨NN￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- short￨L￨JJ￨O￨- term￨L￨NN￨O￨- projections￨L￨NNS￨O￨- for￨L￨IN￨O￨- its￨L￨PRP$￨O￨- future￨L￨JJ￨DATE￨- development￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- increased￨L￨VBD￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- ,￨L￨,￨O￨- improved￨L￨VBD￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- PPE￨U￨NNP￨O￨- for￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- personnel￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pharmaceutical￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- survival￨L￨NN￨O￨- in￨L￨IN￨O￨- hospitalized￨L￨VBN￨O￨A patients￨L￨NNS￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- simultaneously￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- hospitalized￨L￨VBN￨O￨A cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- βH￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- increased￨L￨VBN￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- PPE￨U￨NNP￨O￨- as￨L￨IN￨O￨- supplies￨L￨NNS￨O￨- and￨L￨CC￨O￨- awareness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- increase￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- eliminating￨L￨VBG￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- post-mortem￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- hospitalized￨L￨VBN￨O￨- patients￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- inappropriate￨L￨JJ￨O￨- funereal￨L￨JJ￨O￨- practices￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- improved￨L￨JJ￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- by￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- diagnosed￨L￨VBN￨O￨- and￨L￨CC￨O￨- hospitalized￨L￨VBN￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- scenario￨L￨NN￨O￨- of￨L￨IN￨O￨- 51￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- 58￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- to￨L￨TO￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- concordant￨L￨JJ￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- it￨L￨PRP￨O￨- takes￨L￨VBZ￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- hospitalized￨L￨VBN￨O￨- by￨L￨IN￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- helpful￨L￨JJ￨O￨- under￨L￨IN￨O￨- these￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- by￨L￨IN￨O￨- providing￨L￨VBG￨O￨- forecasts￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- that￨L￨DT￨O￨- account￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- and￨L￨CC￨O￨- non-linear￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- projecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- proposed￨L￨VBN￨O￨- interventions￨L￨NNS￨O￨- before￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- implemented￨L￨VBN￨O￨- .￨L￨.￨O￨- +Third￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- both￨L￨CC￨O￨- a￨L￨DT￨O￨- simultaneous￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- decrease￨L￨VB￨O￨- in￨L￨IN￨O￨- βH￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- post-mortem￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- hospitalized￨L￨VBN￨O￨A cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- hospitalized￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- wildlife￨L￨NN￨O￨A ,￨L￨,￨O￨- CMR￨U￨NN￨O￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- well￨L￨RB￨O￨- suited￨L￨VBN￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- survival￨L￨NN￨O￨- rate￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- capture￨L￨NN￨O￨- or￨L￨CC￨O￨- encounter￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- particularly￨L￨RB￨O￨- important￨L￨JJ￨O￨- development￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- multi-state￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- transition￨L￨NN￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- uninfected￨L￨JJ￨O￨A states￨L￨NNS￨O￨- and￨L￨CC￨O￨- which￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- scientists￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- abiotic￨L￨JJ￨O￨- and￨L￨CC￨O￨- biotic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- influence￨L￨VBP￨O￨- the￨L￨DT￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- .￨L￨.￨O￨- +Such￨U￨PDT￨O￨- a￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- description￨L￨NN￨O￨- inevitably￨L￨RB￨O￨- requires￨L￨VBZ￨O￨- a￨L￨DT￨O￨- thorough￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- govern￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- wildlife￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- parameters￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- survival￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- pathogen-induced￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- virulence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- parasites￨L￨NNS￨O￨- can￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- that￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- uninfected￨L￨JJ￨O￨A animals￨L￨NNS￨O￨- often￨L￨RB￨O￨- have￨L￨VBP￨O￨- different￨L￨JJ￨O￨- capture￨L￨NN￨O￨- or￨L￨CC￨O￨- encounter￨L￨NN￨O￨- rates￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +CMR￨U￨NNP￨O￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- allow￨L￨VBP￨O￨- scientists￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- control￨L￨NN￨O￨- for￨L￨IN￨O￨- possible￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- detection￨L￨NN￨O￨- bias￨L￨NN￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- uninfected￨L￨JJ￨O￨A hosts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- r￨L￨NN￨O￨- eff￨L￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨A size￨L￨NN￨O￨A is￨L￨VBZ￨O￨- bimodal￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- roughly￨L￨RB￨O￨- Gaussian￨U￨JJ￨MISC￨- peak￨L￨NN￨O￨- centered￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- peak￨L￨NN￨O￨- for￨L￨IN￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- terminal￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- ”￨L￨''￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- fail￨L￨VB￨O￨- to￨L￨TO￨O￨- propagate￨L￨VB￨O￨- significantly￨L￨RB￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- peaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- separated￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- exceeds￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- progresses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- characterized￨L￨VBN￨O￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨A results￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Results￨U￨NNS￨O￨- we￨L￨PRP￨O￨- compute￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨A size￨L￨NN￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- regimes￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- and￨L￨CC￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- most￨L￨RBS￨O￨- significantly￨L￨RB￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- if￨L￨IN￨O￨- r￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- d￨L￨NN￨O￨- I/dt￨U￨NN￨O￨- <￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- will￨L￨MD￨O￨- decline￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- seed￨L￨NN￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ≤￨L￨NN￨O￨- I￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- will￨L￨MD￨O￨- occur￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compute￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- non-interacting￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨A case￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- that￨L￨IN￨O￨- organisms￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- faster￨L￨RBR￨O￨- life￨L￨NN￨O￨- history￨L￨NN￨O￨- are￨L￨VBP￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- short￨L￨JJ￨O￨- lived￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- shorter￨L￨JJR￨O￨- generation￨L￨NN￨O￨- times￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- larger￨L￨JJR￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- offspring￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- larger￨L￨JJR￨O￨- effective￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- might￨L￨MD￨O￨- at￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- expect￨L￨VBP￨O￨A that￨L￨IN￨O￨- a￨L￨DT￨O￨- beneficial￨L￨JJ￨O￨- insertion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- those￨L￨DT￨O￨- ERVs￨U￨NNS￨MISC￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- endogenous￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- element￨L￨NN￨O￨- derived￨L￨VBN￨O￨- immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EDI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- would￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- beneficial￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- would￨L￨MD￨O￨- spread￨L￨VB￨O￨- to￨L￨TO￨O￨- fixation￨L￨NN￨O￨- faster￨L￨RBR￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- than￨L￨IN￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- slower￨L￨JJR￨O￨- life￨L￨NN￨O￨- history￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- alternative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- ERV￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- influence￨L￨VB￨O￨- our￨L￨PRP$￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- active￨L￨JJ￨O￨- ERVs￨U￨NNS￨MISC￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- length￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- how￨L￨WRB￨O￨- long￨L￨RB￨O￨- does￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- take￨L￨VB￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- endogenous￨L￨JJ￨O￨- retroviral￨L￨JJ￨O￨- insertion￨L￨NN￨O￨- to￨L￨TO￨O￨- reach￨L￨VB￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- enough￨L￨JJ￨O￨- frequency￨L￨NN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- few￨L￨JJ￨O￨- whole￨L￨JJ￨O￨- genomes￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- sequenced￨L￨VBN￨O￨- ?￨L￨.￨O￨- )￨L￨-RRB-￨O￨- +Intuitively￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨- active￨L￨JJ￨O￨- ERVs￨U￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- incorporation/loss￨L￨NN￨O￨- —￨L￨:￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- varies￨L￨VBZ￨O￨- with￨L￨IN￨O￨- life￨L￨NN￨O￨A history￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- long￨L￨JJ￨O￨- they￨L￨PRP￨O￨- take￨L￨VBP￨O￨- to￨L￨TO￨O￨- run￨L￨VB￨O￨- their￨L￨PRP$￨O￨- course￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- fixation￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- locus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- call￨L￨VBP￨O￨- the￨L￨DT￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- severe￨L￨JJ￨O￨- footrot￨L￨NN￨O￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- spread￨L￨VBN￨O￨- to￨L￨TO￨O￨- six￨L￨CD￨NUMBER￨- counties￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- 16￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sheep￨L￨NN￨O￨A flocks￨L￨NNS￨O￨- if￨L￨IN￨O￨- no￨L￨DT￨O￨- elimination￨L￨NN￨O￨- programme￨L￨NN￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- initiated￨L￨VBN￨O￨- .￨L￨.￨O￨- +nodosus￨L￨NN￨O￨- strain￨L￨NN￨O￨- than￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- benign￨L￨JJ￨O￨- strain.Severe￨L￨NN￨O￨- footrot￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- diagnosed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- county￨L￨NN￨O￨A of￨L￨IN￨O￨- Rogaland￨U￨NNP￨LOCATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- south￨L￨JJ￨O￨- west￨L￨NN￨O￨- of￨L￨IN￨O￨- Norway￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- had￨L￨VBD￨O￨- spread￨L￨VBN￨O￨- to￨L￨TO￨O￨- two￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- 19￨L￨CD￨NUMBER￨- counties￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 119￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- sheep￨L￨NN￨O￨A flocks￨L￨NNS￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- diagnosed￨L￨VBN￨O￨- with￨L￨IN￨O￨- severe￨L￨JJ￨O￨- footrot￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- curb￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨A footrot￨L￨NN￨O￨- was￨L￨VBD￨O￨- by￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- within￨L￨IN￨O￨- county￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- that￨L￨IN￨O￨- severe￨L￨JJ￨O￨- footrot￨L￨NN￨O￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- spread￨L￨VBN￨O￨- to￨L￨TO￨O￨- 16￨L￨CD￨NUMBER￨- counties￨L￨NNS￨O￨- and￨L￨CC￨O￨- 64￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sheep￨L￨NN￨O￨A flocks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- these￨L￨DT￨O￨- findings￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- scrutinize￨L￨VB￨O￨- in￨L￨IN￨O￨- greater￨L￨JJR￨O￨- detail￨L￨NN￨O￨- how￨L￨WRB￨O￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- moreover￨L￨RB￨O￨- ,￨L￨,￨O￨- whether￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- particular￨L￨JJ￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨A that￨L￨WDT￨O￨- promote￨L￨VBP￨O￨- or￨L￨CC￨O￨- hinder￨L￨VBP￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- recent￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨A contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨- strongly￨L￨RB￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- disease2345￨L￨NN￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- looked￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- successive￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- strains￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- strain￨L￨NN￨O￨- modifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- manner￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- strain11121314￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨A contact￨L￨NN￨O￨A network￨L￨NN￨O￨- that￨L￨WDT￨O￨- facilitates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- lowers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fixation￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- invading￨L￨VBG￨O￨- strain￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- analytical￨L￨JJ￨O￨- and￨L￨CC￨O￨- simulation￨L￨NN￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- evolution￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- and￨L￨CC￨O￨- idealized￨L￨JJ￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- numerous￨L￨JJ￨O￨- researches￨L￨VBZ￨O￨- that￨L￨IN￨O￨- have￨L￨VBP￨O￨- discovered￨L￨VBN￨O￨- meteorological￨L￨JJ￨O￨A factors￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- various￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- drivers￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- or￨L￨CC￨O￨- its￨L￨PRP$￨O￨- seasonal￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- climates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Possible￨U￨JJ￨O￨- drivers￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- include￨L￨VBP￨O￨- meteorological￨L￨JJ￨O￨A variations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- small￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A could￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- amplification￨L￨NN￨O￨- and￨L￨CC￨O￨- damping￨L￨VBG￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- oscillations￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- sustain￨L￨VB￨O￨- a￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- subtropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- relationship￨L￨NN￨O￨- with￨L￨IN￨O￨- meteorological￨L￨JJ￨O￨A factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A hospitalization￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- P&I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- associated￨L￨VBN￨O￨- mortality￨L￨NN￨O￨- were￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 29￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 4.1￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- 100,000￨L￨CD￨NUMBER￨- person-years￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- highly￨L￨RB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- only￨L￨RB￨O￨- rarely￨L￨RB￨O￨- originate￨L￨VB￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- be￨L￨VB￨O￨- they￨L￨PRP￨O￨- pathogenic￨L￨JJ￨O￨- disease1213￨L￨NN￨O￨- ,￨L￨,￨O￨- innovative￨L￨JJ￨O￨- ideas14￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- chatter15￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- deep￨L￨JJ￨O￨- intellectual￨L￨JJ￨O￨- hunger￨L￨NN￨O￨- and￨L￨CC￨O￨- practical￨L￨JJ￨O￨- utility￨L￨NN￨O￨- in￨L￨IN￨O￨- accurately￨L￨RB￨O￨- measuring￨L￨VBG￨O￨- and￨L￨CC￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- spreading￨L￨NN￨O￨A process￨L￨NN￨O￨A without￨L￨IN￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- inevitably￨L￨RB￨O￨- reaches￨L￨VBZ￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- connected￨L￨JJ￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- seed￨L￨NN￨O￨- node￨L￨NN￨O￨- predicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- before￨L￨IN￨O￨- half￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- large￨L￨JJ￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reached￨L￨VBN￨O￨- .￨L￨.￨O￨- +Thirty￨U￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- innovation￨L￨NN￨O￨- have￨L￨VBP￨O￨- refined￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- nodes￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- influential￨L￨JJ￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- almost￨L￨RB￨O￨- any￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- network￨L￨NN￨O￨- via￨L￨IN￨O￨- features￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- betweenness￨L￨NN￨O￨- centrality23￨L￨NN￨O￨- ,￨L￨,￨O￨- eigenvalue￨L￨JJ￨O￨- centrality4￨L￨NN￨O￨- ,￨L￨,￨O￨- degree5￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- k-shell6￨L￨NN￨O￨- .￨L￨.￨O￨- +Yet￨U￨RB￨O￨- highly￨L￨RB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- rare￨L￨JJ￨O￨- by￨L￨IN￨O￨- definition￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- just￨L￨RB￨O￨- listed￨L￨VBN￨O￨- measures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- informative￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- vast￨L￨JJ￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- node￨L￨NN￨O￨- 's￨L￨POS￨O￨- spreading￨L￨VBG￨O￨- power￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- push￨L￨VB￨O￨- a￨L￨DT￨O￨- spreading￨L￨NN￨O￨A process￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- highly￨L￨RB￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- varying￨L￨VBG￨O￨- birth￨L￨NN￨O￨A rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- models￨L￨NNS￨O￨- allowing￨L￨VBG￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- levels￨L￨NNS￨O￨- can￨L￨MD￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- switching￨L￨NN￨O￨- from￨L￨IN￨O￨- annual￨L￨JJ￨SET￨- epidemics￨L￨NNS￨O￨- to￨L￨TO￨O￨- irregular￨L￨JJ￨O￨- and￨L￨CC￨O￨- multiennial￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- in￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- immunizing￨L￨VBG￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- long-term￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- birth￨L￨NN￨O￨A and￨L￨CC￨O￨- immigration￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- immune￨L￨JJ￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- μ￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- δ￨L￨VB￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- lose￨L￨VBP￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- analyse￨L￨VBP￨O￨- the￨L￨DT￨O￨- buffering￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- framework￨L￨NN￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- standard￨L￨JJ￨O￨- models￨L￨NNS￨O￨- predict￨L￨VBP￨O￨- that￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- should￨L￨MD￨O￨- become￨L￨VB￨O￨- less￨L￨RBR￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- birth￨L￨NN￨O￨A rate￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- buffering￨L￨VBG￨O￨- increases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- slope￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- regression￨L￨NN￨O￨- line￨L￨NN￨O￨- of￨L￨IN￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- birth￨L￨NN￨O￨A rate￨L￨NN￨O￨- against￨L￨IN￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- buffering￨L￨VBG￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- demographics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- To￨U￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproductive￨L￨JJ￨O￨A ratio￨L￨NN￨O￨A R0￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-infected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- type￨L￨NN￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproductive￨L￨JJ￨O￨A ratio￨L￨NN￨O￨A R0￨U￨NN￨O￨- for￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- resulted￨L￨VBD￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 1.757￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 1.9￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- corrected￨L￨VBN￨O￨- and￨L￨CC￨O￨- uncorrected￨L￨JJ￨O￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- We￨U￨PRP￨O￨- obtained￨L￨VBD￨O￨- robust￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- Ebola￨U￨NNP￨MISC￨- outbreak￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- close￨L￨JJ￨O￨- agreement￨L￨NN￨O￨- between￨L￨IN￨O￨- our￨L￨PRP$￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +2015Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Ebola￨U￨NNP￨O￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- reemerged￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- crisis￨L￨NN￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- isolated￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- also￨L￨RB￨O￨- observed￨L￨VBD￨O￨- globally￨L￨RB￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- outbreak￨L￨NN￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Article￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Estimating￨U￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproductive￨L￨JJ￨O￨A ratio￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨ORGANIZATION￨- LeoneAdnan￨U￨NNP￨O￨- Khan1￨U￨NN￨O￨- ,￨L￨,￨O￨- Mahim￨U￨NNP￨O￨- Naveed2￨U￨NN￨O￨- ,￨L￨,￨O￨- Muhammad￨U￨NNP￨PERSON￨- Dur-e-Ahmad3￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Mudassar￨U￨NNP￨PERSON￨- Imran4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 4:13￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Khan￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨O￨- Central￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- predictions￨L￨NNS￨O￨- leveraged￨L￨VBD￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- previous￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models34￨L￨NN￨O￨- that￨L￨WDT￨O￨- encapsulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- EVD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- tracking￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- interactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- including￨L￨VBG￨O￨- Susceptible￨U￨NNP￨O￨- ,￨L￨,￨O￨- Exposed￨U￨VBN￨O￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨O￨- and￨L￨CC￨O￨- Removed￨U￨VBN￨O￨- types￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- EVD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨A occurs￨L￨VBZ￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- average￨L￨JJ￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- T.￨U￨FW￨O￨- +The￨U￨DT￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- denoted￨L￨VBN￨O￨A as￨L￨IN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- between￨L￨IN￨O￨- states￨L￨NNS￨O￨- A￨U￨DT￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- remission￨L￨NN￨O￨- rate￨L￨NN￨O￨- r.￨L￨NNP￨O￨- Mortality￨U￨NNP￨O￨- rates￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- respective￨L￨JJ￨O￨- states￨L￨NNS￨O￨- are￨L￨VBP￨O￨- denoted￨L￨VBN￨O￨- m￨L￨NN￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- m￨L￨NN￨O￨- B.￨U￨NNP￨O￨- All￨U￨NNP￨O￨- rates￨L￨NNS￨O￨- may￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- calendar￨L￨NN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- age￨L￨NN￨O￨- a.￨L￨NN￨O￨- Living￨U￨VBG￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- aged￨L￨VBD￨O￨- a￨L￨DT￨O￨- at￨L￨IN￨O￨- calendar￨L￨NN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- are￨L￨VBP￨O￨- either￨L￨RB￨O￨- in￨L￨IN￨O￨- state￨L￨NN￨O￨- A￨U￨NN￨O￨- or￨L￨CC￨O￨- state￨L￨NN￨O￨- B.￨U￨NNP￨O￨- +The￨U￨DT￨O￨- transitions￨L￨NNS￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- compartment￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- are￨L￨VBP￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- rates￨L￨NNS￨O￨A that￨L￨WDT￨O￨- may￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- calendar￨L￨NN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- age-structured￨L￨JJ￨O￨- models￨L￨NNS￨O￨- also￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- a￨L￨DT￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- argue￨L￨VBP￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- multi-host￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- at￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- levels￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- population-level￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- shared￨L￨VBN￨O￨- by￨L￨IN￨O￨- all￨L￨DT￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- species￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sampled￨L￨VBN￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- niche￨L￨NN￨O￨- breadth￨L￨NN￨O￨- ,￨L￨,￨O￨- sociality￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- abundance￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- individual￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- parasite￨L￨JJ￨O￨A acquisition￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- age￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- sex￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- immunocompetence￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Unlike￨U￨IN￨O￨- host-parasite￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- attempt￨L￨VBP￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- parasite￨L￨JJ￨O￨A spread￨L￨NN￨O￨- among￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- species￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Epidemiological￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- unipartite￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- contain￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- edges￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- or￨L￨CC￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- individual-based￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- meaningful￨L￨JJ￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨NN￨O￨A in￨L￨IN￨O￨- question￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Forecasting￨U￨NN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A activity￨L￨NN￨O￨A could￨L￨MD￨O￨- inform￨L￨VB￨O￨- decisions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- and￨L￨CC￨O￨- assist￨L￨VB￨O￨- with￨L￨IN￨O￨- stockpiling￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- planning￨L￨NN￨O￨- of￨L￨IN￨O￨- additional￨L￨JJ￨O￨- hospital￨L￨NN￨O￨- bed￨L￨NN￨O￨- capacity￨L￨NN￨O￨- to￨L￨TO￨O￨- meet￨L￨VB￨O￨- high￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- demand￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Serfling￨U￨VBG￨PERSON￨- regression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- originally￨L￨RB￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Serfling￨U￨VBG￨ORGANIZATION￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A baseline￨L￨NN￨O￨- establishment￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- estimation￨L￨NN￨O￨- using￨L￨VBG￨O￨- cleaned￨L￨VBN￨O￨- historical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- harmonic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A activity￨L￨NN￨O￨A during￨L￨IN￨O￨- all￨L￨DT￨O￨- non-epidemic￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- stationary￨L￨JJ￨O￨- from￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- to￨L￨TO￨DURATION￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- this￨L￨DT￨O￨- adjusted￨L￨JJ￨O￨A Serfling￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- events￨L￨NNS￨O￨- over￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- non-adjusted￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨DATE￨- week￨L￨NN￨DATE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A isolations￨L￨NNS￨O￨- each￨L￨DT￨O￨- season￨L￨NN￨O￨- was￨L￨VBD￨O￨- commonly￨L￨RB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- peak￨L￨NN￨O￨- week￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +PVs￨U￨NNS￨O￨- contain￨L￨VBP￨O￨- a￨L￨DT￨O￨- circular￨L￨JJ￨O￨- double-stranded￨L￨JJ￨O￨- DNA￨U￨NN￨MISC￨- genome￨L￨NN￨O￨- of￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 8￨L￨CD￨NUMBER￨- kb￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- organized￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- an￨L￨DT￨O￨- upstream￨L￨JJ￨O￨- regulatory￨L￨JJ￨O￨- region￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- URR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- harbouring￨L￨VBG￨O￨- transcription￨L￨NN￨O￨- factor-binding￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- and￨L￨CC￨O￨- controlling￨L￨VBG￨O￨- gene￨L￨NN￨O￨- expression￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- an￨L￨DT￨O￨- early￨L￨JJ￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- encoding￨L￨VBG￨O￨- for￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- genes￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- including￨L￨VBG￨O￨- viral￨L￨JJ￨O￨- replication￨L￨NN￨O￨- and￨L￨CC￨O￨- cell￨L￨NN￨O￨- transformation￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- late￨L￨JJ￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- encoding￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- L1￨U￨NN￨O￨- and￨L￨CC￨O￨- L2￨U￨NN￨O￨- capsid￨L￨NN￨O￨- proteins￨L￨NNS￨O￨A which￨L￨WDT￨O￨- self-assemble￨L￨VBP￨O￨- to￨L￨TO￨O￨- yield￨L￨VB￨O￨- the￨L￨DT￨O￨- virion￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- late-phase￨L￨NN￨O￨- L1￨U￨NN￨O￨- and￨L￨CC￨O￨- L2￨U￨NN￨O￨- proteins￨L￨NNS￨O￨A encapsidate￨L￨VBP￨O￨- newly￨L￨RB￨O￨- synthesized￨L￨VBN￨O￨- viral￨L￨JJ￨O￨- genomes￨L￨NNS￨O￨- and￨L￨CC￨O￨- virions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- shed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- uppermost￨L￨NN￨O￨- layers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epithelium￨L￨NN￨O￨- The￨U￨DT￨O￨- best-studied￨L￨JJS￨O￨- PV￨U￨NN￨O￨- is￨L￨VBZ￨O￨- HPV16￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mucosotropic￨L￨JJ￨O￨- PV￨U￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- anogenital￨L￨JJ￨O￨- cancers￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- clinical￨L￨JJ￨O￨- manifestations￨L￨NNS￨O￨- of￨L￨IN￨O￨- PV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨A genotype￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- genotype￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- epithelium￨L￨NN￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- phenotype￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- cell￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- nutritional￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- life￨L￨NN￨O￨A cycle￨L￨NN￨O￨A described￨L￨VBN￨O￨- below￨L￨IN￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- HPV16￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- although￨L￨IN￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- PVs￨U￨NNS￨O￨- ,￨L￨,￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- productive/silent￨L￨JJ￨O￨- ,￨L￨,￨O￨- chronic/acute￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- evolved￨L￨VBN￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- vary￨L￨VB￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- PV￨U￨NN￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- examined￨L￨VBN￨O￨- the￨L￨DT￨O￨- relationships￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- structures￨L￨NNS￨O￨- ,￨L￨,￨O￨- few￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- hierarchical￨L￨JJ￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- directly￨L￨RB￨O￨- from￨L￨IN￨O￨- census￨L￨NN￨O￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- modeled￨L￨VBD￨O￨- physical￨L￨JJ￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A using￨L￨VBG￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- urban￨L￨JJ￨O￨- traffic￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- built￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- actual￨L￨JJ￨O￨- census￨L￨NN￨O￨- ,￨L￨,￨O￨- land-use￨L￨NN￨O￨- and￨L￨CC￨O￨- population-mobility￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Every￨U￨DT￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- demographical￨L￨JJ￨O￨- profile￨L￨NN￨O￨- contains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- hierarchical￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- cross-district￨L￨JJ￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A between￨L￨IN￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- age-structured￨L￨JJ￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A on￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- for￨L￨IN￨O￨- studies￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- associations￨L￨NNS￨O￨- between￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨A factors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- with￨L￨IN￨O￨- GLMs￨U￨NNS￨O￨- and￨L￨CC￨O￨- GAMs￨U￨NNS￨O￨- ,￨L￨,￨O￨- aiming￨L￨VBG￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- methodological￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- analyses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Time￨U￨NNP￨O￨- series￨L￨NN￨O￨A analysis￨L￨NN￨O￨- usually￨L￨RB￨O￨- follows￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- or￨L￨CC￨O￨- community￨L￨NN￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- requires￨L￨VBZ￨O￨- health￨L￨NN￨O￨- outcome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dependent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- exposure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- independent￨L￨JJ￨RELIGION￨- )￨L￨-RRB-￨O￨- variables￨L￨NNS￨O￨- measured￨L￨VBN￨O￨- repeatedly￨L￨RB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- on￨L￨IN￨O￨- daily￨L￨JJ￨SET￨- or￨L￨CC￨O￨- weekly￨L￨JJ￨SET￨- basis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- differences￨L￨NNS￨O￨- might￨L￨MD￨O￨- consequently￨L￨RB￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- when￨L￨WRB￨O￨- applying￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A method￨L￨NN￨O￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- no￨L￨DT￨O￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- has￨L￨VBZ￨O￨- summarized￨L￨VBN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- considerations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Though￨U￨IN￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A analysis￨L￨NN￨O￨- in￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- studies￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- non-infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- being￨L￨VBG￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- manner￨L￨NN￨O￨- .￨L￨.￨O￨- +Time￨U￨NNP￨O￨- series￨L￨NN￨O￨A regression￨L￨NN￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- practiced￨L￨VBN￨O￨- in￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- molecular￨L￨JJ￨O￨- research￨L￨NN￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- has￨L￨VBZ￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- schistosome￨L￨NN￨O￨- parasite￨L￨NN￨O￨A Schistosoma￨U￨NN￨O￨- mansoni￨L￨NNS￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- New￨U￨NNP￨LOCATION￨- World￨U￨NNP￨LOCATION￨- snail￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- Biomphalaria￨U￨NN￨O￨- glabrata￨L￨NN￨O￨- ,￨L￨,￨O￨- recently￨L￨RB￨DATE￨- aided￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨- sequenced￨L￨VBN￨O￨- genomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- species￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- transcriptomic￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +mansoni￨L￨NN￨O￨- from￨L￨IN￨O￨- natural￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Guadeloupe￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- West￨U￨NNP￨LOCATION￨- Indies￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- 40￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- snails￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- matter￨L￨NN￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- parasite￨L￨JJ￨O￨A miracidia￨L￨NN￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- challenge￨L￨VB￨O￨- them￨L￨PRP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Among￨U￨IN￨O￨- 289￨L￨CD￨NUMBER￨- snails￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- R￨U￨NN￨O￨- allele￨L￨NN￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- GRC￨U￨NNP￨ORGANIZATION￨- locus￨L￨NN￨O￨- grc1￨L￨NN￨O￨- is￨L￨VBZ￨O￨- strongly￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- resistance￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- fashion￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Colombian￨U￨JJ￨NATIONALITY￨- National￨U￨NNP￨ORGANIZATION￨- Epidemiological￨U￨NNP￨ORGANIZATION￨- Surveillance￨U￨NNP￨ORGANIZATION￨- System￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- SIVIGILA￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- estimated￨L￨VBN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- was￨L￨VBD￨O￨- 65.6￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- 100,000￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- reported￨L￨VBN￨O￨- severe￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- death￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- severity￨L￨NN￨O￨- :￨L￨:￨O￨- non-severe￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A with￨L￨IN￨O￨- or￨L￨CC￨O￨- without￨L￨IN￨O￨- warning￨L￨VBG￨O￨- signs￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- severe￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- encompasses￨L￨VBZ￨O￨- DHF￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- DSS￨U￨NN￨ORGANIZATION￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- countries￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- notified￨L￨VBN￨O￨- in￨L￨IN￨O￨- excess￨L￨NN￨O￨- of￨L￨IN￨O￨- 1.6￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- symptomatic￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- categorized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- :￨L￨:￨O￨- undifferentiated￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- dengue￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- DF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- dengue￨L￨JJ￨O￨- haemorrhagic￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- DHF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Historically￨U￨NNP￨O￨- ,￨L￨,￨O￨- Colombia￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- most￨L￨RBS￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- first￨L￨JJ￨ORDINAL￨- recognized￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- both￨L￨DT￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- management.Keywordseconomic￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- epidemiological￨L￨JJ￨O￨- economics￨L￨NNS￨O￨- incentives￨L￨NNS￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- Economic￨U￨NNP￨O￨- Epidemiology￨U￨NNP￨O￨- and￨L￨CC￨O￨- Epidemiological￨U￨JJ￨O￨- EconomicsEconomic￨U￨JJ￨O￨- behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- play￨L￨VB￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 464￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 475￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asMerging￨L￨NN￨O￨- Economics￨U￨NNP￨O￨- and￨L￨CC￨O￨- Epidemiology￨U￨NNP￨O￨- to￨L￨TO￨O￨- Improve￨U￨VB￨O￨- the￨L￨DT￨O￨- Prediction￨U￨NN￨O￨- and￨L￨CC￨O￨- Management￨U￨NN￨O￨- of￨L￨IN￨O￨- Infectious￨U￨JJ￨O￨- DiseaseAuthorsAuthors￨U￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsCharles￨L￨NNS￨O￨- PerringsCarlos￨U￨NNP￨MISC￨- Castillo-ChavezGerardo￨U￨NNP￨MISC￨- ChowellPeter￨U￨NNP￨MISC￨- DaszakEli￨U￨NNP￨MISC￨- P.￨U￨NNP￨MISC￨- Classical￨U￨JJ￨MISC￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- standard￨L￨NN￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- and￨L￨CC￨O￨- managing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- assume￨L￨VB￨O￨- that￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- frequency￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- addresses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- feedbacks￨L￨NNS￨O￨- between￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- decisions￨L￨NNS￨O￨- driving￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- contact￨L￨NN￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- reason￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A —￨L￨:￨O￨- typically￨L￨RB￨O￨- lists￨L￨NNS￨O￨- of￨L￨IN￨O￨- anonymized￨L￨JJ￨O￨- id￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- times￨L￨NNS￨O￨- when￨L￨WRB￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- close￨L￨RB￨O￨- enough￨L￨RB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- spread￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- point￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reason￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- showing￨L￨VBG￨O￨- who￨L￨WP￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- whom￨L￨WP￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- what￨L￨WP￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- representation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- time￨L￨NN￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Structure￨U￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- refers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- differs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨A network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- can￨L￨MD￨O￨- happen￨L￨VB￨O￨- with￨L￨IN￨O￨- any￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- equal￨L￨JJ￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- e.g.￨L￨FW￨O￨- a￨L￨FW￨O￨- broad￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- interevent￨L￨JJ￨O￨- times￨L￨NNS￨O￨- slows￨L￨VBZ￨O￨- down￨L￨RP￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- describing￨L￨VBG￨O￨- who￨L￨WP￨O￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- whom￨L￨WP￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Six￨U￨CD￨NUMBER￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- models￨L￨NNS￨O￨- included￨L￨VBD￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- minimum￨L￨NN￨O￨A and￨L￨CC￨O￨- maximum￨L￨JJ￨O￨- temperatures￨L￨NNS￨O￨- estimated￨L￨VBN￨O￨- across￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- ;￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 15￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 22￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 30￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- tadpole￨L￨NN￨O￨- sampling￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- analyses￨L￨NNS￨O￨- were￨L￨VBD￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- using￨L￨VBG￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- average￨L￨JJ￨O￨- minimum￨L￨JJ￨O￨A and￨L￨CC￨O￨- maximum￨L￨JJ￨O￨- temperatures￨L￨NNS￨O￨- across￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 15￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 22￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 30￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- tadpole￨L￨VB￨O￨- sampling￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Site￨U￨NN￨O￨- was￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- factor￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- average￨L￨JJ￨O￨- minimum￨L￨NN￨O￨A and￨L￨CC￨O￨- maximum￨L￨NN￨O￨- daily￨L￨JJ￨SET￨- water￨L￨NN￨O￨- temperatures￨L￨NNS￨O￨- ,￨L￨,￨O￨- tadpole￨L￨NN￨O￨- abundance￨L￨NN￨O￨- and￨L￨CC￨O￨- tadpole￨L￨NN￨O￨- development￨L￨NN￨O￨- as￨L￨IN￨O￨- covariates￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- seventh￨L￨JJ￨ORDINAL￨- model￨L￨NN￨TITLE￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- include￨L￨VB￨O￨- any￨L￨DT￨O￨- temperature￨L￨NN￨O￨A measurement￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- averaged￨L￨VBD￨O￨- Bd￨U￨NNP￨O￨- loads￨L￨NNS￨O￨- of￨L￨IN￨O￨- tadpoles￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- interconnected￨L￨JJ￨O￨A small-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- rewiring￨L￨NN￨O￨- probability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- interconnected￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- decreases￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- rewiring￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- small-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- increases￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- above￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨A ,￨L￨,￨O￨- λ￨L￨NN￨O￨- ≥￨L￨NN￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- will￨L￨MD￨O￨- spread￨L￨VB￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- will￨L￨MD￨O￨- ultimately￨L￨RB￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- non-zero￨L￨JJ￨O￨- steady-state￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- density￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ρ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rewiring￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interconnected￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- illustrated￨L￨VBN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- constraint￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interconnection￨L￨NN￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- lattices￨L￨NNS￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A threshold￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- density￨L￨NN￨O￨- .￨L￨.￨O￨- +Variations￨U￨NNS￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- circulating￨L￨VBG￨O￨- respiratory￨L￨JJ￨O￨A virus￨L￨NN￨O￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- circulating￨L￨VBG￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strain￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- climatic￨L￨JJ￨O￨- variability￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- driving￨L￨VBG￨O￨- force￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- availability￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- limiting￨L￨VBG￨O￨- resource￨L￨NN￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- role￨L￨NN￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- explored￨L￨VBN￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- RSV￨U￨NN￨O￨- .￨L￨.￨O￨- +Every￨U￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infects￨L￨VBZ￨O￨A approximately￨L￨RB￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- and￨L￨CC￨O￨- 5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- adults￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- RSV￨U￨NN￨O￨- infects￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- children￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- three￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- life￨L￨NN￨O￨- ;￨L￨:￨O￨- re-infections￨L￨NNS￨O￨- by￨L￨IN￨O￨- these￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- very￨L￨RB￨O￨- common￨L￨JJ￨O￨- during￨L￨IN￨O￨- early￨L￨JJ￨O￨- childhood￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Also￨U￨RB￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- suggested￨L￨VBN￨O￨- that￨L￨IN￨O￨- interference￨L￨NN￨O￨- between￨L￨IN￨O￨- RSV￨U￨NN￨O￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A may￨L￨MD￨O￨- occur￨L￨VB￨O￨- ;￨L￨:￨O￨- several￨L￨JJ￨O￨- reports￨L￨NNS￨O￨- have￨L￨VBP￨O￨- described￨L￨VBN￨O￨- the￨L￨DT￨O￨- interruption￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- circulation￨L￨NN￨O￨- by￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Influenza￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- respiratory￨L￨JJ￨O￨A syncytial￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RSV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- leading￨L￨VBG￨O￨- etiologic￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- of￨L￨IN￨O￨- acute￨L￨JJ￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ARI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- reported￨L￨VBN￨O￨- that￨L￨IN￨O￨- RSV￨U￨NN￨O￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A exhibit￨L￨VBP￨O￨- an￨L￨DT￨O￨- alternating￨L￨VBG￨O￨- pattern￨L￨NN￨O￨- in￨L￨IN￨O￨- San￨U￨NNP￨CITY￨- Luis￨U￨NNP￨CITY￨- Potosí￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- SLP￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- drug￨L￨NN￨O￨A variety￨L￨NN￨O￨- delays￨L￨NNS￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- increased￨L￨VBN￨O￨- drug￨L￨NN￨O￨- variety￨L￨NN￨O￨- comes￨L￨VBZ￨O￨- with￨L￨IN￨O￨- additional￨L￨JJ￨O￨- operational￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sourced￨L￨JJ￨O￨- treatments￨L￨NNS￨O￨- ,￨L￨,￨O￨- increased￨L￨VBN￨O￨- drug￨L￨NN￨O￨A variety￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- higher￨L￨JJR￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- procuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- increased￨L￨VBD￨O￨- inventory￨L￨NN￨O￨- holding￨L￨NN￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- cases￨L￨NNS￨O￨- may￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- increased￨L￨VBN￨O￨- healthcare￨L￨NN￨O￨- worker￨L￨NN￨O￨- training￨L￨NN￨O￨- costs￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- studies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- tradeoff￨L￨NN￨O￨- between￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨- and￨L￨CC￨O￨- operational￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- when￨L￨WRB￨O￨- using￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Also￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- demand￨L￨NN￨O￨- is￨L￨VBZ￨O￨- uncertain￨L￨JJ￨O￨- ,￨L￨,￨O￨- wider￨L￨JJR￨O￨- drug￨L￨NN￨O￨A variety￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- implies￨L￨VBZ￨O￨- higher￨L￨JJR￨O￨- safety￨L￨NN￨O￨- stocks￨L￨NNS￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- higher￨L￨JJR￨O￨- inventory￨L￨NN￨O￨- holding￨L￨VBG￨O￨- costs￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- method￨L￨NN￨O￨- combining￨L￨VBG￨O￨- hierarchical￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- personal￨L￨JJ￨O￨A contact￨L￨NN￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- agent-based￨L￨JJ￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- diffusion￨L￨NN￨O￨- within￨L￨IN￨O￨- terminal￨L￨JJ￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- hierarchical￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- personal￨L￨JJ￨O￨A contact￨L￨NN￨O￨- network￨L￨NN￨O￨- was￨L￨VBD￨O￨- defined￨L￨VBN￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- complex￨L￨NN￨O￨- relationship￨L￨NN￨O￨- of￨L￨IN￨O￨- passengers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Influences￨U￨NNPS￨MISC￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- terminal￨L￨JJ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- hierarchical￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- personal￨L￨JJ￨O￨A contact￨L￨NN￨O￨- networkQuan￨L￨NN￨O￨- Shao1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Meng￨U￨NN￨O￨- Jia1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 15:257￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Shao￨U￨NNP￨O￨- and￨L￨CC￨O￨- Jia￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨O￨- Central￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- quantitatively￨L￨RB￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- influences￨L￨NNS￨O￨A of￨L￨IN￨O￨- passenger￨L￨NN￨O￨- source￨L￨NN￨O￨- ,￨L￨,￨O￨- immunity￨L￨NN￨O￨- difference￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- relation￨L￨NN￨O￨- structure￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- terminal￨L￨JJ￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- improved￨L￨VBN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- crystals￨L￨NNS￨O￨- clearly￨L￨RB￨O￨- varied￨L￨VBD￨O￨- in￨L￨IN￨O￨- shape￨L￨NN￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨- as￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- progressed￨L￨VBN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- CaOx￨U￨NN￨O￨- crystals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- present￨L￨JJ￨DATE￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- plant￨L￨NN￨O￨- surface￨L￨NN￨O￨A ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- inside￨L￨JJ￨O￨- stem￨L￨NN￨O￨- tissue￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- hyphal￨L￨JJ￨O￨- conglomerations￨L￨NNS￨O￨- within￨L￨IN￨O￨- lesions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- CaOx￨U￨NN￨O￨- crystals￨L￨NNS￨O￨- after￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- S.￨U￨NNP￨O￨- napus￨L￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- surface￨L￨NN￨O￨A of￨L￨IN￨O￨- sunflower￨L￨NN￨O￨- hypocotyls￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- penetration￨L￨NN￨O￨- sites￨L￨NNS￨O￨- on￨L￨IN￨O￨- leaves￨L￨NNS￨O￨- and￨L￨CC￨O￨- roots￨L￨NNS￨O￨- of￨L￨IN￨O￨- carrot￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- CaOx￨U￨NN￨O￨- crystals￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- S.￨U￨NNP￨O￨- +sclerotiorum￨L￨NN￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- lost￨L￨VBN￨O￨A the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- oxalic￨L￨JJ￨O￨- acid￨L￨NN￨O￨- also￨L￨RB￨O￨- have￨L￨VBP￨O￨- lost￨L￨VBN￨O￨- their￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +sclerotiorum￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- stems￨L￨VBZ￨O￨- of￨L￨IN￨O￨- Brassica￨U￨NNP￨LOCATION￨- carinata￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Ethiopian￨U￨JJ￨NATIONALITY￨- mustard￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- calcium￨L￨NN￨O￨- oxalate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CaOx￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- crystals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- observed￨L￨VBN￨O￨A .￨L￨.￨O￨- +Multiple￨U￨JJ￨O￨- viral￨L￨JJ￨O￨- lineages￨L￨NNS￨O￨- co-circulate￨L￨VBP￨O￨- in￨L￨IN￨O￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- swine￨L￨NNS￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ‘￨L￨``￨O￨- classical￨L￨JJ￨O￨- ’￨L￨''￨O￨- Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- pandemic￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ‘￨L￨``￨O￨- triple￨L￨JJ￨O￨- reassortant￨L￨NN￨O￨- ’￨L￨''￨O￨- Citation￨U￨NNP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- ,￨L￨,￨O￨- swine￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- avian￨L￨JJ￨O￨- segments￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ‘￨L￨``￨O￨- delta￨L￨NN￨O￨- ’￨L￨''￨O￨- (￨L￨-LRB-￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- viruses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- H1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- these￨L￨DT￨O￨- findings￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- build￨L￨VBP￨O￨- a￨L￨DT￨O￨- meta-population￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- dissemination￨L￨NN￨O￨- of￨L￨IN￨O￨- swIAVs￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- scale￨L￨NN￨O￨- and￨L￨CC￨O￨- identify￨L￨VB￨O￨- regions￨L￨NNS￨O￨- at￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- co-invasion￨L￨NN￨O￨- of￨L￨IN￨O￨- divergent￨L￨JJ￨O￨- lineages￨L￨NNS￨O￨A ,￨L￨,￨O￨- increased￨L￨VBD￨O￨- total￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- with￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- potential￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- swine￨L￨NNS￨O￨A are￨L￨VBP￨O￨- spatially￨L￨RB￨O￨- separated￨L￨VBN￨O￨- into￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- and￨L￨CC￨O￨- European￨U￨JJ￨NATIONALITY￨- swIAV￨L￨NN￨O￨- lineages￨L￨NNS￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- of￨L￨IN￨O￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- and￨L￨CC￨O￨- European￨U￨JJ￨NATIONALITY￨- origin￨L￨NN￨O￨- both￨L￨CC￨O￨- circulate￨L￨VBP￨O￨- in￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- virus￨L￨NN￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- composition￨L￨NN￨O￨- that￨L￨WDT￨O￨- had￨L￨VBD￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- swine￨L￨NNS￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- genome￨L￨NN￨O￨- segments￨L￨NNS￨O￨- of￨L￨IN￨O￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- triple￨L￨JJ￨O￨- reassortant￨L￨NN￨O￨- swine￨L￨NNS￨O￨- virus￨L￨NN￨O￨- origin￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PB2￨U￨NN￨O￨- ,￨L￨,￨O￨- PB1￨U￨NN￨O￨- ,￨L￨,￨O￨- PA￨U￨NN￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- HA￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- NP￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- NS￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- genome￨L￨NN￨O￨- segments￨L￨NNS￨O￨- of￨L￨IN￨O￨- Eurasian￨U￨JJ￨MISC￨- avian-like￨L￨JJ￨O￨- swine￨L￨NNS￨O￨- virus￨L￨NN￨O￨- origin￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NA￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- MP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- reassortant￨L￨NN￨O￨- H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- virus￨L￨NN￨O￨- with￨L￨IN￨O￨- gene￨L￨NN￨O￨- segments￨L￨NNS￨O￨- from￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- swine￨L￨NNS￨O￨A virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- swIAV￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- lineages￨L￨NNS￨O￨- emerged￨L￨VBD￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- initiating￨L￨VBG￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 21st￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- observing￨L￨VBG￨O￨- the￨L￨DT￨O￨- tweet￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- correction￨L￨NN￨O￨- tweet￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- mentions￨L￨VBZ￨O￨- clearly￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A tweets￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- chemically￨L￨RB￨O￨- contaminated￨L￨VBN￨O￨- rain￨L￨NN￨O￨- were￨L￨VBD￨O￨- scientifically￨L￨RB￨O￨- false￨L￨JJ￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- submitted￨L￨VBN￨O￨- at￨L￨IN￨O￨- 19:30￨L￨CD￨TIME￨- on￨L￨IN￨TIME￨- March￨U￨NNP￨DATE￨- 11￨L￨CD￨DATE￨- ,￨L￨,￨O￨- just￨L￨RB￨O￨- 90￨L￨CD￨DURATION￨- minutes￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- appearance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- rumor￨L￨NN￨O￨- tweet￨L￨NN￨O￨- .￨L￨.￨O￨- +Note￨U￨VB￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- user￨L￨NN￨O￨- who￨L￨WP￨O￨- actually￨L￨RB￨O￨- started￨L￨VBD￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A ,￨L￨,￨O￨- because￨L￨IN￨O￨- some￨L￨DT￨O￨- users￨L￨NNS￨O￨- who￨L￨WP￨O￨- tweeted￨L￨VBD￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- have￨L￨VBP￨O￨- already￨L￨RB￨O￨- deleted￨L￨VBN￨O￨- their￨L￨PRP$￨O￨- tweets￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- appear￨L￨VB￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Obviously￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- correction￨L￨NN￨O￨- tweet￨L￨NN￨O￨- could￨L￨MD￨O￨- not￨L￨RB￨O￨- stop￨L￨VB￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- show￨L￨VBP￨O￨- an￨L￨DT￨O￨- overview￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- rumor￨L￨NN￨O￨A diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- we￨L￨PRP￨O￨- explain￨L￨VBP￨O￨- how￨L￨WRB￨O￨- a￨L￨DT￨O￨- correction￨L￨NN￨O￨- tweet￨L￨NN￨O￨- sent￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- city￨L￨NN￨O￨- hall￨L￨NN￨O￨- account￨L￨NN￨O￨- diffused￨L￨VBD￨O￨- enormously￨L￨RB￨O￨- by￨L￨IN￨O￨- retweets￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- this￨L￨DT￨O￨- stage￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A tweets￨L￨NNS￨O￨- grew￨L￨VBD￨O￨- much￨L￨JJ￨O￨- faster￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor-correction￨L￨JJ￨O￨- tweets￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +H3N2￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- also￨L￨RB￨O￨- exhibit￨L￨VBP￨O￨- strong￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- in￨L￨IN￨O￨- temperate￨L￨JJ￨O￨- climate￨L￨NN￨O￨- regions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Australia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- New￨U￨NNP￨COUNTRY￨- Zealand￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- mainly￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- lineages￨L￨NNS￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨DT￨O￨- H1N1￨U￨NN￨O￨- and￨L￨CC￨O￨- H3N2￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- well￨L￨RB￨O￨- documented￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- scale￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- equivalent￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨O￨- virus￨L￨NN￨O￨- lineages￨L￨NNS￨O￨A —￨L￨:￨O￨- B/Yamagata/16￨U￨NN￨O￨- /￨L￨:￨O￨- 88-like￨L￨JJ￨O￨- and￨L￨CC￨O￨- B/Victoria/2￨U￨NN￨O￨- /￨L￨:￨O￨- 87-like￨L￨JJ￨O￨- ,￨L￨,￨O￨- henceforth￨L￨JJ￨O￨- termed￨L￨VBN￨O￨- the￨L￨DT￨O￨- Yamagata￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Victoria￨U￨NNP￨CITY￨- viruses￨L￨NNS￨O￨- —￨L￨:￨O￨- are￨L￨VBP￨O￨- poorly￨L￨RB￨O￨- understood￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- similar￨L￨JJ￨O￨- but￨L￨CC￨O￨- weaker￨L￨JJR￨O￨- evolutionary￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- H1N1￨U￨NN￨O￨- viruses￨L￨NNS￨O￨A that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- circulated￨L￨VBN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- previous￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- (￨L￨-LRB-￨O￨- 1918￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1957￨L￨CD￨DATE￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2009￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- short-term￨L￨JJ￨O￨- co-circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- diverging￨L￨VBG￨O￨- virus￨L￨NN￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NNP￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- two￨L￨CD￨NUMBER￨- subtypes￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- and￨L￨CC￨O￨- H3N2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- lineages￨L￨NNS￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- co-circulate￨L￨VBP￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- cause￨L￨VB￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- type￨L￨NN￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- viruses￨L￨NNS￨O￨A are￨L￨VBP￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- similarities￨L￨NNS￨O￨- in￨L￨IN￨O￨- genome￨L￨NN￨O￨- organization￨L￨NN￨O￨- and￨L￨CC￨O￨- protein￨L￨NN￨O￨- structure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- exhibit￨L￨VBP￨O￨- important￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- ecology￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Increasingly￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- perceived￨L￨VBN￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- exploit￨L￨VB￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- sources￨L￨NNS￨O￨A in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- ensuring￨L￨VBG￨O￨- decision-making￨L￨NN￨O￨- on￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- policies￨L￨NNS￨O￨- geared￨L￨VBN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- progressively￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- as￨L￨RB￨O￨- many￨L￨JJ￨O￨- diverse￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- requirement￨L￨NN￨O￨- ,￨L￨,￨O￨- supported￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- continued￨L￨JJ￨O￨- progress￨L￨NN￨O￨- in￨L￨IN￨O￨- computational￨L￨JJ￨O￨- power￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- encouraged￨L￨VBN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- increasingly￨L￨RB￨O￨A complex￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- require￨L￨VBP￨O￨- rich￨L￨JJ￨O￨- arrays￨L￨NNS￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- guarantee￨L￨VB￨O￨- parameter￨L￨NN￨O￨- identifiability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- irrespective￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- modellers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- faced￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- task￨L￨NN￨O￨- of￨L￨IN￨O￨- integrating￨L￨VBG￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- many￨L￨JJ￨O￨- heterogeneous￨L￨JJ￨O￨- sources￨L￨NNS￨O￨A of￨L￨IN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Policy￨U￨NN￨O￨- makers￨L￨NNS￨O￨- want￨L￨VBP￨O￨- ‘￨L￨``￨O￨- defendable￨L￨JJ￨O￨- ’￨L￨''￨O￨- models￨L￨NNS￨O￨- that￨L￨IN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- realistically￨L￨RB￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- ,￨L￨,￨O￨- crucially￨L￨RB￨O￨- ,￨L￨,￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- outputs￨L￨NNS￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- all￨L￨DT￨O￨- relevant￨L￨JJ￨O￨A available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- typically￨L￨RB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- data￨L￨NNS￨O￨- source￨L￨NN￨O￨- directly￨L￨RB￨O￨- informing￨L￨VBG￨O￨- each￨L￨DT￨O￨- relevant￨L￨JJ￨O￨A parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +Current￨U￨JJ￨DATE￨- birth-death￨L￨JJ￨O￨- models￨L￨NNS￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- phylodynamic￨L￨JJ￨O￨- inference￨L￨NN￨O￨- assume￨L￨VB￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- sampling￨L￨NN￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- history￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- biased￨L￨VBN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- quantities￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A when￨L￨WRB￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- misspecified￨L￨VBN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- sampling￨L￨NN￨O￨A has￨L￨VBZ￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- sampling￨L￨NN￨O￨- protocols￨L￨NNS￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- sequences￨L￨NNS￨O￨- at￨L￨IN￨O￨- specific￨L￨JJ￨O￨- points￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- result￨L￨NN￨O￨- in￨L￨IN￨O￨- more￨L￨JJR￨O￨- accurate￨L￨JJ￨O￨- inference￨L￨NN￨O￨- using￨L￨VBG￨O￨- coalescent￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- vast￨L￨JJ￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- phylodynamic￨L￨JJ￨O￨A studies￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- a￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- coalescent￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- specifies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- changes￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- are￨L￨VBP￨O￨- deterministic￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- Frost￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Volz￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +New￨U￨NNP￨O￨- conceptual￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- added￨L￨VBN￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- may￨L￨MD￨O￨- shape￨L￨VB￨O￨- a￨L￨DT￨O￨- phylogeny￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- ‘￨L￨``￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A ’￨L￨''￨O￨- relates￨L￨VBZ￨O￨- to￨L￨TO￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +Publicly￨U￨RB￨O￨- available￨L￨JJ￨O￨- software￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- BEAST￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- enabled￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- complex￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨A models￨L￨NNS￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- objectives￨L￨NNS￨O￨- were￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- construction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- phantom￨L￨JJ￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- iron￨L￨NN￨O￨- overload￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- liver￨L￨NN￨O￨A by￨L￨IN￨O￨- MRI￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- validated￨L￨VBN￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- LIC￨U￨NN￨ORGANIZATION￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- MRI￨U￨NNP￨O￨- devices￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- phantom￨L￨JJ￨O￨- and￨L￨CC￨O￨- patients￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- goal￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- phantom￨L￨JJ￨O￨- with￨L￨IN￨O￨- various￨L￨JJ￨O￨- different￨L￨JJ￨O￨- concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- iron￨L￨NN￨O￨- solution￨L￨NN￨O￨- that￨L￨WDT￨O￨- gave￨L￨VBD￨O￨- SIRs￨U￨NNS￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- with￨L￨IN￨O￨- moderate￨L￨JJ￨O￨A or￨L￨CC￨O￨- high￨L￨JJ￨O￨- iron￨L￨NN￨O￨- overload￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- phantoms￨L￨NNS￨O￨- simulating￨L￨VBG￨O￨- liver￨L￨NN￨O￨A with￨L￨IN￨O￨- iron￨L￨NN￨O￨- overload￨L￨NN￨O￨- in￨L￨IN￨O￨- MRI￨U￨NNP￨MISC￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- transferability￨L￨NN￨O￨- of￨L￨IN￨O￨- results￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- calibrate￨L￨VB￨O￨- different￨L￨JJ￨O￨- equipment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- attractive￨L￨JJ￨O￨- for￨L￨IN￨O￨- ethical￨L￨JJ￨O￨- ,￨L￨,￨O￨- financial￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- practical￨L￨JJ￨O￨- reasons￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Outbreaks￨U￨NNS￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Middle￨U￨NNP￨LOCATION￨- East￨U￨NNP￨LOCATION￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨- coronavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MERS-CoV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- monkeypox￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- have￨L￨VBP￨O￨- generally￨L￨RB￨O￨- occurred￨L￨VBN￨O￨- as￨L￨IN￨O￨- ‘￨L￨``￨O￨- stuttering￨L￨JJ￨O￨- chains￨L￨NNS￨O￨A ’￨L￨POS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- generating￨L￨VBG￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- linked￨L￨VBN￨O￨- clusters￨L￨NNS￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- without￨L￨IN￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- sustained￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- existing￨L￨VBG￨O￨- techniques￨L￨NNS￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- from￨L￨IN￨O￨- outbreak￨L￨NN￨O￨A size￨L￨NN￨O￨A data￨L￨NNS￨O￨- generally￨L￨RB￨O￨- represent￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- using￨L￨VBG￨O￨- single-type￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- made￨L￨VBD￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- observation￨L￨NN￨O￨- by￨L￨IN￨O￨- developing￨L￨VBG￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- age-structured￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- stuttering￨L￨NN￨O￨- transmission￨L￨NN￨O￨- chains￨L￨NNS￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- combined￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- multi-type￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- we￨L￨PRP￨O￨- derived￨L￨VBD￨O￨- an￨L￨DT￨O￨- expression￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨A size￨L￨NN￨O￨A distribution￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- age-stratified￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- depended￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- physical￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- POLYMOD￨U￨NN￨O￨- survey￨L￨NN￨O￨- in￨L￨IN￨O￨- Great￨U￨NNP￨COUNTRY￨- Britain￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Pre-existing￨U￨JJ￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- older￨L￨JJR￨O￨- age￨L￨NN￨O￨A groups￨L￨NNS￨O￨A can￨L￨MD￨O￨- alter￨L￨VB￨O￨- this￨L￨DT￨O￨- pattern￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- it￨L￨PRP￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- separate￨L￨VB￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- into￨L￨IN￨O￨- its￨L￨PRP$￨O￨- pathogenand￨L￨NN￨O￨- population-specific￨L￨JJ￨O￨- components￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- computational￨L￨JJ￨O￨A enzymology￨L￨NN￨O￨- is￨L￨VBZ￨O￨- examined.KeywordsMathematical￨L￨JJ￨O￨- biologyEpidemiological￨L￨JJ￨O￨- modelsCellular￨L￨JJ￨O￨- physiological￨L￨JJ￨O￨- modelsCancer￨L￨NN￨O￨- modelsMaximum￨L￨NN￨O￨- entropyMolecular￨L￨JJ￨O￨- dynamicsForce￨L￨NN￨O￨- fieldsSolvation￨L￨NN￨O￨- free￨L￨JJ￨O￨- energiesQuantum￨L￨NN￨O￨- mechanicsComputational￨L￨JJ￨O￨- enzymology￨L￨NN￨O￨- IntroductionMathematical￨U￨NNP￨O￨- ,￨L￨,￨O￨- computational￨L￨JJ￨O￨- and￨L￨CC￨O￨- physical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- in￨L￨IN￨O￨- biology￨L￨NN￨O￨- and￨L￨CC￨O￨- medicine￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- phenomena￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- down￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- atoms￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- biomolecule￨L￨NN￨O￨- .￨L￨.￨O￨- +2014Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractA￨U￨NNP￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- topics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- reviewed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨A modeling￨L￨NN￨O￨- in￨L￨IN￨O￨- biology￨L￨NN￨O￨- ,￨L￨,￨O￨- covering￨L￨VBG￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- scales￨L￨NNS￨O￨- from￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- organisms￨L￨NNS￨O￨- to￨L￨TO￨O￨- electrons￨L￨NNS￨O￨- in￨L￨IN￨O￨- atoms￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- technique￨L￨NN￨O￨- of￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- covered￨L￨VBN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- special￨L￨JJ￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- force￨L￨VB￨O￨- fields￨L￨NNS￨O￨- for￨L￨IN￨O￨- protein￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- solvation￨L￨NN￨O￨- free￨L￨JJ￨O￨- energies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨A methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- areas￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- cell￨L￨NN￨O￨- physiology￨L￨NN￨O￨- and￨L￨CC￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- surveyed￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- utility￨L￨NN￨O￨- of￨L￨IN￨O￨- quantum￨L￨NN￨O￨- mechanical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨A in￨L￨IN￨O￨- biophysical￨L￨JJ￨O￨- and￨L￨CC￨O￨- biochemical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- explored￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- complete￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models20￨L￨NN￨O￨- have￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- valuable￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- some￨L￨DT￨O￨- instances￨L￨NNS￨O￨- ,￨L￨,￨O￨- estimates￨L￨NNS￨O￨A of￨L￨IN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- in￨L￨IN￨O￨- agreement￨L￨NN￨O￨- ,￨L￨,￨O￨- implying￨L￨VBG￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- used￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- data￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- independent￨L￨JJ￨RELIGION￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨A rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- corroborate￨L￨VB￨O￨- previous￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- case￨L￨NN￨O￨- reporting￨L￨VBG￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- analysis￨L￨NN￨O￨- by￨L￨IN￨O￨- Althaus￨U￨NNP￨PERSON￨- modeled￨L￨VBD￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- mean￨L￨JJ￨O￨- 5.3￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- before￨L￨IN￨O￨- cases￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- by￨L￨IN￨O￨- Fisman￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Epidemiology￨U￨NN￨MISC￨- of￨L￨IN￨MISC￨- Trypanosoma￨U￨FW￨MISC￨- evansi￨L￨FW￨O￨- and￨L￨CC￨O￨- Trypanosoma￨U￨FW￨PERSON￨- vivax￨L￨NN￨O￨- in￨L￨IN￨O￨- domestic￨L￨JJ￨O￨A animals￨L￨NNS￨O￨- from￨L￨IN￨O￨- selected￨L￨VBN￨O￨- districts￨L￨NNS￨O￨- of￨L￨IN￨O￨- Tigray￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Afar￨U￨NNP￨LOCATION￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- Northern￨U￨JJ￨MISC￨- EthiopiaHadush￨U￨NN￨MISC￨- Birhanu1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Regassa￨U￨NN￨O￨- Fikru2￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mussa￨U￨NNP￨PERSON￨- Said5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Weldu￨U￨NNP￨O￨- Kidane1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Tadesse￨U￨NNP￨PERSON￨- Gebrehiwot1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Ashenafi￨U￨NNP￨PERSON￨- Hagos4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Tola￨U￨NNP￨O￨- Alemu4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Tesfaye￨U￨NNP￨PERSON￨- Dawit6￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Dirk￨U￨NNP￨PERSON￨- Berkvens3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Bruno￨U￨NNP￨PERSON￨- Maria￨U￨NNP￨PERSON￨- Goddeeris2￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Philippe￨U￨NNP￨PERSON￨- Büscher3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 8:212￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Birhanu￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨O￨- Central￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- investigates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- non-tsetse￨L￨JJ￨O￨- transmitted￨L￨JJ￨O￨- animal￨L￨NN￨O￨- trypanosomosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NTTAT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- Trypanosoma￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- T.￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- evansi￨L￨NNS￨O￨- and￨L￨CC￨O￨- T.￨U￨FW￨O￨- vivax￨L￨NN￨O￨- in￨L￨IN￨O￨- domestic￨L￨JJ￨O￨A animals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tsetse-free￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- Northern￨U￨JJ￨LOCATION￨- Ethiopia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Afar￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Tigray￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +evansi￨L￨NN￨O￨- and￨L￨CC￨O￨- RoTat￨U￨NN￨O￨- 1.2￨L￨CD￨NUMBER￨- immune￨L￨JJ￨O￨- trypanolysis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ITL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- buffy￨L￨JJ￨O￨- coat￨L￨NN￨O￨- specimens￨L￨NNS￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨A for￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- diagnosis￨L￨NN￨O￨- with￨L￨IN￨O￨- T.￨U￨FW￨O￨- evansi￨L￨FW￨O￨- type￨L￨NN￨O￨- A￨U￨NN￨O￨- specific￨L￨JJ￨O￨- RoTat￨U￨NN￨O￨- 1.2￨L￨CD￨NUMBER￨- PCR￨U￨NN￨O￨- ,￨L￨,￨O￨- T.￨U￨FW￨O￨- +Plasma￨U￨NN￨O￨- was￨L￨VBD￨O￨- collected￨L￨VBN￨O￨A for￨L￨IN￨O￨- serodiagnosis￨L￨NN￨O￨- with￨L￨IN￨O￨- CATT/T￨U￨NN￨O￨- .￨L￨.￨O￨- +Examples￨U￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- pathogen￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- respond￨L￨VBP￨O￨- to￨L￨TO￨O￨- provisioning￨L￨VBG￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- anthropogenic￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- provided￨L￨VBN￨O￨- ,￨L￨,￨O￨- pathogens￨L￨NNS￨O￨- affected￨L￨VBD￨O￨- and￨L￨CC￨O￨- observed￨L￨VBD￨O￨- impacts￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- conceptual￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- how￨L￨WRB￨O￨- provisioning￨L￨VBG￨O￨- affects￨L￨VBZ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- wildlife￨L￨NN￨O￨A and￨L￨CC￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- practical￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- growing￨L￨VBG￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- anthropogenic￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- can￨L￨MD￨O￨- alter￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- pathogen￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- either￨L￨CC￨O￨- increased￨L￨VBN￨O￨- or￨L￨CC￨O￨- decreased￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- wildlife￨L￨NN￨O￨A and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- provisioning￨L￨VBG￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- particular￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- pathogen￨L￨NN￨O￨- interaction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Table1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- next￨L￨RB￨O￨- conduct￨L￨VB￨O￨- a￨L￨DT￨O￨- meta-analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- to￨L￨TO￨O￨- characterise￨L￨VB￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- outcomes￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- provisioning￨L￨VBG￨O￨- and￨L￨CC￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- pathogen￨L￨NN￨O￨A and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- whether￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- increase￨L￨VBP￨O￨- or￨L￨CC￨O￨- decrease￨L￨VBP￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- anthropogenic￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- especially￨L￨RB￨O￨- important￨L￨JJ￨O￨- given￨L￨VBN￨O￨- that￨L￨IN￨O￨- provisioning￨L￨VBG￨O￨- frequently￨L￨RB￨O￨- brings￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- into￨L￨IN￨O￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- could￨L￨MD￨O￨- facilitate￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- shifts￨L￨NNS￨O￨- and￨L￨CC￨O￨- novel￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- emergence￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- consequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- wildlife￨L￨NN￨O￨A conservation￨L￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- health￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- start￨L￨VBP￨O￨- by￨L￨IN￨O￨- reviewing￨L￨VBG￨O￨- empirical￨L￨JJ￨O￨- support￨L￨NN￨O￨- for￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- mechanisms￨L￨NNS￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- provisioning￨L￨VBG￨O￨- can￨L￨MD￨O￨- affect￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- pathogen￨L￨NN￨O￨A interactions￨L￨NNS￨O￨- by￨L￨IN￨O￨- altering￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- host￨L￨NN￨TITLE￨- immune￨L￨JJ￨O￨- defences￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- host￨L￨NN￨TITLE￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- movement￨L￨NN￨O￨- behaviours￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- host￨L￨NN￨TITLE￨- demography￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- contaminated￨L￨VBN￨O￨- environment￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- FMDV￨U￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- used￨L￨VBD￨O￨- calves￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- vaccinated￨L￨VBN￨O￨- and￨L￨CC￨O￨- calves￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- vaccinated￨L￨VBN￨O￨- 1￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- inoculation￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨- contact￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Quantification￨U￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- foot-and-mouth￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- environment￨L￨NN￨O￨A contaminated￨L￨VBN￨O￨- with￨L￨IN￨O￨- secretions￨L￨NNS￨O￨- and￨L￨CC￨O￨- excretions￨L￨NNS￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- calvesCarla￨L￨NN￨MISC￨- Bravo￨U￨NNP￨MISC￨- de￨L￨IN￨MISC￨- Rueda1￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mart￨U￨NNP￨O￨- CM￨U￨NN￨O￨- de￨L￨IN￨O￨- Jong2Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Phaedra￨U￨NNP￨PERSON￨- L￨U￨NNP￨O￨- Eblé1￨U￨NN￨O￨- and￨L￨CC￨O￨- Aldo￨U￨NNP￨O￨- Dekker1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 46:43￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Bravo￨U￨NNP￨O￨- de￨L￨IN￨O￨- Rueda￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨O￨- Central￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- was￨L￨VBD￨O￨- done￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- linear￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- route￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2R￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- environment￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- included￨L￨VBD￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- FMDV￨U￨NN￨O￨- survival￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- .￨L￨.￨O￨- +2015Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractFoot-and-mouth￨U￨NNP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FMDV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- can￨L￨MD￨O￨- contaminate￨L￨VB￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨A with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- secretions￨L￨NNS￨O￨- and￨L￨CC￨O￨- excretions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Secretions￨U￨NNS￨O￨- and￨L￨CC￨O￨- excretions￨L￨NNS￨O￨- from￨L￨IN￨O￨- all￨L￨DT￨O￨- calves￨L￨NNS￨O￨- were￨L￨VBD￨O￨- tested￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- FMDV￨U￨NN￨O￨- by￨L￨IN￨O￨- virus￨L￨NN￨O￨- isolation￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨A FMDV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Red￨U￨NNP￨O￨- Queen￨U￨NNP￨TITLE￨- manifests￨L￨VBZ￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- experimental￨L￨JJ￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- silico￨L￨NN￨O￨- studies914212223￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- illustrations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- demonstrate￨L￨VBP￨O￨- fluctuating￨L￨VBG￨O￨- Red￨U￨NNP￨O￨- Queen￨U￨NNP￨TITLE￨- dynamics￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- parasites￨L￨NNS￨O￨A exceed￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- valuable￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨A types￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- qualitative￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- Red￨U￨NNP￨O￨- Queen￨U￨NNP￨TITLE￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- include￨L￨VBP￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- circulating￨L￨VBG￨O￨- bacteria￨L￨NNS￨O￨- away￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- targets￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- antigens￨L￨NNS￨O￨- ;￨L￨:￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- decline￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- levels￨L￨NNS￨O￨- ;￨L￨:￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- VE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and/or￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- shift￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- acellular￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- ;￨L￨:￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- manufactured￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨- with￨L￨IN￨O￨- lower￨L￨JJR￨O￨- efficacy￨L￨NN￨O￨- ;￨L￨:￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- decline￨L￨NN￨O￨- of￨L￨IN￨O￨- natural￨L￨NN￨O￨- boosting￨L￨VBG￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- reduced￨L￨VBN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- naturally￨L￨RB￨O￨- circulating￨L￨VBG￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- bacteria￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- successful￨L￨JJ￨O￨- mass-vaccination￨L￨NN￨O￨- ;￨L￨:￨O￨- 5￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- An￨U￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- reporting￨L￨NN￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- improved￨L￨VBN￨O￨- diagnostics￨L￨NNS￨O￨- and￨L￨CC￨O￨- surveillance￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- includes￨L￨VBZ￨O￨- both￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- and￨L￨CC￨O￨- naturally-induced￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨A waning￨L￨VBG￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- vaccination￨L￨NN￨O￨- schedule￨L￨NN￨O￨- administered￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underreporting￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- decreased￨L￨VBN￨O￨- infectiousness￨L￨NN￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- experienced￨L￨VBN￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- parsimonious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- best￨L￨JJS￨O￨- fitting￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Model￨U￨NNP￨TITLE￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- efficacy￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- whole-cell￨L￨JJ￨O￨- and￨L￨CC￨O￨- acellular￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨- of￨L￨IN￨O￨- whole-cell￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- and￨L￨CC￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- fit￨L￨VBP￨O￨- the￨L￨DT￨O￨- output￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- 20￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨A of￨L￨IN￨O￨- age-stratified￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- National￨U￨NNP￨O￨- Notifiable￨U￨JJ￨O￨- Diseases￨U￨NNS￨CAUSE_OF_DEATH￨- Surveillance￨U￨NNP￨O￨- System￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- NNDSS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- hybrid￨L￨NN￨O￨A epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- exploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- optimum￨L￨JJ￨O￨- balance￨L￨NN￨O￨- between￨L￨IN￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- are￨L￨VBP￨O￨- local￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- only￨L￨RB￨O￨- infect￨L￨VBP￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- target￨L￨NN￨O￨- nodes3￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- fully-mixed￨L￨JJ￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- infect￨L￨VB￨O￨- any￨L￨DT￨O￨- other￨L￨JJ￨O￨- node41￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- based￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- analysis31￨L￨NN￨O￨- ,￨L￨,￨O￨- hybrid￨L￨NN￨O￨A epidemics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- structured￨L￨JJ￨O￨- populations8￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- structured￨L￨JJ￨O￨- households91011￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- networked￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- with￨L￨IN￨O￨- “￨L￨``￨O￨- two￨L￨CD￨NUMBER￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨- ”￨L￨''￨O￨- 121314￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Early￨U￨RB￨O￨- relevant￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- investigated￨L￨VBD￨O￨- epidemics￨L￨NNS￨O￨- spreading￨L￨VBG￨O￨A in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- nodes￨L￨NNS￨O￨- mix￨L￨VBP￨O￨- at￨L￨IN￨O￨- both￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- “￨L￨``￨O￨- two￨L￨CD￨NUMBER￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- 7￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- hybrid￨L￨NN￨O￨A epidemics￨L￨NNS￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- larger￨L￨JJR￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- methods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- purely￨L￨RB￨O￨- analytical￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- very￨L￨RB￨O￨- reliable￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- others￨L￨NNS￨O￨- are￨L￨VBP￨O￨- mathematical￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- population￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- separately￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- using￨L￨VBG￨O￨- outbreak￨L￨NN￨O￨A data￨L￨NNS￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- estimate￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- means￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨A and￨L￨CC￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +ASF￨U￨NN￨ORGANIZATION￨- outbreaks￨L￨NNS￨O￨A are￨L￨VBP￨O￨- not￨L￨RB￨O￨- reported￨L￨VBN￨O￨- quickly￨L￨RB￨O￨- enough￨L￨RB￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- collection￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- required￨L￨VBN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- describe￨L￨VBP￨O￨- different￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- R￨U￨NN￨O￨- from￨L￨IN￨O￨- outbreak￨L￨NN￨O￨A data￨L￨NNS￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- across￨L￨IN￨O￨- different￨L￨JJ￨O￨- geographical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Estimates￨U￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- fundamental￨L￨JJ￨O￨- in￨L￨IN￨O￨- underpinning￨L￨VBG￨O￨- rational￨L￨JJ￨O￨A control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- This￨U￨DT￨O￨- review￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- quick￨L￨JJ￨O￨- guide￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- computational￨L￨JJ￨O￨A approaches￨L￨NNS￨O￨- that￨L￨WDT￨O￨- apply￨L￨VBP￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- principles￨L￨NNS￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- selection￨L￨NN￨O￨- to￨L￨TO￨O￨- real￨L￨JJ￨O￨- life￨L￨NN￨O￨- problems￨L￨NNS￨O￨- –￨L￨:￨O￨- from￨L￨IN￨O￨- drug￨L￨NN￨O￨- target￨L￨NN￨O￨- validation￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- design￨L￨NN￨O￨- and￨L￨CC￨O￨- protein￨L￨NN￨O￨- engineering￨L￨NN￨O￨- to￨L￨TO￨O￨- applications￨L￨NNS￨O￨- in￨L￨IN￨O￨- agriculture￨L￨NN￨O￨- ,￨L￨,￨O￨- ecology￨L￨NN￨O￨- and￨L￨CC￨O￨- conservation￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- Darwin￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- selection￨L￨NN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- remains￨L￨VBZ￨O￨- relevant￨L￨JJ￨O￨- today￨L￨NN￨DATE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- solid￨L￨JJ￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- computational￨L￨JJ￨O￨A research￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +2015Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Today￨U￨NNP￨DATE￨- computational￨L￨JJ￨O￨- molecular￨L￨JJ￨O￨A evolution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vibrant￨L￨JJ￨O￨- research￨L￨NN￨O￨- field￨L￨NN￨O￨- that￨L￨WDT￨O￨- benefits￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- and￨L￨CC￨O￨- complex￨L￨JJ￨O￨- new￨L￨JJ￨O￨- generation￨L￨NN￨O￨- sequencing￨L￨NN￨O￨- data￨L￨NNS￨O￨- –￨L￨:￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- full￨L￨JJ￨O￨- genomes￨L￨NNS￨O￨- and￨L￨CC￨O￨- proteomes￨L￨NNS￨O￨- to￨L￨TO￨O￨- microbiomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- metabolomes￨L￨NNS￨O￨- and￨L￨CC￨O￨- epigenomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- molecular￨L￨JJ￨O￨A clock￨L￨NN￨O￨- served￨L￨VBD￨O￨- as￨L￨IN￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- Kimura￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- neutral￨L￨JJ￨IDEOLOGY￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- selection￨L￨NN￨O￨- had￨L￨VBD￨O￨- no￨L￨DT￨O￨- significant￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- shaping￨L￨VBG￨O￨- genomes￨L￨NNS￨O￨- with￨L￨IN￨O￨- most￨L￨JJS￨O￨- genetic￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- being￨L￨VBG￨O￨- selectively￨L￨RB￨O￨- neutral￨L￨JJ￨IDEOLOGY￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- I￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- computational￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- selection￨L￨NN￨O￨- in￨L￨IN￨O￨- molecular￨L￨JJ￨O￨A sequences￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- argue￨L￨VBP￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- heuristic￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- placement￨L￨NN￨O￨- of￨L￨IN￨O￨- sensors￨L￨NNS￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- for￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- properly￨L￨RB￨O￨- placed￨L￨VBN￨O￨- sensors￨L￨NNS￨O￨- can￨L￨MD￨O￨- detect￨L￨VB￨O￨- contagious￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- before￨L￨IN￨O￨- they￨L￨PRP￨O￨- happen￨L￨VB￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- by￨L￨IN￨O￨- taking￨L￨VBG￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- informative￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Borrowing￨U￨VBG￨O￨- the￨L￨DT￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- amplification￨L￨NN￨O￨- of￨L￨IN￨O￨- stimuli￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- excitable￨L￨JJ￨O￨- elements￨L￨NNS￨O￨- are￨L￨VBP￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A :￨L￨:￨O￨- the￨L￨DT￨O￨- stimuli￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- excitable￨L￨JJ￨O￨- system￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- treated￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- detected￨L￨VBN￨O￨- influence￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- occurring￨L￨VBG￨O￨- simultaneously￨L￨RB￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- and￨L￨CC￨O￨- distinguish￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- recent￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- inferred￨L￨VBN￨O￨- by￨L￨IN￨O￨- placing￨L￨VBG￨O￨- sensors￨L￨NNS￨O￨A in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- this￨L￨DT￨O￨- idea￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- deploy￨L￨VB￨O￨- excitable￨L￨JJ￨O￨- sensor￨L￨NN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨A systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- violation￨L￨NN￨O￨- on￨L￨IN￨O￨- inferences￨L￨NNS￨O￨- and￨L￨CC￨O￨- projections￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- performed￨L￨VBD￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- generated￨L￨VBD￨O￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- fit￨L￨VB￨O￨A the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- raw￨L￨JJ￨O￨- and￨L￨CC￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- curves￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- inexpensive￨L￨JJ￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- common￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- formulate￨L￨VB￨O￨- deterministic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- fit￨L￨VB￨O￨A these￨L￨DT￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- least￨L￨JJS￨O￨- squares￨L￨NNS￨O￨- or￨L￨CC￨O￨- related￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- such￨L￨PDT￨O￨- an￨L￨DT￨O￨- exercise￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- itself￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- deterministic￨L￨JJ￨O￨A ,￨L￨,￨O￨- all￨L￨DT￨O￨- discrepancies￨L￨NNS￨O￨- between￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- prediction￨L￨NN￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- effect￨L￨NN￨O￨- ascribed￨L￨VBD￨O￨- to￨L￨TO￨O￨- measurement￨L￨NN￨O￨- error￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- fit￨L￨JJ￨O￨A ,￨L￨,￨O￨- many￨L￨JJ￨O￨- have￨L￨VBP￨O￨- opted￨L￨VBN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- trajectories￨L￨NNS￨O￨- to￨L￨TO￨O￨- cumulative￨L￨JJ￨O￨- case￨L￨NN￨O￨- counts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Central￨U￨NNP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- Kingman￨U￨NNP￨CITY￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- parametric￨L￨JJ￨O￨- coalescent￨L￨NN￨O￨A of￨L￨IN￨O￨- Griffiths￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Tavaré￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sampled￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- fixed￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- irrespective￨L￨RB￨O￨- of￨L￨IN￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- generation￨L￨NN￨O￨- Wright￨U￨NNP￨PERSON￨- –￨L￨:￨O￨- Fisher￨U￨NNP￨PERSON￨- or￨L￨CC￨O￨- Moran￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨JJ￨O￨A approximation￨L￨NN￨O￨- assuming￨L￨VBG￨O￨- an￨L￨DT￨O￨- exponentially￨L￨RB￨O￨- varying￨L￨VBG￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- fails￨L￨VBZ￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- retrieve￨L￨VB￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- coalescent￨L￨JJ￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- replacing￨L￨VBG￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- function￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- ensemble￨L￨NN￨O￨- of￨L￨IN￨O￨- trajectories￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- sampled￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- BD￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨JJ￨O￨A approximation￨L￨NN￨O￨- yields￨L￨VBZ￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- hypothesize￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coalescent￨L￨NN￨O￨A often￨L￨RB￨O￨- being￨L￨VBG￨O￨- violated￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- stochastically￨L￨RB￨O￨- changing￨L￨VBG￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mildly￨L￨RB￨O￨- transmissible￨L￨JJ￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- plant-based￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- produced￨L￨VBD￨O￨- per￨L￨IN￨O￨- week￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- severe￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- decreased￨L￨VBN￨O￨- by￨L￨IN￨O￨- 60￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- if￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- was￨L￨VBD￨O￨- available￨L￨JJ￨O￨- within￨L￨IN￨O￨- 3￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨A of￨L￨IN￨O￨- strain￨L￨NN￨O￨- identification￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- transmissible￨L￨JJ￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 2.0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- delay￨L￨NN￨O￨- of￨L￨IN￨O￨- 3￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨A does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- change￨L￨VB￨O￨- clinical￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨- vaccine￨L￨NN￨O￨- availability￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- age-and￨L￨JJ￨O￨- risk-structured￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- Canada￨U￨NNP￨COUNTRY￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- plant-produced￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- deployment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- within￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨A )￨L￨-RRB-￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- egg-based￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- timeline￨L￨NN￨O￨- .￨L￨.￨O￨- +2015Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Traditional￨U￨JJ￨O￨- processes￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- production￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- producing￨L￨VBG￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- deployed￨L￨VBN￨O￨- sooner￨L￨RBR￨O￨- than￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨A after￨L￨IN￨O￨- strain￨L￨NN￨O￨- identification￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Early￨U￨JJ￨MISC￨- vaccine￨L￨NN￨O￨A availability￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- advance￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenzaAmy￨L￨NN￨O￨- L￨U￨NN￨O￨- Greer1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 8:191￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Greer￨U￨NNP￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨O￨- Central￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- instead￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- regulatory￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- networked￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- endogenous￨L￨JJ￨O￨- bursty￨L￨JJ￨O￨A activity￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- problem￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- posed￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- node￨L￨NN￨O￨- l￨L￨NN￨O￨- that￨L￨WDT￨O￨- changes￨L￨VBZ￨O￨- state￨L￨NN￨O￨- following￨L￨VBG￨O￨- Poisson￨U￨NNP￨PERSON￨- processes￨L￨NNS￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- instantaneous￨L￨JJ￨O￨- activation￨L￨NN￨O￨A rate￨L￨NN￨O￨- —￨L￨:￨O￨- which￨L￨WDT￨O￨- encodes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- alternation￨L￨NN￨O￨- of￨L￨IN￨O￨- activation￨L￨NN￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- —￨L￨:￨O￨- and￨L￨CC￨O￨- inactivation￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- active￨L￨JJ￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- produces￨L￨VBZ￨O￨- events￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- endogenous￨L￨JJ￨O￨- inter-event￨L￨JJ￨O￨- time￨L￨NN￨O￨A probability￨L￨NN￨O￨A distribution￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- testing￨L￨NN￨O￨A strategy￨L￨NN￨O￨- from￨L￨IN￨O￨- baseline￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 16.8￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- overall￨L￨JJ￨O￨- testing￨L￨NN￨O￨- coverage￨L￨NN￨O￨- ;￨L￨:￨O￨- 0.4￨L￨CD￨NUMBER￨- partners￨L￨NNS￨O￨- notified￨L￨VBN￨O￨- and￨L￨CC￨O￨- tested/treated￨L￨VBN￨O￨- per￨L￨IN￨O￨- treated￨L￨VBN￨O￨- positive￨L￨JJ￨O￨- index￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- PID￨U￨NN￨O￨- and￨L￨CC￨O￨- TFI￨U￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Increasing￨U￨VBG￨O￨- overall￨L￨JJ￨O￨- testing￨L￨NN￨O￨A coverage￨L￨NN￨O￨- by￨L￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- from￨L￨IN￨O￨- baseline￨L￨NN￨O￨- to￨L￨TO￨O￨- 25.2￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- 21￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- fewer￨L￨JJR￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- young￨L￨JJ￨O￨- women￨L￨NNS￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- (￨L￨-LRB-￨O￨- PID￨U￨NN￨O￨- :￨L￨:￨O￨- 703￨L￨CD￨NUMBER￨- fewer￨L￨JJR￨O￨- ;￨L￨:￨O￨- TFI￨U￨NN￨O￨- :￨L￨:￨O￨- 88￨L￨CD￨NUMBER￨- fewer￨L￨JJR￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +2015Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Chlamydia￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- bacterial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Scotland￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- potentially￨L￨RB￨O￨- serious￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- pelvic￨L￨JJ￨O￨- inflammatory￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- PID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- tubal￨L￨JJ￨O￨- factor￨L￨NN￨O￨- infertility￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TFI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- women￨L￨NNS￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Impact￨U￨NN￨MISC￨- and￨L￨CC￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨- testing￨L￨NN￨O￨A in￨L￨IN￨O￨- Scotland￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- studyKatharine￨L￨NN￨O￨- J￨U￨NN￨O￨- Looker6Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Lesley￨U￨NNP￨PERSON￨- A￨U￨NNP￨O￨- Wallace7￨U￨NN￨O￨- and￨L￨CC￨O￨- Katherine￨U￨NNP￨PERSON￨- ME￨U￨NNP￨STATE_OR_PROVINCE￨- Turner6￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 12:2￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Looker￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨O￨- Central￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- testing￨L￨NN￨O￨A and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- PID￨U￨NN￨O￨- and￨L￨CC￨O￨- TFI￨U￨NN￨O￨- in￨L￨IN￨O￨- Scotland￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- uncertain￨L￨JJ￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 71￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 56￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- as￨L￨IN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- partnership￨L￨NN￨O￨A network￨L￨NN￨O￨- :￨L￨:￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- AuthorsAuthors￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- affiliationsKa￨L￨NNP￨O￨- Yin￨U￨NNP￨O￨- LeungMirjam￨U￨NNP￨O￨- KretzschmarOdo￨U￨NNP￨O￨- DiekmannOpen￨U￨NNP￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1.4￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 10￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractWe￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- Infectious￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBD￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- homosexual￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Officials￨U￨NNS￨O￨- conducting￨L￨VBG￨O￨- the￨L￨DT￨O￨- contest￨L￨NN￨O￨- found￨L￨VBD￨O￨- each￨L￨DT￨O￨- entry￨L￨NN￨O￨- informative￨L￨JJ￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- capabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modeling￨L￨NN￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- public￨L￨JJ￨O￨- policy￨L￨NN￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- consensus￨L￨NN￨O￨- was￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A forecasting￨L￨NN￨O￨- still￨L￨RB￨O￨- has￨L￨VBZ￨O￨- too￨L￨RB￨O￨- much￨L￨JJ￨O￨- uncertainty￨L￨NN￨O￨- to￨L￨TO￨O￨- base￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- policy￨L￨NN￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- our￨L￨PRP$￨O￨- entry￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- contest￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- forecast￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- historical￨L￨JJ￨O￨- U.S.￨U￨NNP￨COUNTRY￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- observations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2014￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A using￨L￨VBG￨O￨- Twitter￨U￨NNP￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- Internet￨U￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- supplement￨L￨VB￨O￨- ILI￨U￨NNP￨O￨- weekly￨L￨RB￨SET￨- reported￨L￨VBD￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- forecast￨L￨NN￨O￨- is￨L￨VBZ￨O￨- dynamically￨L￨RB￨O￨- adjusted￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- filter￨L￨NN￨O￨- as￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- worm￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- hybrid￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- code￨L￨NN￨O￨- analysis￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- revealed￨L￨VBN￨O￨- the￨L￨DT￨O￨- worm￨L￨NN￨O￨- applied￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- spreading￨L￨VBG￨O￨- mechanisms￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- global￨L￨JJ￨O￨- random￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- local￨L￨JJ￨O￨- network￨L￨NN￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- neighbourhood￨L￨NN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- we￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- explains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- critically￨L￨RB￨O￨- hybrid￨L￨JJ￨O￨A epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- spreading￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- setting￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- metopopulation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critically￨L￨RB￨O￨- hybrid￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- and￨L￨CC￨ORDINAL￨- second￨L￨JJ￨ORDINAL￨- spreading￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- ineffective￨L￨JJ￨O￨- if￨L￨IN￨O￨- used￨L￨VBN￨O￨- alone￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- mechanism￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- show￨L￨VB￨O￨- later￨L￨RB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- when￨L￨WRB￨O￨- mixed￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- fully-mixed￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A models￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- spread￨L￨VB￨O￨- between￨L￨IN￨O￨- any￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +Whereas￨U￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- spreading￨L￨VBG￨O￨A models￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- neighbours￨L￨NNS￨O￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- spread￨L￨VB￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- connections￨L￨NNS￨O￨- among￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- observational￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- tracking￨L￨VBG￨O￨- actual￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- spread￨L￨VBN￨O￨- differently￨L￨RB￨O￨- :￨L￨:￨O￨- apart￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- contagion￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- other￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 26￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- homophily￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- reinforcement￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- trees￨L￨NNS￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- unveil￨L￨VB￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A spreading￨L￨NN￨O￨A in￨L￨IN￨O￨- blog￨L￨NN￨O￨- communities￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- users￨L￨NNS￨O￨- ’￨L￨POS￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- disseminating￨L￨VBG￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- recent￨L￨JJ￨O￨- empirical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- information￨L￨NN￨O￨- flows￨L￨VBZ￨O￨- in￨L￨IN￨O￨- blogspaces￨L￨NNS￨O￨- have￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- evidences￨L￨NNS￨O￨- that￨L￨WDT￨O￨- information￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- diffuse￨L￨JJ￨O￨- via￨L￨IN￨O￨- social￨L￨JJ￨O￨- links￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 32￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 34￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- opposes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- prevailing￨L￨VBG￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- information￨L￨NN￨O￨A spreading￨L￨NN￨O￨A is￨L￨VBZ￨O￨- confined￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- instances￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- classified￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- :￨L￨:￨O￨- social￨L￨JJ￨O￨A spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- occurs￨L￨VBZ￨O￨- following￨L￨VBG￨O￨- social￨L￨JJ￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- self-promotion￨L￨NN￨O￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- references￨L￨NNS￨O￨- of￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- posts￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- broadcast￨L￨NN￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- distinguishes￨L￨VBZ￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- large￨L￨JJ￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- prevented￨L￨VBN￨O￨- with￨L￨IN￨O￨- contact￨L￨NN￨O￨- investigations￨L￨NNS￨O￨- and￨L￨CC￨O￨- moderate￨L￨JJ￨O￨A contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- by￨L￨IN￨O￨- having￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- high￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ≥￨L￨CD￨PERCENT￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- moderate￨L￨JJ￨O￨- to￨L￨TO￨O￨- low￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- clustering￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ≤￨L￨CD￨NUMBER￨- 0.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- aged￨L￨VBN￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- or￨L￨CC￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- 18￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- moderate￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 85￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- or￨L￨CC￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- immunity￨L￨NN￨O￨- clustering￨L￨NN￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ≤￨L￨CD￨NUMBER￨- 18￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- delay￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- traced￨L￨VBN￨O￨- .￨L￨.￨O￨- +Without￨U￨IN￨O￨- contact￨L￨NN￨O￨- investigations￨L￨NNS￨O￨- ,￨L￨,￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- prevented￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- immunity￨L￨NN￨O￨- clustering￨L￨NN￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ≤￨L￨CD￨NUMBER￨- 18￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- moderate￨L￨JJ￨O￨A contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ;￨L￨:￨O￨- but￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- coverage￨L￨NN￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- immunity￨L￨NN￨O￨- clustering￨L￨NN￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ≤￨L￨CD￨NUMBER￨- 18￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- completely￨L￨RB￨O￨- prevent￨L￨VB￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- simulated￨L￨JJ￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- clustering￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- investigations￨L￨NNS￨O￨- with￨L￨IN￨O￨- delays￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- behaviors￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- health￨L￨NN￨O￨- department￨L￨NN￨O￨- ’s￨L￨POS￨O￨- response￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A ,￨L￨,￨O￨- individual￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- response￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- for￨L￨IN￨O￨- CaliforniaFengchen￨U￨NNP￨PERSON￨- Liu￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Wayne￨U￨NNP￨PERSON￨- T￨U￨NN￨O￨- A￨U￨DT￨O￨- Enanoria￨U￨JJ￨O￨- †￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jennifer￨U￨NNP￨PERSON￨- Zipprich3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Seth￨U￨NNP￨PERSON￨- Blumberg1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Kathleen￨U￨NNP￨PERSON￨- Harriman3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Sarah￨U￨NNP￨PERSON￨- F￨U￨NN￨O￨- Ackley1￨U￨NN￨O￨- ,￨L￨,￨O￨- William￨U￨NNP￨PERSON￨- D￨U￨NNP￨PERSON￨- Wheaton4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Justine￨U￨NNP￨PERSON￨- L￨U￨NNP￨PERSON￨- Allpress4￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Travis￨U￨NNP￨O￨- C￨U￨NNP￨O￨- Porco1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- †￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 15:447￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Liu￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨O￨- Central￨U￨NNP￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- examined￨L￨VBN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨A tracing￨L￨VBG￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- clustered￨L￨VBN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- explicitly￨L￨RB￨O￨- modeled￨L￨VBD￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- response￨L￨NN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- curse￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Pharaoh￨U￨NNP￨TITLE￨- ”￨L￨''￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- sit￨L￨VB￨O￨- and￨L￨CC￨O￨- wait￨L￨VB￨O￨- ”￨L￨''￨O￨- hypothesis￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- predicts￨L￨VBZ￨O￨- that￨L￨IN￨O￨- free-living￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- lifespan￨L￨NN￨O￨- exceeds￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- constrained￨L￨VBN￨O￨- by￨L￨IN￨O￨- virulence￨L￨NN￨O￨- ,￨L￨,￨O￨- enabling￨L￨VBG￨O￨A them￨L￨PRP￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- at￨L￨IN￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- virulence￨L￨NN￨O￨- and￨L￨CC￨O￨- continue￨L￨VB￨O￨- transmitting￨L￨VBG￨O￨- to￨L￨TO￨O￨- further￨L￨RB￨O￨- sensitive￨L￨JJ￨O￨- hosts1011121314￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- combining￨L￨VBG￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- trials￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- custom￨L￨NN￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- characterise￨L￨VB￨O￨A the￨L￨DT￨O￨- most￨L￨RBS￨O￨- influential￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- fungal￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- ’s￨L￨POS￨O￨- outbreak￨L￨NN￨O￨- using￨L￨VBG￨O￨- S.￨U￨NNP￨O￨- Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- alternate￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- methods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- incubation￨L￨NN￨O￨- duration￨L￨NN￨O￨- .￨L￨.￨O￨- +Free-living￨U￨JJ￨O￨- infectious￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- spores￨L￨NNS￨O￨- and￨L￨CC￨O￨- zoospores￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- lengthen￨L￨VBP￨O￨- the￨L￨DT￨O￨- timespan￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- enabling￨L￨VBG￨O￨A contact￨L￨NN￨O￨- with￨L￨IN￨O￨- greater￨L￨JJR￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- hosts9￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- modifications￨L￨NNS￨O￨- include￨L￨VBP￨O￨- species￨L￨NNS￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- depleted￨L￨VBN￨O￨- populations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- struggle￨L￨VBP￨O￨- to￨L￨TO￨O￨- survive￨L￨VB￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- tolerant￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A thriving￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- community￨L￨NN￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- transmit￨L￨VB￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- agent￨L￨NN￨O￨- without￨L￨IN￨O￨- any￨L￨DT￨O￨- clinical￨L￨JJ￨O￨- signs￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- addresses￨L￨NNS￨O￨- this￨L￨DT￨O￨- shortcoming￨L￨NN￨O￨- by￨L￨IN￨O￨- reviewing￨L￨VBG￨O￨- previous￨L￨JJ￨O￨- KA￨U￨NN￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- presenting￨L￨VBG￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- methodology￨L￨NN￨O￨- and￨L￨CC￨O￨- supervising￨L￨VBG￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- conducting￨L￨VBG￨O￨- KA￨U￨NN￨O￨- within￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- organizations￨L￨NNS￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- provides￨L￨VBZ￨O￨- well-defined￨L￨JJ￨O￨- constructs￨L￨NNS￨O￨- and￨L￨CC￨O￨- guiding￨L￨VBG￨O￨- principles￨L￨NNS￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- that￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- organizations￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- deviate￨L￨VB￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- proper￨L￨JJ￨O￨- path￨L￨NN￨O￨- of￨L￨IN￨O￨- KA￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- frameworks￨L￨NNS￨O￨A and￨L￨CC￨O￨- methodologies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- KM￨U￨NNP￨O￨- as￨L￨IN￨O￨- depicted￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- numerous￨L￨JJ￨O￨- enterprises￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- unable￨L￨JJ￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- their￨L￨PRP$￨O￨- KM￨U￨NNP￨O￨- projects￨L￨NNS￨O￨- despite￨L￨IN￨O￨- large￨L￨JJ￨O￨- monetary￨L￨JJ￨O￨- investments￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- conducting￨L￨VBG￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- KA￨U￨NN￨O￨- within￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- organizations￨L￨NNS￨O￨A will￨L￨MD￨O￨- be￨L￨VB￨O￨- provided￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Research￨U￨NNP￨ORGANIZATION￨- Method￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Proposed￨U￨VBN￨O￨- Solution￨U￨NN￨O￨- sections￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- different￨L￨JJ￨O￨- KA￨U￨NN￨O￨- frameworks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- frameworks￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Jafari￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Lusa￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Zhang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- none￨L￨NN￨O￨- adequately￨L￨RB￨O￨- fulfill￨L￨VBP￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- conducting￨L￨VBG￨O￨- KA￨U￨NN￨O￨- within￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- organizations￨L￨NNS￨O￨A .￨L￨.￨O￨- +Although￨U￨IN￨O￨- several￨L￨JJ￨O￨- EIA￨U￨NN￨ORGANIZATION￨- frameworks￨L￨NNS￨O￨A are￨L￨VBP￨O￨- directed￨L￨VBN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Zachman￨U￨NNP￨PERSON￨- framework￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- shapes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infrastructure￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- EIAs￨U￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- a￨L￨DT￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- metapopulation￨L￨NN￨O￨- persistence￨L￨NN￨O￨- analytically￨L￨RB￨O￨- ,￨L￨,￨O￨- highlighting￨L￨VBG￨O￨- that￨L￨IN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- dimensions￨L￨NNS￨O￨- ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- patches￨L￨NNS￨O￨A ,￨L￨,￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dispersal￨L￨NN￨O￨- kernel￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- patch￨L￨NN￨O￨- value￨L￨NN￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- key￨L￨JJ￨O￨- to￨L￨TO￨O￨- determining￨L￨VBG￨O￨- persistence￨L￨NN￨O￨- .￨L￨.￨O￨- +Hanski￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Ovaskainen￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- extended￨L￨VBD￨O￨- this￨L￨DT￨O￨- formulation￨L￨NN￨O￨- to￨L￨TO￨O￨- realistic￨L￨JJ￨O￨- landscapes￨L￨NNS￨O￨- ,￨L￨,￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- patches￨L￨NNS￨O￨A ,￨L￨,￨O￨- each￨L￨DT￨O￨- having￨L￨VBG￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- “￨L￨``￨O￨- value￨L￨NN￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- dispersal￨L￨NN￨O￨- whose￨L￨WP$￨O￨- strength￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- patches￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- intuition￨L￨NN￨O￨- forms￨L￨VBZ￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- of￨L￨IN￨O￨- metapopulation￨L￨NN￨O￨- theory￨L￨NN￨O￨- :￨L￨:￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- local￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- occupying￨L￨VBG￨O￨- patches￨L￨NNS￨O￨A of￨L￨IN￨O￨- suitable￨L￨JJ￨O￨- habitat￨L￨NN￨O￨- might￨L￨MD￨O￨- undergo￨L￨VB￨O￨- extinction￨L￨NN￨O￨- ,￨L￨,￨O￨- persistence￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- level￨L￨NN￨O￨- —￨L￨:￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- patch￨L￨NN￨O￨- —￨L￨:￨O￨- as￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- disperse￨L￨VB￨O￨- between￨L￨IN￨O￨- patches￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- recolonize￨L￨VB￨O￨- empty￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- finally￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- arranging￨L￨VBG￨O￨- the￨L￨DT￨O￨- patches￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- perfect￨L￨JJ￨O￨- grid￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨RB￨O￨- often￨L￨RB￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨- of￨L￨IN￨O￨- protected￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- yields￨L￨VBZ￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- persistence￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- distribute￨L￨VBP￨O￨- the￨L￨DT￨O￨- patches￨L￨NNS￨O￨- randomly￨L￨RB￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- more￨L￨JJR￨O￨- fruitful￨L￨JJ￨O￨- avenue￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- N￨U￨NN￨O￨- patches￨L￨NNS￨O￨A ,￨L￨,￨O￨- distribute￨L￨VB￨O￨- them￨L￨PRP￨O￨- randomly￨L￨RB￨O￨- in￨L￨IN￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- connect￨L￨VB￨O￨- any￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- patches￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- closer￨L￨JJR￨O￨- than￨L￨IN￨O￨- some￨L￨DT￨O￨- threshold￨L￨NN￨O￨- distance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- EVD￨U￨NN￨O￨- and￨L￨CC￨O￨- Marburg￨U￨NNP￨MISC￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- extracted￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- details￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- provided￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- point￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- confidence￨L￨NN￨O￨A intervals￨L￨NNS￨O￨- ,￨L￨,￨O￨- ranges￨L￨NNS￨O￨- ,￨L￨,￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- total￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- encompassing￨L￨VBG￨O￨- confirmed￨L￨VBN￨O￨- ,￨L￨,￨O￨- suspected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- retrospectively￨L￨RB￨O￨- diagnosed￨L￨VBD￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- EVD￨U￨NN￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- inferential￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +All￨U￨DT￨O￨- searches￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- search￨L￨NN￨O￨- terms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Ebola￨U￨NNP￨O￨- ,￨L￨,￨O￨- Marburg￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- EHF￨U￨NN￨O￨- ,￨L￨,￨O￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- MHF￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- EBOV￨U￨NN￨O￨- ,￨L￨,￨O￨- Ebola￨U￨NNP￨LOCATION￨- Zaire￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Ebola￨U￨NNP￨O￨- Sudan￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Ebola￨U￨NNP￨LOCATION￨- Reston￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Ebola￨U￨NNP￨O￨- Bundibugyo￨U￨NNP￨O￨- ,￨L￨,￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- parameterization￨L￨NN￨O￨- ,￨L￨,￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- case￨L￨NN￨O￨A fatality￨L￨NN￨O￨A rate￨L￨NN￨O￨A ,￨L￨,￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CFR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- serial￨L￨NN￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- delay￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- on￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- databases￨L￨NNS￨O￨- :￨L￨:￨O￨- ScienceDirect￨U￨NNP￨O￨- ,￨L￨,￨O￨- ResearchGate￨U￨NNP￨O￨- ,￨L￨,￨O￨- Google￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- GoogleScholar￨U￨NNP￨O￨- ,￨L￨,￨O￨- BioOne￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Web￨U￨NN￨O￨- of￨L￨IN￨O￨- Science￨U￨NNP￨O￨- and￨L￨CC￨O￨- PubMed￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- collect￨L￨VB￨O￨- all￨L￨DT￨O￨- published￨L￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- reprinted￨L￨VBN￨O￨- in￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- tables￨L￨NNS￨O￨- containing￨L￨VBG￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- corresponding￨L￨JJ￨O￨- confidence￨L￨NN￨O￨A intervals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- EVD￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- aim￨L￨NN￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- perform￨L￨VB￨O￨- a￨L￨DT￨O￨- meta-analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- rather￨L￨RB￨O￨- to￨L￨TO￨O￨- compile￨L￨VB￨O￨- and￨L￨CC￨O￨- document￨L￨VB￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- parameter￨L￨NN￨O￨A estimates￨L￨VBZ￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- EVD￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- 40￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- manuscript￨L￨NN￨O￨- and￨L￨CC￨O￨- tables￨L￨NNS￨O￨- include￨L￨VBP￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- confidence￨L￨NN￨O￨A intervals￨L￨NNS￨O￨- and￨L￨CC￨O￨- ranges￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- referenced￨L￨VBN￨O￨- publications￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- available￨L￨JJ￨O￨- online￨L￨NN￨O￨- only￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Data￨U￨NNS￨O￨- Citation￨U￨NNP￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- dog￨L￨NN￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- increasing￨L￨VBG￨O￨- dog￨L￨NN￨O￨- immunization￨L￨NN￨O￨- coverage￨L￨NN￨O￨- rate￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- rabies￨L￨NNP￨O￨A in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- culling￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- replaced￨L￨VBN￨O￨- by￨L￨IN￨O￨- immunization￨L￨NN￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dog-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- both￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stray￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- human￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Guangdong￨U￨NNP￨STATE_OR_PROVINCE￨- Province￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- subpopulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- dogs￨L￨NNS￨O￨- and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A among￨L￨IN￨O￨- dogs￨L￨NNS￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- that￨L￨IN￨O￨- 85￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- –￨L￨:￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- rabies￨L￨NNP￨O￨A cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- dog￨L￨NN￨O￨- bites￨L￨VBZ￨O￨- in￨L￨IN￨O￨- mainland￨L￨NN￨O￨- China￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,769￨L￨CD￨NUMBER￨- human￨L￨JJ￨O￨- rabies￨L￨NNP￨O￨A cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- [￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- 2,012￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +Parameter￨U￨NN￨O￨- A￨U￨NN￨O￨- represents￨L￨VBZ￨O￨A the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- additional￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨O￨- ;￨L￨:￨O￨- ω￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- vaccine￨L￨NN￨O￨- wanes￨L￨VBZ￨O￨- ;￨L￨:￨O￨- μ￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- β￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- ;￨L￨:￨O￨- p￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- recruited￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- vaccinated￨L￨VBN￨O￨- ;￨L￨:￨O￨- τ￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- σ￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- exposed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- constructing￨L￨VBG￨O￨- the￨L￨DT￨O￨- Lyapunov￨U￨NN￨PERSON￨- function￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- generalization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Poincaré-Bendixson￨U￨NNP￨LOCATION￨- criterion￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- Section￨U￨NNP￨O￨- 5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A P￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Obviously￨U￨RB￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- always￨L￨RB￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A P￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- /￨L￨:￨O￨- μ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- pA￨L￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 0,0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- *￨L￨SYM￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- no￨L￨DT￨O￨- real￨L￨JJ￨O￨- equilibria￨L￨NNS￨O￨- ;￨L￨:￨O￨- when￨L￨WRB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- *￨L￨SYM￨O￨- <￨L￨JJR￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- endemic￨L￨JJ￨O￨- equilibria￨L￨NNS￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- *￨L￨SYM￨O￨- and￨L￨CC￨O￨- P￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- *￨L￨SYM￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ≥￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A P￨U￨NN￨O￨- *￨L￨NN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- of￨L￨IN￨O￨- January￨U￨NNP￨DATE￨- 12￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2015￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 8,362￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 10,150￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- 3,556￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 3,067￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- officially￨L￨RB￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- countries￨L￨NNS￨O￨- mostly￨L￨RB￨O￨- afflicted￨L￨VBD￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- concern￨L￨NN￨O￨- of￨L￨IN￨O￨- further￨L￨JJ￨O￨- international￨L￨JJ￨O￨- spread￨L￨NN￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- ceased￨L￨VBN￨O￨- .4￨L￨CD￨NUMBER￨- Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- instrumental￨L￨JJ￨O￨- in￨L￨IN￨O￨- providing￨L￨VBG￨O￨- guidance￨L￨NN￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨DATE￨- future￨L￨JJ￨DATE￨- projections￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- important￨L￨JJ￨O￨- ongoing￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- crises￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- might￨L￨MD￨O￨- have￨L￨VB￨O￨- towards￨L￨IN￨O￨- transmission￨L￨NN￨O￨- control￨L￨NN￨O￨- .5￨L￨CD￨NUMBER￨- Models￨U￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- distinguished￨L￨VBN￨O￨- to￨L￨TO￨O￨- four￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- categories￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- realism￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- consequently￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- difficulty￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Deterministic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- integro￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- partial￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- “￨L￨``￨O￨- continuum￨L￨NN￨O￨- models￨L￨NNS￨O￨- ”￨L￨''￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- coarse-grained￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- relaxing￨L￨VBG￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨A of￨L￨IN￨O￨- continuum￨L￨NN￨O￨- models￨L￨NNS￨O￨- about￨L￨IN￨O￨- infinite￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- incorporate￨L￨VBP￨O￨- stochastic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- variables￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- individual-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- “￨L￨``￨O￨- memory￨L￨NN￨O￨- ”￨L￨''￨O￨- import￨L￨NN￨O￨- the￨L￨DT￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- population￨L￨NN￨O￨- while￨L￨IN￨O￨- relaxing￨L￨VBG￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- about￨L￨IN￨O￨- structural￨L￨JJ￨O￨- uniformity￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- interactions￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- complex￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- “￨L￨``￨O￨- social￨L￨JJ￨O￨- ”￨L￨''￨O￨- network-based￨L￨JJ￨O￨- or￨L￨CC￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- emphasize￨L￨VBP￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- nature￨L￨NN￨O￨- and￨L￨CC￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- delayed￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Althaus13￨U￨NN￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- vital￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- EBOV￨U￨NN￨O￨- in￨L￨IN￨O￨- West￨U￨JJ￨MISC￨- African￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- correspondingly￨L￨RB￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- and￨L￨CC￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +12￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- outbreak￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- early￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- estimated￨L￨VBD￨O￨- a￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- African￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- international￨L￨JJ￨O￨A threat￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- longer￨L￨RBR￨O￨- time-scale￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Methods￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- employing￨L￨VBG￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- Equation-Free￨U￨NNP￨O￨- approach15￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- estimations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- to￨L￨TO￨O￨- death￨L￨NN￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨A fatality￨L￨NN￨O￨A rate￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- per-contact￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- movement￨L￨NN￨O￨- data￨L￨NNS￨O￨- extracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- registration￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- cellular￨L￨JJ￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- geographic￨L￨JJ￨O￨A area￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- centrality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- areas￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- extracted￨L￨VBN￨O￨- by￨L￨IN￨O￨- building￨L￨VBG￨O￨- a￨L￨DT￨O￨- movement￨L￨NN￨O￨- network￨L￨NN￨O￨- between￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- geographic￨L￨JJ￨O￨A areas￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- summarize￨L￨VB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- considering￨L￨VBG￨O￨- three￨L￨CD￨NUMBER￨- characterizing￨L￨VBG￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨A mobility￨L￨NN￨O￨A and￨L￨CC￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- geographic￨L￨JJ￨O￨A metapopulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- people￨L￨NNS￨O￨- move￨L￨VBP￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- geographic￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- and￨L￨CC￨O￨- spread￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- competing￨L￨VBG￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A spreading￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- livestock￨L￨NN￨O￨A ,￨L￨,￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- knowledge￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- farms￨L￨NNS￨O￨- or￨L￨CC￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- aggregated￨L￨JJ￨O￨- movements￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- farm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- sampling￨L￨NN￨O￨- approach￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- where￨L￨WRB￨O￨- larger￨L￨JJR￨O￨- farms￨L￨NNS￨O￨- or￨L￨CC￨O￨- farms￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- movements￨L￨NNS￨O￨- are￨L￨VBP￨O￨- sampled￨L￨VBN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- played￨L￨VBN￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- through￨L￨IN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- livestock￨L￨NN￨O￨A movements￨L￨NNS￨O￨- for￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- FMD￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- bTB￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- bluetongue￨L￨NN￨O￨- virus￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- full￨L￨JJ￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- datasets￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- readily￨L￨RB￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- partial￨L￨JJ￨O￨- samples￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A across￨L￨IN￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- through￨L￨IN￨O￨- livestock￨L￨NN￨O￨A movements￨L￨NNS￨O￨- when￨L￨WRB￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- partial￨L￨JJ￨O￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- FMD￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- early￨L￨JJ￨O￨- dissemination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- detected￨L￨VBN￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- mainly￨L￨RB￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- long-distance￨L￨JJ￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- livestock￨L￨NN￨O￨A between￨L￨IN￨O￨- farms￨L￨NNS￨O￨- and￨L￨CC￨O￨- through￨L￨IN￨O￨- markets￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- compliance￨L￨NN￨O￨- with￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- ETU￨U￨NN￨O￨- capacity￨L￨NN￨O￨- in￨L￨IN￨O￨- Lofa￨U￨NNP￨LOCATION￨- County￨U￨NNP￨LOCATION￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- insufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- stop￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨A had￨L￨VBD￨O￨- population￨L￨NN￨O￨- behavior￨L￨NN￨O￨- not￨L￨RB￨O￨- changed￨L￨VBD￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- network-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- combine￨L￨VBP￨O￨- isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- ETUs￨U￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- public￨L￨NN￨O￨- 's￨L￨POS￨O￨- cooperation￨L￨NN￨O￨- with￨L￨IN￨O￨- preventative￨L￨JJ￨O￨- measures￨L￨NNS￨O￨A to￨L￨TO￨O￨- control￨L￨VB￨O￨- EVD￨U￨NNP￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- fit￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- weekly￨L￨JJ￨SET￨- case￨L￨NN￨O￨- counts￨L￨VBZ￨O￨A from￨L￨IN￨O￨- Lofa￨U￨NNP￨LOCATION￨- County￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Liberia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- social￨L￨JJ￨O￨- mobilization￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- ETUs￨U￨NNS￨O￨- in￨L￨IN￨O￨- containing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- an￨L￨DT￨O￨- early￨L￨JJ￨O￨- Lofa￨U￨NNP￨LOCATION￨- County￨U￨NNP￨LOCATION￨- EVD￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨A was￨L￨VBD￨O￨- controlled￨L￨VBN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- imported￨L￨VBN￨O￨- case￨L￨NN￨O￨- launched￨L￨VBD￨O￨- a￨L￨DT￨O￨- much￨L￨JJ￨O￨- larger￨L￨JJR￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- late-May￨L￨JJ￨DATE￨- 26￨L￨CD￨DATE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- 623￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- 27￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- identified￨L￨VBD￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- co-existence￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A A￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- interhemispheric￨L￨JJ￨O￨- synchronized￨L￨VBN￨O￨- pattern￨L￨NN￨O￨- for￨L￨IN￨O￨- subtype￨L￨NN￨O￨- A￨U￨NN￨O￨- H3N2￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- latitudinal￨L￨JJ￨O￨- gradients￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- timing￨L￨NN￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- denote￨L￨VBP￨O￨- H1N1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- -￨L￨:￨O￨- pandemic￨L￨JJ￨O￨A seasonal￨L￨JJ￨O￨- A￨U￨NN￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- H1N1pdm￨U￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- strain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1pdm09￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- H3N2￨U￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- H3N2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- pandemic￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- strain￨L￨NN￨O￨- confronted￨L￨VBD￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- a￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- global￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- recent￨L￨JJ￨O￨- study11￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- dominant￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A A￨U￨NN￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- earlier￨L￨RBR￨O￨- in￨L￨IN￨O￨- Southern￨U￨NNP￨O￨- Asia￨U￨NNP￨CITY￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- 16￨L￨CD￨NUMBER￨- widespread￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- both￨L￨DT￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- eight￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- presumably￨L￨RB￨O￨- being￨L￨VBG￨O￨- complete￨L￨JJ￨O￨- skips6￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- illustrate￨L￨VB￨O￨- how￨L￨WRB￨O￨- this￨L￨DT￨O￨- can￨L￨MD￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- addressing￨L￨VBG￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- serious￨L￨JJ￨O￨- issues￨L￨NNS￨O￨- still￨L￨RB￨O￨- plaguing￨L￨VBG￨O￨- society￨L￨NN￨O￨- despite￨L￨IN￨O￨A better-than-ever￨L￨JJ￨O￨- science￨L￨NN￨O￨- ,￨L￨,￨O￨- measurement￨L￨NN￨O￨- opportunities￨L￨NNS￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- technology￨L￨NN￨O￨- .2￨L￨NN￨NUMBER￨- Crowd￨U￨NN￨O￨- Disasters￨U￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- How￨U￨WRB￨O￨- to￨L￨TO￨O￨- Avoid￨U￨VB￨MISC￨- ThemTragic￨U￨NNP￨MISC￨- crowd￨L￨NN￨O￨- disasters￨L￨NNS￨CAUSE_OF_DEATH￨- repeatedly￨L￨RB￨O￨- occur￨L￨VBP￨O￨- despite￨L￨IN￨O￨- strict￨L￨JJ￨O￨- codes￨L￨NNS￨O￨- and￨L￨CC￨O￨- guidelines￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- organization￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- events￨L￨NNS￨O￨- .￨L￨.￨O￨- +Surprisingly￨U￨RB￨O￨- ,￨L￨,￨O￨- well-designed￨L￨JJ￨O￨- self-regulation￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- outperforms￨L￨VBZ￨O￨- classical￨L￨JJ￨O￨- top￨L￨NN￨O￨- down￨L￨IN￨O￨- control.The￨L￨NN￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- an￨L￨DT￨O￨- overview￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- scientific￨L￨JJ￨O￨A understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- crowd￨L￨NN￨O￨- disasters￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- crime￨L￨NN￨O￨- ,￨L￨,￨O￨- terrorism￨L￨NN￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- wars￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- gained￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- perspective￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 158￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 735￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 781￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asSaving￨L￨NN￨O￨- Human￨U￨JJ￨O￨- Lives￨U￨NNS￨O￨- :￨L￨:￨O￨- What￨U￨WP￨O￨- Complexity￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- and￨L￨CC￨O￨- Information￨U￨NNP￨ORGANIZATION￨- Systems￨U￨NNP￨ORGANIZATION￨- can￨L￨MD￨O￨- ContributeAuthorsAuthors￨U￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsDirk￨L￨NNP￨O￨- HelbingDirk￨U￨NNP￨MISC￨- BrockmannThomas￨U￨NNP￨MISC￨- ChadefauxKarsten￨U￨NNP￨MISC￨- DonnayUlf￨U￨NNP￨MISC￨- BlankeOlivia￨U￨NNP￨MISC￨- Woolley-MezaMehdi￨U￨NNP￨MISC￨- MoussaidAnders￨U￨NNP￨MISC￨- JohanssonJens￨U￨NNP￨MISC￨- KrauseSebastian￨U￨NNP￨MISC￨- SchutteMatjaž￨U￨NNP￨MISC￨- PercOpen￨U￨NNP￨MISC￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 05￨L￨CD￨NUMBER￨A Citation￨U￨NNP￨O￨- 92￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 8.9￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 72￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractWe￨U￨NN￨O￨- discuss￨L￨VBP￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- crowd￨L￨NN￨O￨- disasters￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- crime￨L￨NN￨O￨- ,￨L￨,￨O￨- terrorism￨L￨NN￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- war￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- conventional￨L￨JJ￨O￨- recipes￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- deterrence￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- not￨L￨RB￨O￨- effective￨L￨JJ￨O￨- and￨L￨CC￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +Topics￨U￨NNS￨O￨- addressed￨L￨VBD￨O￨A range￨L￨NN￨O￨- from￨L￨IN￨O￨- crowd￨L￨NN￨O￨- disasters￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- crime￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- terrorism￨L￨NN￨CRIMINAL_CHARGE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- wars￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- MGARCH-DCC￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- regressions￨L￨NNS￨O￨- on￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- discover￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- finding￨L￨NN￨O￨- that￨L￨IN￨O￨- human￨L￨JJ￨O￨- contact￨L￨NN￨O￨- play￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- transmitting￨L￨VBG￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- undertake￨L￨VBP￨O￨- to￨L￨TO￨O￨- conduct￨L￨VB￨O￨- our￨L￨PRP$￨O￨- forecasts￨L￨NNS￨O￨- for￨L￨IN￨O￨- EGARCH￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- estimates￨L￨VBZ￨O￨- implements￨L￨VBZ￨O￨- ;￨L￨:￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A incurred￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- deadly￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- two￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- November￨U￨NNP￨DATE￨- and￨L￨CC￨O￨- December￨U￨NNP￨DATE￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- The￨U￨DT￨MISC￨- Ebola￨U￨NNP￨MISC￨- contagion￨L￨NN￨O￨- and￨L￨CC￨O￨- forecasting￨L￨NN￨O￨- virus￨L￨NN￨O￨A :￨L￨:￨O￨- evidence￨L￨NN￨O￨- from￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- African￨U￨JJ￨NATIONALITY￨- countriesSelmi￨L￨NN￨O￨- Nadhem1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Hachicha￨U￨NN￨O￨- D￨U￨NN￨O￨- Nejib1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 5:16￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Nadhem￨U￨NNP￨O￨- and￨L￨CC￨O￨- Nejib￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- regression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- these￨L￨DT￨O￨- relationships￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- incorporate￨L￨VB￨O￨- non-linear￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- people￨L￨NNS￨O￨- becoming￨L￨VBG￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- news￨L￨NN￨O￨- media￨L￨NNS￨O￨- induced￨L￨VBD￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- topic￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- incorporates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- eventual￨L￨JJ￨O￨- boredom￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- topic￨L￨NN￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- matter￨L￨NN￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- news￨L￨NN￨O￨- videos￨L￨NNS￨O￨- are￨L￨VBP￨O￨- subsequently￨L￨RB￨O￨- aired￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- cross-check￨L￨NN￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- verify￨L￨VBP￨O￨- that￨L￨IN￨O￨- public￨L￨JJ￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- reflected￨L￨VBN￨O￨- by￨L￨IN￨O￨- Internet￨U￨NN￨MISC￨- searches￨L￨NNS￨O￨- and￨L￨CC￨O￨- tweets￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- appear￨L￨VB￨O￨- to￨L￨TO￨O￨- induce￨L￨VB￨O￨- news￨L￨NN￨O￨- media￨L￨NNS￨O￨- stories￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- topic￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- proxy￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- news￨L￨NN￨O￨- media￨L￨NNS￨O￨A coverage￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- Ebola￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- obvious￨L￨JJ￨O￨- shortcomings￨L￨NNS￨O￨- are￨L￨VBP￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- real￨L￨JJ￨O￨- journeys￨L￨NNS￨O￨- typically￨L￨RB￨O￨- involve￨L￨VBP￨O￨- multiple￨L￨JJ￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- transportation￨L￨NN￨O￨A instead￨L￨RB￨O￨- of￨L￨IN￨O￨- agents￨L￨NNS￨O￨- all￨L￨DT￨O￨- travelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- way￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- neighboring￨L￨VBG￨O￨- stations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- different￨L￨JJ￨O￨- distances￨L￨NNS￨O￨- that￨L￨WDT￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- identical￨L￨JJ￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- adjacent￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- real￨L￨JJ￨O￨- journeys￨L￨NNS￨O￨- are￨L￨VBP￨O￨- round-trip￨L￨JJ￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- destination￨L￨NN￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- shows￨L￨VBZ￨O￨- schematically￨L￨RB￨O￨- an￨L￨DT￨O￨- inter-city￨L￨JJ￨O￨- transportation￨L￨NN￨O￨A network￨L￨NN￨O￨- emphasizing￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- link￨L￨NN￨O￨- inhomogeneity￨L￨NN￨O￨- :￨L￨:￨O￨- Links￨U￨NNP￨O￨- of￨L￨IN￨O￨- faster￨L￨RBR￨O￨- transportation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dashed￨L￨VBN￨O￨- lines￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- airlines￨L￨NNS￨O￨- and￨L￨CC￨O￨- high-speed￨L￨JJ￨O￨- trains￨L￨NNS￨O￨- ,￨L￨,￨O￨- connecting￨L￨VBG￨O￨- major￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- of￨L￨IN￨O￨- slower￨L￨JJR￨O￨- transportation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- solid￨L￨JJ￨O￨- lines￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- highways￨L￨NNS￨O￨- ,￨L￨,￨O￨- connecting￨L￨VBG￨O￨- to￨L￨TO￨O￨- surrounding￨L￨VBG￨O￨- cities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- blue￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- via￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- highway￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- journey￨L￨NN￨O￨- starts￨L￨VBZ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- city￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- intended￨L￨JJ￨O￨- destination￨L￨NN￨O￨- j￨L￨NN￨O￨- through￨L￨IN￨O￨- intermediate￨L￨JJ￨O￨- places￨L￨NNS￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- that￨L￨WDT￨O￨- takes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- necessarily￨L￨RB￨O￨- invoke￨L￨VBP￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- cities￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mode￨L￨NN￨O￨- of￨L￨IN￨O￨- transportation￨L￨NN￨O￨A .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨A greatly￨L￨RB￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- traveling￨L￨VBG￨O￨- speed￨L￨NN￨O￨- and￨L￨CC￨O￨- frequency￨L￨NN￨O￨- are￨L￨VBP￨O￨- key￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- integrated￨L￨VBN￨O￨- travel￨L￨NN￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ITN￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- accounts￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- transportation￨L￨NN￨O￨A by￨L￨IN￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- of￨L￨IN￨O￨- genomic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- a￨L￨DT￨O￨- valuable￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- for￨L￨IN￨O￨- given￨L￨VBN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- and￨L￨CC￨O￨- sampling￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- accumulation￨L￨NN￨O￨- of￨L￨IN￨O￨- mutation￨L￨NN￨O￨- both￨L￨CC￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- test￨L￨VB￨O￨- hypotheses￨L￨NNS￨O￨- about￨L￨IN￨O￨- transmission￨L￨NN￨O￨- routes￨L￨NNS￨O￨- and￨L￨CC￨O￨- evolutionary￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨A .￨L￨.￨O￨- +While￨U￨IN￨O￨- R￨U￨NN￨O￨- packages￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- genomic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- within-host￨L￨NN￨O￨- diversity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- realistic￨L￨JJ￨O￨- individual-level￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨A and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- lacking￨L￨VBG￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- both￨L￨CC￨O￨- within-host￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- routes￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- of￨L￨IN￨O￨- sequence￨L￨NN￨O￨A data￨L￨NNS￨O￨A from￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenge￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- this￨L￨DT￨O￨- represents￨L￨VBZ￨O￨- sampling￨L￨NN￨O￨- from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- ,￨L￨,￨O￨- independently￨L￨RB￨O￨- evolving￨L￨VBG￨O￨- within-host￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- suffice￨L￨VB￨O￨- to￨L￨TO￨O￨- neglect￨L￨NN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- when￨L￨WRB￨O￨- considering￨L￨VBG￨O￨- evolutionary￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- frequently￨L￨RB￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- microevolution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- applied￨L￨VBD￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- three￨L￨CD￨NUMBER￨- scenarios￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- exportations￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- asymptomatic￨L￨JJ￨O￨A polio￨L￨NNP￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- currently￨L￨RB￨DATE￨- polio-infected￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- poliovirus￨L￨NN￨O￨- to￨L￨TO￨O￨- Saudi￨U￨NNP￨COUNTRY￨- Arabia￨U￨NNP￨COUNTRY￨- via￨L￨IN￨O￨- Hajj￨U￨NNP￨LOCATION￨- pilgrims￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- importation￨L￨NN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- poliovirus￨L￨NN￨O￨- into￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- ongoing￨L￨JJ￨O￨- importations￨L￨NNS￨O￨- of￨L￨IN￨O￨- poliovirus￨L￨NN￨O￨- into￨L￨IN￨O￨- polio-free￨L￨JJ￨O￨- countries￨L￨NNS￨O￨A ,￨L￨,￨O￨- on￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- WHO￨U￨WP￨ORGANIZATION￨- ’s￨L￨VBZ￨O￨- Director-General￨U￨NNP￨TITLE￨- declared￨L￨VBD￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨- poliovirus￨L￨NN￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- emergency￨L￨NN￨O￨- of￨L￨IN￨O￨- international￨L￨JJ￨O￨- concern￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- an￨L￨DT￨O￨- upsurge￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- five￨L￨CD￨NUMBER￨- previously￨L￨RB￨O￨- polio-free￨L￨JJ￨O￨- countries￨L￨NNS￨O￨A ,￨L￨,￨O￨- triggered￨L￨VBN￨O￨- by￨L￨IN￨O￨- importation￨L￨NN￨O￨- of￨L￨IN￨O￨- WPV￨U￨NN￨O￨- via￨L￨IN￨O￨- travelers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- estimated￨L￨VBD￨O￨- 665￨L￨CD￨NUMBER￨- polio￨L￨NNP￨O￨- exportations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- >￨L￨JJR￨O￨- 99￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- were￨L￨VBD￨O￨- asymptomatic￨L￨JJ￨O￨A )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- 78.3￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- originated￨L￨VBN￨O￨- from￨L￨IN￨O￨- Pakistan￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- accurate￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- topology￨L￨NN￨O￨- similarity￨L￨NN￨O￨A is￨L￨VBZ￨O￨- fundamental￨L￨JJ￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- science￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- link￨L￨NN￨O￨- prediction3￨L￨NN￨O￨- ,￨L￨,￨O￨- personalized￨L￨VBN￨O￨- recommendation4￨L￨NN￨O￨- ,￨L￨,￨O￨- spurious￨L￨JJ￨O￨- link￨L￨NN￨O￨- identification56￨L￨NN￨O￨- ,￨L￨,￨O￨- backbone￨L￨NN￨O￨- extraction789￨L￨NN￨O￨- ,￨L￨,￨O￨- community￨L￨NN￨O￨- detection1011￨L￨NN￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- coarse-graining1213￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- solve￨L￨VB￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- local￨L￨JJ￨O￨- similarity￨L￨NN￨O￨A metrics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- inferring￨L￨VBG￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- networks33￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- other￨L￨JJ￨O￨- words￨L￨NNS￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- receiving￨L￨VBG￨O￨- similar￨L￨JJ￨O￨- information/virus￨L￨NN￨O￨- in￨L￨IN￨O￨- spreading￨L￨NN￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- connected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- features￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- similarity￨L￨NN￨O￨A between￨L￨IN￨O￨- nodes1￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- required￨L￨VBN￨O￨- sample￨L￨NN￨O￨A size￨L￨NN￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- trial￨L￨NN￨O￨- investigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- relative￨L￨JJ￨O￨- risk￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- sequelae.Mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Sample￨U￨NNP￨MISC￨- size￨L￨NN￨O￨- considerations￨L￨NNS￨O￨- using￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- with￨L￨IN￨O￨- Chlamydia￨U￨NN￨O￨- trachomatis￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- sequelae￨L￨NN￨O￨- pelvic￨L￨JJ￨O￨- inflammatory￨L￨JJ￨O￨A diseaseSereina￨L￨NN￨O￨- A￨U￨DT￨O￨- Herzog1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Nicola￨U￨NNP￨MISC￨- Low2￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- Andrea￨U￨NNP￨O￨- Berghold1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 15:233￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- intervention￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- investigates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- sample￨L￨NN￨O￨A size￨L￨NN￨O￨A calculations￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- randomised￨L￨JJ￨O￨- controlled￨L￨JJ￨O￨- trial￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RCT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- Chlamydia￨U￨NN￨MISC￨- trachomatis￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- pelvic￨L￨JJ￨O￨- inflammatory￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- PID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- assumed￨L￨VBN￨O￨- event￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- effect￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨A size￨L￨NN￨O￨A calculation￨L￨NN￨O￨- implicitly￨L￨RB￨O￨- determined￨L￨VBD￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- PID￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- examined￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- assumptions￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨A size￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- published￨L￨VBN￨O￨- RCT￨U￨NN￨O￨- that￨L￨WDT￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨- screening￨L￨NN￨O￨- on￨L￨IN￨O￨- PID￨U￨NN￨O￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- natural￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- display￨L￨VB￨O￨- complex￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- extrinsic￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- environmental￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- elevated￨L￨JJ￨O￨- temperatures￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- intrinsic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- ;￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- significantly￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- water￨L￨NN￨O￨A temperatures￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- high￨L￨JJ￨O￨- UV￨U￨NN￨O￨- radiation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- decline￨L￨NN￨O￨- in￨L￨IN￨O￨- water￨L￨NN￨O￨- quality￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- densities￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- coral￨L￨NN￨O￨- bleaching￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 32￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- utilized￨L￨VBD￨O￨- Partially￨U￨RB￨O￨- Observed￨U￨VBN￨O￨- Markov￨U￨NNP￨PERSON￨- Process￨U￨VB￨O￨- (￨L￨-LRB-￨O￨- POMP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- suited￨L￨VBN￨O￨- for￨L￨IN￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- variables￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- ;￨L￨:￨O￨- rather￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- partially￨L￨RB￨O￨- observed￨L￨VBN￨O￨- through￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatially-replicated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- reports￨L￨NNS￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- prevaccine￨L￨NN￨O￨- era￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- and￨L￨CC￨O￨- built￨L￨VBN￨O￨- mechanistic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- incorporate￨L￨VBP￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨- the￨L￨DT￨O￨- unobservable￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- low￨L￨JJ￨O￨- global￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- polio￨L￨NNP￨O￨- (￨L￨-LRB-￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- rarity￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- limits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A data￨L￨NNS￨O￨A with￨L￨IN￨O￨- which￨L￨WDT￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- examined￨L￨VBD￨O￨- monthly￨L￨JJ￨SET￨- polio￨L￨NNP￨O￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨ORGANIZATION￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Service￨U￨NNP￨ORGANIZATION￨- Morbidity￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Mortality￨U￨NNP￨ORGANIZATION￨- Weekly￨U￨NNP￨ORGANIZATION￨- Reports￨U￨NNP￨ORGANIZATION￨- as￨L￨IN￨O￨- compiled￨L￨VBN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 48￨L￨CD￨NUMBER￨- contiguous￨L￨JJ￨O￨- US￨U￨NNP￨COUNTRY￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- District￨U￨NNP￨STATE_OR_PROVINCE￨- of￨L￨IN￨STATE_OR_PROVINCE￨- Columbia￨U￨NNP￨STATE_OR_PROVINCE￨- (￨L￨-LRB-￨O￨- Fig￨U￨NNP￨O￨- 1A￨L￨NN￨O￨- and￨L￨CC￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- data￨L￨NNS￨O￨- provided￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Supporting￨U￨VBG￨O￨- Information￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- components￨L￨NNS￨O￨- incorporating￨L￨VBG￨O￨- polio￨L￨NNP￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- seasonality￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- symptomatology￨L￨NN￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- and￨L￨CC￨O￨- birth￨L￨NN￨O￨A rates￨L￨NNS￨O￨A .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- progress￨L￨NN￨O￨- in￨L￨IN￨O￨- overall￨L￨JJ￨O￨- urban￨L￨JJ￨O￨A sanitation￨L￨NN￨O￨- access￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- equity￨L￨NN￨O￨- as￨L￨IN￨O￨- indicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- WHO/UNICEF￨U￨NN￨ORGANIZATION￨- Joint￨U￨NNP￨ORGANIZATION￨- Monitoring￨U￨VBG￨ORGANIZATION￨- Programme￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- JMP￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- metrics￨L￨NNS￨O￨- ,￨L￨,￨O￨- residents￨L￨NNS￨O￨- of￨L￨IN￨O￨- urbanising￨L￨NN￨O￨- ,￨L￨,￨O￨- unplanned￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- of￨L￨IN￨O￨- SSA￨U￨NN￨ORGANIZATION￨- experience￨L￨NN￨O￨- persistently￨L￨RB￨O￨- elevated￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risks￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- poor￨L￨JJ￨O￨- sanitation￨L￨NN￨O￨- infrastructure￨L￨NN￨O￨- that￨L￨WDT￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- reliably￨L￨RB￨O￨- sequester￨L￨VB￨O￨- excreta￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- human￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- .6￨L￨NN￨NUMBER￨- 7￨L￨CD￨NUMBER￨- Although￨U￨IN￨O￨- open￨L￨JJ￨O￨- defaecation￨L￨NN￨O￨- and￨L￨CC￨O￨- ‘￨L￨``￨O￨- unimproved￨L￨JJ￨O￨- ’￨L￨''￨O￨- sanitation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- prevalent￨L￨JJ￨O￨- in￨L￨IN￨O￨- urban￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- in￨L￨IN￨O￨- SSA￨U￨NNP￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- rural￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- categories￨L￨NNS￨O￨- apply￨L￨VBP￨O￨- to￨L￨TO￨O￨- one-third￨L￨NN￨ORDINAL￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- urban￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- proportion￨L￨NN￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- changed￨L￨VBN￨O￨- significantly￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- two￨L￨CD￨DURATION￨- decades￨L￨NNS￨DURATION￨- .5￨L￨CD￨NUMBER￨- Although￨U￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- without￨L￨IN￨O￨- adequate￨L￨JJ￨O￨- sanitation￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- lower￨L￨JJR￨O￨- in￨L￨IN￨O￨- urban￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- rural￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- unsafe￨L￨JJ￨O￨- excreta￨L￨NN￨O￨- disposal￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- much￨L￨RB￨O￨- greater￨L￨JJR￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- dense￨L￨JJ￨O￨- urban￨L￨JJ￨O￨- population￨L￨NN￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- low-density￨L￨JJ￨O￨- rural￨L￨JJ￨O￨- population￨L￨NN￨O￨- where￨L￨WRB￨O￨- open￨L￨JJ￨O￨- defaecation￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- largely￨L￨RB￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- boundaries￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- habitation￨L￨NN￨O￨- .￨L￨.￨O￨- +Limited￨U￨JJ￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- prevents￨L￨VBZ￨O￨- stratified￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- important￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- shared￨L￨VBN￨O￨- latrine￨L￨NN￨O￨- type￨L￨NN￨O￨- and￨L￨CC￨O￨- ages￨L￨NNS￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- cohort￨L￨NN￨O￨- now￨L￨RB￨DATE￨- includes￨L￨VBZ￨O￨- children￨L￨NNS￨O￨- from￨L￨IN￨O￨- 29￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- 48￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- at￨L￨IN￨O￨- baseline￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- risks￨L￨NNS￨O￨A of￨L￨IN￨O￨- enteric￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- very￨L￨RB￨O￨- different￨L￨JJ￨O￨- if￨L￨IN￨O￨- child￨L￨NN￨O￨- age￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- narrowly￨L￨RB￨O￨- defined￨L￨VBN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- imprecisely￨L￨RB￨O￨- known￨L￨VBN￨O￨- and￨L￨CC￨O￨- context-specific￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- poor￨L￨JJ￨O￨- sanitation￨L￨NN￨O￨- specifically￨L￨RB￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- high￨L￨JJ￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- sanitation￨L￨NN￨O￨- serves￨L￨VBZ￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨- barrier￨L￨NN￨O￨- against￨L￨IN￨O￨- faecal￨L￨JJ￨O￨- contamination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- environment20￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- outcomes￨L￨NNS￨O￨- .21￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- are￨L￨VBP￨O￨- undertaking￨L￨VBG￨O￨- a￨L￨DT￨O￨- controlled￨L￨JJ￨O￨- before-and-after￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- CBA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- urban￨L￨JJ￨O￨A sanitation￨L￨NN￨O￨- intervention￨L￨NN￨O￨- in￨L￨IN￨O￨- Maputo￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Mozambique￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- primary￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- as￨L￨IN￨O￨- summarised￨L￨JJ￨O￨- below￨L￨IN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- controlled￨L￨JJ￨O￨- before-and-after￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- CBA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- residual￨L￨JJ￨O￨- confounding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- shared￨L￨JJ￨O￨- sanitation￨L￨NN￨O￨- on￨L￨IN￨O￨- enteric￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨A can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- eliminated￨L￨VBN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- for￨L￨IN￨O￨- confounding￨L￨VBG￨O￨- variables￨L￨NNS￨O￨- that￨L￨WDT￨O￨- change￨L￨VBP￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- CBA￨U￨NN￨ORGANIZATION￨- trial￨L￨NN￨O￨- is￨L￨VBZ￨O￨- intended￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- decentralised￨L￨JJ￨O￨- urban￨L￨JJ￨O￨A sanitation￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- combined￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- enteric￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- .￨L￨.￨O￨- +pertussis￨L￨NN￨CAUSE_OF_DEATH￨- isolates￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- evidence￨L￨NN￨O￨- in￨L￨IN￨O￨- support￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- B.￨U￨NNP￨O￨- Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- age-specific￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- UK￨U￨NNP￨COUNTRY￨- are￨L￨VBP￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ;￨L￨:￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- phylodynamic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- sequences￨L￨NNS￨O￨- indicates￨L￨VBZ￨O￨- more￨L￨JJR￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- bacterial￨L￨JJ￨O￨- population￨L￨NN￨O￨- than￨L￨IN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- suggested￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- pattern￨L￨NN￨O￨- expected￨L￨VBN￨O￨- with￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ;￨L￨:￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- asymptomatic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- bias￨L￨NN￨O￨- assessments￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- B.￨U￨NNP￨O￨- pertussis-free￨L￨JJ￨O￨- weeks￨L￨NNS￨DURATION￨- ;￨L￨:￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- asymptomatic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- can￨L￨MD￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- B.￨U￨NNP￨O￨- +Recent￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- suggested￨L￨VBN￨O￨- a￨L￨DT￨O￨- fourth￨L￨JJ￨ORDINAL￨- mechanism￨L￨NN￨O￨- :￨L￨:￨O￨- asymptomatic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- vaccinated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- currently￨L￨RB￨DATE￨- used￨L￨VBN￨O￨- acellular￨L￨JJ￨O￨- B.￨U￨NNP￨MISC￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- vaccines￨L￨NNS￨O￨- .￨L￨.￨O￨- +Acquisition￨U￨NN￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- patients￨L￨NNS￨O￨- treated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ward￨L￨NN￨O￨- ,￨L￨,￨O￨- mainly￨L￨RB￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- transiently￨L￨RB￨O￨- contaminated￨L￨VBN￨O￨- hands￨L￨NNS￨O￨- of￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- workers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- cross-transmission￨L￨JJ￨O￨- acquisition￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- review￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- highlighted￨L￨VBD￨O￨- a￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- using￨L￨VBG￨O￨A mathematical￨L￨JJ￨O￨A modelling￨L￨NN￨O￨- because￨L￨IN￨O￨- such￨L￨JJ￨O￨- information￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- designing￨L￨VBG￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Algorithms￨U￨NNS￨O￨- for￨L￨IN￨O￨- data￨L￨NN￨O￨- analysis￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- hidden￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- HMMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- making￨L￨VBG￨O￨- inferences￨L￨NNS￨O￨- about￨L￨IN￨O￨- an￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨- event￨L￨NN￨O￨- and￨L￨CC￨O￨- estimating￨L￨VBG￨O￨- transmission￨L￨NN￨O￨A parameters￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Alternatively￨U￨RB￨O￨- ,￨L￨,￨O￨- acquisition￨L￨NN￨O￨A may￨L￨MD￨O￨- result￨L￨VB￨O￨- from￨L￨IN￨O￨- sources￨L￨NNS￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- cross-transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- sporadic￨L￨JJ￨O￨- acquisition￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- colonisation￨L￨NN￨O￨- already￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- at￨L￨IN￨O￨- admission￨L￨NN￨O￨- and￨L￨CC￨O￨- de￨L￨FW￨O￨- novo￨L￨FW￨O￨- colonisation￨L￨NN￨O￨- from￨L￨IN￨O￨- patient￨L￨NN￨O￨- ’s￨L￨POS￨O￨- gastrointestinal￨L￨JJ￨O￨- flora￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Estimating￨U￨VBG￨O￨- transmission￨L￨NN￨O￨A parameters￨L￨NNS￨O￨A using￨L￨VBG￨O￨- hospital￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- circulation￨L￨NN￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Mayotte￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- risk￨L￨NN￨O￨- assessment￨L￨NN￨O￨A procedure￨L￨NN￨O￨- evaluated￨L￨VBD￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- persistence￨L￨NN￨O￨- as￨L￨IN￨O￨- “￨L￨``￨O￨- low￨L￨JJ￨O￨- ”￨L￨''￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ruminants￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- dispersal￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- would￨L￨MD￨O￨- slow￨L￨VB￨O￨- down￨L￨RP￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- low￨L￨JJ￨O￨- vector￨L￨NN￨O￨- activity￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- assessment￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- wild￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- theoretical￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- had￨L￨VBD￨O￨- already￨L￨RB￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- RVF￨U￨NN￨O￨- could￨L￨MD￨O￨- persist￨L￨VB￨O￨- at￨L￨IN￨DURATION￨- least￨L￨JJS￨DURATION￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- cattle￨L￨NNS￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- vector￨L￨NN￨O￨A populations￨L￨NNS￨O￨A of￨L￨IN￨O￨- constant￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- Culex￨U￨NNP￨O￨- and￨L￨CC￨O￨- Aedes￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- being￨L￨VBG￨O￨- able￨L￨JJ￨O￨- of￨L￨IN￨O￨- vertical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Persistence￨U￨NN￨O￨- was￨L￨VBD￨O￨- also￨L￨RB￨O￨- possible￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- model￨L￨NN￨TITLE￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- low￨L￨JJ￨O￨A and￨L￨CC￨O￨- high￨L￨JJ￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- RVF￨U￨NN￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- emphasised￨L￨VBD￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- test￨L￨VB￨O￨- their￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- against￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Concerning￨U￨VBG￨O￨- RVF￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- vector￨L￨NN￨O￨A populations￨L￨NNS￨O￨A of￨L￨IN￨O￨- constant￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- RVF￨U￨NN￨O￨- incidence￨L￨NN￨O￨- remained￨L￨VBD￨O￨- high￨L￨JJ￨O￨- among￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A born￨L￨VBN￨O￨- in￨L￨IN￨O￨- Mayotte￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- 12.9￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- IC95￨U￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- =￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 9.6￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- 16.2￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- was￨L￨VBD￨O￨- suspected￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- become￨L￨VBN￨O￨- endemic￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Nyabadza￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- presented￨L￨VBD￨O￨A a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- HIV/AIDS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- applied￨L￨VBD￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- South￨U￨JJ￨NATIONALITY￨- African￨U￨JJ￨NATIONALITY￨- situation￨L￨NN￨O￨- and￨L￨CC￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- condoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- sexual￨L￨JJ￨O￨- partner￨L￨NN￨O￨- acquisition￨L￨NN￨O￨- ,￨L￨,￨O￨- behavior￨L￨NN￨O￨- change￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- ;￨L￨:￨O￨- their￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- controlled￨L￨VBN￨O￨- through￨L￨IN￨O￨- these￨L￨DT￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- presented￨L￨VBD￨O￨A work￨L￨NN￨O￨- demonstrating￨L￨VBG￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- in￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- City￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- work￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- conceptual￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- short-term￨L￨JJ￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Merli￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- presented￨L￨VBD￨O￨A an￨L￨DT￨O￨- exploration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- reflected￨L￨VBD￨O￨- the￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨- surrounding￨L￨VBG￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- analyses￨L￨NNS￨O￨- used￨L￨VBN￨O￨- showed￨L￨VBD￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Hyman￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Stanley￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- generated￨L￨VBD￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨A and￨L￨CC￨O￨- anticipate￨L￨VB￨O￨- its￨L￨PRP$￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Naresh￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- calculated￨L￨VBD￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- immigration￨L￨NN￨O￨- among￨L￨IN￨O￨- HIV-infected￨U￨JJ￨MISC￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- findings￨L￨NNS￨O￨- revealed￨L￨VBD￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- flow￨L￨NN￨O￨- of￨L￨IN￨O￨- immigrating￨L￨VBG￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- all￨L￨DT￨O￨- information￨L￨NN￨O￨- items￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- probabilities￨L￨NNS￨O￨- ,￨L￨,￨O￨- penalties￨L￨NNS￨O￨- ,￨L￨,￨O￨- required￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- chosen￨L￨VBN￨O￨- decision￨L￨NN￨O￨- making￨L￨VBG￨O￨- algorithm￨L￨NN￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- available￨L￨JJ￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- decision￨L￨NN￨O￨- task￨L￨NN￨O￨- is￨L￨VBZ￨O￨- solved￨L￨VBN￨O￨A under￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- ignorance￨L￨NN￨O￨- .￨L￨.￨O￨- +Management￨U￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- common￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- environment￨L￨NN￨O￨- and￨L￨CC￨O￨- safety￨L￨NN￨O￨- problems￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- and￨L￨CC￨O￨- solved￨L￨VBN￨O￨A via￨L￨IN￨O￨- group￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- best￨L￨JJS￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- public￨L￨JJ￨O￨- goods￨L￨NNS￨O￨- games￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- of￨L￨IN￨O￨- decision-making￨L￨JJ￨O￨- tasks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- single￨L￨JJ￨O￨- root￨L￨NN￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- decision￨L￨NN￨O￨A trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- III￨U￨NNP￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- probabilities￨L￨NNS￨O￨- ,￨L￨,￨O￨- penalties￨L￨NNS￨O￨- ,￨L￨,￨O￨- plausibility￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- e.g￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨- is￨L￨VBZ￨O￨- handled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- fuzzy￨L￨JJ￨O￨- sets￨L￨NNS￨O￨A ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- fuzzy￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- see.e.g￨L￨NN￨O￨- .￨L￨.￨O￨- +Problems￨U￨NNS￨O￨- under￨L￨IN￨O￨- partial￨L￨JJ￨O￨- ignorance￨L￨NN￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- solved￨L￨VBN￨O￨A by￨L￨IN￨O￨- Bayes￨U￨NNP￨PERSON￨- '￨L￨POS￨O￨- Theorem￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Bayesian￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- see.e.g￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Optimizing￨U￨VBG￨MISC￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- population-based￨L￨JJ￨O￨- chlamydia￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- screening￨L￨NN￨O￨A among￨L￨IN￨O￨- young￨L￨JJ￨O￨- women￨L￨NNS￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- system￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- approachYu￨L￨NN￨O￨- Teng1￨U￨NN￨O￨- ,￨L￨,￨O￨- Nan￨U￨NN￨PERSON￨- Kong2Email￨U￨NN￨PERSON￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Wanzhu￨U￨NN￨O￨- Tu3￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 15:639￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Chlamydia￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- CT￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- reported￨L￨VBN￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- parameter￨L￨NN￨O￨- optimization￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- resultant￨L￨JJ￨O￨- PDE-based￨U￨JJ￨MISC￨- system￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- care￨L￨NN￨O￨- spending￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- screening￨L￨NN￨O￨A and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- costs￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- program￨L￨NN￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- anticipated￨L￨VBN￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- treating￨L￨VBG￨O￨- the￨L￨DT￨O￨- sequelae￨L￨NN￨O￨- afterwards￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- age-dependent￨L￨JJ￨O￨- screening￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- population-based￨L￨JJ￨O￨- chlamydia￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- screening￨L￨NN￨O￨- among￨L￨IN￨O￨- young￨L￨JJ￨O￨- women￨L￨NNS￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- age-dependent￨L￨JJ￨O￨- screening￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- frequent￨L￨JJ￨O￨- testing￨L￨NN￨O￨- for￨L￨IN￨O￨- certain￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- higher￨L￨JJR￨O￨- risk￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- cost-saving￨L￨JJ￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- CT￨U￨NNP￨STATE_OR_PROVINCE￨- natural￨L￨JJ￨O￨- progress￨L￨NN￨O￨- ,￨L￨,￨O￨- screening￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +Very￨U￨RB￨O￨- little￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- without￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- asymptomatic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- difficulties￨L￨NNS￨O￨- in￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨A of￨L￨IN￨O￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Assessment￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- control￨L￨NN￨O￨- by￨L￨IN￨O￨- isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- specific￨L￨JJ￨O￨- age￨L￨NN￨O￨A groups￨L￨NNS￨O￨A can￨L￨MD￨O￨- guide￨L￨VB￨O￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- and￨L￨CC￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- target￨L￨VB￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- data￨L￨NNS￨O￨A on￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- serological￨L￨JJ￨O￨- survey￨L￨NN￨O￨- in￨L￨IN￨O￨- Changsha￨U￨NNP￨LOCATION￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- then￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- isolating￨L￨VBG￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨A groups￨L￨NNS￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- data￨L￨NNS￨O￨A included￨L￨VBD￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- enrolled￨L￨VBN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- serosurvey￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- most￨L￨JJS￨O￨- empirical￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- large￨L￨JJ￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- average￨L￨JJ￨O￨- statistics￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- reference￨L￨NN￨O￨- when￨L￨WRB￨O￨- determining￨L￨VBG￨O￨- universal￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- evidence￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- that￨L￨WDT￨O￨- spreading￨L￨VBG￨O￨- modes￨L￨NNS￨O￨- differ￨L￨VBP￨O￨A as￨L￨IN￨O￨- information￨L￨NN￨O￨- types￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- linked￨L￨VBN￨O￨- “￨L￨``￨O￨- friends￨L￨NNS￨O￨- ”￨L￨''￨O￨- a￨L￨DT￨O￨- user￨L￨NN￨O￨- has￨L￨VBZ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- much￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- popular￨L￨JJ￨O￨- messages￨L￨NNS￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fractional￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- friends￨L￨NNS￨O￨- needs￨L￨VBZ￨O￨- more￨L￨JJR￨O￨- repeated￨L￨JJ￨O￨- signals￨L￨NNS￨O￨- before￨L￨IN￨O￨- sharing￨L￨VBG￨O￨- a￨L￨DT￨O￨- message￨L￨NN￨O￨A than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- friends￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- purple￨L￨JJ￨O￨- dots￨L￨NNS￨O￨- are￨L￨VBP￨O￨- users￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- shared￨L￨VBN￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- green￨L￨JJ￨O￨- lines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- paths￨L￨NNS￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨- has￨L￨VBZ￨O￨- spread￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- susceptible￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- frequently￨L￨RB￨O￨A used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- green￨L￨JJ￨O￨A energy￨L￨NN￨O￨- utilization￨L￨NN￨O￨- and￨L￨CC￨O￨- power￨L￨NN￨O￨- consumption￨L￨NN￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- strategic￨L￨JJ￨O￨- game￨L￨NN￨O￨- and￨L￨CC￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- distributed￨L￨VBN￨O￨- algorithm￨L￨NN￨O￨- that￨L￨WDT￨O￨- solves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- strategic￨L￨JJ￨O￨- game￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- regret￨L￨NN￨O￨- matching￨L￨VBG￨O￨- procedure￨L￨NN￨O￨- to￨L￨TO￨O￨- enhance￨L￨VB￨O￨- energy￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- green￨L￨JJ￨O￨A energy￨L￨NN￨O￨- utilization￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- adopt￨L￨VBP￨O￨- the￨L￨DT￨O￨- energy￨L￨NN￨O￨- depleting￨L￨VBG￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EDR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- metric￨L￨JJ￨O￨- for￨L￨IN￨O￨- BS￨U￨NN￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- below￨L￨IN￨O￨- where￨L￨WRB￨O￨- R￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- EDR￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- BS￨U￨NN￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmit￨L￨VB￨O￨- power￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨- power￨L￨NN￨O￨- consumption￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- allocated￨L￨VBN￨O￨- green￨L￨JJ￨O￨- energy￨L￨NN￨O￨- in￨L￨IN￨O￨- BS￨U￨NNP￨O￨- m.￨L￨NNP￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- algorithm￨L￨NN￨O￨- achieves￨L￨VBZ￨O￨- an￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pilot￨L￨NN￨TITLE￨- power￨L￨NN￨O￨- selection￨L￨NN￨O￨- game￨L￨NN￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- optimum￨L￨JJ￨O￨- green￨L￨JJ￨O￨A energy￨L￨NN￨O￨- utilization￨L￨NN￨O￨- and￨L￨CC￨O￨- power￨L￨NN￨O￨- consumption￨L￨NN￨O￨- reduction￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- pilot￨L￨NN￨TITLE￨- power￨L￨NN￨O￨- selection￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- regret￨L￨NN￨O￨- matching￨L￨VBG￨O￨- procedure￨L￨NN￨O￨- for￨L￨IN￨O￨- green￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- convergence￨L￨NN￨O￨- and￨L￨CC￨O￨- comparative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- Intelligent￨U￨JJ￨O￨- Cell￨U￨NN￨O￨- brEathing￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ICE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- algorithm￨L￨NN￨O￨- that￨L￨WDT￨O￨- maximizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- utilization￨L￨NN￨O￨- of￨L￨IN￨O￨- green￨L￨JJ￨O￨A energy￨L￨NN￨O￨- through￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- cell￨L￨NN￨O￨- breathing￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- actors￨L￨NNS￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- layers￨L￨NNS￨O￨A make￨L￨VBP￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- process￨L￨NN￨O￨- more￨L￨RBR￨O￨- efficient￨L￨JJ￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- increase￨L￨VBP￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- above￨L￨IN￨O￨- that￨L￨DT￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- isolated￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- real-world￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- isolated￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- act￨L￨VB￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- layers￨L￨NNS￨O￨A ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- go￨L￨VB￨O￨- to￨L￨TO￨O￨- work￨L￨VB￨O￨- or￨L￨CC￨O￨- visit￨L￨VB￨O￨- friends￨L￨NNS￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- to￨L￨TO￨O￨- stay￨L￨VB￨O￨- at￨L￨IN￨O￨- home￨L￨NN￨O￨- or￨L￨CC￨O￨- be￨L￨VB￨O￨- hospitalized￨L￨VBN￨O￨- .￨L￨.￨O￨- +Yagan￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 38￨L￨CD￨NUMBER￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- multilayer￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- act￨L￨VBP￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- layers￨L￨NNS￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- commonly-used￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- reproducing￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model1819￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- 4￨L￨CD￨NUMBER￨- questions￨L￨NNS￨O￨- :￨L￨:￨O￨- What￨U￨WP￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- estimate￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- stratified￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- —￨L￨:￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- simple￨L￨JJ￨O￨- random￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- sections￨L￨NNS￨O￨A —￨L￨:￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- residential￨L￨JJ￨O￨- survey￨L￨NN￨O￨- records￨L￨NNS￨O￨- are￨L￨VBP￨O￨- first￨L￨JJ￨ORDINAL￨- partitioned￨L￨VBN￨O￨- into￨L￨IN￨O￨- mutually-exclusive￨L￨JJ￨O￨- strata￨L￨NN￨O￨- with￨L￨IN￨O￨- non-overlapping￨L￨JJ￨O￨- ranges￨L￨NNS￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- persons￨L￨NNS￨O￨- per￨L￨IN￨O￨- residential￨L￨JJ￨O￨- structure￨L￨NN￨O￨- ?￨L￨.￨O￨- ”￨L￨''￨O￨- +The￨U￨DT￨O￨- ground￨L￨NN￨O￨- truth￨L￨NN￨O￨- survey￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- 20￨L￨CD￨NUMBER￨- sections￨L￨NNS￨O￨A will￨L￨MD￨O￨- provide￨L￨VB￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- using￨L￨VBG￨O￨- different￨L￨JJ￨O￨- stratification￨L￨NN￨O￨- protocols￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- estimate￨L￨NN￨O￨- achievable￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- will￨L￨MD￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- stratified￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- sampling￨L￨NN￨O￨- protocol￨L￨NN￨O￨- ,￨L￨,￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- random￨L￨JJ￨O￨- selection￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- select￨L￨VB￨O￨- the￨L￨DT￨O￨- 4￨L￨CD￨NUMBER￨- sections￨L￨NNS￨O￨A on￨L￨IN￨O￨- each￨L￨DT￨O￨- simulation￨L￨NN￨O￨- trial￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- exploit￨L￨VB￨O￨- this￨L￨DT￨O￨- prior￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- an￨L￨DT￨O￨- improved￨L￨JJ￨O￨- stratification￨L￨NN￨O￨- protocol￨L￨NN￨O￨- for￨L￨IN￨O￨- re-estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- estimate￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- random￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIT￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- four-dimensional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- Λ￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨A ;￨L￨:￨O￨- μ￨L￨NN￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- 20￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- μ￨L￨NN￨O￨- 30￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- nonnegative￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- and￨L￨CC￨O￨- denote￨L￨VBP￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease-caused￨L￨JJ￨O￨- death￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨- an￨L￨DT￨O￨- SEIT￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- apply￨L￨VB￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- T￨U￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨A ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- treated/recovered￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- these￨L￨DT￨O￨- various￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- on￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨A a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- fitted￨L￨JJ￨O￨- probabilistically￨L￨RB￨O￨- to￨L￨TO￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Along￨U￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- SEIT￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- develop￨L￨VB￨O￨- EVD￨U￨NN￨O￨- by￨L￨IN￨O￨- contacting￨L￨VBG￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨A or￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- least￨L￨JJS￨O￨- square￨L￨NN￨O￨- method￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- by￨L￨IN￨O￨- onset￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨A data￨L￨NNS￨O￨- in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- weekly￨L￨NN￨SET￨A reported￨L￨VBD￨O￨- EVD￨U￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Liberia￨U￨NNP￨COUNTRY￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- ℛ0￨U￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- dynamical￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- ,￨L￨,￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- studied￨L￨VBN￨O￨- various￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- interventions￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- hospitalization￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- cases￨L￨NNS￨O￨- after￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- at￨L￨IN￨O￨- hospital￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- estimated￨L￨VBN￨O￨- with￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- 2.7￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨A %￨L￨NN￨PERCENT￨- Confidence￨U￨NN￨O￨- Interval￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- CI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- 1.9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 2.8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Congo￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 2.7￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- :￨L￨:￨O￨- 2.5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Uganda￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Legrand￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- revisit￨L￨VB￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- known￨L￨JJ￨O￨- Ebola￨U￨NNP￨MISC￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- ℛ0￨U￨NN￨O￨- ≈￨L￨CD￨NUMBER￨- 1.34￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨A %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- :￨L￨:￨O￨- 0.92￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 2.11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- are￨L￨VBP￨O￨- working￨L￨VBG￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- algorithm￨L￨NN￨O￨A to￨L￨TO￨O￨- cover￨L￨VB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- only￨L￨RB￨O￨- partial￨L￨JJ￨O￨- information￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- diagnosed￨L￨VBD￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- particle￨L￨NN￨O￨- filtering￨L￨VBG￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- It￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Pt￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- detection￨L￨NN￨O￨- map￨L￨NN￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- population￨L￨NN￨O￨- It￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- posterior￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- population￨L￨NN￨O￨- Pt￨U￨NN￨O￨- .￨L￨.￨O￨- +Cycle￨U￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- possible￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A parasite￨L￨NN￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- To￨U￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasite￨L￨NN￨O￨- intervention￨L￨NN￨O￨- points￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- regional￨L￨JJ￨O￨- control￨L￨NN￨O￨- program￨L￨NN￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- The￨U￨DT￨O￨- global￨L￨JJ￨O￨- effort￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- line￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- world￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- health￨L￨NN￨O￨- concept￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- then￨L￨RB￨O￨- a￨L￨DT￨O￨- globally￨L￨RB￨O￨- defined￨L￨VBN￨O￨- ‘‘￨L￨``￨O￨- one-size-fits-all￨L￨JJ￨O￨- ’’￨L￨''￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- inefficient￨L￨JJ￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A parasite￨L￨NN￨O￨- intervention￨L￨NN￨O￨- points￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- regional￨L￨JJ￨O￨- control￨L￨NN￨O￨- program￨L￨NN￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- The￨U￨DT￨O￨- global￨L￨JJ￨O￨- effort￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- line￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- world￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- health￨L￨NN￨O￨- concept￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- then￨L￨RB￨O￨- a￨L￨DT￨O￨- globally￨L￨RB￨O￨- defined￨L￨VBN￨O￨- ‘‘￨L￨``￨O￨- one-size-fits-all￨L￨JJ￨O￨- ’’￨L￨''￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- inefficient￨L￨JJ￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- interventions￨L￨NNS￨O￨- targeted￨L￨VBN￨O￨- at￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- through￨L￨IN￨O￨- destruction￨L￨NN￨O￨- of￨L￨IN￨O￨- breeding￨L￨VBG￨O￨- sites￨L￨NNS￨O￨- and￨L￨CC￨O￨- prophylaxis/treatment/use￨L￨NN￨O￨- of￨L￨IN￨O￨- nets￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨A period￨L￨NN￨O￨A ,￨L￨,￨O￨- number￨L￨NN￨O￨- infected￨L￨VBN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- immuned￨L￨VBN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- Ro￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- more￨L￨RBR￨O￨- immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- wil￨L￨NN￨O￨- llead￨L￨NN￨O￨- to￨L￨TO￨O￨- Ro1￨U￨NN￨O￨- until￨L￨IN￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- control￨L￨NN￨O￨- program￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- point￨L￨NN￨O￨- Ro￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Taking￨U￨VBG￨O￨- β￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- bites￨L￨VBZ￨O￨- per￨L￨IN￨O￨- person￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- ;￨L￨:￨O￨- β1￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A vectors￨L￨NNS￨O￨- ;￨L￨:￨O￨- β2￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- under￨L￨IN￨O￨- intervention￨L￨NN￨O￨- and￨L￨CC￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- vectors￨L￨NNS￨O￨- ;￨L￨:￨O￨- β3￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- vectors￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- S￨U￨NN￨O￨- =￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- =￨L￨JJ￨O￨- population￨L￨NN￨O￨- under￨L￨IN￨O￨- intervention￨L￨NN￨O￨- ,￨L￨,￨O￨- D￨U￨NN￨O￨- =￨L￨JJ￨O￨- dead￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +Intervention￨U￨NN￨O￨- will￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- when￨L￨WRB￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- equals￨L￨VBZ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- Ih￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- Im￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Ro￨U￨NN￨O￨- ∝￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- γ￨L￨NN￨O￨- ;￨L￨:￨O￨- Ro￨U￨NN￨O￨- =￨L￨JJ￨O￨- b/γ￨L￨NN￨O￨- where￨L￨WRB￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- to￨L￨TO￨O￨- mosquitoes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- reviewed￨L￨VBD￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- reflected￨L￨VBN￨O￨- in￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- structures￨L￨NNS￨O￨- and￨L￨CC￨O￨- parameterizations￨L￨NNS￨O￨- ,￨L￨,￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- their￨L￨PRP$￨O￨- suitability￨L￨NN￨O￨- to￨L￨TO￨O￨- answer￨L￨VB￨O￨- current￨L￨JJ￨DATE￨- questions￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- optimal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- formulation￨L￨NN￨O￨- and￨L￨CC￨O￨- scheduling￨L￨NN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- were￨L￨VBD￨O￨- selected￨L￨VBN￨O￨- for￨L￨IN￨O￨- review￨L￨NN￨O￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- characterized￨L￨VBD￨O￨- an￨L￨DT￨O￨- aspect￨L￨NN￨O￨- of￨L￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- immunity￨L￨NN￨O￨- differently￨L￨RB￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- although￨L￨IN￨O￨- not￨L￨RB￨O￨- an￨L￨DT￨O￨- exhaustive￨L￨JJ￨O￨- list￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- published￨L￨VBN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Authors￨U￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- drivers￨L￨NNS￨O￨- of￨L￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- explore￨L￨VB￨O￨- alternative￨L￨JJ￨O￨- explanations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- resurgence￨L￨NN￨O￨- and￨L￨CC￨O￨- predict￨L￨VBP￨O￨- potential￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Parameters￨U￨NNS￨O￨- with￨L￨IN￨O￨- biological￨L￨JJ￨O￨- ,￨L￨,￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiologic￨L￨JJ￨O￨- interpretations￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- chosen￨L￨VBN￨O￨- compartmental￨L￨JJ￨O￨- break-down￨L￨NN￨O￨- ,￨L￨,￨O￨- define￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- whole￨L￨JJ￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨A made￨L￨VBD￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- under￨L￨IN￨O￨- study￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- processes￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- within￨L￨IN￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A )￨L￨-RRB-￨O￨- within￨L￨IN￨O￨- that￨L￨DT￨O￨- population￨L￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Clinical￨U￨JJ￨O￨- trial￨L￨NN￨O￨- evidence￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- pneumococcal￨L￨JJ￨O￨A polysaccharide￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PPV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- traditionally￨L￨RB￨O￨- recommended￨L￨VBN￨O￨- for￨L￨IN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- adults￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- elderly￨L￨JJ￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- effective￨L￨JJ￨O￨- against￨L￨IN￨O￨- IPD￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- NPP￨U￨NN￨ORGANIZATION￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- clear￨L￨JJ￨O￨- .￨L￨.￨O￨- +IPD￨U￨NNP￨ORGANIZATION￨- generally￨L￨RB￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- hospitalization￨L￨NN￨O￨- ,￨L￨,￨O￨- requiring￨L￨VBG￨O￨- significant￨L￨JJ￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- expenditures￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- estimated￨L￨VBN￨O￨- that￨L￨IN￨O￨- non-invasive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- non-bacteraemic￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨A pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- NPP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- total￨L￨JJ￨O￨- cost￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- literature￨L￨NN￨O￨- search￨L￨NN￨O￨- was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- articles￨L￨NNS￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- PCV13￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- in￨L￨IN￨O￨- adults￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- elderly￨L￨JJ￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- double-blind￨L￨JJ￨O￨- ,￨L￨,￨O￨- randomized￨L￨VBN￨O￨- placebo-controlled￨L￨JJ￨O￨- trial￨L￨NN￨O￨A conducted￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- CAPiTA￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- reported￨L￨VBN￨O￨- that￨L￨IN￨O￨- PCV13￨U￨NN￨O￨- is￨L￨VBZ￨O￨- effective￨L￨JJ￨O￨- against￨L￨IN￨O￨- IPD￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- 45￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- episode￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- type￨L￨NN￨O￨- NPP￨U￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- extensive￨L￨JJ￨O￨- highlight￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- framework￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- both￨L￨CC￨O￨- cross￨L￨VBP￨O￨- community￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- exchange￨L￨NN￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- between￨L￨IN￨O￨- communities￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- case￨L￨NN￨O￨- is￨L￨VBZ￨O￨- specific￨L￨JJ￨O￨- to￨L￨TO￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Optimal￨U￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- only￨L￨RB￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- recently￨L￨RB￨DATE￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- when￨L￨WRB￨O￨- comparing￨L￨VBG￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- separate￨L￨JJ￨O￨- Indian￨U￨JJ￨NATIONALITY￨- communities￨L￨NNS￨O￨- of￨L￨IN￨O￨- Bogra￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Calcutta￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- preventive￨L￨JJ￨O￨- and￨L￨CC￨O￨- control￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- explained￨L￨VBN￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- with￨L￨IN￨O￨- regard￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- connected￨L￨JJ￨O￨- communities￨L￨NNS￨O￨A as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- note￨L￨VB￨O￨- that￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- single￨L￨JJ￨O￨- community￨L￨NN￨O￨- settings￨L￨NNS￨O￨- was￨L￨VBD￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- controls￨L￨NNS￨O￨- since￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- typically￨L￨RB￨O￨- follows￨L￨VBZ￨O￨- such￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- game￨L￨NN￨O￨A presented￨L￨VBD￨O￨- the￨L￨DT￨O￨- player￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- pre-selected￨L￨JJ￨O￨- small￨L￨JJ￨O￨- section￨L￨NN￨O￨- of￨L￨IN￨O￨- genome￨L￨NN￨O￨- sequence￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- KW1￨U￨NN￨O￨- reference￨L￨NN￨O￨- strain￨L￨NN￨O￨- and￨L￨CC￨O￨- rows￨L￨NNS￨O￨- of￨L￨IN￨O￨- sequence￨L￨NN￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- test￨L￨NN￨O￨- variants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- DNA￨U￨NN￨O￨- sequence￨L￨NN￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- string￨L￨NN￨O￨- of￨L￨IN￨O￨- colored￨L￨VBN￨O￨- leaves￨L￨NNS￨O￨- .￨L￨.￨O￨- +Subsequently￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- and￨L￨CC￨O￨- released￨L￨VBD￨O￨- Fraxinus￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Facebook-based￨U￨JJ￨MISC￨- game￨L￨NN￨O￨A ,￨L￨,￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- non-specialists￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- genetic￨L￨JJ￨O￨- variant￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- from￨L￨IN￨O￨- DNA￨U￨NN￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- OADB￨U￨NN￨O￨- project￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- game￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- player￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- alignment￨L￨NN￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- her/him￨L￨NN￨O￨- to￨L￨TO￨O￨- claim￨L￨VB￨O￨- the￨L￨DT￨O￨- puzzle￨L￨NN￨O￨- as￨L￨IN￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- and￨L￨CC￨O￨- score￨L￨NN￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- Fraxinus￨U￨NNP￨MISC￨- game￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- alignment￨L￨NN￨O￨- comparisons￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- the￨L￨DT￨O￨- game￨L￨NN￨O￨- received￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- replicate￨L￨VB￨O￨- player￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- stored￨L￨VBD￨O￨- player￨L￨NN￨O￨- names￨L￨NNS￨O￨- ,￨L￨,￨O￨- scores￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- alignments￨L￨NNS￨O￨- for￨L￨IN￨O￨- later￨L￨JJ￨O￨A analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +accounted￨L￨VBN￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- contexts￨L￨NNS￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- 6￨L￨CD￨NUMBER￨- compartments￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- hospitalized￨L￨VBN￨O￨A ,￨L￨,￨O￨- dead-but-not-yet-buried￨L￨JJ￨O￨- ,￨L￨,￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Interventions￨U￨NNS￨O￨- were￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- completely￨L￨RB￨O￨- efficient￨L￨JJ￨O￨- from￨L￨IN￨O￨- their￨L￨PRP$￨O￨- onset￨L￨NN￨O￨- :￨L￨:￨O￨- no￨L￨DT￨O￨- transmission￨L￨NN￨O￨- occurred￨L￨VBD￨O￨- at￨L￨IN￨O￨- burials￨L￨NNS￨O￨- and￨L￨CC￨O￨- hospitals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- community￨L￨NN￨O￨- transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- reduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplier￨L￨NN￨O￨- estimated￨L￨VBN￨O￨A by￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- fitting￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- we￨L￨PRP￨O￨- reviewed￨L￨VBD￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- historical￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EBOV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- outbreaks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- estimated￨L￨VBN￨O￨A parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- Technical￨U￨NNP￨O￨- Appendix￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- interesting￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- propagation￨L￨NN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- probable￨L￨JJ￨O￨- network￨L￨NN￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- [￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Later￨U￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- examining￨L￨VBG￨O￨- a￨L￨DT￨O￨- node-based￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Youssef￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Scoglio￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spectrum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- network￨L￨NN￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- computers￨L￨NNS￨O￨- communicate￨L￨VBP￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- is￨L￨VBZ￨O￨- frequently￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- propagate￨L￨VB￨O￨- viruses￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- recognized￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- significant￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- sharp￨L￨JJ￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- establishing￨L￨VBG￨O￨- a￨L￨DT￨O￨- node-based￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- make￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨A topology￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- whether￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- decline￨L￨VBP￨O￨- toward￨L￨IN￨O￨- extinction￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨A eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Forecasts￨U￨NNS￨O￨- were￨L￨VBD￨O￨- done￨L￨VBN￨O￨- separately￨L￨RB￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- 4￨L￨CD￨NUMBER￨- ILI￨U￨NN￨O￨- +￨L￨CC￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- H1N1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- combining￨L￨VBG￨O￨- seasonal￨L￨JJ￨O￨- and￨L￨CC￨O￨- pandemic￨L￨JJ￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- H3N2￨U￨NN￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- combining￨L￨VBG￨O￨- all￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- real-time￨L￨JJ￨O￨- forecast￨L￨NN￨O￨A system￨L￨NN￨O￨- for￨L￨IN￨O￨- U.S.￨U￨NNP￨COUNTRY￨- cities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- initialized￨L￨VBN￨O￨- at￨L￨IN￨O￨- Week￨U￨NN￨DURATION￨- 40￨L￨CD￨NUMBER￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- week￨L￨NN￨DURATION￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- U.S.￨U￨NNP￨ORGANIZATION￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- begin￨L￨VBP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- initial￨L￨JJ￨O￨- attempt￨L￨NN￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨A the￨L￨DT￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- U.S.￨U￨NNP￨COUNTRY￨- cities￨L￨NNS￨O￨- proved￨L￨VBD￨O￨- unfruitful￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S2￨U￨NN￨O￨- Fig￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- built￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- forecast￨L￨NN￨O￨A systems￨L￨NNS￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- ILI￨U￨NNP￨O￨- +￨L￨CC￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- international￨L￨JJ￨O￨- news￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- can￨L￨MD￨O￨- attribute￨L￨VB￨O￨- these￨L￨DT￨O￨- biases￨L￨NNS￨O￨- to￨L￨TO￨O￨- supranational￨L￨JJ￨O￨- power￨L￨NN￨O￨- structures￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- incentive￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- can￨L￨MD￨O￨- bias￨L￨NN￨O￨- mass￨L￨NN￨O￨- media￨L￨NNS￨O￨A through￨L￨IN￨O￨- economic￨L￨JJ￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- forces￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 62￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- collect￨L￨VBP￨O￨- a￨L￨DT￨O￨- dataset￨L￨NN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- variables￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- induced￨L￨VBN￨O￨- biases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- appearance￨L￨NN￨O￨A of￨L￨IN￨O￨- TTs￨U￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- that￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- perform￨L￨VBP￨O￨- a￨L￨DT￨O￨- confirmatory￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- test￨L￨VB￨O￨- systemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- subjective￨L￨JJ￨O￨- biases￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- media￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- exploratory￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- TTs￨U￨NNS￨O￨- and￨L￨CC￨O￨- mass￨L￨NN￨O￨- media￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- detecting￨L￨VBG￨O￨- temporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- TT￨U￨NN￨O￨- appearance￨L￨NN￨O￨- that￨L￨WDT￨O￨- reveal￨L￨VBP￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨A influence￨L￨VBP￨O￨- across￨L￨IN￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- gathered￨L￨VBD￨O￨- a￨L￨DT￨O￨- dataset￨L￨NN￨O￨A of￨L￨IN￨O￨- Local￨U￨JJ￨O￨- TTs￨U￨NNS￨O￨- in￨L￨IN￨O￨- Twitter￨U￨NNP￨O￨- :￨L￨:￨O￨- Phrases￨U￨NNS￨O￨- or￨L￨CC￨O￨- words￨L￨NNS￨O￨- that￨L￨WDT￨O￨- appear￨L￨VBP￨O￨- in￨L￨IN￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- frequency￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- country￨L￨NN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- simulated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- across￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- transmission￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1.9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- recent￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemics￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 31-33￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- moderate￨L￨JJ￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 2.4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 7.5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- spread￨L￨NN￨O￨- is￨L￨VBZ￨O￨- rapid￨L￨JJ￨O￨- both￨L￨CC￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- communities￨L￨NNS￨O￨A .￨L￨.￨O￨- +Community￨U￨NNP￨O￨- structure￨L￨NN￨O￨A —￨L￨:￨O￨- aggregation￨L￨NN￨O￨- into￨L￨IN￨O￨- highly￨L￨RB￨O￨- intraconnected￨L￨JJ￨O￨- but￨L￨CC￨O￨- loosely￨L￨RB￨O￨- interconnected￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- —￨L￨:￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- drive￨L￨VB￨O￨- multiwave￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- through￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- group￨L￨NN￨O￨- before￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- in￨L￨IN￨O￨- another￨L￨DT￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- fate￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- —￨L￨:￨O￨- whether￨L￨IN￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- multiple￨L￨JJ￨O￨- waves￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- —￨L￨:￨O￨- depends￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A but￨L￨CC￨O￨- also￨L￨RB￨O￨- ,￨L￨,￨O￨- critically￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- or￨L￨CC￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- bridge￨L￨NN￨O￨- superspreaders￨L￨NNS￨O￨- who￨L￨WP￨O￨- forge￨L￨VBP￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Q￨U￨NNP￨O￨- ranges￨L￨VBZ￨O￨- from￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- randomly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- 0.3￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- substantial￨L￨JJ￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- successfully￨L￨RB￨O￨- used￨L￨VBN￨O￨- meteorological￨L￨JJ￨O￨A inputs￨L￨NNS￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- vector-borne￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 26￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- including￨L￨VBG￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- Aedes￨U￨NNS￨O￨- mosquitoes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- vectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- both￨L￨CC￨O￨- found￨L￨VBD￨O￨- meteorological￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨- DF￨U￨NN￨O￨- cases￨L￨NNS￨O￨- but￨L￨CC￨O￨- suspect￨L￨VBP￨O￨- that￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- circulating￨L￨VBG￨O￨- serotype￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- strain￨L￨NN￨O￨- play￨L￨VBP￨O￨- a￨L￨DT￨O￨- larger￨L￨JJR￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Process-based￨U￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- versus￨L￨CC￨O￨- meteorological￨L￨JJ￨O￨A factors￨L￨NNS￨O￨- on￨L￨IN￨O￨- DENV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- built￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- using￨L￨VBG￨O￨- temperature￨L￨NN￨O￨- dependent￨L￨JJ￨O￨A maturation￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- precipitation￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- 1.7￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A fever￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- DF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- including￨L￨VBG￨O￨- 21,206￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Puerto￨U￨NNP￨LOCATION￨- Rico￨U￨NNP￨CRIMINAL_CHARGE￨- NumericCitation￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +Nodes￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- innermost￨L￨JJS￨O￨- core￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- shell￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- k￨L￨NN￨O￨- value￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- probable￨L￨JJ￨O￨- to￨L￨TO￨O￨- trigger￨L￨VB￨O￨- out￨L￨RP￨O￨- an￨L￨DT￨O￨- economic￨L￨JJ￨O￨- crisis10￨L￨NN￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- k-shell￨L￨NN￨O￨- method￨L￨NN￨O￨- decomposes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- into￨L￨IN￨O￨- ordered￨L￨VBN￨O￨- shells￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- periphery￨L￨NN￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- core￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- influential￨L￨JJ￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- periphery￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- spreading￨L￨NN￨O￨- dynamics29￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- tree￨L￨NN￨O￨A is￨L￨VBZ￨O￨- calculated￨L￨VBN￨O￨- from￨L￨IN￨O￨- its￨L￨PRP$￨O￨- prior￨L￨JJ￨O￨- probability￨L￨NN￨O￨- —￨L￨:￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- either￨L￨CC￨O￨- Kingman￨U￨NNP￨CITY￨- ’s￨L￨POS￨O￨- coalescent￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- ,￨L￨,￨O￨- more￨L￨RBR￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- —￨L￨:￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- likelihood￨L￨NN￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- inferred￨L￨VBN￨O￨- tree￨L￨NN￨O￨A becomes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nuisance￨L￨NN￨O￨- variable￨L￨NN￨O￨- over￨L￨IN￨O￨- which￨L￨WDT￨O￨- one￨L￨PRP￨NUMBER￨- must￨L￨MD￨O￨- integrate￨L￨VB￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- critical￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- premise￨L￨NN￨O￨- of￨L￨IN￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- fit￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- more￨L￨JJR￨O￨- data￨L￨NNS￨O￨A sets￨L￨NNS￨O￨A under￨L￨IN￨O￨- varying￨L￨VBG￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- finding￨L￨VBG￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- minimize￨L￨VBP￨O￨- the￨L￨DT￨O￨- discrepancy￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- and￨L￨CC￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- my￨L￨PRP$￨O￨- colleagues￨L￨NNS￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- adapted￨L￨VBD￨O￨- a￨L￨DT￨O￨- tree￨L￨NN￨O￨A kernel￨L￨NN￨O￨- from￨L￨IN￨O￨- computational￨L￨JJ￨O￨- linguistics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- distance￨L￨NN￨O￨- measure￨L￨NN￨O￨- for￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- phylogenetic￨L￨JJ￨O￨- tree￨L￨NN￨O￨- shapes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- cost￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- intervention￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- response￨L￨NN￨O￨- :￨L￨:￨O￨- More￨U￨JJR￨O￨- formally￨L￨RB￨O￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- c￨L￨NN￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- cost￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- person￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- formulation￨L￨NN￨O￨- differs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- previous￨L￨JJ￨O￨- cost-effectiveness￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- cost￨L￨NN￨O￨A beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- people￨L￨NNS￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- response￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- response￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- cost￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- itself￨L￨PRP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- response￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- these￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨A are￨L￨VBP￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- emphasize￨L￨VBP￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- changing￨L￨VBG￨O￨- connectivity2930￨L￨NN￨O￨- ,￨L￨,￨O￨- adaptive￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- emphasize￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- response￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- state3536￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨- timings￨L￨NNS￨O￨- of￨L￨IN￨O￨- events3738￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- extreme￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- in￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- may￨L￨MD￨O￨- vanish￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨- limit￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- arbitrarily￨L￨RB￨O￨- low￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- can￨L￨MD￨O￨- still￨L￨RB￨O￨- spread1119￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- threshold￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- many￨L￨JJ￨O￨- factors￨L￨NNS￨O￨A including￨L￨VBG￨O￨A the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- behavioral￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- heterogeneous￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A can￨L￨MD￨O￨- make￨L￨VB￨O￨- networks￨L￨NNS￨O￨- more￨L￨RBR￨O￨- vulnerable￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive27￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- network￨L￨NN￨O￨- heterogenity￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- moment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨A chosen￨L￨VBN￨O￨A node￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- critical￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨A caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- departure￨L￨NN￨O￨- from￨L￨IN￨O￨- saddle￨L￨NN￨O￨- points￨L￨NNS￨O￨- far￨L￨RB￨O￨- from￨L￨IN￨O￨- bifurcations￨L￨NNS￨O￨- as￨L￨IN￨O￨- saddle-escape￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- also￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- normal￨L￨JJ￨O￨- form￨L￨NN￨O￨- example￨L￨NN￨O￨- for￨L￨IN￨O￨- passage￨L￨NN￨O￨- near￨L￨IN￨O￨- a￨L￨DT￨O￨- saddle￨L￨NN￨O￨- ;￨L￨:￨O￨- we￨L￨PRP￨O￨- remark￨L￨VBP￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- example￨L￨NN￨O￨- is￨L￨VBZ￨O￨- generic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- that￨L￨WDT￨O￨- mathematical￨L￨JJ￨O￨- theory￨L￨NN￨O￨- guarantees￨L￨NNS￨O￨- that￨L￨IN￨O￨- other￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- nondegenerate￨L￨JJ￨O￨- saddles￨L￨NNS￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- coordinate￨L￨VB￨O￨- changes￨L￨NNS￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- notion￨L￨NN￨O￨- of￨L￨IN￨O￨- equivalence￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics4￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- simple￨L￨JJ￨O￨- low-dimensional￨L￨JJ￨O￨- ,￨L￨,￨O￨- modular￨L￨JJ￨O￨- or￨L￨CC￨O￨- symmetric￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- effective￨L￨JJ￨O￨- few-variable￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- systems￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- early-warnings￨L￨JJ￨O￨- signs￨L￨NNS￨O￨- ,￨L￨,￨O￨- saddle-escape￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨A may￨L￨MD￨O￨- occur1516￨L￨VB￨O￨- but￨L￨CC￨O￨- are￨L￨VBP￨O￨- relatively￨L￨RB￨O￨- rare￨L￨JJ￨O￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- to￨L￨TO￨O￨- saddles￨L￨NNS￨O￨- in￨L￨IN￨O￨- high-dimensional￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- many-variable￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- critical￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨A that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- consider￨L￨VB￨O￨- that￨L￨DT￨O￨- many￨L￨JJ￨O￨- real-world￨L￨JJ￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- reside￨L￨VB￨O￨- in￨L￨IN￨O￨- stable￨L￨JJ￨O￨- states￨L￨NNS￨O￨- .￨L￨.￨O￨- +Warning￨U￨NN￨O￨- signs￨L￨NNS￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- bifurcation-induced￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨A detect￨L￨VBP￨O￨- the￨L￨DT￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- restoring￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- either￨L￨CC￨O￨- through￨L￨IN￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- statistics￨L￨NNS￨O￨- of￨L￨IN￨O￨- noise-induced￨L￨JJ￨O￨- fluctuations178￨L￨NN￨O￨- or￨L￨CC￨O￨- by￨L￨IN￨O￨- direct￨L￨JJ￨O￨- measurement￨L￨NN￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- rates910￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- such￨L￨JJ￨O￨- perturbation-induced￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨A if￨L￨IN￨O￨- it￨L￨PRP￨O￨- resides￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- saddle￨L￨NN￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- state￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- stable￨L￨JJ￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- perturbations￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- unstable￨L￨JJ￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Chile￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- latitudinal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- peak￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- activity￨L￨NN￨O￨- was￨L￨VBD￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- specific￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A but￨L￨CC￨O￨- not￨L￨RB￨O￨- with￨L￨IN￨O￨- winter￨L￨NN￨DATE￨- vacations￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- activity￨L￨NN￨O￨- was￨L￨VBD￨O￨- already￨L￨RB￨O￨- subsiding￨L￨VBG￨O￨- when￨L￨WRB￨O￨- schools￨L￨NNS￨O￨- closed￨L￨VBD￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- pandemic￨L￨JJ￨O￨A A/H1N1￨U￨NN￨O￨- transmission￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- regional￨L￨JJ￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- school￨L￨NN￨O￨- terms￨L￨NNS￨O￨- and￨L￨CC￨O￨- weak￨L￨JJ￨O￨- child-mobility￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- staggered￨L￨JJ￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- fall￨L￨NN￨DATE￨- pandemic￨L￨JJ￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- US￨U￨NNP￨COUNTRY￨- cities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- retrieved￨L￨VBD￨O￨- and￨L￨CC￨O￨- compiled￨L￨VBD￨O￨- daily￨L￨RB￨SET￨- specific￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A ,￨L￨,￨O￨- precipitation￨L￨NN￨O￨- and￨L￨CC￨O￨- temperature￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- period￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Global￨U￨JJ￨O￨- Land￨U￨NNP￨O￨- Data￨U￨NNP￨O￨- Assimilation￨U￨NNP￨O￨- System￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- populous￨L￨JJ￨O￨- city￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +Cumulative￨U￨JJ￨O￨- case￨L￨NN￨O￨- proportions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨A divided￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- spring￨L￨NN￨DATE￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- summer￨L￨NN￨DATE￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- fall￨L￨VB￨O￨- waves￨L￨NNS￨O￨- by￨L￨IN￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- pandemic￨L￨NN￨O￨- in￨L￨IN￨O￨- Canada￨U￨NNP￨COUNTRY￨- was￨L￨VBD￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- school￨L￨NN￨O￨- terms￨L￨NNS￨O￨- and￨L￨CC￨O￨- specific￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Their￨U￨PRP$￨O￨- demonstrated￨L￨VBN￨O￨- efficacy￨L￨NN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- and￨L￨CC￨O￨- adults￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- overcome￨L￨VB￨O￨- the￨L￨DT￨O￨- drawbacks￨L￨NNS￨O￨- of￨L￨IN￨O￨- wrongly￨L￨RB￨O￨- predicting￨L￨VBG￨O￨- which￨L￨WDT￨O￨- B￨U￨NN￨O￨- lineage￨L￨NN￨O￨A will￨L￨MD￨O￨- predominate￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨JJ￨O￨- year￨L￨NN￨DURATION￨- .3￨L￨NN￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Quadrivalent￨U￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- benefit￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- shown￨L￨VBN￨O￨- by￨L￨IN￨O￨- recent￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- .6￨L￨VBP￨NUMBER￨- –￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- none￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- studies￨L￨NNS￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- ,￨L￨,￨O￨- past￨L￨JJ￨DATE￨- experiences￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- those￨L￨DT￨O￨- recommendations￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- season￨L￨NN￨O￨- .1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- resulting￨L￨VBG￨O￨- mismatched￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- and￨L￨CC￨O￨- fails￨L￨VBZ￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A .2￨L￨NN￨NUMBER￨- New￨U￨NNP￨O￨- quadrivalent￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccines￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- QIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- contain￨L￨VBP￨O￨- both￨L￨DT￨O￨- circulating￨L￨VBG￨O￨- B￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- key￨L￨JJ￨O￨- factor￨L￨NN￨O￨- in￨L￨IN￨O￨- QIV￨U￨NN￨O￨- evaluation￨L￨NN￨O￨- ,￨L￨,￨O￨- often￨L￨RB￨O￨- overlooked￨L￨VBD￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- cross-protection￨L￨NN￨O￨- against￨L￨IN￨O￨- a￨L￨DT￨O￨- mismatched￨L￨JJ￨O￨- B￨U￨NN￨O￨- lineage￨L￨NN￨O￨A conferred￨L￨VBD￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- trivalent￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccines￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- TIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- obviously￨L￨RB￨O￨- limiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- added￨L￨VBN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- QIV￨U￨NN￨O￨- over￨L￨IN￨O￨- TIV￨U￨NN￨ORGANIZATION￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Table1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨O￨- lineage￨L￨NN￨O￨A contained￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- TIV￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨JJ￨O￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- primary￨L￨JJ￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- dose￨L￨NN￨O￨A of￨L￨IN￨O￨- OCV￨U￨NN￨O￨- where￨L￨WRB￨O￨- one-dose￨L￨JJ￨O￨- reactive￨L￨JJ￨O￨- campaigns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- as￨L￨RB￨O￨- large￨L￨JJ￨O￨- an￨L￨DT￨O￨- impact￨L￨NN￨O￨- as￨L￨IN￨O￨- two-dose￨L￨JJ￨O￨- campaigns￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- experience￨L￨NN￨O￨A sampling￨L￨NN￨O￨- ,￨L￨,￨O￨- Fleeson￨U￨NN￨PERSON￨- NumericCitation￨U￨NN￨PERSON￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- people￨L￨NNS￨O￨- pass￨L￨VBP￨O￨- through￨L￨IN￨O￨- all￨L￨DT￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- personality￨L￨NN￨O￨- states￨L￨NNS￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- daily￨L￨JJ￨SET￨- lives￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- tendency￨L￨NN￨O￨- of￨L￨IN￨O￨- personality￨L￨NN￨O￨- states￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- stable￨L￨JJ￨O￨- and￨L￨CC￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- trait￨L￨NN￨O￨- level￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- within-person￨L￨NN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- personality￨L￨NN￨O￨- states￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- attributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- situational￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- stable￨L￨JJ￨O￨- dispositions￨L￨NNS￨O￨- captured￨L￨VBN￨O￨- by￨L￨IN￨O￨- traits￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- collected￨L￨VBD￨O￨- high-resolution￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- daily￨L￨JJ￨SET￨- face-to-face￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- among￨L￨IN￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- organization￨L￨NN￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- experience￨L￨NN￨O￨A sampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- Big-Five￨U￨JJ￨MISC￨- personality￨L￨NN￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- affective￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- emotional￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- states￨L￨NNS￨O￨- using￨L￨VBG￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- Positive￨U￨JJ￨O￨- and￨L￨CC￨O￨- Negative￨U￨JJ￨O￨- Affect￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- differ￨L￨VBP￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- tendencies￨L￨NNS￨O￨- to￨L￨TO￨O￨- experience￨L￨VB￨O￨- given￨L￨VBN￨O￨- psychological￨L￨JJ￨O￨A states￨L￨NNS￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- states￨L￨NNS￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- situational￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- stable￨L￨JJ￨O￨- traits￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- dispositions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Yet￨U￨RB￨O￨- ,￨L￨,￨O￨- sociological￨L￨JJ￨O￨- and￨L￨CC￨O￨- psychological￨L￨JJ￨O￨A theory￨L￨NN￨O￨- has￨L￨VBZ￨O￨- long￨L￨RB￨O￨- recognized￨L￨VBN￨O￨- that￨L￨IN￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨- often￨L￨RB￨O￨- involves￨L￨VBZ￨O￨- changes￨L￨NNS￨O￨- across￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- ordinal￨L￨JJ￨O￨- state￨L￨NN￨O￨- structure￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- people￨L￨NNS￨O￨- transition￨L￨NN￨O￨- among￨L￨IN￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- higher￨L￨JJR￨O￨- or￨L￨CC￨O￨- lower￨L￨JJR￨O￨- extraversion￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- existing￨L￨VBG￨O￨- contagion￨L￨NN￨O￨- models￨L￨NNS￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- social-situational￨L￨JJ￨O￨- influences￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- neglect￨L￨NN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- psychological￨L￨JJ￨O￨A state￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- far￨L￨RB￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- network-based￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- has￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- both￨L￨CC￨O￨- generates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- limited-duration￨L￨NN￨O￨- immunity￨L￨NN￨O￨- that￨L￨WDT￨O￨- eventually￨L￨RB￨O￨- lapses￨L￨VBZ￨O￨- back￨L￨RB￨O￨- into￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- due￨L￨JJ￨O￨- either￨L￨CC￨O￨- to￨L￨TO￨O￨- genetic￨L￨JJ￨O￨- drift￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- antigenic￨L￨JJ￨O￨- drift￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- T-cell￨U￨NN￨MISC￨- memory￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- also￨L￨RB￨O￨- carrying￨L￨VBG￨O￨- a￨L￨DT￨O￨- non-trivial￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease-induced￨L￨JJ￨O￨- mortality￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Disease-induced￨U￨JJ￨O￨- mortality￨L￨NN￨O￨A itself￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- especially￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- when￨L￨WRB￨O￨- non-disease-related￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- function￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- drastically￨L￨RB￨O￨- diminished￨L￨VBN￨O￨- by￨L￨IN￨O￨- disease-induced￨L￨JJ￨O￨- structural￨L￨JJ￨O￨- compromise￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- exactly￨L￨RB￨O￨- such￨L￨JJ￨O￨- disconnection￨L￨NN￨O￨- acts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- diminish￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- by￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- effective￨L￨JJ￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Almost￨U￨RB￨O￨- all￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- behave￨L￨VB￨O￨- differently￨L￨RB￨O￨- on￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- simple￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- structures￨L￨NNS￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- fully￨L￨RB￨O￨- mixed￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- reflecting￨L￨VBG￨O￨A different￨L￨JJ￨O￨- potential￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- among￨L￨IN￨O￨- various￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Of￨U￨IN￨O￨- course￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- that￨L￨WDT￨O￨- carries￨L￨VBZ￨O￨- a￨L￨DT￨O￨- non-trivial￨L￨JJ￨O￨- mortality￨L￨NN￨O￨A risk￨L￨NN￨O￨- ,￨L￨,￨O￨- frequent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- network￨L￨NN￨O￨- will￨L￨MD￨O￨- eventually￨L￨RB￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- removal￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- mortality￨L￨NN￨O￨A probability￨L￨NN￨O￨- ,￨L￨,￨O￨- f￨L￨FW￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- protection￨L￨NN￨O￨- loss￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- r.￨L￨NN￨O￨- +Our￨U￨PRP$￨O￨- framework￨L￨NN￨O￨- outputs￨L￨VBZ￨O￨- a￨L￨DT￨O￨- distribution￨L￨NN￨O￨- over￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- histograms￨L￨NNS￨O￨- ,￨L￨,￨O￨- credible￨L￨JJ￨O￨- intervals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- point￨L￨NN￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- season￨L￨NN￨O￨A ’s￨L￨POS￨O￨- onset￨L￨NN￨O￨- ,￨L￨,￨O￨- peak￨L￨NN￨O￨- week￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- peak￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- individual￨L￨JJ￨O￨- wILI￨L￨NN￨O￨- measurements￨L￨NNS￨O￨- ;￨L￨:￨O￨- existing￨L￨VBG￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- analogues￨L￨NNS￨O￨- generate￨L￨VBP￨O￨- separate￨L￨JJ￨O￨- point￨L￨NN￨O￨- predictions￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- wILI￨L￨NN￨O￨- measurement￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- take￨L￨VBP￨O￨- a￨L￨DT￨O￨- nonmechanistic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- generating￨L￨VBG￨O￨- possibilities￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- season￨L￨NN￨O￨A ’s￨L￨POS￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- using￨L￨VBG￨O￨- modified￨L￨VBN￨O￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- seasons￨L￨NNS￨O￨- ’￨L￨POS￨O￨- curves￨L￨NNS￨O￨- ,￨L￨,￨O￨- incorporating￨L￨VBG￨O￨- adjustments￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- ,￨L￨,￨O￨- pace￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- informed￨L￨VBN￨O￨- by￨L￨IN￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- historical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- accommodating￨L￨VBG￨O￨- noise￨L￨NN￨O￨- in￨L￨IN￨O￨- observations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- method￨L￨NN￨O￨- models￨L￨NNS￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- generating￨L￨VBG￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- nonparametrically￨L￨RB￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- smooth￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- fairly￨L￨RB￨O￨- close￨L￨JJ￨O￨- fits￨L￨NNS￨O￨- to￨L￨TO￨O￨- historical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- relying￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- transformations￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- curves￨L￨NNS￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- ILI￨U￨NN￨O￨- this￨L￨DT￨O￨- season￨L￨NN￨O￨A .￨L￨.￨O￨- +Past￨U￨JJ￨DATE￨- forecasting￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- usually￨L￨RB￨O￨- take￨L￨VBP￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- parametric￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- [￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- condition￨L￨NN￨O￨- on￨L￨IN￨O￨- partial￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A activity￨L￨NN￨O￨- levels￨L￨NNS￨O￨- one￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- ten￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2014￨L￨CD￨DATE￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- hosted￨L￨VBD￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- Predict￨U￨VB￨O￨- the￨L￨DT￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- Season￨U￨NN￨MISC￨- Challenge￨U￨NN￨MISC￨- ”￨L￨''￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- encouraged￨L￨VBD￨O￨- teams￨L￨NNS￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- epidemic￨L￨JJ￨O￨- progression￨L￨NN￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- to￨L￨TO￨O￨- policy￨L￨NN￨O￨- makers￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- digital￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- search￨L￨NN￨O￨- engine￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- predictors￨L￨NNS￨O￨- for￨L￨IN￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- k-core￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- PageRank￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- many￨L￨JJ￨O￨- others￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- were￨L￨VBD￨O￨- tested￨L￨VBN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thanks￨U￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- records￨L￨NNS￨O￨- in￨L￨IN￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- action￨L￨NN￨O￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- now￨L￨RB￨DATE￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- mechanisms￨L￨NNS￨O￨- by￨L￨IN￨O￨- directly￨L￨RB￨O￨- observing￨L￨VBG￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- social￨L￨JJ￨O￨A mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- link￨L￨NN￨O￨- formation￨L￨NN￨O￨- driving￨L￨VBG￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- and￨L￨CC￨O￨- predict￨L￨VB￨O￨- complex￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- in￨L￨IN￨O￨- society￨L￨NN￨O￨- .￨L￨.￨O￨- +Identifying￨U￨VBG￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨A on￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- its￨L￨PRP$￨O￨- practical￨L￨JJ￨O￨- application￨L￨NN￨O￨- in￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- their￨L￨PRP$￨O￨- behaviors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- demanded￨L￨VBN￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- influential￨L￨JJ￨O￨A people￨L￨NNS￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- information￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Perhaps￨U￨RB￨O￨- surprisingly￨L￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- causes￨L￨VBZ￨O￨- exceptionally￨L￨RB￨O￨- severe￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- because￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- preventative￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- morbidity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- moderate￨L￨JJ￨O￨- ,￨L￨,￨O￨- disease-induced￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- slightly￨L￨RB￨O￨- elevated￨L￨JJ￨O￨- in￨L￨IN￨O￨- animals￨L￨NNS￨O￨- up￨L￨IN￨DURATION￨- to￨L￨TO￨DURATION￨- one￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vaccines￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- against￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- FMDV￨U￨NN￨O￨- serotypes￨L￨NNS￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- serology￨L￨NN￨O￨- data￨L￨NNS￨O￨- matched￨L￨VBN￨O￨- with￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- age￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- record￨L￨NN￨O￨- of￨L￨IN￨O￨- historical￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- animals￨L￨NNS￨O￨A are￨L￨VBP￨O￨- sampled￨L￨VBN￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- event￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- cross-sectional￨L￨JJ￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- FOI￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- age-specific￨L￨JJ￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- animals￨L￨NNS￨O￨A have￨L￨VBP￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- that￨L￨WDT￨O￨- vary￨L￨VBP￨O￨- with￨L￨IN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- address￨L￨VB￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- immune￨L￨JJ￨O￨A response￨L￨NN￨O￨A against￨L￨IN￨O￨- FMDV￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- fit￨L￨VBP￨O￨- contrasting￨L￨VBG￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- FMDV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- serology￨L￨NN￨O￨- data￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- catalytic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- reversible￨L￨JJ￨O￨- catalytic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- serology￨L￨NN￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- indicate￨L￨VBP￨O￨- past￨L￨IN￨DATE￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- FMDV￨U￨NN￨O￨- for￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Far￨U￨NNP￨LOCATION￨- North￨U￨NNP￨LOCATION￨- Region￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Cameroon￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- five￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- seven￨L￨CD￨NUMBER￨- serotypes￨L￨NNS￨O￨A are￨L￨VBP￨O￨- present￨L￨JJ￨DATE￨- either￨L￨CC￨O￨- endemically￨L￨RB￨O￨- or￨L￨CC￨O￨- intermittently￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- accurate￨L￨JJ￨O￨- measurement￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- antibody￨L￨NN￨O￨A waning￨L￨VBG￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- critical￨L￨JJ￨O￨- for￨L￨IN￨O￨- inference￨L￨NN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- analysis￨L￨NN￨O￨- showing￨L￨VBG￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- collection￨L￨NN￨O￨- affect￨L￨VB￨O￨- likelihood-based￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- cross-sectional￨L￨JJ￨O￨- seroepidemiology￨L￨NN￨O￨- study￨L￨NN￨O￨- will￨L￨MD￨O￨- give￨L￨VB￨O￨- us￨L￨PRP￨O￨- details￨L￨NNS￨O￨- on￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- dynamics￨L￨NNS￨O￨- if￨L￨IN￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- lifelong￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- inferred￨L￨VBN￨O￨A dynamics￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- coarsely￨L￨RB￨O￨- broken￨L￨VBN￨O￨- up￨L￨RP￨O￨- by￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- unless￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- ages￨L￨NNS￨O￨- are￨L￨VBP￨O￨- specified￨L￨VBN￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- decimal￨L￨JJ￨O￨- places￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- certain￨L￨JJ￨O￨- intuitive￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- revisited￨L￨VBN￨O￨- when￨L￨WRB￨O￨- dynamical￨L￨JJ￨O￨- inference￨L￨NN￨O￨A is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- serological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- reason￨L￨NN￨O￨- being￨L￨VBG￨O￨- that￨L￨IN￨O￨- observations￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- SSE￨U￨NN￨ORGANIZATION￨- study￨L￨NN￨O￨- are￨L￨VBP￨O￨- made￨L￨VBN￨O￨- on￨L￨IN￨O￨- recovered/susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Normally￨U￨RB￨O￨- such￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- inferred￨L￨VBN￨O￨A by￨L￨IN￨O￨- fitting￨L￨NN￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- reported￨L￨VBD￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- procedure￨L￨NN￨O￨- would￨L￨MD￨O￨- infer￨L￨VB￨O￨- a￨L￨DT￨O￨- reporting￨L￨NN￨O￨- parameter￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- host￨L￨NN￨TITLE￨- compartments￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- exposed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- mounted￨L￨VBD￨O￨- a￨L￨DT￨O￨- full￨L￨JJ￨O￨- antibody￨L￨NN￨O￨A response￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- specific￨L￨JJ￨O￨- antibody￨L￨NN￨O￨- levels￨L￨NNS￨O￨- would￨L￨MD￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- i￨L￨FW￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- immunological￨L￨JJ￨O￨- assay￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- in￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- search￨L￨NN￨O￨- for￨L￨IN￨O￨- effective￨L￨JJ￨O￨- control￨L￨NN￨O￨A measures￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- build￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- among￨L￨IN￨O￨- human￨L￨JJ￨O￨- beings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Althaus￨U￨NNP￨PERSON￨- presented￨L￨VBD￨O￨- a￨L￨DT￨O￨- susceptible-exposed-infectious-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- fitted￨L￨VBD￨O￨A the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- for￨L￨IN￨O￨- EVD￨U￨NN￨O￨- in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Liberia20￨U￨NNP￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- fitting￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- perform￨L￨VBP￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- estimation￨L￨NN￨O￨A and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +constructed￨L￨VBN￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- EVD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- fitted￨L￨VBD￨O￨A it￨L￨PRP￨O￨- to￨L￨TO￨O￨- historical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- R019￨U￨NN￨O￨- .￨L￨.￨O￨- +considered￨L￨VBN￨O￨- different￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- burial￨L￨NN￨O￨- ceremonies￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- EVD￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨A of￨L￨IN￨O￨- R010￨U￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- feasible￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- patch￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- a￨L￨DT￨O￨- compartment-based￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- capturing￨L￨VBG￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- patch￨L￨NN￨O￨- dissemination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- trend￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- or￨L￨CC￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- by￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- patch￨L￨NN￨O￨- dissemination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- effective￨L￨JJ￨O￨- or￨L￨CC￨O￨- ineffective￨L￨JJ￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- approaches￨L￨VBZ￨O￨- an￨L￨DT￨O￨- acceptably￨L￨RB￨O￨- low￨L￨JJ￨O￨- value￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- fundamentally￨L￨RB￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- patch￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- centralized￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- central￨L￨JJ￨O￨- node￨L￨NN￨O￨- disseminates￨L￨VBZ￨O￨- new￨L￨JJ￨O￨- patches￨L￨NNS￨O￨- directly￨L￨RB￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distributed￨L￨VBN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- every￨L￨DT￨O￨- newly￨L￨RB￨O￨- patched￨L￨VBN￨O￨- node￨L￨NN￨O￨- forwards￨L￨RB￨O￨- the￨L￨DT￨O￨- patches￨L￨NNS￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- or￨L￨CC￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- well-designed￨L￨JJ￨O￨- protocol￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +All￨U￨DT￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- capture￨L￨VBP￨O￨- the￨L￨DT￨O￨- centralized￨L￨JJ￨O￨- patch￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A mechanism￨L￨NN￨O￨- .￨L￨.￨O￨- +RNA￨U￨NN￨O￨- sequencing￨L￨NN￨O￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- 11￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 40￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- single-end￨L￨JJ￨O￨- raw￨L￨JJ￨O￨- reads￨L￨VBZ￨O￨A of￨L￨IN￨O￨- 100￨L￨CD￨NUMBER￨- bp￨L￨NN￨O￨- per￨L￨IN￨O￨- sample￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Summary￨U￨NNP￨O￨- of￨L￨IN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- sequencing￨L￨NN￨O￨- reads￨L￨VBZ￨O￨- ,￨L￨,￨O￨- mapped￨L￨VBD￨O￨- reads￨L￨VBZ￨O￨- ,￨L￨,￨O￨- mapping￨L￨VBG￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- detected￨L￨VBN￨O￨- genes￨L￨NNS￨O￨- and￨L￨CC￨O￨- transcriptome￨L￨NN￨O￨- coverage￨L￨NN￨O￨- TreatmentsRaw￨U￨NNP￨O￨- readsMapped￨L￨NNP￨O￨- reads￨L￨VBZ￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- reads￨L￨VBZ￨O￨- MappedDetected￨U￨NNP￨O￨- genesTranscriptome￨L￨NNP￨O￨- coveragedpiPhenotypeBird￨L￨NNP￨O￨- #￨L￨#￨O￨- 1Non-challenged140￨L￨NN￨O￨- ,958,94932,154,54680.3￨L￨CD￨PERCENT￨- ,98687.59￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 1Non-challenged217￨L￨NN￨O￨- ,774,23513,758,51478.7￨L￨CD￨PERCENT￨- ,27583.44￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 1Non-challenged317￨L￨NN￨O￨- ,409,36413,812,51080.7￨L￨CD￨PERCENT￨- ,14082.65￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 1Non-challenged438￨L￨NN￨O￨- ,557,15626,754,84370.6￨L￨CD￨PERCENT￨- ,85986.85￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 1Resistant121￨L￨NN￨O￨- ,110,68315,919,75578.6￨L￨CD￨PERCENT￨- ,43284.36￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 1Resistant219￨L￨NN￨O￨- ,457,69314,734,51279.8￨L￨CD￨PERCENT￨- ,37484.02￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 1Resistant331￨L￨NN￨O￨- ,249,43424,654,20380.4￨L￨CD￨PERCENT￨- ,93687.30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 1Resistant426￨L￨NN￨O￨- ,426,43721,574,69883.0￨L￨CD￨PERCENT￨- ,64085.57￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 1Susceptible126￨L￨NN￨O￨- ,940,89220,423,34979.3￨L￨CD￨PERCENT￨- ,75986.27￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 1Susceptible216￨L￨NN￨O￨- ,227,83711,585,44679.1￨L￨CD￨PERCENT￨- ,95481.56￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 1Susceptible323￨L￨NN￨O￨- ,554,06918,481,53879.8￨L￨CD￨PERCENT￨- ,71386.00￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 1Susceptible419￨L￨NN￨O￨- ,045,54815,352,57382.2￨L￨CD￨PERCENT￨- ,40984.22￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Non-challenged140￨L￨NN￨O￨- ,113,45031,164,13779.5￨L￨CD￨PERCENT￨- ,96687.48￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Non-challenged215￨L￨NN￨O￨- ,799,65712,039,80180.0￨L￨CD￨PERCENT￨- ,94781.52￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Non-challenged320￨L￨NN￨O￨- ,791,30416,735,99781.8￨L￨CD￨PERCENT￨- ,23583.21￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Non-challenged427￨L￨NN￨O￨- ,189,81721,665,45781.1￨L￨CD￨PERCENT￨- ,55384.95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Resistant120￨L￨NN￨O￨- ,286,50514,862,43279.8￨L￨CD￨PERCENT￨- ,29683.56￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Resistant211￨L￨NN￨O￨- ,761,4208,652,65880.0￨L￨CD￨PERCENT￨- ,54379.16￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Resistant318￨L￨NN￨O￨- ,361,29314,341,04280.2￨L￨CD￨PERCENT￨- ,28183.48￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Resistant416￨L￨NN￨O￨- ,590,84613,386,03180.7￨L￨CD￨PERCENT￨- ,03882.06￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Susceptible122￨L￨NN￨O￨- ,585,43417,629,30880.7￨L￨CD￨PERCENT￨- ,46784.56￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Susceptible211￨L￨NN￨O￨- ,789,7168,534,11078.7￨L￨CD￨PERCENT￨- ,83980.89￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Susceptible317￨L￨NN￨O￨- ,874,00413,601,65377.9￨L￨CD￨PERCENT￨- ,49584.73￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 5Susceptible415￨L￨NN￨O￨- ,429,65912,406,17082.0￨L￨CD￨PERCENT￨- ,16382.79￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Note￨U￨NN￨O￨- :￨L￨:￨O￨- dpi￨L￨NNS￨O￨- :￨L￨:￨O￨- day￨L￨NN￨DURATION￨- post-infection￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- from￨L￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- this￨L￨DT￨O￨- parsimonious￨L￨JJ￨O￨A assumption￨L￨NN￨O￨- may￨L￨MD￨O￨- differ￨L￨VB￨O￨- greatly￨L￨RB￨O￨- from￨L￨IN￨O￨- models￨L￨NNS￨O￨- featuring￨L￨VBG￨O￨- heterogeneous￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- policies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- made￨L￨VBN￨O￨- increasing￨L￨VBG￨O￨- contributions￨L￨NNS￨O￨A to￨L￨TO￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- network￨L￨NN￨O￨- modeling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- outlined￨L￨VBN￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- how￨L￨WRB￨O￨- well￨L￨RB￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- time￨L￨NN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- simulated￨L￨JJ￨O￨A data￨L￨NNS￨O￨A .￨L￨.￨O￨- +Heterogeneity￨U￨NN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨A age￨L￨NN￨O￨A groups￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- factor￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨A generated￨L￨VBN￨O￨A by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- during￨L￨IN￨O￨- his/her￨L￨JJ￨O￨- entire￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- period￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- totally￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Complex￨U￨JJ￨O￨- network￨L￨NN￨O￨- research￨L￨NN￨O￨- turns￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- or￨L￨CC￨O￨- less￨L￨RBR￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- related￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- :￨L￨:￨O￨- first￨L￨RB￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- taking￨L￨VBG￨O￨- place￨L￨NN￨O￨- on￨L￨IN￨O￨- static￨L￨JJ￨O￨- complex￨L￨NN￨O￨A networks￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- manner￨L￨NN￨O￨- that￨L￨WDT￨O￨- makes￨L￨VBZ￨O￨- judicious￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- known￨L￨JJ￨O￨- topological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- second￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- topological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- emerge￨L￨VBP￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- subsequently￨L￨RB￨O￨- evolve￨L￨VB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- purposes￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- prior￨L￨JJ￨O￨- information￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- influenza-like￨L￨JJ￨O￨- illnesses￨L￨NNS￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- build￨L￨VB￨O￨- prior￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- are￨L￨VBP￨O￨- useful￨L￨JJ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- Bayes￨U￨NNP￨PERSON￨- factors￨L￨NNS￨O￨- for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- outbreak￨L￨NN￨O￨- detection￨L￨NN￨O￨- using￨L￨VBG￨O￨- regression￨L￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Bayes￨U￨NNP￨LOCATION￨- factors￨L￨NNS￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- Hoeting￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- key￨L￨NN￨O￨- difference￨L￨NN￨O￨- from￨L￨IN￨O￨- most￨L￨JJS￨O￨- other￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- historical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- alone￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- rather￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Bayesian￨U￨JJ￨O￨- methods￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Smith￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Spiegelhalter￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- present￨L￨VB￨DATE￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- selection￨L￨NN￨O￨A criteria￨L￨NNS￨O￨- for￨L￨IN￨O￨- linear￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- Bayes￨U￨NNP￨LOCATION￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- age￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨O￨- severe￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- skewed￨L￨JJ￨O￨- towards￨L￨IN￨O￨- young￨L￨JJ￨O￨A infants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- <￨L￨JJR￨O￨- 6m￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- around￨L￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- RSV￨U￨NN￨O￨- associated￨L￨VBN￨O￨- hospitalisations￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- attributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- small￨L￨JJ￨O￨- airway￨L￨NN￨O￨- blockage￨L￨NN￨O￨- through￨L￨IN￨O￨- inflammation￨L￨NN￨O￨- and￨L￨CC￨O￨- sloughing￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- epithelial￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- clear￨L￨JJ￨O￨- direct￨L￨JJ￨O￨- benefits￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- gained￨L￨VBN￨O￨- from￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- older￨L￨JJR￨O￨- children￨L￨NNS￨O￨- since￨L￨IN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- severe￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A occurs￨L￨VBZ￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- 6￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- life￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- cohort￨L￨NN￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- Kenya￨U￨NNP￨COUNTRY￨- has￨L￨VBZ￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- severe￨L￨JJ￨O￨- risk￨L￨NN￨O￨- in￨L￨IN￨O￨- young￨L￨JJ￨O￨A children￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- principally￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- age￨L￨NN￨O￨- at￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- their￨L￨PRP$￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- experience￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- what￨L￨WP￨O￨- extent￨L￨NN￨O￨- older￨L￨JJR￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- will￨L￨MD￨O￨- confer￨L￨VB￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- vulnerable￨L￨JJ￨O￨- young￨L￨JJ￨O￨A infant￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- immunisation￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- on￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- infants￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- largely￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- transferred￨L￨VBN￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- risk￨L￨NN￨O￨- or￨L￨CC￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- the￨L￨DT￨O￨- small-world￨L￨JJ￨O￨- property￨L￨NN￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- have￨L￨VB￨O￨- an￨L￨DT￨O￨- infinite￨L￨JJ￨O￨- topological￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- ,￨L￨,￨O￨- naturally￨L￨RB￨O￨- occurring￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- always￨L￨RB￨O￨- finite￨L￨JJ￨O￨A ,￨L￨,￨O￨- exhibit￨L￨VBP￨O￨- cutoffs￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- GPs￨U￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expected￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- inhomogeneous￨L￨JJ￨O￨- topology17￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- large-world￨L￨JJ￨O￨- HMNs￨U￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- imply￨L￨VBP￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨A topological￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- activity￨L￨NN￨O￨- exhibit￨L￨VBP￨O￨- power-law￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- rare￨L￨JJ￨O￨- region￨L￨NN￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- effects￨L￨NNS￨O￨- can￨L￨MD￨O￨- make￨L￨VB￨O￨- a￨L￨DT￨O￨- discontinuous￨L￨JJ￨O￨- transition￨L￨NN￨O￨- continuous￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- generate￨L￨VB￨O￨- so-called￨L￨JJ￨O￨- Griffiths￨U￨NNP￨PERSON￨- phases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- GP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 13￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- critical-like￨L￨JJ￨O￨- power-law￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- appears￨L￨VBZ￨O￨- over￨L￨IN￨O￨- an￨L￨DT￨O￨- extended￨L￨JJ￨O￨- region￨L￨NN￨O￨A around￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- including￨L￨VBG￨O￨- more￨L￨JJR￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- —￨L￨:￨O￨- going￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- fully￨L￨RB￨O￨- mixed￨L￨JJ￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A network￨L￨NN￨O￨A representation￨L￨NN￨O￨- —￨L￨:￨O￨- changes￨L￨NNS￨O￨- different￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- predicted￨L￨VBN￨O￨- final￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- given￨L￨VBN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- breaking￨L￨NN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- assuming￨L￨VBG￨O￨- more￨L￨JJR￨O￨- knowledge￨L￨NN￨O￨- .￨L￨.￨O￨- +10￨L￨CD￨NUMBER￨- —￨L￨:￨O￨- so￨L￨IN￨O￨- the￨L￨DT￨O￨- fully￨L￨RB￨O￨- mixed￨L￨JJ￨O￨- models￨L￨NNS￨O￨- keep￨L￨VBP￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- contact￨L￨NN￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- will￨L￨MD￨O￨- take￨L￨VB￨O￨- place￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- data￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- capturing￨L￨VBG￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A network￨L￨NN￨O￨A representation345￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- single￨L￨JJ￨O￨- wave￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- S-shaped￨U￨JJ￨MISC￨- cumulative￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- turning￨L￨NN￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- fitting￨L￨NN￨O￨A to￨L￨TO￨O￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- selected￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Those￨U￨DT￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- become￨L￨VB￨O￨- more￨L￨RBR￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- employing￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- and￨L￨CC￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨A infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- including￨L￨VBG￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- turning￨L￨VBG￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- final￨L￨JJ￨O￨A size￨L￨NN￨O￨A for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- H1N1￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- SARS￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Dengue￨U￨JJ￨MISC￨- NumericCitation￨U￨NN￨MISC￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- Richards￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- cumulative￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- turning￨L￨VBG￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- final￨L￨JJ￨O￨A size￨L￨NN￨O￨A by￨L￨IN￨O￨- cumulated￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ;￨L￨:￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- purely￨L￨RB￨O￨- empirical￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- others￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- basis￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- realized￨L￨VBN￨O￨- by￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +How￨U￨WRB￨O￨- to￨L￨TO￨O￨- select￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- emerging￨L￨VBG￨O￨A infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- ?￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Spontaneous￨U￨JJ￨MISC￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- virtual￨L￨JJ￨O￨- experimentAdam￨L￨NN￨O￨- Kleczkowski1￨U￨NN￨O￨- ,￨L￨,￨O￨- Savi￨U￨NNP￨PERSON￨- Maharaj1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Susan￨U￨NNP￨PERSON￨- Rasmussen2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Lynn￨U￨NNP￨PERSON￨- Williams3￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Nicole￨U￨NNP￨MISC￨- Cairns2￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 15:973￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Studies￨U￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨- during￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- decisive￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨A driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- risk￨L￨NN￨O￨- attitude￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- which￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- reduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- study￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨- game￨L￨NN￨O￨- setting￨L￨VBG￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A response￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- showed￨L￨VBD￨O￨- by￨L￨IN￨O￨- simulation￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- response￨L￨NN￨O￨A ,￨L￨,￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- cautious￨L￨JJ￨O￨- risk￨L￨NN￨O￨- attitude￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- quickly￨L￨RB￨O￨- suppress￨L￨VB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Two￨U￨CD￨NUMBER￨- hundred￨L￨CD￨NUMBER￨- thirty￨L￨CD￨NUMBER￨- participants￨L￨NNS￨O￨- played￨L￨VBD￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨- game￨L￨NN￨O￨A simulating￨L￨VBG￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- established￨L￨VBN￨O￨- that￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A occurs￨L￨VBZ￨O￨- in￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- forms￨L￨NNS￨O￨- :￨L￨:￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- sudden￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- relatively￨L￨RB￨O￨- disease-free￨L￨JJ￨O￨- region￨L￨NN￨O￨- and￨L￨CC￨O￨- primarily￨L￨RB￨O￨- inland￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- endemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- recurring￨L￨VBG￨O￨- essentially￨L￨RB￨O￨- annually￨L￨RB￨SET￨- and￨L￨CC￨O￨- predominantly￨L￨RB￨O￨- along￨L￨IN￨O￨- coastal￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- mixed-mode￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- occurrence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- rainfall￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A was￨L￨VBD￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- Tanzania￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- conclusion￨L￨NN￨O￨- was￨L￨VBD￨O￨- that￨L￨IN￨O￨- temperature￨L￨NN￨O￨- is￨L￨VBZ￨O￨- significantly￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- degree￨L￨NN￨O￨- Celsius￨U￨NNP￨MISC￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- air￨L￨NN￨O￨- temperature￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- relative￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- predictive￨L￨JJ￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A study￨L￨NN￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- examined￨L￨VBD￨O￨- diarrheal￨L￨NN￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- Botswana￨U￨NNP￨COUNTRY￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- 30-year￨L￨JJ￨DURATION￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- several￨L￨JJ￨O￨- climatic￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- rainfall￨L￨NNS￨O￨- ,￨L￨,￨O￨- minimum￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vapor￨L￨NN￨O￨- pressure￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- KwaZulu-Natal￨U￨NNP￨LOCATION￨- in￨L￨IN￨O￨- South￨U￨NNP￨COUNTRY￨- Africa￨U￨NNP￨COUNTRY￨- were￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- statistically￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- sea￨L￨NN￨O￨- surface￨L￨NN￨O￨- temperature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SST￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- precipitation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- coastal￨L￨JJ￨O￨- phytoplankton￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- being￨L￨VBG￨O￨- the￨L￨DT￨O￨- surrogate￨L￨JJ￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- zooplankton￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- vibrio￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- earlier￨L￨RBR￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Bay￨U￨NNP￨CITY￨- of￨L￨IN￨LOCATION￨- Bengal￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Association￨U￨NNP￨O￨- of￨L￨IN￨O￨- climate￨L￨NN￨O￨- variables￨L￨NNS￨O￨- with￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- unexplored￨L￨JJ￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- attempted￨L￨VBN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- quantitatively￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- CM￨U￨NN￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- assign￨L￨VBP￨O￨A the￨L￨DT￨O￨- PWID￨U￨NNP￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- HCV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- attributes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- enrollment￨L￨NN￨O￨- in￨L￨IN￨O￨- antiviral/vaccine￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- harm￨L￨NN￨O￨- reduction￨L￨NN￨O￨- programs￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- imprisonment￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Dynamic￨U￨NNP￨O￨- modeling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- useful￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- simultaneously￨L￨RB￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- aforementioned￨L￨JJ￨O￨- complexities￨L￨NNS￨O￨- inherent￨L￨JJ￨O￨A in￨L￨IN￨O￨- forecasting￨L￨NN￨O￨- HCV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- prevalence￨L￨NN￨O￨- among￨L￨IN￨O￨- PWID￨U￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- categories￨L￨NNS￨O￨- —￨L￨:￨O￨- Compartmental￨U￨JJ￨O￨- Models￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- CM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Agent-Based￨U￨JJ￨O￨- or￨L￨CC￨O￨- Individual-Based￨U￨JJ￨MISC￨- Models￨U￨NNS￨MISC￨- (￨L￨-LRB-￨O￨- ABMs/IBMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Factors￨U￨NNS￨O￨- contributing￨L￨VBG￨O￨A to￨L￨TO￨O￨- HCV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- acquisition￨L￨NN￨O￨- and￨L￨CC￨O￨- successful￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- among￨L￨IN￨O￨- PWID￨U￨NNP￨O￨- are￨L￨VBP￨O￨- complex￨L￨JJ￨O￨- and￨L￨CC￨O￨- occur￨L￨VB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- geographic￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- risk￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- injection￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨- locations￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- studies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- further￨L￨JJ￨O￨- supported￨L￨VBN￨O￨A by￨L￨IN￨O￨- high￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- HCV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- outbreaks￨L￨NNS￨O￨- among￨L￨IN￨O￨- younger￨L￨JJR￨O￨- PWID￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- HCV￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- have￨L￨VBP￨O￨- steadily￨L￨RB￨O￨- declined￨L￨VBN￨O￨- in￨L￨IN￨O￨- older￨L￨JJR￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- on￨L￨IN￨O￨- those￨L￨DT￨O￨- elements￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- appropriately￨L￨RB￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- diagnosis￨L￨NN￨O￨A and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- what￨L￨WDT￨O￨- elements￨L￨NNS￨O￨- of￨L￨IN￨O￨- better￨L￨JJR￨O￨- diagnosis￨L￨NN￨O￨- or￨L￨CC￨O￨- treatment￨L￨NN￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- greatest￨L￨JJS￨O￨- population-level￨L￨JJ￨O￨- impact￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- yet￨L￨RB￨O￨- remain￨L￨VBP￨O￨- poorly￨L￨RB￨O￨- understood￨L￨VBN￨O￨- at￨L￨IN￨O￨- present￨L￨JJ￨DATE￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- “￨L￨``￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- ”￨L￨''￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- techniques￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- will￨L￨MD￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨A designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- or￨L￨CC￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- population-level￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- epidemiological￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- incorporate￨L￨VBP￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- words￨L￨NNS￨O￨- ,￨L￨,￨O￨- interventions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- faster￨L￨RBR￨O￨- diagnosis￨L￨NN￨O￨A of￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- also￨L￨RB￨O￨- benefit￨L￨VBP￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- depicts￨L￨VBZ￨O￨- a￨L￨DT￨O￨- simplified￨L￨VBN￨O￨A compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- subdivided￨L￨VBN￨O￨- into￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- never￨L￨RB￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- but￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- currently￨L￨RB￨DATE￨- infectious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- latent￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- actively￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- symptomatic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- impact￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- diagnostic￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- on￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- will￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- its￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- deployed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- measures￨L￨NNS￨O￨- consist￨L￨VBP￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- a￨L￨DT￨O￨- whole-flock￨L￨JJ￨O￨- cull￨L￨NN￨O￨- or￨L￨CC￨O￨- genotyping￨L￨VBG￨O￨- all￨L￨DT￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- culling￨L￨VBG￨O￨- the￨L￨DT￨O￨- animals￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- genotype￨L￨NN￨O￨A and￨L￨CC￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- brain￨L￨NN￨O￨- stem￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- culled￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨DURATION￨- least￨L￨JJS￨DURATION￨- 12￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- for￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- positivity￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- rapid￨L￨JJ￨O￨- tests￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Dutch￨U￨JJ￨NATIONALITY￨- culled-flocks￨L￨NNS￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2003￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- consist￨L￨VBP￨O￨- of￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- genotyping￨L￨NN￨O￨- results￨L￨NNS￨O￨- and￨L￨CC￨O￨- scrapie￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- test￨L￨NN￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- animals￨L￨NNS￨O￨A that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- culled￨L￨VBN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mandatory￨L￨JJ￨O￨- scrapie￨L￨NN￨O￨- control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- 69￨L￨CD￨NUMBER￨- flocks￨L￨NNS￨O￨- of￨L￨IN￨O￨- origin￨L￨NN￨O￨- of￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- index￨L￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- accumulated￨L￨VBN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- EU￨U￨NNP￨ORGANIZATION￨- statutory￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- genotyping￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- partial￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- culling￨L￨NN￨O￨- and￨L￨CC￨O￨- testing￨L￨NN￨O￨- of￨L￨IN￨O￨- flocks￨L￨NNS￨O￨- of￨L￨IN￨O￨- origin￨L￨NN￨O￨- of￨L￨IN￨O￨- scrapie-positive￨L￨JJ￨O￨- animals￨L￨NNS￨O￨A .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- identified￨L￨VBD￨O￨- PrP￨U￨NN￨O￨- genotype￨L￨NN￨O￨A and￨L￨CC￨O￨- allele￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- as￨L￨IN￨O￨- flock-level￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- for￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- case-control￨L￨JJ￨O￨- study￨L￨NN￨O￨- comprising￨L￨VBG￨O￨- 293￨L￨CD￨NUMBER￨- flocks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Subsequently￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- occupations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- summarized￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- locations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- analyzed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- interventions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- isolation￨L￨NN￨O￨- and￨L￨CC￨O￨- immunization￨L￨NN￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- discussed￨L￨VBN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- emergency￨L￨NN￨O￨A is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- artificial￨L￨JJ￨O￨- Beijing￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- environment￨L￨NN￨O￨- factors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- always￨L￨RB￨O￨- neglect￨L￨NN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- always￨L￨RB￨O￨- led￨L￨VBD￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- amazingly￨L￨RB￨O￨- increased￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- medical￨L￨JJ￨O￨- workers￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- discussed￨L￨VBN￨O￨A .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- roles￨L￨NNS￨O￨A ,￨L￨,￨O￨- behavior￨L￨NN￨O￨- schedules￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- designed￨L￨VBN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- considered￨L￨VBN￨O￨- graph￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- homogeneously￨L￨RB￨O￨- mixing￨L￨VBG￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- limit￨L￨NN￨O￨- theorems￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- ignorants￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- spreader￨L￨NN￨TITLE￨A tells￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rumour￨L￨NN￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- (￨L￨-LRB-￨O￨- nearest￨L￨JJS￨O￨- )￨L￨-RRB-￨O￨- ignorant￨L￨JJ￨O￨- neighbours￨L￨NNS￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- spreader￨L￨NN￨TITLE￨- becomes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stifler￨L￨NN￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- action￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- (￨L￨-LRB-￨O￨- nearest￨L￨JJS￨O￨- neighbour￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- stifler￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- α￨L￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- interacting￨L￨VBG￨O￨- particle￨L￨NN￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumour￨L￨NN￨O￨- by￨L￨IN￨O￨- agents￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- graph￨L￨NN￨O￨A ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- n￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- node￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- set￨L￨VBN￨O￨- {￨L￨-LRB-￨O￨- 0,1,2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- 0￨L￨CD￨NUMBER￨- stands￨L￨NNS￨O￨- for￨L￨IN￨O￨- ignorant￨L￨JJ￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- spreader￨L￨NN￨TITLE￨A and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- stifler￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- this￨L￨DT￨O￨- intuition￨L￨NN￨O￨- of￨L￨IN￨O￨- cascade￨L￨NN￨O￨A growth￨L￨NN￨O￨- wherein￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- of￨L￨IN￨O￨- tweets￨L￨NNS￨O￨- or￨L￨CC￨O￨- users￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- believed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- :￨L￨:￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- joined￨L￨VBN￨O￨- the￨L￨DT￨O￨- cascade￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- could￨L￨MD￨O￨- potentially￨L￨RB￨O￨- do￨L￨VB￨O￨- so￨L￨RB￨O￨- Infected￨U￨JJ￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- :￨L￨:￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- joined￨L￨VBN￨O￨- the￨L￨DT￨O￨- cascade￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- Recovered￨U￨VBN￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- :￨L￨:￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- left￨L￨VBN￨O￨- the￨L￨DT￨O￨- cascade￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- now￨L￨RB￨DATE￨- participate￨L￨VB￨O￨- in￨L￨IN￨O￨- another￨L￨DT￨O￨- cascade￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Shown￨U￨VBN￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- governing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- join￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- cumulative￨L￨JJ￨O￨- cascade￨L￨NN￨O￨A population￨L￨NN￨O￨- ,￨L￨,￨O￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- joined￨L￨VBN￨O￨- the￨L￨DT￨O￨- cascade￨L￨NN￨O￨- by￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- left￨L￨VBN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- either￨L￨RB￨O￨- currently￨L￨RB￨DATE￨- infected￨L￨VBN￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- adopt￨L￨VBP￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- approach￨L￨NN￨O￨- wherein￨L￨WRB￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- a￨L￨DT￨O￨- user￨L￨NN￨O￨- ’s￨L￨POS￨O￨- interaction￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- protest￨L￨NN￨O￨- information￨L￨NN￨O￨- cascade￨L￨NN￨O￨A using￨L￨VBG￨O￨- a￨L￨DT￨O￨- similarly￨L￨RB￨O￨- conceived￨L￨VBN￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- participation￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- assumption￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- will￨L￨MD￨O￨- experience￨L￨VB￨O￨- a￨L￨DT￨O￨- cost￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- joining￨L￨VBG￨O￨- a￨L￨DT￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- cascade￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- cost￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- classify￨L￨VB￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cascade￨L￨NN￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- evolves￨L￨VBZ￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- improve￨L￨VBP￨O￨- on￨L￨IN￨O￨- vanilla￨L￨NN￨O￨- temporal￨L￨JJ￨O￨- features￨L￨NNS￨O￨- by￨L￨IN￨O￨- representing￨L￨VBG￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- cascade￨L￨NN￨O￨A behavior￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- sets￨L￨NNS￨O￨- .￨L￨.￨O￨- +Biologically￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- controlled￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- assays￨L￨NNS￨O￨- ,￨L￨,￨O￨- UCBSV￨U￨NN￨ORGANIZATION￨- isolates￨L￨NNS￨O￨A induce￨L￨VBP￨O￨- systemic￨L￨JJ￨O￨- mosaic￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- in￨L￨IN￨O￨- Nicotiana￨U￨NN￨LOCATION￨- benthamiana￨L￨NN￨O￨- without￨L￨IN￨O￨- necrotic￨L￨JJ￨O￨- local￨L￨JJ￨O￨- lesions￨L￨NNS￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- CBSV￨U￨NN￨ORGANIZATION￨- isolates￨L￨NNS￨O￨- cause￨L￨VBP￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +CBSD￨U￨NN￨ORGANIZATION￨- is￨L￨VBZ￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- single-stranded￨L￨JJ￨O￨- RNA￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ssRNA￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- Cassava￨U￨NNP￨O￨- brown￨L￨JJ￨O￨- streak￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CBSV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Ugandan￨U￨JJ￨NATIONALITY￨- cassava￨L￨NN￨O￨- brown￨L￨JJ￨O￨- streak￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- UCBSV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- belonging￨L￨VBG￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- genus￨L￨NN￨O￨- Ipomovirus￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- family￨L￨NN￨O￨- Potyviridae￨U￨NNP￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- genome￨L￨NN￨O￨- of￨L￨IN￨O￨- UCBSV￨U￨NN￨O￨- is￨L￨VBZ￨O￨- larger￨L￨JJR￨O￨- (￨L￨-LRB-￨O￨- 9069￨L￨CD￨NUMBER￨- nt￨L￨NNS￨O￨- as￨L￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- MLB3￨U￨NN￨O￨- isolate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- than￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- CBSV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 8995￨L￨CD￨NUMBER￨- nt￨L￨NNS￨O￨- for￨L￨IN￨O￨- isolate￨L￨JJ￨O￨- TZ￨U￨NN￨O￨- :￨L￨:￨O￨- Kor6￨U￨NN￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- wider￨L￨JJR￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- isolates￨L￨NNS￨O￨A of￨L￨IN￨O￨- CBSV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 79.3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 95.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- at￨L￨IN￨O￨- nt￨L￨NN￨O￨- level￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- than￨L￨IN￨O￨- UCBSV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 86.3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 99.3￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- complete￨L￨JJ￨O￨- genomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- CBSV￨U￨NN￨O￨- and￨L￨CC￨O￨- UCBSV￨U￨NN￨O￨- isolates￨L￨NNS￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- sequenced￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- and￨L￨CC￨O￨- sizes￨L￨NNS￨O￨- range￨L￨VBP￨O￨- from￨L￨IN￨O￨- 8,900￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 10,818￨L￨CD￨NUMBER￨- nt￨L￨NNS￨O￨- in￨L￨IN￨O￨- length￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- highly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- cassava￨L￨NN￨O￨- cultivars￨L￨NNS￨O￨- accumulate￨L￨VBP￨O￨- higher￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨A RNA￨U￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- CBSV￨U￨NN￨O￨- and￨L￨CC￨O￨- UCBSV￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- successive￨L￨JJ￨O￨- generations￨L￨NNS￨O￨A provided￨L￨VBD￨O￨- the￨L￨DT￨O￨- proportions￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- types￨L￨NNS￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- the￨L￨DT￨O￨- stable￨L￨JJ￨O￨- composition￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mixture￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- types￨L￨NNS￨O￨- that￨L￨WDT￨O￨- one￨L￨PRP￨NUMBER￨- would￨L￨MD￨O￨- expect￨L￨VB￨O￨- to￨L￨TO￨O￨- see￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- allowed￨L￨VBN￨O￨- to￨L￨TO￨O￨- grow￨L￨VB￨O￨- at￨L￨IN￨O￨- low￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- generations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- envisaged￨L￨VBN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- is￨L￨VBZ￨O￨- discussed￨L￨VBN￨O￨- further￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Discussion￨U￨NN￨O￨- section￨L￨NN￨O￨- We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- generalization￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- calculating￨L￨VBG￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- multiple￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨- reflecting￨L￨VBG￨O￨- individual￨L￨JJ￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- sex￨L￨NN￨O￨- and￨L￨CC￨O￨- perhaps￨L￨RB￨O￨- other￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- sex￨L￨NN￨O￨A ,￨L￨,￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- important￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- equals￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- per￨L￨IN￨O￨- a￨L￨DT￨O￨- currently￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- totally￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Generalization￨U￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- several￨L￨JJ￨O￨- categories￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A with￨L￨IN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- survival￨L￨NN￨O￨- or￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨- by￨L￨IN￨O￨- Diekmann￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- quantifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- infected￨L￨JJ￨O￨A individual￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- chimpanzees￨L￨NNS￨O￨- have￨L￨VBP￨O￨- anatomic￨L￨JJ￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- immunological￨L￨JJ￨O￨- similarities￨L￨NNS￨O￨- with￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- their￨L￨PRP$￨O￨- use￨L￨NN￨O￨- is￨L￨VBZ￨O￨- essential￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- .12￨L￨CD￨NUMBER￨- Unfortunately￨U￨RB￨O￨- ,￨L￨,￨O￨- chimpanzees￨L￨NNS￨O￨- are￨L￨VBP￨O￨- expensive￨L￨JJ￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- manage￨L￨VB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- involve￨L￨VB￨O￨- emotional￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- and￨L￨CC￨O￨- ethical￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- .12￨L￨CD￨NUMBER￨- Instead￨U￨RB￨O￨- ,￨L￨,￨O￨- cattle￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Mycobacterium￨U￨NN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- bovis￨L￨NN￨O￨- and￨L￨CC￨O￨- usually￨L￨RB￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- very￨L￨RB￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- important￨L￨JJ￨O￨- information￨L￨NN￨O￨- for￨L￨IN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- development￨L￨NN￨O￨- .13￨L￨CD￨NUMBER￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- disadvantage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- their￨L￨PRP$￨O￨- largest￨L￨JJS￨O￨- limitation￨L￨NN￨O￨- :￨L￨:￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- Mycobacterium￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- M.￨U￨NN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- hominis￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .13￨L￨CD￨NUMBER￨- Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- require￨L￨VBP￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- expensive￨L￨JJ￨O￨- equipment￨L￨NN￨O￨- .13￨L￨CD￨NUMBER￨- Sheeps￨U￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- respiratory￨L￨JJ￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- lung￨L￨NN￨O￨- function￨L￨NN￨O￨- because￨L￨IN￨O￨- these￨L￨DT￨O￨- aspects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- easily￨L￨RB￨O￨- measurable￨L￨JJ￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- animals￨L￨NNS￨O￨- .12￨L￨CD￨NUMBER￨- Unfortunately￨U￨RB￨O￨- ,￨L￨,￨O￨- limited￨L￨JJ￨O￨- molecular￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- and￨L￨CC￨O￨- difficult￨L￨JJ￨O￨- handling￨L￨NN￨O￨- limit￨L￨NN￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- such￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- .12￨L￨CD￨NUMBER￨- Rabbits￨U￨NNS￨O￨- and￨L￨CC￨O￨- guinea￨L￨NN￨COUNTRY￨- pigs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- easy￨L￨JJ￨O￨- to￨L￨TO￨O￨- handle￨L￨VB￨O￨- and￨L￨CC￨O￨- particularly￨L￨RB￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- studies￨L￨NNS￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- .13￨L￨CD￨NUMBER￨- Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- high￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- suitable￨L￨JJ￨O￨- reagents￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- difficult￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- manipulation￨L￨NN￨O￨- limit￨L￨VB￨O￨- their￨L￨PRP$￨O￨- use￨L￨NN￨O￨- .13￨L￨CD￨NUMBER￨- Cotton￨U￨NN￨O￨- rats￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- viral￨L￨JJ￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- semipermissive￨L￨JJ￨O￨- for￨L￨IN￨O￨- viral￨L￨JJ￨O￨- replication￨L￨NN￨O￨- and￨L￨CC￨O￨- allow￨L￨VB￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- .12￨L￨CD￨NUMBER￨- Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- quite￨L￨RB￨O￨- fragile￨L￨JJ￨O￨- and￨L￨CC￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- handle￨L￨VB￨O￨- .12￨L￨CD￨NUMBER￨- Certainly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- animal￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- mice￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- these￨L￨DT￨O￨- reasons￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- young￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- Mycoplasma￨U￨NN￨MISC￨- pneumoniae￨L￨FW￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- retrospectively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- .2￨L￨NN￨NUMBER￨- There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- much￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- causal￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- respiratory￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- exacerbations￨L￨NNS￨O￨- .3￨L￨NN￨NUMBER￨- Respiratory￨U￨JJ￨O￨- viruses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- >￨L￨JJR￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- exacerbation￨L￨NN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- children4￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- 44￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- adults￨L￨NNS￨O￨- ,5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- rhinoviruses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- RVs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- ,￨L￨,￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- 60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- -66￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .3￨L￨NN￨NUMBER￨- A￨U￨DT￨O￨- strong￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- association￨L￨NN￨O￨- of￨L￨IN￨O￨- RVs￨U￨NNS￨O￨- with￨L￨IN￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- exacerbations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- sided￨L￨VBN￨O￨- by￨L￨IN￨O￨- evidence￨L￨NN￨O￨- supporting￨L￨VBG￨O￨- that￨L￨IN￨O￨- RVs￨U￨NNS￨O￨- spread￨L￨VBN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- upper￨L￨JJ￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- airways￨L￨NNS￨O￨- ,￨L￨,￨O￨- inducing￨L￨VBG￨O￨- inflammation￨L￨NN￨O￨- .6￨L￨CD￨NUMBER￨- Both￨U￨CC￨O￨- infected￨L￨JJ￨O￨- bronchial￨L￨JJ￨O￨- and￨L￨CC￨O￨- pulmonary￨L￨JJ￨O￨- epithelial￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- produce￨L￨VBP￨O￨- inflammatory￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- enhance￨L￨VBP￨O￨- airway￨L￨NN￨O￨- inflammation￨L￨NN￨O￨- and￨L￨CC￨O￨- obstruction￨L￨NN￨O￨- .7￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- RV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- asthmatics￨L￨NNS￨O￨- induced￨L￨VBD￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- typical￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- exacerbating￨L￨VBG￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- lung￨L￨NN￨O￨- function￨L￨NN￨O￨- impairment￨L￨NN￨O￨- ,￨L￨,￨O￨- worsening￨L￨VBG￨O￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- increased￨L￨VBD￨O￨- bronchial￨L￨JJ￨O￨- reactivity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- eosinophilic￨L￨JJ￨O￨- airway￨L￨NN￨O￨- inflammation￨L￨NN￨O￨- .8￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- exacerbation￨L￨NN￨O￨- severity￨L￨NN￨O￨- was￨L￨VBD￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- immunological￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- to￨L￨TO￨O￨- deficient￨L￨JJ￨O￨- interferon￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IFN￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- γ￨L￨NN￨O￨- and￨L￨CC￨O￨- interleukin￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IL￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- -10￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- increased￨L￨VBN￨O￨- IL-4￨U￨NN￨MISC￨- ,￨L￨,￨O￨- IL-5￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- IL-13.8￨U￨NN￨O￨- The￨U￨DT￨O￨- viral￨L￨JJ￨O￨A load￨L￨NN￨O￨A related￨L￨JJ￨O￨- to￨L￨TO￨O￨- clinical￨L￨JJ￨O￨- and￨L￨CC￨O￨- functional￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- asthmatic￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- in￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- controls￨L￨NNS￨O￨- ,￨L￨,￨O￨- revealing￨L￨VBG￨O￨- relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- viral￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- exacerbations￨L￨NNS￨O￨- .8￨L￨CD￨NUMBER￨- Bronchial￨U￨JJ￨O￨- mucosal￨L￨JJ￨O￨- biopsies￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- bronchoscopies￨L￨NNS￨O￨- of￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- RV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- asthmatics￨L￨NNS￨O￨- revealed￨L￨VBD￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- epithelial￨L￨JJ￨O￨- eosinophils￨L￨NNS￨O￨- .9￨L￨CD￨NUMBER￨- Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- RV￨U￨NN￨O￨- colds￨L￨NNS￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- burden￨L￨NN￨O￨- in￨L￨IN￨O￨- submucosal￨L￨JJ￨O￨- lymphocytes￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- peripheral￨L￨JJ￨O￨- blood￨L￨NN￨O￨- lymphopenia￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- histamine￨L￨NN￨O￨- responsiveness￨L￨NN￨O￨- .9￨L￨CD￨NUMBER￨- A￨U￨DT￨O￨- further￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- RV-induced￨U￨JJ￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- exacerbations￨L￨NNS￨O￨- demonstrated￨L￨VBD￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- important￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- neutrophils￨L￨NNS￨O￨- and￨L￨CC￨O￨- CD681￨U￨NN￨O￨- macrophages￨L￨NNS￨O￨- in￨L￨IN￨O￨- bronchial￨L￨JJ￨O￨- mucosa￨L￨NN￨O￨- of￨L￨IN￨O￨- asthmatics￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- healthy￨L￨JJ￨O￨- controls￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- inflammation￨L￨NN￨O￨- was￨L￨VBD￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- viral￨L￨JJ￨O￨A load￨L￨NN￨O￨A and￨L￨CC￨O￨- correlated￨L￨VBD￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- lung￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- underlying￨L￨VBG￨O￨- a￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- RV-induced￨U￨JJ￨O￨- inflammation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- exacerbations￨L￨NNS￨O￨- .10￨L￨CD￨NUMBER￨- Similarly￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- demonstrated￨L￨VBD￨O￨- a￨L￨DT￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- viral￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- COPD￨U￨NN￨O￨- exacerbations￨L￨NNS￨O￨- .11￨L￨CD￨NUMBER￨- Since￨U￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- naturally￨L￨RB￨O￨- occurring￨L￨VBG￨O￨- COPD￨U￨NN￨O￨- exacerbations￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- and￨L￨CC￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- virus-induced￨L￨JJ￨O￨- COPD￨U￨NN￨O￨- exacerbations￨L￨NNS￨O￨- ,￨L￨,￨O￨- experimental￨L￨JJ￨O￨- RV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- COPD￨U￨NN￨O￨- patients￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- .11￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- experimental￨L￨JJ￨O￨- RV16￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- produced￨L￨VBD￨O￨- typical￨L￨JJ￨O￨- COPD￨U￨NN￨O￨- exacerbations￨L￨NNS￨O￨- '￨L￨POS￨O￨- clinical￨L￨JJ￨O￨- features￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- worse￨L￨JJR￨O￨- airflow￨L￨NN￨O￨- obstruction￨L￨NN￨O￨- and￨L￨CC￨O￨- respiratory￨L￨JJ￨O￨- symptoms/inflammation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- both￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- systemic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- COPD￨U￨NN￨O￨- patients￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- controls￨L￨NNS￨O￨- .11￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- COPD￨U￨NN￨O￨- patients￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- asthmatics￨L￨NNS￨O￨- ,￨L￨,￨O￨- exacerbation￨L￨NN￨O￨- severity￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- immunologic￨L￨JJ￨O￨- alterations￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- neutrophils￨L￨NNS￨O￨- .11￨L￨CD￨NUMBER￨- Symptoms￨U￨NNS￨O￨- and￨L￨CC￨O￨- inflammatory￨L￨JJ￨O￨- markers￨L￨NNS￨O￨- were￨L￨VBD￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- .11￨L￨CD￨NUMBER￨- Interestingly￨U￨RB￨O￨- ,￨L￨,￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- was￨L￨VBD￨O￨- higher￨L￨JJR￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- IFN￨U￨NN￨O￨- production￨L￨NN￨O￨- was￨L￨VBD￨O￨- lower￨L￨JJR￨O￨- in￨L￨IN￨O￨- COPD￨U￨NN￨O￨- patients￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- healthy￨L￨JJ￨O￨- controls￨L￨NNS￨O￨- .11￨L￨CD￨NUMBER￨- Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- impaired￨L￨JJ￨O￨- IFN-γ￨U￨NN￨O￨- production￨L￨NN￨O￨- and￨L￨CC￨O￨- neutrophilic￨L￨JJ￨O￨- inflammation￨L￨NN￨O￨- may￨L￨MD￨O￨- play￨L￨VB￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- RV-induced￨U￨JJ￨O￨- COPD￨U￨NN￨O￨- exacerbations￨L￨NNS￨O￨- .11￨L￨CD￨NUMBER￨- Even￨U￨RB￨O￨- if￨L￨IN￨O￨- human￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- truest￨L￨JJS￨O￨- representations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- offer￨L￨VBP￨O￨- answers￨L￨NNS￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- many￨L￨JJ￨O￨- weak￨L￨JJ￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rationale￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- in￨L￨FW￨O￨- vitro￨L￨FW￨O￨- and￨L￨CC￨O￨- animal￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- portray￨L￨VBP￨O￨- RSV￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- as￨L￨IN￨O￨- linked￨L￨VBN￨O￨- more￨L￨JJR￨O￨- to￨L￨TO￨O￨- immunologic￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- than￨L￨IN￨O￨- to￨L￨TO￨O￨- viral￨L￨JJ￨O￨A load￨L￨NN￨O￨A .1￨L￨CD￨NUMBER￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- premises￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- demonstrated￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- RSV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- symptoms￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- immunologic￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- .1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- study￨L￨NN￨O￨- suffers￨L￨VBZ￨O￨- from￨L￨IN￨O￨- some￨L￨DT￨O￨- limitations￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- recent￨L￨JJ￨O￨- study￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨- datasets31￨L￨NN￨O￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- per￨L￨FW￨O￨- capita￨L￨NN￨O￨- social￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- scales￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨A size￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- substrate￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- phenomena￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- ideas￨L￨NNS￨O￨- and￨L￨CC￨O￨- behaviors123￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- common￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- in￨L￨IN￨O￨- RD￨U￨NNP￨O￨- metapopulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- particles￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- equal￨L￨JJ￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- of31￨L￨NN￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- city￨L￨NN￨O￨A scales￨L￨NNS￨O￨- as￨L￨IN￨O￨- where￨L￨WRB￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨- ’s￨L￨POS￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- large￨L￨JJ￨O￨- body￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- evolves￨L￨VBZ￨O￨- antigenically￨L￨RB￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- how￨L￨WRB￨O￨- point￨L￨NN￨O￨- mutations￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- 's￨L￨POS￨O￨- hemagglutinin￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- protein￨L￨NN￨O￨- allow￨L￨VBP￨O￨- for￨L￨IN￨O￨- immune￨L￨JJ￨O￨- escape￨L￨NN￨CRIMINAL_CHARGE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- virus￨L￨NN￨O￨- strains￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- immunologically￨L￨RB￨O￨- to￨L￨TO￨O￨- shape￨L￨VB￨O￨- this￨L￨DT￨O￨- subtype￨L￨NN￨O￨- 's￨L￨POS￨O￨- evolutionary￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- term￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- interference￨L￨NN￨O￨- effects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- possible￨L￨JJ￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- extensive￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- linkage￨L￨NN￨O￨- across￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- 's￨L￨POS￨O￨- HA￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- arise￨L￨VB￨O￨- from￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- background￨L￨NN￨O￨- fitness￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- fitness￨L￨NN￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- mutations￨L￨NNS￨O￨A .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 1997￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- found￨L￨VBD￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nonsynonymous￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- on￨L￨IN￨O￨- tip￨L￨NN￨O￨- branches￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HA￨U￨NNP￨O￨- phylogeny￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- ,￨L￨,￨O￨- indicative￨L￨JJ￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- strain￨L￨NN￨O￨- selection￨L￨NN￨O￨- bias￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- transiently￨L￨RB￨O￨- circulating￨L￨VBG￨O￨- deleterious￨L￨JJ￨O￨- mutations￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- viral￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Together￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- purifying￨L￨VBG￨O￨- selection￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- sufficiently￨L￨RB￨O￨- strong￨L￨JJ￨O￨- to￨L￨TO￨O￨- immediately￨L￨RB￨O￨- eliminate￨L￨VB￨O￨- deleterious￨L￨JJ￨O￨- mutations￨L￨NNS￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A/H3N2￨U￨NN￨O￨- virus￨L￨NN￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- circulates￨L￨VBZ￨O￨- among￨L￨IN￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- feature￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- any￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- mass-action￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- —￨L￨:￨O￨- indeed￨L￨RB￨O￨- ,￨L￨,￨O￨- earlier￨L￨JJR￨O￨- applications￨L￨NNS￨O￨- pertained￨L￨VBD￨O￨- to￨L￨TO￨O￨- inhomogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨A in￨L￨IN￨O￨- predator￨L￨NN￨O￨- –￨L￨:￨O￨- prey￨L￨NN￨O￨- systems￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- mixing￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ’￨L￨POS￨O￨- that￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- nonlinearity￨L￨NN￨O￨- have￨L￨VBP￨O￨- primarily￨L￨RB￨O￨- been￨L￨VBN￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- TSIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- rubella￨L￨NN￨O￨- and￨L￨CC￨O￨- dengue￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- no￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- TSIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- been￨L￨VBN￨O￨- assessed￨L￨VBN￨O￨- ,￨L￨,￨O￨- leaving￨L￨VBG￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- inhomogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨A varies￨L￨VBZ￨O￨- across￨L￨IN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- question￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- time-series￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- TSIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Finkenstädt￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Grenfell￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- to￨L￨TO￨O￨- offer￨L￨VB￨O￨- an￨L￨DT￨O￨- accurate￨L￨JJ￨O￨- and￨L￨CC￨O￨- straightforward￨L￨JJ￨O￨- way￨L￨NN￨O￨A to￨L￨TO￨O￨- statistically￨L￨RB￨O￨- connect￨L￨VB￨O￨- mechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- time-series￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- other￨L￨JJ￨O￨- features￨L￨NNS￨O￨- ,￨L￨,￨O￨- TSIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- readily￨L￨RB￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- inhomogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- phenomenological￨L￨JJ￨O￨- way￨L￨NN￨O￨- by￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- densities￨L￨NNS￨O￨- nonlinearly￨L￨RB￨O￨- .￨L￨.￨O￨- +Applied￨U￨NNP￨O￨- to￨L￨TO￨O￨- discrete-time￨L￨JJ￨O￨- models￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- TSIR￨U￨NN￨O￨- ,￨L￨,￨O￨- mixing￨L￨VBG￨O￨A parameters￨L￨NNS￨O￨- also￨L￨RB￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- interpretation￨L￨NN￨O￨- as￨L￨IN￨O￨- corrections￨L￨NNS￨O￨- for￨L￨IN￨O￨- approximating￨L￨VBG￨O￨- a￨L￨DT￨O￨- truly￨L￨RB￨O￨- continuous-time￨L￨JJ￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Co-infections￨U￨NNS￨O￨- may￨L￨MD￨O￨- result￨L￨VB￨O￨- when￨L￨WRB￨O￨- hosts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- independently￨L￨RB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- parasites￨L￨NNS￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- parasite￨L￨JJ￨O￨- species￨L￨NNS￨O￨- facilitate￨L￨VBP￨O￨- co-occurrence￨L￨NN￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- The￨U￨DT￨MISC￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- multiparasitism￨L￨NN￨O￨- :￨L￨:￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- co-infections￨L￨NNS￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- animal￨L￨JJ￨O￨- healthElise￨L￨NN￨O￨- Vaumourin1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Gwenaël￨U￨NNP￨PERSON￨- Vourc￨U￨NNP￨PERSON￨- ’￨L￨POS￨O￨- h1￨L￨NN￨O￨- ,￨L￨,￨O￨- Patrick￨U￨NNP￨PERSON￨- Gasqui1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Muriel￨U￨NNP￨PERSON￨- Vayssier-Taussat2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 8:545￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractMost￨U￨NNP￨O￨- parasites￨L￨NNS￨O￨A co-occur￨L￨VBP￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- parasites￨L￨NNS￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- multiparasitism￨L￨NN￨O￨- has￨L￨VBZ￨O￨- only￨L￨RB￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- recognised￨L￨VBN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- also￨L￨RB￨O￨- identifies￨L￨VBZ￨O￨- new￨L￨JJ￨O￨- research￨L￨NN￨O￨- directions￨L￨NNS￨O￨- to￨L￨TO￨O￨- pursue.KeywordsMultiparasitismInteractionsAssociationsMechanismsObservationsModelling￨L￨JJ￨O￨- BackgroundMore￨U￨NN￨O￨- than￨L￨IN￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- known￨L￨JJ￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- multitude￨L￨NN￨O￨- of￨L￨IN￨O￨- taxa￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- parasites￨L￨NNS￨O￨A ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- organisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- survive￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- interactions￨L￨NNS￨O￨A can￨L￨MD￨O￨- have￨L￨VB￨O￨- important￨L￨JJ￨O￨- repercussions￨L￨NNS￨O￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨- or￨L￨CC￨O￨- animal￨L￨JJ￨O￨- health￨L￨NN￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- alter￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- duration￨L￨NN￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- risks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- clinical￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Interactions￨U￨NNS￨O￨- among￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A strongly￨L￨RB￨O￨- influence￨L￨VBP￨O￨- parasite￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- play￨L￨VB￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- structuring￨L￨VBG￨O￨- parasite￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- both￨L￨CC￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- among￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Model-based￨U￨JJ￨MISC￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- MDA￨U￨NN￨ORGANIZATION￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- typical￨L￨JJ￨O￨- low-risk￨L￨JJ￨O￨- and￨L￨CC￨O￨- higher-risk￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A prevalence￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- substantially￨L￨RB￨O￨- reduced￨L￨VBN￨O￨- within￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- only￨L￨RB￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- community￨L￨NN￨O￨- participation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- >￨L￨JJR￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- annual￨L￨JJ￨SET￨- MDA￨U￨NN￨ORGANIZATION￨- .￨L￨.￨O￨- +MDA￨U￨NN￨ORGANIZATION￨- success￨L￨NN￨O￨- in￨L￨IN￨O￨- achieving￨L￨VBG￨O￨- very￨L￨RB￨O￨- low￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A prevalence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- treatment￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- frequency￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- requires￨L￨VBZ￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- adults￨L￨NNS￨O￨- and￨L￨CC￨O￨- children￨L￨NNS￨O￨- be￨L￨VB￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- drug￨L￨NN￨O￨- delivery￨L￨NN￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Calibrated￨U￨VBN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- project￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- frequency￨L￨NN￨O￨- and￨L￨CC￨O￨- coverage￨L￨NN￨O￨A of￨L￨IN￨O￨- MDA￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨O￨- schistosomiasis￨L￨NN￨O￨- haematobia￨L￨NN￨O￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- present-day￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- uncertainties￨L￨NNS￨O￨- of￨L￨IN￨O￨- parasite￨L￨JJ￨O￨- biology￨L￨NN￨O￨- and￨L￨CC￨O￨- input￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- implementing￨L￨VBG￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- Roadmap￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Neglected￨U￨NNP￨ORGANIZATION￨- Tropical￨U￨JJ￨ORGANIZATION￨- Diseases￨U￨NNS￨ORGANIZATION￨- it￨L￨PRP￨O￨- would￨L￨MD￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- policymaking￨L￨VBG￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- projections￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- Schistosoma￨U￨NN￨LOCATION￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- MDA-treated￨U￨JJ￨O￨- areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨DURATION￨A years￨L￨NNS￨DURATION￨A .￨L￨.￨O￨- +MDA￨U￨NN￨ORGANIZATION￨- alone￨L￨RB￨O￨- is￨L￨VBZ￨O￨- unlikely￨L￨JJ￨O￨- to￨L￨TO￨O￨- interrupt￨L￨VB￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- once￨L￨RB￨DATE￨- mass￨L￨NN￨O￨- treatment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- suspended￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨A of￨L￨IN￨O￨- human￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- rebound￨L￨VB￨O￨- to￨L￨TO￨O￨- pre-control￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- 25￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 30￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- hidden￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- Ebola￨U￨NN￨MISC￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- affected￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- using￨L￨VBG￨O￨- country￨L￨NN￨O￨- and￨L￨CC￨O￨- sub-country￨L￨JJ￨O￨- confirmed￨L￨VBD￨O￨A case￨L￨NN￨O￨- counts￨L￨NNS￨O￨- available￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- including￨L￨VBG￨O￨- Ebola￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- particular￨L￨JJ￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- decreases￨L￨VBZ￨O￨- below￨L￨IN￨O￨- 1.0￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨A cases￨L￨NNS￨O￨- using￨L￨VBG￨O￨- standard￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- definitions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- were￨L￨VBD￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- week￨L￨NN￨DURATION￨- for￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Guinea￨U￨NNP￨COUNTRY￨- from￨L￨IN￨O￨- January￨U￨NNP￨DATE￨- 5￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2014￨L￨CD￨DATE￨- to￨L￨TO￨O￨- July￨U￨NNP￨DATE￨- 29￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2015￨L￨CD￨DATE￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +Weekly￨U￨NNP￨SET￨- country-and￨L￨NN￨O￨- subcountry-specific￨L￨JJ￨O￨- confirmed￨L￨VBD￨O￨A case￨L￨NN￨O￨- count￨L￨NN￨TITLE￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨ORGANIZATION￨- Global￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Observatory￨U￨NNP￨ORGANIZATION￨- 's￨L￨POS￨O￨- patient￨L￨NN￨O￨- database￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- examined￨L￨VBD￨O￨- international￨L￨JJ￨O￨- reported￨L￨VBN￨O￨- Ebola￨U￨NNP￨MISC￨- case￨L￨NN￨O￨A data￨L￨NNS￨O￨A to￨L￨TO￨O￨- determine￨L￨VB￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- became￨L￨VBD￨O￨- subcritical￨L￨JJ￨O￨- in￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- Guinea￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Reduced￨U￨VBN￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- only￨L￨RB￨O￨- be￨L￨VB￨O￨- maintained￨L￨VBN￨O￨- if￨L￨IN￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨A sufficiently￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- successful￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- antibiotic￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- long￨L￨JJ￨O￨- term￨L￨NN￨O￨- reductions￨L￨NNS￨O￨- in￨L￨IN￨O￨- overall￨L￨JJ￨O￨- transmission.The￨L￨NN￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- drug￨L￨NN￨O￨- administration￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MDA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- reduction￨L￨NN￨O￨- measures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- successfully￨L￨RB￨O￨- control￨L￨VB￨O￨- and￨L￨CC￨O￨- eliminate￨L￨VB￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- :￨L￨:￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- trachoma￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- schistosomiasis￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- onchocerciasis￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- lymphatic￨L￨JJ￨O￨- filariasis￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Though￨U￨IN￨O￨- the￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- V.￨U￨NNP￨O￨- cholerae￨L￨VBP￨O￨- O1￨U￨NN￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- and￨L￨CC￨O￨- multiply￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- influx￨L￨NN￨O￨- of￨L￨IN￨O￨- nutrients￨L￨NNS￨O￨- into￨L￨IN￨O￨- surface￨L￨NN￨O￨A waters￨L￨NNS￨O￨- after￨L￨IN￨O￨- rainfall￨L￨NNS￨O￨- events￨L￨NNS￨O￨- or￨L￨CC￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- water￨L￨NN￨O￨- temperature￨L￨NN￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- recurrent￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- after￨L￨IN￨O￨- interepidemic￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- where￨L￨WRB￨O￨- very￨L￨RB￨O￨- few￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +cholerae￨L￨NN￨O￨- O1￨U￨NN￨O￨- is￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- surface￨L￨NN￨O￨A water￨L￨NN￨O￨- as￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- continue￨L￨VBP￨O￨- to￨L￨TO￨O￨- decline￨L￨VB￨O￨- ,￨L￨,￨O￨- none￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- reservoirs￨L￨NNS￨O￨- in￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +cholerae￨L￨NN￨O￨- O1￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- aquatic￨L￨JJ￨O￨- environment￨L￨NN￨O￨- has￨L￨VBZ￨O￨- left￨L￨VBN￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨- scientific￨L￨JJ￨O￨- community￨L￨NN￨O￨- divided￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- causative￨L￨JJ￨O￨- bacterium￨L￨NN￨O￨- has￨L￨VBZ￨O￨- established￨L￨VBN￨O￨- environmental￨L￨JJ￨O￨- reservoirs￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- surface￨L￨NN￨O￨A waters￨L￨NNS￨O￨- of￨L￨IN￨O￨- Haiti￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- assist￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- planning￨L￨NN￨O￨- and￨L￨CC￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- Haiti￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- MA-LDA￨U￨NN￨LOCATION￨- ,￨L￨,￨O￨- topics￨L￨NNS￨O￨A are￨L￨VBP￨O￨- extracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- messages￨L￨NNS￨O￨- only￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- predefined￨L￨JJ￨O￨- comment￨L￨NN￨O￨- count￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- retweet￨L￨NN￨O￨- count￨L￨NN￨TITLE￨- because￨L￨IN￨O￨- hot￨L￨JJ￨O￨- topics￨L￨NNS￨O￨- related￨L￨JJ￨O￨- messages￨L￨NNS￨O￨- are￨L￨VBP￨O￨- always￨L￨RB￨O￨- retweeted￨L￨VBN￨O￨- and￨L￨CC￨O￨- commented￨L￨VBN￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- frequencies￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formalize￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- hot￨L￨JJ￨O￨- topic￨L￨NN￨O￨A extraction￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- generative￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- probabilistic￨L￨JJ￨O￨- generative￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- LDA￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- called￨L￨VBD￨O￨- MA-LDA￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- innovative￨L￨JJ￨O￨- topic￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- exploit￨L￨VB￨O￨- time￨L￨NN￨O￨- information￨L￨NN￨O￨- of￨L￨IN￨O￨- messages￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- attribute￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- filter￨L￨NN￨O￨- out￨L￨IN￨O￨- the￨L￨DT￨O￨- hot￨L￨JJ￨O￨- topic￨L￨NN￨O￨A related￨L￨JJ￨O￨- words￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- MA-LDA￨U￨NN￨O￨- to￨L￨TO￨O￨- extract￨L￨VB￨O￨- hot￨L￨JJ￨O￨- topics￨L￨NNS￨O￨A .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- necessarily￨L￨RB￨O￨- make￨L￨VBP￨O￨- simplifying￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- nevertheless￨L￨RB￨O￨- provide￨L￨VB￨O￨- general￨L￨JJ￨TITLE￨- insights￨L￨NNS￨O￨- .28￨L￨CD￨NUMBER￨- For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- positive￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- non-local￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- works￨L￨VBZ￨O￨- beyond￨L￨IN￨O￨- neighbor￨L￨NN￨O￨- nucleosomes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- cooperative￨L￨JJ￨O￨- .7￨L￨CD￨NUMBER￨- Our￨U￨PRP$￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- bistable￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- idealized￨L￨JJ￨O￨- HM￨U￨NNS￨O￨- locus￨L￨NN￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- dependence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- silencers￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- simple￨L￨JJ￨O￨- barriers￨L￨NNS￨O￨- to￨L￨TO￨O￨- inhibit￨L￨VB￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- silencing￨L￨NN￨O￨- modifications￨L￨NNS￨O￨- .26￨L￨CD￨NUMBER￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- robust￨L￨JJ￨O￨- ,￨L￨,￨O￨- being￨L￨VBG￨O￨- very￨L￨RB￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- small￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- HM￨U￨NNS￨O￨- locus￨L￨NN￨O￨- by￨L￨IN￨O￨- explicitly￨L￨RB￨O￨- including￨L￨VBG￨O￨- binding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- complex￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- multiple￨L￨JJ￨O￨- nucleosome￨L￨JJ￨O￨- modification￨L￨NN￨O￨- states￨L￨NNS￨O￨- that￨L￨WDT￨O￨- arise￨L￨VBP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- dimeric￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nucleosome￨L￨JJ￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- ubiquitous￨L￨JJ￨O￨- antisilencing￨L￨JJ￨O￨- nucleosome￨L￨JJ￨O￨- modification￨L￨NN￨O￨- by￨L￨IN￨O￨- Dot1￨U￨NN￨O￨- .29￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- simple￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- SIR￨U￨NN￨O￨- complexes￨L￨NNS￨O￨- bound￨L￨VBD￨O￨- to￨L￨TO￨O￨- separate￨L￨VB￨O￨- nucleosomes￨L￨NNS￨O￨- aid￨L￨NN￨O￨- bistability￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- localization￨L￨NN￨O￨- of￨L￨IN￨O￨- SIR￨U￨NN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- silencers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- barriers￨L￨NNS￨O￨- .￨L￨.￨O￨- +SIR￨U￨NN￨O￨- silencing￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- simpler￨L￨JJR￨O￨- than￨L￨IN￨O￨- analogous￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨A eukaryotes￨L￨NNS￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- clearly￨L￨RB￨O￨- nucleosome-based￨L￨JJ￨O￨- ,￨L￨,￨O￨- free￨L￨JJ￨O￨- of￨L￨IN￨O￨- DNA￨U￨NN￨MISC￨- methylation￨L￨NN￨O￨- and￨L￨CC￨O￨- RNAi￨U￨NN￨MISC￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- contribute￨L￨VBP￨O￨- to￨L￨TO￨O￨- heritable￨L￨JJ￨O￨- bistability￨L￨NN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- Sir￨U￨NNP￨O￨- silencing￨L￨NN￨O￨- center￨L￨NN￨O￨- around￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A loop￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- deacetylation￨L￨NN￨O￨- of￨L￨IN￨O￨- H4K16￨U￨NN￨O￨- by￨L￨IN￨O￨- Sir2￨U￨NN￨O￨- creates￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- affinity￨L￨NN￨O￨- nucleosomal￨L￨JJ￨O￨- binding￨L￨NN￨O￨- sites￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Sir2-Sir3-Sir4￨U￨NN￨O￨- complex￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- bind￨L￨VB￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- HM￨U￨NNS￨O￨- loci￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Sir￨U￨NNP￨O￨- silencing￨L￨NN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- Saccharomyces￨U￨FW￨O￨- cerevisiae￨L￨FW￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- characterized￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- epigenetic￨L￨JJ￨O￨- regulation￨L￨NN￨O￨A by￨L￨IN￨O￨- nucleosome￨L￨JJ￨O￨- modification￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- a￨L￨DT￨O￨- realistic￨L￨JJ￨O￨- and￨L￨CC￨O￨- faithful￨L￨JJ￨O￨- reconstruction￨L￨NN￨O￨- of￨L￨IN￨O￨- economic￨L￨JJ￨O￨A and￨L￨CC￨O￨- financial￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- improved￨L￨JJ￨O￨- procedure￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨- links￨L￨NNS￨O￨- directionality￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- we￨L￨PRP￨O￨- implement￨L￨VBP￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- and￨L￨CC￨O￨- self-consistent￨L￨JJ￨O￨- prescription￨L￨NN￨O￨- to￨L￨TO￨O￨- assign￨L￨VB￨O￨- link￨L￨NN￨O￨- weights￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- more￨L￨RBR￨O￨- recent￨L￨JJ￨O￨- approach1011￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- builds￨L￨VBZ￨O￨- on￨L￨IN￨O￨- even￨L￨RB￨O￨- earlier￨L￨JJR￨O￨- results12￨L￨NN￨O￨- ,￨L￨,￨O￨- instead￨L￨RB￨O￨- uses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- topological￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- an￨L￨DT￨O￨- ensemble￨L￨NN￨O￨A of￨L￨IN￨O￨- graphs￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- CM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 13￨L￨CD￨NUMBER￨- —￨L￨:￨O￨- where￨L￨WRB￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Lagrange￨U￨NNP￨LOCATION￨- multipliers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- define￨L￨VBP￨O￨- it￨L￨PRP￨O￨- are￨L￨VBP￨O￨- replaced￨L￨VBN￨O￨- by￨L￨IN￨O￨- fitnesses￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- known￨L￨JJ￨O￨- intrinsic￨L￨JJ￨O￨- node-specific￨L￨JJ￨O￨- features14￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- will￨L￨MD￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- weighted￨L￨JJ￨O￨A directed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- graphs￨L￨NNS￨O￨- composed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨VBN￨O￨- V￨U￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- directed￨L￨VBN￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- —￨L￨:￨O￨- whose￨L￨WP$￨O￨- generic￨L￨JJ￨O￨- element￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- that￨L￨WDT￨O￨- runs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- node￨L￨NN￨O￨- j￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- a￨L￨DT￨O￨- binary￨L￨JJ￨O￨- network￨L￨NN￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- economic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- ones￨L￨NNS￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- accurately￨L￨RB￨O￨- reconstructed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨A degrees￨L￨NNS￨O￨- only182526￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- average￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observables￨L￨NNS￨O￨- computed￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- CM-induced￨U￨JJ￨MISC￨- ensemble￨L￨NN￨O￨A are￨L￨VBP￨O￨- then￨L￨RB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- network￨L￨NN￨O￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Cost-effectiveness￨U￨NN￨MISC￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- quadrivalent￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccines￨L￨NNS￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- Canada￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨ORGANIZATION￨- KingdomEdward￨U￨NNP￨ORGANIZATION￨- W.￨U￨NNP￨ORGANIZATION￨- Bauch7￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 15:465￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- adoption￨L￨NN￨O￨- of￨L￨IN￨O￨- quadrivalent￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- QIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- replace￨L￨VB￨O￨- trivalent￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- immunization￨L￨NN￨O￨- programs￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- growing￨L￨VBG￨O￨- worldwide￨L￨RB￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- helping￨L￨VBG￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨O￨- lineage￨L￨NN￨O￨- mismatch￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- analysis￨L￨NN￨O￨- assessed￨L￨VBN￨O￨- potential￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- impacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- country-wide￨L￨JJ￨O￨- switch￨L￨NN￨O￨A from￨L￨IN￨O￨- TIV￨U￨NN￨ORGANIZATION￨- to￨L￨TO￨O￨- QIV￨U￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- Canada￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- third-party￨L￨JJ￨O￨- payer￨L￨NN￨O￨- perspective￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- considered￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- strategies￨L￨NNS￨O￨- :￨L￨:￨O￨- Children￨U￨NNP￨O￨- aged￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- who￨L￨WP￨O￨- receive￨L￨VBP￨O￨- the￨L￨DT￨O￨- live-attenuated￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- LAIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- switch￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- quadrivalent￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- QLAIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- >￨L￨JJR￨O￨- 18￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- switch￨L￨VBP￨O￨- from￨L￨IN￨O￨- TIV￨U￨NN￨ORGANIZATION￨- to￨L￨TO￨O￨- QIV￨U￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- that￨L￨WDT￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- relations￨L￨NNS￨O￨- started￨L￨VBD￨O￨- using￨L￨VBG￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- issues￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- opinion￨L￨NN￨O￨- leaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- diffusion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- finding￨L￨VBG￨O￨- out￨L￨RP￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- encourage￨L￨VB￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- word￨L￨NN￨O￨- out￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- regular￨L￨JJ￨O￨- consumers￨L￨NNS￨O￨- encourage￨L￨VBP￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- innovations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- discover￨L￨VB￨O￨- whether￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complementary￨L￨JJ￨O￨- or￨L￨CC￨O￨- substitute￨L￨JJ￨O￨- effect￨L￨NN￨O￨- between￨L￨IN￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨- and￨L￨CC￨O￨- traditional￨L￨JJ￨O￨- marketing￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- advertising￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Concerning￨U￨VBG￨O￨- the￨L￨DT￨O￨- studies￨L￨NNS￨O￨- reported￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- marketing￨L￨NN￨O￨- and￨L￨CC￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- innovation￨L￨NN￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- extant￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- probably￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- account￨L￨NN￨O￨- for￨L￨IN￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- adopters￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- across￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g￨L￨FW￨O￨- .￨L￨.￨O￨- +Modeling￨U￨VBG￨O￨- social￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- using￨L￨VBG￨O￨- network￨L￨NN￨O￨A models￨L￨NNS￨O￨A requires￨L￨VBZ￨O￨- taking￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- conditions￨L￨NNS￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- adaptive￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨A dynamic￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- modeled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- rewiring￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨A contagion￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- adoption￨L￨NN￨O￨- process￨L￨NN￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- over￨L￨IN￨O￨- or￨L￨CC￨O￨- underestimated￨L￨VBD￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- not￨L￨RB￨O￨- considering￨L￨VBG￨O￨- network￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- remarkable￨L￨JJ￨O￨- application￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- explained￨L￨VBD￨O￨- —￨L￨:￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- switching￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- :￨L￨:￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- ,￨L￨,￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- were￨L￨VBD￨O￨- cyclical￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- biennial￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- becoming￨L￨VBG￨O￨- highly￨L￨RB￨O￨- irregular￨L￨JJ￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- magnitude￨L￨NN￨O￨- following￨L￨VBG￨O￨- large￨L￨JJ￨O￨A scale￨L￨NN￨O￨A immunization￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- history￨L￨NN￨O￨A is￨L￨VBZ￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- by￨L￨IN￨O￨- dividing￨L￨VBG￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- immune￨L￨JJ￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- more￨L￨RBR￨O￨- refined￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- age-distributed￨L￨JJ￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- leading￨L￨VBG￨O￨- key￨L￨NN￨O￨- to￨L￨TO￨O￨- interpret￨L￨VB￨O￨- and￨L￨CC￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- contagion￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- leitmotiv￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- papers￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- microscopic￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- powerful￨L￨JJ￨O￨- and￨L￨CC￨O￨- fascinating￨L￨JJ￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- strictly￨L￨RB￨O￨- necessary￨L￨JJ￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- instead￨L￨RB￨O￨- essentially￨L￨RB￨O￨- regulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- those￨L￨DT￨O￨- papers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- was￨L￨VBD￨O￨- entirely￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- D-dimensional￨U￨JJ￨MISC￨- lattice￨L￨NN￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- lattice￨L￨NN￨O￨- was￨L￨VBD￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- attractive￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- age-class￨L￨NN￨O￨- ,￨L￨,￨O￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- reproducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- assortative￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Diary-based￨U￨JJ￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- surveys￨L￨NNS￨O￨- also￨L￨RB￨O￨- highlight￨L￨VBP￨O￨- the￨L￨DT￨O￨- homophily￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- :￨L￨:￨O￨- people￨L￨NNS￨O￨- strongly￨L￨RB￨O￨- prefer￨L￨VBP￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- similar￨L￨JJ￨O￨- people￨L￨NNS￨O￨- and￨L￨CC￨O￨- specially￨L￨RB￨O￨- with￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- age-class￨L￨JJ￨O￨- ,￨L￨,￨O￨- i.e￨L￨IN￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- assortative￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- shown￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- diagonal￨L￨JJ￨O￨- elements￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A matrices￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Polymod￨U￨NNP￨O￨- survey￨L￨NN￨O￨- all￨L￨DT￨O￨- over￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- on￨L￨IN￨O￨- age-dependent￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- also￨L￨RB￨O￨- reveal￨L￨VBP￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨A age￨L￨NN￨O￨A have￨L￨VBP￨O￨- very￨L￨RB￨O￨- different￨L￨JJ￨O￨- social￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- with￨L￨IN￨O￨- relevant￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- classes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- verify￨L￨VBP￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨A numerically￨L￨RB￨O￨- by￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- classical￨L￨JJ￨O￨- rejection￨L￨NN￨O￨- sampling￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- ∼￨L￨CD￨NUMBER￨- 500￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- faster￨L￨RBR￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- processes￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- ranges￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- here￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NNP￨O￨- 5￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- “￨L￨``￨O￨- Comparison￨U￨NN￨O￨- of￨L￨IN￨O￨- Gillespie￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- rejection￨L￨NN￨O￨- sampling￨L￨NN￨O￨- algorithms￨L￨NNS￨O￨- ”￨L￨''￨O￨- we￨L￨PRP￨O￨- validate￨L￨VBP￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨A through￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- rejection￨L￨NN￨O￨- sampling￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- ;￨L￨:￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- compare￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- speeds￨L￨NNS￨O￨- for￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIS￨U￨NN￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- synthetic￨L￨JJ￨O￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Section￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- “￨L￨``￨O￨- Stochastic￨U￨NNP￨O￨- processes￨L￨VBZ￨O￨- on￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ”￨L￨''￨O￨- defines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- simulated￨L￨JJ￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- contagion￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- class￨L￨NN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- use￨L￨VB￨O￨- in￨L￨IN￨O￨- examples￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- difficulty￨L￨NN￨O￨- in￨L￨IN￨O￨- adapting￨L￨VBG￨O￨- the￨L￨DT￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨A to￨L￨TO￨O￨- time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- rates￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- normalizing￨L￨VBG￨O￨- time￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- instantaneous￨L￨JJ￨O￨- cumulative￨L￨JJ￨O￨- transition￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨A that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- Poisson￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- processes￨L￨VBZ￨O￨- on￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Main￨U￨NNP￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- Distribution￨U￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- by￨L￨IN￨O￨- type￨L￨NN￨O￨- and￨L￨CC￨O￨- overall￨L￨JJ￨O￨- case-fatality￨L￨JJ￨O￨- ratios￨L￨NNS￨O￨- per￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- Where￨U￨WRB￨O￨- the￨L￨DT￨O￨- distinction￨L￨NN￨O￨- between￨L￨IN￨O￨- probable￨L￨JJ￨O￨A ,￨L￨,￨O￨- confirmed￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- suspected￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- was￨L￨VBD￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- case-fatality￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- and￨L￨CC￨O￨- %￨L￨NN￨O￨- female￨L￨NN￨O￨- were￨L￨VBD￨O￨- calculated￨L￨VBN￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- probable￨L￨JJ￨O￨- and￨L￨CC￨O￨- confirmed￨L￨VBD￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- devastating￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- has￨L￨VBZ￨O￨- resulted￨L￨VBN￨O￨- in￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- ten￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨A reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- previous￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- will￨L￨MD￨O￨- ultimately￨L￨RB￨O￨- provide￨L￨VB￨O￨- improved￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- EVD￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Map￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Democratic￨U￨JJ￨COUNTRY￨- Republic￨U￨NN￨COUNTRY￨- of￨L￨IN￨COUNTRY￨- the￨L￨DT￨COUNTRY￨- Congo￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- DRC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- circles￨L￨NNS￨O￨- are￨L￨VBP￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- probable￨L￨JJ￨O￨A and￨L￨CC￨O￨- confirmed￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- per￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- values￨L￨NNS￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- table￨L￨NN￨O￨- for￨L￨IN￨O￨- Yambuku￨U￨NNP￨LOCATION￨- were￨L￨VBD￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- our￨L￨PRP$￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- cases￨L￨NNS￨O￨A during￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 262/318￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- summarises￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨A and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- analysis￨L￨NN￨O￨- was￨L￨VBD￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- three￨L￨CD￨NUMBER￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- monthly￨L￨JJ￨SET￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- in￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- high-quality￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- collected￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- reported￨L￨VBD￨O￨A cases￨L￨NNS￨O￨A of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- reported￨L￨VBD￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- EV-A71￨U￨NN￨O￨- and￨L￨CC￨O￨- CVA16￨U￨NN￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- patients￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- meteorological￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- analysis￨L￨NN￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- bimodal￨L￨JJ￨O￨A seasonal￨L￨JJ￨O￨- peaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- attributable￨L￨JJ￨O￨- to￨L￨TO￨O￨- EV-A71￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimum￨L￨JJ￨O￨- least￨L￨JJS￨O￨- squares￨L￨NNS￨O￨- fitting￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- LSF￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- curves￨L￨NNS￨O￨- calculated￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- 1-year￨L￨JJ￨DURATION￨- and￨L￨CC￨O￨- 6-month￨L￨JJ￨DURATION￨- cycles￨L￨NNS￨O￨- reproduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- bimodal￨L￨JJ￨O￨A cycles￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- clearly￨L￨RB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- HFMD￨U￨NN￨O￨- and￨L￨CC￨O￨- EV-A71￨U￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- in￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- ChinaBanghua￨U￨NNP￨O￨- Chen1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Ayako￨U￨NNP￨PERSON￨- Sumi2Email￨U￨NNP￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Shin￨U￨NNP￨PERSON￨- ’￨L￨POS￨O￨- ichi￨L￨JJ￨O￨- Toyoda3￨U￨NN￨O￨- ,￨L￨,￨O￨- Quan￨U￨JJ￨O￨- Hu4Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Dunjin￨U￨NNP￨O￨- Zhou4￨U￨NN￨O￨- ,￨L￨,￨O￨- Keiji￨U￨NNP￨PERSON￨- Mise5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Junchan￨U￨NNP￨O￨- Zhao6￨U￨NNP￨O￨- and￨L￨CC￨O￨- Nobumichi￨U￨NNP￨MISC￨- Kobayashi2￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 15:495￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Hand￨U￨VB￨O￨- ,￨L￨,￨O￨- foot￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- mouth￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- HFMD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A caused￨L￨VBN￨O￨A by￨L￨IN￨O￨- a￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- enteroviruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- Coxsackievirus￨U￨NNP￨O￨- A16￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- CVA16￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Enterovirus￨U￨NN￨O￨- A71￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- EV-A71￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨DURATION￨- peak￨L￨JJ￨DURATION￨- months￨L￨NNS￨DURATION￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- LSF￨U￨NNP￨ORGANIZATION￨- curves￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- HFMD￨U￨NNP￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- those￨L￨DT￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- EV-A71￨U￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨A reports￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- hospitalizations￨L￨NNS￨O￨- ,￨L￨,￨O￨- deaths￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- incorporated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- directly￨L￨RB￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-exposed-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- [￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 32￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 33￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- :￨L￨:￨O￨- This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- provided￨L￨VBN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vast￨L￨JJ￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- hand￨L￨NN￨O￨- washing￨L￨VBG￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A practices￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- moderate￨L￨JJ￨O￨- to￨L￨TO￨O￨- extreme￨L￨JJ￨O￨- total￨L￨JJ￨O￨- isolation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- at￨L￨IN￨O￨- all￨L￨DT￨O￨- times￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- are￨L￨VBP￨O￨- integral￨L￨JJ￨O￨- in￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- contracting￨L￨NN￨O￨- and￨L￨CC￨O￨- transmitting￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- same￨L￨JJ￨O￨- phenomenon￨L￨NN￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- with￨L￨IN￨O￨- health￨L￨NN￨O￨- events￨L￨NNS￨O￨- –￨L￨:￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- precautions￨L￨NNS￨O￨- against￨L￨IN￨O￨- becoming￨L￨VBG￨O￨- ill￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- health￨L￨NN￨O￨- threat￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- individual￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- reports￨L￨NNS￨O￨- may￨L￨MD￨O￨- diminsh￨L￨VB￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- distancing￨L￨NN￨O￨A practices￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- relaxed￨L￨VBN￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- affecting￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- better￨L￨RBR￨O￨- control￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- media￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- uptake￨L￨NN￨O￨- and￨L￨CC￨O￨- waning￨L￨VBG￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨A practices￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- needed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Mass￨U￨JJ￨STATE_OR_PROVINCE￨- media￨L￨NNS￨O￨- campaigns￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- and￨L￨CC￨O￨- effective￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- drug￨L￨NN￨O￨- therapy￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨A measures￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- such￨L￨JJ￨O￨- reduced￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- show￨L￨VB￨O￨- how￨L￨WRB￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- derive￨L￨VB￨O￨- analytical￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- stable￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- to￨L￨TO￨O￨- stable￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- impossible￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- system￨L￨NN￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨A .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- gives￨L￨VBZ￨O￨- an￨L￨DT￨O￨- overview￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- fuzzy￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- their￨L￨PRP$￨O￨- combinations￨L￨NNS￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- optimising￨L￨VBG￨O￨- data￨L￨NNS￨O￨- mining￨L￨NN￨O￨- of￨L￨IN￨O￨- gene￨L￨NN￨O￨A expression￨L￨NN￨O￨- and￨L￨CC￨O￨- microarray￨L￨NN￨O￨- datasets￨L￨NNS￨O￨- to￨L￨TO￨O￨- recover￨L￨VB￨O￨- GRNs￨U￨NNS￨O￨- .￨L￨.￨O￨- +Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- transcriptional￨L￨JJ￨O￨- and￨L￨CC￨O￨- translational￨L￨JJ￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨A in￨L￨IN￨O￨- GRN￨U￨NNP￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- such￨L￨JJ￨O￨- delays￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- paradigmatic￨L￨JJ￨O￨- two-gene￨L￨JJ￨O￨- activator-inhibitor￨L￨NN￨O￨- GRN￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- choice￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨A unusual￨L￨JJ￨O￨- signals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- abnormal￨L￨JJ￨O￨- increases￨L￨NNS￨O￨- of￨L￨IN￨O￨- deaths￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- health￨L￨NN￨O￨- indicator￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- since￨L￨IN￨O￨- their￨L￨PRP$￨O￨- performances￨L￨NNS￨O￨- greatly￨L￨RB￨O￨- vary￨L￨VBP￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- factors￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- signal￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- detected￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- onset￨L￨NN￨O￨- ,￨L￨,￨O￨- magnitude￨L￨NN￨O￨- ,￨L￨,￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- progression￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- indicator￨L￨NN￨O￨- monitored￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- shape￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- variation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- itself￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- data￨L￨NNS￨O￨- source￨L￨NN￨O￨- ,￨L￨,￨O￨- data￨L￨NNS￨O￨- quality￨L￨NN￨O￨- ,￨L￨,￨O￨- processing￨L￨NN￨O￨- frequency￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- historical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- containing￨L￨VBG￨O￨- known￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- events￨L￨NNS￨O￨- a￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨A ,￨L￨,￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- performances￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- possible￨L￨JJ￨O￨- using￨L￨VBG￨O￨- simulation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨A abnormal￨L￨JJ￨O￨- increases￨L￨NNS￨O￨- of￨L￨IN￨O￨- mortality￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- was￨L￨VBD￨O￨- evaluated￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +used￨L￨VBN￨O￨- in￨L￨IN￨O￨- silico￨L￨NN￨O￨- modeling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- agent-based￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- existing￨L￨VBG￨O￨- experimental￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- mouse￨L￨NN￨O￨- lung￨L￨NN￨O￨- and￨L￨CC￨O￨- liver￨L￨NN￨O￨A with￨L￨IN￨O￨- F￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- report￨L￨VBP￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- tularemia￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- framework￨L￨NN￨O￨A with￨L￨IN￨O￨- births￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- framework￨L￨NN￨O￨A to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- live￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- against￨L￨IN￨O￨- tularemia￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +F.￨U￨NNP￨O￨- tularensis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- an￨L￨DT￨O￨- exceptionally￨L￨RB￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- unicellular￨L￨JJ￨O￨- organisms￨L￨NNS￨O￨A to￨L￨TO￨O￨- mammals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Collected￨U￨VBN￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- tularemia￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simulation￨L￨NN￨O￨- was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- bias￨L￨NN￨O￨- and￨L￨CC￨O￨- precision￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨A for￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- relatedness￨L￨NN￨O￨- among￨L￨IN￨O￨- group￨L￨NN￨O￨- mates￨L￨NNS￨O￨- on￨L￨IN￨O￨- bias￨L￨NN￨O￨- and￨L￨CC￨O￨- precision￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- that￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- linear￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- GLM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- relative￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨A for￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- genetic￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- that￨L￨WDT￨O￨- aim￨L￨VBP￨O￨- at￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- individual￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- infected/not-infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- solely￨L￨RB￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- susceptibility￨L￨NN￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨A on￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨- on￨L￨IN￨O￨- individual￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- breeding￨L￨NN￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- genes￨L￨NNS￨O￨A that￨L￨WDT￨O￨- influence￨L￨VBP￨O￨- both￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- high￨L￨JJ￨O￨- income￨L￨NN￨O￨- countries￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Canada￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- and￨L￨CC￨O￨- Australia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Indigenous￨U￨JJ￨O￨- people￨L￨NNS￨O￨- suffered￨L￨VBD￨O￨- disproportionately￨L￨RB￨O￨- from￨L￨IN￨O￨- severe￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- isolated￨L￨VBN￨O￨- communities￨L￨NNS￨O￨- experienced￨L￨VBD￨O￨- extremely￨L￨RB￨O￨- high￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- .3￨L￨NN￨NUMBER￨- In￨U￨IN￨O￨- northern￨L￨JJ￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- Canada￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- Indigenous￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- First￨U￨JJ￨ORGANIZATION￨- Nations￨U￨NNS￨ORGANIZATION￨- ,￨L￨,￨O￨- Inuit￨U￨NNP￨O￨- ,￨L￨,￨O￨- Métis￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- communities￨L￨NNS￨O￨- have￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- medical￨L￨JJ￨O￨- care￨L￨NN￨O￨- facilities￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- accessible￨L￨JJ￨O￨- only￨L￨RB￨O￨- by￨L￨IN￨O￨- air￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- residents￨L￨NNS￨O￨- with￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- health￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- diabetes￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- worse￨L￨JJR￨O￨- outcomes￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .3￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- pH1N1￨L￨NN￨O￨- occurred￨L￨VBD￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- remote￨L￨JJ￨O￨- First￨U￨JJ￨ORDINAL￨- Nations￨U￨NNS￨O￨- reserve￨L￨NN￨O￨- in￨L￨IN￨O￨- northern￨L￨JJ￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- spread￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- of￨L￨IN￨O￨- concern￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- severe￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- community￨L￨NN￨O￨- members￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- remote￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- medical￨L￨JJ￨O￨- care￨L￨NN￨O￨- services￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- uncertainty￨L￨NN￨O￨- at￨L￨IN￨O￨- that￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- pH1N1￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- ,￨L￨,￨O￨- non‐pharmacological￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- mitigation￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- was￨L￨VBD￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- intensive￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- therapy￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- neuraminidase￨L￨NN￨O￨- inhibitor￨L￨NN￨O￨- oseltamivir￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- administered￨L￨VBN￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- meeting￨L￨VBG￨O￨- criteria￨L￨NNS￨O￨- for￨L￨IN￨O￨- “￨L￨``￨O￨- influenza‐like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- ”￨L￨''￨O￨- +We￨U￨PRP￨O￨- sought￨L￨VBD￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- community￨L￨NN￨O￨A outbreak￨L￨NN￨O￨- to￨L￨TO￨O￨- parameterize￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- growth￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- Richards￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- traditional￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .5￨L￨CD￨NUMBER￨- Our￨U￨PRP$￨O￨- objectives￨L￨NNS￨O￨- were￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- attempt￨L￨VB￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- pH1N1￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- isolated￨L￨VBN￨O￨- First￨U￨NNP￨ORDINAL￨- Nations￨U￨NNP￨O￨- reserve￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- non‐pharmacological￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- project￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- expected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- aggressive￨L￨JJ￨O￨- pharmacological￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- created￨L￨VBD￨O￨- a￨L￨DT￨O￨- composite￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- by￨L￨IN￨O￨- pooling￨L￨VBG￨O￨- laboratory‐confirmed￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨DT￨O￨- cases￨L￨NNS￨O￨- across￨L￨IN￨O￨- cities￨L￨NNS￨O￨- ,￨L￨,￨O￨- regions￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- seasons￨L￨NNS￨O￨A after￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- regional￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- timing￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- composite￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- various￨L￨JJ￨O￨- hypotheses￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨- and￨L￨CC￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- midpoint￨L￨NN￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨DATE￨- week￨L￨NN￨DATE￨- when￨L￨WRB￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- reaches￨L￨VBZ￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- determined￨L￨VBN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- reporting￨L￨VBG￨O￨- geographical￨L￨JJ￨O￨- unit￨L￨NN￨O￨- :￨L￨:￨O￨- Canadian￨U￨JJ￨NATIONALITY￨- province￨L￨NN￨O￨- ,￨L￨,￨O￨- Canadian￨U￨JJ￨NATIONALITY￨- CMA￨U￨NN￨ORGANIZATION￨- or￨L￨CC￨O￨- CA￨U￨NNP￨STATE_OR_PROVINCE￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- 50￨L￨CD￨NUMBER￨- laboratory‐confirmed￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A A￨U￨NN￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- region￨L￨NN￨O￨- and￨L￨CC￨O￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Distribution￨U￨NN￨O￨- of￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨DT￨O￨- confirmations￨L￨NNS￨O￨- for￨L￨IN￨O￨- Canada￨U￨NNP￨COUNTRY￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- national‐level￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- midpoint￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- seasons￨L￨NNS￨O￨A where￨L￨WRB￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- influenza‐positive￨L￨JJ￨O￨- specimens￨L￨NNS￨O￨- were￨L￨VBD￨O￨- antigenically￨L￨RB￨O￨- similar￨L￨JJ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Distribution￨U￨NN￨O￨- of￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨DT￨O￨- confirmations￨L￨NNS￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- census￨L￨NN￨O￨- metropolitan￨L￨JJ￨O￨- area￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CMA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- level￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- midpoint￨L￨NN￨O￨- for￨L￨IN￨O￨- dominant￨L￨JJ￨O￨- A￨U￨NN￨O￨- seasons￨L￨NNS￨O￨A .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compared￨L￨VBD￨O￨- composite￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨A curves￨L￨NNS￨O￨A across￨L￨IN￨O￨- jurisdictions￨L￨NNS￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- calendar￨L￨NN￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- whether￨L￨IN￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- systematic￨L￨JJ￨O￨- irregularities￨L￨NNS￨O￨- in￨L￨IN￨O￨- testing￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +Modeling￨U￨VBG￨O￨- behavior￨L￨NN￨O￨A is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- micro￨L￨JJ￨O￨- level￨L￨NN￨O￨- through￨L￨IN￨O￨- computational￨L￨JJ￨O￨- neuroscience￨L￨NN￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- macro￨L￨NN￨O￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- society￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- through￨L￨IN￨O￨- computational￨L￨JJ￨O￨- psychology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Instead￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relational￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- multidimensional￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- behavior￨L￨NN￨O￨A must￨L￨MD￨O￨- be￨L￨VB￨O￨- studied￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- umbrella￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- computational￨L￨JJ￨O￨- science￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- three￨L￨CD￨NUMBER￨- attributes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- essential￨L￨JJ￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- behavior￨L￨NN￨O￨A .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- behavior￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- modeling￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- variables￨L￨NNS￨O￨- in￨L￨IN￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- researcher￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- to￨L￨TO￨O￨- what￨L￨WP￨O￨- extent￨L￨NN￨O￨- realistic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- relational￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- multidimensional￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Haemophilus￨U￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- serotype￨L￨NN￨O￨- b￨L￨NN￨O￨- herd￨L￨NN￨O￨- protection￨L￨NN￨O￨A threshold￨L￨NN￨O￨- Human￨U￨JJ￨O￨- Papillomavirus￨U￨NN￨O￨- incremental￨L￨JJ￨O￨- cost-effectiveness￨L￨NN￨O￨- ratio￨L￨NN￨O￨- pneumococcal￨L￨JJ￨O￨- conjugate￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- Quality￨U￨NNP￨O￨- Adjusted￨U￨NNP￨O￨- Life￨U￨NNP￨O￨- Years￨U￨NNS￨DURATION￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- rotavirus￨L￨NN￨O￨- gastroenteritis￨L￨NN￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- Susceptible-Infected-Recovery￨U￨NNP￨ORGANIZATION￨- United￨U￨NNP￨ORGANIZATION￨- States￨U￨NNPS￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- America￨U￨NNP￨ORGANIZATION￨- Vaccination￨U￨NN￨ORGANIZATION￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- well-recognized￨L￨JJ￨O￨- way￨L￨NN￨O￨- of￨L￨IN￨O￨- protecting￨L￨VBG￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- against￨L￨IN￨O￨- communicable￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- further￨L￨RBR￨O￨- complicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- indirect￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- include￨L￨VBP￨O￨- additional￨L￨JJ￨O￨- protection￨L￨NN￨O￨A of￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- herd￨L￨NN￨O￨- protection￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and/or￨L￨CC￨O￨- negative￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- reappearance￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- manifested￨L￨VBN￨O￨- under￨L￨IN￨O￨- certain￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- short-term￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- decline￨L￨VB￨O￨- among￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- subjects￨L￨NNS￨O￨- because￨L￨IN￨O￨- these￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- will￨L￨MD￨O￨- mount￨L￨VB￨O￨- an￨L￨DT￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- antigen￨L￨NN￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- themselves￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- =￨L￨JJ￨O￨- direct￨L￨JJ￨O￨- protection￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- spectacular￨L￨JJ￨O￨- herd￨L￨NN￨O￨- protection￨L￨NN￨O￨A effects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- among￨L￨IN￨O￨- those￨L￨DT￨O￨- normally￨L￨RB￨O￨- not￨L￨RB￨O￨- considered￨L￨VBN￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- but￨L￨CC￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- transmitters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- direct￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- protection￨L￨NN￨O￨A ,￨L￨,￨O￨- it￨L￨PRP￨O￨- also￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- indirect￨L￨JJ￨O￨- population￨L￨NN￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- embedded￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- lattices￨L￨NNS￨O￨- are￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- illustrate￨L￨VB￨O￨- that￨L￨DT￨O￨- RyR2￨U￨NN￨O￨- clusters￨L￨NNS￨O￨- can￨L￨MD￨O￨- exhibit￨L￨VB￨O￨- equal￨L￨JJ￨O￨- Ca2￨U￨NN￨O￨- +￨L￨CC￨O￨- spark￨L￨VB￨O￨- probability￨L￨NN￨O￨- despite￨L￨IN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- channels￨L￨NNS￨O￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- shape￨L￨NN￨O￨- .￨L￨.￨O￨- +L-type￨U￨JJ￨O￨- Ca2￨U￨NN￨O￨- +￨L￨CC￨O￨- channels￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- LCCs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- packed￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- 100￨L￨CD￨NUMBER￨- Ca2￨U￨NN￨O￨- +￨L￨CC￨O￨- -￨L￨:￨O￨- sensitive￨L￨JJ￨O￨- Ca2￨U￨NN￨O￨- +￨L￨CC￨O￨- -￨L￨:￨O￨- release￨L￨NN￨O￨- channels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- ryanodine￨L￨NN￨O￨- receptors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- RyR2s￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- co-located￨L￨VBN￨O￨- at￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- subcellular￨L￨JJ￨O￨- junctions￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- cell￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Binding￨U￨NN￨O￨- of￨L￨IN￨O￨- Ca2￨U￨NN￨O￨- +￨L￨CC￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- closely-apposed￨L￨JJ￨O￨- RyR2s￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- increases￨L￨VBZ￨O￨- their￨L￨PRP$￨O￨- open￨L￨JJ￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- release￨L￨NN￨O￨A of￨L￨IN￨O￨- Ca2￨U￨NN￨O￨- +￨L￨CC￨O￨- from￨L￨IN￨O￨- JSR￨U￨NNP￨ORGANIZATION￨- stores￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- Ca2￨U￨NN￨O￨- +￨L￨CC￨O￨- -￨L￨:￨O￨- induced￨L￨VBN￨O￨- Ca2￨U￨NN￨O￨- +￨L￨CC￨O￨- release￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CICR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Relationship￨U￨NN￨O￨- of￨L￨IN￨O￨- cluster￨L￨NN￨O￨A size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- triangles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- maximum￨L￨NN￨O￨- eigenvalue￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- circles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- Ca2￨U￨NN￨O￨- +￨L￨CC￨O￨- spark￨L￨VB￨O￨- probability￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 3D￨L￨NN￨O￨- spark￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Representative￨U￨JJ￨TITLE￨- simulations￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- 3D￨L￨NN￨O￨- spark￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- showing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- open￨L￨JJ￨O￨- channels￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- 49￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- configuration￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- newly￨L￨RB￨O￨- infected￨L￨JJ￨O￨- single￨L￨JJ￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- where￨L￨WRB￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- squared￨L￨VBN￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Importantly￨U￨RB￨O￨- they￨L￨PRP￨O￨- also￨L￨RB￨O￨- extend￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- beyond￨L￨IN￨O￨- edge-triangle￨L￨JJ￨O￨- configuration￨L￨NN￨O￨A networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- further￨L￨JJ￨O￨- generalisation￨L￨NN￨O￨- that￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- cliques￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- fully￨L￨RB￨O￨- connected￨L￨VBN￨O￨- subgraphs￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- above￨L￨IN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- household￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- derive￨L￨VBP￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- edge-triangle￨L￨JJ￨O￨- configuration￨L￨NN￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Cliques￨U￨NNS￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- n￨L￨NN￨O￨- are￨L￨VBP￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- analogy￨L￨NN￨O￨A with￨L￨IN￨O￨- triangles-size￨L￨JJ￨O￨- n￨L￨NN￨O￨- clique￨L￨VBG￨O￨- corners￨L￨NNS￨O￨- are￨L￨VBP￨O￨- counted￨L￨VBN￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- stubs￨L￨NNS￨O￨- and￨L￨CC￨O￨- triangle￨L￨NN￨O￨- corners￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- drug-susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- drug-resistant￨L￨JJ￨O￨- isolates￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- whether￨L￨IN￨O￨- an￨L￨DT￨O￨- aggressive￨L￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- better￨L￨JJR￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- prevention￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- moderate￨L￨JJ￨O￨A approach￨L￨NN￨O￨- for￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- being￨L￨VBG￨O￨- treated￨L￨VBN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- DR￨U￨NN￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- definition￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- minimum￨L￨NN￨O￨- inhibitory￨L￨JJ￨O￨- concentration￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MIC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- DS￨U￨NN￨O￨- strain￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- slower￨L￨JJR￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- reflecting￨L￨VBG￨O￨- fitness￨L￨NN￨O￨- costs￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- mutation￨L￨NN￨O￨- or￨L￨CC￨O￨- acquisition￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨A genes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- recent￨L￨JJ￨O￨- debate￨L￨NN￨O￨- over￨L￨IN￨O￨- aggressive￨L￨JJ￨O￨- and￨L￨CC￨O￨- moderate￨L￨JJ￨O￨A approaches￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- been￨L￨VBN￨O￨- centered￨L￨VBN￨O￨- on￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨RBS￨O￨- importantly￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- even￨L￨RB￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- very￨L￨RB￨O￨- strong￨L￨JJ￨O￨- competition￨L￨NN￨O￨- ,￨L￨,￨O￨- different￨L￨JJ￨O￨- realistic￨L￨JJ￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- can￨L￨MD￨O￨- support￨L￨VB￨O￨- the￨L￨DT￨O￨- aggressive￨L￨JJ￨O￨- or￨L￨CC￨O￨- moderate￨L￨JJ￨O￨A approach￨L￨NN￨O￨- as￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- external￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨- by￨L￨IN￨O￨- others￨L￨NNS￨O￨- for￨L￨IN￨O￨- periodicity￨L￨NN￨O￨- in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- :￨L￨:￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- survival￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- pathogen￨L￨NN￨O￨- outside￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- host￨L￨NN￨TITLE￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨A changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- defence￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Interactions￨U￨NNS￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- and￨L￨CC￨O￨- subtypes￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- surely￨L￨RB￨O￨- play￨L￨VBP￨O￨- some￨L￨DT￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- cyclical￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- replacement￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- strain￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- and￨L￨CC￨O￨- show￨L￨VB￨O￨- how￨L￨WRB￨O￨- strain￨L￨NN￨O￨A interactions￨L￨NNS￨O￨- alone￨L￨RB￨O￨- can￨L￨MD￨O￨- generate￨L￨VB￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- total￨L￨JJ￨O￨- and￨L￨CC￨O￨- strain-specific￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Detailed￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- illustrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- strain￨L￨NN￨O￨A in￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- cycles￨L￨NNS￨O￨- irregularly￨L￨RB￨O￨- among￨L￨IN￨O￨- years￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- infectivity￨L￨NN￨O￨- enhancement￨L￨NN￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- deliberate￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- another￨L￨DT￨O￨- strain￨L￨NN￨O￨A to￨L￨TO￨O￨- previously￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +C￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- upper￨L￨JJ￨O￨- row￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- update￨L￨VBP￨O￨- rules￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- three-state￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- automaton￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- lead￨L￨NN￨O￨- to￨L￨TO￨O￨- spiral￨L￨NN￨O￨- wave￨L￨NN￨O￨A formation￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- wave￨L￨NN￨O￨- front￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- layer￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- excited￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- depicted￨L￨VBN￨O￨- in￨L￨IN￨O￨- black￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- adjacent￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- refractory￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- depicted￨L￨VBN￨O￨- in￨L￨IN￨O￨- gray￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- deep￨L￨JJ￨O￨- link￨L￨NN￨O￨- between￨L￨IN￨O￨- excitability￨L￨NN￨O￨- and￨L￨CC￨O￨- wave￨L￨NN￨O￨A propagation￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- look￨L￨VB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- algorithmic￨L￨JJ￨O￨- fashion￨L￨NN￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- highly￨L￨RB￨O￨- stylized￨L￨JJ￨O￨- ,￨L￨,￨O￨- minimal￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- excitable￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- can￨L￨MD￨O￨- reproduce￨L￨VB￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- schematics￨L￨NNS￨O￨- of￨L￨IN￨O￨- wave￨L￨NN￨O￨- propagation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- principle￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- wave￨L￨NN￨O￨- front￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- self-sustained￨L￨JJ￨O￨- spiral￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig￨U￨NN￨O￨- 1C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +B￨U￨NN￨O￨- :￨L￨:￨O￨- Snapshots￨U￨NNS￨O￨- of￨L￨IN￨O￨- spiral￨L￨NN￨O￨- wave￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- from￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- left￨L￨VBN￨O￨- to￨L￨TO￨O￨- right￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- cAMP￨L￨NN￨O￨- signaling￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Dictyostelium￨U￨NNP￨MISC￨- discoideum￨L￨NN￨O￨- colony￨L￨NN￨O￨- ,￨L￨,￨O￨- local￨L￨JJ￨O￨- contraction￨L￨NN￨O￨- in￨L￨IN￨O￨- neonatal￨L￨JJ￨O￨- rat￨L￨NN￨O￨- cardiac￨L￨JJ￨O￨- monolayer￨L￨NN￨O￨- cultures￨L￨NNS￨O￨- ,￨L￨,￨O￨- MinD￨U￨NN￨O￨- protein￨L￨NN￨O￨- density￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- lipid￨L￨NN￨O￨- bilayer￨L￨NN￨O￨- and￨L￨CC￨O￨- simulated￨L￨JJ￨O￨- cytokine￨L￨NN￨O￨- levels￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- two-dimensional￨L￨JJ￨O￨- grid￨L￨NN￨O￨- of￨L￨IN￨O￨- cells￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- wave￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- manifest￨L￨VBP￨O￨- in￨L￨IN￨O￨- biology￨L￨NN￨O￨- in￨L￨IN￨O￨- situations￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- circular￨L￨JJ￨O￨- "￨L￨``￨O￨- target￨L￨NN￨O￨- "￨L￨''￨O￨- wavefronts￨L￨NNS￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- sinoatrial￨L￨JJ￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- heart￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- open-ended￨L￨JJ￨O￨- ,￨L￨,￨O￨- spiral￨L￨NN￨O￨- waves￨L￨NNS￨O￨- of￨L￨IN￨O￨- signaling￨L￨NN￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- frog￨L￨NN￨O￨- Xenopus￨U￨NN￨MISC￨- laevis￨L￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +Spot￨U￨NN￨O￨- and￨L￨CC￨O￨- stripe￨L￨NN￨O￨- Turing￨U￨NN￨MISC￨- patterns￨L￨NNS￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- coupled￨L￨VBN￨O￨- Schnakenberg￨U￨NNP￨PERSON￨- elements￨L￨NNS￨O￨- ;￨L￨:￨O￨- target￨L￨NN￨O￨- wave￨L￨NN￨O￨A formation￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- central￨L￨JJ￨O￨- pacemaker￨L￨NN￨O￨- and￨L￨CC￨O￨- established￨L￨JJ￨O￨- spiral￨L￨NN￨O￨- wave￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- coupled￨L￨VBN￨O￨- FitzHugh-Nagumo￨U￨NNP￨O￨- oscillators￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- adaptive￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- put￨L￨VBD￨O￨- forward￨L￨RB￨O￨- many￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A characteristics￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- “￨L￨``￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨- world￨L￨NN￨O￨- ”￨L￨''￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- like￨L￨IN￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Infected￨U￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Susceptible￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Social￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- complex￨L￨NN￨O￨- giant￨L￨JJ￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- connected￨L￨VBD￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- two-fifths￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- acted￨L￨VBD￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- platform￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A in￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- emergency￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- easily￨L￨RB￨O￨- cause￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- false￨L￨JJ￨O￨- facts￨L￨NNS￨O￨- or￨L￨CC￨O￨- rumors￨L￨NNS￨O￨- and￨L￨CC￨O￨- bring￨L￨VB￨O￨- about￨L￨RP￨O￨- a￨L￨DT￨O￨- serious￨L￨JJ￨O￨- panic￨L￨NN￨O￨- without￨L￨IN￨O￨- efficient￨L￨JJ￨O￨- management￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- realized￨L￨VBN￨O￨- that￨L￨IN￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- variable￨L￨JJ￨O￨- network￨L￨NN￨O￨- 's￨L￨POS￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamically￨L￨RB￨O￨- changing￨L￨VBG￨O￨- spread￨L￨NN￨O￨- paths￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- interactive￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- and￨L￨CC￨O￨- group￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- impacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- making￨L￨VBG￨O￨- a￨L￨DT￨O￨- proper￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- emergency￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- increasing￨L￨VBG￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨A makes￨L￨VBZ￨O￨- existing￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- and￨L￨CC￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- process￨L￨NN￨O￨- adequately￨L￨RB￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- modifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- dynamic￨L￨NN￨O￨- by￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- introducing￨L￨VBG￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- budget￨L￨NN￨O￨A b￨L￨NN￨O￨- that￨L￨WDT￨O￨- increases￨L￨VBZ￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- unit￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- constraining￨L￨VBG￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- partially￨L￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- budget￨L￨NN￨O￨- to￨L￨TO￨O￨- cover￨L￨VB￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- healing￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- disease-induced￨L￨JJ￨O￨- resource￨L￨NN￨O￨- constraints￨L￨NNS￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- longer￨L￨JJR￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Important￨U￨JJ￨O￨- progress￨L￨NN￨O￨- in￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- made￨L￨VBN￨O￨- using￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- capture￨L￨VBP￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- dependence￨L￨NN￨O￨- on￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨A rates567￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- took￨L￨VBD￨O￨- an￨L￨DT￨O￨- in-depth￨L￨JJ￨O￨- look￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- heterosexual￨L￨JJ￨O￨- HIV-1￨U￨NN￨MISC￨- subtype￨L￨NN￨O￨A C￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- South￨U￨NNP￨COUNTRY￨- Africa￨U￨NNP￨COUNTRY￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- longitudinally￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- coalescence￨L￨NN￨O￨- and￨L￨CC￨O￨- molecular￨L￨JJ￨O￨- clock￨L￨NN￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- the￨L￨DT￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- HIV-1￨U￨NN￨MISC￨- subtype￨L￨NN￨O￨A C￨U￨NN￨O￨- pandemic21011￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- others￨L￨NNS￨O￨- have￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- the￨L￨DT￨O￨- regional￨L￨JJ￨O￨- HIV-1￨U￨NN￨MISC￨- subtype￨L￨NN￨O￨- C￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- East￨U￨NNP￨O￨- Africa12￨U￨NNP￨O￨- and￨L￨CC￨O￨- South￨U￨NNP￨O￨- America13￨U￨NNP￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- viral￨L￨JJ￨O￨- isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV-1￨U￨NN￨O￨- in￨L￨IN￨O￨- South￨U￨NNP￨COUNTRY￨- Africa￨U￨NNP￨COUNTRY￨- was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- Division￨U￨NN￨MISC￨- of￨L￨IN￨MISC￨- Medical￨U￨JJ￨MISC￨- Virology￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- Stellenbosch￨U￨NNP￨ORGANIZATION￨- University￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Tygerberg￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Cape￨U￨NNP￨CITY￨- Town￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- South￨U￨NNP￨O￨- Africa14￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- became￨L￨VBD￨O￨- a￨L￨DT￨O￨- repository￨L￨NN￨O￨- of￨L￨IN￨O￨- samples￨L￨NNS￨O￨A for￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- testing￨L￨NN￨O￨- from￨L￨IN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- early￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- used￨L￨VBD￨O￨- only￨L￨RB￨O￨- contemporary￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- no￨L￨DT￨O￨- in-depth￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨- investigation￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- conducted￨L￨VBN￨O￨- on￨L￨IN￨O￨- sequence￨L￨NN￨O￨A data￨L￨NNS￨O￨A sampled￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- South￨U￨NNP￨COUNTRY￨- Africa￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- standard￨L￨JJ￨O￨- IGE￨U￨NN￨O￨- models￨L￨NNS￨O￨- seem￨L￨VBP￨O￨- suitable￨L￨JJ￨O￨- to￨L￨TO￨O￨- simultaneously￨L￨RB￨O￨- evaluate￨L￨VB￨O￨- whether￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- are￨L￨VBP￨O￨- under￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A control￨L￨NN￨O￨- ,￨L￨,￨O￨- Lipschutz-Powell￨U￨NN￨PERSON￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- underestimate￨L￨VBP￨O￨- infectivity￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- variances￨L￨NNS￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- fully￨L￨RB￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- underlying￨L￨VBG￨O￨- this￨L￨DT￨O￨- trait￨L￨NN￨O￨- :￨L￨:￨O￨- IGE￨U￨NN￨O￨- models￨L￨NNS￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- phenotype￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- phenotype￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- IGE￨U￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- group￨L￨NN￨O￨- members￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Bijma￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- livestock￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- dnIGE￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- provides￨L￨VBZ￨O￨- accurate￨L￨JJ￨O￨- heritability￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- and￨L￨CC￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A risk￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- scenarios￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- realistic￨L￨JJ￨O￨- for￨L￨IN￨O￨- livestock￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- times￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- accurately￨L￨RB￨O￨- known￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- hereafter￨L￨RB￨O￨- denoted￨L￨VBN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨- indirect￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- dnIGE￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- takes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- combines￨L￨VBZ￨O￨- quantitative￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- IGE￨U￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- principles￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- statistical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- Bayesian￨U￨JJ￨O￨- inferential￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- estimate￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- genetic￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- traits￨L￨NNS￨O￨- are￨L￨VBP￨O￨- under￨L￨IN￨O￨- polygenic￨L￨JJ￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dnIGE￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- improve￨L￨VB￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- genetic￨L￨JJ￨O￨A risks￨L￨NNS￨O￨- when￨L￨WRB￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨- policies￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- must￨L￨MD￨O￨- establish￨L￨VB￨O￨- a￨L￨DT￨O￨- behavioural￨L￨JJ￨O￨A baseline￨L￨NN￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- private￨L￨JJ￨O￨- actions￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- their￨L￨PRP$￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Empirical￨U￨JJ￨O￨- efforts￨L￨NNS￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- one-off￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- wake￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨A [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- infer￨L￨VB￨O￨- potential￨L￨JJ￨O￨- avoidance￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- ex￨L￨FW￨O￨- post￨L￨NN￨O￨- from￨L￨IN￨O￨- observed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- standard￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- voluntary￨L￨JJ￨O￨- avoidance￨L￨NN￨O￨- behaviour￨L￨NN￨O￨A mitigates￨L￨VBZ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- implies￨L￨VBZ￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- between￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- pathogens￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- A/H1N1￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- behavioural￨L￨JJ￨O￨A shifts￨L￨NNS￨O￨- was￨L￨VBD￨O￨- of￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- magnitude￨L￨NN￨O￨- to￨L￨TO￨O￨- alter￨L￨VB￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- USA￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- simulation￨L￨NN￨O￨- to￨L￨TO￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- benefits￨L￨NNS￨O￨A of￨L￨IN￨O￨- avoidance￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- additional￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- 100￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- simulations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- testing￨L￨NN￨O￨A frequency￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- scenario￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- MSM￨U￨NN￨O￨- tests￨L￨NNS￨O￨- on￨L￨IN￨O￨- average￨L￨JJ￨O￨- every￨L￨DT￨SET￨- 90￨L￨CD￨SET￨- days￨L￨NNS￨SET￨- ,￨L￨,￨O￨- neither￨L￨CC￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- error￨L￨NN￨O￨- for￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- nor￨L￨CC￨O￨- the￨L￨DT￨O￨- interpretation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- 3-year￨L￨JJ￨DURATION￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- scenarios￨L￨NNS￨O￨- changed￨L￨VBD￨O￨- as￨L￨IN￨O￨- more￨L￨JJR￨O￨- simulations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- added￨L￨VBN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- simulated￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- testing￨L￨NN￨O￨A frequency￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- testing￨L￨NN￨O￨- intervention￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- varied￨L￨VBN￨O￨- as￨L￨IN￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- Panel￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Supplementary￨U￨NNP￨O￨- Data￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- complete￨L￨JJ￨O￨- cohorts￨L￨NNS￨O￨- were￨L￨VBD￨O￨- simulated￨L￨JJ￨O￨- 20￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- inherent￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- 3-year￨L￨JJ￨DURATION￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- summarized￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- interaction￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- parameterized￨L￨VBN￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- national￨L￨JJ￨O￨- online￨L￨NN￨O￨- survey￨L￨NN￨O￨- of￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- testing￨L￨NN￨O￨A frequency￨L￨NN￨O￨- on￨L￨IN￨O￨- 3-year￨L￨JJ￨DURATION￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- testing￨L￨NN￨O￨- frequency￨L￨NN￨O￨- interacts￨L￨VBZ￨O￨- with￨L￨IN￨O￨- viral￨L￨JJ￨O￨- suppression￨L￨NN￨O￨- ,￨L￨,￨O￨- test￨L￨NN￨O￨- sensitivity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- seeking￨L￨VBG￨O￨- testing￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- increased￨L￨VBN￨O￨- awareness￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- increased￨L￨VBN￨O￨- testing￨L￨NN￨O￨A frequency￨L￨NN￨O￨- are￨L￨VBP￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- reduced￨L￨VBN￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- viral￨L￨JJ￨O￨- suppression￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- diagnosed￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- testing￨L￨NN￨O￨A frequency￨L￨NN￨O￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- are￨L￨VBP￨O￨- increasing￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- relatively￨L￨RB￨O￨- little￨L￨JJ￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- diagnosed￨L￨VBD￨O￨- persons￨L￨NNS￨O￨- achieving￨L￨VBG￨O￨- viral￨L￨JJ￨O￨- suppression￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- estimates￨L￨NNS￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- proportion￨L￨NN￨O￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- decreased￨L￨VBN￨O￨- to￨L￨TO￨O￨- 35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diagnosed￨L￨VBN￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- even￨L￨RB￨O￨- lower￨L￨JJR￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- subgroups￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Risk￨U￨NN￨O￨- perception￨L￨NN￨O￨- is￨L￨VBZ￨O￨- central￨L￨JJ￨O￨- to￨L￨TO￨O￨- most￨L￨JJS￨O￨- health￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- theories￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- line￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- meta-analysis￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- >￨L￨JJR￨O￨- 15,000￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- revealed￨L￨VBD￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- association￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- summary￨L￨NN￨O￨A effect￨L￨NN￨O￨- size￨L￨NN￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- pooling￨L￨VBG￨O￨- effect￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- across￨L￨IN￨O￨- studies￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- uptake￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- perceived￨L￨VBN￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- summary￨L￨NN￨O￨- effect￨L￨NN￨O￨- size￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- range￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0.26￨L￨CD￨NUMBER￨- [￨L￨-LRB-￨O￨- -0.12￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- 0.45￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.24￨L￨CD￨NUMBER￨- [￨L￨-LRB-￨O￨- 0.15￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- 0.36￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- lesser￨L￨JJR￨O￨- extent￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 31￨L￨CD￨NUMBER￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.16￨L￨CD￨NUMBER￨- [￨L￨-LRB-￨O￨- -0.18￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- 0.39￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- meta-analysis￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +β￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ;￨L￨:￨O￨- Ω￨U￨NNP￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- change￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- opinion￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- from￨L￨IN￨O￨- positive￨L￨JJ￨O￨- to￨L￨TO￨O￨- negative￨L￨JJ￨O￨- Ω￨U￨NN￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- negative￨L￨JJ￨O￨- to￨L￨TO￨O￨- positive￨L￨JJ￨O￨- Ω￨U￨NN￨O￨- ′￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- δ￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- suffering￨L￨VBG￨O￨- side￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- from￨L￨IN￨O￨- either￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- δ￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- δ￨L￨NN￨O￨- ;￨L￨:￨O￨- θ￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- vaccinate￨L￨VBP￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- are￨L￨VBP￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- both￨L￨DT￨O￨- their￨L￨PRP$￨O￨- epidemiological￨L￨JJ￨O￨- status￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ;￨L￨:￨O￨- I￨U￨PRP￨O￨- :￨L￨:￨O￨- infected￨L￨VBN￨O￨- ;￨L￨:￨O￨- R￨U￨NN￨O￨- :￨L￨:￨O￨- recovered￨L￨VBN￨O￨- through￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ;￨L￨:￨O￨- R￨U￨NN￨O￨- :￨L￨:￨O￨- recovered￨L￨VBN￨O￨- naturally￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- compartment￨L￨NN￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- opinion￨L￨NN￨O￨A of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- positive￨L￨JJ￨O￨- :￨L￨:￨O￨- subscript￨L￨JJ￨O￨- p￨L￨NN￨O￨- ;￨L￨:￨O￨- non-shaded￨L￨JJ￨O￨- colours￨L￨NNS￨O￨- ;￨L￨:￨O￨- negative￨L￨JJ￨O￨- :￨L￨:￨O￨- subscript￨L￨JJ￨O￨- n￨L￨NN￨O￨- ;￨L￨:￨O￨- shaded￨L￨JJ￨O￨- colours￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- follows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- will￨L￨MD￨O￨- vaccinate￨L￨VB￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- opinion￨L￨NN￨O￨A .￨L￨.￨O￨- +C￨U￨NN￨O￨- and￨L￨CC￨O￨- C￨U￨NN￨O￨- are￨L￨VBP￨O￨- compartments￨L￨NNS￨O￨- that￨L￨WDT￨O￨- indicate￨L￨VBP￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- recalled￨L￨VBD￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- having￨L￨VBG￨O￨- suffered￨L￨VBN￨O￨- negative￨L￨JJ￨O￨A side￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- from￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- reported￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- globally￨L￨RB￨O￨- eradicate￨L￨VB￨O￨- HIV/AIDS￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- money￨L￨NN￨O￨- spent￨L￨VBN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- must￨L￨MD￨O￨- aim￨L￨VB￨O￨- at￨L￨IN￨O￨- eradicating￨L￨VBG￨O￨- HIV/AIDS￨U￨NN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨A has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- sustaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- counterintuitive￨L￨JJ￨O￨- finding￨L￨NN￨O￨- by￨L￨IN￨O￨- Xiao￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- mobility￨L￨NN￨O￨A rates￨L￨NNS￨O￨- among￨L￨IN￨O￨- HIV/AIDS-infected￨U￨JJ￨O￨- individuals￨L￨NNS￨O￨- on￨L￨IN￨O￨- mainland￨L￨NN￨O￨- China￨U￨NNP￨COUNTRY￨- decreased￨L￨VBD￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Arino￨U￨NNP￨O￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A NumericCitation￨U￨NNP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- two-region￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- rates￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- considers￨L￨VBZ￨O￨- sequence￨L￨NN￨O￨- combinations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- exhibit￨L￨VBP￨O￨- the￨L￨DT￨O￨- minimum￨L￨NN￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- mutation￨L￨NN￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- sub-trees￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- connecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- pathogen￨L￨NN￨O￨- strains￨L￨NNS￨O￨- ;￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- consider￨L￨VB￨O￨- a￨L￨DT￨O￨- pseudo-likelihood￨L￨NN￨O￨- computed￨L￨VBD￨O￨- for￨L￨IN￨O￨- only￨L￨RB￨O￨- observed￨L￨VBN￨O￨- sequences￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- genuine￨L￨JJ￨O￨- joint￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- considers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- two-step￨L￨JJ￨O￨- inference￨L￨NN￨O￨- procedure￨L￨NN￨O￨- ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- a￨L￨DT￨O￨- phylogeny￨L￨NN￨O￨- is￨L￨VBZ￨O￨- first￨L￨JJ￨ORDINAL￨- constructed￨L￨VBN￨O￨- independently￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A network￨L￨NN￨O￨A before￨L￨IN￨O￨- conducting￨L￨VBG￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Developments￨U￨NNS￨O￨- in￨L￨IN￨O￨- Bayesian￨U￨JJ￨MISC￨- data-augmentation￨L￨NN￨O￨- methodology￨L￨NN￨O￨- for￨L￨IN￨O￨- spatio-temporal￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- or￨L￨CC￨O￨- so￨L￨RB￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- allow￨L￨VBP￨O￨A key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- risk￨L￨VB￨O￨- assessment￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- inferred￨L￨VBN￨O￨- from￨L￨IN￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- genetic￨L￨JJ￨O￨- change￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- occur￨L￨VBP￨O￨- on￨L￨IN￨O￨- comparable￨L￨JJ￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- joint￨L￨JJ￨O￨A analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- valuable￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- concerning￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Unfortunately￨U￨RB￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- typically￨L￨RB￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- typically￨L￨RB￨O￨- allow￨L￨VB￨O￨- very￨L￨RB￨O￨- precise￨L￨JJ￨O￨- inference￨L￨NN￨O￨A of￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Also￨U￨RB￨O￨- note￨L￨NN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- individual￨L￨JJ￨O￨- i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- G￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- variant￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- universal￨L￨JJ￨O￨- master￨L￨NN￨O￨- sequence￨L￨NN￨O￨- G￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Multiple￨U￨JJ￨O￨- and￨L￨CC￨O￨- Single￨U￨JJ￨O￨- Primary￨U￨JJ￨O￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- Model￨U￨NNP￨TITLE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨DURATION￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- data￨L￨NNS￨O￨- gathering￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- such￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- ,￨L￨,￨O￨- analyse￨L￨VB￨O￨- and￨L￨CC￨O￨- publish￨L￨VB￨O￨- data￨L￨NNS￨O￨A sets￨L￨NNS￨O￨A describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- contexts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks142021222324￨L￨NN￨O￨- :￨L￨:￨O￨- nodes￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- is￨L￨VBZ￨O￨- drawn￨L￨VBN￨O￨- between￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- contact25￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- herd￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- sampled￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- will￨L￨MD￨O￨- thus￨L￨RB￨O￨- be￨L￨VB￨O￨- underestimated￨L￨VBN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Note￨U￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- transportation￨L￨NN￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- transportation￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- worldwide￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza-like￨L￨JJ￨O￨- illnesses￨L￨NNS￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- arrival￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread45￨L￨NN￨O￨- .￨L￨.￨O￨- )￨L￨-RRB-￨O￨- +Anthropogenic￨U￨JJ￨O￨- environmental￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- threaten￨L￨VBP￨O￨- human￨L￨JJ￨O￨- health￨L￨NN￨O￨- by￨L￨IN￨O￨- causing￨L￨VBG￨O￨A food￨L￨NN￨O￨- and￨L￨CC￨O￨- water￨L￨NN￨O￨- scarcity￨L￨NN￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- risks￨L￨NNS￨O￨- for￨L￨IN￨O￨- natural￨L￨JJ￨CAUSE_OF_DEATH￨- disasters￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- displacements￨L￨NNS￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- directly￨L￨RB￨O￨- incapacitating￨L￨VBG￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- cause￨L￨VBP￨O￨- people￨L￨NNS￨O￨- lacking￨L￨VBG￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- lay￨L￨VB￨O￨- sick￨L￨JJ￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- viraemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- parasitaemic￨L￨JJ￨O￨- phases￨L￨NNS￨O￨- ,￨L￨,￨O￨- rendering￨L￨VBG￨O￨- them￨L￨PRP￨O￨- more￨L￨RBR￨O￨- prone￨L￨JJ￨O￨- to￨L￨TO￨O￨- further￨L￨JJ￨O￨- vector￨L￨NN￨O￨- bites￨L￨VBZ￨O￨- and￨L￨CC￨O￨- causing￨L￨VBG￨O￨A increased￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vectors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Definitions￨U￨NNS￨O￨- of￨L￨IN￨O￨- EID￨U￨NNP￨O￨- vary￨L￨VBP￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- increasing￨L￨VBG￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- tendency￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- geographically￨L￨RB￨O￨- ,￨L￨,￨O￨- cause￨L￨VB￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨A incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- species￨L￨NNS￨O￨- or￨L￨CC￨O￨- new￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ;￨L￨:￨O￨- or￨L￨CC￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- within￨L￨IN￨O￨- any￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 24￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- of￨L￨IN￨O￨- improved￨L￨VBN￨O￨- living￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- and￨L￨CC￨O￨- increased￨L￨VBD￨O￨A access￨L￨NN￨O￨- to￨L￨TO￨O￨- medications￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- deaths￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- trended￨L￨VBN￨O￨- downwards￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- centuries￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- giving￨L￨VBG￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- degenerative￨L￨JJ￨O￨- and￨L￨CC￨O￨- lifestyle￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- combined￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨- health￨L￨NN￨O￨A ,￨L￨,￨O￨- animal￨L￨NN￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- livelihoods￨L￨NNS￨O￨- make￨L￨VBP￨O￨- them￨L￨PRP￨O￨- especially￨L￨RB￨O￨- costly￨L￨JJ￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- face-to-face￨L￨JJ￨O￨- human￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- transmitted￨L￨VBN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- make￨L￨VBP￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨A structures￨L￨NNS￨O￨A from￨L￨IN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2011￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Potter￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Hens￨U￨NNS￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- 2013￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- estimate￨L￨NN￨O￨- household￨L￨NN￨O￨- network￨L￨NN￨O￨A structures￨L￨NNS￨O￨A by￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- contact￨L￨NN￨O￨- diaries￨L￨NNS￨O￨- administered￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- multicountry￨L￨JJ￨O￨- survey￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- estimated￨L￨VBN￨O￨- household￨L￨NN￨O￨A and￨L￨CC￨O￨- school￨L￨NN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- improving￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- specification￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- forecasting￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- these￨L￨DT￨O￨- areas￨L￨NNS￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Additional￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- wireless￨L￨JJ￨O￨- sensors￨L￨NNS￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A and￨L￨CC￨O￨- describe￨L￨VBP￨O￨- network￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- hospitals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Vanhems￨U￨FW￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- estimate￨L￨NN￨O￨- network￨L￨NN￨O￨A structures￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- school￨L￨NN￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- contact￨L￨NN￨O￨- diaries￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- friendship￨L￨NN￨O￨- network￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Although￨U￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- speculative￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- possess￨L￨VB￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- level￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- plausibility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- price-sensitivity￨L￨NN￨O￨- of￨L￨IN￨O￨- demand￨L￨NN￨O￨- for￨L￨IN￨O￨- bed￨L￨NN￨O￨- nets￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- free￨L￨JJ￨O￨- bed￨L￨NN￨O￨- net￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- targeted￨L￨VBN￨O￨- to￨L￨TO￨O￨- undernutritioned￨L￨JJ￨O￨- children￨L￨NNS￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- suffering￨L￨VBG￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- undernutrition￨L￨NN￨O￨- and￨L￨CC￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- sub-Saharan￨L￨JJ￨O￨- Africa￨U￨NNP￨LOCATION￨- )￨L￨-RRB-￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- subject￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- randomized￨L￨JJ￨O￨- trial￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- hypoendemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- mesoendemic￨L￨JJ￨O￨- setting￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- constructed￨L￨VBN￨O￨- with￨L￨IN￨O￨- superinfection￨L￨NN￨O￨- and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- portion￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- undernutrition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- weight-for-age￨L￨JJ￨O￨- z￨L￨SYM￨O￨- scores￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- isolate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- supplementary￨L￨JJ￨O￨- food￨L￨NN￨O￨- on￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- confounding￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- portion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- undernutrition￨L￨NN￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- randomized￨L￨JJ￨O￨- trial￨L￨NN￨O￨- of￨L￨IN￨O￨- supplementary￨L￨JJ￨O￨- feeding￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- baseline￨L￨NN￨O￨- bed￨L￨NN￨O￨- net￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- for￨L￨IN￨O￨- children￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- supplementary￨L￨JJ￨O￨- food￨L￨NN￨O￨- given￨L￨VBN￨O￨- to￨L￨TO￨O￨- underweight￨L￨JJ￨O￨- children￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A mortality￨L￨NN￨O￨- by￨L￨IN￨O￨- 7.2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22.9￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- entomological￨L￨JJ￨O￨- inoculation￨L￨NN￨O￨- rate￨L￨NN￨O￨- ranges￨L￨NNS￨O￨- from￨L￨IN￨O￨- 500￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 1.0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- children￨L￨NNS￨O￨- under￨L￨IN￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- diarrhoea￨L￨NN￨CAUSE_OF_DEATH￨- cause￨L￨VBP￨O￨- 17￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 15￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 12￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- identifying￨L￨VBG￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- highly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- children￨L￨NNS￨O￨- for￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- preventive￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- obvious￨L￨JJ￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- examples￨L￨NNS￨O￨- above￨L￨IN￨O￨- .￨L￨.￨O￨- +Targeting￨U￨NN￨O￨- insecticide-treated￨L￨JJ￨O￨- bed￨L￨NN￨O￨- nets￨L￨NNS￨O￨- to￨L￨TO￨O￨- undernutritioned￨L￨JJ￨O￨- children￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- fewer￨L￨JJR￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A deaths￨L￨NNS￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- bed￨L￨NN￨O￨- nets￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- hypoendemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- mesoendemic￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- include￨L￨VBP￨O￨- localized￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- more￨L￨RBR￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- notifications.￨L￨NN￨O￨- ,￨L￨,￨O￨- At￨U￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- policy￨L￨NN￨O￨- makers￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- news￨L￨NN￨O￨- outlets￨L￨NNS￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- attributed￨L￨VBN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- increased￨L￨VBN￨O￨- migration￨L￨NN￨O￨A ,￨L￨,￨O￨- noting￨L￨VBG￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- migrant￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- higher￨L￨JJR￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- economic￨L￨JJ￨O￨- crises￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- policy￨L￨NN￨O￨- –￨L￨:￨O￨- e.g.￨L￨FW￨O￨- in￨L￨IN￨O￨- prevention￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- –￨L￨:￨O￨- that￨L￨IN￨O￨- can￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- disease.￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- Second￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- migration￨L￨NN￨O￨A itself￨L￨PRP￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- composition￨L￨NN￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- :￨L￨:￨O￨- as￨L￨IN￨O￨- people￨L￨NNS￨O￨- move￨L￨VBP￨O￨- between￨L￨IN￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- can￨L￨MD￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- profiles￨L￨NNS￨O￨- change￨L￨VBP￨O￨- .￨L￨.￨O￨- +Box￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Economic￨U￨NNP￨O￨- crises￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- conceptual￨L￨JJ￨O￨- framework￨L￨NN￨O￨- Conceptualizing￨U￨VBG￨O￨- how￨L￨WRB￨O￨- crises￨L￨NNS￨O￨- can￨L￨MD￨O￨- affect￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A among￨L￨IN￨O￨- migrants￨L￨NNS￨O￨- presents￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- analytic￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- migrant￨L￨NN￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- could￨L￨MD￨O￨- become￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- country￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- succeeds￨L￨VBZ￨O￨- in￨L￨IN￨O￨- slowing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- cluster￨L￨NN￨O￨A ,￨L￨,￨O￨- mixing￨L￨VBG￨O￨- between￨L￨IN￨O￨- clusters￨L￨NNS￨O￨- will￨L￨MD￨O￨- decrease￨L￨VB￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- outcomes￨L￨NNS￨O￨- across￨L￨IN￨O￨- clusters￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- a￨L￨DT￨O￨- treatment￨L￨NN￨O￨- effect￨L￨NN￨O￨- will￨L￨MD￨O￨- decrease￨L￨VB￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- false￨L￨JJ￨O￨- discovery￨L￨NN￨O￨- will￨L￨MD￨O￨- increase￨L￨VB￨O￨- .￨L￨.￨O￨- +Probabilistic￨U￨JJ￨O￨- sensitivity￨L￨NN￨O￨- analysis￨L￨NN￨O￨- was￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- inputs￨L￨NNS￨O￨- on￨L￨IN￨O￨- potential￨L￨JJ￨O￨- outcomes.ResultsAssuming￨L￨JJ￨O￨- current￨L￨JJ￨DATE￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- better￨L￨JJR￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- adjuvanted￨L￨JJ￨O￨- versus￨L￨CC￨O￨- non-adjuvanted￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- against￨L￨IN￨O￨- any￨L￨DT￨O￨- strain￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- 35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- better￨L￨JJR￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- non-adjuvanted￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- against￨L￨IN￨O￨- matched￨L￨VBN￨O￨- B￨U￨NN￨O￨- versus￨L￨CC￨O￨- mismatched￨L￨JJ￨O￨- B￨U￨NN￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- aTIV￨L￨NN￨O￨- in￨L￨IN￨O￨- persons￨L￨NNS￨O￨A aged￨L￨VBN￨O￨- ≥￨L￨SYM￨O￨- 65￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- QIV￨U￨NN￨O￨- in￨L￨IN￨O￨- persons￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 65￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- could￨L￨MD￨O￨- reduce￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- 11,166￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 1,329,200￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- hospitalizations￨L￨NNS￨O￨- by￨L￨IN￨O￨- 1365￨L￨CD￨DATE￨- –￨L￨:￨O￨- 43,674￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- by￨L￨IN￨O￨- 421￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11,320￨L￨CD￨NUMBER￨- versus￨L￨CC￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- QIV￨U￨NN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- cohorts￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- products￨L￨NNS￨O￨- require￨L￨VBP￨O￨- clinical￨L￨JJ￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- evaluation￨L￨NN￨O￨- to￨L￨TO￨O￨- aid￨L￨VB￨O￨- policy￨L￨NN￨O￨- decisions.MethodsTo￨L￨NN￨O￨- address￨L￨NN￨O￨- this￨L￨DT￨O￨- need￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- two-part￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- elderly￨L￨JJ￨O￨- persons￨L￨NNS￨O￨A with￨L￨IN￨O￨- adjuvanted￨L￨JJ￨O￨- trivalent￨L￨JJ￨O￨- inactivated￨L￨VBN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- aTIV￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- conventional￨L￨JJ￨O￨- trivalent￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- TIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- quadrivalent￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- QIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- vaccines￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 459￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 487￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asA￨L￨NN￨O￨- Novel￨U￨JJ￨ORGANIZATION￨- Dynamic￨U￨NNP￨ORGANIZATION￨- Model￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Economic￨U￨NNP￨ORGANIZATION￨- Analysis￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Influenza￨U￨NNP￨ORGANIZATION￨- Vaccination￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ElderlyAuthorsAuthors￨U￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsMark￨L￨NNP￨O￨- MullikinLitjen￨U￨NNP￨O￨- TanJeroen￨U￨NNP￨O￨- P.￨U￨NNP￨O￨- JansenMarc￨U￨NNP￨O￨- Van￨U￨NNP￨O￨- RanstNorbert￨U￨NNP￨O￨- FarkasEckhardt￨U￨NNP￨O￨- PetriOpen￨U￨NNP￨O￨- AccessOriginal￨U￨NNP￨O￨- ResearchFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 09￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1.1￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 8￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractIntroductionNew￨U￨NN￨O￨- vaccines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- being￨L￨VBG￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- immunization￨L￨NN￨O￨- in￨L￨IN￨O￨- elderly￨L￨JJ￨O￨- persons￨L￨NNS￨O￨A aged￨L￨JJ￨O￨- ≥￨L￨SYM￨O￨- 65￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Elderly￨U￨JJ￨O￨- aTIV￨L￨NN￨O￨- or￨L￨CC￨O￨- QIV￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- was￨L￨VBD￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- improved￨L￨VBN￨O￨- outcomes￨L￨NNS￨O￨A over￨L￨IN￨O￨- non-adjuvanted￨L￨JJ￨O￨- TIV￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- low￨L￨JJ￨O￨- match￨L￨NN￨O￨- seasons￨L￨NNS￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- intensity￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- licensed￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- or￨L￨CC￨O￨- treatment￨L￨NN￨O￨- for￨L￨IN￨O￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- around￨L￨IN￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- declined￨L￨VBN￨O￨- since￨L￨IN￨O￨- its￨L￨PRP$￨O￨- peak￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- .2￨L￨NN￨NUMBER￨- As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- challenging￨L￨VBG￨O￨- to￨L￨TO￨O￨- run￨L￨VB￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- III￨U￨CD￨NUMBER￨- vaccine￨L￨NN￨O￨- trials￨L￨NNS￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨A of￨L￨IN￨O￨- candidate￨L￨NN￨TITLE￨- vaccines￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- currently￨L￨RB￨DATE￨- in￨L￨IN￨O￨- development￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- apply￨L￨VB￨O￨- for￨L￨IN￨O￨- licensure￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- randomised￨L￨JJ￨O￨- controlled￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- trial￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A efficacy￨L￨NN￨O￨A ,￨L￨,￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- and￨L￨CC￨O￨- control￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- trial￨L￨NN￨O￨- protocol￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CIs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- computed￨L￨VBN￨O￨- as￨L￨IN￨O￨- score￨L￨NN￨O￨- CIs￨U￨NNS￨O￨- .14￨L￨CD￨NUMBER￨- These￨U￨DT￨O￨- standard￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- calculations￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- constant￨L￨JJ￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- arms￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- violated￨L￨VBN￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- declining￨L￨VBG￨O￨- .￨L￨.￨O￨- +Measured￨U￨VBN￨O￨- vaccine￨L￨NN￨O￨A efficacy￨L￨NN￨O￨A —￨L￨:￨O￨- the￨L￨DT￨O￨- median￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- in￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- non-extinct￨L￨JJ￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- case￨L￨NN￨O￨- occurred￨L￨VBD￨O￨- in￨L￨IN￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- or￨L￨CC￨O￨- intervention￨L￨NN￨O￨- arms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- otherwise￨L￨RB￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- defined￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +False-positive￨U￨JJ￨O￨- rate￨L￨NN￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- or￨L￨CC￨O￨- negative￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- effect￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- detected￨L￨VBN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- has￨L￨VBZ￨O￨- no￨L￨DT￨O￨- efficacy￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- non-extinct￨L￨JJ￨O￨- at￨L￨IN￨O￨- that￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A trial￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- arms￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individually￨L￨RB￨O￨- randomised￨L￨VBN￨O￨- controlled￨L￨JJ￨O￨- trial12￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- EVD￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- figure￨L￨NN￨O￨- 1D￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- ratio￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- circulating￨L￨VBG￨O￨A virus￨L￨NN￨O￨- types￨L￨NNS￨O￨- right￨L￨RB￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- virtually￨L￨RB￨O￨- impossible￨L￨JJ￨O￨- without￨L￨IN￨O￨- regular￨L￨JJ￨O￨- virological￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨A ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- AR￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- morbidity￨L￨NN￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- divided￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- circulating￨L￨VBG￨O￨A virus￨L￨NN￨O￨- type￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- before￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- that￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A mainly￨L￨RB￨O￨- reduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- only￨L￨RB￨O￨- slightly￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- analysing￨L￨VBG￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 2009￨L￨CD￨DATE￨- in￨L￨IN￨O￨- Oita￨U￨NNP￨LOCATION￨- City￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Japan￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- reactive￨L￨JJ￨O￨- closures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- effective￨L￨JJ￨O￨- for￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- absenteeism￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- students￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- population￨L￨NN￨O￨- was￨L￨VBD￨O￨- still￨L￨RB￨O￨- unclear￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- reactive￨L￨JJ￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A during￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 2009￨L￨CD￨DATE￨- [￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- concluding￨L￨VBG￨O￨- that￨L￨IN￨O￨- at￨L￨IN￨DURATION￨- least￨L￨JJS￨DURATION￨- 5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- are￨L￨VBP￨O￨- required￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- ideal￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- should￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- delay￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨A incidence￨L￨NN￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- students￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- and￨L￨CC￨O￨- decrease￨L￨VB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- complex￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- mood￨L￨NN￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- bipolar￨L￨JJ￨O￨- disorder￨L￨NN￨O￨A may￨L￨MD￨O￨- be￨L￨VB￨O￨- advanced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- quantitative￨L￨JJ￨O￨- analytic￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- those￨L￨DT￨O￨- developed￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- physical￨L￨JJ￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- biological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Descriptive￨U￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- bipolar￨L￨JJ￨O￨- disorder￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- reveal￨L￨VBP￨O￨- that￨L￨IN￨O￨- simple￨L￨JJ￨O￨- time-series￨L￨NNS￨O￨- approaches￨L￨NNS￨O￨- may￨L￨MD￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- robust￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- and￨L￨CC￨O￨- corroborate￨L￨VB￨O￨- clinical￨L￨JJ￨O￨- judgement￨L￨NN￨O￨- on￨L￨IN￨O￨- bipolar￨L￨JJ￨O￨- disorder￨L￨NN￨O￨- mood￨L￨NN￨O￨- stability￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- mood￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- developing￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- limit￨L￨NN￨O￨- cycle￨L￨NN￨O￨- oscillators￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- mental￨L￨JJ￨O￨- health￨L￨NN￨O￨- disorder￨L￨NN￨O￨A .￨L￨.￨O￨- +Bipolar￨U￨JJ￨O￨- disorder￨L￨NN￨O￨A is￨L￨VBZ￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- pathological￨L￨JJ￨O￨- mood￨L￨NN￨O￨- instability￨L￨NN￨O￨- including￨L￨VBG￨O￨- episodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- extreme￨L￨JJ￨O￨- low￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- depressed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- mood￨L￨NN￨O￨- and￨L￨CC￨O￨- elevated￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- manic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- mood￨L￨NN￨O￨- ,￨L￨,￨O￨- interspersed￨L￨VBN￨O￨- with￨L￨IN￨O￨- less￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- but￨L￨CC￨O￨- still￨L￨RB￨O￨- problematic￨L￨JJ￨O￨- mood￨L￨NN￨O￨- fluctuations￨L￨NNS￨O￨- or￨L￨CC￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- relative￨L￨JJ￨O￨- mood￨L￨NN￨O￨- stability￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- recent￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- mood￨L￨NN￨O￨- instabilities￨L￨NNS￨O￨- in￨L￨IN￨O￨- 23￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- highlighted￨L￨VBD￨O￨- that￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- above￨L￨IN￨O￨- and￨L￨CC￨O￨- below￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- ‘￨L￨``￨O￨- average￨L￨JJ￨O￨- ’￨L￨''￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- mood￨L￨NN￨O￨- are￨L￨VBP￨O￨- described￨L￨VBN￨O￨- differently￨L￨RB￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- DMV￨U￨NN￨ORGANIZATION￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- pilot￨L￨NN￨TITLE￨- whales￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Globicephala￨U￨FW￨O￨- spp.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- southwestern￨L￨JJ￨O￨- Pacific￨U￨NNP￨LOCATION￨- Ocean￨U￨NNP￨LOCATION￨- to￨L￨TO￨O￨- recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- among￨L￨IN￨O￨- dolphins￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Mediterranean￨U￨NNP￨LOCATION￨- Sea￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Atlantic￨U￨NNP￨LOCATION￨- Ocean￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Gulf￨U￨NNP￨LOCATION￨- of￨L￨IN￨LOCATION￨- Mexico￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- GoM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- these￨L￨DT￨O￨- different￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- elusive￨L￨JJ￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- important￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- for￨L￨IN￨O￨- DMV￨U￨NN￨ORGANIZATION￨- spread￨L￨NN￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- still￨L￨RB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- travel￨L￨VB￨O￨- while￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨A population￨L￨NN￨O￨A .￨L￨.￨O￨- +Another￨U￨DT￨O￨- important￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- betweenness￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- calculated￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- times￨L￨NNS￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- lies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨A paths￨L￨NNS￨O￨A over￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- paths￨L￨NNS￨O￨- .￨L￨.￨O￨- +Degree￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨A ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- firstly￨L￨RB￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Freeman￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A for￨L￨IN￨O￨- spreading￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- significance￨L￨NN￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- rumor￨L￨NN￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- edges￨L￨NNS￨O￨A are￨L￨VBP￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- attributes￨L￨NNS￨O￨- or￨L￨CC￨O￨- weights￨L￨NNS￨O￨- ,￨L￨,￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- simply￨L￨RB￨O￨- either￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- or￨L￨CC￨O￨- absent￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +And￨U￨CC￨O￨- then￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- random-walk-based￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A called￨L￨VBN￨O￨- LeaderRank￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- identify￨L￨VB￨O￨- leaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- better￨L￨RBR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- PageRank￨U￨NN￨O￨- algorithm￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- divide￨L￨VB￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- 0.6475￨L￨CD￨NUMBER￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- cases￨L￨NNS￨O￨- with￨L￨IN￨O￨- low-level￨L￨JJ￨O￨- and￨L￨CC￨O￨- moderate￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- New￨U￨NNP￨ORGANIZATION￨- South￨U￨NNP￨ORGANIZATION￨- Wales￨U￨NNP￨ORGANIZATION￨- Population￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Survey￨U￨NN￨O￨- which￨L￨WDT￨O￨- collected￨L￨VBD￨O￨- all-age￨L￨JJ￨O￨- community-level￨L￨JJ￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Four￨U￨CD￨NUMBER￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- were￨L￨VBD￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- asymptomatic￨L￨JJ￨O￨- ;￨L￨:￨O￨- low-level￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨A ;￨L￨:￨O￨- moderate￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- hospitalisation￨L￨NN￨O￨- required￨L￨VBN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- subscript￨L￨JJ￨O￨- letters￨L￨NNS￨O￨- ‘￨L￨``￨O￨- A￨U￨DT￨O￨- ’￨L￨''￨O￨- ,￨L￨,￨O￨- ‘￨L￨``￨O￨- L’￨U￨NNP￨O￨- ,￨L￨,￨O￨- ‘￨L￨``￨O￨- M￨U￨NN￨O￨- ’￨L￨''￨O￨- and￨L￨CC￨O￨- ‘￨L￨``￨O￨- H￨U￨NN￨O￨- ’￨L￨''￨O￨- respectively￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relative￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- effective￨L￨JJ￨O￨- contact￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- parameters￨L￨NNS￨O￨- μ￨L￨NN￨O￨- were￨L￨VBD￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- proportions￨L￨NNS￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- asymptomatic￨L￨JJ￨O￨- class￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- A￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1.0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨- decreasing￨L￨VBG￨O￨- as￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨A increased￨L￨VBD￨O￨- .￨L￨.￨O￨- +*￨L￨SYM￨O￨- Subscripts￨U￨NNPS￨O￨- denote￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- categories￨L￨NNS￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- low-level￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- L￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- moderate￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- M￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- hospitalised￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- H￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proportional￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨A compartments￨L￨NNS￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- published￨L￨VBN￨O￨- observational￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pdm09￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- first￨L￨JJ￨ORDINAL￨- divide￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- great￨L￨JJ￨O￨- many￨L￨JJ￨O￨- super￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- k￨L￨NN￨O￨- spreaders￨L￨NNS￨O￨A are￨L￨VBP￨O￨- chosen￨L￨VBN￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- super￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- centrality￨L￨NN￨O￨- index￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- one￨L￨CD￨NUMBER￨- chooses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- top￨L￨JJ￨O￨- k￨L￨NN￨O￨- influential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- as￨L￨IN￨O￨- spreaders￨L￨NNS￨O￨A according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- centrality￨L￨NN￨O￨- index￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- transfer￨L￨NN￨O￨- probability￨L￨NN￨O￨- between￨L￨IN￨O￨- any￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- k-medoid￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- benchmark￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- all￨L￨DT￨O￨- pathogens￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- environmental￨L￨JJ￨O￨A variation￨L￨NN￨O￨- indirectly￨L￨RB￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- or￨L￨CC￨O￨- during￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- opportunist￨L￨NN￨O￨- pathogens￨L￨NNS￨O￨- can￨L￨MD￨O￨- spend￨L￨VB￨O￨- several￨L￨JJ￨O￨- generations￨L￨NNS￨O￨- between￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- events￨L￨NNS￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- outside￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- environment￨L￨NN￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- such￨L￨JJ￨O￨- their￨L￨PRP$￨O￨- growth￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- directly￨L￨RB￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- various￨L￨JJ￨O￨- abiotic￨L￨JJ￨O￨- and￨L￨CC￨O￨- biotic￨L￨JJ￨O￨- pressures￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- generality￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- inspect￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- targets￨L￨NNS￨O￨- for￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨A variation￨L￨NN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- pathogen￨L￨NN￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- outside￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- infective￨L￨JJ￨O￨- dose￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨A fluctuations￨L￨NNS￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- either￨L￨CC￨O￨- infection-free￨L￨RB￨O￨- ,￨L￨,￨O￨- persistent￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- can￨L￨MD￨O￨- arise￨L￨VB￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- ask￨L￨VB￨O￨- how￨L￨WRB￨O￨- environmental￨L￨JJ￨O￨A variation￨L￨NN￨O￨- translates￨L￨VBZ￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- free-living￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- densities￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- former￨L￨JJ￨O￨- reflects￨L￨VBZ￨O￨- purely￨L￨RB￨O￨- environmental￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- proliferation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- interaction￨L￨NN￨O￨- parameter￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- virulence￨L￨NN￨O￨- .￨L￨.￨O￨- +pertussis￨L￨NN￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- to￨L￨TO￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- longer￨L￨JJR￨O￨- periodic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- line￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- B.￨U￨NNP￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- our￨L￨PRP$￨O￨- findings￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- regions￨L￨NNS￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- both￨L￨CC￨O￨- low￨L￨JJ￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- decreased￨L￨VBD￨O￨- in￨L￨IN￨O￨- periodicity￨L￨NN￨O￨- following￨L￨VBG￨O￨- immunization￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- annual￨L￨JJ￨SET￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- thirteen￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- Chile￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- 1952￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spatial-temporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- Pertussis￨U￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 1995￨L￨CD￨DATE￨- was￨L￨VBD￨O￨- characterized￨L￨VBN￨O￨A by￨L￨IN￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- 4￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- cycle￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DATE￨- two￨L￨CD￨DATE￨- decades￨L￨NNS￨DATE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1990￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resurgence￨L￨NN￨O￨- without￨L￨IN￨O￨- significant￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- resurging￨L￨VBG￨O￨- in￨L￨IN￨O￨- several￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- different￨L￨JJ￨O￨- R0￨U￨NN￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- classical￨L￨JJ￨O￨- swine￨L￨NNS￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CSFV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- diagnostic￨L￨JJ￨O￨- tool￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- genome￨L￨NN￨O￨- or￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- virus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- marker￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- viraemia￨L￨NN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- oropharyngeal￨L￨NN￨O￨- or￨L￨CC￨O￨- rectal￨L￨JJ￨O￨- fluids￨L￨NNS￨O￨- ,￨L￨,￨O￨- clinical￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- newly￨L￨RB￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- during￨L￨IN￨O￨- its￨L￨PRP$￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- quantitative￨L￨JJ￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- very￨L￨RB￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨A impact￨L￨NN￨O￨A of￨L￨IN￨O￨- different￨L￨JJ￨O￨- components￨L￨NNS￨O￨- in￨L￨IN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- moment￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- pigs￨L￨NNS￨O￨A were￨L￨VBD￨O￨- lacking￨L￨VBG￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- were￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- assumed￨L￨VBN￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- L￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- 3￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- model￨L￨NN￨TITLE￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- model￨L￨NN￨TITLE￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- 5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- model￨L￨NN￨TITLE￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- allow￨L￨VB￨O￨- T￨U￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- because￨L￨IN￨O￨- animals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- euthanized￨L￨VBN￨O￨- for￨L￨IN￨O￨- welfare￨L￨NN￨O￨- reasons￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- censored￨L￨VBN￨O￨- values￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- ±￨L￨SYM￨O￨- standard￨L￨JJ￨O￨- deviation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- s.d.￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- 7￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- ±￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- ±￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- 3￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- ±￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ·￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- days￨L￨NNS￨DURATION￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- inoculated￨L￨VBN￨O￨- ,￨L￨,￨O￨- within-pen￨L￨NN￨O￨- and￨L￨CC￨O￨- between-pen￨L￨JJ￨O￨- contact￨L￨NN￨O￨- pigs￨L￨NNS￨O￨A ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- within-pen￨L￨NN￨O￨- and￨L￨CC￨O￨- between-pen￨L￨JJ￨O￨- contact￨L￨NN￨O￨- pigs￨L￨NNS￨O￨A generally￨L￨RB￨O￨- started￨L￨VBD￨O￨- to￨L￨TO￨O￨- excrete￨L￨VB￨O￨- ASFV￨U￨NN￨O￨- genome￨L￨NN￨O￨- through￨L￨IN￨O￨- nasal￨L￨JJ￨O￨- and￨L￨CC￨O￨- oral￨L￨JJ￨O￨- fluid￨L￨NN￨O￨- samples￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- showing￨L￨VBG￨O￨- viraemia￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- established￨L￨VBN￨O￨- a￨L￨DT￨O￨- live￨L￨JJ￨O￨- cell￨L￨NN￨O￨A imaging￨L￨NN￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- simultaneously￨L￨RB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- DENV￨U￨NN￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- IFN￨U￨NN￨ORGANIZATION￨- response￨L￨NN￨O￨- and￨L￨CC￨O￨- quantified￨L￨VBD￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- processes￨L￨NNS￨O￨- by￨L￨IN￨O￨- data-driven￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- key￨L￨JJ￨O￨- topics￨L￨NNS￨O￨- for￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- research￨L￨NN￨O￨- that￨L￨WDT￨O￨- will￨L￨MD￨O￨- unify￨L￨VB￨O￨- recent￨L￨JJ￨O￨- developments￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- powerful￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- immunological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .2￨L￨NN￨NUMBER￨- Multiple-strain￨U￨JJ￨O￨- models2￨L￨NN￨O￨- .1￨L￨NN￨NUMBER￨- InfluenzaMathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- long￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨A through￨L￨IN￨O￨- cross-immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- recent￨L￨JJ￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- includes￨L￨VBZ￨O￨- extending￨L￨VBG￨O￨- the￨L￨DT￨O￨- flexibility￨L￨NN￨O￨- and￨L￨CC￨O￨- biological￨L￨JJ￨O￨- realism￨L￨NN￨O￨- of￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- interface￨L￨NN￨O￨- with￨L￨IN￨O￨- data.KeywordsTransmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- Evolution￨U￨NN￨O￨- Cross-immunity￨U￨NN￨O￨- Multi-strain￨U￨JJ￨O￨- pathogens￨L￨NNS￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- Mathematics￨U￨NNP￨O￨- Subject￨U￨NNP￨O￨- Classification37N25￨U￨NNP￨O￨- Dynamical￨U￨NNP￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- biology￨L￨NN￨O￨- 92B￨L￨NN￨O￨- Mathematical￨U￨JJ￨O￨- Biology￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionMany￨U￨NNP￨O￨- human￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- categorized￨L￨VBN￨O￨- into￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- strains￨L￨NNS￨O￨A ,￨L￨,￨O￨- each￨L￨DT￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- its￨L￨PRP$￨O￨- antigenic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Examining￨U￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- interaction￨L￨NN￨O￨A on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- posed￨L￨VBN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- theoretically￨L￨RB￨O￨- and￨L￨CC￨O￨- biologically.Population￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- generate￨L￨VB￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- drive￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- test￨L￨NN￨O￨- new￨L￨JJ￨O￨- hypotheses￨L￨NNS￨O￨- about￨L￨IN￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- strains￨L￨NNS￨O￨A that￨L￨WDT￨O￨- occurs￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- cross-immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨- must￨L￨MD￨O￨- balance￨L￨VB￨O￨- biological￨L￨JJ￨O￨- realism￨L￨NN￨O￨- with￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- tractability￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- higher-order￨L￨JJ￨O￨- structure￨L￨NN￨O￨- realised￨L￨VBD￨O￨- either￨L￨CC￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- loops￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- or￨L￨CC￨O￨- by￨L￨IN￨O￨- generating￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- subgraphs￨L￨NNS￨O￨- but￨L￨CC￨O￨- with￨L￨IN￨O￨- identical￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- clustering￨L￨NN￨O￨A ,￨L￨,￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- non-negligible￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics.KeywordsNetwork￨L￨NN￨MISC￨- Subgraph￨U￨NNP￨MISC￨- Motif￨U￨NNP￨MISC￨- High-order￨U￨JJR￨MISC￨- structure￨L￨NN￨O￨- Epidemic￨U￨JJ￨O￨- Electronic￨U￨JJ￨O￨- supplementary￨L￨JJ￨O￨- materialThe￨L￨NN￨O￨- online￨L￨NN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- doi￨L￨FW￨O￨- :￨L￨:￨O￨- 10.1007￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- s00285-015-0884-1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- contains￨L￨VBZ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- authorized￨L￨VBN￨O￨- users.Mathematics￨L￨NNS￨O￨- Subject￨U￨JJ￨O￨- Classification05C82￨U￨NN￨O￨- 37N25￨L￨CD￨NUMBER￨- 60J28￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionNetwork￨U￨NNP￨ORGANIZATION￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- revolutionised￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- way￨L￨NN￨O￨- of￨L￨IN￨O￨- thinking￨L￨VBG￨O￨- about￨L￨IN￨O￨- complex￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- processing￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- brain￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- formation￨L￨NN￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- clustering￨L￨NN￨O￨A of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- or￨L￨CC￨O￨- transitivity￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- propensity￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- neighbour￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- connected￨L￨VBN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- pervasive￨L￨JJ￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- continues￨L￨VBZ￨O￨- to￨L￨TO￨O￨- pose￨L￨VB￨O￨- many￨L￨JJ￨O￨- significant￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- viewpoint￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- generation￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- more￨L￨RBR￨O￨- so￨L￨RB￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- well-performing￨L￨JJ￨O￨- approximate￨L￨JJ￨O￨- models.To￨L￨NN￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- either￨L￨RB￨O￨- use￨L￨VB￨O￨- empirical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- or￨L￨CC￨O￨- synthetic￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- generated￨L￨VBN￨O￨- from￨L￨IN￨O￨- theoretical￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- tunable￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- looking￨L￨VBG￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- higher-order￨L￨JJ￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- possible￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- correlations￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- between￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- approach￨L￨NN￨O￨- offers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- unattainable￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- arrangement￨L￨NN￨O￨- of￨L￨IN￨O￨- subgraphs￨L￨NNS￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- classical￨L￨JJ￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- variance￨L￨NN￨O￨- and￨L￨CC￨O￨- clustering￨L￨NN￨O￨A .￨L￨.￨O￨- +By￨U￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- worm￨L￨NN￨O￨A propagation￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- Anderson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- May￨U￨NNP￨DATE￨- have￨L￨VBP￨O￨- thoroughly￨L￨RB￨O￨- explained￨L￨VBN￨O￨- the￨L￨DT￨O￨- behavioural￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- parasites￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Susceptible-Exposed-Infectious-Recovered-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- presented￨L￨VBN￨O￨- by￨L￨IN￨O￨- Mishra￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Saina￨U￨NNP￨PERSON￨- have￨L￨VBP￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporary￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- worm￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Worm￨U￨NN￨O￨- propagation￨L￨NN￨O￨A models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- propagation￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- appropriate￨L￨JJ￨O￨- defence￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- against￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- worm￨L￨NN￨O￨A propagation￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- worm￨L￨NN￨O￨- ’s￨L￨POS￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- defensive￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- papers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- noted￨L￨VBN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- phylogenies￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- history￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reconstructed￨L￨VBN￨O￨- by￨L￨IN￨O￨- augmenting￨L￨VBG￨O￨- the￨L￨DT￨O￨- internal￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- tree￨L￨NN￨O￨A for￨L￨IN￨O￨- samples￨L￨NNS￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- lineage￨L￨NN￨O￨- was￨L￨VBD￨O￨- located￨L￨JJ￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- linked￨L￨VBD￨O￨- up￨L￨RP￨O￨- individual￨L￨JJ￨O￨- within-host￨L￨NN￨O￨- phylogenies￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- tree￨L￨NN￨O￨A structure￨L￨NN￨O￨- to￨L￨TO￨O￨- build￨L￨VB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- tree￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- lineages￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- entire￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- prospect￨L￨NN￨O￨- of￨L￨IN￨O￨- acquiring￨L￨VBG￨O￨- complete￨L￨JJ￨O￨- or￨L￨CC￨O￨- nearly￨L￨RB￨O￨- complete￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- datasets￨L￨NNS￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- naturally￨L￨RB￨O￨- suggests￨L￨VBZ￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- that￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- tree￨L￨NN￨O￨A ,￨L￨,￨O￨- determining￨L￨VBG￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- or￨L￨CC￨O￨- premises￨L￨NN￨O￨- infected￨L￨JJ￨O￨- which￨L￨WDT￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- treat￨L￨NN￨O￨- mutation￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- none￨L￨NN￨O￨- occurring￨L￨VBG￨O￨- within-host￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Morelli￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- extended￨L￨VBN￨O￨- by￨L￨IN￨O￨- Mollentze￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- within-host￨L￨NN￨O￨- mutation￨L￨NN￨O￨- ,￨L￨,￨O￨- still￨L￨RB￨O￨- only￨L￨RB￨O￨- allows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- lineage￨L￨NN￨O￨A to￨L￨TO￨O￨- exist￨L￨VB￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A development￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- measured￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- prevented￨L￨VBD￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- over￨L￨IN￨O￨- up￨L￨RB￨DURATION￨- to￨L￨TO￨DURATION￨- 30￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- baseline￨L￨NN￨O￨- .￨L￨.￨O￨- +Compartmental￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- heterosexual￨L￨JJ￨O￨- and￨L￨CC￨O￨- MSM￨U￨NN￨ORGANIZATION￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A development￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- reduced￨L￨VBN￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A against￨L￨IN￨O￨- other￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- –￨L￨:￨O￨- 40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- protection￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- regions￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- dominant￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- subtypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- clade￨L￨NN￨O￨- C￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- in￨L￨IN￨O￨- SF￨U￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- clade￨L￨NN￨O￨- B￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- in￨L￨IN￨O￨- SA￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- clade￨L￨NN￨O￨- specific￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- men-who-have-sex-with-men￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- MSM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- San￨U￨NNP￨CITY￨- Francisco￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- SF￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- South￨U￨NNP￨COUNTRY￨- Africa￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- SA￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- modeled￨L￨VBD￨O￨- a￨L￨DT￨O￨- clade-specific￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- effective￨L￨JJ￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- predominant￨L￨JJ￨O￨- circulating￨L￨VBG￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- we￨L￨PRP￨O￨- analyzed￨L￨VBD￨O￨- :￨L￨:￨O￨- clade￨L￨NN￨O￨- C￨U￨NN￨O￨- for￨L￨IN￨O￨- SA￨U￨NNP￨O￨- and￨L￨CC￨O￨- clade￨L￨NN￨O￨- B￨U￨NN￨O￨- for￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- SF￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- evidence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- schools￨L￨NNS￨O￨A and￨L￨CC￨O￨- other￨L￨JJ￨O￨- gathering￨L￨NN￨O￨- places￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- airborne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- only￨L￨RB￨O￨- recently￨L￨RB￨DATE￨- that￨L￨IN￨O￨- Chao￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- dengue￨L￨JJ￨O￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- schools￨L￨NNS￨O￨- plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- rise￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- seroconversion￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- formal￨L￨JJ￨O￨- schooling￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- attends￨L￨VBZ￨O￨- school￨L￨NN￨O￨A 5￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- daily￨L￨JJ￨SET￨- 5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- a￨L￨DT￨DURATION￨- week￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- increases￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- 30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- average￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- duplicates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Appendix￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Evidence￨U￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- immediately￨L￨RB￨O￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- school￨L￨NN￨O￨A year￨L￨NN￨DURATION￨- is￨L￨VBZ￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- students￨L￨NNS￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- México￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- considering￨L￨VBG￨O￨- high￨L￨JJ￨O￨- school￨L￨NN￨O￨A or￨L￨CC￨O￨- higher￨L￨JJR￨O￨- educational￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- .￨L￨.￨O￨- +Like￨U￨IN￨O￨- several￨L￨JJ￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- distinguish￨L￨VBP￨O￨- between￨L￨IN￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- infector￨L￨NN￨O￨- 's￨L￨POS￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- looking￨L￨VBG￨O￨- forward￨L￨RB￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- when￨L￨WRB￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- occur￨L￨VBP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- infectee￨L￨NN￨O￨- 's￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- looking￨L￨VBG￨O￨- backward￨L￨RB￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infector￨L￨NN￨O￨- was￨L￨VBD￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- —￨L￨:￨O￨- we￨L￨PRP￨O￨- call￨L￨VBP￨O￨- these￨L￨DT￨O￨- forward￨L￨RB￨O￨- and￨L￨CC￨O￨- backward￨L￨RB￨O￨- generation￨L￨NN￨O￨A intervals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- figure￨L￨NN￨O￨- 1c￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Nishiura￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- explained￨L￨VBD￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- compartmental￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- observed￨L￨VBN￨O￨- mean￨L￨NN￨O￨- generation￨L￨NN￨O￨A intervals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- change￨L￨VB￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- bias￨L￨NN￨O￨- this￨L￨DT￨O￨- can￨L￨MD￨O￨- introduce￨L￨VB￨O￨- in￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- f￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- over￨L￨IN￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- forward￨L￨RB￨O￨- generation￨L￨NN￨O￨A intervals￨L￨NNS￨O￨- for￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- s￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmitting￨L￨VBG￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- s￨L￨NNS￨O￨- +￨L￨CC￨O￨- τ￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- an￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- generation￨L￨NN￨O￨A interval￨L￨NN￨O￨- whose￨L￨WP$￨O￨- distribution￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- after￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- change￨L￨VB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- progresses￨L￨VBZ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- are￨L￨VBP￨O￨- linked￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨A interval￨L￨NN￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- interval￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- when￨L￨WRB￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infector￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infector￨L￨NN￨O￨- was￨L￨VBD￨O￨- infected￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- small￨L￨JJ￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- sick￨L￨JJ￨O￨A people￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- studied￨L￨VBN￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- big￨L￨JJ￨O￨- enough￨L￨RB￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sick￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- call￨L￨VB￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- into￨L￨IN￨O￨- question￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- SEIL￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- sick￨L￨JJ￨O￨A compartment￨L￨NN￨O￨- of￨L￨IN￨O￨- 103￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨A into￨L￨IN￨O￨- different￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- specific￨L￨JJ￨O￨- fluxes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- fixed￨L￨VBN￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- published￨L￨VBN￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- fundamentally￨L￨RB￨O￨A conceived￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- top-down￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- with￨L￨IN￨O￨- regards￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- SEIR-type￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- extrapolated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- individual-level￨L￨NN￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- Goltsev￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 14￨L￨CD￨NUMBER￨- study￨L￨NN￨O￨- the￨L￨DT￨O￨- localization￨L￨NN￨O￨- in￨L￨IN￨O￨- power-law￨L￨NN￨O￨- distributed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- scaling￨L￨NN￨O￨- as￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- q￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ~￨L￨SYM￨O￨- q￨L￨SYM￨O￨- −￨L￨SYM￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- leading￨L￨VBG￨O￨- eigenvalue￨L￨NN￨O￨- Λ1￨U￨NN￨O￨- is￨L￨VBZ￨O￨- essentially￨L￨RB￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- between￨L￨IN￨O￨- 〈￨L￨CD￨NUMBER￨- q2￨L￨NN￨O￨- 〉￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 〈￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- 〉￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- qmax￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨A degree￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network911￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- localization￨L￨NN￨O￨A properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- PEV￨U￨NN￨O￨- for￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- power-law￨L￨NN￨O￨- distributed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- picture￨L￨NN￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- than￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- believed￨L￨VBN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- concept￨L￨NN￨O￨- is￨L￨VBZ￨O￨- mathematically￨L￨RB￨O￨- encoded￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvector￨L￨NN￨O￨- centrality4￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- component￨L￨NN￨O￨- f￨L￨FW￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- principal￨L￨JJ￨TITLE￨- eigenvector￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PEV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- f￨L￨SYM￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨A eigenvalue￨L￨NN￨O￨- Λ1￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- A￨U￨NN￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- point￨L￨VBP￨O￨- out￨L￨RP￨O￨- a￨L￨DT￨O￨- weakness￨L￨NN￨O￨- of￨L￨IN￨O￨- EC￨U￨NNP￨ORGANIZATION￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- centrality￨L￨NN￨O￨- for￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- power-law￨L￨NN￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 5/2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exceedingly￨L￨RB￨O￨- large￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨A hub16￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- illustrated￨L￨VBD￨O￨- through￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- fitted￨L￨VBN￨O￨A on￨L￨IN￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- substantial￨L￨JJ￨O￨- underestimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- and￨L￨CC￨O￨- forecasts￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aimed￨L￨VBD￨O￨A to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- overcome￨L￨VB￨O￨- previously￨L￨RB￨DATE￨- identified￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- limitations￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- not-used￨L￨JJ￨O￨- district￨L￨NN￨O￨- level￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- homogenous￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- across￨L￨IN￨O￨- districts￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ,￨L￨,￨O￨- mainly￨L￨RB￨O￨- deterministic￨L￨JJ￨O￨- ,￨L￨,￨O￨- SEIR￨U￨NN￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Exposed￨U￨VBN￨O￨- ,￨L￨,￨O￨- Infected￨U￨JJ￨O￨- ,￨L￨,￨O￨- Recovered￨U￨VBN￨O￨- compartments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- published￨L￨VBN￨O￨- that￨L￨IN￨O￨- aimed￨L￨VBN￨O￨A to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- especially￨L￨RB￨O￨- the￨L￨DT￨O￨- ones￨L￨NNS￨O￨- early￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨A on￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cumulative￨L￨JJ￨O￨- national￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- two-stage￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- publicly￨L￨RB￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- might￨L￨MD￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- for￨L￨IN￨O￨- operational￨L￨JJ￨O￨A decisions￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- effort￨L￨NN￨O￨- of￨L￨IN￨O￨- 4￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- lost￨L￨VBD￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨DATE￨- may￨L￨MD￨DATE￨- correspond￨L￨VB￨O￨- to￨L￨TO￨O￨- four￨L￨CD￨NUMBER￨- closures￨L￨NNS￨O￨A of￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- each￨L￨DT￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- closures￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- each￨L￨DT￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- closure￨L￨NN￨O￨- lasting￨L￨JJ￨O￨- four￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- ;￨L￨:￨O￨- of￨L￨IN￨O￨- course￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- closures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- allowed￨L￨VBN￨O￨- only￨L￨RB￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- period￨L￨NN￨O￨- established￨L￨VBN￨O￨- by￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 180￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- see￨L￨VBP￨O￨- Methods￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- large￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- trigger￨L￨NN￨O￨- and￨L￨CC￨O￨- large￨L￨JJ￨O￨- timeout￨L￨NN￨O￨- between￨L￨IN￨O￨- consecutive￨L￨JJ￨O￨- closures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- applied￨L￨VBN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- school/class￨L￨NN￨O￨- may￨L￨MD￨O￨- close￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- shorter￨L￨JJR￨O￨- total￨L￨JJ￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- presents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- closure￨L￨NN￨O￨A strategy￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- delay￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- weeks￨L￨NNS￨DURATION￨- lost￨L￨VBD￨O￨- per￨L￨IN￨O￨- student￨L￨NN￨TITLE￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- correspondence￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- weeks￨L￨NNS￨DURATION￨- lost￨L￨VBD￨O￨- spanning￨L￨VBG￨O￨- from￨L￨IN￨O￨- around￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- considered￨L￨VBN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- implementations￨L￨NNS￨O￨- yield￨L￨VBP￨O￨- large￨L￨JJ￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- reduction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 45￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- Fig￨U￨NN￨O￨- 1a￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- peak￨L￨NN￨O￨- incidence￨L￨NN￨O￨- reduction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- -10-80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- Fig￨U￨NN￨O￨- 1b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- peak￨L￨JJ￨O￨- delay￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- -2-18￨L￨CD￨NUMBER￨- weeks￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- Fig￨U￨NN￨O￨- 1c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- no￨L￨DT￨O￨- intervention￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- that￨L￨IN￨O￨- different￨L￨JJ￨O￨- closure￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- reactive￨L￨JJ￨O￨- ,￨L￨,￨O￨- gradual￨L￨JJ￨O￨- ,￨L￨,￨O￨- county￨L￨NN￨O￨- and￨L￨CC￨O￨- national￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- would￨L￨MD￨O￨- have￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- Kingdom￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- extensive￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- closures￨L￨NNS￨O￨A ,￨L￨,￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- closure￨L￨NN￨O￨- event￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- timeout￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- consecutive￨L￨JJ￨O￨- closures￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- absent￨L￨JJ￨O￨- students￨L￨NNS￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- for￨L￨IN￨O￨- triggering￨L￨VBG￨O￨- closure￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨ORGANIZATION￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- provide￨L￨VB￨O￨- specific￨L￨JJ￨O￨- recommendations￨L￨NNS￨O￨- and￨L￨CC￨O￨- left￨L￨VBD￨O￨- any￨L￨DT￨O￨- decision￨L￨NN￨O￨- on￨L￨IN￨O￨- closing￨L￨VBG￨O￨- schools￨L￨NNS￨O￨- to￨L￨TO￨O￨- national￨L￨JJ￨O￨- or￨L￨CC￨O￨- local￨L￨JJ￨O￨- authorities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- policies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- either￨L￨CC￨O￨- favorable￨L￨JJ￨O￨- or￨L￨CC￨O￨- against￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- implementations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- measure￨L￨NN￨O￨- was￨L￨VBD￨O￨- applied￨L￨VBN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Japan￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Russia￨U￨NNP￨COUNTRY￨- also￨L￨RB￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- tradition￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨A policies￨L￨NNS￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- typically￨L￨RB￨O￨- adopt￨L￨VB￨O￨- a￨L￨DT￨O￨- gradual￨L￨JJ￨O￨- closure￨L￨NN￨O￨- strategy￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- affected￨L￨VBN￨O￨- classes￨L￨NNS￨O￨- close￨L￨RB￨O￨- first￨L￨RB￨ORDINAL￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- grades￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- finally￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- school￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- well￨L￨RB￨O￨- studied￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infectious-Recovery￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- compartment￨L￨NN￨O￨- S￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- force￨L￨NN￨O￨- stopping￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- outbreak￨L￨NN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨A period￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- time-dependent￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨A period￨L￨NN￨O￨A τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- onset￨L￨NN￨O￨- to￨L￨TO￨O￨- hospitalization￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- defines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- provide￨L￨VBP￨O￨- predictions￨L￨NNS￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨A different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- time￨L￨NN￨O￨- periods￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- calculate￨L￨VBP￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A numbers￨L￨NNS￨O￨A R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Liberia￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- Ebola￨U￨NNP￨MISC￨- data￨L￨NNS￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- NBS-LRR-mediated￨U￨JJ￨MISC￨- resistance￨L￨NN￨O￨- triggered￨L￨VBN￨O￨- by￨L￨IN￨O￨- aphids￨L￨NNS￨O￨- :￨L￨:￨O￨- viruses￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- adapt￨L￨VB￨O￨A ;￨L￨:￨O￨- aphids￨L￨NNS￨O￨- adapt￨L￨VBP￨O￨- via￨L￨IN￨O￨- different￨L￨JJ￨O￨- mechanismsNathalie￨L￨NN￨O￨- Boissot1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Sophie￨U￨NNP￨PERSON￨- Thomas1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Véronique￨U￨NNP￨O￨- Chovelon1￨U￨NN￨O￨- and￨L￨CC￨O￨- Hervé￨U￨NN￨O￨- Lecoq2BMC￨U￨NN￨O￨- Plant￨U￨NN￨O￨- BiologyBMC￨U￨NN￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 16:25￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Aphids￨U￨NNPS￨O￨- are￨L￨VBP￨O￨- serious￨L￨JJ￨O￨- pest￨L￨NN￨O￨- on￨L￨IN￨O￨- crops￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- melon￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- gene￨L￨NN￨O￨A that￨L￨WDT￨O￨- confers￨L￨VBZ￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- aphids￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- deployed￨L￨VBN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- melon-producing￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- aphid￨L￨NN￨O￨- colony￨L￨NN￨O￨- development￨L￨NN￨O￨- on￨L￨IN￨O￨- Vat-carrying￨U￨JJ￨O￨- plants￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- agrosystems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- characterized￨L￨VBD￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- aphid￨L￨NN￨O￨- and￨L￨CC￨O￨- virus￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- aphid￨L￨NN￨O￨- diversity￨L￨NN￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- aphids￨L￨NNS￨O￨- and￨L￨CC￨O￨- viruses￨L￨NNS￨O￨- may￨L￨MD￨O￨- adapt￨L￨VB￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- Vat￨U￨NN￨O￨- gene￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Vat￨U￨NN￨O￨- gene￨L￨NN￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- NBS-LRR￨U￨NN￨O￨- gene￨L￨NN￨O￨- that￨L￨WDT￨O￨- confers￨L￨VBZ￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- aphid￨L￨NN￨O￨- species￨L￨NNS￨O￨- Aphis￨U￨NNP￨O￨- gossypii￨L￨NNS￨O￨- and￨L￨CC￨O￨- exhibits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- unusual￨L￨JJ￨O￨- characteristic￨L￨NN￨O￨- of￨L￨IN￨O￨- also￨L￨RB￨O￨- conferring￨L￨VBG￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- non-persistently￨L￨JJ￨O￨- transmitted￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- inoculated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- aphid￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- research￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- expand￨L￨VB￨O￨- their￨L￨PRP$￨O￨- application￨L￨NN￨O￨- areas￨L￨NNS￨O￨- to￨L￨TO￨O￨- topic￨L￨NN￨O￨- discussion￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- web￨L￨NN￨O￨A ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- social￨L￨JJ￨O￨- media￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- web￨L￨NN￨O￨- forums.KeywordsInformation￨L￨NN￨O￨- diffusionEpidemic￨L￨JJ￨O￨- modelContagionWeb￨L￨NN￨O￨- forumSocial￨L￨JJ￨O￨- media￨L￨NNS￨O￨- BackgroundSocial￨U￨NNP￨O￨- media￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- blogs￨L￨NNS￨O￨- ,￨L￨,￨O￨- discussion￨L￨NN￨O￨- forums￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- networking￨L￨NN￨O￨- sites￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- new￨L￨JJ￨O￨- channels￨L￨NNS￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- share￨L￨VB￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- express￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- opinions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- topic￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- in￨L￨IN￨O￨- web￨L￨NN￨O￨A forums￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- frequently￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- previous￨L￨JJ￨O￨- research￨L￨NN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- both￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- knowledge￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- social￨L￨JJ￨O￨- media￨L￨NNS￨O￨- ,￨L￨,￨O￨- web￨L￨NN￨O￨A forums￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- people￨L￨NNS￨O￨- in￨L￨IN￨O￨- online￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- disseminate￨L￨VBP￨O￨- and￨L￨CC￨O￨- receive￨L￨VBP￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- environment￨L￨NN￨O￨- for￨L￨IN￨O￨- examining￨L￨VBG￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Epidemic￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- in￨L￨IN￨O￨- web￨L￨NN￨O￨A forums￨L￨NNS￨O￨- :￨L￨:￨O￨- experiments￨L￨NNS￨O￨- in￨L￨IN￨O￨- marketing￨L￨NN￨O￨- exchange￨L￨NN￨O￨- and￨L￨CC￨O￨- political￨L￨JJ￨O￨- dialogJiyoung￨L￨NN￨O￨- Woo1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- and￨L￨CC￨O￨- Hsinchun￨U￨NN￨MISC￨- Chen2￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 5:66￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Woo￨U￨NNP￨O￨- and￨L￨CC￨O￨- Chen￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- fitting￨L￨JJ￨O￨- results￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- plausible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- topic￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- perform￨L￨VBP￨O￨- experiments￨L￨NNS￨O￨- on￨L￨IN￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- K-truss￨U￨NN￨MISC￨- subgraph￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- show￨L￨VB￨O￨- better￨L￨JJR￨O￨- spreading￨L￨NN￨O￨- behavior￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- –￨L￨:￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- previously￨L￨RB￨DATE￨- used￨L￨VBN￨O￨- importance￨L￨NN￨O￨- criteria￨L￨NNS￨O￨- –￨L￨:￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- faster￨L￨JJR￨O￨- and￨L￨CC￨O￨- wider￨L￨JJR￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- K-truss￨U￨NN￨MISC￨- subgraph￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- Kitsak￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 22￨L￨CD￨NUMBER￨- argued￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- significant￨L￨JJ￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- linked￨L￨VBN￨O￨- neighbours￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- coreness￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- 's￨L￨POS￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- than￨L￨IN￨O￨- degree￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- coreness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A is￨L￨VBZ￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- k-core￨L￨NN￨O￨- decomposition23￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- larger￨L￨JJR￨O￨- coreness￨L￨NN￨O￨- value￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- centrally￨L￨RB￨O￨- located￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- H-index￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- value￨L￨NN￨O￨- h￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- h￨L￨NN￨O￨- neighbours￨L￨NNS￨O￨A of￨L￨IN￨O￨- degree￨L￨NN￨O￨- no￨L￨RB￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- h.￨L￨NN￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- H-index￨U￨NN￨MISC￨- concept￨L￨NN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- how￨L￨WRB￨O￨- important￨L￨JJ￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- network30￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- finding￨L￨NN￨O￨- was￨L￨VBD￨O￨- in￨L￨IN￨O￨- sharp￨L￨JJ￨O￨- contrast￨L￨NN￨O￨- with￨L￨IN￨O￨- prototype￨L￨NN￨O￨- SIR￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- which￨L￨WDT￨O￨- ignore￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- surrounding￨L￨VBG￨O￨A infected-susceptible￨L￨JJ￨O￨- pairs￨L￨NNS￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- predict￨L￨VBP￨O￨- large￨L￨JJ￨O￨- invasions￨L￨NNS￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- if￨L￨IN￨O￨- 7￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Continuous￨U￨JJ￨O￨- transitions￨L￨NNS￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- obtained￨L￨VBN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- extended￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- involving￨L￨VBG￨O￨- context-dependent￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- each￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- enhanced￨L￨VBN￨O￨- or￨L￨CC￨O￨- diminished￨L￨VBN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected/spreader￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- surrounding￨L￨VBG￨O￨A the￨L￨DT￨O￨- transmitter-receiver￨L￨NN￨O￨- pair910￨L￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- location￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨- threshold￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- DK￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- variants8￨L￨NN￨O￨- predict￨L￨VBP￨O￨A that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- phenomenon￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- smoothly￨L￨RB￨O￨- with￨L￨IN￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pair￨L￨NN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- to￨L￨TO￨O￨- macroscopic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- invasions￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- fully￨L￨RB￨O￨- explained￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- microscopic￨L￨JJ￨O￨- contagions￨L￨NNS￨O￨- between￨L￨IN￨O￨- pairs￨L￨NNS￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- this￨L￨DT￨O￨- analogy￨L￨NN￨O￨A ,￨L￨,￨O￨- compartmental￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- Suceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- phenomena123￨L￨NN￨O￨- .￨L￨.￨O￨- +Such￨U￨PDT￨O￨- a￨L￨DT￨O￨- template￨L￨NN￨O￨- could￨L￨MD￨O￨- promote￨L￨VB￨O￨- an￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- various￨L￨JJ￨O￨- stakeholders￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- developers￨L￨NNS￨O￨- ,￨L￨,￨O￨- government￨L￨NN￨O￨- analysts￨L￨NNS￨O￨- ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- practitioners￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- epidemiologists￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- preconceptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- backgrounds￨L￨NNS￨O￨- ,￨L￨,￨O￨- expertise￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- needs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- foster￨L￨VB￨O￨- greater￨L￨JJR￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A as￨L￨IN￨O￨- tools￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- epidemiological￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- well-accepted￨L￨JJ￨O￨- technique￨L￨NN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- management￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A do￨L￨VBP￨O￨- not￨L￨RB￨O￨- progress￨L￨VB￨O￨- beyond￨L￨IN￨O￨- a￨L￨DT￨O￨- research￨L￨NN￨O￨- study￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- accepted￨L￨VBN￨O￨- as￨L￨IN￨O￨- tools￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- operational￨L￨JJ￨O￨- setting￨L￨NN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- management￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- learning￨L￨VBG￨O￨- and￨L￨CC￨O￨- planning￨L￨VBG￨O￨- tools￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- facilitate￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- decision-making￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- address￨L￨VB￨O￨- these￨L￨DT￨O￨- challenges￨L￨NNS￨O￨- ,￨L￨,￨O￨- Los￨U￨NNP￨ORGANIZATION￨- Alamos￨U￨NNP￨ORGANIZATION￨- National￨U￨NNP￨ORGANIZATION￨- Laboratory￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- LANL￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- framework￨L￨NN￨O￨- and￨L￨CC￨O￨- lexicon￨L￨NN￨O￨- for￨L￨IN￨O￨- characterizing￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prediction￨L￨NN￨O￨- ,￨L￨,￨O￨- forecasting￨L￨NN￨O￨- and/or￨L￨CC￨O￨- monitoring￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A epidemiology￨L￨NN￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- health￨L￨NN￨O￨- promotion￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- to￨L￨TO￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- system￨L￨NN￨O￨- design￨L￨NN￨O￨- and￨L￨CC￨O￨- operation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- computer￨L￨NN￨O￨- simulation￨L￨NN￨O￨- procedure￨L￨NN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- LF￨U￨NN￨O￨- to￨L￨TO￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- assembled￨L￨VBN￨O￨- from￨L￨IN￨O￨- 18￨L￨CD￨NUMBER￨- sites￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- LF￨U￨NN￨O￨- endemic￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Asia￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Papua￨U￨NNP￨COUNTRY￨- New￨U￨NNP￨COUNTRY￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- reflecting￨L￨VBG￨O￨- different￨L￨JJ￨O￨- ecological￨L￨JJ￨O￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- impacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- complexity￨L￨NN￨O￨- on￨L￨IN￨O￨- filarial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- robustness￨L￨NN￨O￨A and￨L￨CC￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- imply￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- combining￨L￨VBG￨O￨- adaptive￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- parasite￨L￨NN￨O￨- transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- robustness￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- design￨L￨NN￨O￨- principle￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- required￨L￨VBN￨O￨- if￨L￨IN￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- enhance￨L￨VBP￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- parasitic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- delineate￨L￨VB￨O￨- options￨L￨NNS￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- their￨L￨PRP$￨O￨- elimination￨L￨NN￨O￨- effectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- regard￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- how￨L￨WRB￨O￨- including￨L￨VBG￨O￨- vector￨L￨NN￨O￨A control￨L￨NN￨O￨- into￨L￨IN￨O￨- MDA￨U￨NN￨ORGANIZATION￨- programs￨L￨NNS￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- offer￨L￨VB￨O￨- a￨L￨DT￨O￨- countermeasure￨L￨NN￨O￨- that￨L￨WDT￨O￨- will￨L￨MD￨O￨- reliably￨L￨RB￨O￨- increase￨L￨VB￨O￨- system￨L￨NN￨O￨- fragility￨L￨NN￨O￨- globally￨L￨RB￨O￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- settings￨L￨NNS￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- control￨L￨NN￨O￨- option￨L￨NN￨O￨- robust￨L￨JJ￨O￨- to￨L￨TO￨O￨- differential￨L￨JJ￨O￨- locality-specific￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- by￨L￨IN￨O￨- simultaneously￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- regime￨L￨NN￨O￨- variability￨L￨NN￨O￨- also￨L￨RB￨O￨- permit￨L￨VBP￨O￨- more￨L￨RBR￨O￨- reliable￨L￨JJ￨O￨- macroscopic￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- firstly￨L￨RB￨O￨- that￨L￨IN￨O￨- LF￨U￨NN￨O￨- elimination￨L￨NN￨O￨A thresholds￨L￨NNS￨O￨- varied￨L￨VBD￨O￨- significantly￨L￨RB￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- 18￨L￨CD￨NUMBER￨- study￨L￨NN￨O￨- communities￨L￨NNS￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- site￨L￨NN￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- initial￨L￨JJ￨O￨- ecological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- metabolic￨L￨JJ￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- ecology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MTE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- offers￨L￨VBZ￨O￨- an￨L￨DT￨O￨- instrument￨L￨NN￨O￨- to￨L￨TO￨O￨- integrate￨L￨VB￨O￨- physiological￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- and￨L￨CC￨O￨- large-scale￨L￨JJ￨O￨- spatiotemporal￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- to￨L￨TO￨O￨- enable￨L￨VB￨O￨- successful￨L￨JJ￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- changes￨L￨NNS￨O￨- to￨L￨TO￨O￨- climatic￨L￨JJ￨O￨- means￨L￨NNS￨O￨- ,￨L￨,￨O￨- variances￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- extremes￨L￨NNS￨O￨- will￨L￨MD￨O￨- affect￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- parasite￨L￨JJ￨O￨A interactions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- how￨L￨WRB￨O￨- non-linearities￨L￨NNS￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- mean￨L￨VB￨O￨- climate￨L￨NN￨O￨- ,￨L￨,￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- weather￨L￨NN￨O￨- and￨L￨CC￨O￨- organismal￨L￨JJ￨O￨- acclimatization￨L￨NN￨O￨- responses￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- climate￨L￨NN￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- parasite￨L￨JJ￨O￨A interactions￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- begin￨L￨VBP￨O￨- by￨L￨IN￨O￨- defining￨L￨VBG￨O￨- performance￨L￨NN￨O￨- curves￨L￨NNS￨O￨- and￨L￨CC￨O￨- show￨L￨VB￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- parasite￨L￨JJ￨O￨A interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- highlighting￨L￨VBG￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- temperature-dependent￨L￨JJ￨O￨- defense￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- of￨L￨IN￨O￨- ectoand￨L￨NN￨O￨- endothermic￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- can￨L￨MD￨O￨- conceptualize￨L￨VB￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- processes￨L￨NNS￨O￨- as￨L￨IN￨O￨- separate￨L￨JJ￨O￨- thermal￨L￨JJ￨O￨- performance￨L￨NN￨O￨- curves￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨NN￨O￨A to￨L￨TO￨O￨- infect￨L￨VB￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 2A￨L￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- predicted￨L￨VBD￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- would￨L￨MD￨O￨- take￨L￨VB￨O￨- 3.5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- brucellosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- to￨L￨TO￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 0.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- adult￨L￨JJ￨O￨- sheep￨L￨NN￨O￨A seropositive￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- mixed-species￨L￨JJ￨O￨- B.￨U￨NNP￨O￨- melitensis-endemic￨L￨JJ￨O￨- farm￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- median￨L￨JJ￨O￨- field-study￨L￨JJ￨O￨- seroprevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- following￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- sheep￨L￨NN￨O￨- and￨L￨CC￨O￨- cattle￨L￨NNS￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- dynamic￨L￨JJ￨O￨- ,￨L￨,￨O￨- differential-equation￨L￨NN￨O￨- ,￨L￨,￨O￨- age-structured￨L￨JJ￨O￨- ,￨L￨,￨O￨- seasonal￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- births￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- whether￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- sheep￨L￨NN￨O￨A and￨L￨CC￨O￨- cattle￨L￨NNS￨O￨- had￨L￨VBD￨O￨- an￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- brucellosis￨L￨NN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- mixed￨L￨JJ￨O￨- species￨L￨NNS￨O￨- farm￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- sheep￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Vaccination￨U￨NN￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- for￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- livestock￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨A :￨L￨:￨O￨- an￨L￨DT￨O￨- age-stratified￨L￨JJ￨O￨- ,￨L￨,￨O￨- seasonal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- brucellosis￨L￨NN￨O￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- settingsWendy￨L￨NN￨O￨- Beauvais1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Imadidden￨U￨JJ￨O￨- Musallam1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Javier￨U￨NNP￨PERSON￨- Guitian1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 9:55￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Brucella￨U￨NNP￨LOCATION￨- melitensis￨L￨NN￨O￨- causes￨L￨VBZ￨O￨- production￨L￨NN￨O￨- losses￨L￨NNS￨O￨- in￨L￨IN￨O￨- ruminants￨L￨NNS￨O￨- and￨L￨CC￨O￨- febrile￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Central￨U￨NNP￨LOCATION￨- Asia￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Middle￨U￨NNP￨LOCATION￨- East￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- elsewhere￨L￨RB￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- reason￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- have￨L￨VBP￨O￨- taken￨L￨VBN￨O￨- measures￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- restricting￨L￨VBG￨O￨- animal￨L￨NN￨O￨- movement￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- controlled￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- during￨L￨IN￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- information￨L￨NN￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- authorities￨L￨NNS￨O￨A to￨L￨TO￨O￨- improve￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- authorities￨L￨NNS￨O￨- should￨L￨MD￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- cattle￨L￨NNS￨O￨A moving￨L￨VBG￨O￨- out￨L￨RP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- highlands￨L￨NNS￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Interesting￨U￨JJ￨O￨- work￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A movement￨L￨NN￨O￨- in￨L￨IN￨O￨- Argentina￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- relates￨L￨VBZ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- live￨L￨JJ￨O￨- cattle￨L￨NNS￨O￨A market￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- hub￨L￨NN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- Italy￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- were￨L￨VBD￨O￨- intended￨L￨VBN￨O￨- for￨L￨IN￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- applications￨L￨NNS￨O￨- like￨L￨IN￨O￨- identification￨L￨NN￨O￨A of￨L￨IN￨O￨- grain￨L￨NN￨O￨- protein￨L￨NN￨O￨- content￨L￨NN￨O￨- genes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- expression￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- fatty￨L￨JJ￨O￨- acid￨L￨NN￨O￨- desaturase￨L￨NN￨O￨- gene￨L￨NN￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- H2O2￨U￨NN￨O￨- during￨L￨IN￨O￨- powdery￨L￨JJ￨O￨- mildew￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- polyploidization￨L￨NN￨O￨- events￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- SNP￨U￨NN￨ORGANIZATION￨- discovery￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨- responsive￨L￨JJ￨O￨- for￨L￨IN￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- starchy￨L￨JJ￨O￨- endosperm￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +De￨U￨NNP￨O￨- novo￨L￨FW￨O￨- assembled￨L￨VBN￨O￨- transcriptomes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- important￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- for￨L￨IN￨O￨- identification￨L￨NN￨O￨A of￨L￨IN￨O￨- functional￨L￨JJ￨O￨- genes￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- metabolic￨L￨JJ￨O￨- pathways￨L￨NNS￨O￨- from￨L￨IN￨O￨- non-model￨L￨JJ￨O￨- plants￨L￨NNS￨O￨- like￨L￨IN￨O￨- Eucalyptus￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- rubber￨L￨NN￨TITLE￨- plant￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- chickpea￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- comparative￨L￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- bread￨L￨NN￨O￨- wheat￨L￨NN￨O￨- non-normalized￨L￨JJ￨O￨- transcriptomes￨L￨NNS￨O￨- using￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- separate￨L￨JJ￨O￨- de￨L￨FW￨O￨- novo￨L￨FW￨O￨- assemblers￨L￨NNS￨O￨- Trinity￨U￨NNP￨O￨- and￨L￨CC￨O￨- Trans-ABySS￨U￨NNP￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- including￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- k-mers￨L￨NNS￨O￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- odd￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- from￨L￨IN￨O￨- 45￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 87￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- provided￨L￨VBN￨O￨- insights￨L￨NNS￨O￨- on￨L￨IN￨O￨- characterization￨L￨NN￨O￨- and￨L￨CC￨O￨- identification￨L￨NN￨O￨A of￨L￨IN￨O￨- new￨L￨JJ￨O￨- wheat￨L￨NN￨O￨- transcripts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Large￨U￨JJ￨O￨- scale￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- transcriptomes￨L￨NNS￨O￨- in￨L￨IN￨O￨- species￨L￨NNS￨O￨- lacking￨L￨VBG￨O￨- a￨L￨DT￨O￨- sequenced￨L￨VBN￨O￨- genome￨L￨NN￨O￨A requires￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reference-free￨L￨JJ￨O￨- reconstruction￨L￨NN￨O￨- of￨L￨IN￨O￨- transcript￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- from￨L￨IN￨O￨- short￨L￨JJ￨O￨- NGS￨U￨NN￨O￨- reads￨L￨VBZ￨O￨- into￨L￨IN￨O￨- contigs￨L￨NNS￨O￨- using￨L￨VBG￨O￨- de￨L￨FW￨O￨- novo￨L￨FW￨O￨- transcriptome￨L￨FW￨O￨- assembly￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- sequenced￨L￨VBN￨O￨- genome￨L￨NN￨O￨- ,￨L￨,￨O￨- transcriptome￨L￨NN￨O￨- sequencing￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- alternative￨L￨NN￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- identification￨L￨NN￨O￨A of￨L￨IN￨O￨- wheat￨L￨NN￨O￨- genes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- mismatch￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- UK￨U￨NNP￨COUNTRY￨- data￨L￨NNS￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- drive￨L￨VB￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- —￨L￨:￨O￨- evidence￨L￨NN￨O￨- from￨L￨IN￨O￨- other￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- clearly￨L￨RB￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- London￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- major￨L￨JJ￨O￨- UK￨U￨NNP￨COUNTRY￨- cities￨L￨NNS￨O￨- remained￨L￨VBD￨O￨- predominantly￨L￨RB￨O￨- biennial￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-chaotic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- covered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- data￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1920￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1940￨L￨CD￨DATE￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- S1￨U￨NN￨O￨- Text￨U￨VB￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- overall￨L￨JJ￨O￨- clockwork￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- secular￨L￨JJ￨RELIGION￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- recruitment￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- uptake￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- in￨L￨IN￨O￨- small￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- predisposes￨L￨VBZ￨O￨- smaller￨L￨JJR￨O￨- towns￨L￨NNS￨O￨- and￨L￨CC￨O￨- cities￨L￨NNS￨O￨A to￨L￨TO￨O￨- be￨L￨VB￨O￨- entrained￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- larger￨L￨JJR￨O￨- metropolitan￨L￨JJ￨O￨- centers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Secular￨U￨JJ￨RELIGION￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- recruitment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- driver￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A periodicity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- birth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- city￨L￨NN￨O￨- when￨L￨WRB￨O￨- fitting￨L￨JJ￨O￨- and￨L￨CC￨O￨- doing￨L￨VBG￨O￨- forward￨L￨RB￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- intensively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- incidence￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- for￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A are￨L￨VBP￨O￨- from￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- —￨L￨:￨O￨- notably￨L￨RB￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- —￨L￨:￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- prevaccination￨L￨NN￨O￨- era￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- stable￨L￨JJ￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- regularly￨L￨RB￨O￨- occurring￨L￨VBG￨O￨- seasonal￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- annual￨L￨JJ￨SET￨- or￨L￨CC￨O￨- biennial￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- compare￨L￨VB￨O￨- these￨L￨DT￨O￨- contexts￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- fit￨L￨VBP￨O￨- a￨L￨DT￨O￨- Time-series￨U￨NNPS￨MISC￨- Susceptible￨U￨NNP￨MISC￨- Infected￨U￨JJ￨MISC￨- Removed￨U￨VBN￨MISC￨- (￨L￨-LRB-￨O￨- TSIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 80￨L￨CD￨NUMBER￨- cities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- systematic￨L￨JJ￨O￨- and￨L￨CC￨O￨- user-friendly￨L￨JJ￨O￨- way￨L￨NN￨O￨- of￨L￨IN￨O￨- building￨L￨NN￨O￨- and￨L￨CC￨O￨- running￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- efficiently￨L￨RB￨O￨A handles￨L￨VBZ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- reduces￨L￨VBZ￨O￨- much￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- boilerplate￨L￨NN￨O￨- code￨L￨NN￨O￨- that￨L￨WDT￨O￨- usually￨L￨RB￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- Broadwick￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- modular￨L￨JJ￨O￨- ,￨L￨,￨O￨- object-oriented￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- efficiently￨L￨RB￨O￨A handles￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- and￨L￨CC￨O￨- provides￨L￨VBZ￨O￨- packages￨L￨NNS￨O￨- for￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- parameter￨L￨NN￨O￨- inference￨L￨NN￨O￨- using￨L￨VBG￨O￨- Approximate￨U￨NNP￨O￨- Bayesian￨U￨NNP￨O￨- Computation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Markov￨U￨NNP￨PERSON￨- Chain￨U￨NNP￨PERSON￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- MCMC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- Broadwick￨U￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- framework￨L￨NN￨O￨A developed￨L￨VBD￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- productivity￨L￨NN￨O￨- of￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- by￨L￨IN￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- framework￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- and￨L￨CC￨O￨- share￨L￨VB￨O￨- complex￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Kao1BMC￨U￨NN￨O￨- BioinformaticsBMC￨U￨NN￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 17:65￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- O￨U￨NN￨O￨- ’￨L￨''￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Modelling￨U￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- often￨L￨RB￨O￨- involves￨L￨VBZ￨O￨- integrating￨L￨VBG￨O￨- the￨L￨DT￨O￨- wealth￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- gathered￨L￨VBN￨O￨- during￨L￨IN￨O￨- modern￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- into￨L￨IN￨O￨- complex￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- or￨L￨CC￨O￨- computational￨L￨JJ￨O￨A models￨L￨NNS￨O￨A of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Incorporating￨U￨VBG￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- into￨L￨IN￨O￨- simple￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- challenging￨L￨JJ￨O￨- ,￨L￨,￨O￨- requiring￨L￨VBG￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- more￨L￨JJR￨O￨- complex￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- more￨L￨RBR￨O￨- efficient￨L￨JJ￨O￨- computational￨L￨JJ￨O￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- studies￨L￨NNS￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- clinical￨L￨JJ￨O￨- judgment￨L￨NN￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨A treatment￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- cost‐effective￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- ,5￨L￨NN￨O￨- while￨L￨IN￨O￨- others￨L￨NNS￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- testing￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- cost‐effective￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- .6￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- studies￨L￨NNS￨O￨- agreed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- cost‐effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- tests￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- accuracy￨L￨NN￨O￨- and￨L￨CC￨O￨- costs￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- status￨L￨NN￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- one￨L￨NN￨NUMBER￨- has￨L￨VBZ￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- thresholds￨L￨NNS￨O￨- of￨L￨IN￨O￨- accuracy￨L￨NN￨O￨- and￨L￨CC￨O￨- costs￨L￨NNS￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- testing￨L￨NN￨O￨- strategy￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- cost‐effective￨L￨JJ￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- clinical￨L￨JJ￨O￨- judgment￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- SCHNAPS￨U￨NN￨O￨- ,7￨L￨CD￨NUMBER￨- an￨L￨DT￨O￨- agent‐level￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- SPLMM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ‐￨L￨NN￨O￨- based￨L￨VBN￨O￨- simulator￨L￨NN￨O￨- running￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- supercomputers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- CLUMEQ￨U￨NNP￨O￨- consortium￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- hybrid￨L￨NN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- decision￨L￨NN￨O￨- analytic￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Figure￨U￨NNP￨O￨- A1￨U￨NN￨O￨- of￨L￨IN￨O￨- Appendix￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- built￨L￨VBN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- expected￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- rapid￨L￨JJ￨O￨- test￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- POC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- diagnosis￨L￨NN￨O￨- and￨L￨CC￨O￨- early￨L￨JJ￨O￨- appropriate￨L￨JJ￨O￨- antiviral￨L￨JJ￨O￨A treatment￨L￨NN￨O￨A of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨DT￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- clinical￨L￨JJ￨O￨- judgment￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- hybrid￨L￨NN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- decision￨L￨NN￨O￨- analytic￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- principal￨L￨JJ￨TITLE￨- questions￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Is￨U￨VBZ￨O￨- an￨L￨DT￨O￨- antiviral￨L￨JJ￨O￨A treatment￨L￨NN￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- POC￨U￨NN￨O￨- test￨L￨NN￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- cost‐effective￨L￨JJ￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- judgment￨L￨NN￨O￨- ?￨L￨.￨O￨- +We￨U￨PRP￨O￨- considered￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- would￨L￨MD￨O￨- seek￨L￨VB￨O￨- medical￨L￨JJ￨O￨- help￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- outpatient￨L￨NN￨O￨- clinic￨L￨NN￨O￨- or￨L￨CC￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- emergency￨L￨NN￨O￨- department￨L￨NN￨O￨- .9￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- patients￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- 48￨L￨CD￨DURATION￨- hours￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- will￨L￨MD￨O￨- get￨L￨VB￨O￨- oseltamivir￨L￨JJ￨O￨- antiviral￨L￨JJ￨O￨A treatment￨L￨NN￨O￨A two￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- a￨L￨DT￨DURATION￨- day￨L￨NN￨DURATION￨- for￨L￨IN￨O￨- five￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- .￨L￨.￨O￨- +and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- At￨U￨IN￨O￨- what￨L￨WP￨O￨- thresholds￨L￨NNS￨O￨- of￨L￨IN￨O￨- POC￨U￨NN￨O￨- test￨L￨NN￨O￨- accuracy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- sensitivity￨L￨NN￨O￨- and￨L￨CC￨O￨- specificity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- cost￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- testing￨L￨NN￨O￨- strategy￨L￨NN￨O￨- cost‐effective￨L￨NN￨O￨- ?￨L￨.￨O￨- +Macro-level￨U￨JJ￨O￨- descriptors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Airline￨U￨NNP￨ORGANIZATION￨- Network￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WAN￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- explains￨L￨VBZ￨O￨- middle￨L￨JJ￨O￨- and￨L￨CC￨O￨- late￨L￨JJ￨O￨- stage￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨A spread￨L￨NN￨O￨- mediated￨L￨VBN￨O￨- by￨L￨IN￨O￨- this￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- necessarily￨L￨RB￨O￨- regard￨L￨VB￨O￨- early￨L￨JJ￨O￨- stage￨L￨NN￨O￨- variation￨L￨NN￨O￨- as￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Based￨U￨VBD￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- WAN￨U￨NNP￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- public￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- measure￨L￨VB￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- airport￨L￨NN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- AEF￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A originating￨L￨VBG￨O￨- at￨L￨IN￨O￨- that￨L￨DT￨O￨- airport￨L￨NN￨O￨- would￨L￨MD￨O￨- generate￨L￨VB￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- which￨L￨WDT￨O￨- transmits￨L￨VBZ￨O￨- from￨L￨IN￨O￨- airport￨L￨NN￨O￨- to￨L￨TO￨O￨- airport￨L￨NN￨O￨- via￨L￨IN￨O￨- scheduled￨L￨VBN￨O￨- commercial￨L￨JJ￨O￨- flights￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- AEF￨U￨VBP￨O￨- powerfully￨L￨RB￨O￨- explains￨L￨VBZ￨O￨- pandemic￨L￨JJ￨O￨A risk￨L￨NN￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- 0.90￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- level￨L￨NN￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨JJ￨O￨- competence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- 0.85￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- until￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Measuring￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- airports￨L￨NNS￨O￨- for￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨A spread￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- airline￨L￨NN￨O￨- networkGlenn￨L￨NN￨O￨- Lawyer1Email￨U￨NN￨O￨- authorBMC￨L￨NN￨O￨- Infectious￨U￨JJ￨O￨- DiseasesBMC￨U￨NN￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 16:70￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Lawyer￨U￨NNP￨TITLE￨- .￨L￨.￨O￨- +Unlike￨U￨IN￨O￨- engineering￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- vulnerability￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- ,￨L￨,￨O￨- mobile￨L￨JJ￨TITLE￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- cyber￨L￨NN￨O￨- games￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- attackers￨L￨NNS￨O￨- intend￨L￨VBP￨O￨- to￨L￨TO￨O￨- compromise￨L￨VB￨O￨- users￨L￨NNS￨O￨- and￨L￨CC￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- defenders￨L￨NNS￨O￨- will￨L￨MD￨O￨- recover￨L￨VB￨O￨- the￨L￨DT￨O￨- compromised￨L￨VBN￨O￨- users￨L￨NNS￨O￨- to￨L￨TO￨O￨- healthy￨L￨JJ￨O￨- state￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- resource￨L￨NN￨O￨A restriction￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- battery￨L￨NN￨CRIMINAL_CHARGE￨- life￨L￨NN￨O￨- ,￨L￨,￨O￨- computational￨L￨JJ￨O￨- power￨L￨NN￨O￨- ,￨L￨,￨O￨- and/or￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- limited￨L￨JJ￨O￨- bandwidth￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- answer￨L￨VB￨O￨- this￨L￨DT￨O￨- question￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- of￨L￨IN￨O￨- attackers￨L￨NNS￨O￨- or￨L￨CC￨O￨- defenders￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- a￨L￨DT￨O￨- winning￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- cyber￨L￨NN￨O￨- game￨L￨NN￨O￨- with￨L￨IN￨O￨- minimum￨L￨JJ￨O￨- resource￨L￨NN￨O￨A consumption￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- ,￨L￨,￨O￨- distributed￨L￨VBN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- existing￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- consider￨L￨VBP￨O￨- cyber￨L￨JJ￨O￨- war￨L￨NN￨CAUSE_OF_DEATH￨- games￨L￨NNS￨O￨- by￨L￨IN￨O￨- proposing￨L￨VBG￨O￨- optimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- of￨L￨IN￨O￨- attackers￨L￨NNS￨O￨- and￨L￨CC￨O￨- defenders￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- consider￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- with￨L￨IN￨O￨- minimum￨L￨JJ￨O￨- resource￨L￨NN￨O￨A consumption￨L￨NN￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Zhu￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Martinez￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- a￨L￨DT￨O￨- cyber￨L￨NN￨O￨- game￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- two-level￨L￨JJ￨O￨- Stackelberg￨U￨NNP￨PERSON￨- game￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- leader-follower￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- inherent￨L￨JJ￨O￨- resource￨L￨NN￨O￨A constraints￨L￨NNS￨O￨- in￨L￨IN￨O￨- discrete-time￨L￨NN￨O￨- ,￨L￨,￨O￨- linear￨L￨JJ￨O￨- time-invariant￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- investigated￨L￨VBD￨O￨- how￨L￨WRB￨O￨- clustering￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- propensity￨L￨NN￨O￨- of￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- connected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- share￨L￨VB￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- neighbour￨L￨NN￨O￨- ,￨L￨,￨O￨- affects￨L￨VBZ￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- phylogenies￨L￨NNS￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- assortative￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- easily-distinguishable￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A graph￨L￨NN￨O￨- ,￨L￨,￨O￨- made￨L￨VBD￨O￨- up￨L￨RP￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- similar￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- study￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- attempt￨L￨NN￨O￨- to￨L￨TO￨O￨- directly￨L￨RB￨O￨- reconstruct￨L￨VB￨O￨- a￨L￨DT￨O￨- sexual￨L￨JJ￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A ,￨L￨,￨O￨- underlying￨L￨VBG￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- information￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- have￨L￨VBP￨O￨- revealed￨L￨VBN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- quick￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- chains￨L￨NNS￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- among￨L￨IN￨O￨- MSMs￨U￨NNS￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- distinct￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨A with￨L￨IN￨O￨- genetically-similar￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- found￨L￨VBD￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- phylogenies￨L￨NNS￨O￨A resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- static￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- interactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- randomly￨L￨RB￨O￨- paired￨L￨JJ￨O￨- particles￨L￨NNS￨O￨A :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- young￨L￨JJ￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- old￨L￨JJ￨O￨- j￨L￨NN￨O￨- of￨L￨IN￨O￨- opposite￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- adopts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- j￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- otherwise￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- w￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- adopts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- i￨L￨FW￨O￨- ;￨L￨:￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- particles￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- particle￨L￨NN￨O￨- has￨L￨VBZ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- convincing￨L￨VBG￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- ;￨L￨:￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- particles￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- nothing￨L￨NN￨O￨- happens￨L￨VBZ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- adoption￨L￨NN￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- particles￨L￨NNS￨O￨A ’￨L￨POS￨O￨- states￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- age￨L￨NN￨O￨- or￨L￨CC￨O￨- persistence￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- span￨L￨NN￨O￨- each￨L￨DT￨O￨- particle￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- current￨L￨JJ￨DATE￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- composed￨L￨VBN￨O￨- by￨L￨IN￨O￨- N￨U￨NN￨O￨- particles￨L￨NNS￨O￨A whose￨L￨WP$￨O￨- dynamic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- each￨L￨DT￨O￨- particle￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- state￨L￨NN￨O￨- L￨U￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- up￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- ↑￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- down￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- ↓￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- age￨L￨NN￨O￨- young￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Y￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- old￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Z￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨A adopts￨L￨VBZ￨O￨- a￨L￨DT￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- time￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- young￨L￨JJ￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adopted￨L￨VBN￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- yet￨L￨RB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- addressed￨L￨VBN￨O￨- :￨L￨:￨O￨- first￨L￨RB￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- and￨L￨CC￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- cross-protection￨L￨NN￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨A and￨L￨CC￨O￨- ,￨L￨,￨O￨- second￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- potential￨L￨JJ￨O￨- serotype￨L￨NN￨O￨- replacement￨L￨NN￨O￨- by￨L￨IN￨O￨- CV-A16￨U￨NN￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- CV-A6￨U￨NN￨O￨- or￨L￨CC￨O￨- CV-A10￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- following￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- EV-A71￨U￨NN￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- decreased￨L￨VBN￨O￨- EV-A71￨U￨NN￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- accompanying￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- cross-immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- CV-A16￨U￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- potential￨L￨JJ￨O￨- increased￨L￨VBN￨O￨- circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- HFMD￨U￨NN￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- co-infection￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- individual￨L￨NN￨O￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- serotypes￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- rarer￨L￨JJR￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- by￨L￨IN￨O￨- chance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- short-term￨L￨JJ￨O￨- cross-protection￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- neutralization￨L￨NN￨O￨- assays￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- partial￨L￨JJ￨O￨- cross-reactivity￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- EV-A71￨U￨NN￨O￨- and￨L￨CC￨O￨- CV-A16￨U￨NN￨O￨- serotypes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- competitive￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- .￨L￨.￨O￨- +Weekly￨U￨NNP￨SET￨- reported￨L￨VBD￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- y-axis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- across￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2013￨L￨CD￨DATE￨- ,￨L￨,￨O￨- x-axis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- aggregated￨L￨VBN￨O￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- 31￨L￨CD￨NUMBER￨- provinces￨L￨NNS￨O￨- of￨L￨IN￨O￨- Mainland￨U￨NNP￨LOCATION￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- adjusted￨L￨VBN￨O￨- for￨L￨IN￨O￨- estimated￨L￨VBN￨O￨- reporting￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- stratified￨L￨VBN￨O￨- by￨L￨IN￨O￨- serotype￨L￨NN￨O￨- :￨L￨:￨O￨- EV-A71￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- green￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- CV-A16￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- red￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- non-EV-A71￨L￨NN￨O￨- and￨L￨CC￨O￨- non-CV-A16￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨A of￨L￨IN￨O￨- enterovirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- blue￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtained￨L￨VBD￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨- laboratory-confirmed￨L￨JJ￨O￨- HFMD￨U￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- sub-sample￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- province￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- virological￨L￨JJ￨O￨- test￨L￨NN￨O￨- results￨L￨VBZ￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- EV-A71￨U￨NN￨O￨- ,￨L￨,￨O￨- CV-A16￨U￨NN￨O￨- ,￨L￨,￨O￨- other￨L￨JJ￨O￨- non-EV-A71￨L￨NN￨O￨- and￨L￨CC￨O￨- non-CV-A16￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨A of￨L￨IN￨O￨- enterovirus￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- negative￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- analyses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- EV-A71-associated￨U￨JJ￨O￨- HFMD￨U￨NN￨O￨- alone￨L￨RB￨O￨- or￨L￨CC￨O￨- all-cause￨L￨JJ￨O￨- HFMD￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- accounted￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- cross-protective￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- serotype￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨A .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- study￨L￨VB￨O￨- an￨L￨DT￨O￨- epidemic-based￨L￨JJ￨O￨- information￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- on￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- distinguished￨L￨VBN￨O￨- from￨L￨IN￨O￨- existing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- layer-switching￨L￨JJ￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- overburden￨L￨NN￨O￨- or￨L￨CC￨O￨- surcharge￨L￨NN￨O￨- for￨L￨IN￨O￨- transmissions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- proceed￨L￨VBP￨O￨- by￨L￨IN￨O￨- crossing￨L￨VBG￨O￨- different￨L￨JJ￨O￨- layers￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- proceeding￨L￨VBG￨O￨- as￨L￨IN￨O￨- confined￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨A .￨L￨.￨O￨- +These￨U￨DT￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- trade-off￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨A and￨L￨CC￨O￨- across￨L￨IN￨O￨- difference￨L￨NN￨O￨- layers￨L￨NNS￨O￨- to￨L￨TO￨O￨- optimize￨L￨VB￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- average￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- over￨L￨IN￨O￨- different￨L￨JJ￨O￨- channels￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- nearly-confined￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- layer-switching￨L￨JJ￨O￨- cost￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- enough￨L￨RB￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aimed￨L￨VBD￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- and￨L￨CC￨O￨- multiannual￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- PUUV-infected￨U￨JJ￨MISC￨- bank￨L￨NN￨O￨- voles￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- presumably￨L￨RB￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- driver￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- NE￨U￨NN￨STATE_OR_PROVINCE￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- PUUV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- PUUV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- indicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- acquisition￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- PUUV-specific￨U￨JJ￨MISC￨- antibodies￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- expected￨L￨VBD￨O￨- to￨L￨TO￨O￨- shed￨L￨VB￨O￨- more￨L￨JJR￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- PUUV￨U￨NN￨O￨- .￨L￨.￨O￨- +S1￨U￨NN￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- 588￨L￨CD￨NUMBER￨- captures￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- known￨L￨JJ￨O￨- serological￨L￨JJ￨O￨- history￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- area￨L￨NN￨O￨- ;￨L￨:￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- animals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- had￨L￨VBD￨O￨- acquired￨L￨VBN￨O￨- or/and￨L￨NN￨O￨- lost￨L￨VBD￨O￨- antibodies￨L￨NNS￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- trapping￨L￨NN￨O￨- sessions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- seropositive￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- old￨L￨JJ￨O￨- enough￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- >￨L￨JJR￨O￨- 8￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- exclude￨L￨VB￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- result￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- MatAb￨U￨NN￨O￨- .￨L￨.￨O￨- +falciparum￨L￨NN￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- merozoites￨L￨NNS￨O￨- emerging￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- schizont￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- committed￨L￨VBN￨O￨- either￨L￨DT￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- route￨L￨NN￨O￨- —￨L￨:￨O￨- invading￨L￨VBG￨O￨- a￨L￨DT￨O￨- red￨L￨JJ￨O￨- blood￨L￨NN￨O￨A cell￨L￨NN￨O￨- and￨L￨CC￨O￨- developing￨L￨VBG￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- sexual￨L￨JJ￨O￨- gametocyte￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- passed￨L￨VBN￨O￨- onto￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- blood￨L￨NN￨O￨- meal￨L￨NN￨O￨- —￨L￨:￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- further￨L￨JJ￨O￨- in-host￨L￨JJ￨O￨- proliferation￨L￨NN￨O￨- by￨L￨IN￨O￨- invading￨L￨VBG￨O￨- a￨L￨DT￨O￨- red￨L￨JJ￨O￨- blood￨L￨NN￨O￨- cell￨L￨NN￨O￨- ,￨L￨,￨O￨- maturing￨L￨VBG￨O￨- into￨L￨IN￨O￨- another￨L￨DT￨O￨- schizont￨L￨NN￨O￨- and￨L￨CC￨O￨- subsequently￨L￨RB￨O￨- bursting￨L￨VBG￨O￨- to￨L￨TO￨O￨- release￨L￨VB￨O￨- more￨L￨JJR￨O￨- merozoites￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- therefore￨L￨RB￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- inferential￨L￨JJ￨O￨- method￨L￨NN￨O￨- by￨L￨IN￨O￨- expanding￨L￨VBG￨O￨- recent￨L￨JJ￨O￨- regression￨L￨NN￨O￨- methods￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- apply￨L￨VB￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- revealing￨L￨VBG￨O￨- unexpected￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- investment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasites￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- highly-controlled￨L￨JJ￨O￨- setting￨L￨NN￨O￨- of￨L￨IN￨O￨- rodent￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Gametocytes￨U￨NNS￨O￨- are￨L￨VBP￨O￨- specialized￨L￨VBN￨O￨- for￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- midgut￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- infect￨L￨VB￨O￨- red￨L￨JJ￨O￨- blood￨L￨NN￨O￨A cells￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- investment￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- costly￨L￨JJ￨O￨- to￨L￨TO￨O￨- within-host￨L￨JJ￨O￨- replication￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Characterizing￨U￨VBG￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- allocation￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- requires￨L￨VBZ￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A data￨L￨NNS￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- gametocyte￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- parasite￨L￨NN￨O￨- proliferation￨L￨NN￨O￨- and￨L￨CC￨O￨- gametocyte￨L￨NN￨O￨- longevity￨L￨NN￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- investment￨L￨NN￨O￨- .￨L￨.￨O￨- +Transmission￨U￨NNP￨O￨- investment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- cohort￨L￨NN￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A that￨L￨WDT￨O￨- commit￨L￨VBP￨O￨- to￨L￨TO￨O￨- differentiation￨L￨NN￨O￨- into￨L￨IN￨O￨- gametocytes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- proportion￨L￨NN￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- conversion￨L￨NN￨O￨- rate￨L￨NN￨O￨- ”￨L￨''￨O￨- by￨L￨IN￨O￨- convention￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- population￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- distinguish￨L￨VBP￨O￨- between￨L￨IN￨O￨- costs￨L￨NNS￨O￨A of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- c￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- capture￨L￨VBP￨O￨- immunization￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- '￨L￨POS￨O￨- implementation￨L￨NN￨O￨- and￨L￨CC￨O￨- operation￨L￨NN￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- increase￨L￨VB￨O￨- exponentially￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- proportional￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- supported￨L￨VBN￨O￨- by￨L￨IN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- see￨L￨VB￨O￨- figure￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- costs￨L￨NNS￨O￨- c￨L￨NN￨O￨- that￨L￨WDT￨O￨- capture￨L￨VBP￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- morbidity￨L￨NN￨O￨- ,￨L￨,￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- productivity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- are￨L￨VBP￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- cost￨L￨NN￨O￨- The￨U￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- setting￨L￨VBG￨O￨- up￨L￨RP￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- in￨L￨IN￨O￨- location￨L￨NN￨O￨- i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- cost￨L￨NN￨O￨- for￨L￨IN￨O￨- high￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- captured￨L￨VBN￨O￨- by￨L￨IN￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- chosen￨L￨VBN￨O￨- to￨L￨TO￨O￨- reflect￨L￨VB￨O￨- that￨L￨IN￨O￨- achieving￨L￨VBG￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- coverage￨L￨NN￨O￨- costs￨L￨VBZ￨O￨- about￨L￨IN￨O￨- five￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- as￨L￨RB￨O￨- much￨L￨JJ￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- coverage￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- strongly￨L￨RB￨O￨- immunizing￨L￨VBG￨O￨- vaccine-preventable￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- coupled￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- motivate￨L￨VB￨O￨- coalition￨L￨NN￨O￨- formation￨L￨NN￨O￨- and￨L￨CC￨O￨- promote￨L￨VB￨O￨- cooperation￨L￨NN￨O￨- among￨L￨IN￨O￨- countries￨L￨NNS￨O￨A in￨L￨IN￨O￨- designing￨L￨VBG￨O￨- and￨L￨CC￨O￨- implementing￨L￨VBG￨O￨- regional￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- forming￨L￨VBG￨O￨- coalitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- deciding￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- joint￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- countries￨L￨NNS￨O￨- can￨L￨MD￨O￨- achieve￨L￨VB￨O￨- higher￨L￨JJR￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨A at￨L￨IN￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- cost￨L￨NN￨O￨- than￨L￨IN￨O￨- when￨L￨WRB￨O￨- acting￨L￨VBG￨O￨- independently￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- under￨L￨IN￨O￨- certain￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- cooperative￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- kind￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- stage￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- k￨L￨NN￨O￨- countries￨L￨NNS￨O￨- comprising￨L￨VBG￨O￨- the￨L￨DT￨O￨- coalition￨L￨NN￨O￨- chooses￨L￨VBZ￨O￨- their￨L￨PRP$￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- that￨L￨WDT￨O￨- minimizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- combined￨L￨JJ￨O￨- costs￨L￨NNS￨O￨A of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coalition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- π￨L￨NN￨O￨- =￨L￨JJ￨O￨- k￨L￨NN￨O￨- because￨L￨IN￨O￨- countries￨L￨NNS￨O￨- are￨L￨VBP￨O￨- identical￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- non-signatories￨L￨NNS￨O￨- '￨L￨POS￨O￨- reaction￨L￨NN￨O￨- function￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- cost￨L￨NN￨O￨- minimization￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- allow￨L￨VBP￨O￨- countries￨L￨NNS￨O￨A to￨L￨TO￨O￨- coordinate￨L￨VB￨O￨- a￨L￨DT￨O￨- regional￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- by￨L￨IN￨O￨- formation￨L￨NN￨O￨- of￨L￨IN￨O￨- coalitions￨L￨NNS￨O￨- through￨L￨IN￨O￨- international￨L￨JJ￨O￨- agreements￨L￨NNS￨O￨- and￨L￨CC￨O￨- apply￨L￨VB￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- govern￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- spreading￨L￨NN￨O￨- influences￨L￨VBZ￨O￨A can￨L￨MD￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- hindering￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- or￨L￨CC￨O￨- accelerating￨L￨VBG￨O￨- innovation8￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- similar￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- further￨L￨JJ￨O￨- applied￨L￨VBN￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks9￨L￨NN￨O￨- ,￨L￨,￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- scientists￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- publications10￨L￨NN￨O￨- ,￨L￨,￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- injection￨L￨NN￨O￨- points￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- microfinance11￨L￨NN￨O￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- drug￨L￨NN￨O￨- targets￨L￨NNS￨O￨- in￨L￨IN￨O￨- directed￨L￨VBN￨O￨- pathway￨L￨NN￨O￨- networks12￨L￨NN￨O￨- ,￨L￨,￨O￨- predicting￨L￨VBG￨O￨- essential￨L￨JJ￨O￨- proteins￨L￨NNS￨O￨- in￨L￨IN￨O￨- protein￨L￨NN￨O￨- interaction￨L￨NN￨O￨- networks13￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +Encoding￨U￨VBG￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- topology￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- Klemm￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 30￨L￨CD￨NUMBER￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvector￨L￨NN￨O￨- centrality￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- dynamical￨L￨JJ￨O￨- influences￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- called￨L￨VBN￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- 33￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- dynamics-sensitive￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- DS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- centrality￨L￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- at￨L￨IN￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- directly￨L￨RB￨O￨- applied￨L￨VBN￨O￨- in￨L￨IN￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- influences￨L￨NNS￨O￨A of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- usually￨L￨RB￨O￨- performs￨L￨VBZ￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvector￨L￨NN￨O￨A centrality29￨L￨NN￨O￨- and￨L￨CC￨O￨- k-shell￨L￨NN￨O￨- index14￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- high￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- eigenvector￨L￨NN￨O￨- centrality￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- one￨L￨NN￨NUMBER￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Figs￨U￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- details￨L￨NNS￨O￨- shown￨L￨VBN￨O￨- later￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- scientists￨L￨NNS￨O￨- argued￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- important￨L￨JJ￨O￨- than￨L￨IN￨O￨- its￨L￨PRP$￨O￨- immediate￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- proposed￨L￨VBN￨O￨- k-shell￨L￨NN￨O￨- index1415￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- variants16171819￨L￨NN￨O￨- as￨L￨IN￨O￨- indicators￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- influences￨L￨NNS￨O￨A .￨L￨.￨O￨- +Little￨U￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- relapses￨L￨NNS￨O￨- in￨L￨IN￨O￨- natural￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- from￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 5￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- experimentally￨L￨RB￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- relapses￨L￨NNS￨O￨- and￨L￨CC￨O￨- multiple￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A ,￨L￨,￨O￨- equilibrium￨L￨NN￨O￨- analysis￨L￨NN￨O￨- was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- was￨L￨VBD￨O￨- generalized￨L￨VBN￨O￨- .￨L￨.￨O￨- +M.￨U￨NNP￨O￨- genitalium￨L￨NNP￨O￨- ’s￨L￨POS￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- and￨L￨CC￨O￨- reproductive￨L￨JJ￨O￨- health￨L￨NN￨O￨- necessitates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- greater￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- natural￨L￨JJ￨O￨A history￨L￨NN￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- untreated￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- symptomatic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- decisions￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- clearance￨L￨NN￨O￨A rates￨L￨NNS￨O￨- from￨L￨IN￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- cohort￨L￨NN￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- students￨L￨NNS￨O￨- in￨L￨IN￨O￨- London￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- of￨L￨IN￨O￨- Ugandan￨U￨JJ￨NATIONALITY￨- sex￨L￨NN￨O￨- workers￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- acquisition￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- recurrent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- recovery￨L￨NN￨O￨- .￨L￨.￨O￨- +genitalium￨L￨NN￨O￨- ’s￨L￨POS￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- in￨L￨IN￨O￨- women￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- clearance￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- intriguingly￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- clearance￨L￨NN￨O￨- rates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- apparently￨L￨RB￨O￨- very￨L￨RB￨O￨- different￨L￨JJ￨O￨- .￨L￨.￨O￨- +S￨U￨NN￨O￨- :￨L￨:￨O￨- Susceptible￨U￨JJ￨O￨- state￨L￨NN￨O￨- ;￨L￨:￨O￨- I￨U￨PRP￨O￨- :￨L￨:￨O￨- Infected￨U￨JJ￨O￨- state￨L￨NN￨O￨- ;￨L￨:￨O￨- λ￨L￨NN￨O￨- :￨L￨:￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A of￨L￨IN￨O￨- low-risk￨L￨JJ￨O￨- group￨L￨NN￨O￨- ;￨L￨:￨O￨- λ￨L￨NN￨O￨- :￨L￨:￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- high-risk￨L￨JJ￨O￨- group￨L￨NN￨O￨- ;￨L￨:￨O￨- γ￨L￨NN￨O￨- :￨L￨:￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +genitalium-positive￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- stable￨L￨JJ￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- hence￨L￨RB￨O￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- λ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- numerous￨L￨JJ￨O￨- plant￨L￨NN￨O￨- pests￨L￨NNS￨O￨- and￨L￨CC￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- emerald￨L￨JJ￨O￨- ash￨L￨JJ￨O￨- borer￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- citrus￨L￨NN￨O￨- greening￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- pine￨L￨VBP￨O￨- shoot￨L￨NN￨O￨- beetle￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- initial￨L￨JJ￨O￨- detection￨L￨NN￨O￨- triggers￨L￨VBZ￨O￨- legislation￨L￨NN￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- quarantine￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- applied￨L￨VBN￨O￨- uniformly￨L￨RB￨O￨- across￨L￨IN￨O￨- an￨L￨DT￨O￨- entire￨L￨JJ￨O￨- administrative￨L￨JJ￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- county￨L￨NN￨O￨A or￨L￨CC￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- a￨L￨DT￨O￨- delay￨L￨NN￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- first￨L￨JJ￨ORDINAL￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- county￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- applying￨L￨VBG￨O￨- quarantine￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- plant￨L￨NN￨O￨- trade￨L￨NN￨O￨- in￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- county￨L￨NN￨O￨- ,￨L￨,￨O￨- centered￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- detected￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Primary￨U￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- secondary￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- plant￨L￨NN￨O￨- pathogen￨L￨NN￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- county￨L￨NN￨O￨A represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- one-dimensional￨L￨JJ￨O￨- landscape￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- invading￨L￨VBG￨O￨- plant￨L￨NN￨O￨- pathogen￨L￨NN￨O￨- that￨L￨WDT￨O￨- tracks￨L￨VBZ￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- initially￨L￨RB￨O￨- uninfected￨L￨JJ￨O￨- county￨L￨NN￨O￨A becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +ramorum￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- confirmed￨L￨VBN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- Californian￨U￨NN￨MISC￨- county￨L￨NN￨O￨A ,￨L￨,￨O￨- legislation￨L￨NN￨O￨- mandates￨L￨NNS￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- nurseries￨L￨NNS￨O￨- across￨L￨IN￨O￨- that￨L￨DT￨O￨- entire￨L￨JJ￨O￨- county￨L￨NN￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- quarantined￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- internet￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨MISC￨- Wide￨U￨NN￨MISC￨- Web￨U￨NN￨MISC￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- sim￨L￨NN￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Pow￨U￨NN￨O￨- k￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨A p￨L￨NN￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- StrictLessThan￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Mul￨U￨NN￨ORGANIZATION￨- gamma￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- 3￨L￨CD￨NUMBER￨- le￨L￨DT￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- c￨L￨NN￨O￨- satisfies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- equality￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- allocating￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- interventions￨L￨NNS￨O￨- across￨L￨IN￨O￨- geographic￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- budget￨L￨NN￨O￨A constraints￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- person-days￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Simulations￨U￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- yield￨L￨NN￨O￨- high-level￨L￨JJ￨O￨- ,￨L￨,￨O￨- qualitative￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- on￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- policies￨L￨NNS￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- policy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- when￨L￨WRB￨O￨- considering￨L￨VBG￨O￨- a￨L￨DT￨O￨- 5-year￨L￨JJ￨DURATION￨- time￨L￨NN￨O￨- horizon￨L￨NN￨O￨- than￨L￨IN￨O￨- when￨L￨WRB￨O￨- considering￨L￨VBG￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- year￨L￨NN￨DURATION￨A ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- that￨L￨WDT￨O￨- interventions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Increasing￨U￨VBG￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- budget￨L￨NN￨O￨A causes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- person-days￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- decrease￨L￨VB￨O￨- linearly￨L￨RB￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- budget￨L￨NN￨O￨- starts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- taper￨L￨VB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- produces￨L￨VBZ￨O￨- an￨L￨DT￨O￨- intervention￨L￨NN￨O￨- plan￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- identifying￨L￨VBG￨O￨- which￨L￨WDT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- region￨L￨NN￨O￨- and￨L￨CC￨O￨- year￨L￨NN￨DURATION￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- 5-year￨L￨JJ￨DURATION￨- planning￨L￨NN￨O￨- horizon￨L￨NN￨O￨- .￨L￨.￨O￨- +Methodology￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Multi-year￨U￨JJ￨MISC￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A intervention￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modelHarry￨L￨NN￨O￨- J￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- six￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- propagation￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- clarify￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hubs￨L￨NNS￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- spreading￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨A on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Spreading￨U￨VBG￨O￨- phenomena￨L￨NNS￨O￨A ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- often￨L￨RB￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- to￨L￨TO￨O￨- encounter￨L￨VB￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- uniform67￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- phenomena￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- N￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- categorize￨L￨VB￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- compartments￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨A spread￨L￨VBN￨O￨A over￨L￨IN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- curve￨L￨NN￨O￨A that￨L￨WDT￨O￨- extremizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- aforementioned￨L￨JJ￨O￨- quantity￨L￨NN￨O￨- in￨L￨IN￨O￨- question.As￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- section￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- procedure￨L￨NN￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- follow￨L￨VB￨O￨- consist￨L￨VB￨O￨- in￨L￨IN￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- leads￨L￨VBZ￨O￨- an￨L￨DT￨O￨- integral￨L￨JJ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- an￨L￨DT￨O￨- extreme￨L￨JJ￨O￨- value.Although￨L￨NN￨O￨- some￨L￨DT￨O￨- variational￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- were￨L￨VBD￨O￨- solved￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- special￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- like￨L￨IN￨O￨- Bernoulli￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- brachistochrone￨L￨NN￨O￨- problem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- “￨L￨``￨O￨- Basic￨U￨JJ￨O￨- idea￨L￨NN￨O￨- of￨L￨IN￨O￨- variational￨L￨JJ￨O￨- calculus￨L￨NN￨O￨- ”￨L￨''￨O￨- section￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- so-called￨L￨JJ￨O￨- isoperimetric￨L￨JJ￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- solved￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- ancient￨L￨JJ￨O￨- Greeks￨U￨NNPS￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- Euler￨U￨NNP￨PERSON￨- who￨L￨WP￨O￨- presented￨L￨VBD￨O￨- the￨L￨DT￨O￨- variational￨L￨JJ￨O￨- calculus￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- coherent￨L￨JJ￨O￨- branch￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- by￨L￨IN￨O￨- discovering￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- extremization￨L￨NN￨O￨- curve.As￨L￨NN￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- section￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Euler￨U￨NNP￨PERSON￨- equation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- quite￨L￨RB￨O￨- complicated￨L￨JJ￨O￨- and￨L￨CC￨O￨- impossible￨L￨JJ￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- it￨L￨PRP￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- although￨L￨IN￨O￨- some￨L￨DT￨O￨- applications￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- specific￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- soluble￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- clear￨L￨JJ￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- searching￨L￨VBG￨O￨- for￨L￨IN￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- approximate￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- reason￨L￨NN￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- focused￨L￨VBD￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- approximate￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- nonlinear￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- algebraic￨L￨JJ￨O￨- and￨L￨CC￨O￨- transcendental￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- integro-differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- reported￨L￨VBN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- those￨L￨DT￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- tanh￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- exp-function￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Adomian￨U￨NNP￨O￨- ’s￨L￨POS￨O￨- decomposition￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ADM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- parameter￨L￨NN￨O￨- expansion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- homotopy￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨A method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HPM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- c￨L￨NN￨O￨- ,￨L￨,￨O￨- 2014a￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- 2015b￨L￨NN￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- homotopy￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HAM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- b￨L￨NN￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- series￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Lie￨U￨NN￨O￨- algebra￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- perturbation￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- among￨L￨IN￨O￨- many￨L￨JJ￨O￨- others.A￨L￨NN￨O￨- particularly￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- job￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- deals￨L￨VBZ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- combined￨L￨VBN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Laplace￨U￨NNP￨CITY￨- transform￨L￨VB￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LTM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Adomian￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- decomposition￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ADM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- named￨L￨VBN￨O￨- the￨L￨DT￨O￨- H2LTM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- reference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- text￨L￨NN￨O￨- Pow￨U￨NN￨O￨- Mul￨U￨NN￨O￨- dx￨L￨NN￨O￨- text￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- left￨L￨VBD￨O￨- Mul￨U￨NN￨PERSON￨- right￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- f￨L￨FW￨O￨- partial￨L￨JJ￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- Pow￨U￨NNP￨O￨- y￨L￨NN￨O￨- prime￨L￨JJ￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Derivative￨U￨JJ￨O￨- f￨L￨FW￨O￨- Tuple￨U￨FW￨ORGANIZATION￨- y￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Some￨U￨DT￨O￨- interesting￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- integral￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- curve￨L￨NN￨O￨A joining￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- given￨L￨VBN￨O￨- points￨L￨NNS￨O￨- ,￨L￨,￨O￨- requires￨L￨VBZ￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- curve￨L￨NN￨O￨- that￨L￨WDT￨O￨- generates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- surface￨L￨NN￨O￨- of￨L￨IN￨O￨- revolution￨L￨NN￨O￨- of￨L￨IN￨O￨- smallest￨L￨JJS￨O￨- area￨L￨NN￨O￨- when￨L￨WRB￨O￨- revolves￨L￨VBZ￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- axis￨L￨NN￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- brachistochrone￨L￨NN￨O￨- ,￨L￨,￨O￨- search￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- vertical￨L￨JJ￨O￨- curve￨L￨NN￨O￨- without￨L￨IN￨O￨- friction￨L￨NN￨O￨- that￨L￨WDT￨O￨- joins￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- fixed￨L￨JJ￨O￨- points￨L￨NNS￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨- slides￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- possible￨L￨JJ￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Basic￨U￨JJ￨O￨- idea￨L￨NN￨O￨- of￨L￨IN￨O￨- variational￨L￨JJ￨O￨- calculusThis￨L￨NN￨O￨- paper￨L￨NN￨O￨- deals￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨A a￨L￨DT￨O￨- function￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- y￨L￨NNP￨O￨- y￨L￨NNP￨O￨- x￨L￨NN￨O￨- with￨L￨IN￨O￨- continues￨L￨VBZ￨O￨- second￨L￨JJ￨ORDINAL￨- derivatives￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- an￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- variational￨L￨JJ￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- extreme￨L￨JJ￨O￨- an￨L￨DT￨O￨- integral￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- its￨L￨PRP$￨O￨- graph￨L￨NN￨O￨- join￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- points￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- left￨L￨VBD￨O￨- and￨L￨CC￨O￨- left￨L￨VBD￨O￨- From￨U￨IN￨O￨- variational￨L￨JJ￨O￨- calculus￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- y￨L￨NN￨O￨- x￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- that￨L￨IN￨O￨- satisfies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- requirements￨L￨NNS￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- satisfies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Euler￨U￨NNP￨PERSON￨- equation￨L￨NN￨O￨- .￨L￨.￨O￨- +R.￨U￨NNP￨O￨- Laguna-Camacho8￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 5:276￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- This￨U￨DT￨O￨- article￨L￨NN￨O￨- proposes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- Laplace￨U￨NNP￨ORGANIZATION￨- Transform-Homotopy￨U￨NNP￨ORGANIZATION￨- Perturbation￨U￨NNP￨ORGANIZATION￨- Method￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- modifications￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- analytical￨L￨JJ￨O￨- approximate￨L￨JJ￨O￨A solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- which￨L￨WDT￨O￨- arise￨L￨VBP￨O￨- from￨L￨IN￨O￨- some￨L￨DT￨O￨- variational￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Modeling￨U￨VBG￨MISC￨- immune￨L￨JJ￨O￨A response￨L￨NN￨O￨A and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- dynamicsJorge￨L￨NN￨O￨- Reyes-Silveyra1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Armin￨U￨NNP￨O￨- R.￨U￨NNP￨O￨- 2016Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- In￨U￨IN￨O￨- recent￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- incorporated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- simplified￨L￨VBN￨O￨- value￨L￨NN￨O￨- that￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- immune￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- further￨L￨RB￨O￨- ,￨L￨,￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- collective￨L￨JJ￨O￨- immune￨L￨JJ￨O￨A response￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- contagion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- collective￨L￨JJ￨O￨- immune￨L￨JJ￨O￨A response￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- superposition￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PIR￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- quality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨A response￨L￨NN￨O￨A determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- chances￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- capable￨L￨JJ￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- annual￨L￨JJ￨SET￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- live￨L￨JJ￨O￨A births￨L￨NNS￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- countries￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- live￨L￨JJ￨O￨- births￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- then￨L￨RB￨O￨- calculated￨L￨VBD￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- live￨L￨JJ￨O￨- births￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- region￨L￨NN￨O￨- which￨L￨WDT￨O￨- were￨L￨VBD￨O￨- occurring￨L￨VBG￨O￨- in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- which￨L￨WDT￨O￨- had￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- RCV￨U￨NN￨O￨- by￨L￨IN￨O￨- given￨L￨VBN￨O￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- countries￨L￨NNS￨O￨- had￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- RCV￨U￨NNP￨O￨- nationally￨L￨RB￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- 83￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- three￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- six￨L￨CD￨NUMBER￨- WHO￨U￨WP￨ORGANIZATION￨- regions￨L￨NNS￨O￨- had￨L￨VBD￨O￨- established￨L￨VBN￨O￨- rubella￨L￨NN￨O￨A control/elimination￨L￨NN￨O￨- and￨L￨CC￨O￨- CRS￨U￨NNP￨O￨- prevention/elimination￨L￨NN￨O￨- goals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- catalytic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- the￨L￨DT￨O￨- seroprevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- force￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- susceptibles￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- estimates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- directly￨L￨RB￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- employed￨L￨VBN￨O￨A mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- geographical￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- H7N9￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- human￨L￨JJ￨O￨A case￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- ‘￨L￨``￨O￨- H7N9￨U￨NN￨O￨- ’￨L￨''￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- in￨L￨IN￨O￨- eastern￨L￨JJ￨O￨- China￨U￨NNP￨COUNTRY￨- on￨L￨IN￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- specific￨L￨JJ￨O￨- and￨L￨CC￨O￨- age￨L￨NN￨O￨- adjusted￨L￨VBN￨O￨- mortality￨L￨NN￨O￨A and￨L￨CC￨O￨- morbidity￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ‘￨L￨``￨O￨- severity￨L￨NN￨O￨- ’￨L￨''￨O￨- include￨L￨VBP￨O￨- case-fatality-ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CFR￨U￨NN￨O￨- =￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate/incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- time-to-death￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- survival￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- SR￨U￨NN￨O￨- =￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate/prevalence￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Scholars￨U￨NNS￨O￨- studying￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- beginning￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- 20th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨A proposed￨L￨VBD￨O￨- that￨L￨IN￨O￨- CFR￨U￨NNP￨O￨- and￨L￨CC￨O￨- SR￨U￨JJ￨O￨- followed￨L￨VBD￨O￨- specific￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- where￨L￨WRB￨O￨- CFRs￨U￨NNS￨O￨- typically￨L￨RB￨O￨- were￨L￨VBD￨O￨- markedly￨L￨RB￨O￨- higher￨L￨JJR￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- lost￨L￨VBD￨O￨- momentum￨L￨NN￨O￨- as￨L￨IN￨O￨- CFR￨U￨NN￨O￨- declined￨L￨VBD￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- restated￨L￨VBD￨O￨- the￨L￨DT￨DATE￨- century￨L￨NN￨DATE￨A old￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- i.e.￨L￨FW￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- substantial￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- CFR￨U￨NNP￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- serial￨L￨JJ￨O￨- passage￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- virulence￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- includes￨L￨VBZ￨O￨- ,￨L￨,￨O￨- CFR￨U￨NNP￨O￨- variation￨L￨NN￨O￨- for￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 20th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨A NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- driven￨L￨VBN￨O￨- eradication￨L￨NN￨O￨- of￨L￨IN￨O￨- small￨L￨JJ￨O￨- pox￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- both￨L￨DT￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- CFR￨U￨NN￨ORGANIZATION￨- declined￨L￨VBD￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- disappearance￨L￨NN￨O￨- ’￨L￨''￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Infectious￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- remain￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- of￨L￨IN￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨A in￨L￨IN￨O￨- many￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Collective￨U￨NNP￨O￨- health￨L￨NN￨O￨A behavior￨L￨NN￨O￨- often￨L￨RB￨O￨- demonstrates￨L￨VBZ￨O￨- counter-intuitive￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- sometimes￨L￨RB￨O￨- resisting￨L￨VBG￨O￨- interventions￨L￨NNS￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- change￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- producing￨L￨VBG￨O￨- effects￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- opposite￨L￨JJ￨O￨- direction￨L￨NN￨O￨- than￨L￨IN￨O￨- intended￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- lowering￨L￨VBG￨O￨- infectivity￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- increased￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- I￨U￨PRP￨O￨- compared￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- behavior￨L￨NN￨O￨- game￨L￨NN￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- decide￨L￨VBP￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- adopt￨L￨VB￨O￨- protective￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- microbial-level￨L￨JJ￨O￨- game￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- bacteria￨L￨NNS￨O￨- attack￨L￨VBP￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Resilience￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- tipping￨L￨VBG￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hydra￨L￨NN￨O￨- effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- :￨L￨:￨O￨- emergent￨L￨JJ￨O￨- collective￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- agent-based￨L￨JJ￨O￨- modelsChristopher￨L￨NN￨O￨- Robert￨U￨NNP￨O￨- Keane1Email￨U￨NNP￨O￨- authorBMC￨L￨NNP￨O￨- Public￨U￨NNP￨O￨- HealthBMC￨U￨NNP￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 16:265￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Keane￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- game￨L￨NN￨O￨A ,￨L￨,￨O￨- health￨L￨NN￨O￨- protection￨L￨NN￨O￨- is￨L￨VBZ￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- free-riding￨L￨NN￨O￨- defectors￨L￨NNS￨O￨- ,￨L￨,￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- rise￨L￨NN￨O￨- in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- long-lasting￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- considered￨L￨VBD￨O￨- 19￨L￨CD￨NUMBER￨- test-negative￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- scenarios￨L￨NNS￨O￨- A￨U￨DT￨O￨- –￨L￨:￨O￨- S￨U￨NN￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨O￨- 2B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- corresponded￨L￨VBD￨O￨- to￨L￨TO￨O￨- assumptions￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- test-negative￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- mild￨L￨JJ￨O￨A ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- test-negative￨L￨JJ￨O￨- mild￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- EV71-HFMD￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- test-negative￨L￨JJ￨O￨- severe/fatal￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- EV71-HFMD￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- separate￨L￨JJ￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- TSIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- EV71-HFMD￨U￨NN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- national￨L￨JJ￨O￨- average￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- around￨L￨IN￨O￨- 27￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- indirect￨L￨JJ￨O￨A protection￨L￨NN￨O￨- from￨L￨IN￨O￨- EV71￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unlikely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- significant￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- considered￨L￨VBD￨O￨- only￨L￨RB￨O￨- children￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- 6￨L￨CD￨DURATION￨- mo￨L￨NN￨DURATION￨- to￨L￨TO￨O￨- 5￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 60￨L￨CD￨DURATION￨- mo￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- because￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- 94￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 96￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- mild￨L￨JJ￨O￨A ,￨L￨,￨O￨- severe￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- fatal￨L￨JJ￨O￨- HFMD￨U￨NN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- occur￨L￨VBP￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- those￨L￨DT￨O￨- aged￨L￨JJ￨O￨- 6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 71￨L￨CD￨DURATION￨- mo￨L￨NN￨DURATION￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- such￨L￨JJ￨O￨- an￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- comprising￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- national￨L￨JJ￨O￨- HFMD￨U￨NN￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨A )￨L￨-RRB-￨O￨- HFMD￨U￨NN￨O￨- virological￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- records￨L￨NNS￨O￨- from￨L￨IN￨O￨- all￨L￨DT￨O￨- 31￨L￨CD￨NUMBER￨- provinces￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- nationwide￨L￨JJ￨O￨- caregiver￨L￨NN￨O￨- survey￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- health￨L￨NN￨O￨- utility￨L￨NN￨O￨- loss￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- EV71-HFMD￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- perform￨L￨VB￨O￨- a￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- analysis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CEA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- routine￨L￨JJ￨O￨- pediatric￨L￨JJ￨O￨- EV71￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- indirect￨L￨JJ￨O￨A protection￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- Shiga￨U￨NN￨O￨- toxin-producing￨L￨JJ￨O￨- Escherichia￨U￨FW￨O￨- coli￨L￨FW￨O￨- O104￨U￨NN￨O￨- :￨L￨:￨O￨- H4￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Federal￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Risk￨U￨NNP￨ORGANIZATION￨- Assessment￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- BfR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- initiated￨L￨VBD￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- open-source￨L￨NN￨O￨- software￨L￨NN￨O￨- tool￨L￨NN￨O￨- “￨L￨``￨O￨- FoodChain-Lab￨U￨NNP￨O￨- ”￨L￨''￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- trace-back￨L￨NN￨O￨- and￨L￨CC￨O￨- trace-forward￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- implicated￨L￨VBN￨O￨- feed￨L￨NN￨O￨- or￨L￨CC￨O￨- food￨L￨NN￨O￨A items￨L￨NNS￨O￨- along￨L￨IN￨O￨- supply￨L￨NN￨O￨- chains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Information￨U￨NN￨O￨- on￨L￨IN￨O￨- food￨L￨NN￨O￨A deliveries￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- collated￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- public￨L￨JJ￨O￨- authorities￨L￨NNS￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- errors￨L￨NNS￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- different￨L￨JJ￨O￨- or￨L￨CC￨O￨- misspelled￨L￨VBN￨O￨- names￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- assigned￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- company￨L￨NN￨O￨- or￨L￨CC￨O￨- product￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- redesigned￨L￨VBN￨O￨- with￨L￨IN￨O￨- new￨L￨JJ￨O￨- features￨L￨NNS￨O￨- facilitating￨L￨VBG￨O￨- efficient￨L￨JJ￨O￨- handling￨L￨NN￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- food￨L￨NN￨O￨A trade￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- illustrated￨L￨VBN￨O￨- here￨L￨RB￨O￨- with￨L￨IN￨O￨- examples￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- hepatitis￨L￨NN￨O￨- A￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- another￨L￨DT￨O￨- investigation￨L￨NN￨O￨- managed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- European￨U￨JJ￨ORGANIZATION￨- Food￨U￨NNP￨ORGANIZATION￨- Safety￨U￨NNP￨ORGANIZATION￨- Authority￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- EFSA￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- invited￨L￨VBD￨O￨- BfR￨U￨NN￨O￨- to￨L￨TO￨O￨- scientifically￨L￨RB￨O￨- support￨L￨VB￨O￨A it￨L￨PRP￨O￨- by￨L￨IN￨O￨- making￨L￨VBG￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- FoodChain-Lab￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- equally￨L￨RB￨O￨- important￨L￨JJ￨O￨- ,￨L￨,￨O￨- challenge￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- working￨L￨VBG￨O￨- example￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- students￨L￨NNS￨O￨A to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨- ,￨L￨,￨O￨- implementation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- without￨L￨IN￨O￨- needing￨L￨VBG￨O￨- to￨L￨TO￨O￨- acquire￨L￨VB￨O￨- expertise￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- daunting￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modeling￨L￨NN￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- invaluable￨L￨JJ￨O￨- tool￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- providing￨L￨VBG￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- periodic￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- un￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- natural￨L￨JJ￨O￨- zombie￨L￨NN￨O￨- histories￨L￨NNS￨O￨- in￨L￨IN￨O￨- popular￨L￨JJ￨O￨- culture￨L￨NN￨O￨A ,￨L￨,￨O￨- instructors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- flexibility￨L￨NN￨O￨- to￨L￨TO￨O￨- cover￨L￨VB￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- without￨L￨IN￨O￨- deviating￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- zombie￨L￨NN￨O￨- mythos￨L￨NNS￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- chief￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- in￨L￨IN￨O￨- teaching￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- to￨L￨TO￨O￨- students￨L￨NNS￨O￨A in￨L￨IN￨O￨- biology￨L￨NN￨O￨- or￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- popularity￨L￨NN￨O￨- of￨L￨IN￨O￨- zombie￨L￨NN￨O￨- fiction￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- an￨L￨DT￨O￨- obvious￨L￨JJ￨O￨A topic￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- classroom￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- analyses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- relied￨L￨VBN￨O￨A on￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- SMSY￨U￨NNP￨O￨- via￨L￨IN￨O￨- Hilborn￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- 1985￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- linear￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- when￨L￨WRB￨O￨- calculating￨L￨VBG￨O￨- optimal￨L￨JJ￨O￨- yield￨L￨NN￨O￨- profiles￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- observation￨L￨NN￨O￨- error￨L￨NN￨O￨- on￨L￨IN￨O￨- biases￨L￨NNS￨O￨- in￨L￨IN￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- test￨L￨NN￨O￨- I￨U￨PRP￨O￨- randomly￨L￨RB￨O￨- selected￨L￨VBD￨O￨- 1,000￨L￨CD￨NUMBER￨- values￨L￨NNS￨O￨- each￨L￨DT￨O￨- for￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- a￨L￨DT￨O￨- ≤￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 10￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- 5￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- b￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- 10￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- solved￨L￨VBD￨O￨A for￨L￨IN￨O￨- SMSY￨U￨NN￨O￨- using￨L￨VBG￨O￨- both￨L￨CC￨O￨- Newton￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- method￨L￨NN￨O￨- as￨L￨IN￨O￨- suggested￨L￨VBN￨O￨- by￨L￨IN￨O￨- Ricker￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1975￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Halley￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- method￨L￨NN￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- write￨L￨VB￨O￨- We￨U￨PRP￨O￨- now￨L￨RB￨DATE￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨A solution￨L￨NN￨O￨- for￨L￨IN￨O￨- SMSY￨U￨NN￨O￨- that￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- a￨L￨DT￨O￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- from￨L￨IN￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- I￨U￨PRP￨O￨- make￨L￨VBP￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Lambert￨U￨NNP￨PERSON￨- W￨U￨NNP￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- W￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨A solution￨L￨NN￨O￨- to￨L￨TO￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +Methodology￨U￨NNP￨O￨- Article￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Learning￨U￨NNP￨O￨- stochastic￨L￨JJ￨O￨- process-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- from￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- and￨L￨CC￨O￨- dataJovan￨L￨NN￨O￨- Tanevski1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Ljupčo￨U￨NNP￨O￨- Todorovski3￨U￨NNP￨O￨- and￨L￨CC￨O￨- Sašo￨U￨NNP￨O￨- Džeroski1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2BMC￨L￨NNP￨O￨- Systems￨U￨NNPS￨O￨- BiologyBMC￨U￨NNP￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 10:30￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Identifying￨U￨VBG￨O￨- a￨L￨DT￨O￨- proper￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- address￨L￨VBP￨O￨- both￨L￨DT￨O￨- structural￨L￨JJ￨O￨- and￨L￨CC￨O￨- parameter￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- problem￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- systems￨L￨NNS￨O￨- approach￨L￨VBP￨O￨- to￨L￨TO￨O￨- biology￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- process-based￨L￨JJ￨O￨- modeling￨L￨NN￨O￨A methods￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- flexible￨L￨JJ￨O￨- modular￨L￨JJ￨O￨- formalisms￨L￨NNS￨O￨- for￨L￨IN￨O￨- specifying￨L￨VBG￨O￨- large￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- of￨L￨IN￨O￨- plausible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- structures￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- their￨L￨PRP$￨O￨- scope￨L￨NN￨O￨- is￨L￨VBZ￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- many￨L￨JJ￨O￨- existing￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- integrate￨L￨VBP￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- simulation￨L￨NN￨O￨- and￨L￨CC￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- parameter￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A ,￨L￨,￨O￨- only￨L￨RB￨O￨- few￨L￨JJ￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- address￨L￨VBP￨O￨- structural￨L￨JJ￨O￨- uncertainty￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- combine￨L￨VBP￨O￨- the￨L￨DT￨O￨- flexibility￨L￨NN￨O￨- of￨L￨IN￨O￨- process-based￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- addressing￨L￨VBG￨O￨- structural￨L￨JJ￨O￨- uncertainty￨L￨NN￨O￨A with￨L￨IN￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- at￨L￨IN￨O￨- extending￨L￨VBG￨O￨- the￨L￨DT￨O￨- scope￨L￨NN￨O￨- of￨L￨IN￨O￨- process-based￨L￨JJ￨O￨- modeling￨L￨NN￨O￨A methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- inductively￨L￨RB￨O￨- learn￨L￨VB￨O￨- stochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- from￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- which￨L￨WDT￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- :￨L￨:￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- effectively￨L￨RB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- online￨L￨JJ￨O￨- communication￨L￨NN￨O￨- network￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- real-world￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- system￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- physical￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- works￨L￨NNS￨O￨- on￨L￨IN￨O￨- modeling￨L￨NN￨O￨- epidemic-like￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- with￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- roles￨L￨NNS￨O￨- played￨L￨VBN￨O￨- by￨L￨IN￨O￨- community￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- affecting￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- community￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- discovered￨L￨VBD￨O￨- the￨L￨DT￨O￨- emergency￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- metacritical￨L￨JJ￨O￨- point￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨A network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- UAU￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- work￨L￨NN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- previous￨L￨JJ￨O￨- works￨L￨NNS￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- taken￨L￨VBN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨A structure￨L￨NN￨O￨A of￨L￨IN￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- into￨L￨IN￨O￨- consideration￨L￨NN￨O￨- .￨L￨.￨O￨- +Interestingly￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- examples￨L￨NNS￨O￨- the￨L￨DT￨O￨- meme￨L￨NN￨O￨- popularity￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- randomly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- meme￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- selected￨L￨VBN￨O￨- n￨L￨NN￨O￨- times￨L￨NNS￨O￨- for￨L￨IN￨O￨- being￨L￨VBG￨O￨- forwarded￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- connected￨L￨JJ￨O￨A neighbors￨L￨NNS￨O￨- ,￨L￨,￨O￨- scales￨L￨NNS￨O￨- approximately￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- power-law4510￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- criticality￨L￨NN￨O￨- .￨L￨.￨O￨- +Even￨U￨RB￨O￨- though￨L￨IN￨O￨- the￨L￨DT￨O￨- heavy-tailed￨L￨JJ￨O￨- distribution￨L￨NN￨O￨A of￨L￨IN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- α￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- those￨L￨DT￨O￨- models￨L￨NNS￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- conditions4510￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- suggested￨L￨VBN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- far￨L￨RB￨O￨- from￨L￨IN￨O￨- describing￨L￨VBG￨O￨- meme￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- on￨L￨IN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- networks￨L￨NNS￨O￨- properly￨L￨RB￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- growing￨L￨VBG￨O￨A network￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- meme￨L￨NN￨O￨- popularity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- various￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- meme￨L￨NN￨O￨- on￨L￨IN￨O￨- many￨L￨JJ￨O￨- real￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- growth￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- meme￨L￨NN￨O￨- popularity￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- CIC￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- growing￨L￨VBG￨O￨A networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- CICGN￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- Report￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- their￨L￨PRP$￨O￨- important￨L￨JJ￨O￨- conceptual￨L￨JJ￨O￨- difference￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- CTMC￨U￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- state￨L￨NN￨O￨- transition￨L￨NN￨O￨- type￨L￨NN￨O￨- occurring￨L￨VBG￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- combined￨L￨JJ￨O￨- linear￨L￨JJ￨O￨- rate￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- term￨L￨NN￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- immigration￨L￨NN￨O￨A and￨L￨CC￨O￨- a￨L￨DT￨O￨- term￨L￨NN￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- births￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- versions￨L￨NNS￨O￨- we￨L￨PRP￨O￨- incorporate￨L￨VBP￨O￨- births￨L￨NNS￨O￨- ,￨L￨,￨O￨- deaths￨L￨NNS￨O￨- and￨L￨CC￨O￨- immigration￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- class￨L￨NN￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- conceptually￨L￨RB￨O￨- distinguish￨L￨VBP￨O￨- between￨L￨IN￨O￨- births￨L￨NNS￨O￨- and￨L￨CC￨O￨- immigration￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- immigration￨L￨NN￨O￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- births￨L￨NNS￨O￨- rates￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- birth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- proportional￨L￨JJ￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- way￨L￨NN￨O￨- requiring￨L￨VBG￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- individual￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨- have￨L￨VBP￨O￨- absorbing￨L￨VBG￨O￨- states￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- quasi-stationary￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- are￨L￨NN￨O￨- of￨L￨IN￨O￨- major￨L￨JJ￨O￨- interest￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- consider￨L￨VB￨O￨- SI￨U￨NNP￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- births￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- immigration￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- generalized￨L￨VBN￨O￨- versions￨L￨NNS￨O￨A of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- SI￨U￨NNP￨O￨- ,￨L￨,￨O￨- SIS￨U￨NNP￨O￨- ,￨L￨,￨O￨- SIR￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- SIRS￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- are￨L￨VBP￨O￨- classified￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- terminology￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- as￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- much￨L￨RB￨O￨- lower￨L￨JJR￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- season￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- likely￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- relatively￨L￨RB￨O￨- high￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- influential￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- static￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- aggregated￨L￨VBN￨O￨- by￨L￨IN￨O￨- season￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- true￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- season￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- previously￨L￨RB￨DATE￨- estimated￨L￨VBD￨O￨- that￨L￨IN￨O￨- only￨L￨RB￨O￨- 4￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Finnish￨U￨JJ￨NATIONALITY￨- population￨L￨NN￨O￨- were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pdm09￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 2010￨L￨CD￨DATE￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- 1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 2011￨L￨CD￨DATE￨- season￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- properly￨L￨RB￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- mitigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- first-season￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- lowering￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- season￨L￨NN￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- dynamic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- needed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- 74-81￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- aged￨L￨VBN￨O￨- less￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- 15￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- vaccinated￨L￨VBN￨O￨- against￨L￨IN￨O￨- A￨U￨DT￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pdm09￨L￨NN￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- season￨L￨NN￨O￨A .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- pathogenic￨L￨JJ￨O￨- for￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- heavily￨L￨RB￨O￨- populated￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- arbovirus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- widespread￨L￨JJ￨O￨- and￨L￨CC￨O￨- serious￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- constitute￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- problems￨L￨NNS￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- tropical￨L￨JJ￨O￨- and￨L￨CC￨O￨- subtropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- where￨L￨WRB￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- appropriate￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- vectors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- present￨L￨JJ￨DATE￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- way￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- abiotic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- abiotic￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- allowed￨L￨VBD￨O￨- to￨L￨TO￨O￨- vary￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨- of￨L￨IN￨O￨- abiotic￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- entomological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- transition￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- aquatic￨L￨JJ￨O￨- phase￨L￨NN￨O￨- ,￨L￨,￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- adult￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨A and￨L￨CC￨O￨- oviposition￨L￨NN￨O￨- rate￨L￨NN￨O￨- vary￨L￨VBP￨O￨- with￨L￨IN￨O￨- temperature￨L￨NN￨O￨- NumericCitation￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- aim￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonally￨L￨RB￨O￨- varying￨L￨VBG￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- precipitation￨L￨NN￨O￨- in￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A epidemics￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A recorded￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- City￨U￨NN￨O￨- of￨L￨IN￨O￨- Campinas￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- for￨L￨IN￨O￨- transmitting￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- successfully￨L￨RB￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- i-th￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- person￨L￨NN￨O￨A per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +That￨U￨DT￨O￨- are￨L￨VBP￨O￨- identical￨L￨JJ￨O￨- means￨L￨NNS￨O￨- that￨L￨WDT￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- equal￨L￨JJ￨O￨- chance￨L￨NN￨O￨A of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- equal￨L￨JJ￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- homogeneous-mixing￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- traditional￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- usually￨L￨RB￨O￨- assume￨L￨VBP￨O￨- homogeneous￨L￨JJ￨O￨A mixing￨L￨VBG￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- others￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- varies￨L￨VBZ￨O￨- from￨L￨IN￨O￨- person￨L￨NN￨O￨A to￨L￨TO￨O￨- person￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- heterogeneous￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Bipolar￨U￨JJ￨O￨- disorder￨L￨NN￨O￨A affects￨L￨VBZ￨O￨- approximately￨L￨RB￨O￨- 1.2￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- worldwide￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- differs￨L￨VBZ￨O￨- from￨L￨IN￨O￨- MD￨U￨NN￨STATE_OR_PROVINCE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- hallmark￨L￨NN￨O￨- of￨L￨IN￨O￨- mania￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- elevated￨L￨JJ￨O￨- mood￨L￨NN￨O￨- or￨L￨CC￨O￨- euphoria￨L￨NN￨O￨- ,￨L￨,￨O￨- hyper-activity￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- sleep￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- optimism￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- frequently￨L￨RB￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- deficit￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- ’s￨L￨POS￨O￨- judgment￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Biomarkers￨U￨NNS￨O￨- should￨L￨MD￨O￨- also￨L￨RB￨O￨- provide￨L￨VB￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- sensitivity￨L￨NN￨O￨- and￨L￨CC￨O￨- specificity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- >￨L￨JJR￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- classification￨L￨NN￨O￨- of￨L￨IN￨O￨- MD￨U￨NN￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- BPD￨U￨NN￨O￨- and￨L￨CC￨O￨- psychotic￨L￨JJ￨O￨- disorders￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- clinically￨L￨RB￨O￨A useful￨L￨JJ￨O￨- .￨L￨.￨O￨- +Major￨U￨JJ￨TITLE￨- depression￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MD￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- bipolar￨L￨JJ￨O￨- disorder￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- BPD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- psychotic￨L￨JJ￨O￨- disorders￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- schizophrenia￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- misdiagnosed￨L￨JJ￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- inadequate￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- and￨L￨CC￨O￨- devastating￨L￨VBG￨O￨- consequences￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- conceptual￨L￨JJ￨O￨- improvement￨L￨NN￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- heterogeneous￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- face￨L￨NN￨O￨- of￨L￨IN￨O￨- previous￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- assumed￨L￨VBD￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- separated￨L￨VBN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- base￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- formalism￨L￨NN￨O￨- on￨L￨IN￨O￨- elementary￨L￨JJ￨O￨- matrix￨L￨NN￨O￨- operations￨L￨NNS￨O￨- with￨L￨IN￨O￨- Boolean￨U￨JJ￨MISC￨- arithmetic￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨A us￨L￨PRP￨O￨- to￨L￨TO￨O￨- integrate￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- unified￨L￨VBN￨O￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- allows￨L￨VBZ￨O￨A us￨L￨PRP￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- numerous￨L￨JJ￨O￨- advances￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A modelling￨L￨NN￨O￨A ,￨L￨,￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- allowed￨L￨VBD￨O￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- other￨L￨JJ￨O￨- words￨L￨NNS￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- accessibility￨L￨NN￨O￨- graph￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- information￨L￨NN￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- path￨L￨NN￨O￨- connects￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- time￨L￨NN￨O￨A period￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- product￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- makes￨L￨NNS￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- via￨L￨IN￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- divided￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- simply￨L￨RB￨O￨- the￨L￨DT￨O￨- inverse￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- timescale￨L￨NN￨O￨- over￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- T￨U￨NN￨O￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- also￨L￨RB￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- r0￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- completely￨L￨RB￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- S0￨U￨NN￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- interacting￨L￨VBG￨O￨- cities￨L￨NNS￨O￨A linked￨L￨VBN￨O￨- via￨L￨IN￨O￨- implied￨L￨VBN￨O￨- transportation￨L￨NN￨O￨- routes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- coupling￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- contribute￨L￨VBP￨O￨- to￨L￨TO￨O￨- tradeoffs￨L￨NNS￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- determine￨L￨VBP￨O￨- optimal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- allocation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- weakly￨L￨RB￨O￨- coupled￨L￨VBN￨O￨- ,￨L￨,￨O￨- stochasticity￨L￨NN￨O￨- can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- spreading￨L￨VBG￨O￨- from￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- cities￨L￨NNS￨O￨A to￨L￨TO￨O￨- uninfected￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- longer￨L￨JJR￨O￨- time￨L￨NN￨O￨- frame￨L￨NN￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- purely￨L￨RB￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨- can￨L￨MD￨O￨- change￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategy￨L￨NN￨O￨- which￨L￨WDT￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- fewest￨L￨JJS￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- greatly￨L￨RB￨O￨- impacting￨L￨VBG￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- cities￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- until￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- lead￨L￨NN￨O￨- to￨L￨TO￨O￨- tradeoffs￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- dictate￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- of￨L￨IN￨O￨- distributing￨L￨VBG￨O￨- limited￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- sophisticated￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- derived￨L￨VBN￨O￨- for￨L￨IN￨O￨- models￨L￨NNS￨O￨- containing￨L￨VBG￨O￨- additional￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- detail￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- more￨L￨RBR￨O￨- refined￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- well-known￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- simple￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- I￨U￨PRP￨O￨- *￨L￨SYM￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- estimation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- instead￨L￨RB￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- existing￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Uganda￨U￨NNP￨COUNTRY￨- that￨L￨WDT￨O￨- killed￨L￨VBD￨O￨- 224￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- how￨L￨WRB￨O￨- presymptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- affects￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- will￨L￨MD￨O￨- go￨L￨VB￨O￨- on￨L￨IN￨O￨- to￨L￨TO￨O￨- cause￨L￨VB￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Crucially￨U￨RB￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- approximation￨L￨NN￨O￨- above￨L￨IN￨O￨- illustrates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨- require￨L￨VBP￨O￨- knowledge￨L￨NN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- currently￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- *￨L￨SYM￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- therefore￨L￨RB￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- held￨L￨VBN￨O￨- constant￨L￨JJ￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- sufficiently￨L￨RB￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- decrease￨L￨VBP￨O￨A to￨L￨TO￨O￨- constant￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- r￨L￨NN￨O￨- blocks￨L￨NNS￨O￨- would￨L￨MD￨O￨- oscillate￨L￨VB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- weakly￨L￨RB￨O￨- dampened￨L￨VBN￨O￨- oscillation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reach￨L￨VB￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- EVD￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- overwhelming￨L￨JJ￨O￨- and￨L￨CC￨O￨- posed￨L￨VBD￨O￨- a￨L￨DT￨O￨- serious￨L￨JJ￨O￨- threat￨L￨NN￨O￨- to￨L￨TO￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- ineffective￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- early-onset￨L￨JJ￨O￨- stage￨L￨NN￨O￨- ,￨L￨,￨O￨- local￨L￨JJ￨O￨- funeral￨L￨JJ￨O￨- customs￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- weak￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- prevention￨L￨NN￨O￨A measures￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- any￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- control￨L￨NN￨O￨- or￨L￨CC￨O￨- prevention￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- number￨L￨NN￨O￨- would￨L￨MD￨O￨- decrease￨L￨VB￨O￨A rapidly￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- constructed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- well￨L￨RB￨O￨- fitted￨L￨JJ￨O￨- and￨L￨CC￨O￨- demonstrated￨L￨VBD￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- effective￨L￨JJ￨O￨- for￨L￨IN￨O￨- prediction￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Changes￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨A number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- A￨U￨NNP￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Liberia￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- C￨U￨NNP￨O￨- ,￨L￨,￨O￨- D￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- E￨U￨NNP￨O￨- ,￨L￨,￨O￨- F￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- NPM￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ELNPM￨U￨NN￨O￨- permits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- coexistence￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- prion￨L￨NN￨O￨- strains.KeywordsNucleated￨L￨JJ￨O￨- polymerization￨L￨NN￨O￨- Prions￨U￨NNS￨O￨- Protein￨U￨NN￨O￨- aggregation￨L￨NN￨O￨- Protein￨U￨NN￨O￨- misfolding￨L￨NN￨O￨- Yeast￨U￨NN￨O￨- Electronic￨U￨JJ￨O￨- supplementary￨L￨JJ￨O￨A materialThe￨L￨NN￨O￨- online￨L￨NN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- doi￨L￨FW￨O￨- :￨L￨:￨O￨- 10.1007￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- s00285-015-0921-0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- contains￨L￨VBZ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- authorized￨L￨VBN￨O￨- users.Research￨L￨NN￨O￨- sponsored￨L￨VBN￨O￨- in￨L￨IN￨O￨- part￨L￨NN￨O￨- by￨L￨IN￨O￨- NSF￨U￨NNP￨ORGANIZATION￨- INSPIRE￨U￨VB￨O￨- Grant￨U￨NNP￨O￨- #￨L￨#￨MONEY￨- 1344279￨L￨CD￨MONEY￨- to￨L￨TO￨O￨- JD￨U￨NNP￨O￨- and￨L￨CC￨O￨- SS￨U￨NNP￨O￨- and￨L￨CC￨O￨- NIH￨U￨NNP￨ORGANIZATION￨- Grant￨U￨NNP￨O￨- 5R01GM100740￨L￨NN￨O￨- to￨L￨TO￨O￨- SS.Mathematics￨U￨NNS￨O￨- Subject￨U￨JJ￨O￨- Classification92B05￨U￨NN￨O￨- 92C45￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionThe￨U￨NNP￨O￨- central￨L￨JJ￨O￨- dogma￨L￨NN￨O￨- of￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- biology￨L￨NN￨O￨- stipulates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- phenotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- organism￨L￨NN￨O￨- ’s￨L￨POS￨O￨- expressed￨L￨VBN￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- genotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vertically￨L￨RB￨O￨- transmitted￨L￨JJ￨O￨- DNA￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Further￨U￨JJ￨O￨- experimental￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- demonstrated￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- phenotypic￨L￨JJ￨O￨- states￨L￨NNS￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- DNA￨U￨NN￨O￨- but￨L￨CC￨O￨- were￨L￨VBD￨O￨- the￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- misfolded￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- prion￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- protein￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dominant￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- prion￨L￨NN￨O￨- aggregate￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- nucleated￨L￨JJ￨O￨- polymerization￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- NPM￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- normal￨L￨JJ￨O￨- protein￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- aggregates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 72￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 1555￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1578￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asA￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- prion￨L￨NN￨O￨- aggregates￨L￨NNS￨O￨- with￨L￨IN￨O￨- chaperone-mediated￨L￨JJ￨O￨- fragmentationAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsJason￨L￨NN￨O￨- K￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- widely￨L￨RB￨O￨- estimated￨L￨VBN￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- other￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- application￨L￨NN￨O￨- in￨L￨IN￨O￨- delineating￨L￨VBG￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- –￨L￨:￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- preventive￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- containing￨L￨VBG￨O￨- HFMD￨U￨NN￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- limited￨L￨VBN￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- distinguish￨L￨VB￨O￨- the￨L￨DT￨O￨- pathogenic￨L￨JJ￨O￨- HFMD￨U￨NN￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- asymptomatic￨L￨JJ￨O￨A but￨L￨CC￨O￨- still￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- attributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- of￨L￨IN￨O￨- serotypes￨L￨NNS￨O￨- as￨L￨IN￨O￨- indicated￨L￨VBN￨O￨- above￨L￨IN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- cope￨L￨VB￨O￨- with￨L￨IN￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- modified￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- symptomatic￨L￨JJ￨O￨A and￨L￨CC￨O￨- severe￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- governing￨L￨VBG￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- from￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- HFMD￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- with￨L￨IN￨O￨- severe￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- back-estimate￨L￨JJ￨O￨- symptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- asymptomatic￨L￨JJ￨O￨A but￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- completely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- made￨L￨VBD￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- wave￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- on￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- to￨L￨TO￨O￨- train￨L￨VB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- asymptomatic￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- symptomatic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- until￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- sequelae￨L￨NN￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- HFMD￨U￨NN￨O￨- ,￨L￨,￨O￨- herpangina￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- severe￨L￨JJ￨O￨- HFMD￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- clinically￨L￨RB￨O￨- distinguish￨L￨VB￨O￨- between￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- EV71￨U￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- CVA16￨U￨NN￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- mention￨L￨VB￨O￨- the￨L￨DT￨O￨- asymptomatic￨L￨JJ￨O￨A but￨L￨CC￨O￨- still￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- HFMD￨U￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Assuming￨U￨VBG￨O￨- that￨L￨DT￨O￨- mosquitoes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- constant￨L￨JJ￨O￨- activity￨L￨NN￨O￨- for￨L￨IN￨O￨- only￨L￨RB￨O￨- 90￨L￨CD￨DURATION￨A days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- five￨L￨CD￨NUMBER￨- potential￨L￨JJ￨O￨- countermeasures￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- restricted￨L￨JJ￨O￨- movement￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- insecticide￨L￨NN￨O￨- application￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- repellents￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- what￨L￨WP￨O￨- conditions￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- urban￨L￨JJ￨O￨- city￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Tokyo￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- vectors￨L￨NNS￨O￨A are￨L￨VBP￨O￨- active￨L￨JJ￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- summer￨L￨NN￨DATE￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- little￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- around￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- Measure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- monotonically￨L￨RB￨O￨- decreases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- for￨L￨IN￨O￨- 90￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- moderate￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- for￨L￨IN￨O￨- 90￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- are￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- five￨L￨CD￨NUMBER￨- countermeasures￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- Measures￨U￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- for￨L￨IN￨O￨- 90￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- substantially￨L￨RB￨O￨- for￨L￨IN￨O￨- small￨L￨JJ￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- potential￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- like￨L￨IN￨O￨- this￨L￨DT￨O￨- could￨L￨MD￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Predicting￨U￨VBG￨O￨- or￨L￨CC￨O￨- investigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- that￨L￨IN￨O￨- different￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- rate/rhythm￨L￨FW￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- ablation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨A of￨L￨IN￨O￨- AF￨U￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- drivers￨L￨NNS￨O￨- of￨L￨IN￨O￨- progression￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- exploited￨L￨VBN￨O￨- by￨L￨IN￨O￨- new￨L￨JJ￨O￨- therapeutic￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- measuring￨L￨NN￨O￨- and￨L￨CC￨O￨- quantifying￨L￨VBG￨O￨- progression￨L￨NN￨O￨- in￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- remote￨L￨JJ￨O￨- monitoring￨L￨NN￨O￨- and￨L￨CC￨O￨- tele-health￨L￨NN￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- output￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- AF￨U￨NN￨O￨- episodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- span￨L￨NN￨O￨- of￨L￨IN￨O￨- decades￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- progression￨L￨NN￨O￨A starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- short￨L￨JJ￨O￨- intermittent￨L￨JJ￨O￨- episodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- AF￨U￨NN￨O￨- that￨L￨WDT￨O￨- gradually￨L￨RB￨O￨- become￨L￨VBP￨O￨- longer￨L￨RBR￨O￨- until￨L￨IN￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- is￨L￨VBZ￨O￨- either￨L￨CC￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- AF￨U￨NN￨O￨- or￨L￨CC￨O￨- dies￨L￨VBZ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- practice￨L￨NN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- determine￨L￨VB￨O￨- a￨L￨DT￨O￨- patient￨L￨NN￨O￨- ’s￨L￨POS￨O￨- status￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- classification￨L￨NN￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- monitoring￨L￨NN￨O￨- and￨L￨CC￨O￨- detailed￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- initiation￨L￨NN￨O￨- and￨L￨CC￨O￨- termination￨L￨NN￨O￨- of￨L￨IN￨O￨- AF￨U￨NN￨O￨- episodes￨L￨NNS￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- required￨L￨VBN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- additional￨L￨JJ￨O￨- classification￨L￨NN￨O￨A of￨L￨IN￨O￨- longstanding￨L￨JJ￨O￨- persistent￨L￨JJ￨O￨- AF￨U￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- used￨L￨VBN￨O￨- clinically￨L￨RB￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- those￨L￨DT￨O￨- patients￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- episodes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- continued￨L￨VBN￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- 1￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- this￨L￨DT￨O￨- term￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- used￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- NICE￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- National￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Care￨U￨NNP￨ORGANIZATION￨- Excellence￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- clinical￨L￨JJ￨O￨- guidelines￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- increased￨L￨VBN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- excitation￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- episodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- AF￨U￨NN￨O￨- acts￨L￨VBZ￨O￨A to￨L￨TO￨O￨- increase￨L￨VB￨O￨- vulnerability￨L￨NN￨O￨- to￨L￨TO￨O￨- further￨L￨JJ￨O￨- episodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- AF-induced￨U￨JJ￨O￨- remodelling￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- put￨L￨VBD￨O￨- forward￨L￨RB￨O￨- a￨L￨DT￨O￨- non-uniform￨L￨JJ￨O￨- sampling￨L￨NN￨O￨A method￨L￨NN￨O￨- that￨L￨WDT￨O￨- favors￨L￨VBZ￨O￨- sampling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- sampled￨L￨VBN￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- sampled￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- obtained￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- friendship￨L￨NN￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- understanding￨L￨VBG￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- outcomes￨L￨NNS￨O￨- between￨L￨IN￨O￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- friendship￨L￨NN￨O￨- data￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- biases￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- sampling￨L￨NN￨O￨A process￨L￨NN￨O￨- might￨L￨MD￨O￨- then￨L￨RB￨O￨- give￨L￨VB￨O￨- hints￨L￨NNS￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- compensate￨L￨VB￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- biases￨L￨NNS￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- contained￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- friendship￨L￨NN￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- accurate￨L￨JJ￨O￨- prediction￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- risk￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spirit￨L￨NN￨O￨- of￨L￨IN￨O￨- ref￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- show￨L￨VB￨O￨- how￨L￨WRB￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- using￨L￨VBG￨O￨- friendship￨L￨NN￨O￨- data￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- underestimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- risk￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A measured￨L￨VBN￨O￨- using￨L￨VBG￨O￨- wearable￨L￨JJ￨O￨- sensors￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expected￨L￨VBN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- participation￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- weak￨L￨JJ￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- friendship￨L￨NN￨O￨- surveys￨L￨NNS￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- ask￨L￨VBP￨O￨- if￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- friendship￨L￨NN￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- sampling￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- consider￨L￨VBP￨O￨- several￨L￨JJ￨O￨- sampling￨L￨NN￨O￨A procedures￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- sampled￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- friendship￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- 56￨L￨CD￨NUMBER￨A real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- studied￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- DMP￨U￨NN￨O￨- method￨L￨NN￨O￨- performs￨L￨VBZ￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- cases￨L￨NNS￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- topology￨L￨NN￨O￨- and￨L￨CC￨O￨- many￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- neighbors￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- localized￨L￨JJ￨O￨- eigenvector￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacent￨L￨JJ￨O￨- matrix￨L￨NN￨O￨- the￨L￨DT￨O￨- QMF￨U￨NN￨O￨- method￨L￨NN￨O￨- often￨L￨RB￨O￨- deviates￨L￨VBZ￨O￨- from￨L￨IN￨O￨- accurate￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- values￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- eigenvector￨L￨JJ￨O￨- localized￨L￨JJ￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- k-core￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- positive￨L￨JJ￨O￨- degree-degree￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- high￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- by￨L￨IN￨O￨- MFL￨U￨NN￨ORGANIZATION￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- accurate￨L￨JJ￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- from￨L￨IN￨O￨- other￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- the￨L￨DT￨O￨- MFL￨U￨NN￨ORGANIZATION￨- method￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- sole￨L￨JJ￨O￨- input￨L￨NN￨O￨- parameter￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- relationships￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- differing￨L￨VBG￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- MFL￨U￨NN￨ORGANIZATION￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- QMF￨U￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- DMP￨U￨NN￨O￨- method￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- which￨L￨WDT￨O￨- more￨L￨RBR￨O￨- closely￨L￨RB￨O￨- describes￨L￨VBZ￨O￨- real-world￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- uncorrelated￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- 56￨L￨CD￨NUMBER￨A real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- MFL￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- DMP￨U￨NN￨O￨- methods￨L￨NNS￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- uncorrelated￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- value￨L￨NN￨O￨- is￨L￨VBZ￨O￨- larger￨L￨JJR￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- QMF￨U￨NN￨O￨- method￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- pediatric￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- symptoms￨L￨NNS￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- include￨L￨VB￨O￨- vomiting￨L￨NN￨O￨- and￨L￨CC￨O￨- diarrhea￨L￨NN￨O￨- .4￨L￨CD￨NUMBER￨- Although￨U￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- commonly￨L￨RB￨O￨- self-limiting￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- progress￨L￨VB￨O￨- to￨L￨TO￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A pneumonia￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- .5￨L￨CD￨NUMBER￨- Influenza-associated￨U￨JJ￨O￨- deaths￨L￨NNS￨O￨- in￨L￨IN￨O￨- USA￨U￨NNP￨COUNTRY￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 0.4￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- 100,000￨L￨CD￨NUMBER￨- persons￨L￨NNS￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- as￨L￨RB￨O￨- high￨L￨JJ￨O￨- as￨L￨IN￨O￨- 17￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- per￨L￨IN￨O￨- 100,000￨L￨CD￨NUMBER￨- persons￨L￨NNS￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- in￨L￨IN￨O￨- those￨L￨DT￨O￨- over￨L￨IN￨O￨- 65￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- .6￨L￨CD￨NUMBER￨- Taubenberger￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Morens￨U￨NNP￨PERSON￨- reviewed￨L￨VBN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemics￨L￨NNS￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨DATE￨- year￨L￨NN￨DATE￨- 1500￨L￨CD￨DATE￨- and￨L￨CC￨O￨- noted￨L￨VBD￨O￨- that￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemics￨L￨NNS￨O￨- often￨L￨RB￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- greater-than-expected￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- even￨L￨RB￨O￨- among￨L￨IN￨O￨- those￨L￨DT￨O￨- without￨L￨IN￨O￨- comorbid￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- .7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- illustrated￨L￨VBD￨O￨- the￨L￨DT￨O￨- rapidity￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- strain￨L￨NN￨O￨- can￨L￨MD￨O￨- develop￨L￨VB￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- limitations￨L￨NNS￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- rapid￨L￨JJ￨O￨- point-of-care￨L￨JJ￨O￨- testing￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .8￨L￨CD￨NUMBER￨- Because￨U￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- causes￨L￨VBZ￨O￨- significant￨L￨JJ￨O￨- morbidity￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- fatal￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- often￨L￨RB￨O￨- presents￨L￨VBZ￨O￨- with￨L￨IN￨O￨- new￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- advance￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- of￨L￨IN￨O￨- value￨L￨NN￨O￨- in￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- timely￨L￨JJ￨O￨- preventive￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- planning￨L￨NN￨O￨- and￨L￨CC￨O￨- interventions￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- when￨L￨WRB￨O￨- outbreaks￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- large￨L￨JJ￨O￨- enough￨L￨RB￨O￨- to￨L￨TO￨O￨- challenge￨L￨VB￨O￨- or￨L￨CC￨O￨- overwhelm￨L￨VB￨O￨- medical￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- facilities￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- trained￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- metric￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- referred￨L￨VBD￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- ILI￨U￨NN￨O￨- +￨L￨CC￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- defined￨L￨VBD￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- product￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- Google￨U￨NNP￨ORGANIZATION￨- Flu￨U￨NNP￨CAUSE_OF_DEATH￨- Trends￨U￨NNPS￨O￨- estimate￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- estimate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- laboratory￨L￨NN￨O￨- data￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- presenting￨L￨VBG￨O￨- with￨L￨IN￨O￨- ILI￨U￨NN￨O￨- who￨L￨WP￨O￨- actually￨L￨RB￨O￨- have￨L￨VBP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Shaman￨U￨NNP￨O￨- et￨L￨FW￨O￨- al13￨L￨FW￨O￨- published￨L￨VBN￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- weeks￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A using￨L￨VBG￨O￨- ensembles￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBD￨O￨- –￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- included￨L￨VBD￨O￨- adjusting￨L￨VBG￨O￨- for￨L￨IN￨O￨- absolute￨L￨JJ￨O￨- humidity￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- models￨L￨NNS￨O￨- may￨L￨MD￨O￨- still￨L￨RB￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- peaks￨L￨VBZ￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- Nsoesie￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al12￨L￨FW￨O￨- noted￨L￨VBD￨O￨A that￨L￨IN￨O￨- such￨L￨JJ￨O￨- web-based￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- might￨L￨MD￨O￨- distort￨L￨VB￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- predicted￨L￨VBN￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- steps￨L￨NNS￨O￨- are￨L￨VBP￨O￨- performed￨L￨VBN￨O￨- to￨L￨TO￨O￨- calibrate￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- acquired￨L￨VBD￨O￨- distinct￨L￨JJ￨O￨- POC￨U￨NN￨O￨- datasets￨L￨NNS￨O￨A at￨L￨IN￨O￨- zip-code￨L￨NN￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- process￨L￨NN￨O￨- POC￨U￨NN￨O￨- datasets￨L￨NNS￨O￨- for￨L￨IN￨O￨- meaningful￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- against￨L￨IN￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- employed￨L￨VBD￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- meta-heuristic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Simulated￨U￨JJ￨O￨- Annealing￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- calibration￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- and￨L￨CC￨O￨- calibrate￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- parsimonious￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- remarkably￨L￨RB￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- peak￨L￨JJ￨O￨- loads￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- calibration￨L￨NN￨O￨- yields￨L￨NNS￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- similar￨L￨JJ￨O￨A to￨L￨TO￨O￨- those￨L￨DT￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- possible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Delayed-SIR￨U￨NN￨O￨- from￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- outputs￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- produce￨L￨VB￨O￨- results￨L￨NNS￨O￨- similar￨L￨JJ￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- POC￨U￨NNP￨O￨- diagnostics￨L￨NNS￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- answer￨L￨VB￨O￨A the￨L￨DT￨O￨- following￨L￨VBG￨O￨- question￨L￨NN￨O￨- :￨L￨:￨O￨- Do￨U￨VB￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- Epidemiology￨U￨NNP￨O￨- models￨L￨NNS￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- documented￨L￨VBN￨O￨- in￨L￨IN￨O￨- POC￨U￨NNP￨O￨- diagnostics￨L￨NNS￨O￨- data￨L￨NNS￨O￨- ?￨L￨.￨O￨- +The￨U￨DT￨O￨- utility￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- enhanced￨L￨VBN￨O￨A if￨L￨IN￨O￨- POC￨U￨NN￨ORGANIZATION￨- diagnostics￨L￨NNS￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- of￨L￨IN￨O￨- observations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- calibrate￨L￨VB￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- estimated￨L￨VBD￨O￨- that￨L￨IN￨O￨- 84￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨A people￨L￨NNS￨O￨- had￨L￨VBD￨O￨- active￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- an￨L￨DT￨O￨- inflammatory￨L￨JJ￨O￨- conjunctivitis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- visual￨L￨JJ￨O￨- impairment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- 7.6￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- were￨L￨VBD￨O￨- severely￨L￨RB￨O￨- visually￨L￨RB￨O￨- impaired￨L￨JJ￨O￨- or￨L￨CC￨O￨- blind￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- trachoma￨L￨NN￨O￨- .1￨L￨CD￨NUMBER￨- Recently￨U￨RB￨DATE￨- revised￨L￨VBN￨O￨- estimates￨L￨NNS￨O￨- have￨L￨VBP￨O￨- halved￨L￨VBN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- with￨L￨IN￨O￨- active￨L￨JJ￨O￨- trachoma￨L￨NN￨O￨- ,￨L￨,￨O￨- probably￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- collection￨L￨NN￨O￨- of￨L￨IN￨O￨- more￨L￨JJR￨O￨- accurate￨L￨JJ￨O￨- data￨L￨NNS￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SAFE￨U￨JJ￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Surgery￨U￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- trichiasis￨L￨NN￨O￨- ,￨L￨,￨O￨- Antibiotic￨U￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- causative￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- Chlamydia￨U￨NN￨O￨- trachomatis￨L￨NN￨O￨- ,￨L￨,￨O￨- Facial￨U￨JJ￨O￨- cleanliness￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Environmental￨U￨NNP￨O￨- improvement￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,2￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- SAFE￨U￨JJ￨O￨- implementation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- socioeconomic￨L￨JJ￨O￨- improvements￨L￨NNS￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- .3￨L￨NN￨NUMBER￨- Yet￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- with￨L￨IN￨O￨- trichiasis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- inward￨L￨JJ￨O￨- turning￨L￨NN￨O￨- of￨L￨IN￨O￨- eyelashes￨L￨NNS￨O￨- causing￨L￨VBG￨O￨- corneal￨L￨NN￨O￨- damage￨L￨NN￨O￨- that￨L￨WDT￨O￨- will￨L￨MD￨O￨- ultimately￨L￨RB￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- blindness￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- currently￨L￨RB￨DATE￨- about￨L￨IN￨O￨- 8.2￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- .3￨L￨NN￨NUMBER￨- The￨U￨DT￨O￨- WHO￨U￨WP￨ORGANIZATION￨- ’s￨L￨VBZ￨O￨- simplified￨L￨VBN￨O￨- grading￨L￨VBG￨O￨- scheme4￨L￨NN￨O￨- discriminates￨L￨VBZ￨O￨- follicular￨L￨JJ￨O￨- and￨L￨CC￨O￨- inflammatory￨L￨JJ￨O￨- trachoma￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TF￨U￨NN￨O￨- and￨L￨CC￨O￨- TI￨U￨NNP￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- estimated￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- high￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨A setting￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- >￨L￨JJR￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- aged￨L￨VBN￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 9￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulated￨L￨JJ￨O￨- the￨L￨DT￨O￨- administration￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- antibiotic￨L￨JJ￨O￨- annual￨L￨JJ￨SET￨- treatment￨L￨NN￨O￨- rounds￨L￨NNS￨O￨- to￨L￨TO￨O￨- populations￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- initial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- level￨L￨NN￨O￨- was￨L￨VBD￨O￨- high￨L￨JJ￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- alliance￨L￨NN￨O￨- primarily￨L￨RB￨O￨- concern￨L￨NN￨O￨- the￨L￨DT￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- prevalent￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- TT￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- formerly￨L￨RB￨O￨- ,￨L￨,￨O￨- incident￨L￨NN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- CO￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨A trachoma￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TF￨U￨NN￨O￨- ,￨L￨,￨O￨- TI￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,8￨L￨CD￨NUMBER￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- explicitly￨L￨RB￨O￨- included￨L￨VBD￨O￨- the￨L￨DT￨O￨- progress￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- such￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- sequelae￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- investigates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- perturbing￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- through￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- schedules￨L￨NNS￨O￨- to￨L￨TO￨O￨- ascertain￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- what￨L￨WDT￨O￨- effect￨L￨NN￨O￨- these￨L￨DT￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- might￨L￨MD￨O￨- have￨L￨VB￨O￨- on￨L￨IN￨O￨- ocular￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- program￨L￨NN￨O￨- goals￨L￨NNS￨O￨A are￨L￨VBP￨O￨- achievable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- long￨L￨RB￨O￨- these￨L￨DT￨O￨- goals￨L￨NNS￨O￨- might￨L￨MD￨O￨- take￨L￨VB￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- examined￨L￨VBD￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- MDA￨U￨NN￨ORGANIZATION￨- alone￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- surgery￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- MDA￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- “￨L￨``￨O￨- transmission￨L￨NN￨O￨- reduction￨L￨NN￨O￨- ,￨L￨,￨O￨- ”￨L￨''￨O￨- on￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- sequelae￨L￨NN￨O￨- prevalence￨L￨NN￨O￨A levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- sequelae￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- directly￨L￨RB￨O￨- reflect￨L￨VB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- reasons￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- multiple￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- inapparent￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- under-reporting￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- misdiagnosis￨L￨NN￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- misreporting￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨- can￨L￨MD￨O￨- create￨L￨VB￨O￨- a￨L￨DT￨O￨- delay￨L￨NN￨O￨- between￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- reporting￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- mis-registration￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- locations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Feasible￨U￨JJ￨O￨- techniques￨L￨NNS￨O￨- to￨L￨TO￨O￨- handle￨L￨VB￨O￨- these￨L￨DT￨O￨- issues￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- index￨L￨NN￨O￨A clusters￨L￨NNS￨O￨- and￨L￨CC￨O￨- serologic￨L￨JJ￨O￨- testing￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- inapparent￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- states￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- incorporating￨L￨VBG￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- its￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- dengue￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- reality￨L￨NN￨O￨- primarily￨L￨RB￨O￨- evaluated￨L￨VBN￨O￨- by￨L￨IN￨O￨- vector￨L￨NN￨O￨- indicators￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- house￨L￨NN￨O￨- index￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- HI￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- container￨L￨NN￨O￨- index￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Breteau￨U￨NNP￨MISC￨- index￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- pupa￨L￨NN￨MISC￨- index￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- adult￨L￨JJ￨O￨- productivity￨L￨NN￨O￨- index￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- vectors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- now￨L￨RB￨DATE￨- widely￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- throughout￨L￨IN￨O￨- tropical￨L￨JJ￨O￨- and￨L￨CC￨O￨- subtropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- about￨L￨IN￨O￨- half￨L￨PDT￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- ’s￨L￨POS￨O￨- population￨L￨NN￨O￨- being￨L￨VBG￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- previously￨L￨RB￨DATE￨- reported￨L￨VBD￨O￨- a￨L￨DT￨O￨- genome-wide￨L￨JJ￨O￨- search￨L￨NN￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- in￨L￨IN￨O￨- cohorts￨L￨NNS￨O￨- of￨L￨IN￨O￨- F2￨U￨NN￨O￨- progeny￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- C3Ou￨U￨NN￨O￨- or￨L￨CC￨O￨- C3￨U￨NN￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨- B6￨U￨NN￨O￨- mice￨L￨NNS￨O￨A that￨L￨WDT￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- locus￨L￨NN￨O￨- on￨L￨IN￨O￨- chromosome￨L￨NN￨O￨- 15￨L￨CD￨NUMBER￨- controlling￨L￨VBG￨O￨- mortality￨L￨NN￨O￨- during￨L￨IN￨O￨- C.￨U￨NNP￨O￨- Further￨U￨JJ￨O￨- genotype￨L￨NN￨O￨- segregation￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- in￨L￨IN￨O￨- F2￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- B6￨U￨NN￨O￨- x￨L￨NN￨O￨- FVB￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- populations￨L￨NNS￨O￨- implicate￨L￨VBP￨O￨- Cri1￨U￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- C3￨U￨NN￨O￨- ,￨L￨,￨O￨- C3Ou￨U￨NN￨O￨- and￨L￨CC￨O￨- FVB￨U￨NN￨O￨- mice￨L￨NNS￨O￨- .￨L￨.￨O￨- +Transcriptome￨U￨NN￨O￨- analysis￨L￨NN￨O￨- in￨L￨IN￨O￨- total￨L￨JJ￨O￨- colonic￨L￨JJ￨O￨- samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- or￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- mice￨L￨NNS￨O￨A identified￨L￨VBD￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- pathogenic￨L￨JJ￨O￨- mechanism￨L￨NN￨O￨- in￨L￨IN￨O￨- C3Ou￨U￨NN￨O￨- and￨L￨CC￨O￨- FVB￨U￨NN￨O￨- mice￨L￨NNS￨O￨- that￨L￨WDT￨O￨- implicates￨L￨VBZ￨O￨- decreased￨L￨VBN￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- colonic￨L￨JJ￨O￨- HCO3￨U￨NN￨O￨- −￨L￨NN￨O￨- /￨L￨:￨O￨- Cl￨U￨NN￨O￨- −￨L￨NN￨O￨- exchanger￨L￨NN￨O￨- Slc26a3￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- carbonic￨L￨JJ￨O￨- anhydrase￨L￨NN￨O￨- IV￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Car4￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- fluid￨L￨JJ￨O￨- loss￨L￨NN￨O￨- in￨L￨IN￨O￨- feces￨L￨NNS￨O￨- and￨L￨CC￨O￨- perturbations￨L￨NNS￨O￨- in￨L￨IN￨O￨- electrolyte￨L￨NN￨O￨- absorption￨L￨NN￨O￨- .￨L￨.￨O￨- +Generation￨U￨NN￨O￨- of￨L￨IN￨O￨- congenic￨L￨JJ￨O￨- mice￨L￨NNS￨O￨A with￨L￨IN￨O￨- an￨L￨DT￨O￨- introgressed￨L￨JJ￨O￨- segment￨L￨NN￨O￨- of￨L￨IN￨O￨- chromosome￨L￨NN￨O￨- 15￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- B6￨U￨NN￨O￨- genome￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- C3Ou￨U￨NN￨O￨- genomic￨L￨JJ￨O￨- background￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- C3Ou.B6-Cri1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- confirmed￨L￨VBD￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- Cri1￨U￨NN￨O￨- with￨L￨IN￨O￨- full￨L￨JJ￨O￨- survival￨L￨NN￨O￨- of￨L￨IN￨O￨- congenic￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- revealed￨L￨VBD￨O￨- that￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- C.￨U￨NNP￨O￨- +rodentium￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- inbred￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- C3H/HeJ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- called￨L￨VBN￨O￨- C3￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- C3H/HeOuJ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- called￨L￨VBN￨O￨- C3Ou￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- FVB￨U￨NN￨O￨- display￨L￨VBP￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- mortality￨L￨NN￨O￨- while￨L￨IN￨O￨- C57BL/6￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- B6￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- mice￨L￨NNS￨O￨A develop￨L￨VBP￨O￨- self-limiting￨L￨JJ￨O￨- colitis￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- proper￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- effect￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- countries￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- complex￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-linear￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- made￨L￨VBN￨O￨- of￨L￨IN￨O￨- interconnected￨L￨JJ￨O￨- multilayer￨L￨JJ￨O￨- networked￨L￨JJ￨O￨- entities￨L￨NNS￨O￨- –￨L￨:￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- hence￨L￨RB￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨- networks5678￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- ref￨L￨NN￨O￨- .￨L￨.￨O￨- +Unlike￨U￨IN￨O￨- users￨L￨NNS￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- users￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨A network￨L￨NN￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- to￨L￨TO￨O￨- interact￨L￨VB￨O￨- with￨L￨IN￨O￨- people￨L￨NNS￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- this￨L￨DT￨O￨- network￨L￨NN￨O￨- an￨L￨DT￨O￨- advantage￨L￨NN￨O￨- over￨L￨IN￨O￨- local￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- ,￨L￨,￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- fitness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- species￨L￨NNS￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- launched￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨A network￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- the￨L￨DT￨O￨- user￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- to￨L￨TO￨O￨- connect￨L￨VB￨O￨- to￨L￨TO￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- local￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- it￨L￨PRP￨O￨- more￨L￨RBR￨O￨- attractive￨L￨JJ￨O￨- to￨L￨TO￨O￨- users￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- mimic￨L￨VB￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- digital￨L￨JJ￨O￨- ecosystem￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- worldwide￨L￨JJ￨O￨- scale￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- local￨L￨JJ￨O￨- network￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- globally￨L￨RB￨O￨- operating￨L￨NN￨O￨- ,￨L￨,￨O￨- international￨L￨JJ￨O￨A network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NNP￨O￨- 1a￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- launched￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- ;￨L￨:￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨A network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- launched￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- delay￨L￨NN￨O￨- Δt￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- county￨L￨NN￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- was￨L￨VBD￨O￨- reconstructed￨L￨VBN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- EV-A71￨U￨NN￨O￨- and￨L￨CC￨O￨- CV-A16￨U￨NN￨O￨- using￨L￨VBG￨O￨- binomial￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- clinically￨L￨RB￨O￨A confirmed￨L￨VBN￨O￨- HFMD￨U￨NN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- sampling￨L￨NN￨O￨- probability￨L￨NN￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- either￨L￨CC￨O￨- EV-A71￨U￨NN￨O￨- or￨L￨CC￨O￨- CA-A16￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- surrounding￨L￨VBG￨O￨- province￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- four-year￨L￨JJ￨DURATION￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2013￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- clinically￨L￨RB￨O￨A and￨L￨CC￨O￨- laboratory￨L￨NN￨O￨- confirmed￨L￨VBD￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- nationwide￨L￨JJ￨O￨- Notifiable￨U￨JJ￨O￨- Infectious￨U￨JJ￨O￨- Diseases￨U￨NNS￨CAUSE_OF_DEATH￨- Reporting￨U￨NNP￨O￨- Information￨U￨NNP￨O￨- System￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- NIDRIS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- maintained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Chinese￨U￨JJ￨ORGANIZATION￨- Center￨U￨NN￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- displays￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- geographic￨L￨JJ￨O￨- gradients￨L￨NNS￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- HFMD38￨U￨NN￨O￨- ,￨L￨,￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- CCS￨U￨NN￨ORGANIZATION￨- across￨L￨IN￨O￨- regions￨L￨NNS￨O￨A could￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- competing￨L￨VBG￨O￨- spatially￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- reduced￨L￨VBN￨O￨- focus￨L￨NN￨O￨- in￨L￨IN￨O￨- coverage￨L￨NN￨O￨- on￨L￨IN￨O￨- zones￨L￨NNS￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- CCS43￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- detailed￨L￨JJ￨O￨- geographic￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- CCS￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ’s￨L￨POS￨O￨- northern￨L￨JJ￨O￨A and￨L￨CC￨O￨- southern￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- using￨L￨VBG￨O￨- both￨L￨CC￨O￨- observed￨L￨VBN￨O￨- and￨L￨CC￨O￨- simulated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- from￨L￨IN￨O￨- TSIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- CCS￨U￨NN￨O￨- for￨L￨IN￨O￨- EV-A71￨U￨NN￨O￨- and￨L￨CC￨O￨- CV-A16￨U￨NN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- county-level￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- southern￨L￨JJ￨O￨- and￨L￨CC￨O￨- northern￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- Xing￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- worst￨L￨JJS￨O￨- month￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- August￨U￨NNP￨DATE￨- in￨L￨IN￨O￨- history￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- asymptomatic￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A cases￨L￨NNS￨O￨- among￨L￨IN￨O￨- tourists￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- 23￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 206￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Dengue￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- dengue￨L￨JJ￨O￨A serotypes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- DENV￨U￨NN￨ORGANIZATION￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- and￨L￨CC￨O￨- subtropics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A cases￨L￨NNS￨O￨- worldwide￨L￨RB￨O￨- ,￨L￨,￨O￨- concern￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨- for￨L￨IN￨O￨- travelers￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- justified￨L￨JJ￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- individual￨L￨JJ￨O￨- risk￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- dengue￨L￨NN￨O￨A is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- much￨L￨JJ￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- asymptomatic￨L￨JJ￨O￨- /￨L￨:￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨DURATION￨- other￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- history￨L￨NN￨O￨A of￨L￨IN￨O￨- Dengue￨U￨NNP￨O￨- in￨L￨IN￨O￨- Rio￨U￨NNP￨LOCATION￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- discuss￨L￨VB￨O￨- potential￨L￨JJ￨O￨- risks￨L￨NNS￨O￨- to￨L￨TO￨O￨- tourists￨L￨NNS￨O￨- amongst￨L￨IN￨O￨- visitors￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- forthcoming￨L￨JJ￨O￨- Rio￨U￨NNP￨O￨- Olympics￨U￨NNPS￨MISC￨- .￨L￨.￨O￨- +Without￨U￨IN￨O￨- aiming￨L￨VBG￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- a￨L￨DT￨O￨- predictive￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- but￨L￨CC￨O￨- rather￨L￨RB￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- what￨L￨WP￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- devised￨L￨VBD￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- EVD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- :￨L￨:￨O￨- SEICR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-infectious-convalescent-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- component￨L￨NN￨O￨- for￨L￨IN￨O￨- convalescent￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- convalescent￨L￨JJ￨O￨- survivors￨L￨NNS￨O￨- who￨L￨WP￨O￨- maintain￨L￨VBP￨O￨- active￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- replication￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extended￨L￨VBD￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-infected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- EVD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- a￨L￨DT￨O￨- component￨L￨NN￨O￨- for￨L￨IN￨O￨- sexual￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- convalescent￨L￨JJ￨O￨- survivors￨L￨NNS￨O￨- who￨L￨WP￨O￨- maintain￨L￨VBP￨O￨- active￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- replication￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Sexual￨U￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A from￨L￨IN￨O￨- convalescent￨L￨JJ￨O￨- survivors￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- likely￨L￨RB￨O￨- a￨L￨DT￨O￨- rare￨L￨JJ￨O￨- event￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- warned￨L￨VBN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- trajectory￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- reports￨L￨NNS￨O￨- suggesting￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- sexual￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- from￨L￨IN￨O￨- convalescent￨L￨JJ￨O￨- survivors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- raised￨L￨VBN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- important￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- sexual￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- βs￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- product￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- βs￨L￨NN￨O￨- =￨L￨JJ￨O￨- ηq￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- consider￨L￨VB￨O￨- separately￨L￨RB￨O￨- :￨L￨:￨O￨- η￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- per￨L￨FW￨O￨- sex￨L￨NN￨O￨- act￨L￨NN￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- from￨L￨IN￨O￨- convalescent￨L￨JJ￨O￨- men￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- q￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- engage￨L￨VBP￨O￨- in￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- intercourse￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨A cases￨L￨NNS￨O￨A increased￨L￨VBD￨O￨- exponentially￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- eastern￨L￨JJ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- Jiangsu￨U￨NNP￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- Zhejiang￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 135￨L￨CD￨NUMBER￨- confirmed￨L￨VBD￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- H7N9￨U￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- 44￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- officially￨L￨RB￨O￨- reported￨L￨VBN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Compared￨U￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- epidemic￨L￨JJ￨O￨- wave￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- later￨L￨JJ￨O￨- waves￨L￨NNS￨O￨A included￨L￨VBD￨O￨- larger￨L￨JJR￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- H7N9￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- spread￨L￨VBN￨O￨- across￨L￨IN￨O￨- wider￨L￨JJR￨O￨- geographical￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- no￨L￨DT￨O￨- further￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- following￨L￨VBG￨DURATION￨- 2￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- virus￨L￨NN￨O￨- re-emerged￨L￨VBD￨O￨- in￨L￨IN￨O￨- Zhejiang￨U￨NNP￨STATE_OR_PROVINCE￨- Province￨U￨NNP￨LOCATION￨- on￨L￨IN￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- large￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- waves￨L￨NNS￨O￨A of￨L￨IN￨O￨- human￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- documented￨L￨VBN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- R￨U￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Rice￨U￨NNP￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- adopts￨L￨VBZ￨O￨- resistance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- genes￨L￨NNS￨O￨A to￨L￨TO￨O￨- combat￨L￨VB￨O￨- against￨L￨IN￨O￨- avirulence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- AVR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- effectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- M.￨U￨NN￨O￨- All￨U￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- currently￨L￨RB￨DATE￨- known￨L￨VBN￨O￨- R￨U￨NN￨O￨- genes￨L￨NNS￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- rice￨L￨NN￨O￨- blast￨L￨NN￨O￨- belong￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- NBS-LRR￨U￨NN￨MISC￨- defense￨L￨NN￨O￨- gene￨L￨NN￨O￨- family￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- consist￨L￨VBP￨O￨- of￨L￨IN￨O￨- cell￨L￨NN￨O￨- surface￨L￨NN￨O￨- leucine-rich￨L￨JJ￨O￨- repeats￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- LRR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- intracellular￨L￨JJ￨O￨- nucleotide￨L￨NN￨O￨- binding￨L￨NN￨O￨- sites￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- NBS￨U￨NNS￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- recognize￨L￨VB￨O￨- specific￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- effectors￨L￨NNS￨O￨- and￨L￨CC￨O￨- trigger￨L￨VB￨O￨- resistance￨L￨NN￨O￨- responses6￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- NBS-LRR￨U￨NN￨MISC￨- defense￨L￨NN￨O￨- genes￨L￨NNS￨O￨A are￨L￨VBP￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- activated￨L￨VBN￨O￨- upon￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- regulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- small￨L￨JJ￨O￨- non-coding￨L￨JJ￨O￨- RNAs￨U￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- microRNAs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- miRNAs￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 78￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- super￨L￨JJ￨O￨- miRNA￨L￨NN￨O￨- family￨L￨NN￨O￨- miR482￨L￨NN￨O￨- targets￨L￨VBZ￨O￨- NBS-LRR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resistance￨L￨NN￨O￨- genes￨L￨NNS￨O￨A with￨L￨IN￨O￨- coiled-coil￨L￨JJ￨O￨- domains￨L￨NNS￨O￨- at￨L￨IN￨O￨- their￨L￨PRP$￨O￨- N￨U￨NN￨O￨- terminus￨L￨NN￨O￨- in￨L￨IN￨O￨- Nicotiana￨U￨NNP￨LOCATION￨- benthamiana14￨L￨NN￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- whether￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- mutants￨L￨NNS￨O￨- with￨L￨IN￨O￨- increased￨L￨VBN￨O￨- TIP￨U￨NN￨O￨- resistance￨L￨NN￨O￨- could￨L￨MD￨O￨- stably￨L￨RB￨O￨- invade￨L￨VB￨O￨A high-risk￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Techniques￨U￨NNS￨O￨- adopted￨L￨VBN￨O￨- from￨L￨IN￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨A analysis￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- SNA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- intensively￨L￨RB￨O￨- applied￨L￨VBN￨O￨- by￨L￨IN￨O￨- veterinary￨L￨JJ￨O￨- epidemiologists￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- livestock￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- network￨L￨NN￨O￨- actors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- central￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- trade￨L￨NN￨O￨A restrictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- or￨L￨CC￨O￨- testing￨L￨NN￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- node￨L￨NN￨O￨- removal￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- revealing￨L￨VBG￨O￨- potential￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- paths￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- German￨U￨JJ￨NATIONALITY￨- pig￨L￨NN￨O￨- trade￨L￨NN￨O￨A network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- actors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- analyzed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- other￨L￨JJ￨O￨- words￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- considered￨L￨VBN￨O￨- network￨L￨NN￨O￨- forms￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- substrate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- via￨L￨IN￨O￨- pig￨L￨NN￨O￨- trade￨L￨NN￨O￨A in￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Premises￨U￨NNS￨O￨- and￨L￨CC￨O￨- animal￨L￨NN￨O￨- movements￨L￨NNS￨O￨- between￨L￨IN￨O￨- premises￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- translated￨L￨VBN￨O￨- into￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- time￨L￨NN￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- collective￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- at￨L￨IN￨O￨- criticality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- transition￨L￨NN￨O￨- point￨L￨NN￨O￨- between￨L￨IN￨O￨- active/inactive￨L￨JJ￨O￨- states￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- diversity￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- excitability￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- proves￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- performance￨L￨NN￨O￨- :￨L￨:￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- task￨L￨NN￨O￨- of￨L￨IN￨O￨- distinguishing￨L￨VBG￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- external￨L￨JJ￨O￨- input￨L￨NN￨O￨- ,￨L￨,￨O￨- quantified￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- range￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- substantially￨L￨RB￨O￨- improved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- numerous￨L￨JJ￨O￨- recent￨L￨JJ￨O￨- works￨L￨NNS￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- optimizing￨L￨VBG￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- criticality￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- network￨L￨NN￨O￨- topologies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Haimoviciet￨U￨NNP￨O￨- al.￨L￨FW￨O￨- ,￨L￨,￨O￨- 2013￨L￨CD￨DATE￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- convenience￨L￨NN￨O￨- identical￨L￨JJ￨O￨- units￨L￨NNS￨O￨A are￨L￨VBP￨O￨- ordinarily￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- nodal￨L￨JJ￨O￨- intrinsic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- collective￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- thus￨L￨RB￨O￨- remains￨L￨VBZ￨O￨- unexplored￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- constructive￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- diversity￨L￨NN￨O￨- in￨L￨IN￨O￨- excitability￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- simple￨L￨JJ￨O￨- bimodal￨L￨JJ￨O￨- and￨L￨CC￨O￨- uniform￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- more￨L￨JJR￨O￨- realistic￨L￨JJ￨O￨- gamma￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- robustness￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- combining￨L￨VBG￨O￨- excitatory￨L￨JJ￨O￨- and￨L￨CC￨O￨- inhibitory￨L￨JJ￨O￨- units￨L￨NNS￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨- with￨L￨IN￨O￨- threshold￨L￨NN￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- refractory￨L￨JJ￨O￨- units￨L￨NNS￨O￨A R￨U￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- units￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨VB￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- refractory￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- enhanced￨L￨VBN￨O￨- network￨L￨NN￨O￨- response￨L￨NN￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- proximity￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- tricritical￨L￨JJ￨O￨- regime￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- critical￨L￨JJ￨O￨- coupling￨L￨NN￨O￨- strength￨L￨NN￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- integrators￨L￨NNS￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- for￨L￨IN￨O￨- diversity￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +established￨L￨VBN￨O￨- a￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- processes￨L￨VBZ￨O￨- coupled￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- inhibitory￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- was￨L￨VBD￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- structures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- respective￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness18￨L￨NN￨O￨- .￨L￨.￨O￨- +studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- asymmetrically￨L￨RB￨O￨- interacting￨L￨VBG￨O￨- spreading￨L￨VBG￨O￨A dynamics￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- processes￨L￨VBZ￨O￨- coupled￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- rise￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- threshold19￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- physical-contact￨L￨JJ￨O￨- layer￨L￨NN￨TITLE￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- to￨L￨TO￨O￨- adopt￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- received￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- communication￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- reinforcement￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- complex￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- adoption￨L￨NN￨O￨A behavior￨L￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- cost￨L￨NN￨O￨- is￨L￨VBZ￨O￨- explored￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- social￨L￨JJ￨O￨- reinforcement￨L￨NN￨O￨- effect￨L￨NN￨O￨- and￨L￨CC￨O￨- optimal￨L￨JJ￨O￨- information￨L￨NN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- which￨L￨WDT￨O￨- entail￨L￨VBP￨O￨- the￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- social￨L￨JJ￨O￨- cost￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- increasing￨L￨VBG￨O￨- recognition￨L￨NN￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- dengue￨L￨NN￨O￨A ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- matching￨L￨VBG￨O￨- to￨L￨TO￨O￨- single￨L￨JJ￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- narrow￨L￨VB￨O￨- down￨L￨RP￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- explanatory￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- matching￨L￨VBG￨O￨- to￨L￨TO￨O￨- multiple￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- at￨L￨IN￨O￨- various￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- and￨L￨CC￨O￨- hierarchical￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- generate￨L￨VBP￨O￨- such￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- key￨L￨JJ￨O￨- elements￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- applied￨L￨VBD￨O￨- a￨L￨DT￨O￨- POM￨U￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- modelling￨L￨NN￨O￨- global￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- proposed￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- serotype￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- were￨L￨VBD￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- dynamical￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- sufficiently￨L￨RB￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- enhanced￨L￨VBN￨O￨- infectiousness￨L￨NN￨O￨- or￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 60￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 130￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- induce￨L￨VB￨O￨- asynchronous￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨A NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- outcome￨L￨NN￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- indicated￨L￨VBN￨O￨- to￨L￨TO￨O￨- underlie￨L￨VB￨O￨- the￨L￨DT￨O￨- manifestation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- epidemic￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- Thailand￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Emphasis￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- on￨L￨IN￨O￨- unravelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- roles￨L￨NNS￨O￨- that￨L￨WDT￨O￨- cross-immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- cross-enhancement￨L￨NN￨O￨- between￨L￨IN￨O￨- serotypes￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- play￨L￨NN￨O￨- in￨L￨IN￨O￨- capturing￨L￨VBG￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- most￨L￨JJS￨O￨- modelling￨L￨JJ￨O￨- endeavours￨L￨NNS￨O￨- have￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- serotypes￨L￨NNS￨O￨A to￨L￨TO￨O￨- have￨L￨VB￨O￨- identical￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- asymmetry￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- serotype￨L￨NN￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- ADE￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Ideally￨U￨RB￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- new￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- detected￨L￨VBN￨O￨- and￨L￨CC￨O￨- recorded￨L￨VBN￨O￨A immediately￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- reality￨L￨NN￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- rarely￨L￨RB￨O￨- possible￨L￨JJ￨O￨- and￨L￨CC￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- recorded￨L￨VBN￨O￨- at￨L￨IN￨O￨- irregular￨L￨JJ￨O￨- intervals￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- points￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- suboptimal￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A variation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- predictable￨L￨JJ￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- antibody￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- such￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- created￨L￨VBN￨O￨- that￨L￨IN￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- Ab￨U￨NN￨O￨- levels￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- titers￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- using￨L￨VBG￨O￨- known￨L￨JJ￨O￨- serological￨L￨JJ￨O￨- response￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- are￨L￨VBP￨O￨- sampled￨L￨VBN￨O￨- repeatedly￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- seroconversion￨L￨NN￨O￨- event￨L￨NN￨O￨- in￨L￨IN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- sampling￨L￨NN￨O￨- events￨L￨NNS￨O￨- provides￨L￨VBZ￨O￨- further￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Temporal￨U￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- Ab￨U￨NN￨O￨- levels￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- another￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- time￨L￨NN￨O￨- since￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- case￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- illustration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- evidence￨L￨NN￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- transmission￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- phylogeny￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- gene￨L￨NN￨O￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- nested￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- ,￨L￨,￨O￨- comprehensive￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- observing￨L￨VBG￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- link￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- organism￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- putative￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- or￨L￨CC￨O￨- discrete￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- event￨L￨NN￨O￨A .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Nesting￨U￨NN￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- '￨L￨POS￨O￨- strain￨L￨NN￨O￨A lineages￨L￨NNS￨O￨- within￨L￨IN￨O￨- another￨L￨DT￨O￨- 's￨L￨POS￨O￨- supports￨L￨VBZ￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- carrying￨L￨VBG￨O￨- the￨L￨DT￨O￨- ancestral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- carrying￨L￨VBG￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- recently￨L￨RB￨DATE￨- diverged￨L￨VBD￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- shown￨L￨VBN￨O￨- here￨L￨RB￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- putative￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- event￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- red￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- person￨L￨NN￨O￨- A￨U￨NN￨O￨- to￨L￨TO￨O￨- person￨L￨NN￨O￨- B.￨U￨NNP￨PERSON￨- Helicobacter￨U￨NNP￨PERSON￨- pylori￨L￨NNP￨O￨- ,￨L￨,￨O￨- Mycobacterium￨U￨FW￨O￨- tuberculosis￨L￨FW￨O￨- and￨L￨CC￨O￨- Burkholderia￨U￨FW￨LOCATION￨- dolosa￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- cystic￨L￨JJ￨O￨- fibrosis￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- several￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- accumulated￨L￨VBN￨O￨- an￨L￨DT￨O￨- adequate￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mutations￨L￨NNS￨O￨- to￨L￨TO￨O￨- track￨L￨VB￨O￨- transmission￨L￨NN￨O￨- across￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- link￨L￨NN￨O￨A may￨L￨MD￨O￨- be￨L￨VB￨O￨- impossible￨L￨JJ￨O￨- to￨L￨TO￨O￨- prove￨L￨VB￨O￨- conclusively￨L￨RB￨O￨- from￨L￨IN￨O￨- genomic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- alone￨L￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- choices￨L￨NNS￨O￨- impact￨L￨NN￨O￨- confidence￨L￨NN￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- directionality￨L￨NN￨O￨- of￨L￨IN￨O￨- microbial￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Available￨U￨JJ￨O￨- data￨L￨NNS￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- higher￨L￨JJR￨O￨- bacterial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- loads￨L￨NNS￨O￨- are￨L￨VBP￨O￨- less￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- resolve￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- dose￨L￨NN￨O￨A of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- remain￨L￨VBP￨O￨- a￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- re-emergent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- following￨L￨VBG￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- some￨L￨DT￨O￨- areas￨L￨NNS￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Kongwa￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Tanzania￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Gurage￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ethiopia￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- rounds￨L￨NNS￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- deployed￨L￨VBN￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- dropped￨L￨VBN￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- aged￨L￨VBN￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 9￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- trachoma￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- routine￨L￨JJ￨O￨- rubella￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- can￨L￨MD￨O￨- prevent￨L￨VB￨O￨- CRS￨U￨NNP￨O￨- ,￨L￨,￨O￨- inadequate￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A may￨L￨MD￨O￨- actually￨L￨RB￨O￨- increase￨L￨VB￨O￨- CRS￨U￨NNP￨O￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- this￨L￨DT￨O￨- occurs￨L￨VBZ￨O￨- because￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- short￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- elimination￨L￨NN￨O￨- effectively￨L￨RB￨O￨- reduces￨L￨VBZ￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- delaying￨L￨NN￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- if￨L￨IN￨O￨- no￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- has￨L￨VBZ￨O￨- occurred￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- y-axis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨DATE￨- first￨L￨RB￨DATE￨- increase￨L￨VB￨O￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- scenario￨L￨NN￨O￨- of￨L￨IN￨O￨- no￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- indicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- horizontal￨L￨JJ￨O￨- grey￨L￨JJ￨O￨- line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- eventually￨L￨RB￨O￨- declining￨L￨VBG￨O￨- when￨L￨WRB￨O￨- incidence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- low￨L￨JJ￨O￨- to￨L￨TO￨O￨- offset￨L￨VB￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Birth￨U￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- Madagascar￨U￨NNP￨COUNTRY￨- remain￨L￨VBP￨O￨- relatively￨L￨RB￨O￨- high￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 30￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- 1000￨L￨CD￨DATE￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- theory￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- high￨L￨JJ￨O￨- birth￨L￨NN￨O￨A rates￨L￨NNS￨O￨A are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- investment￨L￨NN￨O￨- for￨L￨IN￨O￨- RCV￨U￨NNP￨O￨- less￨L￨JJR￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- priority￨L￨NN￨O￨- .￨L￨.￨O￨- +Further￨U￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- birth￨L￨NN￨O￨A rates￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- high￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- move￨L￨VB￨O￨- beyond￨L￨IN￨O￨- coverage￨L￨NN￨O￨- levels￨L￨NNS￨O￨- that￨L￨WDT￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- CRS￨U￨NNP￨O￨- burden￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- point￨L￨NN￨O￨- levels￨L￨NNS￨O￨- fell￨L￨VBD￨O￨- again￨L￨RB￨O￨- ;￨L￨:￨O￨- currently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- doses￨L￨NNS￨O￨- delivered￨L￨VBN￨O￨- divided￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- today￨L￨NN￨DATE￨- hovers￨L￨VBZ￨O￨- around￨L￨IN￨O￨- 85￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- Madagascar￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A with￨L￨IN￨O￨- 38￨L￨CD￨NUMBER￨- set￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- considered￨L￨VBD￨O￨- human￨L￨JJ￨O￨- ,￨L￨,￨O￨- rat￨L￨NN￨O￨- and￨L￨CC￨O￨- flea￨L￨NN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- assumed￨L￨VBD￨O￨- perfect￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- underestimated￨L￨VBN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- 350￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- both￨L￨CC￨O￨- rodent-to-human￨L￨NN￨O￨- and￨L￨CC￨O￨- human-to-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- plague￨L￨VB￨O￨A ,￨L￨,￨O￨- that￨L￨IN￨O￨- incorporates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- human-to-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- household￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- ignores￨L￨VBZ￨O￨- the￨L￨DT￨O￨- zoonotic￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- altogether￨L￨RB￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- noted￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- acknowledged￨L￨VBD￨O￨- shortfalls￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- exclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- latency￨L￨NN￨O￨- period￨L￨NN￨O￨- between￨L￨IN￨O￨- catching￨L￨VBG￨O￨- plague￨L￨VB￨O￨A and￨L￨CC￨O￨- becoming￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- perfect￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- between￨L￨IN￨O￨- villagers￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- epidemiological￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- approach￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- is￨L￨VBZ￨O￨- taken￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- times￨L￨NNS￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- plague￨L￨VB￨O￨A victims￨L￨NNS￨O￨- became￨L￨VBD￨O￨- infectious￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- approached￨L￨VBN￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- augmentation￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Eyam￨U￨NNP￨LOCATION￨- plague￨L￨VB￨O￨A NumericCitation￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infectious￨L￨JJ￨O￨- –￨L￨:￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- mentioned￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- explained￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- doses￨L￨NNS￨O￨- available￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- vaccine￨L￨NN￨O￨- releasing￨L￨VBG￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- starting￨L￨VBG￨O￨- date￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- deployment￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- vaccine￨L￨NN￨O￨- deployment￨L￨NN￨O￨- methods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- doses￨L￨NNS￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- feel￨L￨VBP￨O￨- that￨L￨IN￨O￨- developing￨L￨VBG￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A distribution￨L￨NN￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- geographic￨L￨JJ￨O￨- districts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- interesting￨L￨JJ￨O￨- and￨L￨CC￨O￨- important￨L￨JJ￨O￨- issues￨L￨NNS￨O￨- for￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- antiviral￨L￨JJ￨O￨- prophylaxis￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- area￨L￨NN￨O￨- or￨L￨CC￨O￨- household￨L￨NN￨O￨- quarantine￨L￨NN￨O￨- or￨L￨CC￨O￨- case￨L￨NN￨O￨- isolation￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- incorporated￨L￨VBN￨O￨A into￨L￨IN￨O￨- various￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- designed￨L￨VBD￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- expansion￨L￨NN￨O￨- under￨L￨IN￨O￨- various￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- deployment￨L￨NN￨O￨A conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- segregation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- incorporated￨L￨VBN￨O￨A into￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- HSEIR-V￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- characterise￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- test￨L￨VB￨O￨- how￨L￨WRB￨O￨- transmission￨L￨NN￨O￨- mode￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- symbiont￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- fitness￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- experimentally￨L￨RB￨O￨- passaged￨L￨VBD￨O￨- M13￨U￨NN￨O￨- and￨L￨CC￨O￨- E.￨U￨FW￨O￨- coli￨L￨FW￨O￨- in￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- replicated￨L￨VBN￨O￨- environments￨L￨NNS￨O￨- that￨L￨WDT￨O￨- differed￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- naïve￨L￨JJ￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨A hosts￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- opportunity￨L￨NN￨O￨- for￨L￨IN￨O￨- horizontal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- passage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- diagrams￨L￨VBZ￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- among￨L￨IN￨O￨- treatments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +coli￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- grown￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- same￨L￨JJ￨DATE￨- day￨L￨NN￨DATE￨- n￨L￨NN￨O￨- plate￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- added￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- supplement￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- treatments￨L￨NNS￨O￨- L￨U￨NN￨O￨- and￨L￨CC￨O￨- M.￨U￨NN￨O￨- Unexpectedly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- ancestral￨L￨JJ￨O￨- M13￨U￨NN￨O￨- increased￨L￨VBD￨O￨- both￨L￨CC￨O￨- bacterial￨L￨JJ￨O￨A growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- bacterial￨L￨JJ￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- phage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mutualist￨L￨NN￨O￨- of￨L￨IN￨O￨- E.￨U￨NNP￨O￨- +Filamentous￨U￨JJ￨O￨- phages￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- powerful￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- symbiosis￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- these￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- a￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨A cell￨L￨NN￨O￨- and￨L￨CC￨O￨- produce￨L￨VBP￨O￨- thousands￨L￨NNS￨O￨- of￨L￨IN￨O￨- progeny￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- without￨L￨IN￨O￨- killing￨L￨VBG￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- resistance￨L￨NN￨O￨A law￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- connected￨L￨JJ￨O￨- network￨L￨NN￨O￨- G￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- partition￨L￨NN￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- resistance￨L￨NN￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- one-dimensional￨L￨JJ￨O￨- structure￨L￨NN￨O￨- entropy￨L￨NN￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- entropy￨L￨NN￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- partition￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- find￨L￨VBP￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- resistance￨L￨NN￨O￨A law￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- connected￨L￨JJ￨O￨- graph￨L￨NN￨O￨- G￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- resistance￨L￨NN￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- two-dimensional￨L￨JJ￨O￨- structure￨L￨NN￨O￨- entropy￨L￨NN￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- local￨L￨JJ￨O￨- resistance￨L￨NN￨O￨A law￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- secure￨L￨VB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- G￨U￨NN￨O￨- by￨L￨IN￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- partition￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- resistance￨L￨NN￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- is￨L￨VBZ￨O￨- maximised￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- PA￨U￨NN￨STATE_OR_PROVINCE￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- resistance￨L￨NN￨O￨A and￨L￨CC￨O￨- security￨L￨NN￨O￨- index￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- both￨L￨DT￨O￨- robust￨L￨JJ￨O￨- to￨L￨TO￨O￨- random￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- and￨L￨CC￨O￨- exponentially￨L￨RB￨O￨- decrease￨L￨VB￨O￨- as￨L￨IN￨O￨- d￨L￨NN￨O￨- increases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Management￨U￨NN￨O￨- of￨L￨IN￨O￨- pest￨L￨NN￨O￨- species￨L￨NNS￨O￨- and￨L￨CC￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- spatially￨L￨RB￨O￨- restricted￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- lakes￨L￨NNS￨O￨- ,￨L￨,￨O￨- ponds￨L￨NNS￨O￨- and￨L￨CC￨O￨- aquaculture￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- often￨L￨RB￨O￨- involves￨L￨VBZ￨O￨- chemical￨L￨NN￨O￨- treatments￨L￨NNS￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- reservoir￨L￨NN￨O￨A hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- future￨L￨JJ￨DATE￨- pathogen￨L￨NN￨O￨- emergence￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- host-specific￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- eradication￨L￨NN￨O￨A can￨L￨MD￨O￨- eliminate￨L￨VB￨O￨- reservoir￨L￨NN￨O￨- or￨L￨CC￨O￨- intermediate￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- or￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- shown￨L￨VBN￨O￨- by￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- being￨L￨VBG￨O￨- reduced￨L￨VBN￨O￨- via￨L￨IN￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- potential￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- establishment￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- generalist￨L￨NN￨O￨- pathogen￨L￨NN￨O￨- following￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- environmental￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- adjacent￨L￨JJ￨O￨A source￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- eradication￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- population￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- adjacent￨L￨JJ￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- species￨L￨NNS￨O￨- composition￨L￨NN￨O￨- ,￨L￨,￨O￨- abundance￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- background￨L￨NN￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- new￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨A prevalence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pressure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- quantities￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- critical￨L￨JJ￨O￨- exponents￨L￨NNS￨O￨- and￨L￨CC￨O￨- amplitude￨L￨NN￨O￨- ratios￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- computed￨L￨VBN￨O￨- in￨L￨IN￨O￨- quite￨L￨RB￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- universality￨L￨NN￨O￨- classes17￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- size￨L￨NN￨O￨- scaling￨L￨NN￨O￨- analysis￨L￨NN￨O￨- will￨L￨MD￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- percolation￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Notable￨U￨JJ￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- contact￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- critical￨L￨JJ￨O￨A properties￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- analysed8910111415￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- time￨L￨NN￨O￨- horizon￨L￨NN￨O￨- with￨L￨IN￨O￨- finite￨L￨JJ￨O￨- size￨L￨NN￨O￨- resources￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- compartments￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Like￨U￨IN￨O￨- the￨L￨DT￨O￨- small-world￨L￨JJ￨O￨- property￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- that￨L￨IN￨O￨- functional￨L￨JJ￨O￨- brain￨L￨NN￨O￨A networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- scale-free￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- became￨L￨VBD￨O￨- popular￨L￨JJ￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- turn￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- millennium78￨L￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- some￨L￨DT￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- functional￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- spatially￨L￨RB￨O￨- coarse-grained￨L￨JJ￨O￨- parcellations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- brain￨L￨NN￨O￨A are￨L￨VBP￨O￨- small￨L￨JJ￨O￨- worlds5￨L￨NNS￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- structural￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- level￨L￨NN￨O￨- the￨L￨DT￨O￨- brain￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- large-world￨L￨JJ￨O￨- network￨L￨NN￨O￨- after￨L￨IN￨O￨- all46￨L￨NN￨O￨- .￨L￨.￨O￨- +Drawing￨U￨VBG￨O￨- parallels￨L￨NNS￨O￨- between￨L￨IN￨O￨- neural￨L￨JJ￨O￨- and￨L￨CC￨O￨- socio-technological￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- neuroscientists￨L￨NNS￨O￨- have￨L￨VBP￨O￨- hypothesized￨L￨VBN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- brain￨L￨NN￨O￨A we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- small-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- structural1￨L￨NN￨O￨- and￨L￨CC￨O￨- functional￨L￨JJ￨O￨- level2￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- reason￨L￨NN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- plausible￨L￨JJ￨O￨- to￨L￨TO￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- functional￨L￨JJ￨O￨A level￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- connectome￨L￨NN￨O￨- ’s￨L￨POS￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- scale-free￨L￨JJ￨O￨- .￨L￨.￨O￨- +Inconsistent￨U￨JJ￨O￨- findings￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- associations￨L￨NNS￨O￨- between￨L￨IN￨O￨- meteorological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- relative￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- studies6789101112131415￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- temperature￨L￨NN￨O￨- of￨L￨IN￨O￨- 21.1￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 26.7￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- ,￨L￨,￨O￨- higher￨L￨JJR￨O￨- relative￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A and￨L￨CC￨O￨- school￨L￨NN￨O￨- period￨L￨NN￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- higher￨L￨JJR￨O￨- HFMD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- mainland￨L￨NN￨O￨- China22￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- therefore￨L￨RB￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- driving￨L￨NN￨O￨- factors￨L￨NNS￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- HFMD￨U￨NN￨O￨- shows￨L￨VBZ￨O￨A less￨L￨JJR￨O￨- obvious￨L￨JJ￨O￨- seasonality￨L￨NN￨O￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- shows￨L￨VBZ￨O￨A the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- HFMD-associated￨U￨JJ￨O￨- hospitalizations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- between￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- and￨L￨CC￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +HFMD￨U￨NN￨O￨- is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- transmissible￨L￨JJ￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- 2.5￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 5.5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +CRTs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- usual￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- replication￨L￨NN￨O￨- and￨L￨CC￨O￨- contemporaneous￨L￨JJ￨O￨- controls￨L￨NNS￨O￨- in￨L￨IN￨O￨- trials￨L￨NNS￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- typically￨L￨RB￨O￨- provide￨L￨VBP￨O￨- both￨L￨CC￨O￨- individual￨L￨JJ￨O￨- protection￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- immediate￨L￨JJ￨O￨- recipients￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- induce￨L￨VBP￨O￨- community￨L￨NN￨O￨- effects￨L￨NNS￨O￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- onward￨L￨RB￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- generic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- stepped￨L￨VBD￨O￨- wedge￨L￨NN￨O￨- cluster-randomized￨L￨JJ￨O￨- trials￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- SWCRTs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- transmission-reducing￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- has￨L￨VBZ￨O￨- spatially￨L￨RB￨O￨- diffuse￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- trials￨L￨NNS￨O￨A were￨L￨VBD￨O￨- then￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- designs￨L￨NNS￨O￨- for￨L￨IN￨O￨- providing￨L￨VBG￨O￨- generalizable￨L￨JJ￨O￨- causal￨L￨JJ￨O￨- inferences￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- measurements￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contamination￨L￨NN￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SolarMal￨U￨JJ￨O￨- example￨L￨NN￨O￨- illustrates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- generic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- incorporating￨L￨VBG￨O￨- spatial￨L￨JJ￨O￨- smoothing￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- such￨L￨JJ￨O￨- trials￨L￨NNS￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- calculation￨L￨NN￨O￨- and￨L￨CC￨O￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- cluster￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- randomization￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Clustering￨U￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- needed￨L￨VBN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- or￨L￨CC￨O￨- where￨L￨WRB￨O￨- effects￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- level￨L￨NN￨O￨- are￨L￨VBP￨O￨- anticipated￨L￨VBN￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- averaged￨L￨VBN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- individual-level￨L￨JJ￨O￨- randomized￨L￨JJ￨O￨A trial￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- considering￨L￨VBG￨O￨- systems￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- understood￨L￨VBN￨O￨- as￨L￨IN￨O￨- interaction￨L￨NN￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- defined￨L￨VBN￨O￨- above￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- would￨L￨MD￨O￨- like￨L￨VB￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- development￨L￨NN￨O￨- process￨L￨NN￨O￨- that￨L￨WDT￨O￨- lets￨L￨VBZ￨O￨- the￨L￨DT￨O￨- modeler￨L￨NN￨TITLE￨- follow￨L￨VB￨O￨- a￨L￨DT￨O￨- procedure￨L￨NN￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- Identify￨U￨VB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- species￨L￨NNS￨O￨A or￨L￨CC￨O￨- compartments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- emphasize￨L￨VBP￨O￨- that￨L￨IN￨O￨- any￨L￨DT￨O￨- practical￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- schema￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- software￨L￨NN￨O￨- tool￨L￨NN￨O￨- could￨L￨MD￨O￨- and￨L￨CC￨O￨- should￨L￨MD￨O￨- bury￨L￨VB￨O￨- these￨L￨DT￨O￨- automated￨L￨VBN￨O￨- rules￨L￨NNS￨O￨A behind￨L￨IN￨O￨- a￨L￨DT￨O￨- non-mathematical￨L￨JJ￨O￨- user￨L￨NN￨O￨- interface￨L￨NN￨O￨- ,￨L￨,￨O￨- separating￨L￨VBG￨O￨- the￨L￨DT￨O￨- scientific￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- process￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematics￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- and￨L￨CC￨O￨- solve￨L￨VB￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- this￨L￨DT￨O￨- accounting￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨A and￨L￨CC￨O￨- interactions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- constitutes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- move￨L￨NN￨O￨- quickly￨L￨RB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- ODEs￨U￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- analyzed￨L￨VBN￨O￨- by￨L￨IN￨O￨- standard￨L￨JJ￨O￨- means￨L￨NNS￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- analytically￨L￨RB￨O￨- or￨L￨CC￨O￨- numerically￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- situations￨L￨NNS￨O￨- ,￨L￨,￨O￨- parcels￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- species￨L￨NNS￨O￨A are￨L￨VBP￨O￨- transformed￨L￨VBN￨O￨- into￨L￨IN￨O￨- parcels￨L￨NNS￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- species￨L￨NNS￨O￨- at￨L￨IN￨O￨- rates￨L￨NNS￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- interaction￨L￨NN￨O￨- rules￨L￨NNS￨O￨- that￨L￨WDT￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- species￨L￨NNS￨O￨- .￨L￨.￨O￨- +Identify￨U￨VB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- species￨L￨NNS￨O￨A ,￨L￨,￨O￨- be￨L￨VB￨O￨- they￨L￨PRP￨O￨- biological￨L￨JJ￨O￨- ,￨L￨,￨O￨- ecological￨L￨JJ￨O￨- ,￨L￨,￨O￨- physical￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- otherwise￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- recently￨L￨RB￨DATE￨- proposed￨L￨VBD￨O￨- an￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- method￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Belief￨U￨NNP￨MISC￨- Propagation￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- BP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 67￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- gave￨L￨VBD￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- exact￨L￨JJ￨O￨- tractable￨L￨JJ￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- inference￨L￨NN￨O￨A problems￨L￨NNS￨O￨- on￨L￨IN￨O￨- acyclic￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- excellent￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- on￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- graphs￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- real￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- problem￨L￨NN￨O￨- addressed￨L￨VBD￨O￨- ranged￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- inference￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- source￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- zero￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- times￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- plus￨L￨CC￨O￨- a￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- partial￨L￨JJ￨O￨- ,￨L￨,￨O￨- noisy￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- snapshot￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- instant￨L￨NN￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- this￨L￨DT￨O￨- discrete￨L￨JJ￨O￨A time￨L￨NN￨O￨A network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- constructed￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- between￨L￨IN￨O￨- states￨L￨NNS￨O￨- defining￨L￨VBG￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time-step￨L￨JJ￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- will￨L￨MD￨O￨- then￨L￨RB￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- semi-continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- inference￨L￨NN￨O￨A framework￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- datasets￨L￨NNS￨O￨- without￨L￨IN￨O￨- any￨L￨DT￨O￨- discretization￨L￨NN￨O￨- approximation￨L￨NN￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- it￨L￨PRP￨O￨- be￨L￨VB￨O￨- implicit￨L￨JJ￨O￨- or￨L￨CC￨O￨- explicit￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- choosing￨L￨VBG￨O￨- initial￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- as￨L￨IN￨O￨- source￨L￨NN￨O￨- spreaders￨L￨NNS￨O￨A to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- maximum￨L￨NN￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- influence￨L￨NN￨O￨- maximization￨L￨NN￨O￨- problem12￨L￨NN￨O￨- .￨L￨.￨O￨- +Pei￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 21￨L￨CD￨NUMBER￨- addressed￨L￨VBD￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- search￨L￨VB￨O￨- for￨L￨IN￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨A by￨L￨IN￨O￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- influential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- strong￨L￨JJ￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- selecting￨L￨VBG￨O￨- top-ranked￨L￨JJ￨O￨- influential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- as￨L￨IN￨O￨- source￨L￨NN￨O￨- spreaders￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- and￨L￨CC￨O￨- classical￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +Very￨U￨RB￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- Morone￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Makse￨U￨NNP￨PERSON￨- presented￨L￨VBD￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- critical￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨A by￨L￨IN￨O￨- mapping￨L￨VBG￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- onto￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- percolation￨L￨NN￨O￨- in￨L￨IN￨O￨- random￨L￨JJ￨O￨- networks36￨L￨NN￨O￨- .￨L￨.￨O￨- +He￨U￨PRP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 37￨L￨CD￨NUMBER￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- multiple￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- community￨L￨NN￨O￨- structures￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- fat-tailed￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- random￨L￨JJ￨O￨- immunization￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- vaccinating￨L￨VBG￨O￨- a￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- chosen￨L￨VBN￨O￨- randomly￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- stopping￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- since￨L￨IN￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- immunization￨L￨NN￨O￨- of￨L￨IN￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- -100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- halt￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- nodes￨L￨NNS￨O￨A are￨L￨VBP￨O￨- called￨L￨VBN￨O￨- hubs￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- high￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- reason￨L￨NN￨O￨- why￨L￨WRB￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- technology￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- fashion￨L￨NN￨O￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- quickly￨L￨RB￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨- than￨L￨IN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- idea￨L￨NN￨O￨- behind￨L￨IN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- MRP￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- removing￨L￨VBG￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A or￨L￨CC￨O￨- immunizing￨L￨VBG￨O￨- susceptible￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- are￨L￨VBP￨O￨- efficient￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- to￨L￨TO￨O￨- fight￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Movement￨U￨NNP￨O￨- restriction￨L￨NN￨O￨- policies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MRPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- popular￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- implemented￨L￨VBD￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- countries￨L￨NNS￨O￨- to￨L￨TO￨O￨- fight￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- animal￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- worldwide￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- removal￨L￨NN￨O￨- or￨L￨CC￨O￨- isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A will￨L￨MD￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- continuing￨L￨VBG￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- effective￨L￨JJ￨O￨- only￨L￨RB￨O￨- under￨L￨IN￨O￨- demanding￨L￨VBG￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- recuperator￨L￨NN￨O￨- for￨L￨IN￨O￨- stopping￨L￨VBG￨O￨- relapsing￨L￨NN￨O￨- and￨L￨CC￨O￨- preventing￨L￨VBG￨O￨A the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- drink￨L￨VB￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- effective￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- alcoholism￨L￨NN￨CAUSE_OF_DEATH￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- preventing￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- drink￨L￨VB￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- recuperator￨L￨NN￨O￨- to￨L￨TO￨O￨- accept￨L￨VB￨O￨- treatment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- refuse￨L￨VB￨O￨- drinking￨L￨NN￨O￨- alcohol.KeywordsAlcoholismThresholdFixed￨L￨JJ￨O￨- weightAdaptive￨L￨JJ￨O￨- weightOptimal￨L￨JJ￨O￨- controlStable￨L￨JJ￨O￨- BackgroundAlcohol￨U￨NN￨O￨- use￨L￨NN￨O￨- and￨L￨CC￨O￨- abuse￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- society￨L￨NN￨O￨- for￨L￨IN￨O￨- centuries￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- The￨U￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- alcoholism￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- relapse￨L￨NN￨O￨- on￨L￨IN￨O￨- weighted￨L￨JJ￨O￨- networksHai-Feng￨L￨JJ￨O￨- Huo1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Ying-Ping￨U￨JJ￨O￨- Liu1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 5:722￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractTwo￨U￨NNP￨O￨- SIRS￨U￨NNP￨O￨- alcoholism￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- relapse￨L￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- fixed￨L￨VBN￨O￨- and￨L￨CC￨O￨- adaptive￨L￨JJ￨O￨- weight￨L￨NN￨O￨A are￨L￨VBP￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- situation￨L￨NN￨O￨- ,￨L￨,￨O￨- alcoholism￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- issue￨L￨NN￨O￨- that￨L￨WDT￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- solved￨L￨VBN￨O￨A urgently.Since￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- mimic￨L￨VB￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- alcoholism￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- provide￨L￨VB￨O￨- useful￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- drinking￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- fixed￨L￨JJ￨O￨- weight￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- StrictLessThan￨U￨NNP￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- alcohol￨L￨NN￨O￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- drinking￨L￨NN￨O￨- crowd￨L￨NN￨O￨- gradually￨L￨RB￨O￨- disappear￨L￨VBP￨O￨- .￨L￨.￨O￨- +Benedict￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- proposed￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- standard￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- alcoholics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- accurate￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- metropolitan￨L￨JJ￨O￨- Melbourne￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- Australia￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨A filter￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- observation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- upon￨L￨IN￨O￨- a￨L￨DT￨O￨- negative￨L￨JJ￨O￨- binomial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- influenza‐like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Flu￨U￨NNP￨CAUSE_OF_DEATH￨- Trends￨U￨NNPS￨O￨- .9￨L￨CD￨NUMBER￨- While￨U￨IN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- no￨L￨RB￨O￨- longer￨L￨RB￨O￨- publishing￨L￨VBG￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- of￨L￨IN￨O￨- August￨U￨NNP￨DATE￨- 20￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- continue￨L￨VBP￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- signal￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- research￨L￨NN￨O￨- purposes￨L￨NNS￨O￨- .10￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- results￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- here￨L￨RB￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- towards￨L￨IN￨O￨- a￨L￨DT￨O￨- decision‐support￨L￨NN￨O￨- tool￨L￨NN￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- use￨L￨VB￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- near‐real￨L￨NN￨O￨- ‐￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- and￨L￨CC￨O￨- beyond￨L￨IN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- recent￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- filtering￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- forecasting￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- 115￨L￨CD￨NUMBER￨- cities￨L￨NNS￨O￨- in￨L￨IN￨O￨- USA￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- timing￨L￨NN￨O￨- forecasts￨L￨NNS￨O￨- were￨L￨VBD￨O￨- comparably￨L￨RB￨O￨- accurate￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- six￨L￨CD￨NUMBER￨- surveyed￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- .11￨L￨CD￨NUMBER￨- It￨U￨PRP￨O￨- was￨L￨VBD￨O￨- also￨L￨RB￨O￨- observed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- particle￨L￨NN￨O￨A filters￨L￨NNS￨O￨- performed￨L￨VBN￨O￨- ‘￨L￨``￨O￨- slightly￨L￨RB￨O￨- better￨L￨JJR￨O￨- predicting￨L￨VBG￨O￨- peaks￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- ’￨L￨''￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- ‘￨L￨``￨O￨- ensemble￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- Kalman￨U￨NN￨PERSON￨- ]￨L￨-RRB-￨O￨- filters￨L￨NNS￨O￨- were￨L￨VBD￨O￨- better￨L￨RB￨O￨- at￨L￨IN￨O￨- indicating￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- peak￨L￨NN￨O￨- had￨L￨VBD￨O￨- already￨L￨RB￨O￨- occurred￨L￨VBN￨O￨- ’￨L￨''￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- recursive￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- estimation￨L￨NN￨O￨- methods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ‘￨L￨``￨O￨- filters￨L￨NNS￨O￨- ’￨L￨POS￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- forecasting￨L￨NN￨O￨A purposes￨L￨NNS￨O￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- often￨L￨RB￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- with￨L￨IN￨O￨- Internet￨U￨NN￨MISC￨- search￨L￨NN￨O￨- query￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- mechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .3￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- While￨U￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- of￨L￨IN￨O￨- practical￨L￨JJ￨O￨- forecasting￨L￨NN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- seasons￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- adapted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- vagaries￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- system￨L￨NN￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ‘￨L￨``￨O￨- observations￨L￨NNS￨O￨- ’￨L￨POS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- collected￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- being￨L￨VBG￨O￨- surveilled￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- activity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- by￨L￨IN￨O￨- averaging￨L￨VBG￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- existing￨L￨VBG￨O￨- trade￨L￨NN￨O￨A connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- node￨L￨NN￨O￨- pairs￨L￨NNS￨O￨- and￨L￨CC￨O￨- analyze￨L￨VB￨O￨- how￨L￨WRB￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- activity￨L￨NN￨O￨- influence￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Previously￨U￨RB￨DATE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- aggregation￨L￨NN￨O￨- of￨L￨IN￨O￨- trade￨L￨NN￨O￨A links￨L￨NNS￨O￨- into￨L￨IN￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- overestimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- probability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 31￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- duration￨L￨NN￨O￨- .￨L￨.￨O￨- +Further￨U￨RB￨O￨- ,￨L￨,￨O￨- SNA￨U￨NNP￨ORGANIZATION￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- utilized￨L￨VBN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- specific￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Methicillin-resistant￨U￨JJ￨O￨- Staphylococcus￨U￨FW￨O￨- aureus￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- MRSA￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- Danish￨U￨JJ￨NATIONALITY￨- pig￨L￨NN￨O￨- trade￨L￨NN￨O￨A network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- strategic￨L￨JJ￨O￨- removal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- would￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- decomposition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- into￨L￨IN￨O￨- fragments￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- would￨L￨MD￨O￨- interrupt￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- chains￨L￨NNS￨O￨- and￨L￨CC￨O￨- prevent￨L￨VB￨O￨- further￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- the￨L￨DT￨O￨- trade￨L￨NN￨O￨A network￨L￨NN￨O￨- ,￨L￨,￨O￨- farms￨L￨NNS￨O￨- with￨L￨IN￨O￨- greater￨L￨JJR￨O￨- trade￨L￨NN￨O￨- activities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- contributors￨L￨NNS￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- are￨L￨VBP￨O￨- also￨L￨RB￨O￨- robust￨L￨JJ￨O￨- enough￨L￨RB￨O￨- in￨L￨IN￨O￨- providing￨L￨VBG￨O￨- strong￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- about￨L￨IN￨O￨- various￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- like￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- ,￨L￨,￨O￨- equilibrium￨L￨NN￨O￨A points￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibria￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- periodic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- solutions￨L￨NNS￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- however￨L￨RB￨O￨- a￨L￨DT￨O￨- difficulty￨L￨NN￨O￨- in￨L￨IN￨O￨- proving￨L￨VBG￨O￨- theoretical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- like￨L￨IN￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨A points￨L￨NNS￨O￨A ,￨L￨,￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- topologies￨L￨NNS￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- popular￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- called￨L￨VBD￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- -￨L￨:￨O￨- Infectious￨U￨JJ￨O￨- -￨L￨:￨O￨- Susceptible￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- then￨L￨RB￨O￨- applied￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- such￨L￨JJ￨O￨- application￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- manner￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- spread￨L￨VBN￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨A of￨L￨IN￨O￨- networks9￨L￨NN￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- useful￨L￨JJ￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A thresholds￨L￨NNS￨O￨A for￨L￨IN￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- SI￨U￨NNP￨O￨- ,￨L￨,￨O￨- SIS￨U￨NNP￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models1314￨L￨NN￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- information￨L￨NN￨O￨- may￨L￨MD￨O￨- include￨L￨VB￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- competing￨L￨VBG￨O￨- interests￨L￨NNS￨O￨- of￨L￨IN￨O￨- societal￨L￨JJ￨O￨- benefit￨L￨NN￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- implementation￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- over-or￨L￨JJ￨O￨- under-vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- prioritize￨L￨VB￨O￨- efforts￨L￨NNS￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- population￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A levels￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- costs￨L￨NNS￨O￨- given￨L￨VBN￨O￨- sub-optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- coverage￨L￨NN￨O￨- was￨L￨VBD￨O￨- varied￨L￨VBN￨O￨- from￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- total￨L￨JJ￨O￨- cost￨L￨NN￨O￨- ;￨L￨:￨O￨- hereafter￨L￨RB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- other￨L￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- by￨L￨IN￨O￨- varying￨L￨VBG￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A required￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- reasons￨L￨NNS￨O￨- above￨L￨IN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- pays￨L￨VBZ￨O￨- particular￨L￨JJ￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- simulation￨L￨NN￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- valuable￨L￨JJ￨O￨- research￨L￨NN￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- exploration￨L￨NN￨O￨- of￨L￨IN￨O￨- fundamental￨L￨JJ￨O￨- laws￨L￨NNS￨O￨- and￨L￨CC￨O￨- trends￨L￨NNS￨O￨- of￨L￨IN￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨A in￨L￨IN￨O￨- airspace￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨A of￨L￨IN￨O￨- airspace￨L￨NN￨O￨- congestion￨L￨NN￨O￨- has￨L￨VBZ￨O￨- traditionally￨L￨RB￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- graphs￨L￨NNS￨O￨- with￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- flights￨L￨NNS￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- connectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- date￨L￨VB￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨A of￨L￨IN￨O￨- delay￨L￨NN￨O￨- or￨L￨CC￨O￨- congestion￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- road￨L￨NN￨O￨- transport￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨A of￨L￨IN￨O￨- congestion￨L￨NN￨O￨- or￨L￨CC￨O￨- delay￨L￨NN￨O￨- in￨L￨IN￨O￨- air￨L￨NN￨O￨- transport￨L￨NN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- limited￨L￨VBN￨O￨- ,￨L￨,￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- airport￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- airspace￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- noted￨L￨VBN￨O￨- also￨L￨RB￨O￨- that￨L￨IN￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨A in￨L￨IN￨O￨- airspace￨L￨NN￨O￨- is￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- that￨L￨DT￨O￨- in￨L￨IN￨O￨- road￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- weight￨L￨NN￨O￨- can￨L￨MD￨O￨- moreover￨L￨RB￨O￨- be￨L￨VB￨O￨- assigned￨L￨VBN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- link￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- CSN￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨- w￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- registered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- sensors￨L￨NNS￨O￨A on￨L￨IN￨O￨- that￨L￨DT￨O￨- day￨L￨NN￨DURATION￨- between￨L￨IN￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- j￨L￨FW￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- CDN￨U￨NN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- reported￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- students￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- diaries￨L￨NNS￨O￨- ,￨L￨,￨O￨- building￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- CDND￨U￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- use￨L￨VB￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- link￨L￨NN￨O￨- a￨L￨DT￨O￨- duration￨L￨NN￨O￨- taken￨L￨VBN￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- list￨L￨NN￨O￨- of￨L￨IN￨O￨- durations￨L￨NNS￨O￨- registered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- sensors￨L￨NNS￨O￨- ,￨L￨,￨O￨- obtaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- CDNS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Methods￨U￨NNS￨O￨- for￨L￨IN￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Quantitative￨U￨JJ￨O￨- comparisons￨L￨NNS￨O￨- between￨L￨IN￨O￨- datasets￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- sensors￨L￨NNS￨O￨A and￨L￨CC￨O￨- self-reported￨L￨JJ￨O￨- diaries￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- and￨L￨CC￨O￨- durations￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- statistics￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- however￨L￨RB￨O￨- scarce￨L￨JJ￨O￨- ,￨L￨,￨O￨- mainly￨L￨RB￨O￨- because￨L￨IN￨O￨- very￨L￨RB￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- combined￨L￨VBN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- data￨L￨NNS￨O￨- collection￨L￨NN￨O￨- means￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- design￨L￨NN￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- contained￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- diaries￨L￨NNS￨O￨- to￨L￨TO￨O￨- build￨L￨VB￨O￨- surrogate￨L￨JJ￨O￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- yield￨L￨VBP￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- risk￨L￨NN￨O￨- as￨L￨IN￨O￨- quantified￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- considering￨L￨VBG￨O￨- as￨L￨IN￨O￨- ground￨L￨NN￨O￨- truth￨L￨NN￨O￨- the￨L￨DT￨O￨- dataset￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- sensors￨L￨NNS￨O￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Interestingly￨U￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- much￨L￨JJ￨O￨- lower￨L￨JJR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- inferred￨L￨VBD￨O￨- from￨L￨IN￨O￨- contact￨L￨NN￨O￨- diaries￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- wearable￨L￨JJ￨O￨- sensors￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- each￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- students￨L￨NNS￨O￨A and￨L￨CC￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- is￨L￨VBZ￨O￨- drawn￨L￨VBN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- j￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- students￨L￨NNS￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- j￨L￨FW￨O￨- is￨L￨VBZ￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- dataset￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- considered￨L￨VBN￨O￨- day￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +,￨L￨,￨O￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- nursing￨L￨NN￨O￨- homes￨L￨NNS￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- antimicrobial-resistant￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- confirmed￨L￨VBN￨O￨- by￨L￨IN￨O￨- studies￨L￨NNS￨O￨- in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- higher￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- pathogens￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- MRSA￨U￨NNP￨O￨- in￨L￨IN￨O￨- nursing￨L￨VBG￨O￨- homes￨L￨NNS￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- hospitals￨L￨NNS￨O￨A and￨L￨CC￨O￨- have￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- “￨L￨``￨O￨- being￨L￨VBG￨O￨- transferred￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- care￨L￨NN￨O￨- institution￨L￨NN￨O￨- ”￨L￨''￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- risk￨L￨NN￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- being￨L￨VBG￨O￨- carrier￨L￨NN￨O￨- of￨L￨IN￨O￨- MRSA￨U￨NNP￨O￨- in￨L￨IN￨O￨- patients￨L￨NNS￨O￨- admitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- sought￨L￨VBD￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- nursing￨L￨NN￨O￨- homes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- positioned￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- healthcare￨L￨NN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- nursing￨L￨NN￨O￨- homes￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- connections￨L￨NNS￨O￨- with￨L￨IN￨O￨- hospitals￨L￨NNS￨O￨A influence￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial-resistant￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- healthcare￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- comparing￨L￨VBG￨O￨- different￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- were￨L￨VBD￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- nursing￨L￨NN￨O￨- homes￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial-resistant￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- strains￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- healthcare￨L￨NN￨O￨A network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- synthetic￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- hospitals￨L￨NNS￨O￨A and￨L￨CC￨O￨- nursing￨L￨NN￨O￨- homes￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- Dutch￨U￨JJ￨NATIONALITY￨- healthcare￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +–￨L￨:￨O￨- Hospitals￨U￨NNS￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- exchange￨L￨NN￨O￨- patients￨L￨NNS￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- healthcare￨L￨NN￨O￨A institutes￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- nursing￨L￨VBG￨O￨- homes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Fast￨U￨JJ￨MISC￨- and￨L￨CC￨O￨- accurate￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- field￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨A of￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- vaccinesLorenzo￨L￨NN￨O￨- Argante1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Michele￨U￨NNP￨PERSON￨- Tizzoni2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Duccio￨U￨NNP￨O￨- Medini3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 14:98￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Estimating￨U￨VBG￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- accuracy￨L￨NN￨O￨- and￨L￨CC￨O￨- precision￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- challenging￨L￨VBG￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- low￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- invasive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- ranges￨L￨VBZ￨O￨- between￨L￨IN￨O￨- 0.5￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 1￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- 100,000￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- North￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- MCML￨U￨NN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- VE￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- MenC￨U￨NN￨O￨- immunization￨L￨NN￨O￨- campaign￨L￨NN￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- good￨L￨JJ￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- results￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- screening￨L￨NN￨O￨A method￨L￨NN￨O￨- and￨L￨CC￨O￨- carriage￨L￨NN￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- confidence￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- and￨L￨CC￨O￨- obtained￨L￨VBN￨O￨- using￨L￨VBG￨O￨- only￨L￨RB￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- within￨L￨IN￨O￨- 2￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- scheduled￨L￨VBN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Vaccine￨U￨NN￨O￨- effectiveness￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- VE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- estimated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- screening￨L￨NN￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- formula￨L￨NN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- vaccinated￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- Monte￨U￨NNP￨LOCATION￨- Carlo￨U￨NNP￨LOCATION￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MCML￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨A of￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- MCML￨U￨NN￨O￨- method￨L￨NN￨O￨A provided￨L￨VBN￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- MenC￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- validated￨L￨VBN￨O￨- against￨L￨IN￨O￨- results￨L￨NNS￨O￨- published￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- related￨L￨JJ￨O￨- work6￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- found￨L￨VBD￨O￨- a￨L￨DT￨O￨- mixed￨L￨JJ￨O￨- phase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- dynamics￨L￨NNS￨O￨- –￨L￨:￨O￨- besides￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- phase￨L￨NN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- isolated￨L￨VBN￨O￨A networks￨L￨NNS￨O￨- –￨L￨:￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- spreads￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- network￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- weak￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- spreads￨L￨VBZ￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- layers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- interconnected￨L￨VBN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- rewiring￨L￨NN￨O￨- rate￨L￨NN￨O￨- beyond￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- phase￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model5￨L￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- multilayered￨L￨JJ￨O￨- interconnected￨L￨JJ￨O￨A systems￨L￨NNS￨O￨- can￨L￨MD￨O￨- support￨L￨VB￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- each￨L￨DT￨O￨- isolated￨L￨VBN￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- so￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- internetwork￨L￨NN￨O￨- correlations￨L￨NNS￨O￨- boost￨L￨VBP￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- two-network￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- interconnected￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- layers￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- adaptation￨L￨NN￨O￨- process￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- rewiring￨L￨NN￨O￨- of￨L￨IN￨O￨- interlayer￨L￨NN￨O￨- links￨L￨NNS￨O￨- can￨L￨MD￨O￨- dramatically￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- layers￨L￨NNS￨O￨A .￨L￨.￨O￨- +Because￨U￨IN￨O￨- we￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- coevolution￨L￨NN￨O￨A mechanisms￨L￨NNS￨O￨- between￨L￨IN￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- from￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- disease-behavior￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- coevolution￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- know￨L￨VB￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- utilize￨L￨VB￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- effectively￨L￨RB￨O￨- suppress￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- make￨L￨VBP￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- coevolution￨L￨NN￨O￨A mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- interacting￨L￨VBG￨O￨- mechanisms￨L￨NNS￨O￨- in￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- here￨L￨RB￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- mechanisms￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- coevolution￨L￨NN￨O￨A processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- demonstrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- asymmetrical￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- dynamics￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- real-world￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- systems￨L￨NNS￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- coevolution￨L￨NN￨O￨A .￨L￨.￨O￨- +Researchers￨U￨NNS￨O￨- have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- metacritical￨L￨JJ￨O￨- point16￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A and￨L￨CC￨O￨- multiplex￨L￨JJ￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- information￨L￨NN￨O￨- propagation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- promoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading17￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- reliability￨L￨NN￨O￨- evaluation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- sensor￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- ’￨L￨POS￨O￨- functionality￨L￨NN￨O￨- as￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- face￨L￨VBP￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- self-replicating￨L￨JJ￨O￨- malicious￨L￨JJ￨O￨- code￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- malware￨L￨NN￨O￨- for￨L￨IN￨O￨- short￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- continuous-time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CTMC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- provides￨L￨VBZ￨O￨- considerable￨L￨JJ￨O￨- flexibility￨L￨NN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- state￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- sensor￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- illustrating￨L￨VBG￨O￨- malware￨L￨NN￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- reliability￨L￨NN￨O￨- evaluation￨L￨NN￨O￨- for￨L￨IN￨O￨- WSNs￨U￨NNS￨O￨- is￨L￨VBZ￨O￨- vital￨L￨JJ￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- guarantee￨L￨VB￨O￨- the￨L￨DT￨O￨- delivery￨L￨NN￨O￨- of￨L￨IN￨O￨- sensed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- sensor￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- sink￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- CTMC￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- insufficient￨L￨JJ￨O￨- for￨L￨IN￨O￨- correctly￨L￨RB￨O￨- treating￨L￨VBG￨O￨- malware￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- often￨L￨RB￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- security￨L￨NN￨O￨- failures￨L￨NNS￨O￨- for￨L￨IN￨O￨- sensor￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- only￨L￨RB￨O￨- once￨L￨RB￨DATE￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- transforming￨L￨VBG￨O￨- from￨L￨IN￨O￨- state￨L￨NN￨O￨- I￨U￨PRP￨O￨- to￨L￨TO￨O￨- state￨L￨NN￨O￨- R￨U￨NN￨O￨- becomes￨L￨VBZ￨O￨- immune￨L￨JJ￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- hence￨L￨RB￨O￨- unable￨L￨JJ￨O￨- to￨L￨TO￨O￨- propagate￨L￨VB￨O￨- malware￨L￨NN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- better￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- factors￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- VDPV￨U￨NN￨O￨- emergence￨L￨NN￨O￨A and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- spread￨L￨NN￨O￨- will￨L￨MD￨O￨- help￨L￨VB￨O￨- the￨L￨DT￨O￨- GPEI￨U￨NN￨ORGANIZATION￨- to￨L￨TO￨O￨- define￨L￨VB￨O￨- a￨L￨DT￨O￨- clear￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- geographic￨L￨JJ￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- tOPV￨L￨NN￨O￨- SIA￨U￨NNP￨O￨- that￨L￨WDT￨O￨- minimises￨L￨VBZ￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- VDPV2￨U￨NN￨O￨- emergence￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- and￨L￨CC￨O￨- immediately￨L￨RB￨O￨- after￨L￨IN￨O￨- OPV2￨U￨NN￨O￨- withdrawal￨L￨NN￨O￨- .￨L￨.￨O￨- +Worldwide￨U￨NNP￨O￨- OPV2￨U￨NN￨O￨- withdrawal￨L￨NN￨O￨- will￨L￨MD￨O￨- put￨L￨VB￨O￨- the￨L￨DT￨O￨- 155￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- currently￨L￨RB￨DATE￨- using￨L￨VBG￨O￨- tOPV￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- routine￨L￨JJ￨O￨- immunisation￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨A of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- VDPV2￨U￨NN￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- associated￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- type￨L￨NN￨O￨- .￨L￨.￨O￨- +SIAs￨U￨NNS￨O￨- with￨L￨IN￨O￨- tOPV￨L￨NN￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- OPV2￨U￨NN￨O￨- withdrawal￨L￨NN￨O￨- would￨L￨MD￨O￨- increase￨L￨VB￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- serotype￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- VDPV2￨U￨NN￨O￨- emergence￨L￨NN￨O￨A and￨L￨CC￨O￨- spread￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- emergent￨L￨JJ￨O￨- VDPVs￨U￨NNS￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- where￨L￨WRB￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- ρ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- absolute￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- VDPV￨U￨NN￨O￨- emergence￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- reversion￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Sabin￨U￨NN￨O￨- virus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- infrequent￨L￨JJ￨O￨- or￨L￨CC￨O￨- poor-coverage￨L￨JJ￨O￨- SIAs￨U￨NNS￨O￨- could￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- limited￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- potentially￨L￨RB￨O￨- an￨L￨DT￨O￨- adverse￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- risk￨L￨NN￨O￨A resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- poliovirus￨L￨NN￨O￨- shedding￨L￨VBG￨O￨- and￨L￨CC￨O￨- seeding￨L￨VBG￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- VDPV￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- non-spatial￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- generation￨L￨NN￨O￨- matrix￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Appendix￨U￨NNP￨O￨- A￨U￨DT￨O￨- for￨L￨IN￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- that￨L￨DT￨O￨- This￨U￨DT￨O￨- quantity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- straight￨L￨JJ￨O￨- forward￨L￨RB￨O￨- to￨L￨TO￨O￨- interpret￨L￨VB￨O￨- biologically￨L￨RB￨O￨- as￨L￨IN￨O￨- R0￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- broken￨L￨VBN￨O￨- into￨L￨IN￨O￨- contributions￨L￨NNS￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- undetected￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- divided￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- exit￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- I￨U￨PRP￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- enter￨L￨VB￨O￨A I￨U￨PRP￨O￨- or￨L￨CC￨O￨- I￨U￨PRP￨O￨- plus￨L￨CC￨O￨- the￨L￨DT￨O￨- exit￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- eventually￨L￨RB￨O￨- enter￨L￨VBP￨O￨- I￨U￨PRP￨O￨- or￨L￨CC￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- this￨L￨DT￨O￨- term￨L￨NN￨O￨- plays￨L￨VBZ￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- components￨L￨NNS￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- left￨L￨VBN￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- enter￨L￨VB￨O￨- the￨L￨DT￨O￨- hospitalized￨L￨VBN￨O￨- class￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- multiplied￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- time￨L￨NN￨O￨- spent￨L￨VBN￨O￨- in￨L￨IN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- F￨U￨NN￨O￨- class￨L￨NN￨O￨- multiplied￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- time￨L￨NN￨O￨- spent￨L￨VBN￨O￨- in￨L￨IN￨O￨- F￨U￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- eventually￨L￨RB￨O￨- enter￨L￨VBP￨O￨- the￨L￨DT￨O￨- F￨U￨NN￨O￨- class￨L￨NN￨O￨- from￨L￨IN￨O￨- any￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- hospitalization￨L￨NN￨O￨- and￨L￨CC￨O￨- safe￨L￨JJ￨O￨A burial￨L￨NN￨O￨- practices￨L￨NNS￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- beds￨L￨NNS￨O￨- in￨L￨IN￨O￨- hospitals￨L￨NNS￨O￨- ,￨L￨,￨O￨- expanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- treatment￨L￨NN￨O￨- units￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ETUs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- accelerating￨L￨VBG￨O￨- case￨L￨NN￨O￨- identification￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- implementing￨L￨VBG￨O￨- a￨L￨DT￨O￨- quarantine￨L￨NN￨O￨- policy￨L￨NN￨O￨- for￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ref￨L￨FW￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- these￨L￨DT￨O￨- different￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- routes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- per￨L￨FW￨O￨- capita￨L￨NN￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- from￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- undetected￨L￨JJ￨O￨- ,￨L￨,￨O￨- hospitalized￨L￨VBN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- funeral￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- contributing￨L￨VBG￨O￨- to￨L￨TO￨O￨- onward￨L￨RB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- including￨L￨VBG￨O￨- those￨L￨DT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- funeral￨L￨JJ￨O￨- class￨L￨NN￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- excluding￨L￨VBG￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- quarantined￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- effectively￨L￨RB￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- maximized￨L￨VBD￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- hospitalization￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- II￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- hospitalization￨L￨NN￨O￨- and￨L￨CC￨O￨- safe￨L￨JJ￨O￨A burial￨L￨NN￨O￨- practices￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- III￨U￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- quarantine￨L￨NN￨O￨- and￨L￨CC￨O￨- safe￨L￨JJ￨O￨- burial￨L￨NN￨O￨- practices￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- research￨L￨NN￨O￨- subjects￨L￨NNS￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨A solution￨L￨NN￨O￨A with￨L￨IN￨O￨- any￨L￨DT￨O￨- positive￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- in￨L￨IN￨O￨- probability￨L￨NN￨O￨- mean￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- probability￨L￨NN￨O￨- mean￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- asymptotical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- ergodicity￨L￨NN￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- deterministic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- disease-induced￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- Λ￨U￨NN￨O￨- denotes￨L￨VBZ￨O￨A the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-related￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- βf￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuously￨L￨RB￨O￨- differentiable￨L￨JJ￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- per￨L￨FW￨O￨- capita￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +constructed￨L￨VBN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- obtained￨L￨VBD￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- global￨L￨JJ￨O￨- positive￨L￨JJ￨O￨A solution￨L￨NN￨O￨A with￨L￨IN￨O￨- any￨L￨DT￨O￨- positive￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- established￨L￨VBD￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- ;￨L￨:￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- or￨L￨CC￨O￨- persists￨L￨VBZ￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- Lyapunov￨U￨NN￨PERSON￨- function￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- Itô￨U￨NN￨PERSON￨- 's￨L￨POS￨O￨- formula￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- establish￨L￨VB￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- interesting￨L￨JJ￨O￨- criteria￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- permanence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Whether￨U￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- stationary￨L￨JJ￨O￨A distribution￨L￨NN￨O￨A only￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- permanent￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- IAV￨U￨NN￨O￨- in￨L￨IN￨O￨- pig￨L￨NN￨O￨- herds￨L￨NNS￨O￨A under￨L￨IN￨O￨- different￨L￨JJ￨O￨- management￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- examined￨L￨VBD￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- persistence￨L￨NN￨O￨- varies￨L￨VBZ￨O￨- with￨L￨IN￨O￨- herd￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- titrated￨L￨VBN￨O￨- against￨L￨IN￨O￨- seroprevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- critical￨L￨JJ￨O￨- herd￨L￨NN￨O￨- size￨L￨NN￨O￨- ’￨L￨''￨O￨- (￨L￨-LRB-￨O￨- CHS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- swine￨L￨NNS￨O￨A herds￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- commonly￨L￨RB￨O￨- found￨L￨VBN￨O￨- ,￨L￨,￨O￨- realistic￨L￨JJ￨O￨- farm￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +How￨U￨WRB￨O￨- is￨L￨VBZ￨O￨- persistence￨L￨NN￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- modifiable￨L￨JJ￨O￨- farm￨L￨NN￨O￨A management￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- assumed￨L￨VBN￨O￨- farrowing￨L￨NN￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- cohorting￨L￨NN￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- into￨L￨IN￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- separation￨L￨NN￨O￨- of￨L￨IN￨O￨- weaners￨L￨NNS￨O￨- ,￨L￨,￨O￨- growers￨L￨NNS￨O￨- ,￨L￨,￨O￨- finishers￨L￨NNS￨O￨- and￨L￨CC￨O￨- piglets￨L￨NNS￨O￨- and￨L￨CC￨O￨- sows￨L￨VBZ￨O￨- into￨L￨IN￨O￨- different￨L￨JJ￨O￨- buildings￨L￨NNS￨O￨- or￨L￨CC￨O￨- sites￨L￨NNS￨O￨- ?￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- some￨L￨DT￨O￨- anecdotal￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- suggest￨L￨VBP￨O￨- swine￨L￨NNS￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- persisting￨L￨VBG￨O￨- at￨L￨IN￨O￨- small￨L￨JJ￨O￨- population￨L￨NN￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- possibly￨L￨RB￨O￨- even￨L￨RB￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- farm￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- pig￨L￨NN￨O￨- farms￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- insufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- fully￨L￨RB￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- and￨L￨CC￨O￨- why￨L￨WRB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- within￨L￨IN￨O￨- swine￨L￨NNS￨O￨A populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- on￨L￨IN￨O￨- viral￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- simply￨L￨RB￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- production￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- by￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- killing￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- clearance￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- free￨L￨JJ￨O￨- virus￨L￨NN￨O￨- particles￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- scenario￨L￨NN￨O￨- analysis￨L￨NN￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A that￨L￨WDT￨O￨- succumb￨L￨VBP￨O￨- to￨L￨TO￨O￨- ASF￨U￨NN￨ORGANIZATION￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- 200￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +ASF￨U￨NNP￨ORGANIZATION￨- has￨L￨VBZ￨O￨- no￨L￨DT￨O￨- cure￨L￨NN￨O￨- or￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- control￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- proper￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- biosecurity￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- pig￨L￨NN￨O￨- confinement￨L￨NN￨O￨- and￨L￨CC￨O￨- movement￨L￨NN￨O￨- restriction￨L￨NN￨O￨- plus￨L￨CC￨O￨- culling￨L￨NN￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A on￨L￨IN￨O￨- infected￨L￨JJ￨O￨- farms￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- surrounding￨L￨VBG￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- proportion￨L￨NN￨O￨- ρ￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A succumb￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- while￨L￨IN￨O￨- those￨L￨DT￨O￨- that￨L￨WDT￨O￨- survive￨L￨VBP￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- carrier￨L￨NN￨O￨- pigs￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1-ρ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- examples￨L￨NNS￨O￨- the￨L￨DT￨O￨- naming￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- was￨L￨VBD￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- “￨L￨``￨O￨- Vac￨U￨NNP￨O￨- _￨L￨SYM￨O￨- 7030￨L￨CD￨NUMBER￨- ”￨L￨''￨O￨- is￨L￨VBZ￨O￨- vaccine￨L￨NN￨O￨- intervention￨L￨NN￨O￨- with￨L￨IN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- day￨L￨NN￨DURATION￨- 30￨L￨CD￨NUMBER￨- after￨L￨IN￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- whereas￨L￨IN￨O￨- “￨L￨``￨O￨- Bio￨U￨NNP￨O￨- _￨L￨NNP￨O￨- 30￨L￨CD￨NUMBER￨- ”￨L￨''￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- biosecurity￨L￨NN￨O￨- intervention￨L￨NN￨O￨- 30￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨A after￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- now￨L￨RB￨DATE￨- entered￨L￨VBN￨O￨- the￨L￨DT￨O￨- post‐pandemic￨L￨JJ￨O￨- period￨L￨NN￨O￨- for￨L￨IN￨O￨- H1N1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2009￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- timely￨L￨JJ￨O￨- to￨L￨TO￨O￨- review￨L￨VB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- studies￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- serial￨L￨NN￨O￨A interval￨L￨NN￨O￨- or￨L￨CC￨O￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- A/H1N1￨U￨NN￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- previous￨L￨JJ￨O￨- pandemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- planning￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- guidance￨L￨NN￨O￨- document￨L￨NN￨O￨- ‘￨L￨``￨O￨- Global￨U￨JJ￨O￨- surveillance￨L￨NN￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- ’￨L￨''￨O￨- released￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- were￨L￨VBD￨O￨- highlighted￨L￨VBN￨O￨- that￨L￨IN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- documented￨L￨VBN￨O￨- quickly￨L￨RB￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- respect￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- symptoms￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- serial￨L￨NN￨O￨A interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- onset￨L￨NN￨O￨- in￨L￨IN￨O￨- primary￨L￨JJ￨O￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- secondary￨L￨JJ￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- ratio/number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- primary￨L￨JJ￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +All￨U￨DT￨O￨- publications￨L￨NNS￨O￨- were￨L￨VBD￨O￨- reviewed￨L￨VBN￨O￨- for￨L￨IN￨O￨- relevance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- finally￨L￨RB￨O￨- retained￨L￨VBD￨O￨- 36￨L￨CD￨NUMBER￨- papers￨L￨NNS￨O￨- presenting￨L￨VBG￨O￨- original￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- serial￨L￨NN￨O￨A interval￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- assumption￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- GT￨U￨NN￨O￨- distribution￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- shorter￨L￨JJR￨O￨- mean￨L￨NN￨O￨- GT￨U￨NN￨O￨- will￨L￨MD￨O￨- likely￨L￨RB￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- smaller￨L￨JJR￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- estimate￨L￨NN￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- criteria￨L￨NNS￨O￨- for￨L￨IN￨O￨- selecting￨L￨VBG￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- most￨L￨RBS￨O￨- connected￨L￨VBN￨O￨- :￨L￨:￨O￨- select￨L￨VB￨O￨A the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- degree￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- random￨L￨JJ￨O￨- :￨L￨:￨O￨- select￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- random￨L￨JJ￨O￨- acquaintance￨L￨NN￨O￨- :￨L￨:￨O￨- select￨L￨VB￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- acquaintance￨L￨NN￨O￨- of￨L￨IN￨O￨- random￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- biased￨L￨VBN￨O￨- toward￨L￨IN￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- designing￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A surveillance￨L￨NN￨O￨A systems￨L￨NNS￨O￨- for￨L￨IN￨O￨- networked￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- seeks￨L￨VBZ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- sensors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- timely￨L￨JJ￨O￨- and￨L￨CC￨O￨- accurate￨L￨JJ￨O￨- indications￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- activity￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- strategies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- illustrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- subset￨L￨NN￨O￨A includes￨L￨VBZ￨O￨- five￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 100￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- red￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨A network￨L￨NN￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- β￨L￨VB￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- 〈￨L￨SYM￨O￨- k￨L￨NN￨O￨- 〉￨L￨NN￨O￨- and￨L￨CC￨O￨- 〈￨L￨NN￨O￨- k2￨L￨NN￨O￨- 〉￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- squared￨L￨VBD￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- traceable￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- perform￨L￨VB￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- interviewing￨L￨VBG￨O￨- ,￨L￨,￨O￨- compiling￨L￨VBG￨O￨- lists￨L￨NNS￨O￨- ,￨L￨,￨O￨- seeking￨L￨VBG￨O￨- out￨L￨RP￨O￨- contacted￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- performing￨L￨VBG￨O￨- monitoring￨L￨NN￨O￨A and￨L￨CC￨O￨- isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- identified￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- grows￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Instead￨U￨RB￨O￨- of￨L￨IN￨O￨- monitoring￨L￨VBG￨O￨A individuals￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- list￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- community-based￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- that￨L￨IN￨O￨- entire￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- be￨L￨VB￨O￨- monitored￨L￨VBN￨O￨- for￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- until￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- ruled￨L￨VBN￨O￨- out￨L￨RP￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- all￨L￨DT￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- perfectly￨L￨RB￨O￨- isolated￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- monitoring￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- policies￨L￨NNS￨O￨- would￨L￨MD￨O￨- evidently￨L￨RB￨O￨- drastically￨L￨RB￨O￨- limit￨L￨VB￨O￨- new￨L￨JJ￨O￨- Ebola￨U￨NNP￨MISC￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- abrupt￨L￨JJ￨O￨- halt￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +C.￨U￨NNP￨O￨- R￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ---￨L￨:￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t.￨L￨NN￨O￨- R￨U￨NN￨O￨- drops￨L￨VBZ￨O￨- before￨L￨IN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 70￨L￨CD￨NUMBER￨- because￨L￨IN￨O￨- policies￨L￨NNS￨O￨A affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- contagion￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- initially￨L￨RB￨O￨- infected￨L￨VBN￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- undergo￨L￨VB￨O￨- A￨U￨DT￨O￨- birth￨L￨NN￨O￨- event￨L￨NN￨O￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- another￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- created￨L￨VBN￨O￨- in￨L￨IN￨O￨- subpopulation￨L￨NN￨O￨A i￨L￨FW￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- death￨L￨NN￨O￨- event￨L￨NN￨O￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- or￨L￨CC￨O￨- removal￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- subpopulation￨L￨NN￨O￨- i￨L￨FW￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- sampling￨L￨NN￨O￨- event￨L￨NN￨O￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨- probability￨L￨NN￨O￨- r￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨- event￨L￨NN￨O￨- yields￨L￨VBZ￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- type-change￨L￨JJ￨O￨- event￨L￨NN￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- from￨L￨IN￨O￨- subpopulation￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- subpopulation￨L￨NN￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- birth￨L￨NN￨O￨- event￨L￨NN￨O￨- among￨L￨IN￨O￨- demes￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- subpopulation￨L￨NN￨O￨- i￨L￨FW￨O￨- causes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- to￨L￨TO￨O￨- arise￨L￨VB￨O￨- in￨L￨IN￨O￨- subpopulation￨L￨NN￨O￨- j￨L￨NN￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- process￨L￨NN￨O￨- terminates￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- no￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- left￨L￨VBN￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- subpopulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2013￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- through￨L￨IN￨O￨- births￨L￨NNS￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- lineages￨L￨NNS￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- or￨L￨CC￨O￨- removal￨L￨NN￨O￨- events￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sampling￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- either￨L￨CC￨O￨- continuously￨L￨RB￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- sampling￨L￨NN￨O￨- rate￨L￨NN￨O￨- and/or￨L￨CC￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- contemporaneous￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- event￨L￨NN￨O￨A at￨L￨IN￨O￨- present￨L￨JJ￨DATE￨- (￨L￨-LRB-￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- ρ￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- sampled￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- multitype￨L￨JJ￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- started￨L￨VBN￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨A of￨L￨IN￨O￨- type￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- brain￨L￨NN￨O￨- critical￨L￨JJ￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- experimentally￨L￨RB￨O￨A characterized￨L￨VBN￨O￨- via￨L￨IN￨O￨- power-law￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- distributed￨L￨VBN￨O￨- neuronal￨L￨JJ￨O￨- avalanches1213141516￨L￨NN￨O￨- or￨L￨CC￨O￨- diverging￨L￨VBG￨O￨- long-range￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- or￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- correlations1718￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- activity￨L￨NN￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- inside￨L￨IN￨O￨A the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- region￨L￨NN￨O￨- also￨L￨RB￨O￨- presents￨L￨VBZ￨O￨- long-range￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- yielding￨L￨VBG￨O￨- Detrended￨U￨NNP￨O￨- Fluctuation￨U￨NN￨O￨- Analysis173738￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- DFA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- exponent￨L￨NN￨O￨- .￨L￨.￨O￨- +Throughout￨U￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- of￨L￨IN￨O￨- avalanche￨L￨NN￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- 1/f￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- 0.2￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- 1.3￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- experimentally￨L￨RB￨O￨A expected1733343536￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- finite￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- avalanche￨L￨NN￨O￨- size￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- cutoffs￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- also￨L￨RB￨O￨- must￨L￨MD￨O￨- diverge￨L￨VB￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- PLs￨U￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨A state22￨L￨NN￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- avalanches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- PL￨U￨NN￨O￨- distributed￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- cutoff￨L￨NN￨O￨- that￨L￨WDT￨O￨- scales￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- inside￨L￨IN￨O￨A the￨L￨DT￨O￨- GP￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- my￨L￨PRP$￨O￨- experience￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- systems/models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- within-host￨L￨NN￨O￨- and￨L￨CC￨O￨- between-host￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- given￨L￨VBN￨O￨- answers￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ”￨L￨''￨O￨- are￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- help￨L￨VBP￨O￨- us￨L￨PRP￨O￨- understand￨L￨VB￨O￨- biology￨L￨NN￨O￨A better￨L￨RBR￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- help￨L￨VBP￨O￨- us￨L￨PRP￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- gene￨L￨NN￨O￨- knockouts/knockins￨L￨NNS￨O￨- ,￨L￨,￨O￨- cell￨L￨NN￨O￨- depletions￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccines￨L￨NNS￨O￨- ,￨L￨,￨O￨- treatments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- some￨L￨DT￨O￨- cases￨L￨NNS￨O￨- mathematical￨L￨JJ￨O￨A models￨L￨NNS￨O￨A generate￨L￨VBP￨O￨- predictions￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- difficult￨L￨JJ￨O￨- or￨L￨CC￨O￨- impossible￨L￨JJ￨O￨- to￨L￨TO￨O￨- test￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- making￨L￨VBG￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- unscientific￨L￨JJ￨O￨- per￨L￨IN￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- scientific￨L￨JJ￨O￨- theory￨L￨NN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- philosophers￨L￨NNS￨O￨- of￨L￨IN￨O￨- science￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- Twentieth￨U￨NNP￨DATE￨- Century￨U￨NNP￨DATE￨- Karl￨U￨NNP￨PERSON￨- Popper￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +I￨U￨PRP￨O￨- hope￨L￨VBP￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- will￨L￨MD￨O￨- generate￨L￨VB￨O￨- the￨L￨DT￨O￨- much￨L￨JJ￨O￨- needed￨L￨VBN￨O￨- discussion￨L￨NN￨O￨- on￨L￨IN￨O￨- uses￨L￨NNS￨O￨- and￨L￨CC￨O￨- misuses￨L￨NNS￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- biology￨L￨NN￨O￨A and￨L￨CC￨O￨- perhaps￨L￨RB￨O￨- will￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- quantitative￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- topic￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨A models￨L￨NNS￨O￨A are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- useful￨L￨JJ￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- important￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- biological￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- .￨L￨.￨O￨- +What￨U￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- in￨L￨IN￨O￨- biology￨L￨NN￨O￨A ?￨L￨.￨O￨- +To￨U￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecasts￨L￨NNS￨O￨- and￨L￨CC￨O￨- improve￨L￨VB￨O￨- their￨L￨PRP$￨O￨- usefulness￨L￨NN￨O￨- to￨L￨TO￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- decision￨L￨NN￨O￨- making￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- organized￨L￨VBN￨O￨- a￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- forecasting￨L￨NN￨O￨A challenge￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- objectives￨L￨NNS￨O￨- of￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecasts￨L￨NNS￨O￨- ,￨L￨,￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- increasing￨L￨VBG￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecasting￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- improving￨L￨VBG￨O￨- the￨L￨DT￨O￨- utility￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecasts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Results￨U￨NNS￨MISC￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- centers￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- prevention￨L￨NN￨O￨- ’s￨L￨POS￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2014￨L￨CD￨DATE￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- Season￨U￨NN￨MISC￨- ChallengeMatthew￨U￨NNP￨MISC￨- Biggerstaff1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- Alper2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Mark￨U￨NNP￨PERSON￨- Dredze3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Spencer￨U￨NNP￨PERSON￨- Fox4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Isaac￨U￨NNP￨PERSON￨- Chun-Hai￨U￨NNP￨PERSON￨- Fung5￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Kyle￨U￨NNP￨PERSON￨- S.￨U￨NNP￨O￨- To￨U￨TO￨O￨- encourage￨L￨VB￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- innovation￨L￨NN￨O￨- in￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecasting￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- organized￨L￨VBN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Unites￨U￨NNP￨O￨- States￨U￨NNPS￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- forecast￨L￨NN￨O￨- was￨L￨VBD￨O￨- due￨L￨JJ￨O￨- on￨L￨IN￨O￨- December￨U￨NNP￨DATE￨- 2￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2013￨L￨CD￨DATE￨- ;￨L￨:￨O￨- 3/13￨L￨CD￨NUMBER￨- forecasts￨L￨NNS￨O￨- received￨L￨VBD￨O￨- correctly￨L￨RB￨O￨- predicted￨L￨VBN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨A within￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- 1/13￨L￨CD￨NUMBER￨- predicted￨L￨VBD￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- within￨L￨IN￨O￨- 1￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- 3/13￨L￨CD￨NUMBER￨- predicted￨L￨VBD￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- ILINet￨U￨NN￨O￨- percentage￨L￨NN￨O￨- within￨L￨IN￨O￨- 1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 4/13￨L￨CD￨NUMBER￨- predicted￨L￨VBD￨O￨- the￨L￨DT￨O￨- season￨L￨NN￨O￨- duration￨L￨NN￨O￨- within￨L￨IN￨O￨- 1￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +Infectious￨U￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- forecasting￨L￨NN￨O￨A combines￨L￨VBZ￨O￨- traditional￨L￨JJ￨O￨- and￨L￨CC￨O￨- internet-derived￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- with￨L￨IN￨O￨- novel￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +Initial￨U￨JJ￨O￨- work￨L￨NN￨O￨- describing￨L￨VBG￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecasting￨L￨NN￨O￨A methods￨L￨NNS￨O￨- was￨L￨VBD￨O￨- promising￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- temporal￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- and￨L￨CC￨O￨- antigenicity￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- never￨L￨RB￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- ,￨L￨,￨O￨- largely￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- specimens￨L￨NNS￨O￨- which￨L￨WDT￨O￨- were￨L￨VBD￨O￨- subjectively￨L￨RB￨O￨- selected￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨A drifts￨L￨NNS￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- ,￨L￨,￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- representative￨L￨JJ￨TITLE￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- strains￨L￨NNS￨O￨- currently￨L￨RB￨DATE￨- circulating￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- information￨L￨NN￨O￨- has￨L￨VBZ￨O￨- seldom￨L￨RB￨O￨- been￨L￨VBN￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- and￨L￨CC￨O￨- antigenic￨L￨JJ￨O￨A surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- date￨L￨NN￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- assessed￨L￨VBN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- and￨L￨CC￨O￨- antigenic￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- network￨L￨NN￨O￨- managed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- routinely￨L￨RB￨O￨- selected￨L￨VBD￨O￨- potentially￨L￨RB￨O￨- drifted￨L￨VBN￨O￨- specimens￨L￨NNS￨O￨- for￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- and￨L￨CC￨O￨- antigenic￨L￨JJ￨O￨A characterization￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- implemented￨L￨VBD￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2014￨L￨CD￨DATE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- randomly￨L￨RB￨O￨- select￨L￨VB￨O￨- a￨L￨DT￨O￨- sample￨L￨NN￨O￨A of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- specimens￨L￨NNS￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- aged￨L￨JJ￨O￨- below￨L￨IN￨O￨- 18￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- adults￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- tertiary￨L￨JJ￨O￨- hospitals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- Island￨U￨NNP￨LOCATION￨- each￨L￨DT￨SET￨- week￨L￨NN￨SET￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- CI￨U￨NN￨O￨- propagation￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- CI￨U￨NN￨MISC￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- name￨L￨VBP￨O￨- Collective￨U￨JJ￨O￨- Influence￨U￨NN￨O￨- Propagation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- CIP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- influence￨L￨VBP￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +1￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨A maximization￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- introduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- Collective￨U￨NNP￨O￨- Influence￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- CI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- localizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- showed￨L￨VBD￨O￨- in1￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- objective￨L￨JJ￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨A eigenvalue￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- non-backtracking￨L￨JJ￨O￨- matrix￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NB￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- occupation￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- encoding￨L￨VBG￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- vacancy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- occupancy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- an￨L￨DT￨O￨- improved￨L￨VBN￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- CI￨U￨NN￨O￨- algorithm￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- keeps￨L￨VBZ￨O￨- the￨L￨DT￨O￨- computational￨L￨JJ￨O￨- complexity￨L￨NN￨O￨- bounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- log￨L￨NN￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- removed￨L￨VBN￨O￨- one-by-one￨L￨RB￨O￨- .￨L￨.￨O￨- +Study￨U￨NNP￨O￨- protocol￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Mass￨U￨NNP￨STATE_OR_PROVINCE￨- mosquito￨L￨NN￨O￨- trapping￨L￨NN￨O￨- for￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A control￨L￨NN￨O￨- in￨L￨IN￨O￨- western￨L￨JJ￨O￨- Kenya￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- study￨L￨NN￨O￨- protocol￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- stepped￨L￨VBN￨O￨- wedge￨L￨NN￨O￨- cluster-randomised￨L￨JJ￨O￨- trialAlexandra￨L￨NN￨O￨- Hiscox￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Tobias￨U￨NNP￨PERSON￨- Homan￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Collins￨U￨NNP￨PERSON￨- K.￨U￨NNP￨PERSON￨- Smith3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- †￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 17:356￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Increasing￨U￨VBG￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- insecticide￨L￨NN￨O￨- resistance￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- outdoor￨L￨JJ￨O￨- ,￨L￨,￨O￨- residual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- threaten￨L￨VBP￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- existing￨L￨VBG￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- tools￨L￨NNS￨O￨- used￨L￨VBN￨O￨- against￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- mosquitoes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods/design￨U￨NN￨O￨- A￨U￨NN￨O￨- stepped￨L￨VBD￨O￨- wedge￨L￨NN￨O￨- cluster-randomised￨L￨JJ￨O￨- trial￨L￨NN￨O￨- design￨L￨NN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- mosquito￨L￨NN￨O￨A trapping￨L￨NN￨O￨- on￨L￨IN￨O￨- Rusinga￨U￨NNP￨LOCATION￨- Island￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- western￨L￨JJ￨O￨- Kenya￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- SolarMal￨U￨NNP￨O￨- project￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- odour-baited￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- traps￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A through￨L￨IN￨O￨- mass￨L￨NN￨O￨- trapping￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- vectors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Over￨U￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 2013￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- all￨L￨DT￨O￨- households￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- island￨L￨NN￨O￨- were￨L￨VBD￨O￨- provided￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- solar-powered￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨A trapping￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- causal￨L￨JJ￨O￨- link￨L￨NN￨O￨- between￨L￨IN￨O￨- ZIKV￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- microcephaly￨L￨NN￨O￨- was￨L￨VBD￨O￨- inferred￨L￨VBN￨O￨- via￨L￨IN￨O￨- several￨L￨JJ￨O￨- independent￨L￨JJ￨RELIGION￨- lines￨L￨NNS￨O￨- of￨L￨IN￨O￨- evidence￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- microcephaly￨L￨RB￨O￨- and￨L￨CC￨O￨- brain￨L￨NN￨O￨A abnormalities￨L￨NNS￨O￨- in￨L￨IN￨O￨- infants￨L￨NNS￨O￨- born￨L￨VBN￨O￨- to￨L￨TO￨O￨- mothers￨L￨NNS￨O￨- with￨L￨IN￨O￨- suspected￨L￨VBN￨O￨- or￨L￨CC￨O￨- confirmed￨L￨VBN￨O￨- ZIKV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- or￨L￨CC￨O￨- second￨L￨JJ￨ORDINAL￨- trimester￨L￨NN￨O￨- of￨L￨IN￨O￨- pregnancy￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- rare￨L￨JJ￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- microcephaly￨L￨NN￨O￨- in￨L￨IN￨O￨- infants￨L￨NNS￨O￨- with￨L￨IN￨O￨- congenital￨L￨JJ￨O￨- Zika￨U￨NN￨O￨- syndrome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CZS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- distinguishing￨L￨VBG￨O￨- it￨L￨PRP￨O￨- from￨L￨IN￨O￨- microcephaly￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- other￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- birth￨L￨NN￨O￨- defects￨L￨VBZ￨O￨- occurring￨L￨VBG￨O￨- in￨L￨IN￨O￨- women￨L￨NNS￨O￨- with￨L￨IN￨O￨- travel-acquired￨L￨JJ￨O￨- ZIKV￨U￨NN￨O￨- ,￨L￨,￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- low￨L￨JJ￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- events￨L￨NNS￨O￨- were￨L￨VBD￨O￨- coincident￨L￨JJ￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- causal￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- biology￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- integrated￨L￨VBN￨O￨- with￨L￨IN￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- reducing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- vector-to-human￨L￨NN￨O￨- and￨L￨CC￨O￨- sexual￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- via￨L￨IN￨O￨- vector￨L￨NN￨O￨A control￨L￨NN￨O￨- and￨L￨CC￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- ,￨L￨,￨O￨- planning￨L￨VBG￨O￨- pregnancy￨L￨NN￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- the￨L￨DT￨O￨- high-transmission￨L￨JJ￨O￨- season￨L￨NN￨O￨- ,￨L￨,￨O￨- launching￨L￨VBG￨O￨- vaccines￨L￨NNS￨O￨- once￨L￨RB￨DATE￨- developed￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reducing￨L￨VBG￨O￨- intrauterine￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- pathology￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- climatic￨L￨JJ￨O￨- ,￨L￨,￨O￨- physiological￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- behavioral￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- influence￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- seasonality￨L￨NN￨O￨- include￨L￨VBP￨O￨- those￨L￨DT￨O￨- that￨L￨WDT￨O￨- impact￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- and/or￨L￨CC￨O￨- vector￨L￨NN￨O￨A susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- host/vector￨L￨NN￨O￨- infectiousness￨L￨NN￨O￨- ,￨L￨,￨O￨- virus￨L￨NN￨O￨- viability￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission-relevant￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- among￨L￨IN￨O￨- hosts/vectors￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- abundance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Lastly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- ZIKV￨U￨NN￨O￨- genome￨L￨NN￨O￨- was￨L￨VBD￨O￨- recovered￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- brain￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- fetus￨L￨NN￨O￨- with￨L￨IN￨O￨- microcephaly￨L￨NN￨O￨- aborted￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- expectant￨L￨JJ￨O￨- mother￨L￨NN￨O￨- infected￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 13th￨L￨JJ￨DATE￨- week￨L￨NN￨DATE￨- of￨L￨IN￨O￨- gestation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- reported￨L￨VBN￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- newborns￨L￨NNS￨O￨- from￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- with￨L￨IN￨O￨- microcephaly￨L￨NN￨O￨- who￨L￨WP￨O￨- died￨L￨VBD￨O￨- shortly￨L￨RB￨O￨- after￨L￨IN￨O￨- birth￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- miscarriages￨L￨NNS￨O￨- ;￨L￨:￨O￨- all￨L￨DT￨O￨- tested￨L￨VBN￨O￨- positive￨L￨JJ￨O￨- for￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Pregnant￨U￨JJ￨O￨- women￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- risk￨L￨NN￨O￨- severe￨L￨JJ￨O￨- fetal￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- brain￨L￨NN￨O￨A abnormalities￨L￨NNS￨O￨- —￨L￨:￨O￨- believed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- disruption￨L￨NN￨O￨- of￨L￨IN￨O￨- brain￨L￨NN￨O￨- development￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- intrauterine￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- —￨L￨:￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- investigation￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- stratified￨L￨VBN￨O￨- by￨L￨IN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- partner￨L￨NN￨O￨A change￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- effects￨L￨NNS￨O￨- and￨L￨CC￨O￨- prospects￨L￨NNS￨O￨- of￨L￨IN￨O￨- elimination￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- represents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- stratified￨L￨VBN￨O￨- into￨L￨IN￨O￨- m￨L￨NN￨O￨- risk￨L￨NN￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- partner￨L￨NN￨O￨A change￨L￨NN￨O￨- rates￨L￨NNS￨O￨- c￨L￨NN￨O￨- ,￨L￨,￨O￨- l￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explicitly￨L￨RB￨O￨- incorporated￨L￨VBD￨O￨- risk￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- sexual￨L￨JJ￨O￨A activity￨L￨NN￨O￨- and￨L￨CC￨O￨- mixing￨L￨VBG￨O￨- between￨L￨IN￨O￨- population￨L￨NN￨O￨- groups￨L￨NNS￨O￨- by￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- activity￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- risk￨L￨NN￨O￨A behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- on￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- group￨L￨NN￨O￨- l￨L￨NN￨O￨- consists￨L￨VBZ￨O￨A of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- treated￨L￨VBN￨O￨- ,￨L￨,￨O￨- A￨U￨DT￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- n￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- stages￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- computer￨L￨NN￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- population￨L￨NN￨O￨- evolving￨L￨VBG￨O￨- under￨L￨IN￨O￨- recurrent￨L￨JJ￨O￨- selective￨L￨JJ￨O￨A sweeps￨L￨NNS￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- positive￨L￨JJ￨O￨- selection￨L￨NN￨O￨- alone￨L￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- occurs￨L￨VBZ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- estimated￨L￨VBN￨O￨- by￨L￨IN￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- effective￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- thus￨L￨RB￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- background￨L￨NN￨O￨- selection￨L￨NN￨O￨- and￨L￨CC￨O￨- metapopulation￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A ,￨L￨,￨O￨- using￨L￨VBG￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reproduce￨L￨VBP￨O￨- other￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- in￨L￨IN￨O￨- H3N2￨U￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- either￨L￨CC￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- incorporated￨L￨VBN￨O￨- in￨L￨IN￨O￨- recurrent￨L￨JJ￨O￨- selective￨L￨JJ￨O￨A sweep￨L￨NN￨O￨- simulation￨L￨NN￨O￨- ,￨L￨,￨O￨- selective￨L￨JJ￨O￨- sweeps￨L￨NNS￨O￨- are￨L￨VBP￨O￨- mostly￨L￨RB￨O￨- hard￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- synonymous￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- census￨L￨NN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- those￨L￨DT￨O￨- mutations￨L￨NNS￨O￨- arise￨L￨VBP￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- much￨L￨RB￨O￨- smaller￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- forces￨L￨NNS￨O￨- before￨L￨IN￨O￨- selective￨L￨JJ￨O￨A sweeps￨L￨NNS￨O￨- further￨L￨RBR￨O￨- reduce￨L￨VB￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +Genetic￨U￨JJ￨O￨- hitchhiking￨L￨VBG￨O￨- fails￨L￨VBZ￨O￨- to￨L￨TO￨O￨- completely￨L￨RB￨O￨- wipe￨L￨VB￨O￨- out￨L￨RP￨O￨- pre-existing￨L￨JJ￨O￨- variation￨L￨NN￨O￨- because￨L￨IN￨O￨- soft￨L￨JJ￨O￨- ,￨L￨,￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- hard￨L￨RB￨O￨- ,￨L￨,￨O￨- selective￨L￨JJ￨O￨A sweeps￨L￨NNS￨O￨- prevail￨L￨VBP￨O￨- under￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- mutation￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Refined￨U￨VBN￨MISC￨- stratified-worm-burden￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- incorporate￨L￨VBP￨O￨- specific￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- snail￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- better￨L￨JJR￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- Schistosoma￨U￨NN￨O￨- diagnosis￨L￨NN￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- controlDavid￨L￨NN￨O￨- Gurarie1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Charles￨U￨NNP￨PERSON￨- H.￨U￨NNP￨PERSON￨- Multiple￨U￨JJ￨PERSON￨- factors￨L￨NNS￨O￨- modify￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- affect￨L￨VB￨O￨- their￨L￨PRP$￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- aggregated￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- worm￨L￨NN￨O￨A burdens￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- parasite￨L￨NN￨O￨- reproduction￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- snail￨L￨NN￨O￨- biology￨L￨NN￨O￨- .￨L￨.￨O￨- +Modeling￨U￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenging￨L￨JJ￨O￨- task￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- more￨L￨JJR￨O￨- accurate￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- ,￨L￨,￨O￨- newer￨L￨JJR￨O￨- models￨L￨NNS￨O￨- should￨L￨MD￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- influential￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- in-host￨L￨JJ￨O￨- biology￨L￨NN￨O￨A ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- diagnostic￨L￨JJ￨O￨- uncertainties￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- To￨U￨TO￨O￨- refine￨L￨VB￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- predictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- modified￨L￨VBD￨O￨- an￨L￨DT￨O￨- earlier￨L￨JJR￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SWB￨U￨NN￨O￨- by￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- factors￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- essential￨L￨JJ￨O￨- in-host￨L￨JJ￨O￨- biology￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- parasite￨L￨NN￨O￨- mating￨L￨NN￨O￨- ,￨L￨,￨O￨- aggregation￨L￨NN￨O￨- ,￨L￨,￨O￨- density-dependent￨L￨JJ￨O￨- fecundity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- random￨L￨JJ￨O￨- egg-release￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- demographically￨L￨RB￨O￨- structured￨L￨VBN￨O￨- host￨L￨NN￨TITLE￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- heterogeneous￨L￨JJ￨O￨- factors￨L￨NNS￨O￨A that￨L￨WDT￨O￨- play￨L￨VBP￨O￨- important￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- perpetuation￨L￨NN￨O￨- of￨L￨IN￨O￨- schistosomiasis￨L￨NN￨O￨- include￨L￨VBP￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- local￨L￨JJ￨O￨- human￨L￨JJ￨O￨- demographics￨L￨NNS￨O￨- and￨L￨CC￨O￨- exposure￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- ,￨L￨,￨O￨- patchy￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- habitats￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨- of￨L￨IN￨O￨- rainfall￨L￨NNS￨O￨- and￨L￨CC￨O￨- temperature￨L￨NN￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- affect￨L￨VBP￨O￨- snail￨L￨NN￨O￨- abundance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- Schistosoma￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- metazoan￨L￨JJ￨O￨- macro-parasites￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- highly￨L￨RB￨O￨- uneven￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- heterogeneous￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- among￨L￨IN￨O￨- its￨L￨PRP$￨O￨- vertebrate￨L￨NN￨O￨- host￨L￨NN￨TITLE￨A populations￨L￨NNS￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- evident￨L￨JJ￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- experimental￨L￨JJ￨O￨- and￨L￨CC￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- S0￨U￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A declines￨L￨VBZ￨O￨- monotonically￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- eventually￨L￨RB￨O￨- disappears￨L￨VBZ￨O￨- ;￨L￨:￨O￨- while￨L￨IN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- increases￨L￨VBZ￨O￨- first￨L￨RB￨ORDINAL￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- decreases￨L￨VBZ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- occurs￨L￨VBZ￨O￨- outbreak￨L￨NN￨O￨- and/or￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- recovered￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- βS￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- this￨L￨DT￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- corresponding￨L￨JJ￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- removed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- possible￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨A are￨L￨VBP￨O￨- linked￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- called￨L￨VBN￨O￨- neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- generalized￨L￨VBN￨O￨- as￨L￨IN￨O￨- below￨L￨IN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨A individuals￨L￨NNS￨O￨A with￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ⋯￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Just￨U￨RB￨O￨- as￨L￨IN￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- approximation￨L￨NN￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- observed￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨A infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- homogeneous￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- too￨L￨RB￨O￨- oversimplified￨L￨JJ￨O￨- and￨L￨CC￨O￨- ignores￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approach￨L￨NN￨O￨- taken￨L￨VBN￨O￨- by￨L￨IN￨O￨- Grzymkowski￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- coauthors￨L￨NNS￨O￨- relied￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- temperature￨L￨NN￨O￨A field￨L￨NN￨O￨- takes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- generating￨L￨NN￨O￨- function￨L￨NN￨O￨- Equality￨U￨NN￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Sum￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- left￨L￨VBD￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- right￨L￨NN￨O￨- Phi￨U￨NNP￨O￨- x￨L￨CC￨O￨- j￨L￨NNP￨O￨- Pow￨U￨NNP￨O￨- factorial￨L￨JJ￨O￨- j￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- A￨U￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- j￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- undetermined￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- and￨L￨CC￨O￨- solidification￨L￨NN￨O￨- front￨L￨JJ￨O￨- Phi￨U￨NNP￨O￨- t￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- through￨L￨IN￨O￨- xi￨L￨NN￨O￨- t￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- satisfying￨L￨VBG￨O￨- the￨L￨DT￨O￨- boundary￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 3a￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- in￨L￨IN￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Closed￨U￨JJ￨MISC￨- solutions￨L￨NNS￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- differential-difference￨L￨JJ￨O￨- equation￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- associated￨L￨VBN￨O￨- plate￨L￨NN￨O￨- solidification￨L￨NN￨O￨- problemOlawanle￨L￨NNP￨O￨- P.￨U￨NNP￨O￨- Johnson2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 5:1273￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractTwo￨U￨NNP￨O￨- distinct￨L￨JJ￨O￨- and￨L￨CC￨O￨- novel￨L￨JJ￨O￨- formalisms￨L￨NNS￨O￨- for￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- exact￨L￨NN￨O￨- closed￨L￨VBD￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- variable-coefficient￨L￨JJ￨O￨- differential-difference￨L￨NN￨O￨- equations￨L￨NNS￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- plate￨L￨NN￨O￨- solidification￨L￨NN￨O￨- problem￨L￨NN￨O￨- are￨L￨VBP￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +Equation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- models￨L￨NNS￨O￨- the￨L￨DT￨O￨- temperature￨L￨NN￨O￨A distribution￨L￨NN￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- solid￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- plate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- x￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- half￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- plate￨L￨NN￨O￨- thickness￨L￨NN￨O￨- ,￨L￨,￨O￨- lambda￨L￨NN￨O￨- its￨L￨PRP$￨O￨- thermal￨L￨JJ￨O￨- conductivity￨L￨NN￨O￨- ,￨L￨,￨O￨- kappa￨L￨NN￨O￨- its￨L￨PRP$￨O￨- latent￨L￨JJ￨O￨- heat￨L￨NN￨O￨- of￨L￨IN￨O￨- fusion￨L￨NN￨O￨- ,￨L￨,￨O￨- gamma￨L￨NN￨O￨- its￨L￨PRP$￨O￨- mass￨L￨NN￨O￨- density￨L￨NN￨O￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- its￨L￨PRP$￨O￨- diffusivity￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Equality￨U￨NN￨O￨- b￨L￨NN￨O￨- lambda￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- propose￨L￨VB￨O￨- a￨L￨DT￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- between￨L￨IN￨O￨- humans￨L￨NNS￨O￨A and￨L￨CC￨O￨- cows￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- BTB￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- situation￨L￨NN￨O￨- and￨L￨CC￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- Urumqi￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- reference￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- exploring￨L￨VBG￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- between￨L￨IN￨O￨- humans￨L￨NNS￨O￨A and￨L￨CC￨O￨- cows￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- established￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- establishing￨L￨VBG￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- were￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- discussion￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 82271￨L￨CD￨NUMBER￨- cows￨L￨NNS￨O￨- were￨L￨VBD￨O￨- quarantined￨L￨VBN￨O￨A using￨L￨VBG￨O￨- tuberculin￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PPD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- intradermal￨L￨JJ￨O￨- allergic￨L￨JJ￨O￨- reaction￨L￨NN￨O￨- for￨L￨IN￨O￨- 8￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- Urumqi￨U￨NNP￨CITY￨- of￨L￨IN￨O￨- 14￨L￨CD￨NUMBER￨- large-scale￨L￨JJ￨O￨- dairy￨L￨NN￨O￨- farms￨L￨NNS￨O￨- and￨L￨CC￨O￨- 8￨L￨CD￨NUMBER￨- counties￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- 333￨L￨CD￨NUMBER￨- positive￨L￨JJ￨O￨- cows￨L￨NNS￨O￨- in￨L￨IN￨O￨- quarantined￨L￨VBN￨O￨A cows￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- positive￨L￨JJ￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 0.40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- relating￨L￨VBG￨O￨- observed￨L￨VBN￨O￨- spreading￨L￨VBG￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- quantity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- idiosyncratic￨L￨JJ￨O￨- network￨L￨NN￨O￨- features￨L￨NNS￨O￨- are￨L￨VBP￨O￨- null￨L￨JJ￨O￨A models￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- which￨L￨WDT￨O￨- separately￨L￨RB￨O￨- destroy￨L￨VBP￨O￨- correlations￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- applied￨L￨VBD￨O￨- null￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- contact￨L￨NN￨O￨- shufflings￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- call￨L￨NN￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MCN￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- were￨L￨VBD￨O￨- mobile￨L￨JJ￨TITLE￨- subscribers￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- were￨L￨VBD￨O￨- placed￨L￨VBN￨O￨- between￨L￨IN￨O￨- caller/callee￨L￨NN￨O￨- pairs￨L￨NNS￨O￨- and￨L￨CC￨O￨- annotated￨L￨JJ￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- call￨L￨NN￨O￨- timestamps￨L￨NNS￨O￨- .￨L￨.￨O￨- +Prior￨U￨RB￨O￨- null￨L￨JJ￨O￨A models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- shuffling￨L￨NN￨O￨- —￨L￨:￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- timestamped￨L￨JJ￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- shuffle￨L￨NN￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ways￨L￨NNS￨O￨- to￨L￨TO￨O￨- retain￨L￨VB￨O￨- certain￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- while￨L￨IN￨O￨- destroying￨L￨VBG￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- limitation￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- shuffled￨L￨VBD￨O￨- null￨L￨JJ￨O￨A models￨L￨NNS￨O￨- as￨L￨IN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- colocation-based￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- draw￨L￨VB￨O￨- any￨L￨DT￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- spatiotemporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- inducement￨L￨NN￨O￨- shuffling￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- state￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- events￨L￨NNS￨O￨- that￨L￨WDT￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- place￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- movement￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- influence￨L￨NN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- meteorological￨L￨JJ￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨A factors￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- temperature￨L￨NN￨O￨- ,￨L￨,￨O￨- rainfall￨L￨NNS￨O￨- and￨L￨CC￨O￨- flooding￨L￨NN￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- abundant￨L￨JJ￨O￨- species￨L￨NNS￨O￨- detected￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Culex￨U￨JJ￨MISC￨- pipiens￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- diversity￨L￨NN￨O￨- and￨L￨CC￨O￨- composition￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- RVF￨U￨NN￨O￨- mosquito￨L￨NN￨O￨- vectors￨L￨NNS￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- area￨L￨NN￨O￨- are￨L￨VBP￨O￨- unknown￨L￨JJ￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- climatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- ecological￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- their￨L￨PRP$￨O￨- population￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Rift￨U￨NNP￨MISC￨- Valley￨U￨NNP￨MISC￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- vector￨L￨NN￨O￨- diversity￨L￨NN￨O￨- and￨L￨CC￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- meteorological￨L￨JJ￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨A factors￨L￨NNS￨O￨A on￨L￨IN￨O￨- Culex￨U￨JJ￨MISC￨- pipiens￨L￨NNS￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Okavango￨U￨NNP￨LOCATION￨- Delta￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- BotswanaHammami￨U￨NNP￨O￨- Pachka￨U￨NNP￨O￨- †￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Tran￨U￨NNP￨O￨- Annelise￨U￨NNP￨O￨- †￨L￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kemp￨U￨NNP￨PERSON￨- Alan5￨U￨NNP￨O￨- ,￨L￨,￨O￨- Tshikae￨U￨NNP￨O￨- Power2￨U￨NNP￨O￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kgori￨U￨NNP￨O￨- Patrick6￨U￨NN￨O￨- ,￨L￨,￨O￨- Chevalier￨U￨NNP￨PERSON￨- Véronique1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Paweska￨U￨NNP￨O￨- Janusz5￨U￨NNP￨O￨- and￨L￨CC￨O￨- Jori￨U￨NNP￨PERSON￨- Ferran￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- †￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 9:434￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- In￨U￨IN￨O￨- Northern￨U￨NNP￨LOCATION￨- Botswana￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- rural￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- ,￨L￨,￨O￨- livestock￨L￨NN￨O￨- ,￨L￨,￨O￨- wildlife￨L￨NN￨O￨- and￨L￨CC￨O￨- large￨L￨JJ￨O￨A numbers￨L￨NNS￨O￨A of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- cohabitate￨L￨VBP￨O￨- around￨L￨IN￨O￨- permanent￨L￨JJ￨O￨- waters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Okavango￨U￨NNP￨LOCATION￨- Delta￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- sub-Saharan￨L￨JJ￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Rift￨U￨NNP￨O￨- Valley￨U￨NNP￨O￨- Fever￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- RVF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- circulate￨L￨VB￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- area￨L￨NN￨O￨A among￨L￨IN￨O￨- wild￨L￨JJ￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- 32￨L￨CD￨NUMBER￨- studies￨L￨NNS￨O￨- assessing￨L￨VBG￨O￨- MDR-TB￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- by￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- demonstrate￨L￨VB￨O￨- an￨L￨DT￨O￨- overall￨L￨JJ￨O￨- association￨L￨NN￨O￨A between￨L￨IN￨O￨- acquired￨L￨VBN￨O￨- MDR-TB￨U￨NN￨O￨- and￨L￨CC￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- co-infection￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- risk￨L￨NN￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- contracting￨L￨VBG￨O￨- primary￨L￨JJ￨O￨- MDR-TB￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Attempts￨U￨NNS￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- made￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- resistance￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- lieu￨L￨NN￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- relied￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- assumptions￨L￨NNS￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- biology￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- considered￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- risk￨L￨NN￨O￨- clusters￨L￨NNS￨O￨A :￨L￨:￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- of￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- EVD￨U￨NN￨O￨- case￨L￨NN￨O￨- occurrence￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- cluster￨L￨NN￨O￨- as￨L￨IN￨O￨- projected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- highest￨L￨JJS￨O￨- incident￨L￨NN￨O￨- cases￨L￨NNS￨O￨- two￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- previously￨L￨RB￨DATE￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- projected￨L￨VBN￨O￨- weekly￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- efficacious￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- vary￨L￨VB￨O￨- between￨L￨IN￨O￨- clusters￨L￨NNS￨O￨A over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- different￨L￨JJ￨O￨- risks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- predicted￨L￨VBN￨O￨- ,￨L￨,￨O￨- randomly￨L￨RB￨O￨- choosing￨L￨VBG￨O￨- a￨L￨DT￨O￨- cluster￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- treated￨L￨VBN￨O￨- fails￨L￨VBZ￨O￨- to￨L￨TO￨O￨- prioritize￨L￨VB￨O￨- those￨L￨DT￨O￨- at￨L￨IN￨O￨- highest￨L￨JJS￨O￨- risk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- undermines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ethical￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SWCT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- design￨L￨NN￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- ring￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- cluster-randomized￨L￨JJ￨O￨- trial￨L￨NN￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- trial￨L￨NN￨O￨- population￨L￨NN￨O￨- was￨L￨VBD￨O￨- made￨L￨VBN￨O￨- up￨L￨IN￨O￨- of￨L￨IN￨O￨- clusters￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- and￨L￨CC￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- laboratory-confirmed￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- or￨L￨CC￨O￨- modeled￨L￨VBN￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- within￨L￨IN￨O￨- districts￨L￨NNS￨O￨- of￨L￨IN￨O￨- SL￨U￨NNP￨O￨- to￨L￨TO￨O￨- assign￨L￨VB￨O￨- clusters￨L￨NNS￨O￨A to￨L￨TO￨O￨- receive￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- OSWCT￨U￨NNP￨O￨- designs￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- stepped-wedge￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- trial￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- SWCT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- another￨L￨DT￨O￨- trial￨L￨NN￨O￨- design￨L￨NN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- test￨L￨VB￨O￨- a￨L￨DT￨O￨- candidate￨L￨NN￨TITLE￨- vaccine￨L￨NN￨O￨- in￨L￨IN￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- SL￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- addresses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rationality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- metrics￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- robustness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- algebraic￨L￨JJ￨O￨A connectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- edge￨L￨NN￨O￨- betweenness￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- investigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- robust￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- generalized￨L￨VBN￨O￨- meshes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- GMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- robustness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- metrics￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- algebraic￨L￨JJ￨O￨A connectivity￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- edge￨L￨NN￨O￨- betweenness￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Wang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Van￨U￨NNP￨PERSON￨- Mieghem￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- designed￨L￨VBN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- two￨L￨CD￨NUMBER￨- heuristic￨L￨NN￨O￨- algorithms￨L￨NNS￨O￨- for￨L￨IN￨O￨- stepwise￨L￨JJ￨O￨- maximizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- algebraic￨L￨JJ￨O￨A connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- edge-growing￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- mesh￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GM￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- grown￨L￨VBN￨O￨- up￨L￨RP￨O￨- by￨L￨IN￨O￨- stepwise￨L￨JJ￨O￨- optimizing￨L￨VBG￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- robustness￨L￨NN￨O￨A .￨L￨.￨O￨- +Subsequently￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- validated￨L￨VBD￨O￨- the￨L￨DT￨O￨- acquired￨L￨VBN￨O￨- CPI￨U￨NNP￨MISC￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- with￨L￨IN￨O￨- real￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- records￨L￨NNS￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨A CPI￨U￨NNP￨MISC￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- idealized￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- commonly￨L￨RB￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- real￨L￨JJ￨O￨- CPI￨U￨NNP￨MISC￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- constructed￨L￨VBN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- time￨L￨NN￨O￨- resolution￨L￨NN￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- CPIs￨U￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- dynamic￨L￨JJ￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- simulate￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- CPI￨U￨NNP￨MISC￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- simulation￨L￨NN￨O￨- was￨L￨VBD￨O￨- set￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- resolution￨L￨NN￨O￨A .￨L￨.￨O￨- +As￨U￨IN￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨A CPI￨U￨NNP￨MISC￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- behavior￨L￨NN￨O￨- in￨L￨IN￨O￨- Chinese￨U￨JJ￨NATIONALITY￨- colleges￨L￨NNS￨O￨- .￨L￨.￨O￨- +Orally￨U￨RB￨O￨- applied￨L￨VBN￨O￨- fipronil￨L￨NN￨O￨- can￨L￨MD￨O￨- remain￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- for￨L￨IN￨O￨- several￨L￨JJ￨DURATION￨- weeks￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- several￨L￨JJ￨DURATION￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- concentration￨L￨NN￨O￨- administered￨L￨VBN￨O￨A (￨L￨-LRB-￨O￨- mg/kg￨L￨NN￨O￨- body￨L￨NN￨O￨- weight￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- fipronil￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- lengthy￨L￨JJ￨O￨- half-life￨L￨NN￨O￨- of￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 128￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- that￨L￨IN￨O￨- sand￨L￨NN￨O￨- fly￨L￨VBP￨O￨- control￨L￨NN￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- be￨L￨VB￨O￨- maintained￨L￨VBN￨O￨- for￨L￨IN￨O￨- several￨L￨JJ￨DURATION￨- months￨L￨NNS￨DURATION￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +Fipronil-based￨U￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- orally￨L￨RB￨O￨- administered￨L￨VBN￨O￨- to￨L￨TO￨O￨- cattle￨L￨NNS￨O￨A and￨L￨CC￨O￨- rodents￨L￨NNS￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- successful￨L￨JJ￨O￨- in￨L￨IN￨O￨- killing￨L￨VBG￨O￨- laboratory-reared￨L￨JJ￨O￨- sand￨L￨NN￨O￨- flies￨L￨NNS￨O￨- under￨L￨IN￨O￨- controlled￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- targeting￨L￨VBG￨O￨- blood-feeding￨L￨JJ￨O￨- adults￨L￨NNS￨O￨- and￨L￨CC￨O￨- larvae￨L￨NNS￨O￨- that￨L￨WDT￨O￨- feed￨L￨VBP￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- feces￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recent￨L￨JJ￨O￨- models￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- VL￨U￨NNP￨O￨- epidemiology￨L￨NN￨O￨- within￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Bihar￨U￨NNP￨CITY￨- have￨L￨VBP￨O￨- examined￨L￨VBN￨O￨- VL￨U￨NNP￨O￨- underreporting￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- antimony￨L￨JJ￨O￨- resistant￨L￨JJ￨O￨- VL￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- VL￨U￨NNP￨O￨- treatment￨L￨NN￨O￨A ,￨L￨,￨O￨- prevention￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- specific￨L￨JJ￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- adulticides￨L￨NNS￨O￨- and￨L￨CC￨O￨- destruction￨L￨NN￨O￨- of￨L￨IN￨O￨- sand￨L￨NN￨O￨- fly￨L￨VBP￨O￨- breeding￨L￨VBG￨O￨- sites￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- could￨L￨MD￨O￨- potentially￨L￨RB￨O￨- supplement￨L￨VB￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- practice￨L￨NN￨O￨- of￨L￨IN￨O￨- IRS￨U￨NNP￨ORGANIZATION￨- by￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- exophilic￨L￨JJ￨O￨- ,￨L￨,￨O￨- cattle-feeding￨L￨JJ￨O￨- adult￨L￨JJ￨O￨- sand￨L￨NN￨O￨- flies￨L￨NNS￨O￨- and￨L￨CC￨O￨- larval￨L￨JJ￨O￨- sand￨L￨NN￨O￨- flies￨L￨VBZ￨O￨- feeding￨L￨VBG￨O￨- on￨L￨IN￨O￨- organic￨L￨JJ￨O￨- matter￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A feces￨L￨NNS￨O￨- .￨L￨.￨O￨- +Phlebotomine￨U￨NNP￨O￨- sand￨L￨NN￨O￨- flies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- small￨L￨JJ￨O￨- Diptera￨U￨NNP￨O￨- ,￨L￨,￨O￨- rarely￨L￨RB￨O￨- exceeding￨L￨VBG￨O￨- a￨L￨DT￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- mm￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- family￨L￨NN￨O￨- Psychodidae￨U￨NN￨O￨- and￨L￨CC￨O￨- subfamily￨L￨NN￨O￨- Phlebotominae￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- holometabolous￨L￨JJ￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- life￨L￨NN￨O￨- stages￨L￨NNS￨O￨- :￨L￨:￨O￨- eggs￨L￨NNS￨O￨- ,￨L￨,￨O￨- larvae￨L￨NNS￨O￨- ,￨L￨,￨O￨- pupae￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- adults￨L￨NNS￨O￨A .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- variables￨L￨NNS￨O￨- that￨L￨WDT￨O￨- drive￨L￨VBP￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- linking￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- survival￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- in￨L￨IN￨O￨- common￨L￨JJ￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- quantitative￨L￨JJ￨O￨- traits￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- virions￨L￨NNS￨O￨- ,￨L￨,￨O￨- unicellular￨L￨JJ￨O￨- parasites￨L￨NNS￨O￨- ,￨L￨,￨O￨- antibodies￨L￨NNS￨O￨- and￨L￨CC￨O￨- lymphocytes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- blood￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Constructing￨U￨VBG￨O￨- mechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- capture￨L￨VBP￨O￨- the￨L￨DT￨O￨- detail￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- fluctuations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- complicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- array￨L￨NN￨O￨- of￨L￨IN￨O￨- effectors￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨A response￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- feedbacks￨L￨NNS￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- keep￨L￨VB￨O￨- potentially￨L￨RB￨O￨- harmful￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- in￨L￨IN￨O￨- check￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- memory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- parasite￨L￨JJ￨O￨- growth￨L￨NN￨O￨- itself￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- evolutionary￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- traits￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- size￨L￨NN￨O￨- at￨L￨IN￨O￨- flowering￨L￨NN￨O￨- of￨L￨IN￨O￨- monocarpic￨L￨JJ￨O￨- plants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- ecological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- exploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- body￨L￨NN￨O￨- size￨L￨NN￨O￨- on￨L￨IN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- capturing￨L￨VBG￨O￨- these￨L￨DT￨O￨- details￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- key￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- traits￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- increases￨L￨VBZ￨O￨- in￨L￨IN￨O￨- size￨L￨NN￨O￨- via￨L￨IN￨O￨- growth￨L￨NN￨O￨- or￨L￨CC￨O￨- losses￨L￨NNS￨O￨- via￨L￨IN￨O￨- shrinkage￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- links￨L￨NNS￨O￨- to￨L￨TO￨O￨- survival￨L￨NN￨O￨- or￨L￨CC￨O￨- fertility￨L￨NN￨O￨- are￨L￨VBP￨O￨- modelled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- generalized￨L￨VBN￨O￨- linear￨L￨JJ￨O￨- regression￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨- house￨L￨NN￨O￨- mice￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Mus￨U￨NN￨O￨- musculus￨L￨NN￨O￨- domesticus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- injections￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨- product￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- lipopolysaccharide￨L￨NN￨O￨- or￨L￨CC￨O￨- LPS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- elicit￨L￨VB￨O￨- innate￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- in￨L￨IN￨O￨- animals24￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- monitored￨L￨VBD￨O￨- nest-sharing￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨- mice￨L￨NNS￨O￨A pre-and￨L￨JJ￨O￨- post-immune￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- changes￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Over￨U￨IN￨O￨- several￨L￨JJ￨DURATION￨- weeks￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- repeated￨L￨VBD￨O￨- all￨L￨DT￨O￨- social￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- different￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- 35￨L￨CD￨NUMBER￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- females￨L￨NNS￨O￨A and￨L￨CC￨O￨- 16￨L￨CD￨NUMBER￨- males￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- 37￨L￨CD￨NUMBER￨- LPS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- females￨L￨NNS￨O￨- and￨L￨CC￨O￨- 20￨L￨CD￨NUMBER￨- males￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- injected￨L￨VBD￨O￨- animals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- overlap￨L￨VBP￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- mice￨L￨NNS￨O￨A sharing￨L￨VBG￨O￨- a￨L￨DT￨O￨- nest￨L￨NN￨O￨- box￨L￨NN￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- community￨L￨NN￨O￨- was￨L￨VBD￨O￨- obliged￨L￨VBN￨O￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- a￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A control￨L￨NN￨O￨- team￨L￨NN￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- standard￨L￨JJ￨O￨- dengue￨L￨NN￨O￨- control￨L￨NN￨O￨- activities￨L￨NNS￨O￨- :￨L￨:￨O￨- entomological￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- breeding￨L￨VBG￨O￨- source￨L￨NN￨O￨- reduction￨L￨NN￨O￨- through￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- inspection￨L￨NN￨O￨- of￨L￨IN￨O￨- houses￨L￨NNS￨O￨- ,￨L￨,￨O￨- larviciding￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- containers￨L￨NNS￨O￨- ,￨L￨,￨O￨- adult￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- density￨L￨NN￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- communication￨L￨NN￨O￨- and￨L￨CC￨O￨- education￨L￨NN￨O￨- on￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- prevention￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- enforcement￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- control￨L￨NN￨O￨- legislation￨L￨NN￨O￨- .￨L￨.￨O￨- +Briefly￨U￨RB￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- routine￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- integrated￨L￨VBN￨O￨- community-based￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- mobilize￨L￨VB￨O￨- all￨L￨DT￨O￨- community￨L￨NN￨O￨- partners￨L￨NNS￨O￨- to￨L￨TO￨O￨- participate￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨NN￨O￨A control￨L￨NN￨O￨- activity￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- administrative￨L￨JJ￨O￨- leadership￨L￨NN￨O￨- and￨L￨CC￨O￨- support￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- density￨L￨NN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- public￨L￨JJ￨O￨- places￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- safe￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Integrated￨U￨NNP￨O￨- community-based￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- required￨L￨VBN￨O￨- every￨L￨DT￨O￨- community￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A fever￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- activity￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- leadership￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- government￨L￨NN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- multi-sectoral￨L￨JJ￨O￨- collaboration￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- was￨L￨VBD￨O￨- established￨L￨VBN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- authority￨L￨NN￨O￨- was￨L￨VBD￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- technical￨L￨JJ￨O￨- organization￨L￨NN￨O￨- and￨L￨CC￨O￨- inspection￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- integrated￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- program￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- collected￨L￨VBD￨O￨- daily￨L￨RB￨SET￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A fever￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- meteorological￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- daily￨L￨JJ￨SET￨- mean￨L￨NN￨O￨- temperature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- °C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- relative￨L￨JJ￨O￨- humidity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- %￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- Guangzhou￨U￨NNP￨CITY￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- January￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2006￨L￨CD￨DATE￨- through￨L￨IN￨O￨- December￨U￨NNP￨DATE￨- 31￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2014￨L￨CD￨DATE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dengue￨L￨JJ￨O￨A cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- province￨L￨NN￨O￨- were￨L￨VBD￨O￨- mainly￨L￨RB￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- imported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- from￨L￨IN￨O￨- surrounding￨L￨VBG￨O￨- dengue￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- and￨L￨CC￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- leveling￨L￨NN￨O￨- off￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- constant￨L￨JJ￨O￨- value￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- community￨L￨NN￨O￨A sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- is￨L￨VBZ￨O￨- linear￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Cumulative￨U￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- log-normal￨L￨JJ￨O￨- plot￨L￨NN￨O￨- of￨L￨IN￨O￨- cumulative￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- versus￨L￨CC￨O￨- simulation￨L￨NN￨O￨- day￨L￨NN￨DURATION￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- community￨L￨NN￨O￨A sizes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 51￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 101￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 201￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Even￨U￨RB￨O￨- though￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- relative￨L￨JJ￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- community￨L￨NN￨O￨A saturation￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- strongly￨L￨RB￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- household￨L￨NN￨O￨- size￨L￨NN￨O￨- H￨U￨NN￨O￨- ,￨L￨,￨O￨- varying￨L￨VBG￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨A mixing￨L￨VBG￨O￨- size￨L￨NN￨O￨- C￨U￨NN￨O￨- would￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- requires￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- fixed￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨A size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- varied￨L￨VBN￨O￨- .￨L￨.￨O￨- +Important￨U￨JJ￨O￨- concepts￨L￨NNS￨O￨- for￨L￨IN￨O￨- structured￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- vaccine-induced￨L￨JJ￨O￨- age-shift￨L￨JJ￨O￨- and￨L￨CC￨O￨- core￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- are￨L￨VBP￨O￨- fundamental￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- that￨L￨WDT￨O￨- arise￨L￨VBP￨O￨A from￨L￨IN￨O￨- this￨L￨DT￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- principle￨L￨NN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- deterministic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- offers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fruitful￨L￨JJ￨O￨- avenue￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- problems￨L￨NNS￨O￨- of￨L￨IN￨O￨- endemicity￨L￨NN￨O￨- .￨L￨.￨O￨- +Deterministic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A epidemiology￨L￨NN￨O￨A .￨L￨.￨O￨- +Important￨U￨JJ￨O￨- challenges￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- with￨L￨IN￨O￨- regard￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- multi-strain￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- arise￨L￨VBP￨O￨A .￨L￨.￨O￨- +Spatially￨U￨RB￨O￨- explicit￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- treated￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨A framework￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- this￨L￨DT￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- suppose￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- between￨L￨IN￨O￨- any￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pair￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- perhaps￨L￨RB￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- infect￨L￨VB￨O￨- others￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- opposite￨L￨JJ￨O￨- sex￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- perhaps￨L￨RB￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- from￨L￨IN￨O￨- male￨L￨JJ￨O￨A to￨L￨TO￨O￨- female￨L￨JJ￨O￨- and￨L￨CC￨O￨- female￨L￨JJ￨O￨- to￨L￨TO￨O￨- male￨L￨NN￨O￨- are￨L￨VBP￨O￨- different￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Global￨U￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- incorporate￨L￨VB￨O￨- individual￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- by￨L￨IN￨O￨- having￨L￨VBG￨O￨- different￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- sex￨L￨NN￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- history￨L￨NN￨O￨- .￨L￨.￨O￨- +Individual-based￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- came￨L￨VBD￨O￨- in￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨A with￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1970s￨L￨NNS￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- developments￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- computer￨L￨NN￨O￨- methodology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- inference￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- general￨L￨JJ￨TITLE￨- metapopulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- allow￨L￨VBP￨O￨A an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- to￨L￨TO￨O￨- belong￨L￨VB￨O￨- to￨L￨TO￨O￨- several￨L￨JJ￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- with￨L￨IN￨O￨- its￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- allow￨L￨VB￨O￨- more￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- the￨L￨DT￨O￨- IBA￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨A as￨L￨IN￨O￨- observed￨L￨VBN￨O￨- on￨L￨IN￨O￨- real￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- them￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IBA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- termed￨L￨VBN￨O￨- discrete-time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- arbitrary￨L￨JJ￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- key￨L￨JJ￨O￨- idea￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- IBA￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- tracking￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- state￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- state￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨A are￨L￨VBP￨O￨- characterised￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- connectivity￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- timings￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- events35￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simple￨L￨JJ￨O￨- and￨L￨CC￨O￨- flexible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- formulation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- that￨L￨IN￨O￨- extends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Holling￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- Types￨U￨NNS￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- wider￨L￨JJR￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- qualitatively￨L￨RB￨O￨- distinct￨L￨JJ￨O￨- behaviours￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- vector￨L￨NN￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- availability￨L￨NN￨O￨A of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- blood-host￨L￨JJ￨O￨- species￨L￨NNS￨O￨- .￨L￨.￨O￨- +2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Ecological￨U￨NNP￨O￨- theory￨L￨NN￨O￨- predicts￨L￨VBZ￨O￨- a￨L￨DT￨O￨- diverse￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- functional￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- to￨L￨TO￨O￨- resource￨L￨NN￨O￨- availability￨L￨NN￨O￨A ;￨L￨:￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- blood￨L￨NN￨O￨- consumption￨L￨NN￨O￨- by￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- vectors￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- simplistic￨L￨JJ￨O￨- ,￨L￨,￨O￨- linear￨L￨JJ￨O￨- response￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ubiquitously￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Epidemiological￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- falciparum￨L￨NN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Chagas￨U￨NNP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- Lyme￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨NN￨O￨- ,￨L￨,￨O￨- often￨L￨RB￨O￨- implicit￨L￨JJ￨O￨- ,￨L￨,￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- functional￨L￨JJ￨O￨A response￨L￨NN￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- spurious￨L￨JJ￨O￨- under-or￨L￨JJ￨O￨- over-estimates￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- ,￨L￨,￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- full￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- life-cycles￨L￨NNS￨O￨- .￨L￨.￨O￨- +Interactions￨U￨NNS￨O￨- between￨L￨IN￨O￨- vector￨L￨NN￨O￨- biting￨L￨VBG￨O￨A behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- uneven￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- between￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- for￨L￨IN￨O￨- Chagas￨U￨NNP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- render￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- more￨L￨RBR￨O￨- resilient￨L￨JJ￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- How￨U￨WRB￨MISC￨- do￨L￨VBP￨O￨- biting￨L￨VBG￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- vectors￨L￨NNS￨O￨- behaviourally￨L￨RB￨O￨- respond￨L￨VBP￨O￨- to￨L￨TO￨O￨- host￨L￨NN￨TITLE￨- availability?Laith￨L￨NN￨O￨- Yakob1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 9:468￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Philips427￨U￨NN￨O￨- and￨L￨CC￨O￨- Karishma￨U￨NN￨MISC￨- Chhabria427BMC￨U￨NN￨MISC￨- NeuroscienceBMC￨U￨NN￨MISC￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 17￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Suppl￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- 54￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2016Published￨L￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Table￨U￨NNP￨O￨- of￨L￨IN￨O￨- contentsA1￨L￨NN￨O￨- Functional￨U￨JJ￨O￨- advantages￨L￨NNS￨O￨- of￨L￨IN￨O￨- cell-type￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- neural￨L￨JJ￨O￨A circuitsTatyana￨L￨NNP￨O￨- O.￨U￨NNP￨O￨- SharpeeA2￨U￨NNP￨O￨- Mesoscopic￨U￨NNP￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- propagating￨L￨VBG￨O￨- waves￨L￨NNS￨O￨- in￨L￨IN￨O￨- visual￨L￨JJ￨O￨- cortexAlain￨L￨NN￨O￨- DestexheA3￨U￨NN￨MISC￨- Dynamics￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- biomarkers￨L￨NNS￨O￨- of￨L￨IN￨O￨- mental￨L￨JJ￨O￨- disordersMitsuo￨L￨NN￨O￨- KawatoF1￨U￨NN￨O￨- Precise￨U￨JJ￨O￨- recruitment￨L￨NN￨O￨- of￨L￨IN￨O￨- spiking￨L￨VBG￨O￨- output￨L￨NN￨O￨- at￨L￨IN￨O￨- theta￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- dendritic￨L￨JJ￨O￨- h-channels￨L￨NNS￨O￨- in￨L￨IN￨O￨- multi-compartment￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- oriens-lacunosum/moleculare￨L￨JJ￨O￨- hippocampal￨L￨JJ￨O￨- interneuronsVladislav￨L￨NN￨O￨- Sekulić￨U￨NN￨O￨- ,￨L￨,￨O￨- Frances￨U￨NNP￨PERSON￨- K.￨U￨NNP￨PERSON￨- McCarley￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jee￨U￨NNP￨PERSON￨- Hyun￨U￨NNP￨PERSON￨- ChoiO3￨U￨NNP￨O￨- Modeling￨U￨VBG￨O￨- auditory￨L￨JJ￨O￨- stream￨L￨NN￨O￨- segregation￨L￨NN￨O￨- ,￨L￨,￨O￨- build-up￨L￨NN￨O￨- and￨L￨CC￨O￨- bistabilityJames￨L￨NNS￨PERSON￨- Rankin￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Pamela￨U￨NNP￨PERSON￨- Osborn￨U￨NNP￨PERSON￨- Popp￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- John￨U￨NNP￨PERSON￨- RinzelO4￨U￨NNP￨O￨- Strong￨U￨JJ￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- tonotopic￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- ensembles￨L￨NNS￨O￨- explains￨L￨VBZ￨O￨- pitch-related￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- auditory￨L￨JJ￨O￨- cortex￨L￨NN￨O￨- evoked￨L￨VBD￨O￨- fieldsAlejandro￨L￨NNP￨O￨- Tabas￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- André￨U￨NNP￨PERSON￨- Rupp￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Emili￨U￨NNP￨O￨- Balaguer-BallesterO5￨U￨NN￨O￨- A￨U￨DT￨O￨- simple￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- retinal￨L￨JJ￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- multi-electrode￨L￨JJ￨O￨- stimulationMatias￨L￨NNS￨O￨- I.￨U￨NN￨PERSON￨- Ibbotson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hamish￨U￨NNP￨PERSON￨- MeffinO6￨U￨NNP￨O￨- Noise￨U￨NNP￨O￨- correlations￨L￨NNS￨O￨- in￨L￨IN￨O￨- V4￨U￨NN￨O￨- area￨L￨NN￨O￨- correlate￨L￨VBP￨O￨- with￨L￨IN￨O￨- behavioral￨L￨JJ￨O￨- performance￨L￨NN￨O￨- in￨L￨IN￨O￨- visual￨L￨JJ￨O￨- discrimination￨L￨NN￨O￨- taskVeronika￨L￨NNP￨O￨- Koren￨U￨NNP￨O￨- ,￨L￨,￨O￨- Timm￨U￨NNP￨PERSON￨- Lochmann￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Valentin￨U￨NNP￨PERSON￨- Dragoi￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Klaus￨U￨NNP￨O￨- ObermayerO7￨U￨NNP￨O￨- Input-location￨U￨NN￨MISC￨- dependent￨L￨JJ￨O￨- gain￨L￨NN￨O￨- modulation￨L￨NN￨O￨- in￨L￨IN￨O￨- cerebellar￨L￨NN￨O￨- nucleus￨L￨NN￨O￨- neuronsMaria￨L￨NN￨O￨- Psarrou￨U￨NN￨O￨- ,￨L￨,￨O￨- Maria￨U￨NNP￨PERSON￨- Schilstra￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Neil￨U￨NNP￨PERSON￨- Davey￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Benjamin￨U￨NNP￨PERSON￨- Torben-Nielsen￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Volker￨U￨NNP￨O￨- SteuberO8￨U￨NNP￨O￨- Analytic￨U￨NNP￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- cable￨L￨NN￨O￨- energy￨L￨NN￨O￨- function￨L￨NN￨O￨- for￨L￨IN￨O￨- cortical￨L￨JJ￨O￨- axons￨L￨NNS￨O￨- and￨L￨CC￨O￨- dendritesHuiwen￨L￨NN￨PERSON￨- Ju￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Jiao￨U￨NNP￨PERSON￨- Yu￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Michael￨U￨NNP￨PERSON￨- L.￨U￨NNP￨PERSON￨- elegans￨L￨NNS￨PERSON￨- interactome￨L￨NN￨O￨- :￨L￨:￨O￨- interactive￨L￨JJ￨O￨- visualization￨L￨NN￨O￨- of￨L￨IN￨O￨- Caenorhabditis￨U￨NN￨O￨- elegans￨L￨NNS￨O￨- worm￨L￨NN￨O￨- neuronal￨L￨JJ￨O￨- networkJimin￨L￨NNP￨O￨- Kim￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Will￨U￨NNP￨PERSON￨- Leahy￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Eli￨U￨NNP￨O￨- ShlizermanO10￨U￨NNP￨O￨- Is￨U￨VBZ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- any￨L￨DT￨O￨- good￨L￨JJ￨O￨- ?￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- because￨L￨IN￨O￨- spillovers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- for￨L￨IN￨O￨- Lassa￨U￨NNP￨O￨- Fever￨U￨NN￨CAUSE_OF_DEATH￨- demonstrates￨L￨VBZ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- rare￨L￨JJ￨O￨- events￨L￨NNS￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- ecological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- with￨L￨IN￨O￨- differing￨L￨VBG￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- periodicity￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- abundance￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- life￨L￨NN￨O￨- histories￨L￨NNS￨O￨- and￨L￨CC￨O￨- periodicity￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- anthropogenic￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- land-use￨L￨NN￨O￨- and￨L￨CC￨O￨- behavioural￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- affecting￨L￨VBG￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- with￨L￨IN￨O￨- reservoir￨L￨NN￨O￨A hosts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Mathematically￨U￨RB￨O￨- ,￨L￨,￨O￨- zoonotic￨L￨JJ￨O￨A spillovers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Cox￨U￨NN￨O￨- processes￨L￨NNS￨O￨- if￨L￨IN￨O￨- stochasticity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- becomes￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- by￨L￨IN￨O￨- self-correcting￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- decreasing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- processes￨L￨VBZ￨O￨- if￨L￨IN￨O￨- depletion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- occurs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- stuttering￨L￨VBG￨O￨- chains￨L￨NNS￨O￨- are￨L￨VBP￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- self-exciting￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- increasing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- previous￨L￨JJ￨O￨- human￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- self-correcting￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- depletion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- S1￨U￨NN￨O￨- in￨L￨IN￨O￨- S2￨U￨NN￨O￨- Text￨U￨VBP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- key￨L￨JJ￨O￨- difference￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨A spillovers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- arise￨L￨VB￨O￨- from￨L￨IN￨O￨- random￨L￨JJ￨O￨- and￨L￨CC￨O￨- independent￨L￨JJ￨RELIGION￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- assuming￨L￨VBG￨O￨- no￨L￨DT￨O￨- depletion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- pool￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- or￨L￨CC￨O￨- humans￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- stuttering￨L￨NN￨O￨- chain￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- arises￨L￨VBZ￨O￨- from￨L￨IN￨O￨- human-to-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- human￨L￨JJ￨O￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨A as￨L￨IN￨O￨- each￨L￨DT￨O￨- infected￨L￨JJ￨O￨- person￨L￨NN￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- trigger￨L￨VB￨O￨- a￨L￨DT￨O￨- chain￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- before￨L￨IN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- contributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨A spillover￨L￨NN￨O￨- and￨L￨CC￨O￨- human-to-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Proliferative￨U￨JJ￨O￨- Kidney￨U￨NN￨CAUSE_OF_DEATH￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- PKD￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- salmonid￨L￨NN￨O￨- fish￨L￨NN￨O￨- ,￨L￨,￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- Tetracapsuloides￨U￨NNS￨MISC￨- bryosalmonae￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- phylum￨L￨NN￨O￨- Cnidaria￨U￨NNP￨O￨- ,￨L￨,￨O￨- class￨L￨NN￨O￨- Malacosporea￨U￨NN￨LOCATION￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- problematic￨L￨JJ￨O￨- for￨L￨IN￨O￨- hatcheries￨L￨NNS￨O￨- and￨L￨CC￨O￨- fish￨L￨NN￨O￨- farms￨L￨NNS￨O￨- ,￨L￨,￨O￨- potentially￨L￨RB￨O￨- reaching￨L￨VBG￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A prevalence￨L￨NN￨O￨A and￨L￨CC￨O￨- high￨L￨JJ￨O￨- mortalities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- affected￨L￨VBN￨O￨- fish￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- PKD￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨A fish￨L￨NN￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- poorly￨L￨RB￨O￨- known￨L￨VBN￨O￨- ,￨L￨,￨O￨- PKD￨U￨NN￨ORGANIZATION￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- factor￨L￨NN￨O￨- contributing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- decline￨L￨NN￨O￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨- salmonid￨L￨NN￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Northern￨U￨NNP￨LOCATION￨- Europe￨U￨NNP￨LOCATION￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- moving￨L￨VBG￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- in￨L￨IN￨O￨- standard￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- shedding￨L￨VBG￨O￨- data￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- either￨L￨CC￨O￨- when￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- dose￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- under￨L￨IN￨O￨- controlled￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- existing￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- enrolled￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨A of￨L￨IN￨O￨- live￨L￨JJ￨O￨- virus￨L￨NN￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- produce￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- shed￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- measured￨L￨VBN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨A level￨L￨NN￨O￨A ,￨L￨,￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- most￨L￨RBS￨O￨- frequently￨L￨RB￨O￨- involve￨L￨VBP￨O￨- a￨L￨DT￨O￨- ‘￨L￨``￨O￨- compartmental￨L￨JJ￨O￨- ’￨L￨''￨O￨- approach￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- progress￨L￨VBP￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- discrete￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- usually￨L￨RB￨O￨- at￨L￨IN￨O￨- constant￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- modern￨L￨JJ￨O￨- computationally￨L￨RB￨O￨- intensive￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- make￨L￨VBP￨O￨A use￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- geometry￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- density￨L￨NN￨O￨- for￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- norovirus￨L￨NN￨O￨- and￨L￨CC￨O￨- Ebola￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨A population-level￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- will￨L￨MD￨O￨- cause￨L￨VB￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- simple￨L￨JJ￨O￨- optimal￨L￨JJ￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- instead￨L￨RB￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- constrain￨L￨VBP￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- lie￨L￨VB￨O￨- close￨L￨RB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- curve￨L￨NN￨O￨- in￨L￨IN￨O￨- parameter￨L￨NN￨O￨A space￨L￨NN￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- good￨L￨JJ￨O￨- news￨L￨NN￨O￨- for￨L￨IN￨O￨- planning￨L￨VBG￨O￨- for￨L￨IN￨O￨- mitigation￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- contact￨L￨NN￨O￨A structure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- :￨L￨:￨O￨- ignoring￨L￨VBG￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- structures￨L￨NNS￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- slightly￨L￨RB￨O￨- conservative￨L￨JJ￨IDEOLOGY￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- vc￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- inference￨L￨NN￨O￨- procedure￨L￨NN￨O￨- for￨L￨IN￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- vc￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨A structure￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- ‘￨L￨``￨O￨- who￨L￨WP￨O￨- contacts￨L￨NNS￨O￨- whom￨L￨WP￨O￨- ’￨L￨''￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- not￨L￨RB￨O￨- available￨L￨JJ￨O￨- or￨L￨CC￨O￨- hard￨L￨JJ￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- quickly￨L￨RB￨O￨- for￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- novelty￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- lies￨L￨VBZ￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- estimators￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- required￨L￨VBN￨O￨- control￨L￨NN￨O￨- effort￨L￨NN￨O￨- vc￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- usually￨L￨RB￨O￨- available￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- ,￨L￨,￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨A structure￨L￨NN￨O￨A .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- ignoring￨L￨VBG￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- contact￨L￨NN￨O￨- pattern￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- effectively￨L￨RB￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- mix￨L￨VBP￨O￨- homogeneously￨L￨RB￨O￨- ,￨L￨,￨O￨- will￨L￨MD￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- slight￨L￨JJ￨O￨- overestimation￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- contact￨L￨NN￨O￨A structure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- far￨L￨RB￨O￨- from￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- justification￨L￨NN￨O￨- for￨L￨IN￨O￨- basing￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- policies￨L￨NNS￨O￨- on￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- derived￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- close￨L￨VB￨O￨- and￨L￨CC￨O￨- intimate￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- bodily￨L￨JJ￨O￨- fluids￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- hard￨L￨JJ￨O￨A to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- who￨L￨WP￨O￨- regularly￨L￨RB￨O￨- has￨L￨VBZ￨O￨- such￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- whom￨L￨WP￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- pulse￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PIR￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- immunized￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- gradually￨L￨RB￨O￨- decreases￨L￨VBZ￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- demographic￨L￨JJ￨O￨- turnover￨L￨NN￨O￨A :￨L￨:￨O￨- births￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- unvaccinated￨L￨JJ￨O￨- entries￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- and￨L￨CC￨O￨- offtake￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- slaughtering￨L￨NN￨O￨- and￨L￨CC￨O￨- sales￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- recommended￨L￨VBN￨O￨- strategy￨L￨NN￨O￨- in￨L￨IN￨O￨- Sahelian￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- target￨L￨NN￨O￨- population￨L￨NN￨O￨- during￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- successive￨L￨JJ￨O￨A years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- round￨L￨NN￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sole￨L￨JJ￨O￨- offspring￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- animals￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- old￨L￨JJ￨DURATION￨- )￨L￨-RRB-￨O￨- during￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- successive￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- passive￨L￨NN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- immaturity￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- immunized￨L￨JJ￨O￨A system￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- animals￨L￨NNS￨O￨- older￨L￨JJR￨O￨- than￨L￨IN￨O￨- three￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- are￨L￨VBP￨O￨- vaccinated￨L￨VBN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- defining￨L￨VBG￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- population￨L￨NN￨O￨- for￨L￨IN￨O￨- PPR￨U￨NNP￨ORGANIZATION￨- vaccination￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- vaccination￨L￨NN￨O￨- round￨L￨NN￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- preferably￨L￨RB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- beginning￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dry￨L￨JJ￨O￨- season￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- November-December￨U￨NN￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- peak￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- when￨L￨WRB￨O￨- grazing￨L￨NN￨O￨- is￨L￨VBZ￨O￨- abundant￨L￨JJ￨O￨- and￨L￨CC￨O￨- animals￨L￨NNS￨O￨A in￨L￨IN￨O￨- good￨L￨JJ￨O￨- health￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- PPRV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- post-vaccination￨L￨JJ￨O￨- PIR￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- only￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- turnover￨L￨NN￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- commute￨L￨NN￨O￨- network￨L￨NN￨O￨- was￨L￨VBD￨O￨- formulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- bipartite￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig￨U￨NN￨O￨- 1D￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- schematic￨L￨JJ￨O￨- diagram￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- accompanying￨L￨VBG￨O￨- each￨L￨DT￨O￨- station￨L￨NN￨O￨A :￨L￨:￨O￨- work/study￨L￨NN￨O￨- area￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- work￨L￨NN￨O￨- population￨L￨NN￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- red￨L￨JJ￨O￨- circles￨L￨NNS￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨O￨- 1D￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- residence￨L￨NN￨O￨- area￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- home￨L￨NN￨O￨- population￨L￨NN￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- blue￨L￨JJ￨O￨- circles￨L￨NNS￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨O￨- 1D￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- M￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1,435￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- stations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Tokyo￨U￨NNP￨CITY￨- metropolitan￨L￨JJ￨O￨- area￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- respectively￨L￨RB￨O￨- gives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- commuters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- use￨L￨VBP￨O￨- i-th￨L￨JJ￨O￨- station￨L￨NN￨O￨A as￨L￨IN￨O￨- the￨L￨DT￨O￨- home￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- commuters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- use￨L￨VBP￨O￨- j-th￨L￨JJ￨O￨- station￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- commuters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- metropolitan￨L￨JJ￨O￨- area￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- largest￨L￨JJS￨O￨- daytime￨L￨JJ￨TIME￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- exceeded￨L￨VBD￨O￨- 5,000￨L￨CD￨NUMBER￨- commuters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- working/studying￨L￨VBG￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- Shinjuku￨U￨NNP￨LOCATION￨- station￨L￨NN￨O￨A with￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- 5,411￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- nighttime￨L￨JJ￨TIME￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- was￨L￨VBD￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- 1,000￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- residing￨L￨VBG￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- Oizumi-gakuen￨U￨JJ￨MISC￨- station￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- 853￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- commuting￨L￨VBG￨O￨- from￨L￨IN￨O￨- their￨L￨PRP$￨O￨- residence￨L￨NN￨O￨- area￨L￨NN￨O￨- at￨L￨IN￨O￨- station￨L￨NN￨O￨A i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- i-th￨L￨JJ￨O￨- home￨L￨NN￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- work/study￨L￨JJ￨O￨- area￨L￨NN￨O￨- at￨L￨IN￨O￨- station￨L￨NN￨O￨- j￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- j-th￨L￨JJ￨O￨- work￨L￨NN￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A.￨U￨NN￨O￨- aegypti￨L￨NNP￨O￨- saw￨L￨VBD￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- resurgence￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨DATE￨- end￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- 20th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- and￨L￨CC￨O￨- populations￨L￨NNS￨O￨- continue￨L￨VBP￨O￨- to￨L￨TO￨O￨- grow￨L￨VB￨O￨- and￨L￨CC￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A fever￨L￨NN￨CAUSE_OF_DEATH￨- following￨L￨VBG￨O￨- ineffectual￨L￨JJ￨O￨- control￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- rapid￨L￨JJ￨O￨- urbanisation￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- worth￨L￨JJ￨O￨- noting￨L￨VBG￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- issue￨L￨NN￨O￨- with￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- three-quarters￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- annual￨L￨JJ￨SET￨- dengue￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- asymptomatic￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- hosts￨L￨NNS￨O￨- continue￨L￨VBP￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- mosquitoes￨L￨NNS￨O￨- whilst￨L￨IN￨O￨- going￨L￨VBG￨O￨- about￨L￨IN￨O￨- their￨L￨PRP$￨O￨- daily￨L￨JJ￨SET￨- routines￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- SIT￨U￨NN￨O￨- vector￨L￨NN￨O￨A control￨L￨NN￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- masked￨L￨VBN￨O￨- by￨L￨IN￨O￨- natural￨L￨JJ￨O￨- density-dependent￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- significant￨L￨JJ￨O￨- reductions￨L￨NNS￨O￨- in￨L￨IN￨O￨- adult￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- broad￨L￨JJ￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- isolation￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- study￨L￨VB￨O￨- ventilation￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- community-level￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- ideally￨L￨RB￨O￨- modeled￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- person￨L￨NN￨O￨- and￨L￨CC￨O￨- location￨L￨NN￨O￨A level￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- entire￨L￨JJ￨O￨- urban￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- urban￨L￨JJ￨O￨A airborne￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- integrating￨L￨VBG￨O￨- the￨L￨DT￨O￨- indoor￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- community￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Wells-Riley￨U￨JJ￨LOCATION￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- local￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- buildings￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- indoor￨L￨JJ￨O￨- spaces￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- visiting￨L￨VBG￨O￨- each￨L￨DT￨O￨- location￨L￨NN￨O￨A type￨L￨NN￨O￨- ;￨L￨:￨O￨- ventilation￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ;￨L￨:￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +Environment￨U￨NNP￨O￨- parameters￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- ventilation￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- location￨L￨NN￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- refined￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- indoor-space￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Indoor￨U￨JJ￨O￨- contact￨L￨NN￨O￨- was￨L￨VBD￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- individuals￨L￨NNS￨O￨- visiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- indoor￨L￨JJ￨O￨- location￨L￨NN￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- systems￨L￨NNS￨O￨- no￨L￨RB￨O￨- longer￨L￨RB￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- clear￨L￨JJ￨O￨- transition￨L￨NN￨O￨- at￨L￨IN￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- causing￨L￨VBG￨O￨- the￨L￨DT￨O￨- catastrophic￨L￨JJ￨O￨- chain￨L￨NN￨O￨- reaction￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- still￨L￨RB￨O￨- show￨L￨VB￨O￨- nonstationary￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- with￨L￨IN￨O￨- intermittent￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨A of￨L￨IN￨O￨- event-occurrences￨L￨NNS￨O￨- at￨L￨IN￨O￨- lower￨L￨JJR￨O￨- reproduction￨L￨NN￨O￨- ratios￨L￨NNS￨O￨- ;￨L￨:￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- is￨L￨VBZ￨O￨- even￨L￨RB￨O￨- smaller￨L￨JJR￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- remain￨L￨VB￨O￨- stationary￨L￨JJ￨O￨- ,￨L￨,￨O￨- producing￨L￨VBG￨O￨- apparently￨L￨RB￨O￨- random￨L￨JJ￨O￨- events￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- consider￨L￨VB￨O￨- extrinsic￨L￨JJ￨O￨- or￨L￨CC￨O￨- spontaneous￨L￨JJ￨O￨A activation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- suggest￨L￨VBP￨O￨- revising￨L￨VBG￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- an￨L￨DT￨O￨- inflow￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- spontaneous￨L￨JJ￨O￨- activity￨L￨NN￨O￨- ρ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- smoothly￨L￨RB￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- accordingly￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- transition￨L￨NN￨O￨- at￨L￨IN￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- softened￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1a￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- transition￨L￨NN￨O￨- between￨L￨IN￨O￨- stationary￨L￨JJ￨O￨- and￨L￨CC￨O￨- nonstationary￨L￨JJ￨O￨- states￨L￨NNS￨O￨- generally￨L￨RB￨O￨- occurs￨L￨VBZ￨O￨- in￨L￨IN￨O￨- every￨L￨DT￨O￨- proliferation￨L￨NN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- cascades￨L￨NNS￨O￨A may￨L￨MD￨O￨- emerge￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- suggest￨L￨VBP￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- systems￨L￨NNS￨O￨- to￨L￨TO￨O￨- oppress￨L￨VB￨O￨- or￨L￨CC￨O￨- promote￨L￨VB￨O￨- the￨L￨DT￨O￨- event-occurrence￨L￨NN￨O￨- bursts￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0.6￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- 0.8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- sequence￨L￨NN￨O￨- appears￨L￨VBZ￨O￨- nonstationary￨L￨JJ￨O￨- ,￨L￨,￨O￨- exhibiting￨L￨VBG￨O￨- spontaneous￨L￨JJ￨O￨A cascades￨L￨NNS￨O￨- of￨L￨IN￨O￨- occurrences￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- pre-vaccination￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- was￨L￨VBD￨O￨- approximately￨L￨RB￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- cohort￨L￨NN￨O￨- ,￨L￨,￨O￨- discounted￨L￨VBN￨O￨- by￨L￨IN￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A occurs￨L￨VBZ￨O￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- a￨L￨DT￨DURATION￨- few￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- birth￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mortality￨L￨NN￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- live￨L￨VB￨O￨- long￨L￨RB￨O￨- enough￨L￨RB￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +Foremost￨U￨JJ￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- problems￨L￨NNS￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- post-honeymoon￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- occurring￨L￨VBG￨O￨- when￨L￨WRB￨O￨- susceptibles￨L￨NNS￨O￨- accumulate￨L￨VBP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- despite￨L￨IN￨O￨- relatively￨L￨RB￨O￨- good￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- outbreak-avoiding￨L￨JJ￨O￨- recommendations￨L￨NNS￨O￨- for￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨- policy￨L￨NN￨O￨- in￨L￨IN￨O￨- high￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- like￨L￨IN￨O￨- ours￨L￨PRP￨O￨- have￨L￨VBP￨O￨- influenced￨L￨VBN￨O￨- vaccination￨L￨NN￨O￨- policy￨L￨NN￨O￨A ,￨L￨,￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- scheduling￨L￨NN￨O￨- supplementary￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIAs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- seasonality￨L￨NN￨O￨- clearly￨L￨RB￨O￨- affects￨L￨VBZ￨O￨- temporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- migration￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- robust￨L￨JJ￨O￨- explanation￨L￨NN￨O￨- for￨L￨IN￨O￨- differences￨L￨NNS￨O￨A in￨L￨IN￨O￨- regions￨L￨NNS￨O￨- '￨L￨POS￨O￨- long-term￨L￨JJ￨O￨- contributions￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- H3N2￨U￨NN￨O￨- would￨L￨MD￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- light￨L￨NN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- potentially￨L￨RB￨O￨- influential￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- among￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- observations￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- ecological￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- climate￨L￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- demography￨L￨NN￨O￨- ,￨L￨,￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- antigenic￨L￨JJ￨O￨A evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- H3N2￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- shapes￨L￨VBZ￨O￨- its￨L￨PRP$￨O￨- global￨L￨JJ￨O￨- migratory￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- affects￨L￨VBZ￨O￨A a￨L￨DT￨O￨- strain￨L￨NN￨O￨- 's￨L￨POS￨O￨- intrinsic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- otherwise￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨A drift￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- R0￨U￨NN￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- mutation￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- diffusion-like￨L￨JJ￨O￨- process￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 10,21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨A evolution￨L￨NN￨O￨- may￨L￨MD￨O￨- vary￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- way￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- turnover￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- Lau￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Yip￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- assume￨L￨VBP￨O￨- only￨L￨RB￨O￨- removals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- kernel￨L￨NN￨O￨A estimator￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approach￨L￨NN￨O￨- also￨L￨RB￨O￨- requires￨L￨VBZ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A times￨L￨NNS￨O￨A to￨L￨TO￨O￨- be￨L￨VB￨O￨- known￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- rarely￨L￨RB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- reality￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- fixed-length￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- times￨L￨NNS￨O￨- are￨L￨VBP￨O￨- immediately￨L￨RB￨O￨- specified￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- removal￨L￨NN￨O￨- times￨L￨NNS￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- Becker￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Yip￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1989￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Becker￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1989￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- consider￨L￨VBP￨O￨- non-parametric￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- general￨L￨JJ￨TITLE￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A periods￨L￨NNS￨O￨A distributed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- allowing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- Chen￨U￨NNP￨PERSON￨- consider￨L￨VB￨O￨- a￨L￨DT￨O￨- related￨L￨JJ￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- kernel￨L￨NN￨O￨A estimation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- depletion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- ignored￨L￨VBN￨O￨- .￨L￨.￨O￨- +Modelling￨U￨VBG￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- successfully￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- within-herd￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- other￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- or￨L￨CC￨O￨- bacteria￨L￨NNS￨O￨- affecting￨L￨VBG￨O￨- pigs￨L￨NNS￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- batch￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- pig￨L￨NN￨O￨- herds￨L￨NNS￨O￨A [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- recently￨L￨RB￨DATE￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- representing￨L￨VBG￨O￨- swIAV￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- US￨U￨NNP￨COUNTRY￨- breeding￨L￨NN￨O￨- and￨L￨CC￨O￨- finishing￨L￨VBG￨O￨- herds￨L￨NNS￨O￨A with￨L￨IN￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- swIAV￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- pig￨L￨NN￨O￨- herds￨L￨NNS￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- stochastic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- more￨L￨RBR￨O￨- suited￨L￨VBN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- swIAV￨L￨NN￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨A herd￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨A size￨L￨NN￨O￨- on￨L￨IN￨O￨- swIAV￨L￨NN￨O￨- persistence￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Vertical￨U￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- between￨L￨IN￨O￨- generations￨L￨NNS￨O￨- of￨L￨IN￨O￨- Aedes￨U￨NNS￨O￨- mosquitoes￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- virus-infected￨L￨JJ￨O￨- Aedes￨U￨NNP￨O￨- eggs￨L￨NNS￨O￨- to￨L￨TO￨O￨- survive￨L￨VB￨O￨- for￨L￨IN￨O￨- up￨L￨RB￨DURATION￨- to￨L￨TO￨DURATION￨- several￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- through￨L￨IN￨O￨- dry￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- mechanism￨L￨NN￨O￨- for￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- through￨L￨IN￨O￨- inter-epizootic￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- RVF￨U￨NN￨MISC￨- ,￨L￨,￨O￨- once￨L￨RB￨DATE￨- livestock￨L￨NN￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- primary￨L￨JJ￨O￨- transovarially-infected￨L￨JJ￨O￨- Aedes￨U￨NNS￨O￨- species￨L￨NNS￨O￨- mosquitoes￨L￨NNS￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- Culex￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- Mansonia￨U￨NNP￨O￨- species￨L￨NNS￨O￨- mosquitoes￨L￨NNS￨O￨- may￨L￨MD￨O￨- transmit￨L￨VB￨O￨- RVFV￨U￨NN￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- mammals￨L￨NNS￨O￨- ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considers￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- mosquito￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- Aedes￨U￨NNP￨O￨- and￨L￨CC￨O￨- Culex￨U￨NNP￨MISC￨- —￨L￨:￨O￨- modeled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- Susceptible-Exposed-Infected￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- —￨L￨:￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- livestock￨L￨NN￨O￨A animals￨L￨NNS￨O￨- —￨L￨:￨O￨- modeled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- Susceptible-Exposed-Infected-Recovery￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- pond￨L￨NN￨O￨- is￨L￨VBZ￨O￨- placed￨L￨VBN￨O￨- under￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- one￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- step￨L￨NN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- associated￨L￨VBN￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨A eggs￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mosquitoes￨U￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- vectors￨L￨NNS￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- RVFV￨U￨NN￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- spread￨L￨VBN￨O￨- by￨L￨IN￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- infected￨L￨JJ￨O￨- tissues￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Long-term￨U￨JJ￨O￨- monitoring￨L￨NN￨O￨- of￨L￨IN￨O￨- spotted￨L￨JJ￨O￨- hyenas￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- revealed￨L￨VBN￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- species￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- host￨L￨NN￨TITLE￨A to￨L￨TO￨O￨- several￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- significantly￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- life￨L￨NN￨O￨- history￨L￨NN￨O￨- traits￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 35￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 40￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 44￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Information￨U￨NN￨O￨- on￨L￨IN￨O￨- sapovirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- or￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- in￨L￨IN￨O￨- free-ranging￨L￨JJ￨O￨- wildlife￨L￨NN￨O￨A is￨L￨VBZ￨O￨- scant￨L￨JJ￨O￨- and￨L￨CC￨O￨- long-term￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- any￨L￨DT￨O￨- wildlife￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- lacking￨L￨VBG￨O￨- .￨L￨.￨O￨- +Its￨U￨PRP$￨O￨- wild￨L￨JJ￨O￨A carnivore￨L￨NN￨O￨- guild￨L￨NN￨O￨- of￨L￨IN￨O￨- 26￨L￨CD￨NUMBER￨- species￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- multi-host￨L￨JJ￨O￨- landscape￨L￨NN￨O￨- for￨L￨IN￨O￨- viral￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 34￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 36￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- spotted￨L￨JJ￨O￨- hyena￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Crocuta￨U￨NN￨O￨- crocuta￨L￨NN￨O￨- ,￨L￨,￨O￨- family￨L￨NN￨O￨- Hyaenidae￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- abundant￨L￨JJ￨O￨- large￨L￨JJ￨O￨- carnivore￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A —￨L￨:￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- PI-SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- online￨L￨JJ￨O￨- TV￨U￨NN￨O￨- series￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- and￨L￨CC￨O￨- test￨L￨NN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- using￨L￨VBG￨O￨- three￨L￨CD￨NUMBER￨- popular￨L￨JJ￨O￨- South￨U￨JJ￨NATIONALITY￨- Korean￨U￨JJ￨NATIONALITY￨- TV￨U￨NN￨O￨- series￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- finds￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A stimulation￨L￨NN￨O￨- would￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- online￨L￨JJ￨O￨- streaming￨L￨NN￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- TV￨U￨NN￨O￨- series￨L￨NN￨O￨- audience￨L￨NN￨O￨- significantly￨L￨RB￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- lock-in￨L￨NN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +TV￨U￨NN￨O￨- series￨L￨NN￨O￨- update￨L￨VBP￨O￨- periods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- fixed￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- viewed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A stimulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- audiences￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- impulsive￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- suppresses￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- TV￨U￨NN￨O￨- series￨L￨NN￨O￨- updates￨L￨NNS￨O￨- stimulate￨L￨VBP￨O￨- diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- major￨L￨JJ￨O￨- online￨L￨JJ￨O￨- video-streaming￨L￨JJ￨O￨- service￨L￨NN￨O￨- suppliers￨L￨NNS￨O￨- buy￨L￨VBP￨O￨- the￨L￨DT￨O￨- broadcast￨L￨NN￨O￨- rights￨L￨NNS￨O￨- of￨L￨IN￨O￨- TV￨U￨NN￨O￨- series￨L￨NN￨O￨A and￨L￨CC￨O￨- sell￨L￨VB￨O￨- inserted￨L￨VBN￨O￨- commercial￨L￨JJ￨O￨- advertisements￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- audiences￨L￨NNS￨O￨- must￨L￨MD￨O￨- view￨L￨VB￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- perform￨L￨VB￨O￨- the￨L￨DT￨O￨- isolated￨L￨VBN￨O￨- contingency￨L￨NN￨O￨- analysis￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨A called￨L￨VBN￨O￨- “￨L￨``￨O￨- temporal￨L￨JJ￨O￨- knockout￨L￨NN￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- TKO￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- super-spreader￨L￨JJ￨O￨- and￨L￨CC￨O￨- immunization￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- measure￨L￨VB￨O￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨- ’s￨L￨POS￨O￨- influence/impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨A called￨L￨VBN￨O￨- “￨L￨``￨O￨- temporal￨L￨JJ￨O￨- knockout￨L￨NN￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- TKO￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- super-spreader￨L￨JJ￨O￨- and￨L￨CC￨O￨- immunization￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- measure￨L￨VB￨O￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨- ’s￨L￨POS￨O￨- influence/impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +TKO￨U￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- network￨L￨NN￨O￨- measure￨L￨NN￨O￨A for￨L￨IN￨O￨- approximating￨L￨VBG￨O￨- influence￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- rather￨L￨RB￨O￨- an￨L￨DT￨O￨- all-things-considered￨L￨JJ￨O￨- empirical￨L￨JJ￨O￨- measurement￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨- ’s￨L￨POS￨O￨- time-dependent￨L￨JJ￨O￨- potential￨L￨NN￨O￨- to￨L￨TO￨O￨- change￨L￨VB￨O￨- propagation￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- for￨L￨IN￨O￨- use￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- benchmark￨L￨NN￨O￨- in￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- network￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- generated￨L￨VBN￨O￨- or￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- used￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- placement￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- these￨L￨DT￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- identified￨L￨VBN￨O￨- best￨L￨JJS￨O￨- measure￨L￨NN￨O￨A of￨L￨IN￨O￨- influence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Danon13￨U￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- extensive￨L￨JJ￨O￨- review￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Identical￨U￨JJ￨MISC￨- synchronization￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- non-autonomous￨L￨JJ￨O￨- unified￨L￨JJ￨O￨- chaotic￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- switchBehnaz￨L￨NN￨O￨- Koocheck￨U￨NNP￨O￨- Shooshtari￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- AbdolMohammad￨U￨NNP￨O￨- Forouzanfar￨U￨NNP￨O￨- †￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- MohammadReza￨U￨NNP￨O￨- Molaei￨U￨NNP￨O￨- †￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- †￨L￨NN￨O￨- Citation￨U￨NNP￨O￨- 5:1667￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- a￨L￨DT￨O￨- non-autonomous￨L￨JJ￨O￨- unified￨L￨JJ￨O￨- chaotic￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- switch￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- Chen￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Lorenz￨U￨NNP￨PERSON￨- systems￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- identical￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- complete￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- synchronization￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- bi-directionally￨L￨RB￨O￨- coupled￨L￨VBN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- identical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- analyze￨L￨VB￨O￨- its￨L￨PRP$￨O￨- stability￨L￨NN￨O￨- by￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- Lyapunov￨U￨NNP￨PERSON￨- characteristic￨L￨JJ￨O￨- exponent￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- seems￨L￨VBZ￨O￨- that￨L￨IN￨O￨- Chaotic￨U￨JJ￨O￨- systems￨L￨NNS￨O￨- oppose￨L￨VBP￨O￨- with￨L￨IN￨O￨- synchronization￨L￨NN￨O￨A ,￨L￨,￨O￨- because￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- identical￨L￨JJ￨O￨- chaotic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- nearly￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- trajectories￨L￨NNS￨O￨- in￨L￨IN￨O￨- phase￨L￨NN￨O￨- space￨L￨NN￨O￨- which￨L￨WDT￨O￨- diverge￨L￨VBP￨O￨- quickly￨L￨RB￨O￨- .￨L￨.￨O￨- +Synchronization￨U￨NN￨O￨- of￨L￨IN￨O￨- chaos￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- happen￨L￨VB￨O￨- when￨L￨WRB￨O￨- some￨L￨DT￨O￨- dissipative￨L￨JJ￨O￨- chaotic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨A are￨L￨VBP￨O￨- coupled￨L￨VBN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- realized￨L￨VBN￨O￨- that￨L￨IN￨O￨- chaotic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- synchronized￨L￨VBN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- address￨L￨VB￨O￨- this￨L￨DT￨O￨- gap￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- multidisciplinary￨L￨JJ￨O￨- dialog￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- established￨L￨VBN￨O￨- virtual￨L￨JJ￨O￨- “￨L￨``￨O￨- Community￨U￨NN￨O￨- of￨L￨IN￨O￨- Practice￨U￨NNP￨O￨- ,￨L￨,￨O￨- ”￨L￨''￨O￨- called￨L￨VBN￨O￨- mod4PH￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Modeling￨U￨VBG￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- enhance￨L￨VB￨O￨- the￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- applications￨L￨NNS￨O￨- for￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- clinical￨L￨JJ￨O￨- decision-making￨L￨JJ￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- such￨L￨JJ￨O￨- glossaries￨L￨NNS￨O￨- define￨L￨VBP￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- terms￨L￨NNS￨O￨- and￨L￨CC￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vocabulary￨L￨NN￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A modeling￨L￨NN￨O￨A literature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- aim￨L￨VB￨O￨- at￨L￨IN￨O￨- standardizing￨L￨VBG￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- lexicon￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- terminology￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mod4PH￨L￨NN￨O￨- group￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- glossary￨L￨NN￨O￨- of￨L￨IN￨O￨- terms￨L￨NNS￨O￨- ,￨L￨,￨O￨- ”￨L￨''￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- use￨L￨NN￨O￨- and￨L￨CC￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A modeling￨L￨NN￨O￨A terms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- glossary￨L￨NN￨O￨- was￨L￨VBD￨O￨- created￨L￨VBN￨O￨- and￨L￨CC￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- summary￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- online￨L￨NN￨O￨- forum￨L￨NN￨O￨- discussions￨L￨NNS￨O￨- surrounding￨L￨VBG￨O￨- the￨L￨DT￨O￨- usage￨L￨NN￨O￨- and￨L￨CC￨O￨- definition￨L￨NN￨O￨A of￨L￨IN￨O￨- key￨L￨JJ￨O￨- terms￨L￨NNS￨O￨- in￨L￨IN￨O￨- modeling￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mod4PH￨L￨NN￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- LinkedIn￨U￨NNP￨O￨- forum￨L￨NN￨O￨- ,￨L￨,￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- from￨L￨IN￨O￨- different￨L￨JJ￨O￨- disciplines￨L￨NNS￨O￨- including￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A modeling￨L￨NN￨O￨A ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- policy￨L￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- disagreement￨L￨NN￨O￨- between￨L￨IN￨O￨- phylogeny￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- history￨L￨NN￨O￨- are￨L￨VBP￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Incomplete￨U￨JJ￨O￨- transmission￨L￨NN￨O￨- bottlenecks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- within-host￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨A variation￨L￨NN￨O￨A is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- from￨L￨IN￨O￨- donor￨L￨NN￨O￨- to￨L￨TO￨O￨- recipient￨L￨JJ￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- non-negligibly￨L￨JJ￨O￨- small￨L￨JJ￨O￨- inoculum￨L￨NN￨O￨- ;￨L￨:￨O￨- this￨L￨DT￨O￨- means￨L￨VBZ￨O￨- lineages￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- shared￨L￨VBN￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- ancestor￨L￨NN￨O￨- since￨L￨IN￨O￨- long￨L￨JJ￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Non-sampled￨U￨JJ￨MISC￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- sampled￨L￨VBN￨O￨A patient￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- linked￨L￨VBN￨O￨- by￨L￨IN￨O￨- direct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- most￨L￨RBS￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- sampled￨L￨VBN￨O￨- patient￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- non-sampled￨L￨JJ￨O￨- intermediate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Multiply￨U￨RB￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- patients￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- erroneously￨L￨RB￨O￨- excluded￨L￨VBN￨O￨- from￨L￨IN￨O￨- some￨L￨DT￨O￨- transmission￨L￨NN￨O￨- chains￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- if￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- patient￨L￨NN￨O￨A are￨L￨VBP￨O￨- not￨L￨RB￨O￨- collected￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1D￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- A￨U￨NNP￨O￨- spatial￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Wild￨U￨NNP￨O￨- Poliovirus￨U￨NNP￨O￨- Type￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- Kano￨U￨NNP￨CITY￨- State￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Nigeria￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- calibration￨L￨NN￨O￨- and￨L￨CC￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- elimination￨L￨NN￨O￨- probabilityKevin￨L￨NN￨O￨- A.￨U￨NN￨O￨- 2016Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Since￨U￨IN￨O￨- the￨L￨DT￨O￨- launch￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Global￨U￨JJ￨O￨- Polio￨U￨NNP￨O￨- Eradication￨U￨NN￨O￨- Initiative￨U￨NNP￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- but￨L￨CC￨O￨- three￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Nigeria￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Pakistan￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Afghanistan￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- apparently￨L￨RB￨O￨- interrupted￨L￨JJ￨O￨- all￨L￨DT￨O￨- wild￨L￨JJ￨O￨A poliovirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- WPV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- article￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- calibration￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨A poliovirus￨L￨NN￨O￨- Type￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- Kano￨U￨NNP￨CITY￨- State￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Nigeria￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- WPV1￨U￨NN￨O￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- 5￨L￨CD￨NUMBER￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- 6￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- WPV1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- drive￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- development￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- susceptible-exposed-infective-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A featuring￨L￨VBG￨O￨- seasonal￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- and￨L￨CC￨O￨- age-dependent￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- calibrated￨L￨VBN￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- resampled￨L￨JJ￨O￨- ,￨L￨,￨O￨- projected￨L￨VBD￨O￨- forward￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- recent￨L￨JJ￨O￨- case￨L￨NN￨O￨- counts￨L￨VBZ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- Type￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- poliovirus￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- eliminated￨L￨VBN￨O￨- in￨L￨IN￨O￨- Kano￨U￨NNP￨CITY￨- state￨L￨NN￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Burkina￨U￨NNP￨PERSON￨- Faso￨U￨NNP￨PERSON￨- experienced￨L￨VBD￨O￨- a￨L￨DT￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨- that￨L￨WDT￨O￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- 54,111￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- high￨L￨JJ￨O￨- estimated￨L￨VBN￨O￨- administrative￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- several￨L￨JJ￨O￨- supplemental￨L￨JJ￨O￨- campaigns￨L￨NNS￨O￨- ;￨L￨:￨O￨- many￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- children￨L￨NNS￨O￨- who￨L￨WP￨O￨- missed￨L￨VBD￨O￨- vaccinations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- locally￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- during￨L￨IN￨O￨- campaigns￨L￨NNS￨O￨- and￨L￨CC￨O￨- contributed￨L￨VBD￨O￨- significantly￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- outbreak9￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- immunized￨L￨VBN￨O￨- to￨L￨TO￨O￨- interrupt￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- scales￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- highly￨L￨RB￨O￨- transmissible￨L￨JJ￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- that￨L￨IN￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- remain￨L￨VBP￨O￨- above￨L￨IN￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- local￨L￨JJ￨O￨- elimination1213￨L￨NN￨O￨- ,￨L￨,￨O￨- emphasizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- accurate￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- measurements￨L￨NNS￨O￨- established￨L￨VBD￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- ,￨L￨,￨O￨- positive￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- largest￨L￨JJS￨O￨- cities￨L￨NNS￨O￨- in￨L￨IN￨O￨- Niger￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- drove￨L￨VBD￨O￨- local￨L￨JJ￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- both￨L￨CC￨O￨- across￨L￨IN￨O￨- cities￨L￨NNS￨O￨- and￨L￨CC￨O￨- within￨L￨IN￨O￨- them￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- Figs￨U￨NNS￨O￨- 1A￨L￨NN￨O￨- and￨L￨CC￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 172728￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Twenty-three￨U￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- response￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- was￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨- by￨L￨IN￨O￨- immunizing￨L￨VBG￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- children￨L￨NNS￨O￨- younger￨L￨JJR￨O￨- than￨L￨IN￨O￨- 60￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- satellite-derived￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- refine￨L￨VB￨O￨- our￨L￨PRP$￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- immunization￨L￨NN￨O￨- campaign￨L￨NN￨O￨A .￨L￨.￨O￨- +A￨U￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- eight￨L￨CD￨NUMBER￨- cities￨L￨NNS￨O￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- finds￨L￨VBZ￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- Delhi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- 48￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- households￨L￨NNS￨O￨A in￨L￨IN￨O￨- slums￨L￨NNS￨O￨- have￨L￨VBP￨O￨- five￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- people￨L￨NNS￨O￨- sleeping￨L￨VBG￨O￨- per￨L￨IN￨O￨- room￨L￨NN￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- 19￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- non-slum￨L￨JJ￨O￨- households￨L￨NNS￨O￨- .5￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- overcrowded￨L￨JJ￨O￨- living￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- facilitate￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- airborne￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .6￨L￨NN￨NUMBER￨- 7￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- high-density￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- developed￨L￨VBN￨O￨- and￨L￨CC￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- poverty￨L￨NN￨O￨- and￨L￨CC￨O￨- higher￨L￨JJR￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- no￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- ,￨L￨,￨O￨- large￨L￨JJ￨O￨- urban￨L￨JJ￨O￨A areas￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- eg￨L￨FW￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- several￨L￨JJ￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- slums￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- their￨L￨PRP$￨O￨- geographic￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- ,￨L￨,￨O￨- compositions￨L￨NNS￨O￨- ,￨L￨,￨O￨- unique￨L￨JJ￨O￨- home￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- agent-resolved￨L￨JJ￨O￨- activity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- differ￨L￨VBP￨O￨A between￨L￨IN￨O￨- slum￨L￨NN￨O￨- and￨L￨CC￨O￨- non-slum￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- from￨L￨IN￨O￨- those￨L￨DT￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- networked￨L￨JJ￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- ignores￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- slums￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- later￨L￨RB￨O￨- use￨L￨VB￨O￨- this￨L￨DT￨O￨- understanding￨L￨VBG￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- appropriate￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- detailed￨L￨VBN￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- slums￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- larger￨L￨JJR￨O￨- urban￨L￨JJ￨O￨A population￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- reside￨L￨VBP￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨A models￨L￨NNS￨O￨A previously￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- are￨L￨VBP￨O￨- compartmental￨L￨JJ￨O￨- constructs￨L￨NNS￨O￨- that￨L￨WDT￨O￨- divide￨L￨VBP￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- chain￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- constructs￨L￨NNS￨O￨- additionally￨L￨RB￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- partial￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- exposure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SEIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Accurate￨U￨JJ￨O￨- forecasts￨L￨NNS￨O￨A of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- incidence￨L￨NN￨O￨- could￨L￨MD￨O￨- thus￨L￨RB￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- management￨L￨NN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- data-driven￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- and￨L￨CC￨O￨- better￨L￨RBR￨O￨- timed￨L￨VBN￨O￨- for￨L￨IN￨O￨- patient￨L￨NN￨O￨- demand￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- validation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- model-inference￨L￨NN￨O￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- forecasting￨L￨VBG￨O￨A the￨L￨DT￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- model-inference￨L￨NN￨O￨- system￨L￨NN￨O￨- developed￨L￨VBD￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- forecasts￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- critical￨L￨JJ￨O￨- RSV￨U￨NN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- core￨L￨NN￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- forecasting￨L￨NN￨O￨A system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- refined￨L￨JJ￨O￨- SOSa-SPSa￨U￨NN￨MISC￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- depicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- sentiment￨L￨NN￨O￨- contagion￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- possibility￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- when￨L￨WRB￨O￨- coming￨L￨VBG￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- pessimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- comes￨L￨VBZ￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- optimistic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- become￨L￨VBP￨O￨- optimistic￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- β￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- whom￨L￨WP￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- come￨L￨VBP￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- spontaneously￨L￨RB￨O￨- become￨L￨VBP￨O￨- optimistic￨L￨JJ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- α￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- whom￨L￨WP￨O￨- the￨L￨DT￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- come￨L￨VBP￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- g￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- become￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- exists￨L￨VBZ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- first￨L￨RB￨ORDINAL￨- extended￨L￨VBD￨O￨- the￨L￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- uninfected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨A spontaneously￨L￨RB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- whom￨L￨WP￨O￨- the￨L￨DT￨O￨- uninfected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- come￨L￨VBN￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- limitation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SOSa-SPSa￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- only￨L￨RB￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- optimists￨L￨NNS￨O￨- and￨L￨CC￨O￨- pessimists￨L￨NNS￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- transform￨L￨VB￨O￨- into￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨A but￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- interact￨L￨VB￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- directly￨L￨RB￨O￨- .￨L￨.￨O￨- +Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- presents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- sentiment￨L￨NN￨O￨- contagion￨L￨NN￨O￨- process￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- pessimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- divided￨L￨VBN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- status￨L￨NN￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- optimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- O￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- pessimistic￨L￨JJ￨O￨- subjects￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- SISa￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- against￨L￨IN￨O￨- our￨L￨PRP$￨O￨- expectations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- can￨L￨MD￨O￨- decrease￨L￨VB￨O￨- significantly￨L￨RB￨O￨- with￨L￨IN￨O￨- population￨L￨NN￨O￨A density￨L￨NN￨O￨A ,￨L￨,￨O￨- possibly￨L￨RB￨O￨- because￨L￨IN￨O￨- higher￨L￨JJR￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- areas￨L￨NNS￨O￨- are￨L￨VBP￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- attributes￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- better￨L￨JJR￨O￨- healthcare￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- work￨L￨NN￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- location-specific￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- better￨L￨JJR￨O￨A model￨L￨NN￨TITLE￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- reason￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- topic￨L￨NN￨O￨- of￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- research￨L￨NN￨O￨- .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- have￨L￨VBP￨O￨- often￨L￨RB￨O￨- been￨L￨VBN￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- homogenously￨L￨RB￨O￨- mix￨L￨VB￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- recent￨L￨JJ￨O￨- EVD￨U￨NN￨O￨- models34567￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- recent￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- migration￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases8￨L￨NN￨O￨- ,￨L￨,￨O￨- homogeneous￨L￨JJ￨O￨A mixing￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- especially￨L￨RB￨O￨- poor￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- for￨L￨IN￨O￨- EVD￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨A understand￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- test￨L￨VB￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- leading￨L￨VBG￨O￨- EVD￨U￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- West￨U￨NNP￨O￨- Africa￨U￨NNP￨O￨- Ebola￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- have￨L￨VBP￨O￨- often￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- via￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨A mixing34567￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- major￨L￨JJ￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- control￨L￨VBP￨O￨- activities￨L￨NNS￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- routine￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- are￨L￨VBP￨O￨- supplemental￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIAs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- periodic￨L￨JJ￨O￨- national￨L￨JJ￨O￨- or￨L￨CC￨O￨- regional￨L￨JJ￨O￨- campaigns￨L￨NNS￨O￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- providing￨L￨VBG￨O￨- vaccine￨L￨NN￨O￨- to￨L￨TO￨O￨- everyone￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- defined￨L￨VBN￨O￨- age￨L￨NN￨O￨- range￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- scatter￨L￨NN￨O￨- in￨L￨IN￨O￨- relative￨L￨JJ￨O￨- fatalities￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- healthcare￨L￨NN￨O￨- measures￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- pulse￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Removed￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinations￨L￨NNS￨O￨- .￨L￨.￨O￨- +QV￨U￨NN￨O￨- =￨L￨JJ￨O￨- ΔV/ΔT￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- pulse￨L￨NN￨O￨A and￨L￨CC￨O￨- a￨L￨DT￨O￨- negative￨L￨JJ￨O￨- or￨L￨CC￨O￨- small￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- value￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- on-time￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- timing￨L￨NN￨O￨A goes￨L￨VBZ￨O￨- beyond￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- but￨L￨CC￨O￨- presumably￨L￨RB￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- rate￨L￨NN￨O￨- drops￨L￨VBZ￨O￨- towards￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- percentage￨L￨NN￨O￨- saturates￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- coverage￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Mereckiene￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 's￨L￨POS￨O￨- NumericCitation￨U￨NNP￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- values￨L￨NNS￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- t￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- denote￨L￨VBP￨O￨- the￨L￨DT￨DURATION￨- weeks￨L￨NNS￨DURATION￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- vaccination￨L￨NN￨O￨A starts￨L￨VBZ￨O￨- and￨L￨CC￨O￨- ends￨L￨VBZ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- being￨L￨VBG￨O￨- counted￨L￨VBN￨O￨- cumulatively￨L￨RB￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- schools￨L￨NNS￨O￨A were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- calibrate￨L￨VB￨O￨- a￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- grades￨L￨NNS￨O￨- and￨L￨CC￨O￨- schools￨L￨NNS￨O￨- using￨L￨VBG￨O￨- Markov￨U￨NNP￨PERSON￨- Chain￨U￨NNP￨O￨- Monte￨U￨NNP￨PERSON￨- Carlo￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- MCMC￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- median￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- schools￨L￨NNS￨O￨A of￨L￨IN￨O￨- 1.16￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 1.40￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- students￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- school￨L￨NN￨O￨- case￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 0.85￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 1.09￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- schools￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- A/H1N1pdm09￨U￨NNP￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- has￨L￨VBZ￨O￨- made￨L￨VBN￨O￨- it￨L￨PRP￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- collect￨L￨VB￨O￨- detailed￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- symptoms￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- primary￨L￨JJ￨O￨- schools￨L￨NNS￨O￨A of￨L￨IN￨O￨- Trento￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- The￨U￨DT￨O￨- discrepancy￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- within-school￨L￨NN￨O￨- transmission￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- household￨L￨NN￨O￨- and￨L￨CC￨O￨- community￨L￨NN￨O￨- transmission￨L￨NN￨O￨- played￨L￨VBD￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- sustaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- school￨L￨NN￨O￨A epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- high￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- between￨L￨IN￨O￨- students￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- class￨L￨NN￨O￨- confirms￨L￨VBZ￨O￨- that￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- within-class￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- key￨L￨JJ￨O￨- to￨L￨TO￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- school￨L￨NN￨O￨A settings￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Theoretically￨U￨RB￨O￨- ,￨L￨,￨O￨- influence￨L￨NN￨O￨A maximization￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- problem￨L￨NN￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- effectively￨L￨RB￨O￨- identify￨L￨VB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- maximize￨L￨VB￨O￨- their￨L￨PRP$￨O￨- spreading￨L￨NN￨O￨- influence￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- much￨L￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- on￨L￨IN￨O￨- measuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- node￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- effectively￨L￨RB￨O￨- identify￨L￨VB￨O￨- multiple￨L￨JJ￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨A are￨L￨VBP￨O￨- still￨L￨RB￨O￨- lacking￨L￨VBG￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- researches￨L￨VBZ￨O￨- in￨L￨IN￨O￨- sociology￨L￨NN￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- selecting￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- degree￨L￨NN￨O￨- as￨L￨IN￨O￨- spreaders￨L￨NNS￨O￨A can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- better￨L￨JJR￨O￨- spreading￨L￨NN￨O￨- influence￨L￨NN￨O￨- than￨L￨IN￨O￨- many￨L￨JJ￨O￨- other￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- attempted￨L￨VBD￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- effective￨L￨JJ￨O￨- multiple￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨A by￨L￨IN￨O￨- generalizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- idea￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coloring￨L￨VBG￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- graph￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Experiments￨U￨NNS￨O￨- are￨L￨VBP￨O￨- performed￨L￨VBN￨O￨- on￨L￨IN￨O￨- several￨L￨JJ￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- outperform￨L￨VB￨O￨- some￨L￨DT￨O￨- centrality-based￨L￨JJ￨O￨- methods￨L￨NNS￨O￨A .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- average￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- become￨L￨VB￨O￨- Then￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- after￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- dengue￨L￨NN￨O￨A should￨L￨MD￨O￨- be￨L￨VB￨O￨- Comparing￨U￨VBG￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- see￨L￨VB￨O￨- that￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- I￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- decrease￨L￨VBP￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- increases￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- we￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- inoculate￨L￨VB￨O￨- against￨L￨IN￨O￨- dengue￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- three￨L￨CD￨NUMBER￨- routes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨- as￨L￨IN￨O￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- Now￨U￨RB￨DATE￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- P￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- P0￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- start￨L￨VBP￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- intuitive￨L￨JJ￨O￨- view￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- dengue￨L￨NN￨O￨A among￨L￨IN￨O￨- humans￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- simple￨L￨JJ￨O￨- static￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- illustrated￨L￨VBD￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- purpose￨L￨NN￨O￨- here￨L￨RB￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- propose￨L￨VB￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- co-infection￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨A and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- with￨L￨IN￨O￨- particular￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- and￨L￨CC￨O￨- implication￨L￨NN￨O￨- for￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- dengue￨L￨NN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- diagram￨L￨NN￨O￨- of￨L￨IN￨O￨- co-infection￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨A and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- among￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- mosquitos￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- adopt￨L￨VBP￨O￨- a￨L￨DT￨O￨- computational￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- step￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- possible￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- :￨L￨:￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- binding￨L￨NN￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- receptor￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- binding￨L￨NN￨O￨- protein￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- receptor￨L￨NN￨O￨- protein￨L￨NN￨O￨- expression￨L￨NN￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- gene￨L￨NN￨O￨- regulatory￨L￨JJ￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- receptor￨L￨NN￨O￨- binding￨L￨NN￨O￨- complexity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- understood￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- amino￨L￨NN￨O￨- acids￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- entry￨L￨NN￨O￨- protein￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- receptor￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- increases￨L￨VBZ￨O￨- ,￨L￨,￨O￨- viruses￨L￨NNS￨O￨- tend￨L￨VBP￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- specialists￨L￨NNS￨O￨- and￨L￨CC￨O￨- target￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- specific￨L￨JJ￨O￨- receptor￨L￨NN￨O￨- .￨L￨.￨O￨- +Commonly￨U￨RB￨O￨- ,￨L￨,￨O￨- viruses￨L￨NNS￨O￨- enter￨L￨VBP￨O￨- host￨L￨NN￨TITLE￨- cells￨L￨NNS￨O￨- by￨L￨IN￨O￨- binding￨L￨NN￨O￨- cell￨L￨NN￨O￨- surface￨L￨NN￨O￨A receptors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Almost￨U￨RB￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- assume￨L￨VB￨O￨- ,￨L￨,￨O￨- first￨L￨RB￨ORDINAL￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- dt￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- dt￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- once￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- any￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computer￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- latency￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- computers￨L￨NNS￨O￨- become￨L￨VBP￨O￨- the￨L￨DT￨O￨- E￨U￨NN￨O￨- ones￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- secondly￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- anti-virus￨L￨JJ￨O￨- software￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- affected￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- completely￨L￨RB￨O￨- and￨L￨CC￨O￨- immediately￨L￨RB￨O￨- eliminated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Next￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- admits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- virus-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- that￨L￨IN￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- virus￨L￨NN￨O￨A eradication￨L￨NN￨O￨- if￨L￨IN￨O￨- R0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- admits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- equilibrium￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- whereas￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A disappears￨L￨VBZ￨O￨- completely￨L￨RB￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- find￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨- models￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨- in￨L￨IN￨O￨- Ref￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- virus￨L￨NN￨O￨A equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- propelled￨L￨VBN￨O￨- by￨L￨IN￨O￨- decisions￨L￨NNS￨O￨- made￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- consume￨L￨VB￨O￨- and￨L￨CC￨O￨- share￨L￨VB￨O￨A the￨L￨DT￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- identified￨L￨VBN￨O￨- by￨L￨IN￨O￨- Christakis￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Fowler￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- outcome￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- structural￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- reflects￨L￨VBZ￨O￨- volition￨L￨NN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- individual￨L￨JJ￨O￨- decisions￨L￨NNS￨O￨- to￨L￨TO￨O￨- consume￨L￨VB￨O￨- ,￨L￨,￨O￨- modify￨L￨VB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- share￨L￨NN￨O￨A information￨L￨NN￨O￨- and￨L￨CC￨O￨- seeks￨L￨VBZ￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- emergent￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- local￨L￨JJ￨O￨- preferences￨L￨NNS￨O￨- with￨L￨IN￨O￨- special￨L￨JJ￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- tie￨L￨JJ￨O￨- strength￨L￨NN￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- the￨L￨DT￨O￨- Diffusion￨U￨NNP￨MISC￨- of￨L￨IN￨MISC￨- Innovations￨U￨NNPS￨MISC￨- we￨L￨PRP￨O￨- adopt￨L￨VBP￨O￨- the￨L￨DT￨O￨- concepts￨L￨NNS￨O￨- communication￨L￨NN￨O￨- channels￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- directionality￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- communication￨L￨NN￨O￨- proximity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- tie￨L￨JJ￨O￨- strength￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- individual￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- modification￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- inflection￨L￨NN￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +Reinvention￨U￨NNP￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- modification￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- levels￨L￨NNS￨O￨- :￨L￨:￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- attribute￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- itself￨L￨PRP￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- an￨L￨DT￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- whether￨L￨IN￨O￨- it￨L￨PRP￨O￨- enhances￨L￨VBZ￨O￨- or￨L￨CC￨O￨- diminishes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- spreads￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- behavior￨L￨NN￨O￨- performed￨L￨VBN￨O￨- by￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- modification￨L￨NN￨O￨- activity￨L￨NN￨O￨- shed￨L￨VBD￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- act￨L￨NN￨O￨- of￨L￨IN￨O￨- modifying￨L￨VBG￨O￨- information￨L￨NN￨O￨A has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- accelerating￨L￨VBG￨O￨- or￨L￨CC￨O￨- decelerating￨L￨VBG￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- conceptually￨L￨RB￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- relatively￨L￨RB￨O￨- well-studied￨L￨JJ￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- locating￨L￨VBG￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- cascade￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- –￨L￨:￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- information￨L￨NN￨O￨- cascade￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- challenging￨L￨JJ￨O￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- because￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- perturbed￨L￨VBN￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨A to￨L￨TO￨O￨- having￨L￨VBG￨O￨- observations￨L￨NNS￨O￨- at￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- times￨L￨NNS￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- having￨L￨VBG￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- “￨L￨``￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- ”￨L￨''￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- –￨L￨:￨O￨- ,￨L￨,￨O￨- –￨L￨:￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- having￨L￨VBG￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- cascades￨L￨NNS￨O￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- sparse￨L￨JJ￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- perturbed￨L￨VBN￨O￨- and￨L￨CC￨O￨- unperturbed￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- situations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- complete￨L￨JJ￨O￨- or￨L￨CC￨O￨- almost￨L￨RB￨O￨- complete￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- perturbed￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- lack￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- spreads￨L￨VBZ￨O￨- [￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- situations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- alone￨L￨RB￨O￨- reasonable￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- an￨L￨DT￨O￨- abstract￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- situations￨L￨NNS￨O￨- above￨L￨IN￨O￨- are￨L￨VBP￨O￨- analogous￨L￨JJ￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- aspects￨L￨NNS￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- perturbation￨L￨NN￨O￨A spread￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- whose￨L￨WP$￨O￨- elements￨L￨NNS￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- known￨L￨VBN￨O￨- complex￨L￨NN￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- wish￨L￨VBP￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- path￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- observation￨L￨NN￨O￨- that￨L￨IN￨O￨- provides￨L￨VBZ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- perturbed￨L￨VBN￨O￨- or￨L￨CC￨O￨- unperturbed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- to￨L￨TO￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- color￨L￨NN￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- the￨L￨DT￨O￨- ranking￨L￨JJ￨O￨- assigned￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨A paths￨L￨NNS￨O￨- approach￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- label￨L￨NN￨O￨- propagation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- exposure￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- larger￨L￨JJR￨O￨- red￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- deemed￨L￨VBN￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- perturbed￨L￨VBN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- darker￨L￨JJR￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- deemed￨L￨VBN￨O￨- less￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- By￨U￨IN￨O￨- using￨L￨VBG￨O￨- shortest￨L￨JJS￨O￨A paths￨L￨NNS￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- propagation￨L￨NN￨O￨- path￨L￨NN￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 11￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 14￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- assigned￨L￨VBN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- perturbed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- because￨L￨IN￨O￨- both￨L￨DT￨O￨- paths￨L￨NNS￨O￨- connecting￨L￨VBG￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 6￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- equally￨L￨RB￨O￨- short￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- all￨L￨DT￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- deemed￨L￨VBN￨O￨- equally￨L￨RB￨O￨- unlikely￨L￨JJ￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- perturbed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- because￨L￨IN￨O￨- no￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- path￨L￨NN￨O￨- traverses￨L￨VBZ￨O￨- them￨L￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Label￨U￨NN￨O￨- propagation￨L￨NN￨O￨- assigns￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- perturbed￨L￨VBN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- to￨L￨TO￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 2-to-5￨L￨JJ￨O￨- path￨L￨NN￨O￨A but￨L￨CC￨O￨- also￨L￨RB￨O￨- to￨L￨TO￨O￨- nodes￨L￨NNS￨O￨- 7￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- no￨L￨DT￨O￨- observed￨L￨VBN￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unperturbed￨L￨JJ￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- formally￨L￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- D￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- on￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- θ￨L￨VBP￨O￨- is￨L￨VBZ￨O￨- replaced￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- of￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨A by￨L￨IN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- ρ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- distance￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- dataset￨L￨NN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ϵ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- tolerance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2011￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- estimated￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- similarity￨L￨NN￨O￨- and￨L￨CC￨O￨- estimated￨L￨VBN￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- relating￨L￨VBG￨O￨- 60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- HIV-infected￨U￨JJ￨O￨- men￨L￨NNS￨O￨A who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MSM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- Kingdom￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- sophisticated￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- complex￨L￨JJ￨O￨- population￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- phylogenies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- inference￨L￨NN￨O￨A of￨L￨IN￨O￨- structural￨L￨JJ￨O￨- network￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- been￨L￨VBN￨O￨- limited￨L￨VBN￨O￨- .￨L￨.￨O￨- +Unfortunately￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- explicitly￨L￨RB￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- tree￨L￨NN￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- normalizing￨L￨VBG￨O￨- constant￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- using￨L￨VBG￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨A network￨L￨NN￨O￨A models￨L￨NNS￨O￨- from￨L￨IN￨O￨- observed￨L￨VBN￨O￨- phylogenetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- better￨L￨RBR￨O￨- relate￨L￨VB￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- major￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- a￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- term￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- acquisition￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- outside￨L￨IN￨O￨A the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- simulation￨L￨NN￨O￨- :￨L￨:￨O￨- rate￨L￨NN￨O￨A of￨L￨IN￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.001￨L￨CD￨DURATION￨- yr￨L￨NN￨DURATION￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- initial￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 1000￨L￨CD￨DATE￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 365/14￨L￨CD￨NUMBER￨- yr￨L￨NN￨DURATION￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- 14￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- spontaneous￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- ξ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.00067￨L￨CD￨DURATION￨- yr￨L￨NN￨DURATION￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- birth￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/60￨L￨CD￨NUMBER￨- yr￨L￨NN￨DURATION￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- example￨L￨NN￨O￨- contains￨L￨VBZ￨O￨- multiple￨L￨JJ￨O￨- ‘￨L￨``￨O￨- sparks￨L￨VBZ￨O￨- ’￨L￨''￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨A to￨L￨TO￨O￨- supercriticality￨L￨NN￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- demonstrating￨L￨VBG￨O￨- that￨L￨IN￨O￨- bifurcation￨L￨NN￨O￨- delay￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- simply￨L￨RB￨O￨- the￨L￨DT￨O￨- waiting￨L￨VBG￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- spark￨L￨VB￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- after￨L￨IN￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- pure￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨A and￨L￨CC￨O￨- prevalence￨L￨NN￨O￨- are￨L￨VBP￨O￨- potentially￨L￨RB￨O￨- of￨L￨IN￨O￨- use￨L￨NN￨O￨- for￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- and￨L￨CC￨O￨- tracking￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- typical￨L￨JJ￨O￨- criticisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- ‘￨L￨``￨O￨- big￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ’￨L￨POS￨O￨- analyses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- as￨L￨IN￨O￨- containing￨L￨VBG￨O￨- biases￨L￨NNS￨O￨- and￨L￨CC￨O￨- tending￨L￨VBG￨O￨- towards￨L￨IN￨O￨- overfitting￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- behavioural￨L￨JJ￨O￨- change￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- media￨L￨NNS￨O￨A by￨L￨IN￨O￨- explicitly￨L￨RB￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- compartment￨L￨NN￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- mass￨L￨NN￨O￨- media￨L￨NNS￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR-type￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- incorporating￨L￨VBG￨O￨- effects￨L￨NNS￨O￨- like￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- criteria￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- media￨L￨NNS￨O￨A function￨L￨NN￨O￨- proposed￨L￨VBN￨O￨- here￨L￨RB￨O￨- fits￨L￨VBZ￨O￨- historical￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- other￨L￨JJ￨O￨- media￨L￨NNS￨O￨- functions￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- become￨L￨VBN￨O￨- popular￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- data￨L￨NNS￨O￨- streams￨L￨NNS￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- Internet￨U￨NN￨MISC￨- and￨L￨CC￨O￨- online￨L￨NN￨O￨- social￨L￨JJ￨O￨- media￨L￨NNS￨O￨A usage￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- data-driven￨L￨JJ￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- couples￨L￨VBZ￨O￨- these￨L￨DT￨O￨- existing￨L￨VBG￨O￨- paradigms￨L￨NNS￨O￨- :￨L￨:￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- media￨L￨NNS￨O￨A engagement￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- behaviour￨L￨NN￨O￨- change￨L￨NN￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- then￨L￨RB￨O￨- be￨L￨VB￨O￨- validated￨L￨VBN￨O￨- against￨L￨IN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- demography￨L￨NN￨O￨A and￨L￨CC￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- strongly￨L￨RB￨O￨- between￨L￨IN￨O￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨DATE￨- may￨L￨MD￨DATE￨- impact￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- limit￨L￨VB￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- conclusions￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- observations￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- country￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- generalized￨L￨VBN￨O￨- to￨L￨TO￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- non-outbreak￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- hospitals￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- outside￨L￨IN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- official￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- zone￨L￨NN￨O￨- ,￨L￨,￨O￨- nosocomial￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- might￨L￨MD￨O￨- arise￨L￨VB￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- patient￨L￨NN￨O￨- or￨L￨CC￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- HCW￨U￨NN￨O￨- is￨L￨VBZ￨O￨- transferred￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- care￨L￨NN￨O￨- center8￨L￨NN￨O￨- or￨L￨CC￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- patient￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- at￨L￨IN￨O￨- hospital￨L￨NN￨O￨- with￨L￨IN￨O￨- nonspecific￨L￨JJ￨O￨- EVD￨U￨NN￨O￨- symptoms￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- hospitals￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- differ￨L￨VB￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- contact￨L￨VB￨O￨- patterns￨L￨NNS￨O￨- between￨L￨IN￨O￨- HCW￨U￨NN￨O￨- and￨L￨CC￨O￨- patients￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- outbreak￨L￨NN￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- symptomatic￨L￨JJ￨O￨- patients￨L￨NNS￨O￨A are￨L￨VBP￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- HCW12￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- facilitated￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- dry￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- patients￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- exhibit￨L￨VB￨O￨- specific￨L￨JJ￨O￨- signs￨L￨NNS￨O￨- of￨L￨IN￨O￨- EVD67￨U￨NN￨O￨- .￨L￨.￨O￨- +Contact￨U￨NN￨O￨- between￨L￨IN￨O￨- EVD￨U￨NN￨O￨- patients￨L￨NNS￨O￨A and￨L￨CC￨O￨- healthcare￨L￨NN￨O￨- workers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- HCW￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- contributes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- hospital￨L￨NN￨O￨- spread5￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- complex￨L￨JJ￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- being￨L￨VBG￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- quickly￨L￨RB￨O￨A and￨L￨CC￨O￨- reliably￨L￨RB￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host-vector-pathogen￨L￨NN￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- perturbations￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- controls￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- connecting￨L￨VBG￨O￨- strategic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- more￨L￨RBR￨O￨- closely￨L￨RB￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨A to￨L￨TO￨O￨- make￨L￨VB￨O￨- qualitative￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- and￨L￨CC￨O￨- yet￨L￨RB￨O￨- retain￨L￨VB￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- what￨L￨WP￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- elements￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- —￨L￨:￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- specific￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- many￨L￨JJ￨O￨- possible￨L￨JJ￨O￨- intervention￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A ,￨L￨,￨O￨- compare￨L￨VBP￨O￨- them￨L￨PRP￨O￨- cost-effectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- do￨L￨VBP￨O￨- so￨L￨RB￨O￨- quickly￨L￨RB￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- lone￨L￨JJ￨O￨- and￨L￨CC￨O￨- combined￨L￨JJ￨O￨- intervention￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A faster￨L￨RBR￨O￨- than￨L￨IN￨O￨- almost￨L￨RB￨O￨- any￨L￨DT￨O￨- other￨L￨JJ￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- argue￨L￨VBP￨O￨- that￨L￨IN￨O￨- collaborations￨L￨NNS￨O￨- between￨L￨IN￨O￨- empiricists￨L￨NNS￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- modelers￨L￨NNS￨O￨- can￨L￨MD￨O￨- more￨L￨RBR￨O￨- efficiently￨L￨RB￨O￨- identify￨L￨VB￨O￨- effective￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨A for￨L￨IN￨O￨- HLB￨U￨NN￨ORGANIZATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- SPIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- planning￨L￨NN￨O￨- horizon￨L￨NN￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- over￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- calculate￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- utilities￨L￨NNS￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- a￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨A decision￨L￨NN￨O￨- —￨L￨:￨O￨- affects￨L￨VBZ￨O￨- behavioral￨L￨JJ￨O￨- change￨L￨NN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- that￨L￨DT￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SPIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Prophylactic￨U￨JJ￨O￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨O￨- ,￨L￨,￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- developed￨L￨VBN￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- couples￨L￨VBZ￨O￨- individual￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨A decisions￨L￨NNS￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SPIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- couples￨L￨NNS￨O￨- two￨L￨CD￨NUMBER￨- sub-models￨L￨NNS￨O￨- :￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Disease￨U￨NNP￨CAUSE_OF_DEATH￨- Dynamics￨U￨NNP￨MISC￨- Model￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- reproducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- another￨L￨DT￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Behavioral￨U￨NNP￨O￨- Decision￨U￨NNP￨O￨- Model￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- agents￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- make￨L￨VBP￨O￨- the￨L￨DT￨O￨- decision￨L￨NN￨O￨- to￨L￨TO￨O￨- engage￨L￨VB￨O￨- in￨L￨IN￨O￨- prophylactic￨L￨NN￨O￨A or￨L￨CC￨O￨- non-prophylactic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +Agents￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- engage￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- status￨L￨NN￨O￨- quo￨L￨NN￨O￨- behavior￨L￨NN￨O￨- while￨L￨IN￨O￨- agents￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- prophylactic￨L￨JJ￨O￨A state￨L￨NN￨O￨- employ￨L￨VBP￨O￨- preventative￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reduce￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- agents￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- vulnerable￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- or￨L￨CC￨O￨- prophylactic￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- statistics￨L￨NNS￨O￨- ,￨L￨,￨O￨- season￨L￨NN￨O￨- exponent￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3,4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- reflects￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stable￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- newly￨L￨RB￨O￨A acute￨L￨JJ￨O￨- human￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- total￨L￨JJ￨O￨- newly￨L￨RB￨O￨- acute￨L￨JJ￨O￨- human￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- we￨L￨PRP￨O￨- all￨L￨DT￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- brucellosis￨L￨NN￨O￨- has￨L￨VBZ￨O￨- seasonal￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- ,￨L￨,￨O￨- hence￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- human￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- significantly￨L￨RB￨O￨- increasing￨L￨VBG￨O￨- annually￨L￨RB￨SET￨- in￨L￨IN￨SET￨- summer￨L￨NN￨DATE￨- and￨L￨CC￨O￨- autumn￨L￨NN￨DATE￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- in￨L￨IN￨O￨- spring￨L￨NN￨DATE￨- and￨L￨CC￨O￨- winter￨L￨NN￨DATE￨A are￨L￨VBP￨O￨- relatively￨L￨RB￨O￨- decreasing￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Eventually￨U￨RB￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Figure￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- conclude￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- newly￨L￨RB￨O￨A acute￨L￨JJ￨O￨- human￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- spring￨L￨NN￨DATE￨- and￨L￨CC￨O￨- winter￨L￨NN￨DATE￨- are￨L￨VBP￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- those￨L￨DT￨O￨- in￨L￨IN￨O￨- summer￨L￨NN￨DATE￨- and￨L￨CC￨O￨- autumn￨L￨NN￨DATE￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- confirmed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨A acute￨L￨JJ￨O￨- human￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Bayingolin￨U￨NNP￨LOCATION￨- Mongol￨U￨NNP￨LOCATION￨- Autonomous￨U￨NNP￨LOCATION￨- Prefecture￨U￨NNP￨LOCATION￨- show￨L￨VBP￨O￨- a￨L￨DT￨O￨- pronounced￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- fluctuation￨L￨NN￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- brucellosis￨L￨NN￨O￨- among￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- ,￨L￨,￨O￨- sheep￨L￨NN￨O￨- ,￨L￨,￨O￨- elk￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨A [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Date￨U￨NN￨O￨- of￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- infected￨L￨JJ￨O￨- case￨L￨NN￨O￨- for￨L￨IN￨O￨- administrative￨L￨JJ￨O￨- units￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- countries￨L￨NNS￨O￨- of￨L￨IN￨O￨- Liberia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Guinea￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- surrounding￨L￨VBG￨O￨- nations￨L￨NNS￨O￨- of￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- openly￨L￨RB￨O￨- accessible￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- 16￨L￨CD￨NUMBER￨- spatial￨L￨JJ￨O￨- models￨L￨NNS￨O￨- reflecting￨L￨VBG￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨A density￨L￨NN￨O￨A ,￨L￨,￨O￨- border￨L￨NN￨O￨- closure￨L￨NN￨O￨- ,￨L￨,￨O￨- long-distance￨L￨JJ￨O￨- dispersal￨L￨NN￨O￨- and￨L￨CC￨O￨- individual￨L￨JJ￨O￨- movement￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- electronic￨L￨JJ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- Methods￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- daily￨L￨JJ￨SET￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- locations￨L￨NNS￨O￨- depended￨L￨VBD￨O￨- on￨L￨IN￨O￨- distance￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨A density￨L￨NN￨O￨A and￨L￨CC￨O￨- international￨L￨JJ￨O￨- border￨L￨NN￨O￨- closures￨L￨NNS￨O￨- between￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- neighbouring￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- available￨L￨JJ￨O￨- proxies￨L￨NNS￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- from￨L￨IN￨O￨- individual￨L￨JJ￨O￨- cell￨L￨NN￨O￨- phone￨L￨NN￨O￨- records￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- were￨L￨VBD￨O￨- a￨L￨DT￨O￨- poor￨L￨JJ￨O￨- predictor￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Blue￨U￨JJ￨O￨- lines￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- best-fit￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- distance￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨A density￨L￨NN￨O￨A and￨L￨CC￨O￨- whether￨L￨IN￨O￨- links￨L￨NNS￨O￨- cross￨L￨VBP￨O￨- the￨L￨DT￨O￨- border￨L￨NN￨O￨- surrounding￨L￨VBG￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- fitted￨L￨VBD￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- beginning￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- ending￨L￨VBG￨O￨- on￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- electronic￨L￨JJ￨O￨A supplementary￨L￨JJ￨O￨A material￨L￨NN￨O￨- ,￨L￨,￨O￨- table￨L￨NN￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Administrative￨U￨JJ￨O￨- units￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨A the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- coloured￨L￨VBN￨O￨- by￨L￨IN￨O￨- date￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 34￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NNP￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 1299￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1308￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asCost-Utility￨L￨NN￨O￨- of￨L￨IN￨O￨- Quadrivalent￨U￨JJ￨O￨- Versus￨U￨NNP￨O￨- Trivalent￨U￨NNP￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- Vaccine￨U￨NNP￨O￨- in￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Using￨U￨VBG￨O￨- an￨L￨DT￨O￨- Individual-Based￨U￨JJ￨MISC￨- Dynamic￨U￨NNP￨MISC￨- Transmission￨U￨NNP￨MISC￨- ModelAuthorsAuthors￨U￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsChristiaan￨L￨NNP￨O￨- DolkMartin￨U￨NNP￨PERSON￨- EichnerRobert￨U￨NNP￨PERSON￨- WelteAnastassia￨U￨NNP￨PERSON￨- AnastassopoulouLaure-Anne￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- BellinghenBarbara￨U￨NNP￨PERSON￨- Poulsen￨U￨NNP￨PERSON￨- NautrupIlse￨U￨NNP￨O￨- Van￨U￨NNP￨O￨- VlaenderenRuprecht￨U￨NNP￨O￨- Schmidt-OttMarkus￨U￨NNP￨O￨- SchwehmMaarten￨U￨NNP￨O￨- PostmaOpen￨U￨NNP￨O￨- AccessOriginal￨U￨NNP￨O￨- Research￨U￨NNP￨O￨- ArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1.7￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 10￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractBackgroundSeasonal￨U￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- primarily￨L￨RB￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨DT￨O￨- strain￨L￨NN￨O￨- subtypes￨L￨NNS￨O￨- and￨L￨CC￨O￨- strains￨L￨NNS￨O￨- from￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- B￨U￨NN￨O￨- lineages￨L￨NNS￨O￨- that￨L￨WDT￨O￨- vary￨L￨VBP￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- .￨L￨.￨O￨- +Quadrivalent￨U￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- QIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- includes￨L￨VBZ￨O￨- both￨L￨DT￨O￨- B-lineage￨U￨JJ￨MISC￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- works￨L￨NNS￨O￨- have￨L￨VBP￨O￨- exploited￨L￨VBN￨O￨- the￨L￨DT￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- awareness￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- none￨L￨NN￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- explored￨L￨VBN￨O￨- the￨L￨DT￨O￨- realistic￨L￨JJ￨O￨- coevolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- layers￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- explored16￨L￨NN￨O￨- ,￨L￨,￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- suited￨L￨VBN￨O￨- underlying￨L￨VBG￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- taking￨L￨VBG￨O￨- place￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨- networks1718192021￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- more￨L￨RBR￨O￨- realistically￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- coevolution￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- awareness￨L￨NN￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨A network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- linked￨L￨VBN￨O￨- with￨L￨IN￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- socioeconomic￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- awareness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- susceptibility35￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- preventive￨L￨JJ￨O￨A isolation￨L￨NN￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- keep￨L￨VB￨O￨- under￨L￨IN￨O￨- control￨L￨NN￨O￨- properly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- specific￨L￨JJ￨O￨- social￨L￨JJ￨O￨- categories￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- with￨L￨IN￨O￨- regards￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- less￨L￨RBR￨O￨- aware￨L￨JJ￨O￨- and￨L￨CC￨O￨- economically￨L￨RB￨O￨- disadvantaged￨L￨JJ￨O￨- other￨L￨JJ￨O￨- than￨L￨IN￨O￨- being￨L￨VBG￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- central￨L￨JJ￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- work￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- propose￨L￨VB￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- introducing￨L￨VBG￨O￨- an￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- preventive￨L￨JJ￨O￨A isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- skill￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- systems￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- and￨L￨CC￨O￨- richness￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- observational￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- should￨L￨MD￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- be￨L￨VB￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- forecast￨L￨NN￨O￨A system￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- method￨L￨NN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- data￨L￨NN￨O￨- and/or￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- epidemic￨L￨JJ￨O￨- features￨L￨NNS￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- forecast￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- either￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- or￨L￨CC￨O￨- optimized￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- state-space￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- address￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- questions￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- what￨L￨WP￨O￨- spatial￨L￨JJ￨O￨- scale￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- granularity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- simulation￨L￨NN￨O￨- does￨L￨VBZ￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- connection￨L￨NN￨O￨- improve￨L￨VB￨O￨- forecast￨L￨NN￨O￨A performance￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- whether￨L￨IN￨O￨- forecast￨L￨NN￨O￨- performance￨L￨NN￨O￨- differs￨L￨VBZ￨O￨- between￨L￨IN￨O￨- interpandemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- pandemic￨L￨JJ￨O￨- seasons￨L￨NNS￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- differing￨L￨VBG￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Addressing￨U￨VBG￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- factor￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- compared￨L￨VBD￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- —￨L￨:￨O￨- three￨L￨CD￨NUMBER￨- ensemble￨L￨NN￨O￨- filters￨L￨NNS￨O￨- and￨L￨CC￨O￨- three￨L￨CD￨NUMBER￨- particle￨L￨NN￨O￨- type￨L￨NN￨O￨- filters￨L￨NNS￨O￨- —￨L￨:￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- forecast￨L￨NN￨O￨A of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- revealed￨L￨VBD￨O￨- key￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- among￨L￨IN￨O￨- those￨L￨DT￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- test￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- network￨L￨NN￨O￨- forecast￨L￨NN￨O￨A system￨L￨NN￨O￨- at￨L￨IN￨O￨- borough￨L￨NN￨O￨- and￨L￨CC￨O￨- neighborhood￨L￨NN￨O￨- spatial￨L￨JJ￨O￨- resolutions￨L￨NNS￨O￨- using￨L￨VBG￨O￨- ILI￨U￨NN￨O￨- +￨L￨CC￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- virulence-transmission￨L￨NN￨O￨- trade-off￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- promising￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- virulence￨L￨NN￨O￨A of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- predictions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- been￨L￨VBN￨O￨- approached￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- piecemeal￨L￨RB￨O￨- manner￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- combining￨L￨VBG￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- ,￨L￨,￨O￨- AIDS-free￨U￨JJ￨O￨- survival￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- SPVL￨U￨NN￨O￨- from￨L￨IN￨O￨- very￨L￨RB￨O￨- different￨L￨JJ￨O￨- cohorts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- functions￨L￨NNS￨O￨- fitted￨L￨VBD￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- well￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- shown￨L￨VBN￨O￨- by￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- non-parametric￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- stratified￨L￨VBN￨O￨- by￨L￨IN￨O￨- SPVL￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1a￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- Kaplan-Meier￨U￨NNP￨O￨- plot￨L￨NN￨O￨- comparing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- prediction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- best￨L￨JJS￨O￨- model￨L￨NN￨TITLE￨- fit￨L￨NN￨O￨- was￨L￨VBD￨O￨- one￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- increases￨L￨VBZ￨O￨- from￨L￨IN￨O￨- 0.019￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- year￨L￨NN￨DURATION￨- to￨L￨TO￨O￨- 0.14￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- year￨L￨NN￨DURATION￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- stepwise￨L￨JJ￨O￨- fashion￨L￨NN￨O￨- as￨L￨IN￨O￨- SPVL￨U￨NN￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- plateaus￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1a￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- ΔAIC￨U￨NN￨O￨- =￨L￨JJ￨O￨- −￨L￨CD￨NUMBER￨- 75.96￨L￨CD￨NUMBER￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- null￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 817￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- HIV-1￨U￨NN￨MISC￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- set-point￨L￨JJ￨O￨- viral￨L￨JJ￨O￨A load￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- SPVL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- stable￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- load￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptomatic￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- trait￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- both￨L￨DT￨O￨- variable￨L￨JJ￨O￨- and￨L￨CC￨O￨- heritable￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- current￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- USRT￨U￨NNP￨ORGANIZATION￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨RB￨ORDINAL￨- comprehensive￨L￨JJ￨O￨- dose￨L￨NN￨O￨- –￨L￨:￨O￨- response￨L￨NN￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A risk￨L￨NN￨O￨- among￨L￨IN￨O￨- medical￨L￨JJ￨O￨- radiation￨L￨NN￨O￨- workers￨L￨NNS￨O￨- using￨L￨VBG￨O￨- individualised￨L￨JJ￨O￨- annual￨L￨JJ￨SET￨- dose￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- badge￨L￨NN￨O￨- dose￨L￨NN￨O￨- measurements￨L￨NNS￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- more￨L￨JJR￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- covering￨L￨VBG￨O￨- ∼￨L￨SYM￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- worker￨L￨NN￨O￨- total￨L￨JJ￨O￨- doses￨L￨NNS￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- work￨L￨NN￨O￨- history￨L￨NN￨O￨- and￨L￨CC￨O￨- practices￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dose￨L￨NN￨O￨- –￨L￨:￨O￨- response￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- using￨L￨VBG￨O￨- internal￨L￨JJ￨O￨- comparisons￨L￨NNS￨O￨- of￨L￨IN￨O￨- excess￨L￨JJ￨O￨- relative￨L￨JJ￨O￨- risk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ERR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- stratified￨L￨VBN￨O￨- by￨L￨IN￨O￨- birth￨L￨NN￨O￨- cohort￨L￨NN￨O￨- and￨L￨CC￨O￨- year￨L￨NN￨DURATION￨- first￨L￨RB￨ORDINAL￨- worked￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- findings￨L￨NNS￨O￨- from￨L￨IN￨O￨- our￨L￨PRP$￨O￨- earlier￨L￨JJR￨O￨- work-history￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Hormonal￨U￨JJ￨O￨- ,￨L￨,￨O￨- reproductive￨L￨JJ￨O￨- ,￨L￨,￨O￨- lifestyle￨L￨NN￨O￨- ,￨L￨,￨O￨- anthropometric￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- known￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- ∼￨L￨CD￨PERCENT￨- 40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Madigan￨U￨NN￨PERSON￨- ;￨L￨:￨O￨- Sprague￨U￨NNP￨LOCATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- our￨L￨PRP$￨O￨- earlier￨L￨JJR￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- USRT￨U￨NNP￨MISC￨- Cohort￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- Mohan￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Doody￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- WeCare￨U￨NNP￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- second￨L￨JJ￨ORDINAL￨- breast￨L￨NN￨O￨- cancers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Langholz￨U￨NN￨LOCATION￨- ;￨L￨:￨O￨- Bernstein￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- examined￨L￨VBD￨O￨- individual￨L￨JJ￨O￨- radiation￨L￨NN￨O￨- exposure￨L￨NN￨O￨- and￨L￨CC￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- risks￨L￨NNS￨O￨- adjusting￨L￨VBG￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- known￨L￨JJ￨O￨- lifestyle￨L￨NN￨O￨- and￨L￨CC￨O￨- reproductive￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- self-reported￨L￨JJ￨O￨- work￨L￨NN￨O￨- history￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- Radiologic￨U￨NNP￨O￨- Technologists￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- USRT￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- experienced￨L￨VBD￨O￨- elevated￨L￨JJ￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Doody￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Mohan￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- breast￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- moderate￨L￨JJ￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- ionising￨L￨VBG￨O￨- radiation￨L￨NN￨O￨- doses￨L￨NNS￨O￨- in￨L￨IN￨O￨- atomic￨L￨JJ￨O￨- bomb￨L￨NN￨O￨- survivors￨L￨NNS￨O￨- and￨L￨CC￨O￨- radiotherapy￨L￨NN￨O￨- patients￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simulation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A that￨L￨WDT￨O￨- fits￨L￨VBZ￨O￨- historical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- trends￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- deaths￨L￨NNS￨O￨- and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- capturing￨L￨VBG￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- behavioral￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- with￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- various￨L￨JJ￨O￨- policy￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- implementation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- decrease￨L￨VB￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- unintended￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- .￨L￨.￨O￨- +Later￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- causal￨L￨JJ￨O￨A loop￨L￨NN￨O￨- diagram￨L￨NN￨O￨- is￨L￨VBZ￨O￨- provided￨L￨VBN￨O￨- that￨L￨IN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- causal￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- key￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- public￨L￨NN￨O￨- ’s￨L￨POS￨O￨- situational￨L￨JJ￨O￨- awareness￨L￨NN￨O￨- and￨L￨CC￨O￨- attention￨L￨NN￨O￨- towards￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- consequently￨L￨RB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨A to￨L￨TO￨O￨- test￨L￨VB￨O￨- various￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- and￨L￨CC￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- adverse￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- sociocultural￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- may￨L￨MD￨O￨- rise￨L￨VB￨O￨- up￨L￨RP￨O￨- to￨L￨TO￨O￨- 4.6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- sociocultural￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- discussed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Rowell￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fatal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- wise￨L￨JJ￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- public￨L￨JJ￨O￨- fear￨L￨NN￨O￨- ;￨L￨:￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contrary￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- author￨L￨NN￨TITLE￨- explains￨L￨VBZ￨O￨- that￨L￨IN￨O￨- fear￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- leveraged￨L￨VBN￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- public￨L￨JJ￨O￨- awareness￨L￨NN￨O￨A about￨L￨IN￨O￨- the￨L￨DT￨O￨- proper￨L￨JJ￨O￨- steps￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- extremely￨L￨RB￨O￨- helpful￨L￨JJ￨O￨- for￨L￨IN￨O￨- testing￨L￨VBG￨O￨- different￨L￨JJ￨O￨- policy￨L￨NN￨O￨A scenarios￨L￨NNS￨O￨- during￨L￨IN￨O￨- such￨L￨JJ￨O￨- crises￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- 7￨L￨CD￨NUMBER￨- by￨L￨IN￨O￨- saving￨L￨VBG￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- management￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- mitigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- event￨L￨NN￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- PRRS￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- field￨L￨NN￨O￨- virus￨L￨NN￨O￨- re-introduction￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- farrow-to-wean￨L￨JJ￨O￨- swine￨L￨NNS￨O￨- herd￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- developed￨L￨VBD￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- included￨L￨VBD￨O￨- herd￨L￨NN￨O￨A closure￨L￨NN￨O￨- with￨L￨IN￨O￨- or￨L￨CC￨O￨- without￨L￨IN￨O￨- gilt￨L￨JJ￨O￨- acclimation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- single￨L￨JJ￨O￨- or￨L￨CC￨O￨- repeated￨L￨VBN￨O￨- mass￨L￨NN￨O￨- immunization￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- modified-live￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- Midwestern￨U￨NN￨LOCATION￨- US￨U￨NNP￨COUNTRY￨- farrow-to-wean￨L￨JJ￨O￨- herd￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- different￨L￨JJ￨O￨- PRRS￨U￨NN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- infected￨L￨JJ￨O￨- PRRS￨U￨NN￨O￨- sites￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- 1,000-sow￨L￨JJ￨MISC￨- farrow-to-wean￨L￨JJ￨MISC￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- herd￨L￨NN￨O￨A as￨L￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- used￨L￨VBN￨O￨- stochastic￨L￨JJ￨O￨- “￨L￨``￨O￨- SIR￨U￨NN￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- ,￨L￨,￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- compartments￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stratified￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- PRRS￨U￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PRRSV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- time-to-extinction￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- 115-sow￨L￨JJ￨O￨- breeding￨L￨NN￨O￨- herd￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- .￨L￨.￨O￨- +Secondary￨U￨JJ￨O￨- objectives￨L￨NNS￨O￨- were￨L￨VBD￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- immunization￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- would￨L￨MD￨O￨- change￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- swine￨L￨NNS￨O￨- farm￨L￨NN￨O￨- .￨L￨.￨O￨- +Subjects￨U￨NNS￨O￨- were￨L￨VBD￨O￨- included￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- inclusion￨L￨NN￨O￨- criteria￨L￨NNS￨O￨- were￨L￨VBD￨O￨- met￨L￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- emergency￨L￨NN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- incidents￨L￨NNS￨O￨- with￨L￨IN￨O￨- ≥￨L￨NN￨O￨- 30￨L￨CD￨NUMBER￨- patients￨L￨NNS￨O￨- ;￨L￨:￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- incidents￨L￨NNS￨O￨- with￨L￨IN￨O￨- specific￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- subtypes￨L￨NNS￨O￨A verified￨L￨VBN￨O￨- by￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- examinations￨L￨NNS￨O￨- including￨L￨VBG￨O￨- virus￨L￨NN￨O￨- isolation￨L￨NN￨O￨- and/or￨L￨CC￨O￨- nucleic￨L￨JJ￨O￨- acid￨L￨NN￨O￨- detection￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- healthcare￨L￨NN￨O￨- authority￨L￨NN￨O￨- intervention￨L￨NN￨O￨- of￨L￨IN￨O￨- ≥￨L￨CD￨NUMBER￨- 5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- criteria￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- ≥￨L￨NN￨O￨- 30￨L￨CD￨NUMBER￨- ILIs￨U￨NNS￨O￨- occurring￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- preschool￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- collective￨L￨JJ￨O￨- organization￨L￨NN￨O￨- within￨L￨IN￨O￨- 1￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- laboratory-confirmed￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A viruses￨L￨NNS￨O￨A through￨L￨IN￨O￨- virus￨L￨NN￨O￨- isolation￨L￨NN￨O￨- or￨L￨CC￨O￨- real-time￨L￨JJ￨O￨- reverse￨L￨JJ￨O￨- transcriptase￨L￨NN￨O￨- polymerase￨L￨NN￨O￨- chain￨L￨NN￨O￨- reaction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RT-PCR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mixed￨L￨JJ￨O￨- type￨L￨NN￨O￨- refers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- mixture￨L￨NN￨O￨- of￨L￨IN￨O￨- ≥￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- virus￨L￨NN￨O￨- types￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- case￨L￨NN￨O￨- sample￨L￨NN￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- ;￨L￨:￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- include￨L￨VB￨O￨- ≥￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- subtypes￨L￨NNS￨O￨- of￨L￨IN￨O￨- type￨L￨NN￨O￨- A￨U￨NN￨O￨- or￨L￨CC￨O￨- ≥￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- subtype￨L￨NN￨O￨- of￨L￨IN￨O￨- type￨L￨NN￨O￨- A￨U￨NN￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- type￨L￨NN￨O￨- B￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A viruses￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- addressed￨L￨VBD￨O￨- this￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- parameterized￨L￨VBN￨O￨- stochastic￨L￨JJ￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- ,￨L￨,￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- SEIBM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- designed￨L￨VBN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- landscape-scale￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 47￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 50￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- multi-species￨L￨NNS￨O￨- wildlife￨L￨NN￨O￨A hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 51￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 52￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- claim￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- adequate￨L￨JJ￨O￨A predictions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- management￨L￨NN￨O￨- activities￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- mitigation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- contingency￨L￨NN￨O￨- planning￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- driving￨L￨VBG￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- adequate￨L￨JJ￨O￨A representation￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- therefore￨L￨RB￨O￨- of￨L￨IN￨O￨- crucial￨L￨JJ￨O￨- importance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Summarizing￨U￨VBG￨O￨- transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- hence￨L￨RB￨O￨- ,￨L￨,￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- allow￨L￨VB￨O￨- inferences￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- stages￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- persist￨L￨VB￨O￨- outside￨L￨IN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- whether￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- IT￨U￨PRP￨O￨- may￨L￨MD￨O￨- require￨L￨VB￨O￨- different￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- mitigation￨L￨NN￨O￨A efforts￨L￨NNS￨O￨- than￨L￨IN￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- DT￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- explanatory￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- assessed￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- included￨L￨VBD￨O￨- susceptible￨L￨JJ￨O￨- animal￨L￨NN￨O￨A densities￨L￨NNS￨O￨- ,￨L￨,￨O￨- weather￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- detection￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- IPs￨U￨NNS￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- 7￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- under￨L￨IN￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- AUC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- 7￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- convex￨L￨NN￨O￨- hull￨L￨NN￨O￨- calculation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Modeling￨U￨NN￨O￨- studies￨L￨NNS￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- in￨L￨IN￨O￨- Australia￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- overseas￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- and/or￨L￨CC￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- FMD￨U￨NN￨ORGANIZATION￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- situations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- widespread￨L￨JJ￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- resources￨L￨NNS￨O￨A for￨L￨IN￨O￨- stamping￨L￨VBG￨O￨- out￨L￨RP￨O￨- are￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- .￨L￨.￨O￨- +Sarandopoulos￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- conducted￨L￨VBD￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- 125￨L￨CD￨NUMBER￨- FMD￨U￨NN￨ORGANIZATION￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- non-endemic￨L￨JJ￨O￨- temperate￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- reported￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- OIE￨U￨NN￨O￨- between￨L￨IN￨O￨- January￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2005￨L￨CD￨DATE￨- and￨L￨CC￨O￨- December￨U￨NNP￨DATE￨- 31￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2013￨L￨CD￨DATE￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- associations￨L￨NNS￨O￨- between￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- size/duration￨L￨NN￨O￨- and￨L￨CC￨O￨- early￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- explanatory￨L￨JJ￨O￨- variables￨L￨NNS￨O￨A .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- New￨U￨NNP￨COUNTRY￨- Zealand￨U￨NNP￨COUNTRY￨- invest￨L￨VB￨O￨- considerable￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- in￨L￨IN￨O￨- preparedness￨L￨NN￨O￨- and￨L￨CC￨O￨- planning￨L￨NN￨O￨- for￨L￨IN￨O￨- emergency￨L￨NN￨O￨- animal￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- maintaining￨L￨VBG￨O￨- vaccine￨L￨NN￨O￨- banks￨L￨NNS￨O￨- for￨L￨IN￨O￨- FMD￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- HCV￨U￨NN￨O￨- incidence￨L￨NN￨O￨- stabilized￨L￨VBD￨O￨- among￨L￨IN￨O￨- heterosexuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- decreased￨L￨VBD￨O￨- among￨L￨IN￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- inject￨L￨VBP￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- .3￨L￨NN￨NUMBER￨- An￨U￨DT￨O￨- international￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- HCV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- HIV‐infected￨U￨JJ￨O￨- MSM￨U￨NN￨ORGANIZATION￨- was￨L￨VBD￨O￨- revealed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨- study￨L￨NN￨O￨- .11￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- high‐risk￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- including￨L￨VBG￨O￨- condomless￨L￨JJ￨O￨- traumatic￨L￨JJ￨O￨- anal￨L￨JJ￨O￨- intercourse￨L￨NN￨O￨- ,￨L￨,￨O￨- fisting￨L￨VBG￨O￨- ,￨L￨,￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- recreational￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- group￨L￨NN￨O￨- sex￨L￨NN￨O￨A .1￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 13￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- SHCS￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- HCV￨U￨NN￨O￨- incidence￨L￨NN￨O￨- coincided￨L￨VBD￨O￨- with￨L￨IN￨O￨- reduced￨L￨VBN￨O￨- self‐reported￨L￨JJ￨O￨- condom￨L￨NN￨O￨- use￨L￨NN￨O￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨O￨- on￨L￨IN￨O￨- antiretroviral￨L￨JJ￨O￨- therapy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ART￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .14￨L￨CD￨NUMBER￨- Effective￨U￨JJ￨O￨- interventions￨L￨NNS￨O￨- to￨L￨TO￨O￨- curb￨L￨VB￨O￨- the￨L￨DT￨O￨- HCV￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- among￨L￨IN￨O￨- HIV‐infected￨U￨JJ￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- remain￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- established￨L￨VBN￨O￨- .￨L￨.￨O￨- +antiretroviral￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- confidence￨L￨NN￨O￨- interval￨L￨NN￨O￨- direct‐acting￨L￨VBG￨O￨- antiviral￨L￨JJ￨O￨- agent￨L￨NN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨- C￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- interquartile￨L￨JJ￨O￨- range￨L￨NN￨O￨- men￨L￨NNS￨O￨A who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- person‐years￨L￨NNS￨O￨- Swiss￨U￨JJ￨NATIONALITY￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- Cohort￨U￨NN￨O￨- Study￨U￨NN￨O￨- The￨U￨DT￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨- C￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HCV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ‐￨L￨RB￨O￨- infected￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- evolved￨L￨VBN￨O￨- quickly￨L￨RB￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- few￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- .1￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- Western￨U￨JJ￨MISC￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- HCV￨U￨NN￨O￨- is￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- among￨L￨IN￨O￨- HIV‐infected￨U￨JJ￨O￨- men￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MSM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .1￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- observed￨L￨VBD￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Swiss￨U￨JJ￨NATIONALITY￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- Cohort￨U￨NN￨MISC￨- Study￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- SHCS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,10￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- steep￨L￨JJ￨O￨- rise￨L￨NN￨O￨- in￨L￨IN￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- HCV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨O￨- without￨L￨IN￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- injection￨L￨NN￨O￨- drug￨L￨NN￨O￨- use￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- without￨L￨IN￨O￨- bias￨L￨NN￨O￨- in￨L￨IN￨O￨- heterogenous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- scholars￨L￨NNS￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- precise￨L￨JJ￨O￨- hierarchical￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- hubs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- firstly￨L￨RB￨O￨- informed￨L￨VBN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- pervades￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- progressive￨L￨JJ￨IDEOLOGY￨- cascade￨L￨NN￨O￨- across￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- degree￨L￨NN￨O￨- classes41￨L￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- results￨L￨NNS￨O￨- have￨L￨VBP￨O￨- manifested￨L￨VBN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- uncorrelated￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- designing￨L￨VBG￨O￨- a￨L￨DT￨O￨- proper￨L￨JJ￨O￨- contact￨L￨NN￨O￨- strategy￨L￨NN￨O￨- can￨L￨MD￨O￨- effectively￨L￨RB￨O￨- promote￨L￨VB￨O￨A the￨L￨DT￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- preferential￨L￨JJ￨O￨- contact￨L￨NN￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PCS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- information￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- informed￨L￨VBN￨O￨A nodes￨L￨NNS￨O￨- densities￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- plant￨L￨NN￨O￨- pathogenic￨L￨JJ￨O￨- fungi￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- genus￨L￨NN￨O￨- Fusarium￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- putative￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- effector￨L￨NN￨O￨- genes￨L￨NNS￨O￨A and/or￨L￨CC￨O￨- secondary￨L￨JJ￨O￨- metabolite￨L￨NN￨O￨- gene￨L￨NN￨O￨- clusters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- regulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- ortholog￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- transcription￨L￨NN￨O￨- factor￨L￨NN￨O￨- :￨L￨:￨O￨- F.￨U￨NNP￨O￨- Also￨U￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- plant￨L￨NN￨O￨- pathogenic￨L￨JJ￨O￨- fungi￨L￨NNS￨O￨- Botrytis￨U￨NNP￨O￨- cinerea￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Reg1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Verticillium￨U￨NNP￨O￨- dahliae￨L￨NNP￨O￨- (￨L￨-LRB-￨O￨- VdSge1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Cladosporium￨U￨NN￨O￨- fulvum￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CfWor1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Zymoseptoria￨U￨NN￨O￨- tritici￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZtWor1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Ustilago￨U￨NNP￨O￨- maydis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- UmRos1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Magnaporthe￨U￨NN￨O￨- oryzae￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MoGti1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- deletion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- gene￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- transcription￨L￨NN￨O￨- factor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- partially￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- perturbs￨L￨VBZ￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- effector￨L￨NN￨O￨- genes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 32￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Ustilago￨U￨NNP￨O￨- maydis￨L￨VBZ￨O￨- the￨L￨DT￨O￨- heterodimer￨L￨NN￨O￨- bE/bW￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- forkhead￨L￨NN￨O￨- transcription￨L￨NN￨O￨- factor￨L￨NN￨O￨- Fox1￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- zinc￨L￨NN￨O￨- finger￨L￨NN￨O￨- transcription￨L￨NN￨O￨- factors￨L￨NNS￨O￨- Rbf1￨U￨NN￨O￨- and￨L￨CC￨O￨- Mzr1￨U￨NN￨O￨- are￨L￨VBP￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- transcriptional￨L￨JJ￨O￨- regulation￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogenicity-related￨L￨JJ￨O￨- genes￨L￨NNS￨O￨A and/or￨L￨CC￨O￨- effector￨L￨NN￨O￨- genes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Leptosphaeria￨U￨NNP￨LOCATION￨- maculans￨L￨NNS￨O￨- and￨L￨CC￨O￨- Stagnospora￨U￨NN￨O￨- nodorum￨L￨NN￨O￨- ,￨L￨,￨O￨- homologs￨L￨NNS￨O￨- of￨L￨IN￨O￨- StuA￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- bHLH￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- basic￨L￨JJ￨O￨- helix-loop-helix￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- transcription￨L￨NN￨O￨- factor￨L￨NN￨O￨- ,￨L￨,￨O￨- regulate￨L￨VBP￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- effector￨L￨NN￨O￨- genes￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- works￨L￨NNS￨O￨- on￨L￨IN￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- have￨L￨VBP￨O￨- greatly￨L￨RB￨O￨- deepened￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- level￨L￨NN￨O￨- and￨L￨CC￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- useful￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- overlooked￨L￨VBN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- what￨L￨WP￨O￨- would￨L￨MD￨O￨- happen￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- aim￨L￨VB￨O￨- for￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- but￨L￨CC￨O￨- only￨L￨RB￨O￨- suppose￨L￨VBP￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- localized￨L￨JJ￨O￨A target￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mixed￨L￨JJ￨O￨- degree￨L￨NN￨O￨- decomposition￨L￨NN￨O￨- method￨L￨NN￨O￨- consider￨L￨VBP￨O￨- both￨L￨DT￨O￨- the￨L￨DT￨O￨- residual￨L￨JJ￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- exhausted￨L￨VBN￨O￨- degree￨L￨NN￨O￨- when￨L￨WRB￨O￨- decomposing￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- rank￨L￨VB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- accordingly27￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- iterative￨L￨JJ￨O￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- method￨L￨NN￨O￨- incorporates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- centrality￨L￨NN￨O￨- information￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- in￨L￨IN￨O￨- ranking￨L￨JJ￨O￨A spreaders28￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- diversity￨L￨NN￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- the￨L￨DT￨O￨- ranking￨L￨JJ￨O￨- method29￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- hiring￨L￨VBG￨O￨- committee￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- know￨L￨VB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- these￨L￨DT￨O￨- PhD￨U￨NN￨O￨- students￨L￨NNS￨O￨A but￨L￨CC￨O￨- the￨L￨DT￨O￨- email￨L￨NN￨O￨- address￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- collaborators￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- published￨L￨VBN￨O￨- papers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- author￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- paper￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- essentially￨L￨RB￨O￨- a￨L￨DT￨O￨- target￨L￨NN￨O￨- spreading￨L￨NN￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- collaboration￨L￨NN￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- one￨L￨PRP￨NUMBER￨- has￨L￨VBZ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- node￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- propagate￨L￨VB￨O￨- such￨L￨JJ￨O￨- information￨L￨NN￨O￨- to￨L￨TO￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- PhD￨U￨NN￨O￨- students￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- towards￨L￨IN￨O￨- localized￨L￨JJ￨O￨A targets￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- attention￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- perceive￨L￨VB￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- govern￨L￨VBP￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨A size￨L￨NN￨O￨A in￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- clarify￨L￨VB￨O￨- how￨L￨WRB￨O￨- each￨L￨DT￨O￨- key￨L￨JJ￨O￨- factor￨L￨NN￨O￨- contributes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- various￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- issue￨L￨NN￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨A size￨L￨NN￨O￨A is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- system￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- composite￨L￨NN￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- non-human￨L￨JJ￨O￨- primates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- primates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- generally￨L￨RB￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- sylvatic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- viruses￨L￨NNS￨O￨A ,￨L￨,￨O￨- this￨L￨DT￨O￨- paradigm￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- scant￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- and￨L￨CC￨O￨- researchers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- have￨L￨VBP￨O￨- repeatedly￨L￨RB￨O￨- cautioned￨L￨VBN￨O￨- that￨L￨IN￨O￨- other￨L￨JJ￨O￨- animal￨L￨JJ￨O￨- species￨L￨NNS￨O￨- may￨L￨MD￨O￨- play￨L￨VB￨O￨- key￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Dengue￨U￨JJ￨O￨- virus￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- DENV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- chikungunya￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- and￨L￨CC￨O￨- spread￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- and￨L￨CC￨O￨- rapidly￨L￨RB￨O￨- across￨L￨IN￨O￨- both￨L￨DT￨O￨- Central￨U￨NNP￨O￨- and￨L￨CC￨O￨- South￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- reaching￨L￨VBG￨O￨- dozens￨L￨NNS￨O￨- of￨L￨IN￨O￨- countries￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- year￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- introduction￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- ZIKV￨U￨NNP￨O￨- was￨L￨VBD￨O￨- first￨L￨JJ￨ORDINAL￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ancestral￨L￨JJ￨O￨- sylvatic￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨- of￨L￨IN￨O￨- YFV￨U￨NN￨O￨- ,￨L￨,￨O￨- CHIKV￨U￨NN￨O￨- and￨L￨CC￨O￨- ZIKV￨U￨NN￨O￨- occur￨L￨VBP￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- DENV￨U￨NN￨O￨- ancestral￨L￨JJ￨O￨- cycle￨L￨NN￨O￨A occurs￨L￨VBZ￨O￨- in￨L￨IN￨O￨- Southeast￨U￨NNP￨LOCATION￨- Asia￨U￨NNP￨CITY￨- with￨L￨IN￨O￨- later￨L￨JJ￨O￨- transport￨L￨NN￨O￨- to￨L￨TO￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- enzootic￨L￨JJ￨O￨- establishment￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- invasion￨L￨NN￨O￨- of￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- by￨L￨IN￨O￨- Zika￨U￨NNP￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- latest￨L￨JJS￨O￨- upheaval￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- decade-long￨L￨JJ￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- viruses￨L￨NNS￨O￨A transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- Aedes￨U￨VBZ￨O￨- aegypti￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- predicted￨L￨VBN￨O￨- well￨L￨RB￨O￨- in￨L￨IN￨O￨- advance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- association￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- neuropathology￨L￨NN￨O￨- and￨L￨CC￨O￨- teratogenicity￨L￨NN￨O￨- were￨L￨VBD￨O￨- only￨L￨RB￨O￨- revealed￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A through￨L￨IN￨O￨- the￨L￨DT￨O￨- Pacific￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- into￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- whether￨L￨IN￨O￨- this￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- difference￨L￨NN￨O￨- alone￨L￨RB￨O￨- can￨L￨MD￨O￨- drive￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- sex-specific￨L￨JJ￨O￨- virulence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen.We￨L￨NN￨O￨- advance￨L￨NN￨O￨- evolutionary￨L￨JJ￨O￨- theory￨L￨NN￨O￨- by￨L￨IN￨O￨- formulating￨L￨VBG￨O￨- and￨L￨CC￨O￨- solving￨L￨VBG￨O￨- analytically￨L￨RB￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model23￨L￨NN￨O￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- vertical￨L￨JJ￨O￨- and￨L￨CC￨O￨- horizontal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- male￨L￨JJ￨O￨A and￨L￨CC￨O￨- female￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- will￨L￨MD￨O￨- explore￨L￨VB￨O￨- which￨L￨WDT￨O￨- factors￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- selection￨L￨NN￨O￨- for￨L￨IN￨O￨- differential￨L￨JJ￨O￨- exploitation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- residing￨L￨VBG￨O￨- in￨L￨IN￨O￨- female￨L￨JJ￨O￨- and￨L￨CC￨O￨- male￨L￨JJ￨O￨A hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- each￨L￨DT￨O￨- sex￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogens￨L￨NNS￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- host￨L￨VBP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- that￨L￨IN￨O￨- natural￨L￨JJ￨O￨- selection￨L￨NN￨O￨- acting￨L￨VBG￨O￨- differently￨L￨RB￨O￨- on￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- in￨L￨IN￨O￨- male￨L￨NN￨O￨A and￨L￨CC￨O￨- female￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- pathogens￨L￨NNS￨O￨- exhibiting￨L￨VBG￨O￨- different￨L￨JJ￨O￨- virulence￨L￨NN￨O￨- in￨L￨IN￨O￨- men￨L￨NNS￨O￨- and￨L￨CC￨O￨- women￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- progression￨L￨NN￨O￨- and￨L￨CC￨O￨- fatality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- virulence￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- affect￨L￨VB￨O￨- sex-specific￨L￨JJ￨O￨- organs￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- substantially￨L￨RB￨O￨- between￨L￨IN￨O￨- men￨L￨NNS￨O￨- and￨L￨CC￨O￨- women12￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- solve￨L￨VBP￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- allowing￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- to￨L￨TO￨O￨- exhibit￨L￨VB￨O￨- different￨L￨JJ￨O￨- virulence￨L￨NN￨O￨A in￨L￨IN￨O￨- men￨L￨NNS￨O￨- and￨L￨CC￨O￨- women￨L￨NNS￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- April￨U￨NNP￨DATE￨- 15￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2016￨L￨CD￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨ORGANIZATION￨- Strategic￨U￨NNP￨ORGANIZATION￨- Advisory￨U￨NNP￨ORGANIZATION￨- Group￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨O￨- Experts￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- SAGE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- immunisation￨L￨NN￨O￨- recommended￨L￨VBD￨O￨- Dengvaxia￨U￨NNP￨PERSON￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- regions￨L￨NNS￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- endemicity￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- indicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- seroprevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- or￨L￨CC￨O￨- greater￨L￨JJR￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- modeled￨L￨VBN￨O￨- reduced￨L￨VBN￨O￨- dengue￨L￨JJ￨O￨A hospitalizations￨L￨NNS￨O￨- by￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- over￨L￨IN￨O￨- 30￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- vaccinating￨L￨VBG￨O￨- yearly￨L￨JJ￨SET￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- 9￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- children￨L￨NNS￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- was￨L￨VBD￨O￨- revisited￨L￨VBN￨O￨- and￨L￨CC￨O￨- published￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- concluding￨L￨VBG￨O￨- that￨L￨IN￨O￨- Dengvaxia￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- given￨L￨VBN￨O￨- ,￨L￨,￨O￨- every￨L￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- 9￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- children￨L￨NNS￨O￨- living￨L￨VBG￨O￨- in￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A endemic￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- reduce￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- significantly￨L￨RB￨O￨- over￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- introduction￨L￨NN￨O￨- and￨L￨CC￨O￨- beyond￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- 21￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- to￨L￨TO￨O￨- 29￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- over￨L￨IN￨O￨- 20￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- modellers￨L￨NNS￨O￨- from￨L￨IN￨O￨- Sanofi￨U￨NNP￨ORGANIZATION￨- Pasteur￨U￨NNP￨ORGANIZATION￨- have￨L￨VBP￨O￨- predicted￨L￨VBN￨O￨- that￨L￨IN￨O￨- Dengvaxia￨U￨NNP￨PERSON￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- by￨L￨IN￨O￨- about￨L￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- within￨L￨IN￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- country￨L￨NN￨O￨- ’s￨L￨POS￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- vaccinated￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- achieving￨L￨VBG￨O￨- a￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- dengue￨L￨JJ￨O￨- prevention￨L￨NN￨O￨- goal￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- 3￨L￨CD￨NUMBER￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- phase￨L￨NN￨O￨- III￨U￨CD￨NUMBER￨- trials￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- high￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- partial￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A immunes￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- high￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- hospitalizations￨L￨NNS￨O￨- during￨L￨IN￨O￨- breakthrough￨L￨NN￨O￨- dengue￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- persons￨L￨NNS￨O￨- who￨L￨WP￨O￨- were￨L￨VBD￨O￨- vaccinated￨L￨VBN￨O￨- when￨L￨WRB￨O￨- seronegative￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- manufacturer￨L￨NN￨TITLE￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- has￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- 25￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- Phase￨U￨NN￨O￨- III￨U￨CD￨NUMBER￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- 66￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- olds￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- outline￨L￨VBP￨O￨- 3￨L￨CD￨NUMBER￨- components￨L￨NNS￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- building￨L￨VBG￨O￨- a￨L￨DT￨O￨- predictive￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- researchers￨L￨NNS￨O￨- and￨L￨CC￨O￨- managers￨L￨NNS￨O￨- should￨L￨MD￨O￨- consider￨L￨VB￨O￨- early￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- wildlife￨L￨NN￨O￨A pathogen￨L￨NN￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- modeling￨L￨NN￨O￨- frame￨L￨NN￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- appropriate￨L￨JJ￨O￨- ,￨L￨,￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- parameters￨L￨NNS￨O￨- or￨L￨CC￨O￨- factors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- making￨L￨VBG￨O￨- preliminary￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- collate￨L￨VB￨O￨- existing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- parameterize￨L￨VB￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- quickly￨L￨RB￨O￨- ,￨L￨,￨O￨- rigorously￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- effectively￨L￨RB￨O￨- synthesizes￨L￨VBZ￨O￨- relevant￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- a￨L￨DT￨O￨- wildlife￨L￨NN￨O￨A pathogen￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- emergence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- essential￨L￨JJ￨O￨- for￨L￨IN￨O￨- informing￨L￨VBG￨O￨- management￨L￨NN￨O￨- at￨L￨IN￨O￨- critical￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- and￨L￨CC￨O￨- ultimately￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- livestock￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- wildlife￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- reluctant￨L￨JJ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- forecasting￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- management￨L￨NN￨O￨A actions￨L￨NNS￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- parameters￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- essential￨L￨JJ￨O￨- component￨L￨NN￨O￨- for￨L￨IN￨O￨- applying￨L￨VBG￨O￨- decision￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- emerging￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- predictive￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- trade-offs￨L￨NNS￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- management￨L￨NN￨O￨A actions￨L￨NNS￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- consequences￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- this￨L￨DT￨O￨- 4-5-3￨L￨CD￨NUMBER￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- can￨L￨MD￨O￨- work￨L￨VB￨O￨- with￨L￨IN￨O￨- managers￨L￨NNS￨O￨- to￨L￨TO￨O￨- rapidly￨L￨RB￨O￨- develop￨L￨VB￨O￨- useful￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- with￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- and￨L￨CC￨O￨- prioritize￨L￨VB￨O￨- information￨L￨NN￨O￨- gathering￨L￨NN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- management￨L￨NN￨O￨A of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- accumulated￨L￨VBN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- temporal￨L￨JJ￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- ,￨L￨,￨O￨- clinical￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- information￨L￨NN￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- valuable￨L￨JJ￨O￨- information￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- exploited￨L￨VBN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- and￨L￨CC￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- One￨U￨CD￨NUMBER￨- feasible￨L￨JJ￨O￨- means￨L￨NNS￨O￨- to￨L￨TO￨O￨- promptly￨L￨RB￨O￨- detect￨L￨VB￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- track￨L￨VB￨O￨- the￨L￨DT￨O￨- progress￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- regional￨L￨JJ￨O￨- or￨L￨CC￨O￨- national￨L￨JJ￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- medical￨L￨JJ￨O￨- centres￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stochastic￨U￨NNP￨MISC￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- populationsRui-Xing￨L￨JJ￨O￨- Ming1￨U￨NN￨O￨- ,￨L￨,￨O￨- Jiming￨U￨VBG￨PERSON￨- Liu2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- William￨U￨NNP￨PERSON￨- K.￨U￨NNP￨PERSON￨- Recent￨U￨JJ￨PERSON￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- stressed￨L￨VBN￨O￨- the￨L￨DT￨O￨- urgency￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- when￨L￨WRB￨O￨- and￨L￨CC￨O￨- where￨L￨WRB￨O￨- outbreaks￨L￨NNS￨O￨- may￨L￨MD￨O￨- emerge￨L￨VB￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A spread￨L￨VBN￨O￨- because￨L￨RB￨O￨- many￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- unknown￨L￨JJ￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- quantitatively￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- such￨L￨JJ￨O￨- information￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- passengers￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- flight￨L￨NN￨O￨- or￨L￨CC￨O￨- number￨L￨NN￨O￨- co-authorship￨L￨NN￨O￨- papers￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- bind￨L￨VBP￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- weight￨L￨NN￨O￨- value￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- edge10￨L￨NN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨A based￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- that￨L￨WDT￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- essence￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨A computes￨L￨VBZ￨O￨- ranking￨L￨JJ￨O￨- score￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- connectivity￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- some￨L￨DT￨O￨- consensus￨L￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- terms￨L￨NNS￨O￨- ,￨L￨,￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- traits￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- essential￨L￨JJ￨O￨- in￨L￨IN￨O￨- determining￨L￨VBG￨O￨- the￨L￨DT￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- ,￨L￨,￨O￨- cause￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- within￨L￨IN￨O￨- human￨L￨JJ￨O￨A populations￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- Citation￨U￨NNP￨MISC￨- Ebola￨U￨NNP￨MISC￨- virus￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- EVD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- continuing￨L￨VBG￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- underlined￨L￨VBN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- better￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- emerge￨L￨VB￨O￨- and￨L￨CC￨O￨- cause￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- traits￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- human￨L￨JJ￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- by￨L￨IN￨O￨- any￨L￨DT￨O￨- transmission￨L￨NN￨O￨- route￨L￨NN￨O￨- other￨L￨JJ￨O￨- than￨L￨IN￨O￨- deliberate￨L￨JJ￨O￨- laboratory￨L￨NN￨O￨- exposure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +Level￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- indicates￨L￨VBZ￨O￨- viruses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- infect￨L￨VB￨O￨- humans￨L￨NNS￨O￨A but￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- from￨L￨IN￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +Level￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- indicates￨L￨VBZ￨O￨- viruses￨L￨NNS￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- humans￨L￨NNS￨O￨A are￨L￨VBP￨O￨- exposed￨L￨VBN￨O￨- but￨L￨CC￨O￨- which￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- infect￨L￨VB￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- placement￨L￨NN￨O￨- position￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- function￨L￨NN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- immunizing￨L￨VBG￨O￨- those￨L￨DT￨O￨- candidate￨L￨NN￨TITLE￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- introduces￨L￨VBZ￨O￨- Dancing￨U￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DWPV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨A placement￨L￨NN￨O￨- strategy￨L￨NN￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- division￨L￨NN￨O￨- into￨L￨IN￨O￨- our￨L￨PRP$￨O￨- solution￨L￨NN￨O￨- .￨L￨.￨O￨- +Researchers￨U￨NNS￨O￨- try￨L￨VBP￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- protection￨L￨NN￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- algorithm￨L￨NN￨O￨- by￨L￨IN￨O￨- modifying￨L￨VBG￨O￨- heuristic￨L￨NN￨O￨- idea￨L￨NN￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- NP-hard￨U￨JJ￨MISC￨- NumericCitation￨U￨NN￨MISC￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- computing￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨A between￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- #￨L￨#￨O￨- p￨L￨NN￨O￨- problem￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- immunization￨L￨NN￨O￨- strategy￨L￨NN￨O￨A should￨L￨MD￨O￨- take￨L￨VB￨O￨- the￨L￨DT￨O￨- benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- time￨L￨NN￨O￨- slot￨L￨NN￨O￨- into￨L￨IN￨O￨- consideration￨L￨NN￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- utilization￨L￨NN￨O￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- typical￨L￨JJ￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- which￨L￨WDT￨O￨- quantify￨L￨VBP￨O￨- how￨L￨WRB￨O￨- much￨L￨RB￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- centrally￨L￨RB￨O￨- positioned￨L￨JJ￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- betweenness￨L￨NN￨O￨- ,￨L￨,￨O￨- closeness￨L￨NN￨O￨- ,￨L￨,￨O￨- local￨L￨JJ￨O￨- rank￨L￨NN￨O￨- ,￨L￨,￨O￨- h-index￨L￨NN￨O￨- ,￨L￨,￨O￨- Katz￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- eigenvector￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- k-shell￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- k-truss￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- percolation￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- accessibility￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- influence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- expected￨L￨VBN￨O￨- force￨L￨NN￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨A the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- quickly￨L￨RB￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Those￨U￨DT￨O￨- interacting￨L￨VBG￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- affecting￨L￨VBG￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- ’s￨L￨POS￨O￨- states￨L￨NNS￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- vertices￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- representing￨L￨VBG￨O￨A the￨L￨DT￨O￨- objects￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- edges￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- representing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- relations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Not￨U￨RB￨O￨- any￨L￨DT￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- important￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- various￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨A importance￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- Darwinian￨U￨JJ￨MISC￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- linked￨L￨VBD￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- genotype￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- frequencies￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- alleles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- surviving￨L￨VBG￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- genotypes￨L￨NNS￨O￨- could￨L￨MD￨O￨- change￨L￨VB￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- selection￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- agent￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- could￨L￨MD￨O￨- occur￨L￨VB￨O￨- if￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- adults￨L￨NNS￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- between￨L￨IN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- exposure￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- the￨L￨DT￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- unnecessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- invoke￨L￨VB￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- allele￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- Darwinian￨U￨JJ￨MISC￨- evolution￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- observed￨L￨VBN￨O￨- mortality￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- plausible￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- mortality￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- mortality￨L￨NN￨O￨- feedbacks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- identify￨L￨VBP￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen-specific￨L￨JJ￨O￨- mortality￨L￨NN￨O￨A rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- starting￨L￨VBG￨O￨- frequencies￨L￨NNS￨O￨- of￨L￨IN￨O￨- protective￨L￨JJ￨O￨- alleles￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 19th￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- mortality￨L￨NN￨O￨- transition￨L￨NN￨O￨- of￨L￨IN￨O￨- Pacific￨U￨NNP￨ORGANIZATION￨- Islanders￨U￨NNPS￨ORGANIZATION￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- non-zero￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- more￨L￨JJR￨O￨- individuals￨L￨NNS￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- lower￨L￨JJR￨O￨- the￨L￨DT￨O￨- mortality￨L￨NN￨O￨A rate￨L￨NN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- that￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- detecting￨L￨VBG￨O￨- subpopulations￨L￨NNS￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨A may￨L￨MD￨O￨- potentially￨L￨RB￨O￨- facilitate￨L￨VB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- impactful￨L￨JJ￨O￨- and￨L￨CC￨O￨- cost-effective￨L￨JJ￨O￨- deployment￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- resources￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- point-of-care￨L￨JJ￨O￨- testing￨L￨NN￨O￨- or￨L￨CC￨O￨- pre-exposure￨L￨JJ￨O￨- prophylaxis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Historically￨U￨NNP￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A has￨L￨VBZ￨O￨- often￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- partition￨L￨NN￨O￨- the￨L￨DT￨O￨- sequence￨L￨NN￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- into￨L￨IN￨O￨- clades￨L￨NNS￨O￨- or￨L￨CC￨O￨- subtypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- different￨L￨JJ￨O￨- investigators￨L￨NNS￨O￨- can￨L￨MD￨O￨- refer￨L￨VB￨O￨- to￨L￨TO￨O￨- similar￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- nomenclature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- seldom￨L￨RB￨O￨- been￨L￨VBN￨O￨- validated￨L￨VBN￨O￨- on￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- where￨L￨WRB￨O￨- actual￨L￨JJ￨O￨- clusters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- different￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A methods￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- empirical￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- .￨L￨.￨O￨- +Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨A methods￨L￨NNS￨O￨- play￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- extensive￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- that￨L￨WDT￨O￨- accumulates￨L￨VBZ￨O￨- in￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Genetic￨U￨JJ￨O￨- clustering￨L￨NN￨O￨A methods￨L￨NNS￨O￨- operate￨L￨VBP￨O￨- on￨L￨IN￨O￨- variation￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- nucleotide￨L￨NN￨O￨- sequencing￨L￨NN￨O￨- or￨L￨CC￨O￨- nucleic￨L￨JJ￨O￨- acid￨L￨NN￨O￨- profiling￨L￨NN￨O￨- of￨L￨IN￨O￨- conspicuous￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- features￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- restriction￨L￨NN￨O￨- fragment￨L￨NN￨O￨- length￨L￨NN￨O￨- polymorphisms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- RFLPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- three￨L￨CD￨NUMBER￨- generations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- iterative￨L￨JJ￨O￨- fitting￨L￨JJ￨O￨A procedure￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- d￨L￨NN￨O￨- had￨L￨VBD￨O￨- stabilized￨L￨VBN￨O￨- sufficiently￨L￨RB￨O￨- to￨L￨TO￨O￨- project￨L￨VB￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- with￨L￨IN￨O￨- reasonable￨L￨JJ￨O￨- accuracy￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- porcine￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- diarrhea￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PEDV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- outbreak￨L￨NN￨O￨A in￨L￨IN￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- decay￨L￨NN￨O￨- and￨L￨CC￨O￨- exponential￨L￨JJ￨O￨- adjustment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IDEA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- modelAmy￨L￨NNP￨O￨- L.￨U￨NNP￨O￨- Using￨U￨VBG￨O￨- our￨L￨PRP$￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- 2-parameter￨L￨JJ￨O￨- IDEA￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- PEDV￨U￨NN￨O￨- on￨L￨IN￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- swine￨L￨NNS￨O￨- farms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- best-fit￨L￨JJS￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- between￨L￨IN￨O￨- farm￨L￨NN￨O￨- transmission￨L￨NN￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨A the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- publically￨L￨RB￨O￨- available￨L￨JJ￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- IDEA￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- projections￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- excellent￨L￨JJ￨O￨A agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- 7-day￨L￨JJ￨DURATION￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- estimate￨L￨NN￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- strongly￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- ambient￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- precipitation￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- predicted￨L￨VBD￨O￨- future￨L￨JJ￨DATE￨- climate￨L￨NN￨O￨- changes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- altered￨L￨JJ￨O￨- rainfall￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- ,￨L￨,￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- Hawaiian￨U￨JJ￨O￨- forest￨L￨NN￨O￨A birds￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- altitudinal￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- on￨L￨IN￨O￨- avian￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- Hawaiian￨U￨JJ￨LOCATION￨- forest￨L￨NN￨O￨A birds￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- previously￨L￨RB￨DATE￨- NumericCitation￨U￨NNP￨O￨- linked￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- climate￨L￨NN￨O￨- projections￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- warm￨L￨JJ￨O￨- and￨L￨CC￨O￨- dry￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- RCP￨U￨NN￨O￨- 4.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- warm￨L￨JJ￨O￨- and￨L￨CC￨O￨- wet￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- A1B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hot￨L￨JJ￨O￨- and￨L￨CC￨O￨- dry￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- RCP￨U￨NN￨O￨- 8.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- futures￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- our￨L￨PRP$￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- mosquito￨L￨NN￨O￨- abundance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- bird￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- until￨L￨IN￨O￨- the￨L￨DT￨DATE￨- end￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- 21st￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- .￨L￨.￨O￨- +Malaria￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- recently￨L￨RB￨DATE￨- increased￨L￨VBN￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- at￨L￨IN￨O￨- high￨L￨JJ￨O￨- elevations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Hawai’i￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- constitute￨L￨VBP￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- remaining￨L￨VBG￨O￨- refugia￨L￨NN￨O￨- for￨L￨IN￨O￨- native￨L￨JJ￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- supporting￨L￨VBG￨O￨- the￨L￨DT￨O￨- concern￨L￨NN￨O￨- that￨L￨IN￨O￨- native￨L￨JJ￨O￨- Hawaiian￨U￨JJ￨MISC￨- forest￨L￨NN￨O￨A birds￨L￨NNS￨O￨- may￨L￨MD￨O￨- suffer￨L￨VB￨O￨- further￨L￨JJ￨O￨- population￨L￨NN￨O￨- declines￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- species￨L￨NNS￨O￨- extinction￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- climate-induced￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 8,11,13,14,22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- comprehensive￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Hawaiian￨U￨JJ￨O￨- forest￨L￨NN￨O￨A bird-malaria￨L￨NN￨O￨- system￨L￨NN￨O￨- illustrates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- transmission￨L￨NN￨O￨- varies￨L￨VBZ￨O￨- across￨L￨IN￨O￨- altitudes￨L￨NNS￨O￨- on￨L￨IN￨O￨- Hawai’i￨U￨NNP￨LOCATION￨- Island￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- from￨L￨IN￨O￨- high￨L￨JJ￨O￨- year-round￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- warm￨L￨JJ￨O￨- lowland￨L￨JJ￨O￨- forests￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- episodic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- at￨L￨IN￨O￨- mid￨L￨JJ￨O￨- elevation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- infrequent￨L￨JJ￨O￨- summer￨L￨NN￨DATE￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- cool￨L￨JJ￨O￨- high￨L￨JJ￨O￨- elevations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Even￨U￨RB￨O￨- though￨L￨IN￨O￨- these￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- not￨L￨RB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- life￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- multitude￨L￨NN￨O￨- of￨L￨IN￨O￨- BCMs￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- setting￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- still￨L￨RB￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- game-theoretical￨L￨JJ￨O￨- foundation￨L￨NN￨O￨- that￨L￨WDT￨O￨- caused￨L￨VBD￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- ‘￨L￨``￨O￨- vaccination￨L￨NN￨O￨- games￨L￨NNS￨O￨A ’￨L￨POS￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- ‘￨L￨``￨O￨- epidemic￨L￨JJ￨O￨- games￨L￨NNS￨O￨- with￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨- ’￨L￨''￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- incorporating￨L￨VBG￨O￨- behavioural￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- as￨L￨IN￨O￨- ‘￨L￨``￨O￨- behavioural￨L￨JJ￨O￨- change￨L￨NN￨O￨- models￨L￨NNS￨O￨- ’￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- BCMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- typically￨L￨RB￨O￨- complement￨L￨VBP￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- attempt￨L￨NN￨O￨- to￨L￨TO￨O￨- mimic￨L￨VB￨O￨- real￨L￨JJ￨O￨A life￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- A/H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- has￨L￨VBZ￨O￨- triggered￨L￨VBN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- to￨L￨TO￨O￨- adapt￨L￨VB￨O￨- their￨L￨PRP$￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- take￨L￨VB￨O￨- preventive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- interest￨L￨NN￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- behaviour￨L￨NN￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- disease-related￨L￨JJ￨O￨- information￨L￨NN￨O￨- into￨L￨IN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- essence￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- BCM￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- responsive￨L￨JJ￨O￨- to￨L￨TO￨O￨- external￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- take￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- preventive￨L￨JJ￨O￨A measures￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- of￨L￨IN￨O￨- contracting￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- HAT￨U￨NN￨O￨- ,￨L￨,￨O￨- multiple￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- including￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- trypanosomes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- scale￨L￨NN￨O￨- migrations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- activity-related￨L￨JJ￨O￨- movements￨L￨NNS￨O￨A through￨L￨IN￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- exposure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- key￨L￨JJ￨O￨- to￨L￨TO￨O￨- HAT￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- agent-based￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- movements￨L￨NNS￨O￨A that￨L￨WDT￨O￨- expose￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- hazards￨L￨NNS￨O￨- that￨L￨WDT￨O￨- vary￨L￨VBP￨O￨- through￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨- has￨L￨VBZ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- risk-mitigation￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- feed￨L￨VB￨O￨- into￨L￨IN￨O￨- policy￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- the￨L￨DT￨O￨- ABM￨U￨NNP￨MISC￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨A activities￨L￨NNS￨O￨- that￨L￨WDT￨O￨- generate￨L￨VBP￨O￨- large￨L￨JJ￨O￨- amounts￨L￨NNS￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- results￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- explored￨L￨VBN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- depth￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- emergent￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +African￨U￨JJ￨NATIONALITY￨- animal￨L￨NN￨O￨- trypanosomiasis￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- AAT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- as￨L￨IN￨O￨- being￨L￨VBG￨O￨- “￨L￨``￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- factors￨L￨NNS￨O￨A restricting￨L￨VBG￨O￨- economic￨L￨JJ￨O￨- development￨L￨NN￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- today￨L￨NN￨DATE￨- ”￨L￨''￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- widespread￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- overstocking￨L￨NN￨O￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- in￨L￨IN￨O￨- tsetse-free￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Important￨U￨JJ￨O￨- research￨L￨NN￨O￨- questions￨L￨NNS￨O￨- explored￨L￨VBN￨O￨- were￨L￨VBD￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- spatial￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- parasite￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pressure￨L￨NN￨O￨A related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- urbanization￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- temporal￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- parasite￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pressure￨L￨NN￨O￨- in￨L￨IN￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- year￨L￨NN￨DATE￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- or￨L￨CC￨O￨- an￨L￨DT￨O￨- age-dependent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pressure￨L￨NN￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- parasite￨L￨NN￨O￨- abundance￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- assuming￨L￨VBG￨O￨- E.￨U￨NNP￨O￨- Methods￨U￨NNS￨O￨- By￨U￨IN￨O￨- developing￨L￨VBG￨O￨- and￨L￨CC￨O￨- comparing￨L￨VBG￨O￨- different￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- we￨L￨PRP￨O￨- characterised￨L￨VBD￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pressure￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨- that￨L￨WDT￨O￨- foxes￨L￨NNS￨O￨- acquired￨L￨VBN￨O￨- after￨L￨IN￨O￨- exposure￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- foxes￨L￨NNS￨O￨- in￨L￨IN￨O￨- Zurich￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- included￨L￨VBD￨O￨- the￨L￨DT￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pressure￨L￨NN￨O￨A with￨L￨IN￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- fox￨L￨NN￨O￨- and￨L￨CC￨O￨- season￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- regulating￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- on￨L￨IN￨O￨- parasite￨L￨NN￨O￨- abundance￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- zoonotic￨L￨JJ￨O￨- parasite￨L￨NN￨O￨A among￨L￨IN￨O￨- the￨L￨DT￨O￨- fox￨L￨NN￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- remarkably￨L￨RB￨O￨- aggregated￨L￨VBN￨O￨- with￨L￨IN￨O￨- few￨L￨JJ￨O￨- heavily￨L￨RB￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- harbouring￨L￨VBG￨O￨- much￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨NN￨O￨- burdens￨L￨NNS￨O￨- and￨L￨CC￨O￨- being￨L￨VBG￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- parasitic￨L￨JJ￨O￨- egg￨L￨NN￨O￨- contamination￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Mathematical￨U￨JJ￨MISC￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- Echinococcus￨U￨NN￨O￨- multilocularis￨L￨NNS￨O￨- abundance￨L￨NN￨O￨A in￨L￨IN￨O￨- foxes￨L￨NNS￨O￨- in￨L￨IN￨O￨- Zurich￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- SwitzerlandBelen￨U￨NNP￨MISC￨- Otero-Abad1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- Simon￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- alleviate￨L￨VB￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- various￨L￨JJ￨O￨- rumor￨L￨NN￨O￨A theories￨L￨NNS￨O￨- from￨L￨IN￨O￨- social￨L￨JJ￨O￨- ,￨L￨,￨O￨- psychological￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- CMC￨U￨NNP￨ORGANIZATION￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- used￨L￨VBD￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- features￨L￨NNS￨O￨- .￨L￨.￨O￨- +Second￨U￨NNP￨ORDINAL￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- report￨L￨VBP￨O￨- findings￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- snapshot￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- identified￨L￨VBN￨O￨- features￨L￨NNS￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A propagation￨L￨NN￨O￨- phases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Rumor-related￨U￨JJ￨O￨- tweets￨L￨NNS￨O￨- were￨L￨VBD￨O￨- extracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- examined￨L￨VBN￨O￨- over￨L￨IN￨O￨- different￨L￨JJ￨O￨- time￨L￨NN￨O￨- windows￨L￨NNS￨O￨- ,￨L￨,￨O￨- form￨L￨VBP￨O￨- the￨L￨DT￨DURATION￨- initial￨L￨JJ￨DURATION￨- 3￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨A to￨L￨TO￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨DURATION￨- 56￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- circulation￨L￨NN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- features￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- rumor￨L￨NN￨O￨A classification￨L￨NN￨O￨- .￨L￨.￨O￨- +Public￨U￨NNP￨O￨- health￨L￨NN￨O￨- decision￨L￨NN￨O￨- makers￨L￨NNS￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- require￨L￨VBP￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- inference￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- fundamental￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- using￨L￨VBG￨O￨- observations￨L￨NNS￨O￨A that￨L￨WDT￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- imperfectly￨L￨RB￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- reported￨L￨VBD￨O￨- disease-related￨L￨JJ￨O￨- illnesses￨L￨NNS￨O￨- serve￨L￨VBP￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- imperfect￨L￨JJ￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- incident￨L￨NN￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- methods￨L￨NNS￨O￨- make￨L￨VBP￨O￨A use￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- involve￨L￨VB￨O￨- Markov￨U￨NNP￨PERSON￨- Chain￨U￨NNP￨O￨- Monte￨U￨NNP￨O￨- Carlo￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- filtering￨L￨VBG￨O￨- techniques￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 32￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- sample￨L￨NN￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨- states￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- individual-level￨L￨JJ￨O￨- data￨L￨NNS￨O￨- required￨L￨VBN￨O￨- by￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- network￨L￨NN￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- compartmental￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- projecting￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- trajectory￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- calibration￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- Multiple￨U￨JJ￨O￨- Shooting￨U￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- Stochastic￨U￨NNP￨O￨- systems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MSS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- utilizes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- noise￨L￨NN￨O￨- approximation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LNA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- state-updating￨L￨JJ￨O￨- procedure￨L￨NN￨O￨- to￨L￨TO￨O￨- approximate￨L￨JJ￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- observations￨L￨NNS￨O￨A while￨L￨IN￨O￨- explicitly￨L￨RB￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- interdependency￨L￨NN￨O￨- between￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- wide￨L￨JJ￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- to￨L￨TO￨O￨- calibrate￨L￨VB￨O￨- these￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- differ￨L￨VBP￨O￨- based￨L￨VBN￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- observations￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- delay￨L￨NN￨O￨- is￨L￨VBZ￨O￨- primarily￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- replication￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- competing￨L￨VBG￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- activation￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨A compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- from￨L￨IN￨O￨- published￨L￨VBN￨O￨- data￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1,22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- between￨L￨IN￨O￨- 0.06￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 3.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- cells￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- proliferate￨L￨VBP￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- predicted￨L￨VBN￨O￨- that￨L￨IN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- recombination￨L￨NN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- circulating￨L￨VBG￨O￨- viral￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- fragments￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- genome￨L￨NN￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- latent￨L￨JJ￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- time￨L￨NN￨O￨- during￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- quasispecies￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- evolutionary￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- active￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- actively￨L￨RB￨O￨- replicating￨L￨VBG￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨A represents￨L￨VBZ￨O￨- long-lived￨L￨JJ￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- growing￨L￨VBG￨O￨- fascination￨L￨NN￨O￨- with￨L￨IN￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- high-dimensional￨L￨JJ￨O￨- complex￨L￨NN￨O￨- system123456￨L￨NN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- huge￨L￨JJ￨O￨- components￨L￨NNS￨O￨A interacting￨L￨VBG￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- usually￨L￨RB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- coupled￨L￨VBN￨O￨- dynamical￨L￨JJ￨O￨- units￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- spreading7￨L￨NN￨O￨- ,￨L￨,￨O￨- neuronal￨L￨JJ￨O￨- networks8￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Kuramoto￨U￨NNP￨O￨- model9￨L￨NN￨O￨- ,￨L￨,￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- self-driven￨L￨JJ￨O￨- particles10￨L￨NN￨O￨- ,￨L￨,￨O￨- percolation￨L￨NN￨O￨- or￨L￨CC￨O￨- cascading￨L￨VBG￨O￨- procedure11121314151617￨L￨NN￨O￨- ,￨L￨,￨O￨- Ising￨U￨JJ￨O￨- model181920212223￨L￨NN￨O￨- and￨L￨CC￨O￨- ecosystems242526￨L￨NN￨O￨- etc￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- Gao￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- proposed￨L￨VBD￨O￨- an￨L￨DT￨O￨- elaborate￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- coding￨L￨VBG￨O￨- the￨L￨DT￨O￨- microcosmic￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- information￨L￨NN￨O￨- between￨L￨IN￨O￨- components￨L￨NNS￨O￨A into￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- the￨L￨DT￨O￨- multi-dimensional￨L￨JJ￨O￨- coupled￨L￨VBN￨O￨- nonlinear￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- simply￨L￨RB￨O￨- reduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- 1D￨L￨NN￨O￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- universal￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- theories￨L￨NNS￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- too￨L￨RB￨O￨- complicated￨L￨VBN￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- accurate￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- coupled￨L￨VBN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- interacting￨L￨VBG￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- usually￨L￨RB￨O￨- highly￨L￨RB￨O￨- heterogenous￨L￨JJ￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- inhomogeneous￨L￨JJ￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- components￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- achievements￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- these￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- structure28￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- heterogenous￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- centrality￨L￨NN￨O￨- and￨L￨CC￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- usually￨L￨RB￨O￨A varies￨L￨VBZ￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- since￨L￨IN￨O￨- permutation￨L￨NN￨O￨- symmetry￨L￨NN￨O￨- breaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- therefore￨L￨RB￨O￨- could￨L￨MD￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- this￨L￨DT￨O￨- distinctiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- as￨L￨IN￨O￨- w￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- difficulty￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- activity￨L￨NN￨O￨- x￨L￨CC￨O￨- converted￨L￨VBN￨O￨- by￨L￨IN￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- resembling￨L￨VBG￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- in￨L￨IN￨O￨- Newtonian￨U￨JJ￨O￨- mechanics￨L￨NNS￨O￨- as￨L￨IN￨O￨- intrinsic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- promote￨L￨VB￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- generalized￨L￨VBN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- other￨L￨JJ￨O￨- than￨L￨IN￨O￨- resilience￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- to￨L￨TO￨O￨- figure￨L￨VB￨O￨- out￨L￨RP￨O￨- the￨L￨DT￨O￨- applicability￨L￨NN￨O￨- and￨L￨CC￨O￨- limitation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reduced￨L￨VBN￨O￨A 1D￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- equation￨L￨NN￨O￨- .￨L￨.￨O￨- +Adding￨U￨VBG￨O￨- another￨L￨DT￨O￨- layer￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- detail￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- agents￨L￨NNS￨O￨A depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- connections￨L￨NNS￨O￨- ,￨L￨,￨O￨- introducing￨L￨VBG￨O￨- time￨L￨NN￨O￨- fluctuations￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- agent￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- relevant￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- either￨L￨CC￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- agents￨L￨NNS￨O￨A are￨L￨VBP￨O￨- well-described￨L￨JJ￨O￨- by￨L￨IN￨O￨- averages￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- result￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- random-mixing￨L￨JJ￨O￨- hypothesis56￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- scheme￨L￨NN￨O￨- ,￨L￨,￨O￨- agents￨L￨NNS￨O￨A are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- vertices￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- connections￨L￨NNS￨O￨- are￨L￨VBP￨O￨- distributed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- adjacency￨L￨NN￨O￨- matrix￨L￨NN￨O￨- A￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- assigned￨L￨VBN￨O￨- network￨L￨NN￨O￨- configuration11￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- satisfies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- 〈￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- 〉￨L￨NN￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- β/γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number7￨L￨NN￨DATE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- formed￨L￨VBN￨O￨- by￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- agents￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- chickens￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- σ1￨L￨NN￨O￨- and￨L￨CC￨O￨- σ2￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- wild‐type￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- barn￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- mutant￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- barn￨L￨NN￨O￨- at￨L￨IN￨O￨- that￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- individual‐based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- in￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- an￨L￨DT￨O￨- expression￨L￨NN￨O￨- for￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- fitness￨L￨NN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- it￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- reduced￨L￨VBN￨O￨A lifespan￨L￨NN￨O￨- of￨L￨IN￨O￨- poultry￨L￨NN￨O￨- on￨L￨IN￨O￨- industrial￨L￨JJ￨O￨- farms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- reduced￨L￨VBN￨O￨- cohort￨L￨NN￨O￨- duration￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- virulence￨L￨NN￨O￨- .￨L￨.￨O￨- +Chickens￨U￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- wild‐type￨L￨JJ￨O￨- strain￨L￨NN￨O￨- shed￨L￨VBD￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨A at￨L￨IN￨O￨- rate￨L￨NN￨O￨- κ1￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- chickens￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- mutant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- shed￨L￨VBD￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- κ2￨L￨NN￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- a￨L￨DT￨O￨- chicken￨L￨NN￨O￨- perishes￨L￨VBZ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- occurs￨L￨VBZ￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- v￨L￨LS￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- chickens￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- wild‐type￨L￨JJ￨O￨- strain￨L￨NN￨O￨- and￨L￨CC￨O￨- v￨L￨LS￨O￨- 2￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- chickens￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- mutant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- ω1￨L￨NN￨O￨- or￨L￨CC￨O￨- ω2￨L￨NN￨O￨- viral￨L￨JJ￨O￨- particles￨L￨NNS￨O￨A are￨L￨VBP￨O￨- released￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- barn￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Ing￨U￨NNP￨O￨- process￨L￨NN￨O￨- has￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- denotes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- well￨L￨RB￨O￨- defined￨L￨VBN￨O￨- linear￨L￨JJ￨O￨- transformation￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- automatically￨L￨RB￨O￨- gather￨L￨VB￨O￨- neighbour￨L￨NN￨O￨A ’s￨L￨POS￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- information￨L￨NN￨O￨- or￨L￨CC￨O￨- called￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- score￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- n￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- gathering￨L￨NN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- properly￨L￨RB￨O￨A chosen￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Ing￨U￨NNP￨O￨- process￨L￨NN￨O￨- will￨L￨MD￨O￨- obtain￨L￨VB￨O￨- more￨L￨RBR￨O￨- exact￨L￨JJ￨O￨- rankings￨L￨NNS￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- H-index28￨U￨NN￨O￨- ,￨L￨,￨O￨- coreness10￨L￨NN￨O￨- ,￨L￨,￨O￨- closeness32￨L￨NN￨O￨- ,￨L￨,￨O￨- betweenness33￨L￨NN￨O￨- ,￨L￨,￨O￨- LeaderRank￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- LR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 34￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- weighted￨L￨JJ￨O￨- LeaderRank￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- WLR￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- 35￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- CR30￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- evaluate￨L￨VB￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- Ing￨U￨NNP￨O￨- score￨L￨NN￨O￨- can￨L￨MD￨O￨- estimate￨L￨VB￨O￨- node￨L￨NN￨O￨A importance￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model31￨L￨NN￨O￨- on￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- representative￨L￨JJ￨TITLE￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- random￨L￨JJ￨O￨- contact￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- between￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- direct￨L￨JJ￨O￨- from￨L￨IN￨O￨- man￨L￨NN￨O￨- to￨L￨TO￨O￨- pig￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- infected￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A have￨L￨VBP￨O￨- equal￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- man￨L￨NN￨O￨- after￨L￨IN￨O￨- slaughter￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- fixed￨L￨VBN￨O￨- at￨L￨IN￨O￨- 1000￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- include￨L￨VBP￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- taeniosis￨L￨NN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- ,￨L￨,￨O￨- health￨L￨NN￨O￨- education￨L￨NN￨O￨- ,￨L￨,￨O￨- improved￨L￨VBD￨O￨- meat￨L￨NN￨O￨- inspection￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- improved￨L￨VBD￨O￨- hygiene￨L￨NN￨O￨- and￨L￨CC￨O￨- sanitation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Gabriël￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Included￨U￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- assessment￨L￨NN￨O￨- should￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- affected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- and￨L￨CC￨O￨- pig￨L￨NN￨O￨- owners￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- lose￨L￨VBP￨O￨- 50￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- pigs￨L￨NNS￨O￨A if￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Trevisan￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- also￨L￨RB￨O￨- demonstrated￨L￨VBN￨O￨- that￨L￨IN￨O￨- confined￨L￨VBN￨O￨- pigs￨L￨NNS￨O￨A had￨L￨VBD￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- free-roaming￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- –￨L￨:￨O￨- control￨L￨JJ￨O￨- study￨L￨NN￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- confirmed￨L￨VBN￨O￨- that￨L￨IN￨O￨- feeding￨L￨VBG￨O￨- potato￨L￨NN￨O￨- peels￨L￨VBZ￨O￨- to￨L￨TO￨O￨- pigs￨L￨NNS￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- risk￨L￨NN￨O￨- in￨L￨IN￨O￨- getting￨L￨VBG￨O￨- porcine￨L￨NN￨O￨- cysticercosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +WHO￨U￨WP￨O￨- considers￨L￨VBZ￨O￨- Taenia￨U￨NNP￨LOCATION￨- solium￨L￨NN￨O￨- taeniosis/cysticercosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TSTC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- an￨L￨DT￨O￨- eradicable￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- its￨L￨PRP$￨O￨- simple￨L￨JJ￨O￨- life￨L￨NN￨O￨- cycle￨L￨NN￨O￨- and￨L￨CC￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- powerful￨L￨JJ￨O￨- and￨L￨CC￨O￨- inexpensive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- tools￨L￨NNS￨O￨A .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- kernel￨L￨NN￨O￨- functions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- unable￨L￨JJ￨O￨- to￨L￨TO￨O￨- tease￨L￨VB￨O￨- apart￨L￨RB￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- indirect￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- those￨L￨DT￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- farm￨L￨NN￨O￨A operators￨L￨NNS￨O￨- .￨L￨.￨O￨- +Statistical￨U￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- long￨L￨RB￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- many￨L￨JJ￨O￨- complex￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- written￨L￨VBN￨O￨- texts￨L￨NNS￨O￨- and￨L￨CC￨O￨- language￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- now￨L￨RB￨DATE￨- include￨L￨VBP￨O￨- network￨L￨NN￨O￨- representations￨L￨NNS￨O￨- of￨L￨IN￨O￨- text￨L￨NN￨O￨A to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- linguistic￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- from￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- physics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- authorship￨L￨NN￨O￨- recognition￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- included￨L￨VBD￨O￨- text￨L￨NN￨O￨A modeling￨L￨NN￨O￨- with￨L￨IN￨O￨- co-occurrence￨L￨NN￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 42￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 47￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Networks￨U￨NNP￨O￨- generated￨L￨VBD￨O￨- from￨L￨IN￨O￨- text￨L￨NN￨O￨A share￨L￨NN￨O￨- several￨L￨JJ￨O￨- features￨L￨NNS￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- complex￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- transportation￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- biological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- co-occurrence￨L￨NN￨O￨- representation￨L￨NN￨O￨- to￨L￨TO￨O￨- probe￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- along￨L￨IN￨O￨- a￨L￨DT￨O￨- text￨L￨NN￨O￨A is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- author￨L￨NN￨TITLE￨- ’s￨L￨POS￨O￨- style￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- GBFP￨U￨NN￨O￨- identifies￨L￨VBZ￨O￨- multiple￨L￨JJ￨O￨- main￨L￨JJ￨O￨- paths￨L￨NNS￨O￨A for￨L￨IN￨O￨- each￨L￨DT￨O￨- case￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- easily￨L￨RB￨O￨- recognizable￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- all￨L￨DT￨O￨- high-persistence￨L￨JJ￨O￨- patents￨L￨NNS￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- approach￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- identify￨L￨VB￨O￨- some￨L￨DT￨O￨- dominantly￨L￨RB￨O￨- important￨L￨JJ￨O￨- patents￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- identified￨L￨VBN￨O￨- main￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- yields￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- network￨L￨NN￨O￨- complexity￨L￨NN￨O￨- that￨L￨WDT￨O￨- makes￨L￨VBZ￨O￨- qualitatively￨L￨RB￨O￨- tracing￨L￨VBG￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- problematic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- method￨L￨NN￨O￨- searches￨L￨NNS￨O￨- backward￨L￨RB￨O￨- and￨L￨CC￨O￨- forward￨L￨RB￨O￨- paths￨L￨NNS￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- genetically￨L￨RB￨O￨- dominant￨L￨JJ￨O￨- patents￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- generate￨L￨VB￨O￨- multiple￨L￨JJ￨O￨- interconnected￨L￨JJ￨O￨- main￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- without￨L￨IN￨O￨- missing￨L￨VBG￨O￨- any￨L￨DT￨O￨- dominantly￨L￨RB￨O￨- important￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- domain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- we￨L￨PRP￨O￨- label￨L￨VBP￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- method￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- backward-forward￨L￨JJ￨O￨- path￨L￨NN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- acronym￨L￨NN￨O￨- GBFP￨U￨NN￨O￨- throughout￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- adopt￨L￨VBP￨O￨- the￨L￨DT￨O￨- genetic￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- persistence￨L￨NN￨O￨- measurement￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GKPM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- suggested￨L￨VBN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- differently￨L￨RB￨O￨- from￨L￨IN￨O￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- paths￨L￨NNS￨O￨A by￨L￨IN￨O￨- forward￨L￨RB￨O￨- and￨L￨CC￨O￨- backward￨L￨RB￨O￨- tracing￨L￨VBG￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- citation-based￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- significant￨L￨JJ￨O￨- trajectories￨L￨NNS￨O￨- ,￨L￨,￨O￨- Hummon￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Doreian￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- first￨L￨RB￨ORDINAL￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- main￨L￨JJ￨O￨A path￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- and￨L￨CC￨O￨- much￨L￨JJ￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- applied￨L￨VBN￨O￨- main￨L￨JJ￨O￨- path￨L￨NN￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- technologies￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- technological￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Phylodynamic￨U￨JJ￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV-1￨U￨NN￨MISC￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- asymmetry￨L￨NN￨O￨- in￨L￨IN￨O￨- viral￨L￨JJ￨O￨- phylogenies￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- indicative￨L￨JJ￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- transmissions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- heterogeneous￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- yield￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨- with￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- mean￨L￨NN￨O￨- cluster￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- shorter￨L￨JJR￨O￨- mean￨L￨VB￨O￨- branch￨L￨NN￨O￨- lengths￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- somewhat￨L￨RB￨O￨- higher￨L￨JJR￨O￨- tree￨L￨NN￨O￨A imbalance￨L￨NN￨O￨- than￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- relatively￨L￨RB￨O￨- homogeneous￨L￨JJ￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Phylodynamics￨U￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- linking￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- with￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- fast￨L￨RB￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- histories￨L￨NNS￨O￨- become￨L￨VBP￨O￨- “￨L￨``￨O￨- recorded￨L￨VBN￨O￨- ”￨L￨''￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- between-host￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- phylogeny￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- phylogenetic￨L￨JJ￨O￨- tree￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Keeping￨U￨VBG￨O￨- track￨L￨NN￨O￨- of￨L￨IN￨O￨- who￨L￨WP￨O￨- transmits￨L￨VBZ￨O￨- to￨L￨TO￨O￨- whom￨L￨WP￨O￨- and￨L￨CC￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- every￨L￨DT￨O￨- individual￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- only￨L￨RB￨O￨- once￨L￨RB￨DATE￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- other￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- history￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- rooted￨L￨JJ￨O￨- tree￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- transmission￨L￨NN￨O￨- tree￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Previously￨U￨RB￨DATE￨- ,￨L￨,￨O￨- Britton￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- O’Neill￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- Erdős-Rényi￨U￨JJ￨MISC￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- it￨L￨PRP￨O￨- using￨L￨VBG￨O￨- recovery￨L￨NN￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- Groendyke￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- changed￨L￨VBN￨O￨- by￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- βf￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- us￨L￨PRP￨O￨- suppose￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- are￨L￨VBP￨O￨- different￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- general￨L￨JJ￨TITLE￨- deterministic￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨A equation￨L￨NN￨O￨A :￨L￨:￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- randomly￨L￨RB￨O￨- fluctuating￨L￨VBG￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- will￨L￨MD￨O￨- manifest￨L￨VB￨O￨- themselves￨L￨PRP￨O￨- mainly￨L￨RB￨O￨- as￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- β￨L￨RB￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- d￨L￨NN￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- change￨L￨NN￨O￨- to￨L￨TO￨O￨- random￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomesBy￨L￨NN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- limit￨L￨NN￨O￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- error￨L￨NN￨O￨A term￨L￨NN￨O￨- error￨L￨NN￨O￨- dt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- i￨L￨FW￨O￨- ≤￨L￨FW￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- normal￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- with￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- mean￨L￨NN￨O￨- and￨L￨CC￨O￨- variance￨L￨NN￨O￨- σ2dt￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- i￨L￨FW￨O￨- ≤￨L￨FW￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- Itô￨U￨NN￨O￨- stochastic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- Model￨U￨NNP￨TITLE￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨A case￨L￨NN￨O￨A where￨L￨WRB￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- q￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- by￨L￨IN￨O￨- Yang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Mao￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- σ1￨L￨NN￨O￨- =￨L￨JJ￨O￨- σ2￨L￨NN￨O￨- =￨L￨JJ￨O￨- σ3￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- j￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- l￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- q￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- also￨L￨RB￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Assume￨U￨VB￨O￨- that￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- H1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- H2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- hold￨L￨VBP￨O￨- ;￨L￨:￨O￨- then￨L￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- +3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- solution￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- will￨L￨MD￨O￨- remain￨L￨VB￨O￨- in￨L￨IN￨O￨- R￨U￨NN￨O￨- +3￨L￨CD￨NUMBER￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨A the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- fully￨L￨RB￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- requires￨L￨VBZ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- partnership￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- arise￨L￨VBP￨O￨- from￨L￨IN￨O￨- reinfection￨L￨NN￨O￨A that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- SIS-type￨U￨JJ￨MISC￨- behaviour￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- inherently￨L￨RB￨O￨- lower-dimensional￨L￨JJ￨O￨- than￨L￨IN￨O￨- their￨L￨PRP$￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- counterparts￨L￨NNS￨O￨- ,￨L￨,￨O￨- potential￨L￨JJ￨O￨- reinfection￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- multiple￨L￨JJ￨O￨- times￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- between￨L￨IN￨O￨- neighbouring￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- makes￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- more￨L￨RBR￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- tractable￨L￨JJ￨O￨- results￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- utilise￨L￨VB￨O￨- such￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- techniques￨L￨NNS￨O￨A to￨L￨TO￨O￨- gain￨L￨VB￨O￨- a￨L￨DT￨O￨- clear￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- STIs￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- other￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- short-duration￨L￨NN￨O￨- immunity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- on￨L￨IN￨O￨- understanding￨L￨NN￨O￨- when￨L￨WRB￨O￨- simple￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- fail￨L￨VBP￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨- or￨L￨CC￨O￨- related￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- discussed￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- exact￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- marginal￨L￨JJ￨O￨A probabilities￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- finite￨L￨JJ￨O￨- explicitly￨L￨RB￨O￨- known￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Much￨U￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- focussed￨L￨VBN￨O￨- on￨L￨IN￨O￨- extending￨L￨VBG￨O￨- such￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- weighted￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- duration￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 35￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 37￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- denominator￨L￨NN￨O￨- that￨L￨WDT￨O￨- on￨L￨IN￨O￨- clustered￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- results￨L￨VBZ￨O￨- from￨L￨IN￨O￨- all￨L￨DT￨O￨- approaches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- approximate￨L￨JJ￨O￨- .￨L￨.￨O￨- +Consider￨U￨VB￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- population￨L￨NN￨O￨- patch￨L￨NN￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- admixture￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- refractory￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- initial￨L￨JJ￨O￨- fractions￨L￨NNS￨O￨- S0￨U￨NN￨O￨- ,￨L￨,￨O￨- I0￨U￨NN￨O￨- and￨L￨CC￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- scenario￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- sub-population￨L￨NN￨O￨- of￨L￨IN￨O￨- refractory￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- cycle￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- entirely￨L￨RB￨O￨- reflected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- S0￨U￨NN￨O￨- ,￨L￨,￨O￨- I0￨U￨NN￨O￨- and￨L￨CC￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- again￨L￨RB￨O￨- ,￨L￨,￨O￨- right￨L￨RB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- prone￨L￨JJ￨O￨- to￨L￨TO￨O￨- spreading￨L￨VBG￨O￨- and￨L￨CC￨O￨- persistance￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- becomes￨L￨VBZ￨O￨- persistent￨L￨JJ￨O￨A in￨L￨IN￨O￨- time7￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- state￨L￨NN￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immediate￨L￨JJ￨O￨- neighbourhood￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- stochastic￨L￨JJ￨O￨- in￨L￨IN￨O￨- nature￨L￨NN￨O￨- and￨L￨CC￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨A states￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- refractory￨L￨JJ￨O￨A stage￨L￨NN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- becomes￨L￨VBZ￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- infect￨L￨VB￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +Liu￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 17￨L￨CD￨NUMBER￨- gave￨L￨VBD￨O￨- a￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- centrality￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Dynamics-Sensitive￨U￨JJ￨O￨- centrality￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- while￨L￨IN￨O￨- only￨L￨RB￨O￨- use￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- influence￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- performs￨L￨VBZ￨O￨- much￨L￨RB￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- some￨L￨DT￨O￨- topological￨L￨JJ￨O￨- structural￨L￨JJ￨O￨- centralities￨L￨NNS￨O￨- like￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- k-shell￨L￨NN￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- comparable￨L￨JJ￨O￨- with￨L￨IN￨O￨- eigenvector￨L￨NN￨O￨- centrality￨L￨NN￨O￨- .￨L￨.￨O￨- +suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvector￨L￨NN￨O￨- centrality￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- dynamical￨L￨JJ￨O￨- influences￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- spreading￨L￨NN￨O￨- model34￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- proof￨L￨NN￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- given￨L￨VBN￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- exist￨L￨VBP￨O￨- a￨L￨DT￨O￨- closed￨L￨JJ￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- scale￨L￨NN￨O￨- and￨L￨CC￨O￨- eigenvector￨L￨NN￨O￨- centrality￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- networks35￨L￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- of￨L￨IN￨O￨- conventional￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- combine￨L￨VBP￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- centrality￨L￨NN￨O￨A closely￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- topological￨L￨JJ￨O￨- structure13141516￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- emphasize￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- closeness￨L￨NN￨O￨- ,￨L￨,￨O￨- betweenness￨L￨NN￨O￨- ,￨L￨,￨O￨- k-shell15￨L￨NN￨O￨- ,￨L￨,￨O￨- H-index16￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- real￨L￨JJ￨O￨- life￨L￨NN￨O￨- many￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- temporal3637383940414243￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- topological￨L￨JJ￨O￨A structure￨L￨NN￨O￨- evolving￨L￨VBG￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- time-order￨L￨NN￨O￨- have￨L￨VBP￨O￨- great￨L￨JJ￨O￨- influence￨L￨NN￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- networks414445￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- versions￨L￨NNS￨O￨- of￨L￨IN￨O￨- centrality￨L￨NN￨O￨A which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes44464748￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- only￨L￨RB￨O￨- take￨L￨VBP￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- an￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- sized￨L￨VBN￨O￨- sample￨L￨NN￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- ILI￨U￨NN￨O￨- seek￨L￨VBP￨O￨- medical￨L￨JJ￨O￨- care￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- sample￨L￨NN￨O￨- can￨L￨MD￨O￨- change￨L￨VB￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- circulating￨L￨VBG￨O￨- virus￨L￨NN￨O￨- subtype￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- season￨L￨NN￨O￨A to￨L￨TO￨O￨- season￨L￨NN￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- country￨L￨NN￨O￨- to￨L￨TO￨O￨- country￨L￨NN￨O￨- ;￨L￨:￨O￨- second￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- medical￨L￨JJ￨O￨- professionals￨L￨NNS￨O￨- participating￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sentinel￨L￨NN￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- physicians￨L￨NNS￨O￨- working￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- or￨L￨CC￨O￨- region￨L￨NN￨O￨- NumericCitation￨U￨NN￨MISC￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- low￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- and￨L￨CC￨O￨- unpredictability￨L￨NN￨O￨- ;￨L￨:￨O￨- third￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- consultations￨L￨NNS￨O￨- happened￨L￨VBD￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- delay￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- available￨L￨JJ￨O￨- at￨L￨IN￨O￨- best￨L￨JJS￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- lag￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨A by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- EISN-ILI￨U￨NN￨MISC￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- modified￨L￨VBN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- MSIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- research￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- mainly￨L￨RB￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- the￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨A ’s￨L￨POS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- ’s￨L￨POS￨O￨- timing￨L￨NN￨O￨- ,￨L￨,￨O￨- neglecting￨L￨VBG￨O￨- timely￨L￨JJ￨O￨- onset￨L￨NN￨O￨- identification￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- few￨L￨JJ￨O￨- other￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- develop￨L￨VBP￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- different￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- it￨L￨PRP￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- with￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- or￨L￨CC￨O￨- just￨L￨RB￨O￨- by￨L￨IN￨O￨- testing￨L￨VBG￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- particularly￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- sensor￨L￨NN￨O￨- worm￨L￨NN￨O￨A by￨L￨IN￨O￨- several￨L￨JJ￨O￨- iterative￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- security￨L￨NN￨O￨- states￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- propagation￨L￨NN￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- only￨L￨RB￨O￨- provide￨L￨VB￨O￨- macroscopic￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨- sensor￨L￨NN￨O￨- worm￨L￨NN￨O￨A ’s￨L￨POS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- scale￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- accurately￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- follows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- transition￨L￨NN￨O￨- scheme￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S-I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- microscopically￨L￨RB￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- prior￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- sensor￨L￨NN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- worm￨L￨NN￨O￨A .￨L￨.￨O￨- +Worm￨U￨NN￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- always￨L￨RB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- imminent￨L￨JJ￨O￨- and￨L￨CC￨O￨- effective￨L￨JJ￨O￨- threats￨L￨NNS￨O￨- against￨L￨IN￨O￨- energy￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- confidentiality￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- service￨L￨NN￨O￨- availability￨L￨NN￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- WSNs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- defending￨L￨VBG￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨- worm￨L￨NN￨O￨A carrier￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- research￨L￨NN￨O￨- modeled￨L￨VBD￨O￨- the￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- attributable￨L￨JJ￨O￨- to￨L￨TO￨O￨- iNTS￨L￨NN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- programmatic￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- NTS￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- utilizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- Expanded￨U￨NNP￨O￨- Program￨U￨NN￨O￨- on￨L￨IN￨O￨- Immunization￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- EPI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- infrastructure￨L￨NN￨O￨- that￨L￨IN￨O￨- successfully￨L￨RB￨O￨- delivered￨L￨VBN￨O￨- Hib￨U￨NN￨O￨- and￨L￨CC￨O￨- pneumococcal￨L￨JJ￨O￨- conjugate￨L￨NN￨O￨A vaccines￨L￨NNS￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- drastically￨L￨RB￨O￨- reduced￨L￨VBN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- invasive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- those￨L￨DT￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- burdens￨L￨NNS￨O￨- of￨L￨IN￨O￨- invasive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- Haemophilus￨U￨JJ￨O￨- influenzae￨L￨NNS￨O￨- type￨L￨NN￨O￨- b￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Hib￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Streptococcus￨U￨NN￨O￨- pneumoniae￨L￨FW￨O￨- have￨L￨VBP￨O￨- plummeted￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- Hib￨U￨NN￨O￨- conjugate￨L￨NN￨O￨A and￨L￨CC￨O￨- multivalent￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨- conjugate￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- recognition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- iNTS￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Numbers￨U￨NNS￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- within￨L￨IN￨O￨- specific￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- pooled￨L￨VBD￨O￨- across￨L￨IN￨O￨- even￨L￨RB￨O￨- years￨L￨NNS￨DURATION￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- HGT￨U￨NNP￨O￨- surveillance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- 2002￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2004￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2006￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2008￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2010￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- with￨L￨IN￨O￨- denominators￨L￨NNS￨O￨- from￨L￨IN￨O￨- INSTAT￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- group-specific￨L￨JJ￨O￨- hospitalization￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- iNTS￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- then￨L￨RB￨O￨- validated￨L￨VBN￨O￨- by￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- iNTS￨L￨NN￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- estimated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- odd￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨A of￨L￨IN￨O￨- HGT￨U￨NN￨O￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- infinite￨L￨JJ￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- vanishes￨L￨VBZ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- percolates￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- non-zero￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- levels￨L￨NNS￨O￨- via￨L￨IN￨O￨- hierarchical￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- from￨L￨IN￨O￨- hub￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- lower￨L￨JJR￨O￨- degree￨L￨NN￨O￨- nodes12￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- SIS￨U￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- maximum￨L￨NN￨O￨- degree￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- cutoff￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- hub￨L￨NN￨O￨A node￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- act￨L￨VBP￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- incessant￨L￨JJ￨O￨- source￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state89￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemics￨U￨NNS￨O￨- on￨L￨IN￨O￨- adaptive￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- exhibit￨L￨VB￨O￨- complex￨L￨JJ￨O￨- emergent￨L￨JJ￨O￨- dynamics3235363738￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- sustained￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨- ,￨L￨,￨O￨- bistability￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hysteresis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- emergent￨L￨JJ￨O￨- topological￨L￨JJ￨O￨- properties32353940￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- heterogeneous￨L￨JJ￨O￨- degree￨L￨NN￨O￨A distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- assortative￨L￨JJ￨O￨- degree￨L￨NN￨O￨- correlations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- SIR￨U￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- differently￨L￨RB￨O￨- from￨L￨IN￨O￨- SIS￨U￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts81011￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- vanishes￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- thermodynamic￨L￨JJ￨O￨- limit￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- degree￨L￨NN￨O￨A increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- true￨L￨JJ￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- unless￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- restriction￨L￨NN￨O￨- on￨L￨IN￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- cognitive￨L￨JJ￨O￨- limitations7￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- transition￨L￨NN￨O￨- point￨L￨NN￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- excitation￨L￨NN￨O￨- propagation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- input￨L￨NN￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- excitation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- injected￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- distant￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- output￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨A in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model111213￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- note￨L￨NN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- excitation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- contribution￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- fold￨L￨NN￨COUNTRY￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- a￨L￨DT￨O￨- relative￨L￨JJ￨O￨- excitation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- minimal￨L￨JJ￨O￨A fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- excited￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- excited￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- usage￨L￨NN￨O￨- of￨L￨IN￨O￨- structural￨L￨JJ￨O￨- components￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- cycles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- producing￨L￨VBG￨O￨- reentrant￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Inspired￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- self-sustained￨L￨JJ￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- neuroscience￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- here￨L￨RB￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- minimal￨L￨JJ￨O￨A discrete￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- excitable￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- relative￨L￨JJ￨O￨- excitation￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- excitations￨L￨NNS￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Quantitatively￨U￨RB￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- smallest￨L￨JJS￨O￨- integer￨L￨NN￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- or￨L￨CC￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- κk￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- acts￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- barrier￨L￨NN￨O￨- for￨L￨IN￨O￨- propagation￨L￨NN￨O￨A ,￨L￨,￨O￨- by￨L￨IN￨O￨- requiring￨L￨VBG￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- n￨L￨NN￨O￨- incoming￨L￨JJ￨O￨- excitations￨L￨NNS￨O￨- to￨L￨TO￨O￨- switch￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- excited￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- work5￨L￨NN￨O￨- ;￨L￨:￨O￨- there￨L￨RB￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- neighboring￨L￨VBG￨O￨- excitation￨L￨NN￨O￨- was￨L￨VBD￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- trigger￨L￨VB￨O￨- transition￨L￨NN￨O￨A to￨L￨TO￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- κ￨L￨VB￨O￨- →￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- an￨L￨DT￨O￨- elementary￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- relatively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- how￨L￨WRB￨O￨- web￨L￨NN￨O￨A malware￨L￨NN￨O￨- spread￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨- ’￨L￨POS￨O￨- security￨L￨NN￨O￨- awareness￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- develop￨L￨VB￨O￨- proper￨L￨JJ￨O￨- prevention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- with￨L￨IN￨O￨- human￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +Hosts￨U￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- web￨L￨NN￨O￨A malware￨L￨NN￨O￨- can￨L￨MD￨O￨- suffer￨L￨VB￨O￨- from￨L￨IN￨O￨- modifications￨L￨NNS￨O￨- of￨L￨IN￨O￨- browser￨L￨NN￨O￨- settings￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- default￨L￨NN￨O￨- homepage￨L￨NN￨O￨- ,￨L￨,￨O￨- search￨L￨NN￨O￨- bars￨L￨NNS￨O￨- ,￨L￨,￨O￨- toolbars￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- cause￨L￨VB￨O￨- user￨L￨NN￨O￨- registry￨L￨NN￨O￨- modification￨L￨NN￨O￨- ,￨L￨,￨O￨- display￨L￨VBP￨O￨- intermittent￨L￨JJ￨O￨- advertising￨L￨NN￨O￨- pop-ups￨L￨NNS￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- transmit￨L￨VB￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- your￨L￨PRP$￨O￨- web-browsing￨L￨JJ￨O￨- habits￨L￨NNS￨O￨- to￨L￨TO￨O￨- advertisers￨L￨NNS￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- third￨L￨JJ￨ORDINAL￨- party￨L￨NN￨O￨- interests￨L￨NNS￨O￨- without￨L￨IN￨O￨- your￨L￨PRP$￨O￨- awareness￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- human￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- influences￨L￨VBZ￨O￨- on￨L￨IN￨O￨- web￨L￨NN￨O￨A malware￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- propagation￨L￨NN￨O￨- when￨L￨WRB￨O￨- user￨L￨NN￨O￨- ’s￨L￨POS￨O￨- security￨L￨NN￨O￨- awareness￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- hyperlinks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- addresses￨L￨NNS￨O￨- of￨L￨IN￨O￨- corresponding￨L￨JJ￨O￨- harmful￨L￨JJ￨O￨- websites￨L￨NNS￨O￨- purporting￨L￨VBG￨O￨- to￨L￨TO￨O￨- proliferate￨L￨VB￨O￨- malware￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- exist￨L￨VB￨O￨- in￨L￨IN￨O￨- short￨L￨JJ￨O￨- messages￨L￨NNS￨O￨- or￨L￨CC￨O￨- spam￨L￨NN￨O￨- emails￨L￨NNS￨O￨- that￨L￨WDT￨O￨- lure￨L￨VBP￨O￨- victims￨L￨NNS￨O￨- to￨L￨TO￨O￨- click￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- malicious￨L￨JJ￨O￨- URLs￨U￨NNS￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- redirect￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- false￨L￨JJ￨O￨- web￨L￨NN￨O￨A page￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- inject￨L￨VB￨O￨- malware￨L￨NN￨O￨- into￨L￨IN￨O￨- their￨L￨PRP$￨O￨- devices￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- recent￨L￨JJ￨O￨- reviews￨L￨NNS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- determinants￨L￨NNS￨O￨- of￨L￨IN￨O￨- spillover￨L￨NN￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- knowledge-gap￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- exists￨L￨VBZ￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- lack￨L￨VBP￨O￨- empirically￨L￨RB￨O￨- validated￨L￨VBN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ecological￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- wildlife￨L￨NN￨O￨A reservoirs￨L￨NNS￨O￨- and￨L￨CC￨O￨- key￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- hantavirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- climate￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- condition￨L￨NN￨O￨- and/or￨L￨CC￨O￨- agricultural￨L￨JJ￨O￨- activity￨L￨NN￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- via￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- reservoir￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- exposure￨L￨NN￨O￨- risk￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- virus￨L￨NN￨O￨- stability￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- untangle￨L￨VB￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- ,￨L￨,￨O￨- combined￨L￨JJ￨O￨- field￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- that￨L￨WDT￨O￨- link￨L￨VBP￨O￨- the￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- wildlife￨L￨NN￨O￨A with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- wildlife￨L￨NN￨O￨- reservoir￨L￨NN￨O￨- are￨L￨VBP￨O￨- essential￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- in￨L￨IN￨O￨- question￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- cause￨L￨VB￨O￨- hantavirus￨L￨NN￨O￨- pulmonary￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- HPS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- hemorrhagic￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- renal￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HFRS￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- range￨L￨VBP￨O￨- between￨L￨IN￨O￨- 0.5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 40￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Hantavirus￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- numerous￨L￨JJ￨O￨- significant￨L￨JJ￨O￨- zoonotic￨L￨JJ￨O￨A outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- HFRS￨U￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- Hantaan￨U￨JJ￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HTNV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- Korean￨U￨NNP￨NATIONALITY￨- War￨U￨NNP￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- HPS￨U￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- Sin￨U￨NNP￨O￨- Nombre￨U￨NNP￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SNV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- group-based￨L￨JJ￨O￨- metric￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- R0￨U￨NN￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- high￨L￨JJ￨O￨- within-group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- within￨L￨IN￨O￨- farm￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- only￨L￨RB￨O￨- low￨L￨JJ￨O￨- between-group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- between￨L￨IN￨O￨- farm￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- R0￨U￨NN￨O￨- can￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- poor￨L￨JJ￨O￨- at￨L￨IN￨O￨- describing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- metapopulations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- farm￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- to￨L￨TO￨O￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- via￨L￨IN￨O￨- livestock￨L￨NN￨O￨- movements￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- technique￨L￨NN￨O￨A ,￨L￨,￨O￨- consider￨L￨VB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- SEIR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- born￨L￨VBN￨O￨- into￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- following￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- they￨L￨PRP￨O￨- enter￨L￨VBP￨O￨- exposed￨L￨VBN￨O￨- state￨L￨NN￨O￨- E￨U￨NN￨O￨- and￨L￨CC￨O￨- incubate￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- progress￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- state￨L￨NN￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- recover￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- state￨L￨NN￨O￨- R.￨U￨NNP￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- *￨L￨SYM￨O￨- takes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- intuitive￨L￨JJ￨O￨- form￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨A rate￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- within-herd￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- within-herd￨L￨JJ￨O￨- persistent￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- R￨U￨NN￨O￨- *￨L￨SYM￨O￨- peaks￨L￨VBZ￨O￨- at￨L￨IN￨O￨- intermediate￨L￨JJ￨O￨- movement￨L￨NN￨O￨A rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- revealing￨L￨VBG￨O￨- ranges￨L￨NNS￨O￨- of￨L￨IN￨O￨- movement￨L￨NN￨O￨- rates￨L￨NNS￨O￨- where￨L￨WRB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- intervention￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- most￨L￨RBS￨O￨- difficult￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨A of￨L￨IN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- related￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- normalization￨L￨NN￨O￨- condition￨L￨NN￨O￨- The￨U￨DT￨O￨- following￨L￨VBG￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obeyed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- :￨L￨:￨O￨- These￨U￨DT￨O￨- equations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- become￨L￨VBP￨O￨- recovered￨L￨VBN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- available￨L￨JJ￨O￨A data￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- newly￨L￨RB￨O￨- infected￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- and￨L￨CC￨O￨- total￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- cumulative￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- agent￨L￨NN￨O￨- based￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- Euclidean￨U￨JJ￨MISC￨- network20￨L￨NN￨O￨- ,￨L￨,￨O￨- mentioned￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- paragraph￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- analysed￨L￨VBN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- data￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Liberia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- extended￨L￨VBD￨O￨- over￨L￨IN￨O￨- approximately￨L￨RB￨O￨- two￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨A data￨L￨NNS￨O￨A for￨L￨IN￨O￨- total￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- cumulative￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- extracted￨L￨VBN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨A reach￨L￨VBP￨O￨- a￨L￨DT￨O￨- saturation￨L￨NN￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- conclude￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- existed￨L￨VBN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- longer￨L￨JJR￨O￨- period￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Guinea￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- list￨L￨VBP￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- traits￨L￨NNS￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A that￨L￨WDT￨O￨- could￨L￨MD￨O￨- amplify￨L￨VB￨O￨- their￨L￨PRP$￨O￨- vulnerability￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- under￨L￨IN￨O￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- likely￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- to￨L￨TO￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- parasite￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- various￨L￨JJ￨O￨- mitigation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- both￨L￨CC￨O￨- parasites￨L￨NNS￨O￨- and￨L￨CC￨O￨- hosts￨L￨NNS￨O￨- adapting￨L￨VBG￨O￨- to￨L￨TO￨O￨- disrupted￨L￨VBN￨O￨- climates￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- 54￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- free-living￨L￨JJ￨O￨- species￨L￨NNS￨O￨- eventually￨L￨RB￨O￨- committed￨L￨VBN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fate￨L￨NN￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A remains￨L￨VBZ￨O￨- uncertain￨L￨JJ￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- significant￨L￨JJ￨O￨- research￨L￨NN￨O￨- profiling￨L￨VBG￨O￨- climate-driven￨L￨JJ￨O￨- biodiversity￨L￨NN￨O￨- loss￨L￨NN￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- turn￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- century￨L￨NN￨DATE￨- .￨L￨.￨O￨- +Identifying￨U￨VBG￨O￨- traits￨L￨NNS￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- predispose￨L￨VB￨O￨- parasites￨L￨NNS￨O￨A to￨L￨TO￨O￨- climate-driven￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- ,￨L￨,￨O￨- separate￨L￨JJ￨O￨- from￨L￨IN￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- would￨L￨MD￨O￨- provide￨L￨VB￨O￨- conservation￨L￨NN￨O￨- a￨L￨DT￨O￨- much￨L￨JJ￨O￨- needed￨L￨VBN￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- risk￨L￨NN￨O￨- assessment￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- robust￨L￨JJ￨O￨- and￨L￨CC￨O￨- applicable￨L￨JJ￨O￨- across￨L￨IN￨O￨- major￨L￨JJ￨O￨- parasitic￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Macroparasites￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- already￨L￨RB￨O￨- uniquely￨L￨RB￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- secondary￨L￨JJ￨O￨- extinctions￨L￨NNS￨O￨- ;￨L￨:￨O￨- theoretical￨L￨JJ￨O￨- work￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- parasite￨L￨NN￨O￨- vulnerability￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- 10￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- extinction￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- and￨L￨CC￨O￨- tertiary￨L￨JJ￨O￨- extinctions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- highlighted￨L￨VBN￨O￨- that￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A can￨L￨MD￨O￨- dilute￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- counterintuitive￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- observe￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- age-specific￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- computationally￨L￨RB￨O￨- expensive￨L￨JJ￨O￨- but￨L￨CC￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- fast￨L￨JJ￨O￨- but￨L￨CC￨O￨- more￨L￨RBR￨O￨- stylized￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- different￨L￨JJ￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- both￨L￨DT￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- calibrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- similar￨L￨JJ￨O￨- results￨L￨NNS￨O￨- under￨L￨IN￨O￨- no￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- goal￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- possible￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- performances￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- agent-based￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- may￨L￨MD￨O￨- differ￨L￨VB￨O￨- significantly￨L￨RB￨O￨- in￨L￨IN￨O￨- practical￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- total￨L￨JJ￨O￨- cost￨L￨NN￨O￨- and￨L￨CC￨O￨- 34￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- strategies￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- each￨L￨DT￨O￨- iteration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- optimization￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- performances￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨- generated￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- evaluated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- experiments￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- mesh-adaptive￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- effective￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A allocation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- objective￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Λ￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ;￨L￨:￨O￨- μ1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- μ2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- disease-induced￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- β1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- β2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- or￨L￨CC￨O￨- infected￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- to￨L￨TO￨O￨- mosquito￨L￨NN￨O￨- ;￨L￨:￨O￨- α1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- saturation￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ;￨L￨:￨O￨- υ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ;￨L￨:￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- K￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- environment￨L￨NN￨O￨- for￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- above￨L￨JJ￨O￨- works￨L￨NNS￨O￨- and￨L￨CC￨O￨- [￨L￨-LRB-￨O￨- 29￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 34￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- lymphatic￨L￨JJ￨O￨- filariasis￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- environment￨L￨NN￨O￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- background￨L￨NN￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- initial￨L￨JJ￨O￨- valueswhere￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- separately￨L￨RB￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ;￨L￨:￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- for￨L￨IN￨O￨- mosquito￨L￨NN￨O￨A population￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Nonautonomous￨U￨JJ￨O￨- phenomenon￨L￨NN￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- often￨L￨RB￨O￨- occurs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨A systems￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- operator￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- globally￨L￨RB￨O￨- asymptotical￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- location￨L￨NN￨O￨- and￨L￨CC￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incursion￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- relate￨L￨VBP￨O￨- to￨L￨TO￨O￨- farm￨L￨NN￨O￨A density￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- movements￨L￨NNS￨O￨- to￨L￨TO￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- area789￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- strain￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus7￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- incursions10￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- human￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- compliance￨L￨NN￨O￨- with￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- movement￨L￨NN￨O￨- restrictions1112￨L￨NN￨O￨- have￨L￨VBP￨O￨- all￨L￨DT￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- farm￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- strict￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- implemented￨L￨VBN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- depopulating￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- premises￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- IPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- tracing￨L￨VBG￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- premises￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- strict￨L￨JJ￨O￨- movement￨L￨NN￨O￨- restrictions￨L￨NNS￨O￨- for￨L￨IN￨O￨- farms￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vicinity￨L￨NN￨O￨- of￨L￨IN￨O￨- IPs￨U￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- line￨L￨NN￨O￨- with￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- and￨L￨CC￨O￨- European￨U￨JJ￨NATIONALITY￨- level￨L￨NN￨O￨- legislation￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- generated￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- vary￨L￨VBP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- taken￨L￨VBN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- an￨L￨DT￨O￨- incursion￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- geographical￨L￨JJ￨O￨- location￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- producer￨L￨NN￨TITLE￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- explore￨L￨VB￨O￨- which￨L￨WDT￨O￨- other￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- would￨L￨MD￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- generated￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- incorporates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- premises￨L￨NNS￨O￨A to￨L￨TO￨O￨- premises￨L￨NNS￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- through￨L￨IN￨O￨- local￨L￨JJ￨O￨- spread￨L￨NN￨O￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- randomly￨L￨RB￨O￨- selected￨L￨VBN￨O￨- farm￨L￨NN￨O￨- in￨L￨IN￨O￨- GB￨U￨NN￨O￨- .￨L￨.￨O￨- +tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- genomes￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- deposited￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- European￨U￨JJ￨NATIONALITY￨- Nucleotide￨U￨NN￨MISC￨- Archive￨U￨NNP￨MISC￨- ;￨L￨:￨O￨- accession￨L￨NN￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- PRJEB12764￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- url￨L￨NN￨O￨- -￨L￨:￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- commands￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- reference￨L￨NN￨O￨- alignment￨L￨NN￨O￨- and￨L￨CC￨O￨- variant￨L￨JJ￨O￨- calling￨L￨VBG￨O￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- text￨L￨NN￨O￨- file￨L￨NN￨O￨- from￨L￨IN￨O￨- Figshare￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.6084￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- m9.figshare￨L￨JJ￨O￨- .3153280￨L￨NN￨NUMBER￨- (￨L￨-LRB-￨O￨- url￨L￨NN￨O￨- -￨L￨:￨O￨- emiology/3153280￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- final￨L￨JJ￨O￨- dataset￨L￨NN￨O￨- of￨L￨IN￨O￨- variants￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- fasta￨L￨NN￨O￨- file￨L￨NN￨O￨- from￨L￨IN￨O￨- Figshare￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- DOI￨U￨NNP￨O￨- :￨L￨:￨O￨- 10.6084￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- m9.figshare￨L￨JJ￨O￨- .3153280￨L￨NN￨NUMBER￨- (￨L￨-LRB-￨O￨- url￨L￨NN￨O￨- -￨L￨:￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- TransPhylo￨U￨NNP￨MISC￨- code￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- update￨L￨VBP￨O￨- written￨L￨VBN￨O￨- specifically￨L￨RB￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- from￨L￨IN￨O￨- GitHub￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- url￨L￨NN￨O￨- -￨L￨:￨O￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- described￨L￨VBN￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- person-to-person￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- from￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- genome￨L￨NN￨O￨- data￨L￨NNS￨O￨- ;￨L￨:￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- an￨L￨DT￨O￨- improvement￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- ’s￨L￨POS￨O￨- underlying￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- time￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- person￨L￨NN￨O￨A was￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- previously￨L￨RB￨DATE￨- developed￨L￨VBD￨O￨- TransPhylo￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Didelot￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- transmissions￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- timing￨L￨NN￨O￨- given￨L￨VBN￨O￨- mutational￨L￨JJ￨O￨- events￨L￨NNS￨O￨- captured￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- time-labelled￨L￨JJ￨O￨- phylogeny￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- used￨L￨VBD￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨- transmissions￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- 33￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2011￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Transmission￨U￨NNP￨O￨- inference￨L￨NN￨O￨- from￨L￨IN￨O￨- genomic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- uses￨L￨VBZ￨O￨- mutations￨L￨NNS￨O￨- –￨L￨:￨O￨- fixed￨L￨JJ￨O￨- or￨L￨CC￨O￨- minor￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Worby￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- Poon￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- shared￨L￨VBN￨O￨- across￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- isolates￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- putative￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- events￨L￨NNS￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- request￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Medical￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- Officer￨U￨NNP￨O￨- leading￨L￨VBG￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- response￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analysed￨L￨VBD￨O￨- Mycobacterium￨U￨NN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨A genomes￨L￨NNS￨O￨- from￨L￨IN￨O￨- 48￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 52￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- a￨L￨DT￨O￨- decline￨L￨NN￨O￨- in￨L￨IN￨O￨- newly￨L￨RB￨O￨- diagnosed￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- truly￨L￨RB￨O￨- signaled￨L￨VBD￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- In￨U￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- travel￨L￨NN￨O￨- data￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- arrival￨L￨NN￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- seeded￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- originating￨L￨VBG￨O￨A country￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- regarded￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- connecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- originating￨L￨VBG￨O￨- country￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +KeywordsBasic￨U￨JJ￨O￨- reproduction￨L￨NN￨O￨- numberEpidemic￨L￨JJ￨O￨- modelsTravel￨L￨NN￨O￨- dataSIR￨L￨NN￨O￨- modelInfluenza￨L￨NN￨O￨- pandemic￨L￨JJ￨O￨- BackgroundIn￨U￨NN￨O￨- responding￨L￨VBG￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 21st￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- reliable￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- phases￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A pandemic￨L￨NN￨O￨A is￨L￨VBZ￨O￨- critical￨L￨JJ￨O￨- .￨L￨.￨O￨- +Method￨U￨NN￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- likelihood-based￨L￨JJ￨O￨- method￨L￨NN￨O￨- using￨L￨VBG￨O￨- arrival￨L￨NN￨O￨A times￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- and￨L￨CC￨O￨- timely￨L￨JJ￨O￨- source￨L￨NN￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmissibility￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- statistically￨L￨RB￨O￨- fit￨L￨VBP￨O￨- each￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- cross-sectional￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- load￨L￨NN￨O￨A ,￨L￨,￨O￨- PCR￨U￨NN￨O￨- and￨L￨CC￨O￨- TF￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- for￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- on￨L￨IN￨O￨- age-specific￨L￨JJ￨O￨- bacterial￨L￨JJ￨O￨- load￨L￨NN￨O￨A ,￨L￨,￨O￨- PCR￨U￨NN￨O￨- and￨L￨CC￨O￨- TF￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- evaluated￨L￨VBN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- trachoma￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Susceptible￨U￨NNP￨O￨- ,￨L￨,￨O￨- Infected￨U￨JJ￨O￨- ,￨L￨,￨O￨- Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- has￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- state￨L￨NN￨O￨A are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- I￨U￨PRP￨O￨- state￨L￨VBP￨O￨- are￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- PCR￨U￨NN￨O￨- detectable￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- Model￨U￨NNP￨TITLE￨- 2￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨A the￨L￨DT￨O￨- same￨L￨JJ￨O￨- structure￨L￨NN￨O￨- as￨L￨IN￨O￨- Model￨U￨NNP￨TITLE￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- we￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- assume￨L￨VB￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- D￨U￨NN￨O￨- state￨L￨NN￨O￨- are￨L￨VBP￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- re-infection￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- human￨L￨JJ￨O￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- combined￨L￨JJ￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- poultry￨L￨NN￨O￨A and￨L￨CC￨O￨- generate￨L￨VB￨O￨- retrospective￨L￨NN￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- incidence￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- poultry￨L￨NN￨O￨- and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- eastern￨L￨JJ￨O￨- and￨L￨CC￨O￨- southern￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- estimate￨L￨NN￨O￨- critical￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- generate￨L￨VB￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- and￨L￨CC￨O￨- pandemic￨L￨JJ￨O￨- human￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- H1N1￨U￨NN￨O￨- ,￨L￨,￨O￨- H3N2￨U￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- temperate￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 18-20￨L￨CD￨DATE￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- subtropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- limited￨L￨JJ￨O￨- ,￨L￨,￨O￨- partial￨L￨JJ￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨A poses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenge￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- and￨L￨CC￨O￨- quantification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- H7N9￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- spillover￨L￨JJR￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- poultry￨L￨NN￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- link￨L￨NN￨O￨- between￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨A and￨L￨CC￨O￨- human￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- LBMs￨U￨NNS￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- because￨L￨IN￨O￨- human￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- cases￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- well￨L￨RB￨O￨- documented￨L￨VBN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- human￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- serve￨L￨VBP￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- sentinel￨L￨NN￨O￨- proxy￨L￨NN￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- among￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- .￨L￨.￨O￨- +Outbreaks￨U￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- cases￨L￨NNS￨O￨- peak￨L￨NN￨O￨- in￨L￨IN￨O￨- winter￨L￨NN￨DATE￨- months￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- geographical￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- eastern￨L￨JJ￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- southern￨L￨JJ￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Finding￨U￨VBG￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- forest￨L￨NN￨O￨A when￨L￨WRB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- present￨L￨JJ￨DATE￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- economically￨L￨RB￨O￨- important￨L￨JJ￨O￨- decision￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- forest￨L￨NN￨O￨- manager￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- arrival￨L￨NN￨O￨- of￨L￨IN￨O￨- pests￨L￨NNS￨O￨- and￨L￨CC￨O￨- pathogens￨L￨NNS￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- losses￨L￨NNS￨O￨- in￨L￨IN￨O￨- market￨L￨NN￨O￨- values￨L￨NNS￨O￨- through￨L￨IN￨O￨- :￨L￨:￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- tree￨L￨NN￨O￨- growth￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- D.￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2016￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- even-aged￨L￨JJ￨O￨- forest￨L￨NN￨O￨- by￨L￨IN￨O￨- creating￨L￨VBG￨O￨- a￨L￨DT￨O￨- generalisable￨L￨JJ￨O￨- ,￨L￨,￨O￨- bioeconomic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- ,￨L￨,￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single-rotation￨L￨JJ￨O￨- Faustmann￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- net￨L￨JJ￨O￨- present￨L￨JJ￨DATE￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- NPV￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- forest￨L￨NN￨O￨- by￨L￨IN￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- one-off￨L￨JJ￨O￨- establishment￨L￨NN￨O￨- cost￨L￨NN￨O￨- and￨L￨CC￨O￨- timber￨L￨NN￨O￨- revenue￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- then￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- non-timber￨L￨JJ￨O￨- benefits￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- cornerstone￨L￨NN￨O￨- of￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- studies￨L￨NNS￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- provision￨L￨NN￨O￨- of￨L￨IN￨O￨- recreational￨L￨JJ￨O￨- services￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- carbon￨L￨NN￨O￨- sequestration￨L￨NN￨O￨- ,￨L￨,￨O￨- taxes￨L￨NNS￨O￨- or￨L￨CC￨O￨- subsidies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- timber￨L￨NN￨O￨- and￨L￨CC￨O￨- carbon￨L￨NN￨O￨- sequestration￨L￨NN￨O￨- benefits￨L￨NNS￨O￨- while￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- biodiversity￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- forest￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- interdependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- provision￨L￨NN￨O￨- of￨L￨IN￨O￨- amenity￨L￨NN￨O￨- services￨L￨NNS￨O￨- from￨L￨IN￨O￨- adjacent￨L￨JJ￨O￨- forests￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- trade-off￨L￨NN￨O￨- between￨L￨IN￨O￨- waiting￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- timber￨L￨NN￨O￨- to￨L￨TO￨O￨- grow￨L￨VB￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- further￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- maximises￨L￨VBZ￨O￨- the￨L￨DT￨O￨- NPV￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- forest￨L￨NN￨O￨A ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- when￨L￨WRB￨O￨- timber￨L￨NN￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- no￨L￨DT￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨VBZ￨O￨- quickly￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- timber￨L￨NN￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- non-zero￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- to￨L￨TO￨O￨- wait￨L￨VB￨O￨- until￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- to￨L￨TO￨O￨- harvest￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- management￨L￨NN￨O￨- decision￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- clear-felling￨L￨JJ￨O￨- and￨L￨CC￨O￨- ask￨L￨VB￨O￨- :￨L￨:￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- multiple-benefit￨L￨JJ￨O￨- forest￨L￨NN￨O￨A ?￨L￨.￨O￨- +Over￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- Bayesian￨U￨JJ￨O￨- inferential￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- enable￨L￨VB￨O￨- statistically￨L￨RB￨O￨- rigorous￨L￨JJ￨O￨- parameterization￨L￨NN￨O￨- of￨L￨IN￨O￨- discrete￨L￨JJ￨O￨A state￨L￨NN￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- semi-Markov￨L￨JJ￨MISC￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- DCTMPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- noisy￨L￨JJ￨O￨- and￨L￨CC￨O￨- incomplete￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- typical￨L￨JJ￨O￨- of￨L￨IN￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- detections￨L￨NNS￨O￨- from￨L￨IN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Information￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- uncertainty￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- key￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- from￨L￨IN￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨A is￨L￨VBZ￨O￨- encoded￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- posterior￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- joint￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- describing￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- missing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- transition￨L￨NN￨O￨- times￨L￨NNS￨O￨- conditional￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- modeling￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Their￨U￨PRP$￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- nature￨L￨NN￨O￨- enables￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- accurate￨L￨JJ￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- than￨L￨IN￨O￨- discrete￨L￨JJ￨O￨A time￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- discrete￨L￨JJ￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ideally￨L￨RB￨O￨- suited￨L￨VBN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- farms￨L￨NNS￨O￨- classified￨L￨VBN￨O￨- into￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- inference￨L￨NN￨O￨- tools￨L￨NNS￨O￨A for￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- make￨L￨VBP￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- data-augmentation￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- missing￨L￨VBG￨O￨- information￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- times￨L￨NNS￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- as￨L￨IN￨O￨- additional￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- inferred￨L￨VBN￨O￨- .￨L￨.￨O￨- +Subsequent￨U￨JJ￨O￨- risk￨L￨NN￨O￨- assessment￨L￨NN￨O￨- can￨L￨MD￨O￨- then￨L￨RB￨O￨- be￨L￨VB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- best￨L￨JJS￨O￨- fits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- suitably￨L￨RB￨O￨- weighted￨L￨JJ￨O￨- outputs￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- quantitatively￨L￨RB￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- disease-behaviour￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- fit￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- dueling￨L￨NN￨O￨- contagion￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- jointly￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +And￨U￨CC￨O￨- while￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- devoted￨L￨VBN￨O￨- considerable￨L￨JJ￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- incentives￨L￨NNS￨O￨- facing￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- deciding￨L￨VBG￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- threat￨L￨NN￨O￨- posed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- contagion￨L￨NN￨O￨A in￨L￨IN￨O￨- question￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- paid￨L￨VBN￨O￨- less￨L￨JJR￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- decisions￨L￨NNS￨O￨- on￨L￨IN￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- perceived￨L￨VBN￨O￨- risks￨L￨NNS￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨A influence￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- may￨L￨MD￨O￨- take￨L￨VB￨O￨- preventative￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- vaccination28￨L￨NN￨O￨- or￨L￨CC￨O￨- reduced￨L￨VBN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- others13￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- behavioural￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- modify￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection323334￨L￨NN￨O￨- .￨L￨.￨O￨- +Yet￨U￨RB￨O￨- ,￨L￨,￨O￨- accumulating￨L￨VBG￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A is￨L￨VBZ￨O￨- common242526￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- comes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- health￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- smoking￨L￨NN￨CAUSE_OF_DEATH￨- cessation27￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- adoption2829￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- reason￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- focus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- on￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- key￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dueling￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- how￨L￨WRB￨O￨- severe￨L￨JJ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- really￨L￨RB￨O￨- is￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- promptly￨L￨RB￨O￨- the￨L￨DT￨O￨- focal￨L￨JJ￨O￨- population￨L￨NN￨O￨- responds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Regional￨U￨NNP￨O￨- rainfall￨L￨NNS￨O￨- was￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- mediates￨L￨VBZ￨O￨- this￨L￨DT￨O￨- long-range￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- ENSO￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- monsoon￨L￨NN￨O￨- rains￨L￨NNS￨O￨- and￨L￨CC￨O￨- river￨L￨NN￨TITLE￨- discharge￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- levels￨L￨NNS￨O￨- in￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Both￨U￨CC￨O￨- statistical￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- and￨L￨CC￨O￨- process-based￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- ENSO￨U￨NNP￨ORGANIZATION￨- on￨L￨IN￨O￨- rural￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- of￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- For￨U￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨A of￨L￨IN￨O￨- Dhaka￨U￨NNP￨CITY￨- itself￨L￨PRP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- capital￨L￨NN￨O￨- of￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- mechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- incorporating￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- lacking￨L￨VBG￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- phenomenological￨L￨JJ￨O￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- thanas￨L￨FW￨O￨- ”￨L￨''￨O￨- or￨L￨CC￨O￨- districts￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- specifically￨L￨RB￨O￨- identified￨L￨VBD￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- within￨L￨IN￨O￨- Dhaka￨U￨NNP￨CITY￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- truly￨L￨RB￨O￨- urban￨L￨JJ￨O￨- core￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨A and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- more￨L￨JJR￨O￨- rural￨L￨JJ￨O￨- periphery￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- former￨L￨JJ￨O￨- exhibiting￨L￨VBG￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- stronger￨L￨JJR￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- ENSO￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +Climate￨U￨NN￨O￨- variability￨L￨NN￨O￨- ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- the￨L￨DT￨O￨- El￨U￨NNP￨MISC￨- Niño-Southern￨U￨NNP￨MISC￨- Oscillation￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- ENSO￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨A the￨L￨DT￨O￨- year-to-year￨L￨JJ￨O￨- variation￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- district￨L￨NN￨O￨A given￨L￨VBN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- ascertain￨L￨VB￨O￨- the￨L￨DT￨O￨- strengths￨L￨NNS￨O￨- and￨L￨CC￨O￨- weaknesses￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- TF￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- data￨L￨NNS￨O￨- contained￨L￨VBD￨O￨- district￨L￨NN￨O￨A level￨L￨NN￨O￨- TF￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- at￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2010￨L￨CD￨DATE￨- .￨L￨.￨O￨- +Available￨U￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- IRS￨U￨NNP￨ORGANIZATION￨- on￨L￨IN￨O￨- VL￨U￨NNP￨O￨- incidence￨L￨NN￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- accurate￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- variant￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- asymptomatic￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- contributors￨L￨NNS￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- annual￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- 10,000￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- was￨L￨VBD￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- feasible￨L￨JJ￨O￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- settings￨L￨NNS￨O￨- that￨L￨WDT￨O￨- experience￨L￨VBP￨O￨- optimal￨L￨JJ￨O￨- IRS￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- onwards￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- baseline￨L￨NN￨O￨- endemicity￨L￨NN￨O￨- of￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- VL￨U￨NN￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- 10,000￨L￨CD￨NUMBER￨- capita￨L￨NN￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- estimated￨L￨VBN￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- VL￨U￨NNP￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- develop￨L￨VBP￨O￨- clinical￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- fitting￨L￨NN￨O￨- a￨L￨DT￨O￨- multi-state￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- to￨L￨TO￨O￨- serological￨L￨JJ￨O￨- and￨L￨CC￨O￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- endemic￨L￨JJ￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Symptomatic￨U￨JJ￨O￨- cases￨L￨NNS￨O￨- can￨L￨MD￨O￨- receive￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- VL￨U￨NN￨O￨- treatments￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- E0￨U￨NN￨O￨- and￨L￨CC￨O￨- E1￨U￨NN￨O￨- treated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- develop￨L￨VB￨O￨A PKDL￨U￨NN￨ORGANIZATION￨- after￨L￨IN￨O￨- some￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- apparent￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- absolute￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- this￨L￨DT￨O￨- putatively￨L￨RB￨O￨- recovered￨L￨VBN￨O￨- stage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- included￨L￨VBN￨O￨- because￨L￨IN￨O￨- some￨L￨DT￨O￨- VL￨U￨NN￨O￨- cases￨L￨NNS￨O￨- seem￨L￨VBP￨O￨- to￨L￨TO￨O￨- harbor￨L￨VB￨O￨- dormant￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- after￨L￨IN￨O￨- treatment￨L￨NN￨O￨- which￨L￨WDT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- late￨L￨JJ￨O￨- post-treatment￨L￨JJ￨O￨- dermatological￨L￨JJ￨O￨- complication￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Warwick￨U￨NNP￨ORGANIZATION￨- developed￨L￨VBD￨O￨- model￨L￨NN￨TITLE￨- W￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- converts￨L￨VBZ￨O￨- their￨L￨PRP$￨O￨- recent￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vector￨L￨NN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- asymptomatic￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- contributors￨L￨NNS￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Erasmus￨U￨NNP￨O￨- MC￨U￨NNP￨O￨- developed￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- VL￨U￨NNP￨O￨- models￨L￨NNS￨O￨- :￨L￨:￨O￨- model￨L￨NN￨TITLE￨- E0￨U￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- symptomatic￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- sole￨L￨JJ￨O￨- contributors￨L￨NNS￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- E1￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- best-performing￨L￨JJS￨O￨- model￨L￨NN￨TITLE￨- from￨L￨IN￨O￨- their￨L￨PRP$￨O￨- recent￨L￨JJ￨O￨- study￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- contributors￨L￨NNS￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- asymptomatic￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- groups￨L￨NNS￨O￨- have￨L￨VBP￨O￨- approached￨L￨VBN￨O￨- modelling￨L￨VBG￨O￨- systematic￨L￨JJ￨O￨A non-adherence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- shall￨L￨MD￨O￨- use￨L￨VB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- catch-all￨L￨JJ￨O￨- term￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- when￨L￨WRB￨O￨- some￨L￨DT￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- repeatedly￨L￨RB￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- receive￨L￨VB￨O￨- treatments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- these￨L￨DT￨O￨- different￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- never￨L￨RB￨O￨- been￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- simulated￨L￨JJ￨O￨- coverage￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- predicted￨L￨VBN￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Early￨U￨RB￨O￨- modelling￨L￨VBG￨O￨- work￨L￨NN￨O￨- for￨L￨IN￨O￨- lymphatic￨L￨JJ￨O￨- filariasis￨L￨NN￨O￨- highlighted￨L￨VBD￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- systematic￨L￨JJ￨O￨A non-adherence￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- program￨L￨NN￨O￨- can￨L￨MD￨O￨- undermine￨L￨VB￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- program￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- untreated￨L￨JJ￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- act￨L￨VBP￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- onward￨L￨RB￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- setting￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- systematic￨L￨JJ￨O￨A non-adherence￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- helminth￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- for￨L￨IN￨O￨- systematic￨L￨JJ￨O￨A non-adherence￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- helminth￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- into￨L￨IN￨O￨- treatment￨L￨NN￨O￨- campaign￨L￨NN￨O￨- coverage￨L￨NN￨O￨- highlight￨L￨VBP￨O￨- the￨L￨DT￨O￨- unreliability￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- coverage￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- further￨L￨RB￨O￨- complicating￨L￨VBG￨O￨- modelling￨L￨NN￨O￨A efforts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- pathogens￨L￨NNS￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- threshold￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- dose￨L￨NN￨O￨A of￨L￨IN￨O￨- childhood￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- ;￨L￨:￨O￨- even￨L￨RB￨O￨- where￨L￨WRB￨O￨- routine￨L￨JJ￨O￨- first￨L￨JJ￨ORDINAL￨- dose￨L￨NN￨O￨- coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- ,￨L￨,￨O￨- primary￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- failure￨L￨NN￨O￨- ,￨L￨,￨O￨- ∼￨L￨SYM￨O￨- 14￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- at￨L￨IN￨O￨- 9￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- interactions￨L￨NNS￨O￨- with￨L￨IN￨O￨- maternal￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- can￨L￨MD￨O￨- limit￨L￨VB￨O￨- immunization￨L￨NN￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- p￨L￨NN￨O￨- threshold￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- where￨L￨WRB￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- remains￨L￨VBZ￨O￨- endemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- maintained￨L￨VBN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- routine￨L￨JJ￨O￨- childhood￨L￨NN￨O￨- dose￨L￨NN￨O￨A and￨L￨CC￨O￨- periodic￨L￨JJ￨O￨- ,￨L￨,￨O￨- age-targeted￨L￨JJ￨O￨- supplemental￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIAs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Though￨U￨IN￨O￨- the￨L￨DT￨O￨- intent￨L￨NN￨O￨- of￨L￨IN￨O￨- campaigns￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- age￨L￨NN￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- immunized￨L￨VBN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- campaigns￨L￨NNS￨O￨- may￨L￨MD￨O￨- differ￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- logistical￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- in￨L￨IN￨O￨- implementation￨L￨NN￨O￨- ,￨L￨,￨O￨- under-estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- vaccination￨L￨NN￨O￨- services￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- illustrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- while￨L￨IN￨O￨- broader￨L￨JJR￨O￨- age￨L￨NN￨O￨- target￨L￨NN￨O￨- SIAs￨U￨NNS￨O￨- necessarily￨L￨RB￨O￨- reduce￨L￨VB￨O￨- R￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- marginal￨L￨JJ￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- campaigns￨L￨NNS￨O￨A depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- context￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- that￨L￨WDT￨O￨- was￨L￨VBD￨O￨- immunized￨L￨VBN￨O￨- by￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- using￨L￨VBG￨O￨- UNICEF￨U￨NNP￨ORGANIZATION￨- /￨L￨:￨O￨- Citation￨U￨NNP￨O￨- for￨L￨IN￨O￨- routine￨L￨JJ￨O￨A and￨L￨CC￨O￨- SIAs￨U￨NNS￨O￨- ,￨L￨,￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Supplementary￨U￨NNP￨O￨- Material￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- propose￨L￨VBP￨O￨- effective￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A into￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- scholars￨L￨NNS￨O￨- used￨L￨VBN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +applied￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- daily￨L￨JJ￨SET￨- contact￨L￨NN￨O￨A activity￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- even￨L￨RB￨O￨- gradual￨L￨JJ￨O￨- and￨L￨CC￨O￨- mild￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- changes￨L￨NNS￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- dramatic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- slowing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contact￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- determine￨L￨VB￨O￨- who￨L￨WP￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- greatly￨L￨RB￨O￨- affect￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreads￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- spread￨L￨VBN￨O￨- through￨L￨IN￨O￨- physical￨L￨JJ￨O￨- contact￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- follows￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- people￨L￨NNS￨O￨- .￨L￨.￨O￨- +Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- surge￨L￨NN￨O￨- in￨L￨IN￨O￨- interest￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A models￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual101112131415￨L￨NN￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- individual￨L￨JJ￨O￨- preemptive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- have￨L￨VBP￨O￨- on￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A over￨L￨IN￨O￨- networks17181920￨L￨NN￨O￨- .￨L￨.￨O￨- +Beyond￨U￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- meet￨L￨VBP￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- contacts￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- preemptive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨A taken￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease16￨L￨NN￨O￨- .￨L￨.￨O￨- +That￨U￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- preemptive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- which￨L￨WDT￨O￨- then￨L￨RB￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A .￨L￨.￨O￨- +These￨U￨DT￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- can￨L￨MD￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- preempt￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨VBN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Keeping￨U￨VBG￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- precision￨L￨NN￨O￨A public￨L￨JJ￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- geospatial￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- in￨L￨IN￨O￨- mind￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨- simulation￨L￨NN￨O￨- based￨L￨VBN￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- hypothetical￨L￨JJ￨O￨- EVD￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- undertaken￨L￨VBN￨O￨- with￨L￨IN￨O￨- following￨L￨VBG￨O￨- objectives￨L￨NNS￨O￨- :￨L￨:￨O￨- To￨U￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- on￨L￨IN￨O￨- 01.01.2017￨L￨CD￨DATE￨- at￨L￨IN￨O￨- New￨U￨NNP￨CITY￨- Delhi￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- EVD￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- span￨L￨NN￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- precision￨L￨NN￨O￨A public￨L￨JJ￨O￨- health￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- simply￨L￨RB￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- improving￨L￨VBG￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- promote￨L￨VBP￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reduce￨L￨VB￨O￨- health￨L￨NN￨O￨- disparities￨L￨NNS￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- emerging￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- technologies￨L￨NNS￨O￨- for￨L￨IN￨O￨- measuring￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- exposures￨L￨NNS￨O￨- ,￨L￨,￨O￨- behaviours￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- developing￨L￨VBG￨O￨- interventional￨L￨JJ￨O￨- policies￨L￨NNS￨O￨- for￨L￨IN￨O￨- targeted￨L￨VBN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- programs￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- health￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- emergent￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- of￨L￨IN￨O￨- precession￨L￨NN￨O￨- public￨L￨JJ￨O￨A health￨L￨NN￨O￨A are￨L￨VBP￨O￨- improving￨L￨VBG￨O￨- methodologies￨L￨NNS￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- modernizing￨L￨VBG￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- targeting￨L￨VBG￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- prevent￨L￨VB￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Geospatial￨U￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- geographic￨L￨JJ￨O￨- information￨L￨NN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- tool￨L￨NN￨O￨- of￨L￨IN￨O￨- precision￨L￨NN￨O￨A public￨L￨JJ￨O￨- health￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- .￨L￨.￨O￨- +Systematic￨U￨JJ￨O￨- computations￨L￨NNS￨O￨- revealed￨L￨VBD￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- interdependent￨L￨JJ￨O￨- links￨L￨NNS￨O￨A so￨L￨IN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- failure￨L￨NN￨O￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- node￨L￨NN￨O￨- causes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- immediate￨L￨JJ￨O￨- failures￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- it￨L￨PRP￨O￨- by￨L￨IN￨O￨- such￨L￨JJ￨O￨- links￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- first-and￨L￨JJ￨O￨- second-order￨L￨JJ￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- crossover￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- arise￨L￨VB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- strength￨L￨NN￨O￨- is￨L￨VBZ￨O￨- changed23￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- vary￨L￨VBP￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- dependency￨L￨NN￨O￨- links￨L￨NNS￨O￨A and￨L￨CC￨O￨- find￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- final￨L￨JJ￨O￨- recovered￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- increases￨L￨VBZ￨O￨- greatly￨L￨RB￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dependency￨L￨NN￨O￨- links￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- high￨L￨JJ￨O￨- .￨L￨.￨O￨- +Concretely￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- increase￨L￨VBP￨O￨- ρ0￨L￨VB￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- change￨L￨VB￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- dependency￨L￨NN￨O￨- links￨L￨NNS￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- changes￨L￨NNS￨O￨- from￨L￨IN￨O￨- first-order￨L￨JJ￨O￨- to￨L￨TO￨O￨- second-order￨L￨NN￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- dependency￨L￨NN￨O￨- links￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- node￨L￨NN￨O￨- adopts￨L￨VBZ￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- pieces￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- received￨L￨VBN￨O￨- from￨L￨IN￨O￨- adopted￨L￨VBN￨O￨A neighbors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- exceeds￨L￨VBZ￨O￨- an￨L￨DT￨O￨- adoption￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- if￨L￨IN￨O￨- its￨L￨PRP$￨O￨- dependency￨L￨NN￨O￨- node￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- adopted￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Canada￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- wildlife￨L￨NN￨O￨- species￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- reservoirs￨L￨NNS￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A because￨L￨IN￨O￨- of￨L￨IN￨O￨- successful￨L￨JJ￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨- in￨L￨IN￨O￨- dogs￨L￨NNS￨O￨- through￨L￨IN￨O￨- widespread￨L￨JJ￨O￨- availability￨L￨NN￨O￨- and￨L￨CC￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- parenteral￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- ,￨L￨,￨O￨- restricted￨L￨JJ￨O￨- animal￨L￨NN￨O￨- movements￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- public￨L￨JJ￨O￨- awareness￨L￨NN￨O￨- and￨L￨CC￨O￨- responsible￨L￨JJ￨O￨- pet￨L￨NN￨O￨- ownership￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- threats￨L￨NNS￨O￨- to￨L￨TO￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- agriculture￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- free-ranging￨L￨JJ￨O￨- wildlife￨L￨NN￨O￨- populations￨L￨NNS￨O￨- posed￨L￨VBN￨O￨- by￨L￨IN￨O￨- RABV￨U￨NN￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A control￨L￨NN￨O￨- targeting￨L￨VBG￨O￨- animal￨L￨NN￨O￨- populations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- implemented￨L￨VBN￨O￨- worldwide￨L￨RB￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- local￨L￨JJ￨O￨- population￨L￨NN￨O￨- reduction￨L￨NN￨O￨- ,￨L￨,￨O￨- parenteral￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- oral￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- 6,000￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- rabies￨L￨NNP￨O￨A are￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- diagnosed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- raccoon￨L￨NN￨O￨- variant￨L￨NN￨O￨- of￨L￨IN￨O￨- RABV￨U￨NN￨O￨- is￨L￨VBZ￨O￨- enzootic￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- trend￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- partly￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- elevated￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- spillover￨L￨NN￨O￨- of￨L￨IN￨O￨- raccoon￨L￨NN￨O￨- variants￨L￨NNS￨O￨- into￨L￨IN￨O￨- other￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- peridomestic￨L￨JJ￨O￨- habits￨L￨NNS￨O￨- ,￨L￨,￨O￨- importance￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- rabies￨L￨NNP￨O￨A reservoir￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- movement￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- understanding￨L￨VBG￨O￨- raccoon￨L￨NN￨O￨- movement￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- study￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- human￨L￨JJ￨O￨- desire￨L￨NN￨O￨- for￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- wildlife￨L￨NN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- concern￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- species￨L￨NNS￨O￨- impacted￨L￨VBN￨O￨- by￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- seasonality￨L￨NN￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨A population￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- decision￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Studying￨U￨VBG￨O￨- financing￨L￨NN￨O￨- issues￨L￨NNS￨O￨- of￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- companies￨L￨NNS￨O￨- and￨L￨CC￨O￨- analyzing￨L￨VBG￨O￨- financing￨L￨NN￨O￨- difference￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- governance￨L￨NN￨O￨- structure￨L￨NN￨O￨- can￨L￨MD￨O￨- effectively￨L￨RB￨O￨- circumvent￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- corporate￨L￨JJ￨O￨- financing￨L￨NN￨O￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- promote￨L￨VB￨O￨- the￨L￨DT￨O￨- improvement￨L￨NN￨O￨- of￨L￨IN￨O￨- legal￨L￨JJ￨O￨- regulations￨L￨NNS￨O￨- specific￨L￨JJ￨O￨- to￨L￨TO￨O￨- listed￨L￨VBN￨O￨A companies￨L￨NNS￨O￨- ’￨L￨POS￨O￨- financing￨L￨NN￨O￨- .￨L￨.￨O￨- +Distinguished￨U￨VBN￨O￨- from￨L￨IN￨O￨- other￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- utilities￨L￨NNS￨O￨- complex￨L￨JJ￨O￨A network￨L￨NN￨O￨A to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- scientific￨L￨JJ￨O￨- companies￨L￨NNS￨O￨- ’￨L￨POS￨O￨- financing￨L￨NN￨O￨- preference￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- governance￨L￨NN￨O￨- structure￨L￨NN￨O￨- on￨L￨IN￨O￨- financing￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- proposes￨L￨VBZ￨O￨- practical￨L￨JJ￨O￨- suggestions￨L￨NNS￨O￨- to￨L￨TO￨O￨- legal￨L￨JJ￨O￨- regulations￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- aspect￨L￨NN￨O￨- of￨L￨IN￨O￨- regulating￨L￨VBG￨O￨- financing￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- and￨L￨CC￨O￨- optimizing￨L￨VBG￨O￨- governance￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- listed￨L￨VBN￨O￨A companies￨L￨NNS￨O￨- ’￨L￨POS￨O￨- financing￨L￨NN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- characteristics￨L￨NNS￨O￨- :￨L￨:￨O￨- first￨L￨RB￨ORDINAL￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- ,￨L￨,￨O￨- internal￨L￨JJ￨O￨- capital￨L￨NN￨O￨- accumulation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- insufficient￨L￨JJ￨O￨- so￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- internal￨L￨JJ￨O￨- financing￨L￨NN￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- governance￨L￨NN￨O￨- structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- taken￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- indicator￨L￨NN￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- among￨L￨IN￨O￨- selected￨L￨VBN￨O￨- listed￨L￨VBN￨O￨A companies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Governance￨U￨NN￨O￨- structure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- affect￨L￨VBP￨O￨- financing￨L￨VBG￨O￨- decision￨L￨NN￨O￨- making￨L￨NN￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- extent￨L￨NN￨O￨- ,￨L￨,￨O￨- different￨L￨JJ￨O￨- governance￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- companies￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- various￨L￨JJ￨O￨- financing￨L￨NN￨O￨- decision￨L￨NN￨O￨- .￨L￨.￨O￨- +Pioneer￨U￨NNP￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- expression￨L￨NN￨O￨A profiles￨L￨NNS￨O￨- of￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- animal￨L￨NN￨O￨- pathogens￨L￨NNS￨O￨- in￨L￨IN￨O￨- infected￨L￨JJ￨O￨- tissues￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- genes￨L￨NNS￨O￨- induced￨L￨VBD￨O￨- more￨L￨RBR￨O￨- strongly￨L￨RB￨O￨- contributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- bacterial￨L￨JJ￨O￨- virulence￨L￨NN￨O￨- and/or￨L￨CC￨O￨- survival￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- gene￨L￨NN￨O￨A expression￨L￨NN￨O￨A in￨L￨IN￨O￨- planta￨L￨NN￨O￨- using￨L￨VBG￨O￨- quantitative￨L￨JJ￨O￨- reporters￨L￨NNS￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- R.￨U￨NNP￨MISC￨- solanacearum￨L￨NN￨O￨- virulence￨L￨NN￨O￨- genes￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- unexpected￨L￨JJ￨O￨- expression￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Changes￨U￨NNS￨O￨- in￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- gene￨L￨NN￨O￨A expression￨L￨NN￨O￨A control￨L￨VBP￨O￨- the￨L￨DT￨O￨- switch￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- commensal￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- parasitic￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- subvert￨L￨VB￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- metabolism￨L￨NN￨O￨- or￨L￨CC￨O￨- development￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- 's￨L￨POS￨O￨- benefit￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +solanacearum￨L￨NN￨O￨- virulence￨L￨NN￨O￨- gene￨L￨NN￨O￨A expression￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- discovery￨L￨NN￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- regulatory￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Epidemiological￨U￨JJ￨O￨- dynamics￨L￨NNS￨O￨- were￨L￨VBD￨O￨- first￨L￨JJ￨ORDINAL￨- captured￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tree￨L￨NN￨O￨- prior￨L￨RB￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- coalescent￨L￨JJ￨O￨A theory￨L￨NN￨O￨- and￨L￨CC￨O￨- assuming￨L￨VBG￨O￨- an￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- flexible￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- effective￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- combining￨L￨VBG￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- estimate￨L￨VB￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- most￨L￨JJS￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- inferred￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- framework￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- observing￨L￨VBG￨O￨- a￨L￨DT￨O￨- phylogeny￨L￨NN￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- managed￨L￨VBD￨O￨- to￨L￨TO￨O￨- express￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- SIS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- “￨L￨``￨O￨- Susceptible-Infected-Susceptible￨U￨JJ￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- “￨L￨``￨O￨- Susceptible-Infected-Removed￨U￨JJ￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A using￨L￨VBG￨O￨- coalescent￨L￨JJ￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- was￨L￨VBD￨O￨- then￨L￨RB￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨A models￨L￨NNS￨O￨A and￨L￨CC￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- R0￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- average￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- 10-year￨L￨JJ￨DURATION￨- time￨L￨NN￨O￨- horizon￨L￨NN￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- IIV4￨U￨NN￨O￨- versus￨L￨CC￨O￨A IIV3￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- vaccinating￨L￨VBG￨O￨- equal￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- discounted￨L￨JJ￨O￨- annual￨L￨JJ￨SET￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- type￨L￨NN￨O￨- B￨U￨NN￨O￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- 1,973,849￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- undiscounted￨L￨JJ￨O￨- 2,325,644￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- fewer￨L￨JJR￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- influenza-related￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- therefore￨L￨RB￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- projected￨L￨VBN￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- IIV4￨U￨NN￨O￨- versus￨L￨CC￨O￨A IIV3￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- prevention￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨JJR￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- societal￨L￨JJ￨O￨- value￨L￨NN￨O￨- and￨L￨CC￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- IIV4￨U￨NN￨O￨- .￨L￨.￨O￨- +Costs￨U￨NNS￨O￨- for￨L￨IN￨O￨- patient￨L￨NN￨O￨- time￨L￨NN￨O￨- lost￨L￨VBD￨O￨- for￨L￨IN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- for￨L￨IN￨O￨- influenza-related￨L￨JJ￨O￨- death￨L￨NN￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- numerator￨L￨NN￨O￨- as￨L￨IN￨O￨- these￨L￨DT￨O￨- time￨L￨NN￨O￨- losses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- captured￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- QALY￨U￨NNP￨O￨- loss￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- ;￨L￨:￨O￨- it￨L￨PRP￨O￨- would￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- double￨L￨JJ￨O￨- counting￨L￨VBG￨O￨- to￨L￨TO￨O￨- also￨L￨RB￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- patient￨L￨NN￨O￨- time￨L￨NN￨O￨- lost￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- numerator￨L￨NN￨O￨- .￨L￨.￨O￨- +AE￨U￨NN￨O￨- ,￨L￨,￨O￨- adverse￨L￨JJ￨O￨- event￨L￨NN￨O￨- ;￨L￨:￨O￨- ICER￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- incremental￨L￨JJ￨O￨- cost-effectiveness￨L￨NN￨O￨- ratio￨L￨NN￨O￨- ;￨L￨:￨O￨- IIV3￨U￨NN￨O￨- ,￨L￨,￨O￨- trivalent￨L￨JJ￨O￨- inactivated￨L￨VBN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨A ;￨L￨:￨O￨- IIV4￨U￨NN￨O￨- ,￨L￨,￨O￨- quadrivalent￨L￨NN￨O￨- inactivated￨L￨VBD￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- ;￨L￨:￨O￨- QALY￨U￨NNP￨O￨- ,￨L￨,￨O￨- quality-adjusted￨L￨JJ￨O￨- life￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +Annual￨U￨JJ￨SET￨- vaccine-related￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- by￨L￨IN￨O￨- $￨L￨$￨MONEY￨- 599￨L￨CD￨MONEY￨- million￨L￨CD￨MONEY￨- (￨L￨-LRB-￨O￨- 5.7￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- IIV4￨U￨NN￨O￨- versus￨L￨CC￨O￨A IIV3￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- these￨L￨DT￨O￨- recent￨L￨JJ￨O￨- progresses￨L￨VBZ￨O￨- in￨L￨IN￨O￨- searching￨L￨VBG￨O￨- for￨L￨IN￨O￨- optimal￨L￨JJ￨O￨A influencers￨L￨NNS￨O￨- in￨L￨IN￨O￨- LTM￨U￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenging￨L￨JJ￨O￨- task￨L￨NN￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- massively￨L￨RB￨O￨- large-scale￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- tens￨L￨NNS￨O￨- of￨L￨IN￨O￨- millions￨L￨NNS￨O￨- nodes￨L￨NNS￨O￨- encountered￨L￨VBN￨O￨- in￨L￨IN￨O￨- modern￨L￨JJ￨O￨- big-data￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- subcritical￨L￨JJ￨O￨- paths￨L￨NNS￨O￨A are￨L￨VBP￨O￨- such￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- along￨L￨IN￨O￨- which￨L￨WDT￨O￨- cascades￨L￨NNS￨O￨- can￨L￨MD￨O￨- propagate￨L￨VB￨O￨- ,￨L￨,￨O￨- CI-TM￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- reliable￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- seeds￨L￨NNS￨O￨- ’￨L￨POS￨O￨- structural￨L￨JJ￨O￨- importance￨L￨NN￨O￨- in￨L￨IN￨O￨- LTM￨U￨NN￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- seed￨L￨NN￨O￨- ’s￨L￨POS￨O￨- contribution￨L￨NN￨O￨- ,￨L￨,￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- collective￨L￨JJ￨O￨- influence￨L￨NN￨O￨- in￨L￨IN￨O￨- threshold￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- CI-TM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- subcritical￨L￨JJ￨O￨- paths￨L￨NNS￨O￨A emanating￨L￨VBG￨O￨- from￨L￨IN￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- enable￨L￨VBP￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- and￨L￨CC￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- guide￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- planning￨L￨NN￨O￨- and￨L￨CC￨O￨- response￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 32￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 34￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- relatively￨L￨RB￨O￨- few￨L￨JJ￨O￨- validated￨L￨VBN￨O￨A CHIKV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- fewer￨L￨JJR￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- validated￨L￨VBN￨O￨- Ae￨U￨NN￨O￨- .￨L￨.￨O￨- +albopictus￨L￨NN￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- environmental￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- temperature￨L￨NN￨O￨- significantly￨L￨RB￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- developmental￨L￨JJ￨O￨- and￨L￨CC￨O￨- metabolic￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- thought￨L￨VBN￨O￨- to￨L￨TO￨O￨- also￨L￨RB￨O￨- influence￨L￨VB￨O￨- egg￨L￨NN￨O￨- production￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- blood￨L￨NN￨O￨- meals￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- extreme￨L￨JJ￨O￨- temperatures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- >￨L￨JJR￨O￨- 40￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- having￨L￨VBG￨O￨- damaging￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- .￨L￨.￨O￨- +albopictus￨L￨JJ￨O￨- population￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- reliable￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- about￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- programs￨L￨NNS￨O￨- at￨L￨IN￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- challenging￨L￨VBG￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- a￨L￨DT￨O￨- CHIKV-infected￨U￨JJ￨MISC￨- vector￨L￨NN￨O￨- bites￨L￨VBZ￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- transmits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- asymptomatic￨L￨JJ￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- begins￨L￨VBZ￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- twelve￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨A with￨L￨IN￨O￨- an￨L￨DT￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- four￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Differences￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- H7N9￨U￨NN￨O￨- and￨L￨CC￨O￨- H5N1￨U￨NN￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- :￨L￨:￨O￨- human￨L￨JJ￨O￨- H5N1￨U￨NN￨O￨- cases￨L￨NNS￨O￨- report￨L￨VBP￨O￨- higher￨L￨JJR￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- higher￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- sick￨L￨JJ￨O￨- or￨L￨CC￨O￨- dead￨L￨JJ￨O￨- birds￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- H7N9￨U￨NN￨O￨- is￨L￨VBZ￨O￨- asymptomatic￨L￨JJ￨O￨- in￨L￨IN￨O￨- birds￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- found￨L￨VBN￨O￨- at￨L￨IN￨O￨- lower￨L￨JJR￨O￨- prevalence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- comparable￨L￨JJ￨O￨- time￨L￨NN￨O￨- frame￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considerably￨L￨RB￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- H7N9￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- aimed￨L￨VBN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- upon￨L￨IN￨O￨- our￨L￨PRP$￨O￨- current￨L￨JJ￨DATE￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- behind￨L￨IN￨O￨- H7N9￨U￨NN￨O￨- and￨L￨CC￨O￨- H5N1￨U￨NN￨O￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- risk￨L￨NN￨O￨A profile￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- virus￨L￨NN￨O￨- subtypes￨L￨NNS￨O￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- mainland￨L￨NN￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- highlight￨L￨VB￨O￨- the￨L￨DT￨O￨- regions￨L￨NNS￨O￨- at￨L￨IN￨O￨- greatest￨L￨JJS￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- experiencing￨L￨VBG￨O￨- AIV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +SDMs￨U￨NNS￨O￨- can￨L￨MD￨O￨- aid￨L￨VB￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- spatial￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- help￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- risk￨L￨NN￨O￨A factors￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- occurrence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reveal￨L￨VBP￨O￨- specific￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- at￨L￨IN￨O￨- highest￨L￨JJS￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- targeted￨L￨VBN￨O￨- for￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- small￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- SDMs￨U￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨A areas￨L￨NNS￨O￨- to￨L￨TO￨O￨- target￨L￨VB￨O￨- for￨L￨IN￨O￨- control￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- H5N1￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- H7N9￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- 24￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- species￨L￨NNS￨O￨- distribution￨L￨NN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SDMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- geographic￨L￨JJ￨O￨- risk￨L￨NN￨O￨A profiles￨L￨NNS￨O￨- for￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- and￨L￨CC￨O￨- H7N9￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- great￨L￨JJ￨O￨- gap￨L￨NN￨O￨- in￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- has￨L￨VBZ￨O￨- however￨L￨RB￨O￨- been￨L￨VBN￨O￨- identified￨L￨VBN￨O￨- for￨L￨IN￨O￨- enzootic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- daily￨L￨JJ￨SET￨- impacting￨L￨VBG￨O￨- the￨L￨DT￨O￨- swine￨L￨NNS￨O￨- sector￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- variation￨L￨NN￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- as￨L￨IN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- assessments￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- conditions.KeywordsVacccinationInfectious￨L￨JJ￨O￨- disesasesReproduction￨L￨NN￨O￨- numberHerd￨L￨NN￨O￨- immunityPig￨L￨NN￨O￨- populations￨L￨NNS￨O￨- BackgroundThe￨U￨NNP￨O￨- main￨L￨JJ￨O￨- pursued￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccines￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- pig￨L￨NN￨O￨- production￨L￨NN￨O￨- and￨L￨CC￨O￨- generally￨L￨RB￨O￨- in￨L￨IN￨O￨- animal￨L￨NN￨O￨- production￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- direct￨L￨JJ￨O￨- protection￨L￨NN￨O￨A .￨L￨.￨O￨- +Beyond￨U￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- protection￨L￨NN￨O￨A conferred￨L￨VBN￨O￨- by￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- indirect￨L￨JJ￨O￨- protection￨L￨NN￨O￨- of￨L￨IN￨O￨- non-immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- ones￨L￨NNS￨O￨- also￨L￨RB￨O￨- contributes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- controlling￨L￨VBG￨O￨- pathogen￨L￨NN￨O￨- spread￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- scale￨L￨NN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity.Pathogen￨L￨NN￨O￨- spread￨L￨NN￨O￨- within￨L￨IN￨O￨- pig￨L￨NN￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- strongly￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- required￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- pathogen￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- several￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- pathogen￨L￨NN￨O￨A shedding￨L￨VBG￨O￨- in￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- animals￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- documented￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- collective￨L￨JJ￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- vaccinations￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- generally￨L￨RB￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- wider￨L￨JJR￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- pathogen￨L￨NN￨O￨A diffusion￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- scale￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- induces￨L￨VBZ￨O￨- an￨L￨DT￨O￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- potentially￨L￨RB￨O￨- decreasing￨L￨VBG￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- immunologically￨L￨RB￨O￨- naïve￨L￨JJ￨O￨- animals￨L￨NNS￨O￨A .￨L￨.￨O￨- +Still￨U￨RB￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- yet-to-be￨L￨JJ￨O￨- elucidated￨L￨VBN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- what￨L￨WP￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- economically￨L￨RB￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- farm￨L￨NN￨O￨- and￨L￨CC￨O￨- regional￨L￨JJ￨O￨A level￨L￨NN￨O￨- ,￨L￨,￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- voluntary￨L￨JJ￨O￨- regional￨L￨JJ￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- may￨L￨MD￨O￨- play￨L￨VB￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- optimize￨L￨VB￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- monitoring￨L￨NN￨O￨- in￨L￨IN￨O￨- infected￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- farm￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- routes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- PRRSv￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Those￨U￨DT￨O￨- unknowns￨L￨NNS￨O￨- include￨L￨VBP￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- updated￨L￨VBN￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- regional￨L￨JJ￨O￨A PRRSv￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- endemically￨L￨RB￨O￨- infected￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- full￨L￨JJ￨O￨- quantification￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- production￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- subclinically￨L￨RB￨O￨- affected￨L￨VBN￨O￨- herds￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- improved￨L￨VBN￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- PRRSv￨U￨NN￨O￨- strains￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- close￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- relatedness￨L￨NN￨O￨- and￨L￨CC￨O￨- linked￨L￨VBN￨O￨- epidemiologically￨L￨RB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- presented￨L￨VBD￨O￨- demonstrate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- quantitative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- routinely￨L￨RB￨O￨- collected￨L￨VBN￨O￨- data￨L￨NNS￨O￨- may￨L￨MD￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- regional￨L￨JJ￨O￨A epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- PRRSv￨U￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- its￨L￨PRP$￨O￨- full￨L￨JJ￨O￨- impact￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- integration￨L￨NN￨O￨- of￨L￨IN￨O￨- phylodynamic￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- of￨L￨IN￨O￨- PRRSv￨U￨NN￨O￨- might￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- prevention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- high-risk￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Novel￨U￨JJ￨MISC￨- analytic￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- porcine￨L￨NN￨O￨- reproductive￨L￨JJ￨O￨- and￨L￨CC￨O￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨A virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PRRSv￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- :￨L￨:￨O￨- lessons￨L￨NNS￨O￨- learned￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- U.S.Julio￨U￨NNP￨O￨- Alvarez1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Pablo￨U￨NNP￨O￨- Valdes-Donoso1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Steven￨U￨NNP￨PERSON￨- Tousignant1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Mohammad￨U￨NNP￨PERSON￨- Alkhamis1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Robert￨U￨NNP￨PERSON￨- Morrison1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Andres￨U￨NNP￨O￨- Perez1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2:3￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ’s￨L￨POS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- porcine￨L￨NN￨O￨- reproductive￨L￨JJ￨O￨- and￨L￨CC￨O￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PRRSv￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- posed￨L￨VBN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pig￨L￨NN￨O￨- industry￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- porcine￨L￨NN￨O￨- reproductive￨L￨JJ￨O￨- and￨L￨CC￨O￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨A virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PRRSv￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- posed￨L￨VBN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pig￨L￨NN￨O￨- industry￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- persistence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- transmissibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- ecological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- like￨L￨IN￨O￨- seasonality￨L￨NN￨O￨- ,￨L￨,￨O￨- interaction￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- circulating￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨A .￨L￨.￨O￨- +Individuals￨U￨NNS￨O￨- mix￨L￨VBP￨O￨- homogeneously￨L￨RB￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- called￨L￨VBN￨O￨- sub-populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- patches￨L￨NNS￨O￨A or￨L￨CC￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- system￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- level￨L￨NN￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- sub-populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- travel￨L￨VBP￨O￨- along￨L￨IN￨O￨- mobility￨L￨NN￨O￨- connections￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- measles￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- may￨L￨MD￨O￨- impact￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- persistence￨L￨NN￨O￨A and￨L￨CC￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- community￨L￨NN￨O￨- size￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- threshold￨L￨NN￨O￨- above￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spatial￨L￨JJ￨O￨A structure￨L￨NN￨O￨A of￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- important￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-trivial￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- also￨L￨RB￨O￨- when￨L￨WRB￨O￨- waning￨L￨VBG￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- regimes￨L￨NNS￨O￨- following￨L￨VBG￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- considered￨L￨VBD￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- V￨U￨NN￨O￨- patches￨L￨NNS￨O￨A ,￨L￨,￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- that￨L￨WDT￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sub-populations￨L￨NNS￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- is￨L￨VBZ￨O￨- linked￨L￨VBN￨O￨- via￨L￨IN￨O￨- mobility￨L￨NN￨O￨- connections￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- one￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- :￨L￨:￨O￨- how￨L￨WRB￨O￨- does￨L￨VBZ￨O￨- the￨L￨DT￨O￨- arrival￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- and￨L￨CC￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- planting￨L￨NN￨O￨- strategy￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- tree￨L￨NN￨O￨- species￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- mixture￨L￨NN￨O￨- ?￨L￨.￨O￨- +Bioeconomic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- useful￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- pests￨L￨NNS￨O￨- and￨L￨CC￨O￨- pathogens￨L￨NNS￨O￨- on￨L￨IN￨O￨- forest￨L￨NN￨O￨- management￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- species￨L￨NNS￨O￨A diversification￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- literature￨L￨NN￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- area￨L￨NN￨O￨- in￨L￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- optimisation￨L￨NN￨O￨- problem￨L￨NN￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- objective￨L￨JJ￨O￨- function￨L￨NN￨O￨- that￨L￨WDT￨O￨- calculates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- present￨L￨JJ￨DATE￨- value￨L￨NN￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- planting￨L￨VBG￨O￨- both￨L￨CC￨O￨- species￨L￨NNS￨O￨A ,￨L￨,￨O￨- when￨L￨WRB￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- ideal￨L￨JJ￨O￨- situation￨L￨NN￨O￨- ’￨L￨''￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- monoculture￨L￨NN￨O￨- of￨L￨IN￨O￨- trees￨L￨NNS￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- A￨U￨DT￨O￨- remaining￨L￨VBG￨O￨- un-infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- forest￨L￨NN￨O￨- manager￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- option￨L￨NN￨O￨- of￨L￨IN￨O￨- planting￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- tree￨L￨NN￨O￨- species￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- species￨L￨NNS￨O￨- A￨U￨DT￨O￨- or￨L￨CC￨O￨- species￨L￨NNS￨O￨- B￨U￨NN￨O￨- or￨L￨CC￨O￨- both￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- rotation￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- note￨L￨NN￨O￨- :￨L￨:￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- rotation￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- create￨L￨VBP￨O￨- a￨L￨DT￨O￨- bioeconomic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- finds￨L￨VBZ￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- planting￨L￨NN￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- tree￨L￨NN￨O￨- species￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- k-shell￨L￨NN￨O￨- decomposition￨L￨NN￨O￨- decomposes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- into￨L￨IN￨O￨- hierarchically￨L￨RB￨O￨- ordered￨L￨VBN￨O￨- shells￨L￨NNS￨O￨- by￨L￨IN￨O￨- recursively￨L￨RB￨O￨- pruning￨L￨NN￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- less￨L￨RBR￨O￨- than￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- shell￨L￨NN￨O￨A index￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Methods￨U￨NNS￨O￨- for￨L￨IN￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- built￨L￨VBN￨O￨- upon￨L￨IN￨O￨- German￨U￨JJ￨NATIONALITY￨- population￨L￨NN￨O￨- counts￨L￨NNS￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨A history￨L￨NN￨O￨- and￨L￨CC￨O￨- was￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- influenza-attributable￨L￨JJ￨O￨- medically￨L￨RB￨O￨- attended￨L￨VBD￨O￨- acute￨L￨JJ￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- I-MAARI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- strain￨L￨NN￨O￨- distribution￨L￨NN￨O￨- using￨L￨VBG￨O￨- Bayesian￨U￨JJ￨MISC￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Is￨U￨VBZ￨MISC￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- modelling￨L￨NN￨O￨- studyFelix￨L￨NN￨O￨- Weidemann1￨U￨NN￨O￨- ,￨L￨,￨O￨- Cornelius￨U￨NNP￨PERSON￨- Remschmidt1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Silke￨U￨NNP￨PERSON￨- Buda2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Udo￨U￨NNP￨PERSON￨- Buchholz2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Bernhard￨U￨NNP￨PERSON￨- Ultsch1￨U￨NN￨O￨- and￨L￨CC￨O￨- Ole￨U￨JJ￨MISC￨- Wichmann1Email￨U￨NN￨MISC￨- authorBMC￨L￨NN￨MISC￨- Infectious￨U￨JJ￨MISC￨- DiseasesBMC￨U￨NN￨MISC￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 17:258￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- children￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- countries￨L￨NNS￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- implemented￨L￨VBN￨O￨- childhood￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- programs￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- overall￨L￨JJ￨O￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- thereby￨L￨RB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- also￨L￨RB￨O￨- challenging￨L￨VBG￨O￨- established￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- the￨L￨DT￨O￨- significant￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- established￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- ask￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- questions￨L￨NNS￨O￨A core￨L￨NN￨O￨- to￨L￨TO￨O￨- understanding￨L￨VBG￨O￨- group￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- for￨L￨IN￨O￨- learning￨L￨VBG￨O￨- in￨L￨IN￨O￨- MOOCs￨U￨NNS￨O￨- :￨L￨:￨O￨- What￨U￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- communication￨L￨NN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- forums￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- does￨L￨VBZ￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- forums￨L￨NNS￨O￨- ?￨L￨.￨O￨- +By￨U￨IN￨O￨- considering￨L￨VBG￨O￨- phylogenies￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- coalescent￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- also￨L￨RB￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- phylogeny￨L￨NN￨O￨- evolving￨L￨VBG￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- defined￨L￨VBN￨O￨- statistical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- phylogenies￨L￨NNS￨O￨- using￨L￨VBG￨O￨- likelihood-based￨L￨JJ￨O￨- inference￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- pairwise￨L￨JJ￨O￨- coalescent￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- naturally￨L￨RB￨O￨- takes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- incomplete￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- to￨L￨TO￨O￨- shape￨L￨VB￨O￨- pathogen￨L￨NN￨O￨- phylogenies￨L￨NNS￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- samples￨L￨NNS￨O￨- together￨L￨RB￨O￨- in￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨A trees￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- previously￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- indicate￨L￨VB￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- phylogenetic￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- can￨L￨MD￨O￨- arise￨L￨VB￨O￨- naturally￨L￨RB￨O￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- no￨L￨DT￨O￨- measurable￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- clustering￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Analogously￨U￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- shifting￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- focus￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- pairs￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- coalescent￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ’s￨L￨POS￨O￨- phylogenetic￨L￨JJ￨O￨- history￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- backwards-time￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- use￨L￨VBP￨O￨- pairwise￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 31￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 33￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- specified￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- evaluate￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- Latin￨U￨JJ￨O￨- hypercube￨L￨NN￨O￨- design￨L￨NN￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- run￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compute￨L￨VBP￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- metrics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- summarize￨L￨VBP￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨A trajectory￨L￨NN￨O￨- of￨L￨IN￨O￨- SPVL￨U￨NN￨ORGANIZATION￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- the￨L￨DT￨O￨- within-couple￨L￨NN￨O￨- transmission￨L￨NN￨O￨A rate￨L￨NN￨O￨A ,￨L￨,￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- “￨L￨``￨O￨- Contact￨U￨NN￨O￨- Structure￨U￨NN￨O￨- ”￨L￨''￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- and￨L￨CC￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Primary￨U￨JJ￨O￨- and￨L￨CC￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ’s￨L￨POS￨O￨- SPVL￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- gives￨L￨VBZ￨O￨- definitions￨L￨NNS￨O￨- ,￨L￨,￨O￨- units￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- models￨L￨NNS￨O￨- explicitly￨L￨RB￨O￨- track￨L￨VBP￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- log10￨L￨NN￨O￨- SPVL￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- denote￨L￨VBP￨O￨A as￨L￨IN￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- progression￨L￨NN￨O￨- to￨L￨TO￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- itself￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- “￨L￨``￨O￨- virulence￨L￨NN￨O￨- ”￨L￨''￨O￨- to￨L￨TO￨O￨- denote￨L￨VB￨O￨- log10￨L￨NN￨O￨- SPVL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Shirreff￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ’s￨L￨POS￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A rate￨L￨NN￨O￨A and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- duration￨L￨NN￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- virus￨L￨NN￨O￨- load￨L￨NN￨O￨- only￨L￨RB￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptomatic￨L￨JJ￨O￨- stage￨L￨NN￨O￨- .￨L￨.￨O￨- +Experiences￨U￨NNS￨O￨- in￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- Marburg￨U￨NNP￨O￨- virus￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Angola￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- EVD￨U￨NNP￨O￨- in￨L￨IN￨O￨- Uganda￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- outbreak￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- emphasize￨L￨VBP￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- promotion￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- context￨L￨NN￨O￨- and￨L￨CC￨O￨- culture￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- work￨L￨NN￨O￨- closely￨L￨RB￨O￨- with￨L￨IN￨O￨- community￨L￨NN￨O￨- leaders￨L￨NNS￨O￨- to￨L￨TO￨O￨- adapt￨L￨VB￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- setting￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Beyond￨U￨IN￨O￨- its￨L￨PRP$￨O￨- humanitarian￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- provision￨L￨NN￨O￨- of￨L￨IN￨O￨- appropriate￨L￨JJ￨O￨- care￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- greater￨L￨JJR￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- beds￨L￨NNS￨O￨- can￨L￨MD￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- curbing￨L￨VBG￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- by￨L￨IN￨O￨- removing￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨A and￨L￨CC￨O￨- isolating￨L￨VBG￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- preventing￨L￨VBG￨O￨- further￨L￨JJ￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- this￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- small￨L￨JJ￨O￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- early￨L￨JJ￨DATE￨A June￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Lofa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- growth￨L￨NN￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- between￨L￨IN￨O￨- early￨L￨JJ￨DATE￨- July￨U￨NNP￨DATE￨- and￨L￨CC￨O￨- late￨L￨JJ￨DATE￨- August￨U￨NNP￨DATE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- EVD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- writing￨L￨VBG￨O￨- ,￨L￨,￨O￨- caused￨L￨VBD￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 11￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- reported￨L￨VBN￨O￨- from￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 28￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- confronted￨L￨VBN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨A ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- typically￨L￨RB￨O￨- work￨L￨VBP￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- by￨L￨IN￨O￨- performing￨L￨VBG￨O￨- assessments￨L￨NNS￨O￨- ,￨L￨,￨O￨- analyzing￨L￨VBG￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- identifying￨L￨VBG￨O￨- resources￨L￨NNS￨O￨- and￨L￨CC￨O￨- interacting￨L￨VBG￨O￨- with￨L￨IN￨O￨- subject￨L￨JJ￨O￨- mater￨L￨NN￨O￨- experts234￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- used￨L￨VBN￨O￨- compartmental￨L￨JJ￨O￨A models￨L￨NNS￨O￨A with￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- like￨L￨IN￨O￨- quarantine￨L￨NN￨O￨- or￨L￨CC￨O￨- isolation￨L￨NN￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- hospitals￨L￨NNS￨O￨- or￨L￨CC￨O￨- cities￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- interventions6789￨L￨NN￨O￨- .￨L￨.￨O￨- +Modeling￨U￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- attractive￨L￨JJ￨O￨- supplemental￨L￨JJ￨O￨- method￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ’s￨L￨POS￨O￨- trajectory￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- control￨L￨NN￨O￨A measures￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- timely￨L￨JJ￨O￨- manner￨L￨NN￨O￨- .￨L￨.￨O￨- +Compartmental￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- historically￨L￨RB￨O￨- common￨L￨JJ￨O￨- ;￨L￨:￨O￨- they￨L￨PRP￨O￨- divide￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- categories￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- expression￨L￨NN￨O￨- of￨L￨IN￨O￨- hospitalization￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- established￨L￨VBN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- A￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨VB￨O￨- the￨L￨DT￨O￨- per￨L￨FW￨O￨- capita￨L￨NN￨O￨- disease-induced￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨A .￨L￨.￨O￨- +They￨U￨PRP￨O￨- chose￨L￨VBD￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- discovered￨L￨VBD￨O￨- the￨L￨DT￨O￨- complicated￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- including￨L￨VBG￨O￨- Saddle-Node￨U￨NNP￨MISC￨- bifurcation￨L￨NN￨O￨A ,￨L￨,￨O￨- Backward￨U￨RB￨O￨- bifurcation￨L￨NN￨O￨- and￨L￨CC￨O￨- Bogdanov-Takens￨U￨NNS￨O￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- codimension￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- contributes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rich￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- hospital￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- respectively￨L￨RB￨O￨A ,￨L￨,￨O￨- Liu￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Cui￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- used￨L￨VBD￨O￨- βe￨L￨NN￨O￨- −￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- c1￨L￨NN￨O￨- −￨L￨SYM￨O￨- c2￨L￨FW￨O￨- f￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- coverage￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- section￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- looking￨L￨VBG￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- backward￨L￨RB￨O￨- bifurcation￨L￨NN￨O￨A of￨L￨IN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- much￨L￨JJ￨O￨- complicated￨L￨JJ￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcation￨L￨NN￨O￨- and￨L￨CC￨O￨- Bogdanov-Takens￨U￨NNS￨MISC￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- codimension￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 3￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- discovered￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- undergoes￨L￨VBZ￨O￨- Saddle-Node￨U￨NNP￨MISC￨- bifurcation￨L￨NN￨O￨A ,￨L￨,￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcation￨L￨NN￨O￨- and￨L￨CC￨O￨- Bogdanov-Takens￨U￨NNS￨MISC￨- bifurcation￨L￨NN￨O￨- ,￨L￨,￨O￨- standing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- collision￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- equilibria￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existance￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- varying￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Serological￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- level￨L￨NN￨O￨- increases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- immunity￨L￨NN￨O￨- wanes￨L￨VBZ￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A increases￨L￨NNS￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- antibody￨L￨NN￨O￨- threshold￨L￨NN￨O￨- defining￨L￨VBG￨O￨- the￨L￨DT￨O￨- protective￨L￨JJ￨O￨- level￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- well￨L￨RB￨O￨- specified￨L￨VBN￨O￨- for￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- debunked￨L￨VBN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- at￨L￨IN￨O￨- 75￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 86￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- mumps￨L￨NNS￨O￨- vaccination￨L￨NN￨O￨A levels￨L￨NNS￨O￨- have￨L￨VBP￨O￨- stayed￨L￨VBN￨O￨- above￨L￨IN￨O￨- that￨L￨DT￨O￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- Scotland￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- 87￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- 94￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 2005￨L￨CD￨DATE￨- saw￨L￨VBD￨O￨- a￨L￨DT￨O￨- sudden￨L￨JJ￨O￨- high￨L￨JJ￨O￨- resurgence￨L￨NN￨O￨- in￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- with￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 4500￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- 8￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- after￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- second￨L￨JJ￨DATE￨- dose￨L￨NN￨O￨- of￨L￨IN￨O￨- MMR￨U￨NN￨ORGANIZATION￨- was￨L￨VBD￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨A program￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- vaccination￨L￨NN￨O￨A and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- added￨L￨VBN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- 67￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- infected￨L￨VBN￨O￨- in￨L￨IN￨O￨- Scotland￨U￨NNP￨COUNTRY￨- were￨L￨VBD￨O￨- fully￨L￨RB￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- doses￨L￨NNS￨O￨A confounded￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- analysis￨L￨NN￨O￨- consisted￨L￨VBD￨O￨- of￨L￨IN￨O￨- interlinked￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- same-sex￨L￨JJ￨O￨- HPV￨U￨NN￨O￨- 6/11/16￨L￨CD￨DATE￨- /￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- population￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- anogenital￨L￨JJ￨O￨- warts￨L￨NNS￨O￨- ,￨L￨,￨O￨- anal￨L￨JJ￨O￨- ,￨L￨,￨O￨- penile￨L￨JJ￨O￨- ,￨L￨,￨O￨- oropharyngeal￨L￨NN￨O￨- ,￨L￨,￨O￨- oral￨L￨JJ￨O￨- cavity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- laryngeal￨L￨NN￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- quality-adjusted￨L￨JJ￨O￨- life￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- (￨L￨-LRB-￨O￨- QALY￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outcomes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Rates￨U￨NNP￨O￨- governing￨L￨VBG￨O￨- transitions￨L￨NNS￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- stages￨L￨NNS￨O￨- were￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- to￨L￨TO￨O￨- age-standardized￨L￨JJ￨O￨- anal￨L￨JJ￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- English￨U￨NNP￨NATIONALITY￨- MSM￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- age-specific￨L￨JJ￨O￨- anal￨L￨JJ￨O￨- HPV￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- 511￨L￨CD￨NUMBER￨- MSM￨U￨NN￨O￨- attending￨L￨VBG￨O￨- a￨L￨DT￨O￨- London-based￨U￨JJ￨O￨- GUM￨U￨NN￨O￨- clinic￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- both￨L￨DT￨O￨- stratified￨L￨VBN￨O￨- by￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- following￨L￨VBG￨O￨- the￨L￨DT￨O￨- initiation￨L￨NN￨O￨- of￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proportionate￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- anal￨L￨JJ￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A incidence￨L￨NN￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- HPV￨U￨NN￨O￨- type￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- pre-vaccination￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- cancers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Summary￨U￨NN￨O￨- of￨L￨IN￨O￨- Demographic￨U￨JJ￨MISC￨- ,￨L￨,￨O￨- Epidemiological￨U￨JJ￨O￨- ,￨L￨,￨O￨- Sexual￨U￨JJ￨O￨- Behavior￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Clinic￨U￨NNP￨O￨- Attendance￨U￨NNP￨O￨- Parameters￨U￨NNP￨O￨- Used￨U￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Models￨U￨NNS￨O￨- Abbreviations￨U￨NNS￨O￨- :￨L￨:￨O￨- CI￨U￨NN￨O￨- ,￨L￨,￨O￨- confidence￨L￨NN￨O￨- interval￨L￨NN￨O￨- ;￨L￨:￨O￨- GUM￨U￨NNP￨O￨- ,￨L￨,￨O￨- genitourinary￨L￨JJ￨O￨- clinic￨L￨NN￨O￨- ;￨L￨:￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- ;￨L￨:￨O￨- HPV￨U￨NNP￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- papillomavirus￨L￨NN￨O￨- ;￨L￨:￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- men￨L￨NNS￨O￨A who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- ;￨L￨:￨O￨- py￨L￨NN￨O￨- ,￨L￨,￨O￨- person-years￨L￨NNS￨O￨- ;￨L￨:￨O￨- RR￨U￨NNP￨O￨- ,￨L￨,￨O￨- relative￨L￨JJ￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +Abbreviations￨U￨NNS￨O￨- :￨L￨:￨O￨- AGW￨U￨NN￨O￨- ,￨L￨,￨O￨- anogenital￨L￨JJ￨O￨- warts￨L￨NNS￨O￨- ;￨L￨:￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- ;￨L￨:￨O￨- HPV￨U￨NNP￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- papillomavirus￨L￨NN￨O￨- ;￨L￨:￨O￨- GUM￨U￨NNP￨O￨- ,￨L￨,￨O￨- genitourinary￨L￨JJ￨O￨- clinic￨L￨NN￨O￨- ;￨L￨:￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- men￨L￨NNS￨O￨A who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- ;￨L￨:￨O￨- QALY￨U￨NNP￨O￨- ,￨L￨,￨O￨- quality-adjusted￨L￨JJ￨O￨- life￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- quantify￨L￨VBP￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Susceptible-Infected-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Susceptible-Infected-Recovered-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- simulation￨L￨NN￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- sophisticated￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- tool￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- demography￨L￨NN￨O￨- and￨L￨CC￨O￨- age-dependent￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- results￨L￨VBZ￨O￨- for￨L￨IN￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 60￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- live￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- old￨L￨JJ￨DURATION￨- children￨L￨NNS￨O￨- in￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- averaged￨L￨VBD￨O￨- over￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- confirm￨L￨VBP￨O￨- this￨L￨DT￨O￨- result￨L￨NN￨O￨- :￨L￨:￨O￨- four￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- seven￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- as￨L￨IN￨O￨- many￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- prevented￨L￨VBN￨O￨- among￨L￨IN￨O￨- non-vaccinated￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- as￨L￨IN￨O￨- among￨L￨IN￨O￨- vaccinees￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- death￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- occur￨L￨VBP￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- frequently￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- unvaccinated￨L￨JJ￨O￨- elderly￨L￨JJ￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- target￨L￨NN￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- ,￨L￨,￨O￨- indirect￨L￨JJ￨O￨A benefits￨L￨NNS￨O￨- can￨L￨MD￨O￨- surpass￨L￨VB￨O￨- direct￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- 20￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 30￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- As￨U￨IN￨O￨- shown￨L￨VBN￨O￨- analytically￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- and￨L￨CC￨O￨- SIRS￨U￨NN￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- indirect￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- effects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- bigger￨L￨JJR￨O￨- than￨L￨IN￨O￨- direct￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- indirect￨L￨JJ￨O￨A effect￨L￨NN￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- “￨L￨``￨O￨- herd￨L￨NN￨O￨- protection￨L￨NN￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- not￨L￨RB￨O￨- everybody￨L￨NN￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- simple￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- to￨L￨TO￨O￨- choose￨L￨VB￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- of￨L￨IN￨O￨- unobserved￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- T￨U￨NN￨O￨- :￨L￨:￨O￨- random￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- :￨L￨:￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- incomplete￨L￨JJ￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- of￨L￨IN￨O￨- unobserved￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- T￨U￨NN￨O￨- are￨L￨VBP￨O￨- drawn￨L￨VBN￨O￨- randomly￨L￨RB￨O￨- ,￨L￨,￨O￨- independently￨L￨RB￨O￨- and￨L￨CC￨O￨- uniformly￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- probability￨L￨NN￨O￨- 1/3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- direct￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- performed￨L￨VBN￨O￨- with￨L￨IN￨O￨- such￨L￨JJ￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- .￨L￨.￨O￨- +density￨L￨NN￨O￨- sampling￨L￨NN￨O￨- :￨L￨:￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- incomplete￨L￨JJ￨O￨- observation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- X￨U￨NN￨O￨- ∈￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- T￨U￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- probability￨L￨NN￨O￨- to￨L￨TO￨O￨- assign￨L￨VB￨O￨- ,￨L￨,￨O￨- independently￨L￨RB￨O￨- and￨L￨CC￨O￨- uniformly￨L￨RB￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Similarity￨U￨NN￨O￨- Sampling￨U￨NN￨O￨- method￨L￨NN￨O￨- consists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- |￨L￨CD￨NUMBER￨- x0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- computing￨L￨VBG￨O￨- an￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- histogram￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- realizations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- contributing￨L￨VBG￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- weight￨L￨NN￨O￨- that￨L￨WDT￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- similarity￨L￨NN￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- actually￨L￨RB￨O￨- observed￨L￨VBN￨O￨- states￨L￨NNS￨O￨- at￨L￨IN￨O￨- T.￨U￨NNP￨O￨- +Among￨U￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Belief￨U￨NNP￨O￨- Propagation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- BP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- very￨L￨RB￨O￨- reliable￨L￨JJ￨O￨- and￨L￨CC￨O￨- efficient￨L￨JJ￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- also￨L￨RB￨O￨- makes￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- easily￨L￨RB￨O￨- reconstruct￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- marginals￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- states￨L￨NNS￨O￨A at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- exploiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- causality￨L￨NN￨O￨- relations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- generated￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- after￨L￨IN￨O￨- T￨U￨NN￨O￨- requires￨L￨VBZ￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- joint￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- |￨L￨CD￨NUMBER￨- x0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨A time￨L￨NN￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- some￨L￨DT￨O￨- later￨L￨JJR￨O￨- time￨L￨NN￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- .￨L￨.￨O￨- +Examples￨U￨NNS￨O￨- include￨L￨VBP￨O￨- algorithms￨L￨NNS￨O￨- in￨L￨IN￨O￨- implantable￨L￨JJ￨O￨- defibrillators￨L￨NNS￨O￨- and￨L￨CC￨O￨- pacemakers￨L￨NNS￨O￨- to￨L￨TO￨O￨- cope￨L￨VB￨O￨- with￨L￨IN￨O￨- irregular￨L￨JJ￨O￨- heartbeats￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- construction￨L￨NN￨O￨- and￨L￨CC￨O￨- fitting￨L￨NN￨O￨- for￨L￨IN￨O￨- prostate￨L￨NN￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- treatment￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- epidemiology￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- artificial￨L￨JJ￨O￨- beta-cell￨L￨NN￨O￨- or￨L￨CC￨O￨- pancreas￨L￨NN￨O￨- project￨L￨NN￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- manage￨L￨VB￨O￨- insulin￨L￨NN￨O￨- and￨L￨CC￨O￨- glucose￨L￨NN￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- type￨L￨NN￨O￨A 1￨L￨CD￨NUMBER￨- diabetes￨L￨NN￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- online￨L￨JJ￨O￨- search￨L￨NN￨O￨- engines￨L￨NNS￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- and￨L￨CC￨O￨- forecast￨L￨VB￨O￨A dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- actively￨L￨RB￨O￨- developing￨L￨VBG￨O￨- research￨L￨NN￨O￨- areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- data￨L￨NNS￨O￨- sciences￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- just￨L￨RB￨O￨- to￨L￨TO￨O￨- name￨L￨VB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- forecasting￨L￨NN￨O￨- with￨L￨IN￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Wikipedia￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- UptoDate￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Correlate￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- approaches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- some￨L￨DT￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- linear￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- generalized￨L￨VBN￨O￨- linear￨L￨JJ￨O￨- regression￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- GLM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- is￨L￨VBZ￨O￨- performed￨L￨VBN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- least￨L￨JJS￨O￨- absolute￨L￨JJ￨O￨- shrinkage￨L￨NN￨O￨- and￨L￨CC￨O￨- selection￨L￨NN￨O￨- operator￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- LASSO￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- penalized￨L￨VBN￨O￨- regression￨L￨NN￨O￨- NumericCitation￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- used￨L￨VBD￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- filters￨L￨NNS￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨A ILI￨U￨NNP￨O￨- +￨L￨CC￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- calculated￨L￨VBN￨O￨- by￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- streams￨L￨NNS￨O￨- of￨L￨IN￨O￨- ILI￨U￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- viral￨L￨JJ￨O￨- detection￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- forecast￨L￨NN￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- related￨L￨JJ￨O￨- deaths￨L￨NNS￨O￨- using￨L￨VBG￨O￨- search￨L￨NN￨O￨- query￨L￨NN￨O￨- from￨L￨IN￨O￨- Yahoo￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- Yuan￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- practical￨L￨JJ￨O￨- and￨L￨CC￨O￨- extremely￨L￨RB￨O￨- challenging￨L￨JJ￨O￨- issue￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- a￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- be￨L￨VB￨O￨- identified￨L￨VBN￨O￨- which￨L￨WDT￨O￨- produce￨L￨VBP￨O￨- sufficient￨L￨JJ￨O￨- observation￨L￨NN￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- sources￨L￨NNS￨O￨A at￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- actually￨L￨RB￨O￨- be￨L￨VB￨O￨- located￨L￨VBN￨O￨- ?￨L￨.￨O￨- +All￨U￨DT￨O￨- these￨L￨DT￨O￨- call￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- efficient￨L￨JJ￨O￨- methodologies￨L￨NNS￨O￨- to￨L￨TO￨O￨- locate￨L￨VB￨O￨- diffusion￨L￨NN￨O￨- sources￨L￨NNS￨O￨A based￨L￨VBN￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- limited￨L￨JJ￨O￨- ,￨L￨,￨O￨- practically￨L￨RB￨O￨- available￨L￨JJ￨O￨- information￨L￨NN￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- of￨L￨IN￨O￨- acquiring￨L￨VBG￨O￨- global￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- output￨L￨NN￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- messenger/sensor￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- as￨L￨IN￨O￨- Nm￨U￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- fully￨L￨RB￨O￨- locate￨L￨VB￨O￨- any￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sources￨L￨NNS￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- way￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- focus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- issue￨L￨NN￨O￨- of￨L￨IN￨O￨- locatability￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- limited￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- sparse￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- observation￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- diffusion￨L￨JJ￨O￨- sources￨L￨NNS￨O￨A locatable￨L￨JJ￨O￨- ?￨L￨.￨O￨- +The￨U￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- Nm￨U￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- nm￨L￨NN￨O￨- ≡￨L￨NN￨O￨- Nm/N￨U￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- characterizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- locatability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- that￨L￨WDT￨O￨- networks￨L￨NNS￨O￨- requiring￨L￨VBG￨O￨- smaller￨L￨JJR￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- nm￨L￨NN￨O￨- are￨L￨VBP￨O￨- deemed￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- stronger￨L￨JJR￨O￨- locatability￨L￨NN￨O￨- of￨L￨IN￨O￨- sources￨L￨NNS￨O￨A .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- ZIKV￨U￨NN￨O￨- ’s￨L￨POS￨O￨- low￨L￨JJ￨O￨- reporting￨L￨NN￨O￨A rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- suitable￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- may￨L￨MD￨O￨- reflect￨L￨VB￨O￨- diverse￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- independent￨L￨JJ￨RELIGION￨- introductions￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- self-sustaining￨L￨JJ￨O￨- local￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Confirmed￨U￨VBD￨O￨- local￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NNP￨O￨- Virus￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- Texas￨U￨NNP￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- Florida￨U￨NNP￨STATE_OR_PROVINCE￨- have￨L￨VBP￨O￨- heightened￨L￨VBN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- and￨L￨CC￨O￨- accurate￨L￨JJ￨O￨- indicators￨L￨NNS￨O￨- of￨L￨IN￨O￨- self-sustaining￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- areas￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- southern￨L￨JJ￨O￨A United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- 268￨L￨CD￨NUMBER￨- reported￨L￨VBD￨O￨- mosquito-borne￨L￨JJ￨O￨- autochthonous￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- local￨L￨JJ￨O￨A )￨L￨-RRB-￨O￨- ZIKV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- occurred￨L￨VBD￨O￨- in￨L￨IN￨O￨- Southern￨U￨NNP￨LOCATION￨- Florida￨U￨NNP￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- Texas￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨- ZIKV￨U￨NN￨O￨- vector￨L￨NN￨O￨- ,￨L￨,￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- over￨L￨IN￨O￨- 30￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- ZIKV￨U￨NN￨O￨- risk￨L￨NN￨O￨- assessment￨L￨NN￨O￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- reporting￨L￨NN￨O￨A ,￨L￨,￨O￨- importations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vector-human￨L￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- importation￨L￨NN￨O￨- risk￨L￨NN￨O￨A was￨L￨VBD￨O￨- concentrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- metropolitan￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- sustained￨L￨JJ￨O￨- ZIKV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- is￨L￨VBZ￨O￨- concentrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- southeastern￨L￨JJ￨O￨- counties￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- Houston￨U￨NNP￨CITY￨- metropolitan￨L￨JJ￨O￨- region￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Texas-Mexico￨U￨NNP￨MISC￨- border￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Numerically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- policy￨L￨NN￨O￨A exhibits￨L￨VBZ￨O￨- switch￨L￨NN￨O￨- points￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- paths￨L￨NNS￨O￨- to￨L￨TO￨O￨- coexistence￨L￨NN￨O￨- equilibria￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- spirals￨L￨NNS￨O￨- ,￨L￨,￨O￨- suggesting￨L￨VBG￨O￨- that￨L￨IN￨O￨- coexistence￨L￨NN￨O￨- equilibria￨L￨NNS￨O￨- are￨L￨VBP￨O￨- never￨L￨RB￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- paths.KeywordsMultiple￨L￨NN￨O￨- strain￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- Economic￨U￨JJ￨O￨- epidemiology￨L￨NN￨O￨- Treatment￨U￨NN￨O￨- Optimal￨U￨JJ￨O￨- control￨L￨NN￨O￨- The￨U￨DT￨O￨- authors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- grateful￨L￨JJ￨O￨- to￨L￨TO￨O￨- seminar￨L￨NN￨O￨- participants￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- University￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Cambridge￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- Royal￨U￨NNP￨ORGANIZATION￨- Economic￨U￨NNP￨ORGANIZATION￨- Society￨U￨NNP￨ORGANIZATION￨- Conference￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Cambridge￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- valuable￨L￨JJ￨O￨- comments.Mathematics￨L￨NNS￨O￨- Subject￨U￨JJ￨O￨- Classification91B55￨U￨NN￨O￨- 91B76￨L￨NN￨O￨- 93C15￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSeveral￨U￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- pose￨L￨VBP￨O￨- a￨L￨DT￨O￨- pressing￨L￨VBG￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- in￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Lyme￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Human￨U￨JJ￨O￨- Papillomavirus￨U￨NN￨O￨- ,￨L￨,￨O￨- Helicobacter￨U￨NNP￨PERSON￨- pylori￨L￨NNP￨PERSON￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- chlamydia￨L￨NN￨O￨- trachomatis￨L￨NN￨O￨- satisfies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- analysed￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- guidance￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- causes.We￨L￨NN￨O￨- analyse￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- policy￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- two-strain￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- both￨L￨CC￨O￨- analytically￨L￨RB￨O￨- and￨L￨CC￨O￨- numerically￨L￨RB￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- results￨L￨NNS￨O￨- lie￨L￨VBP￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- intervention￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- less￨L￨JJR￨O￨- infectious￨L￨JJ￨O￨- strain￨L￨NN￨O￨- dies￨L￨VBZ￨O￨- out.We￨L￨NN￨O￨- provide￨L￨VB￨O￨- numerical￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- look￨L￨VB￨O￨- for￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- policy￨L￨NN￨O￨A along￨L￨IN￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +Optimal￨U￨JJ￨O￨- policy￨L￨NN￨O￨A determines￨L￨VBZ￨O￨- what￨L￨WP￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- social￨L￨JJ￨IDEOLOGY￨- welfare￨L￨NN￨IDEOLOGY￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- chlamydia￨L￨NN￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Traditional￨U￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- influenza-like￨L￨JJ￨O￨- illnesses￨L￨NNS￨O￨- reports￨L￨NNS￨O￨- ,￨L￨,￨O￨- lag￨L￨NN￨O￨- behind￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- 2￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- information￨L￨NN￨O￨- contained￨L￨VBD￨O￨- in￨L￨IN￨O￨- cloud-based￨L￨JJ￨O￨- electronic￨L￨JJ￨O￨- health￨L￨NN￨O￨- records￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- EHR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- Internet￨U￨NNP￨MISC￨- users￨L￨NNS￨O￨- ’￨L￨POS￨O￨- search￨L￨NN￨O￨- activity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- near￨L￨JJ￨O￨- real-time￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- with￨L￨IN￨O￨- historical￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A activity￨L￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- national￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- forecasts￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- up￨L￨RP￨DURATION￨- to￨L￨TO￨DURATION￨- 4￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- ahead￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- publication￨L￨NN￨O￨- of￨L￨IN￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- reports￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- extend￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- originally￨L￨RB￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- track￨L￨VB￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A using￨L￨VBG￨O￨- Google￨U￨NNP￨ORGANIZATION￨- searches￨L￨NNS￨O￨- ,￨L￨,￨O￨- named￨L￨VBN￨O￨- ARGO￨U￨NNP￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- combine￨L￨VB￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- EHR￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- Internet￨U￨NN￨MISC￨- searches￨L￨NNS￨O￨- with￨L￨IN￨O￨- historical￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- activities￨L￨NNS￨O￨- .￨L￨.￨O￨- +spumarius￨L￨NN￨O￨- by￨L￨IN￨O￨- half￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- 500￨L￨CD￨NUMBER￨- m.Using￨L￨NN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- map￨L￨NN￨O￨- of￨L￨IN￨O￨- olive￨L￨JJ￨O￨- orchards￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- generated￨L￨VBD￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- X.￨U￨NNP￨O￨- fastidiosa￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- pathways￨L￨NNS￨O￨- in￨L￨IN￨O￨- Puglia￨U￨NNP￨LOCATION￨- by￨L￨IN￨O￨- connecting￨L￨VBG￨O￨- all￨L￨DT￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- olive￨L￨JJ￨O￨- orchards￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨- ’s￨L￨POS￨O￨- reach￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- km￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- apart￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- measured￨L￨VBN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- closest￨L￨JJS￨O￨- sides￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- orchards￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Network￨U￨NNP￨O￨- analysis￨L￨NN￨O￨- reveals￨L￨VBZ￨O￨- why￨L￨WRB￨O￨- Xylella￨U￨NNP￨ORGANIZATION￨- fastidiosa￨L￨NNP￨ORGANIZATION￨- will￨L￨MD￨O￨- persist￨L￨VB￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- Giovanni￨U￨NNP￨PERSON￨- Strona￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Corrie￨U￨NNP￨PERSON￨- Jacobien￨U￨NNP￨PERSON￨- Carstens￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Pieter￨U￨NNP￨PERSON￨- S.￨U￨NNP￨PERSON￨- Here￨U￨RB￨PERSON￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- much￨L￨RB￨O￨- the￨L￨DT￨O￨- landscape￨L￨NN￨O￨- layout￨L￨NN￨O￨- in￨L￨IN￨O￨- Puglia￨U￨NNP￨LOCATION￨- contributed￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Xylella￨U￨NNP￨O￨- fastidiosa￨L￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- what￨L￨WP￨O￨- clues￨L￨NNS￨O￨- it￨L￨PRP￨O￨- holds￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- options￨L￨NNS￨O￨A for￨L￨IN￨O￨- eradicating￨L￨VBG￨O￨- or￨L￨CC￨O￨- containing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic.The￨L￨NN￨O￨- list￨L￨NN￨O￨- of￨L￨IN￨O￨- insects￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- theoretically￨L￨RB￨O￨- serve￨L￨VB￨O￨- as￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- for￨L￨IN￨O￨- X.￨U￨NNP￨O￨- fastidiosa￨L￨NNP￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- olive￨L￨JJ￨O￨- orchards￨L￨NNS￨O￨- of￨L￨IN￨O￨- Southern￨U￨NNP￨LOCATION￨- Italy￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- meadow￨L￨NN￨O￨- splittlebug￨L￨NN￨O￨- ,￨L￨,￨O￨- Philaenus￨U￨NN￨O￨- spumarius￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Linnaeus￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- 1758￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- abundant￨L￨JJ￨O￨- xylem-fluid￨L￨JJ￨O￨- feeding￨L￨NN￨O￨- hemipteran￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- area6￨L￨NN￨O￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Impact￨U￨NN￨O￨- of￨L￨IN￨O￨- Hepatitis￨U￨NNP￨CAUSE_OF_DEATH￨- C￨U￨NNP￨CAUSE_OF_DEATH￨- Treatment￨U￨NN￨O￨- as￨L￨IN￨O￨- Prevention￨U￨NNP￨O￨- for￨L￨IN￨O￨- People￨U￨NNS￨O￨- Who￨U￨WP￨O￨- Inject￨U￨VB￨O￨- Drugs￨U￨NNS￨CRIMINAL_CHARGE￨- is￨L￨VBZ￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- contact￨L￨VB￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- Cornelia￨U￨NNP￨PERSON￨- Metzig￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Julian￨U￨NNP￨PERSON￨- Surey3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marie￨U￨NNP￨PERSON￨- Francis3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jim￨U￨NNP￨PERSON￨- Conneely4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ibrahim￨U￨NNP￨PERSON￨- Abubakar3￨U￨NN￨O￨- ,5,6￨L￨CD￨NUMBER￨- &￨L￨CC￨O￨- Peter￨U￨NNP￨PERSON￨- J.￨U￨NNP￨PERSON￨- White￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,7￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 1833￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNS￨O￨- EpidemiologyViral￨U￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- AbstractTreatment￨U￨NN￨O￨- as￨L￨IN￨O￨- Prevention￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- TasP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- using￨L￨VBG￨O￨- directly-acting￨L￨JJ￨O￨- antivirals￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- advocated￨L￨VBN￨O￨- for￨L￨IN￨O￨- Hepatitis￨U￨NNP￨CAUSE_OF_DEATH￨- C￨U￨NNP￨CAUSE_OF_DEATH￨- Virus￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- HCV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- inject￨L￨VBP￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨A (￨L￨-LRB-￨O￨- PWID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- treatment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- expensive￨L￨JJ￨O￨- and￨L￨CC￨O￨- TasP￨U￨NN￨ORGANIZATION￨- ’s￨L￨POS￨O￨- effectiveness￨L￨NN￨O￨- is￨L￨VBZ￨O￨- uncertain￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- all￨L￨DT￨O￨- network￨L￨NN￨O￨- types￨L￨NNS￨O￨- TasP￨U￨NN￨O￨- ’s￨L￨POS￨O￨- effectiveness￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- treated￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- change￨L￨VBP￨O￨- risk￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- treatment￨L￨NN￨O￨A coverage￨L￨NN￨O￨- :￨L￨:￨O￨- higher￨L￨JJR￨O￨- coverage￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- fewer￨L￨JJR￨O￨- total￨L￨NN￨O￨- treatments￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- health￨L￨NN￨O￨- gain￨L￨NN￨O￨- .￨L￨.￨O￨- +IntroductionHepatitis￨U￨NN￨MISC￨- C￨U￨NN￨MISC￨- Virus￨U￨NN￨MISC￨- (￨L￨-LRB-￨O￨- HCV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- inject￨L￨VBP￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨A (￨L￨-LRB-￨O￨- PWID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- priority￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- London￨U￨NNP￨CITY￨- being￨L￨VBG￨O￨- around￨L￨IN￨O￨- 43￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +[￨L￨-LRB-￨O￨- Aldridge￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- summarizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- project￨L￨NN￨O￨- that￨L￨WDT￨O￨- evaluated￨L￨VBD￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- centrally￨L￨RB￨O￨- organized￨L￨VBN￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- for￨L￨IN￨O￨- footrot￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Swiss￨U￨JJ￨NATIONALITY￨- sheep￨L￨NN￨O￨A population￨L￨NN￨O￨- .￨L￨.￨O￨- +Outline￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- research￨L￨NN￨O￨- project￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- –￨L￨:￨O￨- benefit￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- centrally￨L￨RB￨O￨- organized￨L￨VBN￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- for￨L￨IN￨O￨- footrot￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Swiss￨U￨JJ￨NATIONALITY￨- sheep￨L￨NN￨O￨A population￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- regions￨L￨NNS￨O￨- also￨L￨RB￨O￨- served￨L￨VBD￨O￨- as￨L￨IN￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- regionalization￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- entropy￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- MEM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- –￨L￨:￨O￨- benefit￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- varying￨L￨VBG￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- questionnaire￨L￨NN￨O￨- was￨L￨VBD￨O￨- sent￨L￨VBN￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- sheep￨L￨NN￨O￨A farmers￨L￨NNS￨O￨- of￨L￨IN￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- revealing￨L￨VBG￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- perceived￨L￨VBN￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- footrot￨L￨NN￨O￨- in￨L￨IN￨O￨- Swiss￨U￨JJ￨NATIONALITY￨- sheep￨L￨NN￨O￨- premises￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- epidemiologic￨L￨JJ￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- management￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- footrot￨L￨NN￨O￨- prevalence￨L￨NN￨O￨A in￨L￨IN￨O￨- Switzerland￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Methodology￨U￨NNP￨O￨- Article￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Clone￨U￨NN￨O￨- temporal￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- sequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- graph￨L￨NN￨O￨- snapshotsMoritz￨L￨NN￨O￨- Hanke1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- and￨L￨CC￨O￨- Ronja￨U￨NN￨O￨- Foraita1BMC￨U￨NN￨O￨- BioinformaticsBMC￨U￨NN￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18:261￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Different￨U￨NNP￨O￨- phenomena￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- genes￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- thought￨L￨VBN￨O￨- of￨L￨IN￨O￨- as￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Focusing￨U￨VBG￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨A as￨L￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- simulated￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- of￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- graph￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- that￨L￨WDT￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- improves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- important￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- in￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- graph￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- ,￨L￨,￨O￨- classical￨L￨JJ￨O￨- vertex￨L￨NN￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- like￨L￨IN￨O￨- closeness￨L￨NN￨O￨- and￨L￨CC￨O￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- single￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Incompletely￨U￨RB￨O￨- observed￨L￨VBN￨O￨- graph￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- lack￨L￨VBP￨O￨- important￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- duration￨L￨NN￨O￨- or￨L￨CC￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- biased￨L￨VBN￨O￨- temporal￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A values￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- implicit￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- sequence￨L￨NN￨O￨- contains￨L￨VBZ￨O￨- all￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- recently￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- do￨L￨VBP￨O￨- allow￨L￨VB￨O￨- mutations￨L￨NNS￨O￨A to￨L￨TO￨O￨- occur￨L￨VB￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- make￨L￨VBP￨O￨- other￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- not￨L￨RB￨O￨- fully￨L￨RB￨O￨- reflecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- above-described￨L￨JJ￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- phenomenological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- distances￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- dominant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- mutations￨L￨NNS￨O￨- can￨L￨MD￨O￨- accumulate￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- clearly￨L￨RB￨O￨- defined￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Much￨U￨JJ￨O￨- progress￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- made￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- development￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- existing￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- either￨L￨CC￨O￨- include￨L￨VBP￨O￨- assumptions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- take￨L￨VB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- process￨L￨NN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- designed￨L￨VBN￨O￨- for￨L￨IN￨O￨- specific￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- fit-for-purpose￨L￨JJ￨O￨- code￨L￨NN￨O￨- for￨L￨IN￨O￨- data￨L￨NN￨O￨- analysis￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- make￨L￨VB￨O￨- limiting￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- sampling￨L￨NN￨O￨A times￨L￨NNS￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- publications￨L￨NNS￨O￨- by￨L￨IN￨O￨- Didelot￨U￨NNP￨PERSON￨- et￨L￨NNP￨O￨- al￨L￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- Ypma￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- revealed￨L￨VBD￨O￨- that￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- relate￨L￨VB￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- is￨L￨VBZ￨O￨- illustrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨O￨- 1A￨L￨NN￨O￨- :￨L￨:￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- four￨L￨CD￨NUMBER￨- unobserved￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- sampling￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- within￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- mutation￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- four￨L￨CD￨NUMBER￨- processes￨L￨NNS￨O￨- indicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- 1￨L￨CD￨NUMBER￨- infecting￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- sampled￨L￨VBN￨O￨- sequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- sampling￨L￨NN￨O￨A ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- coalescence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- mutation￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- most￨L￨JJS￨O￨- or￨L￨CC￨O￨- all￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- are￨L￨VBP￨O￨- sampled￨L￨VBN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- nucleotides￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- single-nucleotide￨L￨JJ￨O￨- polymorphisms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SNPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- resolve￨L￨VB￨O￨- transmission￨L￨NN￨O￨- clusters￨L￨NNS￨O￨- ,￨L￨,￨O￨- individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- complete￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- considered￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- scenarios￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- baseline￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- no￨L￨DT￨O￨- intervention￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- scenario￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- school-based￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- all￨L￨DT￨O￨- students￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- school￨L￨NN￨O￨A were￨L￨VBD￨O￨- vaccinated￨L￨VBN￨O￨- once￨L￨RB￨DATE￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- cases￨L￨NNS￨O￨- were￨L￨VBD￨O￨- beyond￨L￨IN￨O￨- a￨L￨DT￨O￨- stated￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- surveillance￨L￨NN￨O￨- study￨L￨NN￨O￨- were￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- at￨L￨IN￨O￨- elementary￨L￨JJ￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- found￨L￨VBD￨O￨- school￨L￨NN￨TITLE￨A nurse￨L￨NN￨TITLE￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- tracking￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- lowering￨L￨VBG￨O￨- annual￨L￨JJ￨SET￨- varicella￨L￨NN￨O￨- incident￨L￨NN￨O￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- primarily￨L￨RB￨O￨- used￨L￨VBN￨O￨- empirical￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- European￨U￨JJ￨NATIONALITY￨- populations￨L￨NNS￨O￨- but￨L￨CC￨O￨- failed￨L￨VBD￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- class￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨A structure￨L￨NN￨O￨- of￨L￨IN￨O￨- student￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +developed￨L￨VBN￨O￨- two￨L￨CD￨NUMBER￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A holidays￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- 22￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- to￨L￨TO￨O￨- 31￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- student￨L￨NN￨TITLE￨- contacts￨L￨NNS￨O￨- during￨L￨IN￨O￨- summer￨L￨NN￨DATE￨- holidays￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Information￨U￨NN￨O￨- includes￨L￨VBZ￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- primary￨L￨JJ￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- secondary￨L￨JJ￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- college￨L￨NN￨O￨- or￨L￨CC￨O￨- university￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- reporting￨L￨VBG￨O￨- date￨L￨NN￨O￨- of￨L￨IN￨O￨- H1N1￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- dates￨L￨NNS￨O￨- of￨L￨IN￨O￨- symptom￨L￨NN￨O￨- onset￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DO￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- interventions￨L￨NNS￨O￨- including￨L￨VBG￨O￨- case￨L￨NN￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- symptomatic￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- environment￨L￨NN￨O￨- disinfection￨L￨NN￨O￨- ,￨L￨,￨O￨- health￨L￨NN￨O￨- education￨L￨NN￨O￨- ,￨L￨,￨O￨- antivirals￨L￨NNS￨O￨- for￨L￨IN￨O￨- treatment￨L￨NN￨O￨- or￨L￨CC￨O￨- prophylaxis￨L￨NN￨O￨- use￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- grade￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- collected￨L￨VBD￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- small-scale￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- at￨L￨IN￨O￨- schools￨L￨NNS￨O￨- in￨L￨IN￨O￨- Changsha￨U￨NNP￨LOCATION￨- city￨L￨NN￨O￨- from￨L￨IN￨O￨- January￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2009￨L￨CD￨DATE￨- to￨L￨TO￨O￨- December￨U￨NNP￨DATE￨- 31￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2013￨L￨CD￨DATE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- common￨L￨JJ￨O￨- countermeasures￨L￨NNS￨O￨- in￨L￨IN￨O￨- school￨L￨NN￨O￨A outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- antivirus￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- .￨L￨.￨O￨- +Typically￨U￨RB￨O￨- ,￨L￨,￨O￨- school￨L￨NN￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- directly￨L￨RB￨O￨- to￨L￨TO￨O￨- county￨L￨NN￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- by￨L￨IN￨O￨- primary￨L￨JJ￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- center￨L￨NN￨O￨- ,￨L￨,￨O￨- school￨L￨NN￨O￨- clinics￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- clinics￨L￨NNS￨O￨- and￨L￨CC￨O￨- hospitals￨L￨NNS￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- observed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- school￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- practice￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- countermeasures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- taken￨L￨VBN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- at￨L￨IN￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- pharmaceutical￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- typically￨L￨RB￨O￨- antivirus￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- non-pharmaceutical￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- isolation￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Influenza￨U￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- spreads￨L￨VBZ￨O￨- fast￨L￨RB￨O￨- at￨L￨IN￨O￨- school￨L￨NN￨O￨A and￨L￨CC￨O￨- often￨L￨RB￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- small-scale￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- Se￨U￨NNP￨O￨- estimates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- methods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- sample￨L￨NN￨O￨- matrix￨L￨NN￨O￨- ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- samples￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- sampling￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- herd￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- output￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- concludes￨L￨VBZ￨O￨- by￨L￨IN￨O￨- discussing￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- specific￨L￨JJ￨O￨- preclinical￨L￨JJ￨O￨- samples￨L￨NNS￨O￨A to￨L￨TO￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- aid￨L￨VB￨O￨- in￨L￨IN￨O￨- reactive￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- comments￨L￨NNS￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- performance￨L￨NN￨O￨- as￨L￨IN￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- transmission￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Se￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- sample￨L￨NN￨O￨- matrices￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨A of￨L￨IN￨O￨- FMDV-infected￨U￨JJ￨O￨- cattle￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- inoculated￨L￨VBN￨O￨- and￨L￨CC￨O￨- contact-infected￨L￨JJ￨O￨- calves￨L￨NNS￨O￨- started￨L￨VBD￨O￨- shedding￨L￨VBG￨O￨A virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- detected￨L￨VBN￨O￨- by￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- quantitative￨L￨JJ￨O￨- reverse￨L￨NN￨O￨- transcription-PCR￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- qPCR￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- 1￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- postinoculation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dpi￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- at￨L￨IN￨O￨- 1￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- postchallenge￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- nasal￨L￨JJ￨O￨- samples￨L￨NNS￨O￨A in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- shedding￨L￨VBG￨O￨- was￨L￨VBD￨O￨- significantly￨L￨RB￨O￨- higher￨L￨JJR￨O￨- (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- <￨L￨JJR￨O￨- 0.05￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- during￨L￨IN￨O￨- this￨L￨DT￨O￨- phase￨L￨NN￨O￨- than￨L￨IN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- preclinical￨L￨JJ￨O￨- or￨L￨CC￨O￨- early￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- phase￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- ants￨L￨NNS￨O￨- display￨L￨VBP￨O￨- a￨L￨DT￨O￨- remarkable￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- synchronization￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- activity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- quasi-periodic￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- physical￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- nestmates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- S1￨U￨NN￨O￨- Video￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- roughly￨L￨RB￨O￨- three￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- four￨L￨CD￨NUMBER￨- peaks￨L￨NNS￨O￨- per￨L￨IN￨O￨- hour￨L￨NN￨DURATION￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- test￨L￨VB￨O￨- whether￨L￨IN￨O￨- STACs￨U￨NNS￨O￨- could￨L￨MD￨O￨- potentially￨L￨RB￨O￨- influence￨L￨VB￨O￨- information￨L￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- automated￨L￨VBN￨O￨- tracking￨L￨NN￨O￨- system￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- barcode￨L￨NN￨O￨- tag￨L￨NN￨O￨- is￨L￨VBZ￨O￨- attached￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- thorax￨L￨NN￨O￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- ant￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- colony￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1a￨L￨NN￨O￨- and￨L￨CC￨O￨- 1b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- acquire￨L￨VB￨O￨- 15￨L￨CD￨NUMBER￨- three-day-long￨L￨JJ￨DURATION￨- records￨L￨NNS￨O￨A of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- physical￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- nests￨L￨NNS￨O￨- of￨L￨IN￨O￨- L￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- colony￨L￨NN￨O￨- exhibits￨L￨VBZ￨O￨- short-term￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- oscillations￨L￨NNS￨O￨A in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- movement￨L￨NN￨O￨- activity￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- g￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- time-ordered￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Both￨U￨CC￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- activity￨L￨NN￨O￨A and￨L￨CC￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- time-series￨L￨NNS￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- λ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 960￨L￨CD￨DURATION￨- seconds￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Synchronized￨U￨NNP￨O￨- and￨L￨CC￨O￨- mixed￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- coupled￨L￨VBN￨O￨A recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- Muhua￨U￨NNP￨PERSON￨- Zheng1￨U￨NN￨PERSON￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ming￨U￨VBG￨PERSON￨- Zhao3￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Byungjoon￨U￨NNP￨O￨- Min2￨U￨NNP￨O￨- &￨L￨CC￨O￨- Zonghua￨U￨NNP￨O￨- Liu1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2424￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- scienceInfluenza￨L￨NN￨O￨- virus￨L￨NN￨O￨- AbstractEpidemic￨U￨JJ￨O￨- spreading￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- are￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- growing￨L￨VBG￨O￨- aspect￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- here￨L￨RB￨O￨- report￨L￨VBP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- coupled￨L￨VBN￨O￨A regions￨L￨NNS￨O￨- or￨L￨CC￨O￨- cities￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- coupled￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- show￨L￨VB￨O￨- either￨L￨CC￨O￨- synchronized￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- pattern￨L￨NN￨O￨- where￨L￨WRB￨O￨- outbreaks￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- simultaneously￨L￨RB￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- networks￨L￨NNS￨O￨- or￨L￨CC￨O￨- mixed￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- pattern￨L￨NN￨O￨- where￨L￨WRB￨O￨- outbreaks￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- network￨L￨NN￨O￨- but￨L￨CC￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- in￨L￨IN￨O￨- another￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- reveal￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- mechanism￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- two-layered￨L￨JJ￨O￨- network￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- coupled￨L￨VBN￨O￨A recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- synchronized￨L￨VBN￨O￨- and￨L￨CC￨O￨- mixed￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- synchronized￨L￨VBN￨O￨- outbreak￨L￨NN￨O￨- pattern￨L￨NN￨O￨- is￨L￨VBZ￨O￨- preferred￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- triggered￨L￨VBN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- coupled￨L￨VBN￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- mixed￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- pattern￨L￨NN￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- average￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- features￨L￨NNS￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- seed￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- best￨L￨JJS￨O￨- correlate￨L￨VBP￨O￨- the￨L￨DT￨O￨- similarity￨L￨NN￨O￨- between￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- discuss￨L￨VB￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- results￨L￨NNS￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- adequacy￨L￨NN￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨A data￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- recurrent￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- aim￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- originating￨L￨VBG￨O￨- from￨L￨IN￨O￨- every￨L￨DT￨O￨- possible￨L￨JJ￨O￨- seed￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- quantify￨L￨VB￨O￨- their￨L￨PRP$￨O￨- similarity￨L￨NN￨O￨A in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- invasion￨L￨NN￨O￨- tree￨L￨NN￨O￨- and￨L￨CC￨O￨- arrival￨L￨NN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- extensive￨L￨JJ￨O￨- side-by-side￨L￨RB￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- France￨U￨NNP￨COUNTRY￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- commuting￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- :￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- extracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- official￨L￨JJ￨O￨- census￨L￨NN￨O￨- survey￨L￨NN￨O￨- and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨A dataset￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- detailed￨L￨JJ￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨A is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- characterizing￨L￨VBG￨O￨- and￨L￨CC￨O￨- forecasting￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- an￨L￨DT￨O￨- essential￨L￨JJ￨O￨- ingredient￨L￨NN￨O￨- for￨L￨IN￨O￨- most￨L￨JJS￨O￨- spatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- at￨L￨IN￨O￨- global￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- national￨L￨JJ￨O￨- or￨L￨CC￨O￨- continental￨L￨JJ￨O￨- scale￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- thoroughly￨L￨RB￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- adequacy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨A network￨L￨NN￨O￨- to￨L￨TO￨O￨- match￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- census￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- With￨U￨IN￨O￨- incorporating￨L￨VBG￨O￨- hospital￨L￨NN￨O￨A isolation￨L￨NN￨O￨- and￨L￨CC￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- medication￨L￨NN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- analyzing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- resisting￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- 10,029￨L￨CD￨NUMBER￨- total￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- 23￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- expect￨L￨VBP￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- EVD￨U￨NN￨O￨- in￨L￨IN￨O￨- 285￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- devising￨L￨VBG￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A eradicationShuo￨L￨NN￨O￨- Jiang￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kaiqin￨U￨NNP￨PERSON￨- Wang￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Chaoqun￨U￨NNP￨PERSON￨- Li￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Guangbin￨U￨NNP￨PERSON￨- Hong￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Xuan￨U￨NNP￨PERSON￨- Zhang1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Menglin￨U￨NNP￨O￨- Shan1￨U￨NN￨O￨- ,￨L￨,￨O￨- Hongbin￨U￨NNP￨PERSON￨- Li3￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Jin￨U￨NN￨O￨- Wang1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- †￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 15:124￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2015￨L￨CD￨DATE￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- EVD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- defines￨L￨VBZ￨O￨- an￨L￨DT￨O￨- unprecedented￨L￨JJ￨O￨- health￨L￨NN￨O￨- threat￨L￨NN￨O￨- for￨L￨IN￨O￨- human￨L￨JJ￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- regional￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- with￨L￨IN￨O￨- our￨L￨PRP$￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- paths￨L￨NNS￨O￨- including￨L￨VBG￨O￨- household￨L￨NN￨O￨- ,￨L￨,￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- hospital￨L￨NN￨O￨A and￨L￨CC￨O￨- unsafe￨L￨JJ￨O￨- funeral￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- and￨L￨CC￨O￨- eradication￨L￨NN￨O￨A pathways￨L￨NNS￨O￨- ,￨L￨,￨O￨- further￨L￨RB￨O￨- fit￨L￨VB￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- total￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- calculated￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- as￨L￨IN￨O￨- 1.754￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- construct￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- devise￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A eradication￨L￨NN￨O￨- plan￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 01￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Voluntary￨U￨NNP￨O￨- Vaccination￨U￨NN￨O￨- through￨L￨IN￨O￨- Self-organizing￨U￨JJ￨O￨- Behaviors￨U￨NNS￨O￨- on￨L￨IN￨O￨- Locally-mixed￨U￨JJ￨MISC￨- Social￨U￨NNP￨MISC￨- Networks￨U￨NNP￨MISC￨- Benyun￨U￨NNP￨MISC￨- Shi1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Hongjun￨U￨NNP￨PERSON￨- Qiu1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Wenfang￨U￨NNP￨O￨- Niu1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yizhi￨U￨NNP￨O￨- Ren1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Hong￨U￨NNP￨O￨- Ding1￨U￨NNP￨O￨- ,2￨L￨NNP￨O￨- &￨L￨CC￨O￨- Dan￨U￨NNP￨O￨- Chen1￨U￨NNP￨O￨- ,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2665￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- science￨L￨NN￨O￨- AbstractVoluntary￨U￨NNP￨O￨- vaccination￨L￨NN￨O￨A reflects￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- weigh￨L￨VBP￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine-preventable￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- carry￨L￨VBP￨O￨- out￨L￨RP￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- locally-mixed￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- voluntary￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- studying￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- self-organizing￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- circumstance￨L￨NN￨O￨- of￨L￨IN￨O￨- voluntary￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccinating￨L￨VBG￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- depends￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- weigh￨L￨VBP￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨A of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- financial￨L￨JJ￨O￨- cost8￨L￨NN￨O￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- side￨L￨NN￨O￨- effects10￨L￨NN￨O￨- ,11,12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- homogeneously￨L￨RB￨O￨- mixing￨L￨VBG￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- depends￨L￨VBZ￨O￨- largely￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- best￨L￨JJS￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- and￨L￨CC￨O￨- incorporate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- externalities￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨A when￨L￨WRB￨O￨- making￨L￨VBG￨O￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- aimed￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- within￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- facilities￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- reviewed￨L￨VBD￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- publications￨L￨NNS￨O￨- which￨L￨WDT￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- described￨L￨VBD￨O￨- the￨L￨DT￨O￨- externalities￨L￨NNS￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- described￨L￨VBN￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- externalities￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- or￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- described￨L￨VBN￨O￨- macro-level￨L￨JJ￨O￨- policy￨L￨NN￨O￨- options￨L￨NNS￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- externalities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- How￨U￨WRB￨MISC￨- externalities￨L￨NNS￨O￨- impact￨L￨VBP￨O￨- an￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨A in￨L￨IN￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- organizationsJenine￨L￨NN￨O￨- R.￨U￨NNP￨O￨- Few￨U￨JJ￨O￨- resources￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- allocated￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- on￨L￨IN￨O￨- global￨L￨JJ￨O￨- ,￨L￨,￨O￨- national￨L￨JJ￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- part￨L￨NN￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- broader￨L￨JJR￨O￨- economic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- externality￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- fully￨L￨RB￨O￨- considered￨L￨VBN￨O￨- when￨L￨WRB￨O￨- determining￨L￨VBG￨O￨- how￨L￨WRB￨O￨- much￨L￨JJ￨O￨- to￨L￨TO￨O￨- invest￨L￨VB￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- AROs￨U￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- stewardship￨L￨NN￨O￨- programs￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- Based￨U￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- findings￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- methodology￨L￨NN￨O￨- that￨L￨WDT￨O￨- healthcare￨L￨NN￨O￨- organizations￨L￨NNS￨O￨- can￨L￨MD￨O￨- use￨L￨VB￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- negative￨L￨JJ￨O￨- externalities￨L￨NNS￨O￨- when￨L￨WRB￨O￨- making￨L￨VBG￨O￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- on￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨A AROs￨U￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- justify￨L￨VB￨O￨- expenditures￨L￨NNS￨O￨- on￨L￨IN￨O￨- programs￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reduce￨L￨VBP￨O￨- AROs￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- to￨L￨TO￨O￨- formally￨L￨RB￨O￨- incorporate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- negative￨L￨JJ￨O￨- externality￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨A associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- use￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- quantifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- externalities￨L￨NNS￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- use￨L￨NN￨O￨- ,￨L￨,￨O￨- combining￨L￨VBG￨O￨- the￨L￨DT￨O￨- attributable￨L￨JJ￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- AROs￨U￨NNS￨O￨- with￨L￨IN￨O￨- time-series￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- showing￨L￨VBG￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- utilization￨L￨NN￨O￨- and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- AROs￨U￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- absolute￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A for￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- week￨L￨NN￨DURATION￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- calculated￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- follow-up￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- plus￨L￨CC￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- older￨L￨JJR￨O￨- than￨L￨IN￨O￨- 6￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- to￨L￨TO￨O￨- week￨L￨NN￨DURATION￨- t￨L￨NN￨O￨- subtracted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- to￨L￨TO￨O￨- week￨L￨NN￨DURATION￨- t￨L￨NN￨O￨- We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- S0￨U￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨NN￨O￨- expected￨L￨VBD￨O￨- duration￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- discussed￨L￨VBN￨O￨- below￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- calculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- rotavirus￨L￨NN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- made￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- assumptions￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- represented￨L￨VBN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- reported￨L￨VBN￨O￨- rotavirus￨L￨NN￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- of￨L￨IN￨O￨- primary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- removed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- severe￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- after￨L￨IN￨O￨- their￨L￨PRP$￨O￨- primary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- adjusted￨L￨VBD￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- for￨L￨IN￨O￨- under-ascertainment￨L￨NN￨O￨- to￨L￨TO￨O￨- arrive￨L￨VB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- balance￨L￨NN￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A :￨L￨:￨O￨- Because￨U￨IN￨O￨- all￨L￨DT￨O￨- children￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- once￨L￨RB￨DATE￨- before￨L￨IN￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- set￨L￨VBD￨O￨- the￨L￨DT￨O￨- time-dependent￨L￨JJ￨O￨- denominator￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- births￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- previous￨L￨JJ￨DURATION￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- infected￨L￨JJ￨O￨- per￨L￨IN￨O￨- primary￨L￨JJ￨O￨- case￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨A as￨L￨IN￨O￨- where￨L￨WRB￨O￨- Î￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- u￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rotavirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- u￨L￨NN￨O￨- and￨L￨CC￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- u￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- interval￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- u￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- calculated￨L￨VBD￨O￨- in￨L￨IN￨O￨- eAppendix￨L￨NN￨O￨- B￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- set￨L￨VBD￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- disentangle￨L￨VB￨O￨- possible￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- weather￨L￨NN￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- factors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- outcome￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- here￨L￨RB￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- modern￨L￨JJ￨O￨- transportation￨L￨NN￨O￨A networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- made￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- integrated￨L￨VBN￨O￨- with￨L￨IN￨O￨- established￨L￨JJ￨O￨- software￨L￨NN￨O￨- packages￨L￨NNS￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- testing￨L￨NN￨O￨- and￨L￨CC￨O￨- deployment￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- data￨L￨NNS￨O￨- generator￨L￨NN￨O￨- that￨L￨WDT￨O￨- models￨L￨NNS￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- contagion￨L￨NN￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- cities￨L￨NNS￨O￨A connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- airline￨L￨NN￨O￨- routes￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- counts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- then￨L￨RB￨O￨- added￨L￨VBN￨O￨- onto￨L￨IN￨O￨- statically￨L￨RB￨O￨- generated￨L￨VBN￨O￨- baseline￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- city￨L￨NN￨O￨A to￨L￨TO￨O￨- produce￨L￨VB￨O￨- a￨L￨DT￨O￨- full￨L￨JJ￨O￨- synthetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- set￨L￨VBN￨O￨- .￨L￨.￨O￨- +Values￨U￨NNS￨O￨- are￨L￨VBP￨O￨- then￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- PMF￨U￨NN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- an￨L￨DT￨O￨- expected￨L￨VBN￨O￨- degree￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- connected￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- city￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- generate￨L￨VBP￨O￨- a￨L￨DT￨O￨- transportation￨L￨NN￨O￨A network￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- Chung-Lu￨U￨NN￨MISC￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- that￨L￨WDT￨O￨- preserves￨L￨VBZ￨O￨- these￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- morbidity￨L￨NN￨O￨- by￨L￨IN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- tradition￨L￨NN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- expansion￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- fitted￨L￨VBD￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- detailed￨L￨JJ￨O￨- local￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- nasopharyngeal￨L￨JJ￨O￨- carriage￨L￨NN￨O￨- and￨L￨CC￨O￨- invasive￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- IPD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- marginal￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- PCV￨U￨NN￨O￨- catch-up￨L￨NN￨O￨- campaign￨L￨NN￨O￨- over￨L￨IN￨O￨- hypothetical￨L￨JJ￨O￨- routine￨L￨JJ￨O￨- cohort￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- setting￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- campaigns￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- dose￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Assessing￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- catch-up￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨A conjugate￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- modelling￨L￨NN￨O￨- study￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- PCV10￨U￨NN￨O￨- introduction￨L￨NN￨O￨- in￨L￨IN￨O￨- Kilifi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- KenyaStefan￨U￨NNP￨O￨- Flasche1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- John￨U￨NNP￨PERSON￨- Ojal1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Olivier￨U￨NNP￨PERSON￨- Le￨U￨NNP￨PERSON￨- Polain￨U￨NNP￨PERSON￨- de￨L￨IN￨O￨- Waroux1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Mark￨U￨NNP￨PERSON￨- Otiende2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Katherine￨U￨NNP￨PERSON￨- L.￨U￨NNP￨PERSON￨- 2017Received￨L￨NNP￨PERSON￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organisation￨U￨NNP￨ORGANIZATION￨- recommends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- catch-up￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨- conjugate￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PCVs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- accelerate￨L￨VB￨O￨- herd￨L￨NN￨O￨- protection￨L￨NN￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- PCV￨U￨NN￨O￨- impact￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- within￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- introduction￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- catch-up￨L￨NN￨O￨- campaign￨L￨NN￨O￨A among￨L￨IN￨O￨- children￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- prevents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- 65￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 48￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 84￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- IPD￨U￨NN￨O￨- cases￨L￨NNS￨O￨- across￨L￨IN￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- PCV￨U￨NN￨O￨- cohort￨L￨NN￨O￨- introduction￨L￨NN￨O￨- alone￨L￨RB￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- In￨U￨IN￨O￨- Kilifi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Kenya￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- PCV10￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- three-dose￨L￨JJ￨O￨- Expanded￨U￨NNP￨O￨- Programme￨U￨NNP￨O￨- on￨L￨IN￨O￨- Immunisation￨U￨NNP￨O￨- infant￨L￨NN￨O￨- schedule￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- catch-up￨L￨NN￨O￨- campaign￨L￨NN￨O￨A in￨L￨IN￨O￨- children￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bat￨L￨NN￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- EV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- birth￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- death￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- competition￨L￨NN￨O￨- for￨L￨IN￨O￨- resources￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- K￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- EV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- retrieval￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- state￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- recovery￨L￨NN￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- rate￨L￨NN￨O￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- Methods￨U￨NNS￨O￨- section￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- and￨L￨CC￨O￨- characterize￨L￨VBP￨O￨- theoretically￨L￨RB￨O￨A an￨L￨DT￨O￨- Ebola￨U￨NN￨MISC￨- zoonotic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bat￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- bats￨L￨NNS￨O￨- population￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- resources￨L￨NNS￨O￨A represented￨L￨VBD￨O￨- effectively￨L￨RB￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- K￨U￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- likewise￨L￨RB￨O￨- ,￨L￨,￨O￨- those￨L￨DT￨O￨- resources￨L￨NNS￨O￨- conditions￨L￨NNS￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bats￨L￨NNS￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- hypothesis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- filovirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- bats￨L￨NNS￨O￨- :￨L￨:￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- older￨L￨JJR￨O￨- juveniles￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- bats￨L￨NNS￨O￨- can￨L￨MD￨O￨- survive￨L￨VB￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- has￨L￨VBZ￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- immunization￨L￨NN￨O￨- with￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨A conjugate￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- which￨L￨WDT￨O￨- protection￨L￨NN￨O￨- applies￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- to￨L￨TO￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity.The￨L￨NN￨O￨- first￨L￨JJ￨ORDINAL￨- licensed￨L￨JJ￨O￨- multivalent￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨- conjugate￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PCV7￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- confers￨L￨VBZ￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- 7￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- >￨L￨JJR￨O￨- 90￨L￨CD￨NUMBER￨- pneumococcal￨L￨JJ￨O￨- capsular￨L￨JJ￨O￨- serotypes3￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- against￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6B￨L￨NN￨O￨- ,￨L￨,￨O￨- 9V￨L￨NN￨O￨- ,￨L￨,￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 18C￨L￨NN￨O￨- ,￨L￨,￨O￨- 19F￨L￨NN￨O￨- and￨L￨CC￨O￨- 23F￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- eliciting￨L￨VBG￨O￨- anti-capsular￨L￨JJ￨O￨- antibodies4￨L￨NN￨O￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Geographic￨U￨NNP￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨A vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- post-PCV7￨L￨JJ￨O￨- Erida￨U￨NNP￨O￨- Gjini￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 3049￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- Bacterial￨U￨JJ￨O￨- infectionStatistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- AbstractAlthough￨U￨NNP￨O￨- mean￨L￨VB￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- multivalent￨L￨JJ￨O￨- pneumococcus￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- intensively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- ,￨L￨,￨O￨- variance￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- VE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- overlooked￨L￨VBN￨O￨- .￨L￨.￨O￨- +Model￨U￨NNP￨TITLE￨- fitting￨L￨JJ￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- dataset￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- site-specific￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- against￨L￨IN￨O￨- acquisition￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- pneumococcal￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- early￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- PCV77￨U￨NN￨O￨- ,8,9,10￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- protective￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- pneumococcal￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- became￨L￨VBD￨O￨- clear￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- colonization￨L￨NN￨O￨- by￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- serotypes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- VT￨U￨NN￨STATE_OR_PROVINCE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- their￨L￨PRP$￨O￨- associated￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- An￨U￨DT￨O￨- Immunization￨U￨NN￨O￨- Strategy￨U￨NN￨O￨- for￨L￨IN￨O￨- Hidden￨U￨NNP￨O￨- Populations￨U￨NNP￨O￨- Saran￨U￨NNP￨O￨- Chen1￨U￨NN￨O￨- na1￨L￨NN￨O￨- &￨L￨CC￨O￨- Xin￨U￨NNP￨O￨- Lu1￨U￨NN￨O￨- ,2,3,4￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 3268￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksEpidemiology￨L￨NN￨O￨- AbstractHidden￨U￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- injecting￨L￨VBG￨O￨- drug￨L￨NN￨O￨- users￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IDUs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- sex￨L￨NN￨O￨- workers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SWs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- men￨L￨NNS￨O￨A who￨L￨WP￨O￨- have￨L￨VBP￨O￨- sex￨L￨NN￨O￨- with￨L￨IN￨O￨- men￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MSM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- at￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- contracting￨L￨NN￨O￨- and￨L￨CC￨O￨- transmitting￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- gonorrhea￨L￨NN￨O￨- ,￨L￨,￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- etc￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- RDS￨U￨NN￨O￨- sampling￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- cost-efficient￨L￨JJ￨O￨- and￨L￨CC￨O￨- feasible￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- intervention￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- for￨L￨IN￨O￨- hidden￨L￨JJ￨O￨A populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- an￨L￨DT￨O￨- innovative￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- sampling￨L￨NN￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- hidden￨L￨JJ￨O￨A populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- Respondent-driven￨U￨JJ￨O￨- Sampling￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- RDS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- RDS￨U￨NN￨O￨- strategy￨L￨NN￨O￨A is￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- steps￨L￨NNS￨O￨- :￨L￨:￨O￨- First￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- RDS￨U￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- degree￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- personal￨L￨JJ￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- sample￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- on￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- reveal￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- RDS￨U￨NN￨O￨- strategy￨L￨NN￨O￨A is￨L￨VBZ￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- There￨U￨EX￨O￨- was￨L￨VBD￨O￨- no￨L￨DT￨O￨- intervention￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- used￨L￨VBN￨O￨- here￨L￨RB￨O￨- provide￨L￨VBP￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- conditions￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- MERS￨U￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Estimation￨U￨NN￨MISC￨- of￨L￨IN￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Middle￨U￨NNP￨LOCATION￨- East￨U￨NNP￨LOCATION￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨A coronavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MERS-CoV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- Hyuk-Jun￨U￨NNP￨O￨- Chang1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 16:79￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- In￨U￨IN￨O￨- South￨U￨NNP￨COUNTRY￨- Korea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- Middle￨U￨NNP￨LOCATION￨- East￨U￨NNP￨LOCATION￨- respiratory￨L￨JJ￨O￨- syndrome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MERS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- estimates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- MERS￨U￨NN￨O￨- coronavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CoV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- MERS￨U￨NNS￨O￨- in￨L￨IN￨O￨- South￨U￨NNP￨COUNTRY￨- Korea￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- South￨U￨NNP￨COUNTRY￨- Korea￨U￨NNP￨COUNTRY￨- MERS￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- uses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ODEs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- fit￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- South￨U￨NNP￨COUNTRY￨- Korea￨U￨NNP￨COUNTRY￨- outbreak￨L￨NN￨O￨A minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- squared￨L￨VBN￨O￨- errors￨L￨NNS￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Economic￨U￨NNP￨O￨- evaluations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- conducted￨L￨VBN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- ways￨L￨NNS￨O￨- :￨L￨:￨O￨- by￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- burden￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- by￨L￨IN￨O￨- aggregating￨L￨VBG￨O￨- influenza-and￨L￨JJ￨O￨- intervention-associated￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- calculating￨L￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- intervention￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A .￨L￨.￨O￨- +Emphasizing￨U￨VBG￨O￨- the￨L￨DT￨O￨- adequacy￨L￨NN￨O￨- of￨L￨IN￨O￨- hospital-resource￨L￨NN￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- allows￨L￨VBZ￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- community￨L￨NN￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨- pandemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- ensure￨L￨VB￨O￨- hospital￨L￨NN￨O￨A resource￨L￨NN￨O￨- adequacy￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- estimates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- upon￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- representative￨L￨JJ￨TITLE￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- municipality￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- closely￨L￨RB￨O￨- resemble￨L￨VBP￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- from￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- Ontario￨U￨NNP￨STATE_OR_PROVINCE￨- cities￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +InFluNet￨U￨NNP￨O￨- combines￨L￨VBZ￨O￨- demographic￨L￨JJ￨O￨- ,￨L￨,￨O￨- hospital￨L￨NN￨O￨A and￨L￨CC￨O￨- intervention￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- under￨L￨IN￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- suggest￨L￨VBP￨O￨- new￨L￨JJ￨O￨- marker￨L￨NN￨TITLE￨- VRTP￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- on￨L￨IN￨O￨- turning￨L￨VBG￨O￨- point￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Scale-free￨U￨JJ￨MISC￨- (￨L￨-LRB-￨O￨- SF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- observe￨L￨VBP￨O￨- the￨L￨DT￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨- effects￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +Volume￨U￨NN￨O￨- 18￨L￨CD￨NUMBER￨A Supplement￨U￨NN￨O￨- 7￨L￨CD￨NUMBER￨- Proceedings￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Tenth￨U￨NNP￨ORDINAL￨- International￨U￨NNP￨O￨- Workshop￨U￨NNP￨O￨- on￨L￨IN￨O￨- Data￨U￨NNP￨O￨- and￨L￨CC￨O￨- Text￨U￨VB￨O￨- Mining￨U￨NN￨O￨- in￨L￨IN￨O￨- Biomedical￨U￨NNP￨MISC￨- Informatics￨U￨NNP￨MISC￨- Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Coupling￨U￨NN￨MISC￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- turning￨L￨VBG￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networksKiseong￨L￨NN￨O￨- Kim1￨U￨NN￨O￨- ,￨L￨,￨O￨- Sangyeon￨U￨NN￨O￨- Lee1￨U￨NN￨O￨- ,￨L￨,￨O￨- Doheon￨U￨NN￨O￨- Lee1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Kwang￨U￨NNP￨PERSON￨- Hyung￨U￨NNP￨PERSON￨- Lee1Email￨U￨NN￨O￨- authorBMC￨L￨NN￨O￨- BioinformaticsBMC￨U￨NN￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Suppl￨U￨NN￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- 250￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- spreading￨L￨NN￨O￨A phenomenon￨L￨NN￨O￨- simulator￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- input￨L￨NN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- performed￨L￨VBD￨O￨- the￨L￨DT￨O￨- experiment￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Susceptible-Infective-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- spreading￨L￨VBG￨O￨A phenomena￨L￨NNS￨O￨- using￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- spreading￨L￨VBG￨O￨- factors￨L￨NNS￨O￨- ;￨L￨:￨O￨- contagiousness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- induced￨L￨VBD￨O￨- the￨L￨DT￨O￨- VRTP￨U￨NNP￨O￨- formula￨L￨NN￨O￨A for￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- exploiting￨L￨VBG￨O￨- such￨L￨JJ￨O￨- time-of-arrival￨L￨JJ￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- taking￨L￨VBG￨O￨- place￨L￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- partially￨L￨RB￨O￨- because￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨A interactions￨L￨NNS￨O￨- serve￨L￨VBP￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- for￨L￨IN￨O￨- material￨L￨NN￨O￨- or￨L￨CC￨O￨- information￨L￨NN￨O￨- exchange￨L￨NN￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- cultural￨L￨JJ￨O￨- fads￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proliferation￨L￨NN￨O￨- of￨L￨IN￨O￨- innovative￨L￨JJ￨O￨- ideas￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- review28￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Towards￨U￨IN￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- null￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- procedure￨L￨NN￨O￨- for￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- data-driven￨L￨JJ￨O￨- fashion￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- conceive￨L￨VBP￨O￨- the￨L￨DT￨O￨- STN￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- convenient￨L￨JJ￨O￨- descriptive￨L￨JJ￨O￨- device￨L￨NN￨O￨- for￨L￨IN￨O￨- explaining￨L￨VBG￨O￨- time-course￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- diffusion￨L￨NN￨O￨- processes￨L￨NNS￨O￨- thereon￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- carry￨L￨VBP￨O￨- out￨L￨RP￨O￨- extensive￨L￨JJ￨O￨- benchmark￨L￨NN￨O￨- tests￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- to￨L￨TO￨O￨- validate￨L￨VB￨O￨- the￨L￨DT￨O￨- reconstruction￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- restrict￨L￨VBP￨O￨- on￨L￨IN￨O￨- reconstructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- STNs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- —￨L￨:￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- generally￨L￨RB￨O￨- taken￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- null￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- preserving￨L￨VBG￨O￨- temporal￨L￨JJ￨O￨- statistics￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- dyads￨L￨NNS￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- but￨L￨CC￨O￨- ignoring￨L￨VBG￨O￨- higher-order￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- across￨L￨IN￨O￨- them15￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- STN￨U￨NN￨O￨- builds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- time-aggregated￨L￨JJ￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- extra￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨A dimension￨L￨NN￨O￨- by￨L￨IN￨O￨- assigning￨L￨VBG￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- link￨L￨NN￨O￨- a￨L￨DT￨O￨- mutually￨L￨RB￨O￨- independent￨L￨JJ￨RELIGION￨- random￨L￨JJ￨O￨- IET￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- denoting￨L￨VBG￨O￨- the￨L￨DT￨O￨- interval￨L￨NN￨O￨- of￨L￨IN￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- events￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- renewal￨L￨NN￨O￨- manner29￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- later￨L￨RB￨O￨- on￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- fundamentally￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- learn￨L￨VB￨O￨- latent￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- discovering￨L￨VBG￨O￨- both￨L￨CC￨O￨- structural￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨A regularities￨L￨NNS￨O￨- in￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- prominence￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- fields￨L￨NNS￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- biology￨L￨NN￨O￨- to￨L￨TO￨O￨- smart￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- ,￨L￨,￨O￨- Bayesian￨U￨JJ￨O￨- inference￨L￨NN￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- challenging￨L￨JJ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- these￨L￨DT￨O￨- are￨L￨VBP￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- discrete￨L￨JJ￨O￨- state￨L￨NN￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- potentially￨L￨RB￨O￨- infinite￨L￨JJ￨O￨A state-space￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- pseudo-marginal￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- algorithms￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- truncation￨L￨NN￨O￨- method￨L￨NN￨O￨- which￨L￨WDT￨O￨- enables￨L￨VBZ￨O￨- a￨L￨DT￨O￨- principled￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- infinite￨L￨JJ￨O￨A state￨L￨NN￨O￨- spaces￨L￨NNS￨O￨- .￨L￨.￨O￨- +Of￨U￨IN￨O￨- particular￨L￨JJ￨O￨- relevance￨L￨NN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- are￨L￨VBP￨O￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- state-space￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organised￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- population￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- Jump￨U￨NNP￨O￨- Processes￨U￨NNP￨O￨- ,￨L￨,￨O￨- pMJP￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨A label￨L￨NN￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- counts￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- entities￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- species￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- efficient￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- joint￨L￨JJ￨O￨- state/parameter￨L￨NN￨O￨- posterior￨L￨NN￨O￨- sampling￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- Jump￨U￨NNP￨O￨- processes￨L￨NNS￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Capasso￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Serio12￨U￨NN￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- into￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- saturation￨L￨NN￨O￨- level￨L￨NN￨O￨- when￨L￨WRB￨O￨- I￨U￨PRP￨O￨- gets￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- Equality￨U￨FW￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- alpha￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- βI￨L￨NN￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- tfrac￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- alpha￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- inhibition￨L￨NN￨O￨- effect￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- when￨L￨WRB￨O￨- their￨L￨PRP$￨O￨- number￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- crowding￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- note￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨- Qixing￨U￨VBG￨O￨- Han1￨U￨NN￨O￨- ,￨L￨,￨O￨- Liang￨U￨NNP￨PERSON￨- Chen2￨U￨NNP￨O￨- &￨L￨CC￨O￨- Daqing￨U￨NNP￨O￨- Jiang3￨U￨NN￨O￨- ,4￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 3996￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsInfectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- AbstractThe￨U￨NNP￨O￨- stochastic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- and￨L￨CC￨O￨- summarized￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- Define￨U￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨A is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- SEIR￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-infected-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- SEIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- investigated￨L￨VBN￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- researchers7￨L￨JJ￨O￨- ,8,9￨L￨NN￨O￨- .￨L￨.￨O￨- +Investigating￨U￨VBG￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- weather￨L￨NN￨O￨- and￨L￨CC￨O￨- climate￨L￨NN￨O￨A on￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- requires￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- disentangle￨L￨VB￨O￨- concurrent￨L￨JJ￨O￨- modes￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmissions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- environmental￨L￨JJ￨O￨- from￨L￨IN￨O￨- human-to-human￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- tease￨L￨VB￨O￨- apart￨L￨RB￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- exposures￨L￨NNS￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- ;￨L￨:￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- identify￨L￨VB￨O￨- and￨L￨CC￨O￨- separate￨L￨JJ￨O￨- socio-economic￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- and￨L￨CC￨O￨- behavioural￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- ;￨L￨:￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- integrate￨L￨VB￨O￨- all￨L￨PDT￨O￨- these￨L￨DT￨O￨- different￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- unified￨L￨VBN￨O￨- perspective￨L￨NN￨O￨- ;￨L￨:￨O￨- v￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- attribute￨L￨NN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- observed￨L￨VBN￨O￨- environmental￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- vi￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- quantify￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- social￨L￨JJ￨O￨- ,￨L￨,￨O￨- economic￨L￨JJ￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- project￨L￨VB￨O￨- the￨L￨DT￨DATE￨- future￨L￨JJ￨DATE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- changes￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exposure￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- directly￨L￨RB￨O￨- or￨L￨CC￨O￨- indirectly￨L￨RB￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- meteorological/climate￨L￨NN￨O￨- variables￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- high￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- drinking￨L￨NN￨O￨- contaminated￨L￨VBN￨O￨- water￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- poor￨L￨JJ￨O￨- water￨L￨NN￨O￨- drainage￨L￨NN￨O￨- management￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- land￨L￨VB￨O￨- use￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- behavioural￨L￨NN￨O￨- and/or￨L￨CC￨O￨- socio-economic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- recreational￨L￨JJ￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- unclean￨L￨JJ￨O￨- water￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Infectious￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- water￨L￨NN￨O￨A are￨L￨VBP￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- “￨L￨``￨O￨- water-system-related￨L￨JJ￨O￨- ”￨L￨''￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- via￨L￨IN￨O￨- aerosols￨L￨NNS￨O￨- from￨L￨IN￨O￨- poorly￨L￨RB￨O￨- managed￨L￨VBN￨O￨- cooling￨L￨VBG￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- Legionellosis￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- water-based￨L￨JJ￨O￨- ”￨L￨''￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- via￨L￨IN￨O￨- aquatic￨L￨JJ￨O￨- vectors￨L￨NNS￨O￨- or￨L￨CC￨O￨- intermediate￨L￨JJ￨O￨- in￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- Schistosomiasis￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- water-borne￨L￨JJ￨O￨- ”￨L￨''￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- via￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- ,￨L￨,￨O￨- parasitic￨L￨JJ￨O￨- and￨L￨CC￨O￨- viral￨L￨JJ￨O￨- oral-faecal￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- ingestion￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- “￨L￨``￨O￨- water-washed￨L￨JJ￨O￨- ”￨L￨''￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- poor￨L￨JJ￨O￨- hygiene￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- insufficient￨L￨JJ￨O￨- water￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- include￨L￨VB￨O￨- oral-faecal￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- hookworm￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- particularly￨L￨RB￨O￨- important￨L￨JJ￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- water￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- those￨L￨DT￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- neglected￨L￨VBN￨O￨- tropical￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- NTD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organisation￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨ORGANIZATION￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- journal￨L￨NN￨O￨- Plos￨U￨NNP￨O￨- NTD￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- recently￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- estimated￨L￨VBD￨O￨- that￨L￨IN￨O￨- leptospirosis￨L￨NN￨O￨- causes￨L￨VBZ￨O￨A 1.03￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- 58,900￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- placing￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- leading￨L￨VBG￨O￨- zoonotic￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- of￨L￨IN￨O￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- in￨L￨IN￨O￨- Central￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- have￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- environmental￨L￨JJ￨O￨- and￨L￨CC￨O￨- socioeconomic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- increase￨L￨VBP￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- leptospirosis￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- volcanic￨L￨JJ￨O￨- origin￨L￨NN￨O￨- soil￨L￨NN￨O￨- ,￨L￨,￨O￨- precipitation￨L￨NN￨O￨- ,￨L￨,￨O￨- higher￨L￨JJR￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- rural￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- greater￨L￨JJR￨O￨- unsatisfied￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- needs￨L￨NNS￨O￨- for￨L￨IN￨O￨- improved￨L￨JJ￨O￨- housing￨L￨NN￨O￨- and￨L￨CC￨O￨- sanitary￨L￨JJ￨O￨- services￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- extreme￨L￨JJ￨O￨A poverty￨L￨NN￨O￨- and￨L￨CC￨O￨- higher￨L￨JJR￨O￨- illiteracy￨L￨NN￨O￨- rates￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Mass￨U￨JJ￨STATE_OR_PROVINCE￨- chemoprophylaxis￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- after￨L￨IN￨O￨- leptospirosis￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- following￨L￨VBG￨O￨- floods￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- or￨L￨CC￨O￨- during￨L￨IN￨O￨- water-sports￨L￨JJ￨O￨- events￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- Latin￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- preventive￨L￨JJ￨O￨- measure￨L￨NN￨O￨- in￨L￨IN￨O￨- high-risk￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- facilities￨L￨NNS￨O￨- was￨L￨VBD￨O￨- difficult￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Rain￨U￨NN￨O￨- and￨L￨CC￨O￨- floods￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- primary￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- for￨L￨IN￨O￨- leptospirosis￨L￨NN￨O￨- and￨L￨CC￨O￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- reported￨L￨VBN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- following￨L￨VBG￨O￨- extreme￨L￨JJ￨O￨A weather￨L￨NN￨O￨- events￨L￨NNS￨O￨- in￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- locales￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Guyana￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Italy￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- New￨U￨NNP￨LOCATION￨- Caledonia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Nicaragua￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Philippines￨U￨NNPS￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- Central￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- have￨L￨VB￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- leptospirosis￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- being￨L￨VBG￨O￨- developing￨L￨VBG￨O￨- activities￨L￨NNS￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- and￨L￨CC￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- highlights￨L￨VBZ￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- of￨L￨IN￨O￨- antibody￨L￨NN￨O￨A loss￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- could￨L￨MD￨O￨- bias￨L￨NN￨O￨- our￨L￨PRP$￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- critical￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- management￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- serological￨L￨JJ￨O￨- data.KeywordsAntibody￨L￨JJ￨O￨- loss￨L￨NN￨O￨- Approximate￨U￨NNP￨O￨- Bayesian￨U￨NNP￨O￨- computation￨L￨NN￨O￨- Brucellosis￨U￨NNP￨O￨- Greater￨U￨NNP￨O￨- Yellowstone￨U￨NNP￨O￨- Ecosystem￨U￨NNP￨O￨- Basic￨U￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Serology￨U￨NNP￨O￨- Electronic￨U￨NNP￨O￨- supplementary￨L￨JJ￨O￨- materialThe￨L￨NN￨O￨- online￨L￨NN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- doi￨L￨FW￨O￨- :￨L￨:￨O￨- 10.1007￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- s10393-017-1235-z￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- contains￨L￨VBZ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- authorized￨L￨VBN￨O￨- users.IntroductionMany￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- monitoring￨L￨NN￨O￨- programs￨L￨NNS￨O￨- in￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- rely￨L￨VBP￨O￨- on￨L￨IN￨O￨- serology￨L￨NN￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- analyses￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- played￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- 's￨L￨POS￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- Network￨U￨NNP￨O￨- analysis￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- potential￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- identifying￨L￨VBG￨O￨- central￨L￨JJ￨O￨- and/or￨L￨CC￨O￨- highly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- holdings￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- nodes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨A movements￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- arcs￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- herd￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- inter-herd￨L￨JJ￨O￨- spread￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- area￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- primarily￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- animal￨L￨JJ￨O￨A contacts￨L￨NNS￨O￨- at￨L￨IN￨O￨- pastures￨L￨NNS￨O￨- or￨L￨CC￨O￨- through￨L￨IN￨O￨- animal￨L￨NN￨O￨- movements￨L￨NNS￨O￨- between￨L￨IN￨O￨- herds￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- planning￨L￨VBG￨O￨- and￨L￨CC￨O￨- defining￨L￨VBG￨O￨- prevention￨L￨NN￨O￨- activities￨L￨NNS￨O￨- but￨L￨CC￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- of￨L￨IN￨O￨- limited￨L￨JJ￨O￨- or￨L￨CC￨O￨- no￨L￨DT￨O￨- value￨L￨NN￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- already￨L￨RB￨O￨- spread￨L￨VBN￨O￨A ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- that￨L￨DT￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- scenario￨L￨NN￨O￨- of￨L￨IN￨O￨- brucellosis￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- grouped￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- are￨L￨VBP￨O￨- embedded￨L￨VBN￨O￨- in￨L￨IN￨O￨- animal￨L￨NN￨O￨A movement￨L￨NN￨O￨- networks￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 15,16￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- classical￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vital￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨A I￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- N￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- above￨L￨IN￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- inflow￨L￨NN￨O￨- of￨L￨IN￨O￨- newborns￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- μN￨L￨NN￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- classes￨L￨NNS￨O￨- at￨L￨IN￨O￨- rates￨L￨NNS￨O￨- μN￨L￨NN￨O￨- ,￨L￨,￨O￨- μI￨L￨NN￨O￨- and￨L￨CC￨O￨- μR￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- continuous-time￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Schröding-prey￨U￨JJ￨MISC￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨A I￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Equality￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨A mu￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- times￨L￨NNS￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- death-adjusted￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Guckenheimer￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Holmes￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- examined￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- non-monotonic￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- also￨L￨RB￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- derived￨L￨VBD￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +Robinson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Holmes￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- discussed￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Schrödinger-prey￨U￨JJ￨MISC￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- undergoes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- flip￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨A and￨L￨CC￨O￨- a￨L￨DT￨O￨- Hopf￨U￨NNP￨O￨- bifurcation￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- center￨L￨NN￨O￨- manifold￨L￨NN￨O￨- theorem￨L￨NN￨O￨- and￨L￨CC￨O￨- bifurcation￨L￨NN￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- present￨L￨VB￨DATE￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- integrated￨L￨VBN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- electronically￨L￨RB￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- in￨L￨IN￨O￨- local￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Western￨U￨JJ￨MISC￨- hemisphere￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- its￨L￨PRP$￨O￨- performance￨L￨NN￨O￨- by￨L￨IN￨O￨- retrospective￨L￨JJ￨O￨- application￨L￨NN￨O￨- on￨L￨IN￨O￨- authentic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- Swedish￨U￨JJ￨NATIONALITY￨- county￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- need￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- adapted￨L￨VBD￨O￨- to￨L￨TO￨O￨- extensive￨L￨JJ￨O￨- but￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- extends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- algorithms￨L￨NNS￨O￨- for￨L￨IN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- winter￨L￨NN￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- seasons￨L￨NNS￨O￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- novel￨L￨JJ￨O￨- method￨L￨NN￨O￨- was￨L￨VBD￨O￨- formally￨L￨RB￨O￨- defined￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- design￨L￨NN￨O￨- rationale￨L￨NN￨O￨- for￨L￨IN￨O￨- integrated￨L￨VBN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨A methods￨L￨NNS￨O￨- specifically￨L￨RB￨O￨- adapted￨L￨VBD￨O￨- for￨L￨IN￨O￨- application￨L￨NN￨O￨- in￨L￨IN￨O￨- local￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- presentation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- integrated￨L￨VBN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨A method￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- summary￨L￨NN￨O￨- label￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- winter￨L￨NN￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- seasons￨L￨NNS￨O￨- and￨L￨CC￨O￨- pandemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- knowledge￨L￨NN￨O￨- need￨L￨NN￨O￨- presently￨L￨RB￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- immediate￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- at￨L￨IN￨O￨- local￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Newborn￨U￨JJ￨O￨- infants￨L￨NNS￨O￨- are￨L￨VBP￨O￨- typically￨L￨RB￨O￨- protected￨L￨VBN￨O￨- from￨L￨IN￨O￨- RSV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- maternal￨L￨JJ￨O￨- antibodies￨L￨NNS￨O￨- until￨L￨IN￨O￨- about￨L￨IN￨DURATION￨- six￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨A of￨L￨IN￨O￨- age￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- RSV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- six￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- six￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Few￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- used￨L￨VBN￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- vaccination￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- RSV￨U￨NN￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- have￨L￨VBP￨O￨- generally￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- RSV￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- perspective￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- newborn￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Spanish￨U￨JJ￨NATIONALITY￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- Valencia￨U￨NNP￨CITY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- RSV￨U￨NN￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- entering￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- temporarily￨L￨RB￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- currently￨L￨RB￨DATE￨- no￨L￨DT￨O￨- licensed￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- RSV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- about￨L￨IN￨DURATION￨- 50￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- research￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- RSV￨U￨NN￨MISC￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- age￨L￨NN￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨O￨- A￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- SNPs￨U￨NNS￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseaseFloor￨L￨NN￨O￨- Biemans1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Mart￨U￨NNP￨ORGANIZATION￨- C.￨U￨NNP￨ORGANIZATION￨- Selection￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- breeding￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- desirable￨L￨JJ￨O￨- traits￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- fight￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- genetic￨L￨JJ￨O￨A )￨L￨-RRB-￨O￨- traits￨L￨NNS￨O￨- :￨L￨:￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +Quantitative￨U￨JJ￨O￨- genetic￨L￨JJ￨O￨A studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- generally￨L￨RB￨O￨- connect￨L￨VBP￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- genotype￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- capture￨L￨NN￨O￨- genetic￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- set￨L￨VBD￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- single￨L￨JJ￨O￨- nucleotide￨L￨NN￨O￨- polymorphisms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SNPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- usually￨L￨RB￨O￨- ignore￨L￨VBP￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- herd￨L￨NN￨O￨- mates￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- limit￨L￨VB￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Optimizing￨U￨NNP￨O￨- sentinel￨L￨NN￨O￨- surveillance￨L￨NN￨O￨A in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- Yuan￨U￨NN￨O￨- Bai1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Bo￨U￨NNP￨PERSON￨- Yang￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Lijuan￨U￨NNP￨PERSON￨- Lin1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jose￨U￨NNP￨PERSON￨- L.￨U￨NNP￨PERSON￨- Herrera3￨U￨NNP￨PERSON￨- ,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Zhanwei￨U￨NNP￨ORGANIZATION￨- Du3￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Petter￨U￨NNP￨ORGANIZATION￨- Holme5￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 4804￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksNetwork￨L￨NN￨O￨- topology￨L￨NN￨O￨- AbstractTo￨U￨NN￨O￨- help￨L￨NN￨O￨- health￨L￨NN￨O￨- policy￨L￨NN￨O￨- makers￨L￨NNS￨O￨- gain￨L￨NN￨O￨- response￨L￨NN￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- threats￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- early￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- calculate￨L￨VBP￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- difference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- lead￨L￨NN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- surveillance￨L￨NN￨O￨A set￨L￨NN￨O￨- and￨L￨CC￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- reaching￨L￨VBG￨O￨- 1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- have￨L￨VBP￨O￨- addressed￨L￨VBN￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- designing￨L￨VBG￨O￨- surveillance￨L￨NN￨O￨A systems￨L￨NNS￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- common￨L￨JJ￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨A is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- carefully￨L￨RB￨O￨- select￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- sentinels￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- sensors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- report￨L￨VB￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- coupled￨L￨JJ￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- unifies￨L￨VBZ￨O￨- both￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- enabling￨L￨VBG￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vector￨L￨NN￨O￨A population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Agent-based￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- take￨L￨VBP￨O￨- almost￨L￨RB￨O￨- the￨L￨DT￨O￨- opposite￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- generalisations￨L￨NNS￨O￨- mentioned￨L￨VBN￨O￨- above￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- simulate￨L￨VBP￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- ‘￨L￨``￨O￨- agent￨L￨NN￨O￨- ’￨L￨''￨O￨- -￨L￨:￨O￨- )￨L￨-RRB-￨O￨- level￨L￨NN￨O￨- processes￨L￨VBZ￨O￨- occurring￨L￨VBG￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- try￨L￨VB￨O￨- to￨L￨TO￨O￨- calibrate￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- matching￨L￨VBG￨O￨- the￨L￨DT￨O￨- aggregate￨L￨NN￨O￨- behaviour￨L￨NN￨O￨A to￨L￨TO￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- behaviour￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- infectious￨L￨JJ￨O￨- ’￨L￨''￨O￨- compartment￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- individuals￨L￨NNS￨O￨- taking￨L￨VBG￨O￨- part￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- it￨L￨PRP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ‘￨L￨``￨O￨- recovered￨L￨VBN￨O￨- ’￨L￨''￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- no￨L￨RB￨O￨- longer￨L￨RB￨O￨- influencing￨L￨VBG￨O￨- others￨L￨NNS￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- part￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨A modify￨L￨VB￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- changing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- move￨L￨VBP￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- .￨L￨.￨O￨- +established￨L￨VBN￨O￨A a￨L￨DT￨O￨- Susceptible-Exposed-Infectious-Quarantined-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIQR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- R0￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- HFMD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- mainland￨L￨NN￨O￨- China￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +established￨L￨VBN￨O￨A a￨L￨DT￨O￨- Susceptible-Exposed-Infectious-Recovered￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- among￨L￨IN￨O￨- young￨L￨JJ￨O￨- children￨L￨NNS￨O￨- in￨L￨IN￨O￨- Khulna￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Bangladesh￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Also￨U￨RB￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- threshold￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HIT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- needed￨L￨VBD￨O￨- to￨L￨TO￨O￨- stop￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- communicable￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Dynamic￨U￨NNP￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- contributed￨L￨VBN￨O￨A greatly￨L￨RB￨O￨- to￨L￨TO￨O￨- estimating￨L￨VBG￨O￨- R0￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +R0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- expected￨L￨VBN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨A case￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- The￨U￨DT￨O￨- switch￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- nine-valent￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- in￨L￨IN￨O￨- Italy￨U￨NNP￨COUNTRY￨- can￨L￨MD￨O￨- further￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- HPV-related￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- cost-effective￨L￨JJ￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Compared￨U￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- with￨L￨IN￨O￨- quadrivalent￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- nine-valent￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- programme￨L￨NN￨O￨- including￨L￨VBG￨O￨- girls￨L￨NNS￨O￨- and￨L￨CC￨O￨- boys￨L￨NNS￨O￨- shows￨L￨VBZ￨O￨- further￨L￨RB￨O￨- reductions￨L￨NNS￨O￨- of￨L￨IN￨O￨- 17￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- 35￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 14￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- anal￨L￨JJ￨O￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- males￨L￨NNS￨O￨- and￨L￨CC￨O￨- females￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- million￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- genital￨L￨JJ￨O￨- warts￨L￨NNS￨O￨- avoided￨L￨VBN￨O￨- after￨L￨IN￨O￨- 100￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Cost-effectiveness￨U￨NN￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nine-valent￨L￨JJ￨O￨- HPV￨U￨NN￨O￨- vaccine￨L￨NN￨O￨A in￨L￨IN￨O￨- ItalyFrancesco￨U￨NNP￨O￨- Saverio￨U￨NNP￨O￨- Mennini1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Paolo￨U￨NNP￨PERSON￨- Bonanni3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Florence￨U￨NNP￨CITY￨- Bianic4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Chiara￨U￨NNP￨PERSON￨- de￨L￨IN￨PERSON￨- Waure5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Gianluca￨U￨NNP￨PERSON￨- Baio6￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Giacomo￨U￨NNP￨PERSON￨- Plazzotta7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Mathieu￨U￨NNP￨PERSON￨- Uhart8Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Alessandro￨U￨NNP￨PERSON￨- Rinaldi9￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Nathalie￨U￨NNP￨PERSON￨- Largeron8￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 15:11￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- In￨U￨IN￨O￨- Italy￨U￨NNP￨COUNTRY￨- HPV￨U￨NNP￨O￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- quadrivalent￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Gardasil￨U￨NNP￨ORGANIZATION￨- ®￨L￨NNP￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- offered￨L￨VBN￨O￨- actively￨L￨RB￨O￨- and￨L￨CC￨O￨- free￨L￨JJ￨O￨- of￨L￨IN￨O￨- charge￨L￨NN￨O￨- to￨L￨TO￨O￨- girls￨L￨NNS￨O￨- aged￨L￨VBN￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- illustration￨L￨NN￨O￨- is￨L￨VBZ￨O￨- from￨L￨IN￨O￨- Castillo-Chavez￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Yakubu￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- built￨L￨VBD￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dispersal￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- among￨L￨IN￨O￨- patches￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- answer￨L￨VB￨O￨A questions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- used￨L￨VBD￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- on￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ODEs￨U￨NNS￨O￨- :￨L￨:￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- sanitation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- provision￨L￨NN￨O￨- of￨L￨IN￨O￨- clean￨L￨JJ￨O￨- water￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- analysed￨L￨VBN￨O￨- ,￨L￨,￨O￨- comparing￨L￨VBG￨O￨- preemptive￨L￨JJ￨O￨- to￨L￨TO￨O￨- responsive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Vaccinations￨U￨NNS￨O￨- are￨L￨VBP￨O￨- currently￨L￨RB￨DATE￨- being￨L￨VBG￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- intervention￨L￨NN￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- in￨L￨IN￨O￨- Haiti￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- extended￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Tien￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Earn￨U￨VB￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- a￨L￨DT￨O￨- multi-patch￨L￨JJ￨O￨- structure￨L￨NN￨O￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨A movement￨L￨NN￨O￨A .￨L￨.￨O￨- +Prior￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- from￨L￨IN￨O￨- Yapp￨U￨NNP￨LOCATION￨- Island￨U￨NNP￨LOCATION￨- suggest￨L￨VBP￨O￨A that￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- asymptomatic￨L￨JJ￨O￨- or￨L￨CC￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- mild￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- initial￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- from￨L￨IN￨O￨- Latin￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- ZIKV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- less￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- and￨L￨CC￨O￨- less￨L￨RBR￨O￨- febrile￨L￨JJ￨O￨- than￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- dengue￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DENV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- described￨L￨VBD￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨A response￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Power￨U￨NN￨O￨- function￨L￨NN￨O￨- which￨L￨WDT￨O￨- described￨L￨VBD￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- said￨L￨VBD￨O￨- response￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- waves￨L￨NNS￨O￨- of￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- and￨L￨CC￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- human￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨A changes￨L￨NNS￨O￨- responding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- ,￨L￨,￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Bootsma￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ferguson￨U￨NNP￨PERSON￨- modelled￨L￨VBD￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨A responses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Hill￨U￨NNP￨O￨- function￨L￨NN￨O￨- which￨L￨WDT￨O￨- described￨L￨VBD￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- also￨L￨RB￨O￨- lacked￨L￨VBD￨O￨- a￨L￨DT￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- functions￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- behavioral￨L￨JJ￨O￨A responses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- which￨L￨WDT￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- included￨L￨VBD￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- did￨L￨VBD￨O￨A not￨L￨RB￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- fit￨L￨NN￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- gathers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- descriptive￨L￨JJ￨O￨- statistics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transportation￨L￨NN￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- rail￨L￨NN￨O￨- transit￨L￨NN￨O￨- stations￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- rail￨L￨NN￨O￨- transit￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- m￨L￨NN￨O￨- ,￨L￨,￨O￨- median￨L￨NN￨O￨- of￨L￨IN￨O￨- in-degrees￨L￨NNS￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- out-degrees￨L￨JJ￨O￨- O￨U￨NN￨O￨- ,￨L￨,￨O￨- averaged￨L￨VBD￨O￨- shortest￨L￨JJS￨O￨- path￨L￨NN￨O￨- distance￨L￨NN￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- c￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- assortativity￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- r￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- public￨L￨JJ￨O￨- transport￨L￨NN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- Beijing￨U￨NNP￨CITY￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- naturally￨L￨RB￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- unweighted￨L￨JJ￨O￨- directed￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- stations￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- directed￨L￨VBN￨O￨- edge￨L￨NN￨O￨- from￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- node￨L￨NN￨O￨- j￨L￨NN￨O￨- means￨L￨VBZ￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- route￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- station￨L￨NN￨O￨- j￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- successor￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- station￨L￨NN￨O￨- i￨L￨FW￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 250￨L￨CD￨NUMBER￨- meters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- for￨L￨IN￨O￨- short￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- Beijing￨U￨NNP￨CITY￨- public￨L￨JJ￨O￨- transport￨L￨NN￨O￨- system￨L￨NN￨O￨- ;￨L￨:￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- without￨L￨IN￨O￨- rail￨L￨NN￨O￨- transit￨L￨NN￨O￨- stations￨L￨NNS￨O￨A ;￨L￨:￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rail￨L￨NN￨O￨- transit￨L￨NN￨O￨- network￨L￨NN￨O￨- ;￨L￨:￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- randomized￨L￨VBN￨O￨- degree-preserving￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aimed￨L￨VBD￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- technique￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible￨U￨NNP￨O￨- –￨L￨:￨O￨- Infected￨U￨JJ￨O￨- –￨L￨:￨O￨- Recovered￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- elementary￨L￨JJ￨O￨A school￨L￨NN￨O￨- students￨L￨NNS￨O￨- in￨L￨IN￨O￨- Oita￨U￨NNP￨LOCATION￨- City￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- absentee￨L￨NN￨O￨- survey￨L￨NN￨O￨- was￨L￨VBD￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- decision-making￨L￨NN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨- or￨L￨CC￨O￨- school￨L￨NN￨O￨- events￨L￨NNS￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- performed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- as￨L￨IN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- A/H1N1pdm￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- elementary￨L￨JJ￨O￨A schools￨L￨NNS￨O￨- of￨L￨IN￨O￨- Oita￨U￨NNP￨LOCATION￨- City￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- aimed￨L￨VBD￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- A/H1N1pdm￨U￨NN￨O￨- pandemic￨L￨NN￨O￨- among￨L￨IN￨O￨- elementary￨L￨JJ￨O￨A school￨L￨NN￨O￨- students￨L￨NNS￨O￨- in￨L￨IN￨O￨- Oita￨U￨NNP￨LOCATION￨- City￨U￨NNP￨LOCATION￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- absentee￨L￨NN￨O￨- survey￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- survey￨L￨NN￨O￨- ,￨L￨,￨O￨- every￨L￨DT￨O￨- public￨L￨JJ￨O￨- elementary￨L￨JJ￨O￨A school￨L￨NN￨O￨- was￨L￨VBD￨O￨- obligated￨L￨VBN￨O￨- to￨L￨TO￨O￨- report￨L￨VB￨O￨- the￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- absentees￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- A/H1N1pdm￨U￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Oita￨U￨NNP￨ORGANIZATION￨- City￨U￨NNP￨ORGANIZATION￨- Board￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Education￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +KeywordsMulti-group￨U￨JJ￨O￨- SVIRI￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelRelapseBasic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A numberGlobal￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stabilityHerpes￨L￨NNS￨O￨- Simplex￨U￨NNP￨O￨- Virus￨U￨NN￨O￨- Type￨U￨NN￨O￨- 2Vaccination￨L￨NN￨O￨- BackgroundHerpes￨U￨NNS￨O￨- Simplex￨U￨NNP￨O￨- Virus￨U￨NN￨O￨- Type￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- HSV-2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- about￨L￨IN￨O￨- 417￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- 15-49￨L￨CD￨DATE￨- worldwide￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- ℜ0￨U￨NN￨O￨- and￨L￨CC￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- ℜ0￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- if￨L￨IN￨O￨- ℜ0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- so￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- compartmental￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- for￨L￨IN￨O￨- HSV-2￨U￨NN￨MISC￨- were￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- was￨L￨VBD￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- connection￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- ℜ0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- through￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A result￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- ℜ0￨U￨NN￨O￨- for￨L￨IN￨O￨- HSV-2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Clustering￨U￨NN￨O￨- provides￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- advantages￨L￨NNS￨O￨- over￨L￨IN￨O￨- flat￨L￨JJ￨O￨- architecture￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- inter-node￨L￨JJ￨O￨- communication￨L￨NN￨O￨- ,￨L￨,￨O￨- network￨L￨NN￨O￨- scalability￨L￨NN￨O￨- ,￨L￨,￨O￨- bandwidth￨L￨NN￨O￨- management￨L￨NN￨O￨- and￨L￨CC￨O￨- allowing￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- sleep￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- energy￨L￨NN￨O￨A savings￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +CH￨U￨NN￨COUNTRY￨- selection￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- single￨L￨JJ￨O￨- criteria￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- residual￨L￨JJ￨O￨- energy￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- poor￨L￨JJ￨O￨- performance￨L￨NN￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- selected￨L￨VBN￨O￨- CH￨U￨NN￨COUNTRY￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- choice￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- current￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- extended￨L￨VBN￨O￨- cluster￨L￨NN￨O￨A head￨L￨NN￨O￨- selection￨L￨NN￨O￨- criteria￨L￨NNS￨O￨- to￨L￨TO￨O￨- five￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- selected￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- cluster￨L￨NN￨O￨- head￨L￨NN￨O￨- using￨L￨VBG￨O￨- ANP￨U￨NN￨ORGANIZATION￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- cluster￨L￨NN￨O￨A has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- cluster￨L￨NN￨O￨- head￨L￨NN￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- forwarding￨L￨NN￨O￨- aggregated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- member￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- base￨L￨NN￨O￨- station￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- directly￨L￨RB￨O￨- or￨L￨CC￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- CHs￨U￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- those￨L￨DT￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- links￨L￨NNS￨O￨- are￨L￨VBP￨O￨- removed￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- above￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- order￨L￨NN￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- giant￨L￨JJ￨O￨A component￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- continuously￨L￨RB￨O￨- ,￨L￨,￨O￨- approaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nonzero￨L￨NN￨O￨- value￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- way￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- it￨L￨PRP￨O￨- finally￨L￨RB￨O￨- collapses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- HPT￨U￨NN￨O￨- occurs￨L￨VBZ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- giant￨L￨JJ￨O￨A cluster￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- transition￨L￨NN￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- susceptible/infective/removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model2￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- percolating￨L￨VBG￨O￨- clusters￨L￨NNS￨O￨- grown￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- CB￨U￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨A the￨L￨DT￨O￨- CB￨U￨NN￨O￨- process￨L￨NN￨O￨- persists￨L￨VBZ￨O￨- for￨L￨IN￨O￨- O￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- 1/3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- become￨L￨VBP￨O￨- vulnerable￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- then￨L￨RB￨O￨- activated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- short￨L￨JJ￨O￨- SC￨U￨NN￨STATE_OR_PROVINCE￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- observing￨L￨VBG￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- wave￨L￨NN￨O￨A ,￨L￨,￨O￨- while￨L￨IN￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- its￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- increases￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- wave￨L￨NN￨O￨A is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- varies￨L￨VBZ￨O￨A between￨L￨IN￨O￨- 1.9￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 2.8￨L￨CD￨NUMBER￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- for￨L￨IN￨O￨- Antioquia￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Colombia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- varies￨L￨VBZ￨O￨- between￨L￨IN￨O￨- 4￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- 26￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- below￨L￨IN￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- in￨L￨IN￨O￨- blunting￨L￨VBG￨O￨- the￨L￨DT￨O￨- ZIKV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- from￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- to￨L￨TO￨O￨- mosquitoes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Asymptomatic￨U￨NNP￨O￨- Transmission￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Dynamics￨U￨NNPS￨MISC￨- of￨L￨IN￨MISC￨- Zika￨U￨NNP￨MISC￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- Seyed￨U￨NNP￨O￨- M.￨U￨NNP￨O￨- Pereira2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Fatima￨U￨NNP￨PERSON￨- Abdirizak3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marek￨U￨NN￨PERSON￨- Laskowski1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Cecile￨U￨NNP￨PERSON￨- Viboud4￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Gerardo￨U￨NNP￨PERSON￨- Chowell￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,4￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 5829￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- French￨U￨JJ￨NATIONALITY￨- Polynesia￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Zika￨U￨NNP￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- widely￨L￨RB￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- where￨L￨WRB￨O￨- Aedes￨U￨NNP￨O￨- Aegypti￨U￨NNP￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- transmitting￨L￨VBG￨O￨A vector￨L￨NN￨O￨- is￨L￨VBZ￨O￨- endemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- now￨L￨RB￨DATE￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- scholars￨L￨NNS￨O￨A have￨L￨VBP￨O￨- paid￨L￨VBN￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- delay￨L￨NN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- partial￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- constructed￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- attention￨L￨NN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- involving￨L￨VBG￨O￨- vertical￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- was￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- members￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- removed￨L￨VBN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- members￨L￨NNS￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- decades￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observed￨L￨VBD￨O￨- that￨L￨IN￨O￨- scholars￨L￨NNS￨O￨- published￨L￨VBN￨O￨- few￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- in￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- journals￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- mathematics￨L￨NNS￨O￨- considering￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- vertical￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- transmitted￨L￨VBN￨O￨- from￨L￨IN￨O￨- parents￨L￨NNS￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- offspring￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 24￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- σ2￨L￨NN￨O￨- >￨L￨JJR￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- easily￨L￨RB￨O￨- see￨L￨VB￨O￨- from￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- thatDividing￨L￨VBG￨O￨- both￨L￨DT￨O￨- sides￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- t￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- haveSince￨L￨VBP￨O￨- lim￨L￨NN￨O￨- sup￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 〈￨L￨CD￨NUMBER￨- M￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 〉￨L￨SYM￨O￨- /￨L￨:￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- <￨L￨JJR￨O￨- σ2￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- ∞￨L￨CD￨NUMBER￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨A number￨L￨NN￨O￨A theorem￨L￨NN￨O￨- for￨L￨IN￨O￨- martingales￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- obtain￨L￨VB￨O￨- that￨L￨IN￨O￨- Then￨U￨RB￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- superior￨L￨JJ￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- sides￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- when￨L￨WRB￨O￨- σ2￨L￨NN￨O￨- >￨L￨JJR￨O￨- β2/2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- pb￨L￨NN￨O￨- ′￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- implies￨L￨VBZ￨O￨- limI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- σ2￨L￨NN￨O￨- >￨L￨JJR￨O￨- max￨L￨NN￨O￨A {￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- β2/2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- pb￨L￨NN￨O￨- ′￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- σ2￨L￨NN￨O￨- <￨L￨JJR￨O￨- β￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- investigates￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- proposes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- four￨L￨CD￨NUMBER￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- restrain￨L￨VB￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A process￨L￨NN￨O￨- :￨L￨:￨O￨- blocking￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- blocking￨L￨VBG￨O￨- edges￨L￨NNS￨O￨- ,￨L￨,￨O￨- distracting￨L￨VBG￨O￨- node￨L￨NN￨O￨- attention￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- propagating￨L￨VBG￨O￨- opposite￨L￨JJ￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Effective￨U￨NNP￨O￨- Methods￨U￨NNS￨O￨- of￨L￨IN￨O￨- Restraining￨U￨VBG￨O￨- Diffusion￨U￨NNP￨O￨- in￨L￨IN￨O￨- Terms￨U￨NNS￨O￨- of￨L￨IN￨O￨- Epidemic￨U￨NNP￨O￨- Dynamics￨U￨NNP￨O￨- Fei￨U￨NNP￨O￨- Xiong1￨U￨NN￨O￨- ,2￨L￨NN￨O￨- &￨L￨CC￨O￨- Zhao-Yi￨U￨NN￨O￨- Li1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 6013￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComplex￨L￨NNP￨O￨- networksStatistical￨L￨JJ￨O￨- physics￨L￨NNS￨O￨- AbstractRemoving￨U￨VBG￨O￨- influential￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- shortcuts￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- restrains￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- method￨L￨NN￨O￨- destroys￨L￨VBZ￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- changes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Propagating￨U￨VBG￨O￨- opposite￨L￨JJ￨O￨- information￨L￨NN￨O￨- can￨L￨MD￨O￨- effectively￨L￨RB￨O￨- prevent￨L￨VB￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- target￨L￨NN￨O￨- information￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- distracting￨L￨VBG￨O￨- node￨L￨NN￨O￨- attention￨L￨NN￨O￨- only￨L￨RB￨O￨- takes￨L￨VBZ￨O￨- effect￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- an￨L￨DT￨O￨- alternative￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- field￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- imposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- node￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- and￨L￨CC￨O￨- slow￨L￨VB￨O￨- down￨L￨RP￨O￨- diffusion￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Information￨U￨NN￨O￨- diffusion￨L￨NN￨O￨A in￨L￨IN￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- was￨L￨VBD￨O￨- explored￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reposting￨L￨VBG￨O￨- behaviors￨L￨NNS￨O￨- were￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- among￨L￨IN￨O￨- node￨L￨NN￨O￨- interactions18￨L￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- very￨L￨RB￨O￨- useful￨L￨JJ￨O￨- to￨L￨TO￨O￨- tailor￨L￨VB￨O￨- mitigation￨L￨NN￨O￨- strategies3.The￨L￨NN￨O￨- San￨U￨NNP￨ORGANIZATION￨- Francisco￨U￨NNP￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- SFDPH￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- maintains￨L￨VBZ￨O￨- legally￨L￨RB￨O￨- mandated￨L￨VBN￨O￨- case-based￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- includes￨L￨VBZ￨O￨- collected￨L￨VBN￨O￨- sociodemographic￨L￨JJ￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- reported￨L￨VBN￨O￨- and￨L￨CC￨O￨- investigated￨L￨VBN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Clients￨U￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- largest￨L￨JJS￨O￨- component￨L￨NN￨O￨- were￨L￨VBD￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- HIV-positive￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- <￨L￨JJR￨O￨- 0.001￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- Chi-square￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- had￨L￨VBN￨O￨- more￨L￨RBR￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- <￨L￨JJR￨O￨- 0.0001￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- ANOVA￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- than￨L￨IN￨O￨- clients￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- smaller￨L￨JJR￨O￨- connected￨L￨JJ￨O￨- components4.A￨L￨NN￨O￨- partner￨L￨NN￨O￨- notification￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PN￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- called￨L￨VBN￨O￨- an￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- notifies￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- directly￨L￨RB￨O￨- or￨L￨CC￨O￨- indirectly￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- his￨L￨PRP$￨O￨- partners￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- neighbors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sexual￨L￨JJ￨O￨A network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- his￨L￨PRP$￨O￨- infectious￨L￨JJ￨O￨- state5￨L￨NN￨O￨- .￨L￨.￨O￨- +4￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨A network￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- community￨L￨NN￨O￨- of￨L￨IN￨O￨- San￨U￨NNP￨CITY￨- Francisco￨U￨NNP￨CITY￨- from￨L￨IN￨O￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- routinely￨L￨RB￨O￨- collected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- SFDPH￨U￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- syphilis￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- possible￨L￨JJ￨O￨- new￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Individual-based￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- successful￨L￨JJ￨O￨- in￨L￨IN￨O￨- relating￨L￨VBG￨O￨- critical￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨A network10￨L￨NN￨O￨- ,11,12,13,14￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- brief￨L￨NN￨O￨- ,￨L￨,￨O￨- previously￨L￨RB￨DATE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- presented￨L￨VBD￨O￨- controlled￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- 6-to￨L￨JJ￨O￨- 8-week-old￨L￨JJ￨DURATION￨- puppy￨L￨NN￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Puppy￨U￨NNP￨O￨- Profiling￨U￨NNP￨O￨- Assessment￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- PPA￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- three￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- stroking￨L￨VBG￨O￨- ,￨L￨,￨O￨- fake￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- ramp￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- stimuli￨L￨NNS￨O￨- presented￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- including￨L￨VBG￨O￨- following￨L￨VBG￨O￨- ,￨L￨,￨O￨- retrieve￨L￨VB￨O￨- ,￨L￨,￨O￨- gentle￨L￨JJ￨O￨- restraint￨L￨NN￨O￨- ,￨L￨,￨O￨- noise￨L￨NN￨O￨- ,￨L￨,￨O￨- tunnel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- usefully￨L￨RB￨O￨- combined￨L￨VBN￨O￨- and￨L￨CC￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- whether￨L￨IN￨O￨- dogs￨L￨NNS￨O￨A completed￨L￨VBN￨O￨- guide￨L￨NN￨TITLE￨- dogs￨L￨NNS￨O￨- training￨L￨VBG￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- a￨L￨DT￨O￨- working￨L￨VBG￨O￨- guide￨L￨NN￨TITLE￨- dog￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- success￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- epidemiological￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- animal￨L￨NN￨O￨- behavior￨L￨NN￨O￨A research￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- survival￨L￨NN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- MSM￨U￨NN￨ORGANIZATION￨- to￨L￨TO￨O￨- Guide￨U￨NNP￨ORGANIZATION￨- Dogs￨U￨NNP￨ORGANIZATION￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- dog￨L￨NN￨O￨- qualifying￨L￨VBG￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- ,￨L￨,￨O￨- movements￨L￨NNS￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- training￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- this￨L￨DT￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- popular￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- survival￨L￨NN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- multistate￨L￨NN￨O￨- modeling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MSM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- guide￨L￨NN￨TITLE￨A dog￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- Guide￨U￨NNP￨ORGANIZATION￨- Dogs￨U￨NNP￨ORGANIZATION￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- prospectively￨L￨RB￨O￨- collecting￨L￨VBG￨O￨- more￨L￨JJR￨O￨- detailed￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- dogs￨L￨NNS￨O￨A during￨L￨IN￨O￨- training￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- and￨L￨CC￨O￨- record￨L￨VB￨O￨- behavior￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- behavior￨L￨NN￨O￨A data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- previously￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- datasets￨L￨NNS￨O￨- from￨L￨IN￨O￨- Guide￨U￨NNP￨ORGANIZATION￨- Dogs￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +Pearson￨U￨NNP￨PERSON￨- method￨L￨NN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- curve￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- weekly￨L￨JJ￨SET￨- A/H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨- isolation￨L￨NN￨O￨- rate￨L￨NN￨O￨- curve￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2009￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- effective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- succeeding￨L￨VBG￨O￨- A/H1N1￨U￨NN￨O￨- clade￨L￨NN￨O￨- 2B-2￨L￨NN￨O￨- ,￨L￨,￨O￨- carrying￨L￨VBG￨O￨- H275Y￨U￨NN￨O￨- mutation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- neuraminidase￨L￨NN￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- around￨L￨IN￨O￨- 1.65￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- ran￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- A/H1N1￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- isolation￨L￨NN￨O￨- rate￨L￨NN￨O￨- through￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2008￨L￨CD￨DATE￨- single-clade￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A and￨L￨CC￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- clade-based￨L￨JJ￨O￨- A/H1N1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2009￨L￨CD￨DATE￨- two-clade￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- viral￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- in￨L￨IN￨O￨- immunocompromised￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A may￨L￨MD￨O￨- impact￨L￨VB￨O￨- larger-scale￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- emergence￨L￨NN￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- categorization￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- importantly￨L￨RB￨O￨- ,￨L￨,￨O￨- incorporates￨L￨VBZ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- evolution￨L￨NN￨O￨- to￨L￨TO￨O￨- reveal￨L￨VB￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- immunocompromised￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- evolution￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- NoV￨U￨NN￨DATE￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- apparent￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- for￨L￨IN￨O￨- immunocompromised￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A to￨L￨TO￨O￨- generate￨L￨VB￨O￨- significant￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- during￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- isolation￨L￨NN￨O￨- and￨L￨CC￨O￨- rarity￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- limits￨L￨VBZ￨O￨- their￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- NoV￨U￨NN￨DATE￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- rapidly￨L￨RB￨O￨- evolving￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- in￨L￨IN￨O￨- chronically￨L￨RB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- immunocompromised￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- components￨L￨NNS￨O￨- .￨L￨.￨O￨- +Importantly￨U￨RB￨O￨- ,￨L￨,￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- ‘￨L￨``￨O￨- immunocompromised￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨A ’￨L￨POS￨O￨- as￨L￨IN￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- more￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- immunodeficienies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- that￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- chronic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- typically￨L￨RB￨O￨- acute￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- constant￨L￨JJ￨O￨- size￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- immunocompromised￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- births￨L￨NNS￨O￨- or￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- kill￨L￨VB￨O￨- hosts￨L￨NNS￨O￨A so￨L￨IN￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- cases￨L￨NNS￨O￨- recover￨L￨VB￨O￨- ,￨L￨,￨O￨- become￨L￨VB￨O￨- immune￨L￨JJ￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- reinfection￨L￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- RVF￨U￨NN￨O￨- emergence￨L￨NN￨O￨- conducted￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Horn￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Africa￨U￨NNP￨ORGANIZATION￨- using￨L￨VBG￨O￨- ecological￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- above-average￨L￨JJ￨O￨- rainfall￨L￨NNS￨O￨- and￨L￨CC￨O￨- vegetation￨L￨NN￨O￨- density￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Normalized￨U￨JJ￨MISC￨- Vegetation￨U￨NNP￨MISC￨- Difference￨U￨NNP￨MISC￨- Index￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- NDVI￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- over￨L￨IN￨O￨- 3￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- 4￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- could￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- RVF￨U￨NN￨O￨- re-emergence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- seem￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- always￨L￨RB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- Madagascar￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Southern￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- other￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- livestock￨L￨NN￨O￨A susceptibility￨L￨NN￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- play￨L￨VB￨O￨- a￨L￨DT￨O￨- role￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- RVF￨U￨NN￨O￨- emergence￨L￨NN￨O￨- that￨L￨WDT￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- livestock￨L￨NN￨O￨A susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- climate￨L￨NN￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- import￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- serological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- livestock￨L￨NN￨O￨A population￨L￨NN￨O￨- was￨L￨VBD￨O￨- purposively￨L￨RB￨O￨- stratified￨L￨VBN￨O￨- in￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- yearly￨L￨JJ￨SET￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- a￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- ∊￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- age-specific￨L￨JJ￨O￨- IgG￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- fitting￨L￨JJ￨O￨- paragraph￨L￨NN￨O￨- and￨L￨CC￨O￨- S1￨U￨NN￨O￨- Text￨U￨VBP￨O￨- for￨L￨IN￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Subsequent￨U￨JJ￨O￨- serological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- in￨L￨IN￨O￨- Mayotte￨U￨NNP￨LOCATION￨- in￨L￨IN￨O￨- livestock￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 2004￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2016￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- no￨L￨DT￨O￨- symptoms￨L￨NNS￨O￨- in￨L￨IN￨O￨- animals￨L￨NNS￨O￨- being￨L￨VBG￨O￨- detected￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨A to￨L￨TO￨O￨- study￨L￨VB￨O￨- RVF￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- looked￨L￨VBD￨O￨- mainly￨L￨RB￨O￨- at￨L￨IN￨O￨- RVF￨U￨NN￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- once￨L￨RB￨DATE￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- they￨L￨PRP￨O￨- assessed￨L￨VBD￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- few￨L￨JJ￨O￨- were￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Early￨U￨NNP￨MISC￨- rigorous￨L￨JJ￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A can￨L￨MD￨O￨- largely￨L￨RB￨O￨- reduce￨L￨VB￨O￨- dengue￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- magnitude￨L￨NN￨O￨- :￨L￨:￨O￨- experience￨L￨NN￨O￨- from￨L￨IN￨O￨- Chaozhou￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- ChinaTao￨U￨NNP￨PERSON￨- Liu￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Guanghu￨U￨NNP￨PERSON￨- Zhu￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jianfeng￨U￨NNP￨PERSON￨- He2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Tie￨U￨NNP￨O￨- Song2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Meng￨U￨NNP￨PERSON￨- Zhang2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hualiang￨U￨NNP￨O￨- Lin1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Jianpeng￨U￨NNP￨PERSON￨- Xiao1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Weilin￨U￨NNP￨PERSON￨- Zeng1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Xing￨U￨NNP￨PERSON￨- Li1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Zhihao￨U￨NNP￨PERSON￨- Li1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Runsheng￨U￨NNP￨O￨- Xie1￨U￨NN￨O￨- ,￨L￨,￨O￨- Haojie￨U￨NN￨O￨- Zhong2￨U￨NN￨O￨- ,￨L￨,￨O￨- Xiaocheng￨U￨NN￨O￨- Wu2￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Wenbiao￨U￨NNP￨O￨- Hu4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Yonghui￨U￨NNP￨O￨- Zhang2Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Wenjun￨U￨NNP￨O￨- Ma1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- †￨L￨CD￨NUMBER￨- Contributed￨U￨VBD￨O￨- equallyBMC￨L￨NNP￨O￨- Public￨U￨NNP￨O￨- HealthBMC￨U￨NNP￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18:90￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- SEIR￨U￨NN￨O￨- modeling￨L￨NN￨O￨- using￨L￨VBG￨O￨- BI￨U￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- actual￨L￨JJ￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A showed￨L￨VBD￨O￨- a￨L￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 1255￨L￨CD￨DATE￨- dengue￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- close￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1250￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- intensified￨L￨VBD￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- reduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- should￨L￨MD￨O￨- such￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- be￨L￨VB￨O￨- initiated￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A outbreaks￨L￨NNS￨O￨- developing￨L￨VBG￨O￨- ?￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Exposed￨U￨VBN￨O￨- ,￨L￨,￨O￨- Infected￨U￨JJ￨O￨- and￨L￨CC￨O￨- Removed￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- timing￨L￨NN￨O￨- on￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- This￨U￨DT￨O￨- study￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- early￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- rigorous￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A interventions￨L￨NNS￨O￨- can￨L￨MD￨O￨- effectively￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- shorten￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- duration￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Role￨U￨NN￨MISC￨- of￨L￨IN￨O￨- meteorological￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- in￨L￨IN￨O￨- reported￨L￨VBN￨O￨- chickenpox￨L￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- ChinaBanghua￨U￨NNP￨O￨- Chen1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Ayako￨U￨NNP￨PERSON￨- Sumi2Email￨U￨NNP￨O￨- authorView￨L￨NNP￨O￨- ORCID￨U￨NNP￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Lei￨U￨NN￨O￨- Wang3￨U￨NN￨O￨- ,￨L￨,￨O￨- Wang￨U￨NNP￨O￨- Zhou4Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Nobumichi￨U￨JJ￨MISC￨- Kobayashi2BMC￨U￨NN￨MISC￨- Infectious￨U￨JJ￨MISC￨- DiseasesBMC￨U￨NN￨MISC￨- series￨L￨NN￨O￨A –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 17:538￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Q￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- were￨L￨VBD￨O￨- positively￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- mean￨L￨NN￨O￨- temperature￨L￨NN￨O￨A and￨L￨CC￨O￨- rainfall￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- city￨L￨NN￨O￨- .￨L￨.￨O￨- +Conversely￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Q￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- were￨L￨VBD￨O￨- negatively￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- mean￨L￨NN￨O￨- temperature￨L￨NN￨O￨A and￨L￨CC￨O￨- rainfall￨L￨NNS￨O￨- of￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨A data￨L￨NNS￨O￨- of￨L￨IN￨O￨- chickenpox￨L￨NN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- Wuhan￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- have￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- peaks￨L￨NNS￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- winter￨L￨NN￨DATE￨- and￨L￨CC￨O￨- another￨L￨DT￨O￨- in￨L￨IN￨O￨- spring￨L￨NN￨DATE￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- a￨L￨DT￨O￨- bimodal￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Impact￨U￨NN￨O￨- of￨L￨IN￨O￨- life￨L￨NN￨O￨- stage-dependent￨L￨JJ￨O￨- dispersal￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- colonization￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- patches￨L￨NNS￨O￨- by￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- and￨L￨CC￨O￨- tick-borne￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- agentsSarah￨L￨NN￨O￨- Kada1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Karen￨U￨NNP￨PERSON￨- D.￨U￨NNP￨O￨- 2017Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- When￨U￨WRB￨O￨- colonization￨L￨NN￨O￨- and￨L￨CC￨O￨- gene￨L￨NN￨O￨- flow￨L￨NN￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- host-mediated￨L￨JJ￨O￨- dispersal￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- factor￨L￨NN￨O￨- affecting￨L￨VBG￨O￨- vector￨L￨NN￨O￨- dispersal￨L￨JJ￨O￨- potential￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- spent￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- blood￨L￨NN￨O￨- meal￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- vary￨L￨VB￨O￨- strongly￨L￨RB￨O￨- among￨L￨IN￨O￨- life￨L￨NN￨O￨- history￨L￨NN￨O￨- stages￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- vector￨L￨NN￨O￨- life￨L￨NN￨O￨A history￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- length￨L￨NN￨O￨- of￨L￨IN￨O￨- blood￨L￨NN￨O￨- meal￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Allee￨U￨JJ￨O￨- effects￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- condition￨L￨NN￨O￨- the￨L￨DT￨O￨- colonization￨L￨NN￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- ;￨L￨:￨O￨- hard￨L￨JJ￨O￨- ticks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- take￨L￨VBP￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- ,￨L￨,￨O￨- long￨L￨JJ￨O￨- blood￨L￨NN￨O￨- meal￨L￨NN￨O￨- per￨L￨IN￨O￨- life￨L￨NN￨O￨- stage￨L￨NN￨O￨- ,￨L￨,￨O￨- should￨L￨MD￨O￨- have￨L￨VB￨O￨- much￨L￨RB￨O￨- higher￨L￨JJR￨O￨- colonization￨L￨NN￨O￨- rates￨L￨NNS￨O￨- than￨L￨IN￨O￨- soft￨L￨JJ￨O￨- ticks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- take￨L￨VBP￨O￨- repeated￨L￨VBN￨O￨- short￨L￨JJ￨O￨- meals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- 2-patch￨L￨JJ￨O￨- vector-pathogen￨L￨JJ￨O￨- population￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- seabird￨L￨NN￨O￨- ticks￨L￨VBZ￨O￨- as￨L￨IN￨O￨- biological￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- how￨L￨WRB￨O￨- vector￨L￨NN￨O￨- colonization￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- shaped￨L￨VBN￨O￨- by￨L￨IN￨O￨- life￨L￨NN￨O￨- stage-dependent￨L￨JJ￨O￨- dispersal￨L￨NN￨O￨A .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- dispersal￨L￨JJ￨O￨A potential￨L￨NN￨O￨- has￨L￨VBZ￨O￨- direct￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- when￨L￨WRB￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- transovarial￨L￨JJ￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- anticipating￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨A has￨L￨VBZ￨O￨- predominantly￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- specific￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- attempt￨L￨NN￨O￨- at￨L￨IN￨O￨- applying￨L￨VBG￨O￨- EWS￨U￨NN￨O￨- to￨L￨TO￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- emergence￨L￨NN￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- –￨L￨:￨O￨- immigration￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- BDI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- viewed￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- possible￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- direct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- modelling￨L￨VBG￨O￨- spillover￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- external￨L￨JJ￨O￨- source￨L￨NN￨O￨- ,￨L￨,￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- chains￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- fed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- pool￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- test￨L￨VBP￨O￨- the￨L￨DT￨O￨- robustness￨L￨NN￨O￨- of￨L￨IN￨O￨- measures￨L￨NNS￨O￨- to￨L￨TO￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- simulating￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨A using￨L￨VBG￨O￨- the￨L￨DT￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIRS￨U￨NN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- varying￨L￨VBG￨O￨- immunology￨L￨NN￨O￨- and￨L￨CC￨O￨- demographics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- exploring￨L￨VBG￨O￨- EWS￨U￨NN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- performance￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- direction￨L￨NN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- transition￨L￨NN￨O￨A is￨L￨VBZ￨O￨- traversed￨L￨VBN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- contrasting￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨ORGANIZATION￨- .￨L￨.￨O￨- +Dynamical￨U￨JJ￨O￨- systems￨L￨NNS￨O￨- theory￨L￨NN￨O￨- states￨L￨VBZ￨O￨- that￨L￨IN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- stable￨L￨JJ￨O￨- system￨L￨NN￨O￨- approaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- tipping￨L￨JJ￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- taken￨L￨VBN￨O￨- to￨L￨TO￨O￨- recover￨L￨VB￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- ;￨L￨:￨O￨- ultimately￨L￨RB￨O￨- diverging￨L￨VBG￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- spatially￨L￨RB￨O￨- and￨L￨CC￨O￨- temporally￨L￨RB￨O￨- clustered￨L￨VBN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A incidence￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- predominance￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- serotype￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨- by￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- aggregated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- limits￨L￨NNS￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- answer￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- research￨L￨NN￨O￨- questions￨L￨NNS￨O￨- :￨L￨:￨O￨- How￨U￨WRB￨O￨- does￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- of￨L￨IN￨O￨- buildings￨L￨NNS￨O￨- influence￨L￨VBP￨O￨- dengue￨L￨JJ￨O￨A incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ?￨L￨.￨O￨- +Interested￨U￨VBN￨O￨- in￨L￨IN￨O￨- addressing￨L￨VBG￨O￨- this￨L￨DT￨O￨- issue￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- objectives￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- are￨L￨VBP￨O￨- twofold￨L￨JJ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- configuration￨L￨NN￨O￨- of￨L￨IN￨O￨- residential￨L￨JJ￨O￨- buildings￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +How￨U￨WRB￨O￨- does￨L￨VBZ￨O￨- mosquito￨L￨NN￨O￨- population￨L￨NN￨O￨- distribution￨L￨NN￨O￨- influence￨L￨NN￨O￨- dengue￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- serotype-specific￨L￨JJ￨O￨- dominance￨L￨NN￨O￨- ?￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- four￨L￨CD￨NUMBER￨- environments￨L￨NNS￨O￨- were￨L￨VBD￨O￨- set￨L￨VBN￨O￨- up￨L￨RP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- mosquito￨L￨NN￨O￨A agents￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- in￨L￨IN￨O￨- specific￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- houses￨L￨NNS￨O￨- ,￨L￨,￨O￨- workplaces￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- schools￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Four￨U￨CD￨NUMBER￨- quantitative￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- risk￨L￨NN￨O￨- assessment￨L￨NN￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- monthly￨L￨JJ￨SET￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- ASF￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- CSF￨U￨NN￨O￨- introduction￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- live￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A and￨L￨CC￨O￨- products￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- of￨L￨IN￨O￨- origin￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- notification￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- addressed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- event￨L￨NN￨O￨- pathways￨L￨NNS￨O￨- :￨L￨:￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- ASF￨U￨NN￨O￨- being￨L￨VBG￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- live￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A ,￨L￨,￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- ASF￨U￨NNP￨O￨- introduction￨L￨NN￨O￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- swine￨L￨NNS￨O￨- products￨L￨NNS￨O￨- ,￨L￨,￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- introduction￨L￨NN￨O￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- live￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- iv￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- CSF￨U￨NN￨O￨- being￨L￨VBG￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- swine￨L￨NNS￨O￨- products￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- ,￨L￨,￨O￨- ASF￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- CSF￨U￨NN￨O￨- introduction￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- at￨L￨IN￨O￨- state￨L￨NN￨O￨- level￨L￨NN￨O￨- by￨L￨IN￨O￨- legal￨L￨JJ￨O￨- imports￨L￨NNS￨O￨- of￨L￨IN￨O￨- live￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A and￨L￨CC￨O￨- swine￨L￨NNS￨O￨- products￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- monthly￨L￨JJ￨SET￨- basis￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- incorporated￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- online￨L￨JJ￨O￨- platform￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- BioPortal￨U￨JJ￨MISC￨- ™￨L￨NN￨O￨- accessible￨L￨JJ￨O￨- at￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- their￨L￨PRP$￨O￨- visualization￨L￨NN￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- developed￨L￨VBD￨O￨- here￨L￨RB￨O￨- will￨L￨MD￨O￨- serve￨L￨VB￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- template￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- introduction￨L￨NN￨O￨A of￨L￨IN￨O￨- other￨L￨JJ￨O￨- TADs￨U￨NNS￨O￨- .￨L￨.￨O￨- +ASF￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- CSF￨U￨NN￨O￨- represent￨L￨VBP￨O￨- a￨L￨DT￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- swine￨L￨NNS￨O￨A industry￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- important￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- if￨L￨IN￨O￨- they￨L￨PRP￨O￨- were￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- swine￨L￨NNS￨O￨- production￨L￨NN￨O￨- countries￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- previous￨L￨JJ￨O￨- health￨L￨NN￨O￨- economic￨L￨JJ￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- universal￨L￨JJ￨O￨- childhood￨L￨NN￨O￨- rotavirus￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- cost￨L￨VBN￨O￨- –￨L￨:￨O￨- effective￨L￨JJ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- societal￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- healthcare￨L￨NN￨O￨- perspective￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- limited￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- The￨U￨NNP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- largely￨L￨RB￨O￨- preventable￨L￨JJ￨O￨- through￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- rotavirus￨L￨NN￨O￨- vaccines￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- of￨L￨IN￨O￨- 81￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- worldwide￨L￨RB￨O￨- ;￨L￨:￨O￨- eight￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- European￨U￨NNP￨ORGANIZATION￨- Union￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- Many￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- clearly￨L￨RB￨O￨- illustrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- whether￨L￨IN￨O￨- these￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- outweigh￨L￨VBP￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- country￨L￨NN￨O￨- –￨L￨:￨O￨- specific￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ongoing￨L￨JJ￨O￨- rotavirus￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A programme￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- study￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- –￨L￨:￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Norwegian￨U￨JJ￨NATIONALITY￨- setting￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- hospitalisation￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- RVGE￨U￨NN￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- at￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- 1000￨L￨CD￨DATE￨A children￨L￨NNS￨O￨- below￨L￨IN￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- primary￨L￨JJ￨O￨- care￨L￨NN￨O￨- consultations￨L￨NNS￨O￨- and￨L￨CC￨O￨- homecare￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- episodes￨L￨NNS￨O￨- was￨L￨VBD￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- hospitalisation￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Effects￨U￨NNS￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- Michele￨U￨NNP￨PERSON￨- Starnini1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Andrea￨U￨NNP￨PERSON￨- Baronchelli3￨U￨NNP￨O￨- &￨L￨CC￨O￨- Romualdo￨U￨NNP￨O￨- Pastor-Satorras4￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 8597￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksPhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractMulti-layered￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- advance￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- study￨L￨NN￨O￨- has￨L￨VBZ￨O￨- shed￨L￨VBN￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- new￨L￨JJ￨O￨- physical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- .￨L￨.￨O￨- +IntroductionRecently￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- science1￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- enriched￨L￨VBN￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- new￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨- :￨L￨:￨O￨- Multiplex￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- 2,3,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- edges￨L￨NNS￨O￨- belong￨L￨VBP￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- layers￨L￨NNS￨O￨A ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- edges￨L￨NNS￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- creation￨L￨NN￨O￨- and￨L￨CC￨O￨- annihilation￨L￨NN￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- interactions￨L￨NNS￨O￨- switching￨L￨VBG￨O￨- on￨L￨IN￨O￨- and￨L￨CC￨O￨- off￨L￨IN￨O￨- with￨L￨IN￨O￨- given￨L￨VBN￨O￨- characteristic￨L￨JJ￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨A representation￨L￨NN￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- observables￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- multilayer￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- ,￨L￨,￨O￨- degree￨L￨NN￨O￨- correlations￨L￨NNS￨O￨- or￨L￨CC￨O￨- layer￨L￨NN￨TITLE￨- overlap2￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- allowed￨L￨VBN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- structural￨L￨JJ￨O￨- characterization￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- networked￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- helped￨L￨VBD￨O￨- clarify￨L￨VB￨O￨- the￨L￨DT￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- them7￨L￨CD￨NUMBER￨- ,8,9,10,11￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨A are￨L￨VBP￨O￨- a￨L￨DT￨O￨- signature￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- ‘￨L￨``￨O￨- multitasking￨L￨VBG￨O￨- ’￨L￨''￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- agents￨L￨NNS￨O￨- ,￨L￨,￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- switching￨L￨NN￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- social￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- uncorrelated￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- layers￨L￨NNS￨O￨- exhibited￨L￨VBN￨O￨- by￨L￨IN￨O￨- real￨L￨JJ￨O￨- social￨L￨JJ￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Egyptian￨U￨NNP￨NATIONALITY￨- rousette￨L￨NN￨O￨- bats￨L￨NNS￨O￨- maintain￨L￨VBP￨O￨- long-term￨L￨JJ￨O￨- protective￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- Marburg￨U￨NNP￨MISC￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- despite￨L￨IN￨O￨- diminished￨L￨JJ￨O￨- antibody￨L￨NN￨O￨- levels￨L￨NNS￨O￨- Amy￨U￨NNP￨PERSON￨- J.￨U￨NNP￨PERSON￨- Towner￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 8763￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Microbial￨U￨NNP￨O￨- ecologyViral￨L￨NNP￨O￨- reservoirsVirus￨L￨NNP￨O￨- –￨L￨:￨O￨- host￨L￨NN￨TITLE￨- interactions￨L￨NNS￨O￨- AbstractAlthough￨U￨NNP￨O￨- bats￨L￨NNS￨O￨- are￨L￨VBP￨O￨- natural￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- for￨L￨IN￨O￨- numerous￨L￨JJ￨O￨- zoonotic￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- immune￨L￨JJ￨O￨- response￨L￨NN￨O￨- following￨L￨VBG￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- maintained￨L￨VBN￨O￨- in￨L￨IN￨O￨- nature￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- reinfection￨L￨NN￨O￨- of￨L￨IN￨O￨- ERBs￨U￨NNS￨MISC￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- MARV￨U￨NNP￨O￨- maintenance￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- challenge￨L￨VBP￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- ERBs￨U￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- “￨L￨``￨O￨- naturally￨L￨RB￨O￨- ”￨L￨''￨O￨- or￨L￨CC￨O￨- experimentally￨L￨RB￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- MARV￨U￨NN￨ORGANIZATION￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨A prior￨L￨RB￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- ERBs￨U￨NNS￨O￨- with￨L￨IN￨O￨- MARV￨U￨NN￨O￨- ,￨L￨,￨O￨- virus-specific￨L￨JJ￨O￨- IgG￨U￨NN￨O￨- antibodies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- induced￨L￨VBN￨O￨- but￨L￨CC￨O￨- rapidly￨L￨RB￨O￨- wane￨L￨VB￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- 3￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨A post-infection￨L￨JJ￨O￨- the￨L￨DT￨O￨- bats￨L￨NNS￨O￨- are￨L￨VBP￨O￨- seronegative￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Egyptian￨U￨JJ￨NATIONALITY￨- rousette￨L￨NN￨O￨- bat￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ERB￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- known￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨A host￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- Marburg￨U￨NNP￨MISC￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MARV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- inference￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- building￨L￨NN￨O￨- on￨L￨IN￨O￨- core￨L￨NN￨O￨- biological￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- experiments￨L￨NNS￨O￨- indicating￨L￨VBG￨O￨- vector￨L￨NN￨O￨- or￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- survival￨L￨NN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- climatic￨L￨JJ￨O￨A variable￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- leveraging￨L￨VBG￨O￨- spatial￨L￨JJ￨O￨- variation￨L￨NN￨O￨- and￨L￨CC￨O￨- range￨L￨NN￨O￨- limits￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- climatic￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- building￨L￨NN￨O￨- mechanistic￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- from￨L￨IN￨O￨- shorter￨L￨JJR￨O￨- time-series￨L￨NNS￨O￨- of￨L￨IN￨O￨- climatic￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- which￨L￨WDT￨O￨- itself￨L￨PRP￨O￨- often￨L￨RB￨O￨- builds￨L￨VBZ￨O￨- on￨L￨IN￨O￨- biological￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- and/or￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- variation￨L￨NN￨O￨- .￨L￨.￨O￨- +Infectious￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- climatic￨L￨JJ￨O￨A conditions￨L￨NNS￨O￨- through￨L￨IN￨O￨- their￨L￨PRP$￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- and￨L￨CC￨O￨- ticks￨L￨VBZ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- pathogen￨L￨NN￨O￨- survival￨L￨NN￨O￨- outside￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- contamination￨L￨NN￨O￨- and￨L￨CC￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- water-borne￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- dampening￨L￨VBG￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- immunity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- disruptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- status￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- malnutrition￨L￨NN￨CAUSE_OF_DEATH￨- linked￨L￨VBN￨O￨- to￨L￨TO￨O￨- droughts￨L￨NNS￨O￨- or￨L￨CC￨O￨- floods￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- disruption￨L￨NN￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- systems￨L￨NNS￨O￨- by￨L￨IN￨O￨- disasters￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- floods￨L￨NNS￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- hurricanes￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- issue￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- while￨L￨IN￨O￨- climate￨L￨NN￨O￨A acts￨L￨VBZ￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- extrinsic￨L￨JJ￨O￨- driver￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- also￨L￨RB￨O￨- have￨L￨VBP￨O￨- intrinsic￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- population-level￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- increasing￨L￨VBG￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨- can￨L￨MD￨O￨- modify￨L￨VB￨O￨- previous￨L￨JJ￨O￨- geographical￨L￨JJ￨O￨- limits￨L￨NNS￨O￨- for￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Appropriately￨U￨RB￨O￨- attributing￨L￨VBG￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- climatic￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- quantifying￨L￨VBG￨O￨- this￨L￨DT￨O￨- relationship￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- step￨L￨NN￨O￨- in￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- climate￨L￨NN￨O￨- change￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Disentangling￨U￨VBG￨O￨- these￨L￨DT￨O￨- drivers￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- careful￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨- and￨L￨CC￨O￨- model-based￨L￨JJ￨O￨- partitioning￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- climate￨L￨NN￨O￨A and￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- while￨L￨IN￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- pathogen￨L￨NN￨O￨- biology￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- carriage￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- serotype￨L￨NN￨O￨A transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- serotype￨L￨NN￨O￨- co-circulation￨L￨NN￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- Brazilian￨U￨JJ￨NATIONALITY￨- multi-serotype￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- v￨L￨LS￨O￨- k￨L￨NN￨O￨- ∞￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- k￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- metastable￨L￨JJ￨O￨- state￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- τ￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨A of￨L￨IN￨O￨- node￨L￨NN￨O￨- k￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- equals￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- y￨L￨NN￨O￨- ∞￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- vulnerability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network.Researchers￨L￨NNPS￨O￨- have￨L￨VBP￨O￨- mainly￨L￨RB￨O￨- concentrated￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- y￨L￨NN￨O￨- ∞￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- metastable￨L￨JJ￨O￨- state￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- against￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- observation￨L￨NN￨O￨- points￨L￨VBZ￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- find￨L￨VB￨O￨- a￨L￨DT￨O￨- topological￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨A of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- rankings￨L￨NNS￨O￨- in￨L￨IN￨O￨- vulnerability￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- different￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- τ￨L￨NN￨O￨- varies￨L￨VBZ￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- a￨L￨DT￨O￨- topological￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- remains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- nodal￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A probability￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- network￨L￨NN￨O￨- topologies￨L￨NNS￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- τ￨L￨NN￨O￨- varies￨L￨VBZ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- vulnerability￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- probability￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- metastable￨L￨JJ￨O￨- state￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- effective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- τ￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- non-vaccine￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- NVTs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- weak￨L￨JJ￨O￨- or￨L￨CC￨O￨- strong￨L￨JJ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- competition￨L￨NN￨O￨- and￨L￨CC￨O￨- carriage￨L￨NN￨O￨A incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- estimated￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- prior￨L￨JJ￨O￨- field￨L￨NN￨O￨- study￨L￨NN￨O￨- within￨L￨IN￨O￨- KHDSS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- post-vaccination￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- carriage￨L￨NN￨O￨A and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- five￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- for￨L￨IN￨O￨- validation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- predictions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Nasopharyngeal￨U￨JJ￨MISC￨- swabs￨L￨NNS￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- and￨L￨CC￨O￨- pneumococcal￨L￨JJ￨O￨- serotype-specific￨L￨JJ￨O￨- carriage￨L￨NN￨O￨A ascertained￨L￨VBD￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- pre-vaccination￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- serotype￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- carriage￨L￨NN￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- a￨L￨DT￨DURATION￨- few￨L￨JJ￨DURATION￨- months￨L￨NNS￨DURATION￨- post-vaccination￨L￨JJ￨O￨- vaccine-type￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨- carriage￨L￨NN￨O￨A and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- had￨L￨VBD￨O￨- dropped￨L￨VBN￨O￨- substantially￨L￨RB￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameterized￨L￨VBN￨O￨- with￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- KHDSS￨U￨NNP￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- pre-vaccination￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨A epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- long-term￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- PCV10￨U￨NN￨O￨- in￨L￨IN￨O￨- Kilifi￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Methods￨U￨NNS￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- :￨L￨:￨O￨- Evaluating￨U￨VBG￨O￨- the￨L￨DT￨O￨- precision￨L￨NN￨O￨- of￨L￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- regression￨L￨NN￨O￨A and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- novel￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- Carsten￨U￨NNP￨PERSON￨- Kirkeby￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Tariq￨U￨NNP￨PERSON￨- Halasa￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Maya￨U￨JJ￨PERSON￨- Gussmann1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Nils￨U￨NNP￨PERSON￨- Toft1￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Kaare￨U￨NNP￨O￨- Græsbøll1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 9496￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- Computational￨U￨JJ￨O￨- modelsData￨L￨NN￨O￨- processing￨L￨NN￨O￨- An￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- Correction￨U￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- was￨L￨VBD￨O￨- published￨L￨VBN￨O￨- on￨L￨IN￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- This￨U￨DT￨O￨- article￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- updated￨L￨VBN￨O￨- AbstractPrecise￨U￨NNP￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- critical￨L￨JJ￨O￨- for￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- most￨L￨JJS￨O￨- tested￨L￨VBN￨O￨- scenarios￨L￨NNS￨O￨- these￨L￨DT￨O￨- new￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- perform￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- or￨L￨CC￨O￨- better￨L￨JJR￨O￨- than￨L￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- regression￨L￨NN￨O￨A ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- long￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- devise￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- new￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- these￨L￨DT￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- frequently￨L￨RB￨O￨- used￨L￨VBN￨O￨- Poisson￨U￨NNP￨PERSON￨- regression￨L￨NN￨O￨A method￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- easily￨L￨RB￨O￨- biased￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- when￨L￨WRB￨O￨- using￨L￨VBG￨O￨- these￨L￨DT￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- simulation￨L￨NN￨O￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A rate￨L￨NN￨O￨A .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- earliest￨L￨JJS￨O￨- models￨L￨NNS￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- population￨L￨NN￨O￨- being￨L￨VBG￨O￨- studied￨L￨VBN￨O￨- was￨L￨VBD￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- consisted￨L￨VBD￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- class￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- direct￨L￨JJ￨O￨A contact￨L￨NN￨O￨- with￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- recovered￨L￨VBN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- spread￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- again￨L￨RB￨O￨- .￨L￨.￨O￨- +Relaxing￨U￨VBG￨O￨- this￨L￨DT￨O￨- assumption￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- employ￨L￨VB￨O￨- a￨L￨DT￨O￨- stage-progression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- linear￨L￨JJ￨O￨- chain￨L￨NN￨O￨- trick￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- like￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- Dengue￨U￨JJ￨O￨- [￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨A of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- substages￨L￨NNS￨O￨- for￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- various￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- being￨L￨VBG￨O￨- analyzed￨L￨VBN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- exact￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨- final￨L￨JJ￨O￨A size￨L￨NN￨O￨A relations￨L￨NNS￨O￨- for￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- ℛ0￨U￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- infective￨L￨JJ￨O￨- individual￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- wholly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- humans￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- vectors￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- mosquitoes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- final￨L￨JJ￨O￨A size￨L￨NN￨O￨A relation￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- that￨L￨WDT￨O￨- also￨L￨RB￨O￨- included￨L￨VBD￨O￨- direct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- Zika￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- Zhao￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 17￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 18￨L￨CD￨NUMBER￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- susceptible-infected-hibernator-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIHR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- incorporated￨L￨VBD￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- memory￨L￨NN￨O￨- and￨L￨CC￨O￨- forgetting￨L￨VBG￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- Lü￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 19￨L￨CD￨NUMBER￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- strengthening￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- external￨L￨JJ￨O￨- social￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- established￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model.Research￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- opinion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- mutual￨L￨JJ￨O￨- relevance￨L￨NN￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- exchange￨L￨NN￨O￨- since￨L￨IN￨O￨- pieces￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- shared￨L￨VBN￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- people￨L￨NNS￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- thought￨L￨VBN￨O￨- of￨L￨IN￨O￨- like￨L￨IN￨O￨- opinions￨L￨NNS￨O￨A .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- information￨L￨NN￨O￨- entropy￨L￨NN￨O￨A Chao￨U￨NNP￨O￨- Wang1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Zong￨U￨NNP￨PERSON￨- Xuan￨U￨NNP￨PERSON￨- Tan2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ye￨U￨PRP￨PERSON￨- Ye1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Lu￨U￨NN￨PERSON￨- Wang1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Kang￨U￨NNP￨PERSON￨- Hao￨U￨NNP￨PERSON￨- Cheong3￨U￨NNP￨O￨- &￨L￨CC￨O￨- Neng-gang￨U￨NNP￨O￨- Xie1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 9615￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Evolutionary￨U￨NNP￨O￨- theoryInformation￨L￨NN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- computation￨L￨NN￨O￨- AbstractRumor￨U￨NN￨O￨- spreading￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- people￨L￨NNS￨O￨- ’s￨L￨POS￨O￨- lives￨L￨NNS￨O￨- ,￨L￨,￨O￨- distorting￨L￨VBG￨O￨- scientific￨L￨JJ￨O￨- facts￨L￨NNS￨O￨- and￨L￨CC￨O￨- influencing￨L￨VBG￨O￨- political￨L￨JJ￨O￨- opinions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- approaches￨L￨NNS￨O￨- include￨L￨VBP￨O￨- research￨L￨NN￨O￨- by￨L￨IN￨O￨- Martins￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 29￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- applied￨L￨VBD￨O￨- the￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- exchange￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- opinions￨L￨NNS￨O￨A and￨L￨CC￨O￨- Mare￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 31￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- studied￨L￨VBD￨O￨- an￨L￨DT￨O￨- opinion￨L￨NN￨O￨- persuasion￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- game￨L￨NN￨O￨- theory.It￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- distortion￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- distortions￨L￨NNS￨O￨- thus￨L￨RB￨O￨- produced￨L￨VBN￨O￨- are￨L￨VBP￨O￨- vital￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- rumors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- information￨L￨NN￨O￨- entropy￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- considerations￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- memory￨L￨NN￨O￨- ,￨L￨,￨O￨- conformity￨L￨NN￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- subjective￨L￨JJ￨O￨- propensity￨L￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- distortions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- trust￨L￨NN￨O￨- that￨L￨IN￨O￨- people￨L￨NNS￨O￨- place￨L￨VBP￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- K￨U￨NN￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- was￨L￨VBD￨O￨- subsequently￨L￨RB￨O￨- analyzed￨L￨VBN￨O￨- regarding￨L￨VBG￨O￨- average￨L￨JJ￨O￨- information￨L￨NN￨O￨- entropy￨L￨NN￨O￨A ,￨L￨,￨O￨- opinion￨L￨NN￨O￨- fragmentation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- linear￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨A models￨L￨NNS￨O￨A we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- section￨L￨NN￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- formwhere￨L￨NN￨O￨- X￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- n￨L￨NN￨O￨- state￨L￨NN￨O￨- variables￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- constant￨L￨JJ￨O￨- inflows￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- M￨U￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- n￨L￨NN￨O￨- ×￨L￨NN￨O￨- n￨L￨NN￨O￨- transition￨L￨NN￨O￨- rate￨L￨NN￨O￨- matrix￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- we￨L￨PRP￨O￨- began￨L￨VBD￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- states￨L￨NNS￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- ,￨L￨,￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- wished￨L￨VBD￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- a￨L￨DT￨O￨- product￨L￨NN￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- would￨L￨MD￨O￨- expect￨L￨VB￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- infectives￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- region￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- inflow￨L￨NN￨O￨- with￨L￨IN￨O￨- rate￨L￨NN￨O￨- Λ￨U￨NN￨O￨- and￨L￨CC￨O￨- outflow￨L￨NN￨O￨- with￨L￨IN￨O￨- rate￨L￨NN￨O￨- μN￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- immigration-death￨L￨JJ￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- elementary￨L￨JJ￨O￨- ordinary￨L￨JJ￨O￨A differential￨L￨JJ￨O￨A equation￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- dN/dt￨L￨NN￨O￨- =￨L￨JJ￨O￨- Λ￨U￨NN￨O￨- −￨L￨NN￨O￨- μN￨L￨NN￨O￨- .￨L￨.￨O￨- )￨L￨-RRB-￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- data￨L￨NNS￨O￨- incompleteness￨L￨NN￨O￨- or￨L￨CC￨O￨- limited￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- measured￨L￨VBN￨O￨- contact￨L￨NN￨O￨- network20￨L￨NN￨O￨- ,21,22,23￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- it￨L￨PRP￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- data-driven￨L￨JJ￨O￨- models￨L￨NNS￨O￨- using￨L￨VBG￨O￨- incomplete￨L￨JJ￨O￨A data20￨L￨NN￨O￨- ,￨L￨,￨O￨- 23,24,25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- importantly￨L￨RB￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- or￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- from￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- information26￨L￨NN￨O￨- ,27,28￨L￨CD￨NUMBER￨- and/or￨L￨CC￨O￨- to￨L￨TO￨O￨- devise￨L￨VB￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- correctly￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- risk￨L￨NN￨O￨- even￨L￨RB￨O￨- from￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- data23￨L￨NN￨O￨- ,￨L￨,￨O￨- 29￨L￨CD￨NUMBER￨- [￨L￨-LRB-￨O￨- Note￨U￨VB￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- wearable￨L￨JJ￨O￨- sensors￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- opposite￨L￨JJ￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- false￨L￨JJ￨O￨- positives￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- propagation￨L￨NN￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- arise￨L￨VB￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- similar￨L￨JJ￨O￨- method￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- work￨L￨VB￨O￨- well￨L￨RB￨O￨- also￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- diaries￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- wearable￨L￨JJ￨O￨- sensors29￨L￨NN￨O￨- :￨L￨:￨O￨- although￨L￨IN￨O￨- not￨L￨RB￨O￨- all￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- diaries￨L￨NNS￨O￨- ,￨L￨,￨O￨- building￨L￨VBG￨O￨- surrogate￨L￨JJ￨O￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- matrix￨L￨NN￨O￨- measured￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- diaries￨L￨NNS￨O￨- and￨L￨CC￨O￨- publicly￨L￨RB￨O￨- available￨L￨JJ￨O￨- statistics￨L￨NNS￨O￨- on￨L￨IN￨O￨- contact￨L￨NN￨O￨- durations￨L￨NNS￨O￨- made￨L￨VBD￨O￨- it￨L￨PRP￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- correctly￨L￨RB￨O￨A estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- using￨L￨VBG￨O￨- surrogate￨L￨JJ￨O￨- data￨L￨NNS￨O￨- built￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- uniform￨L￨JJ￨O￨- population￨L￨NN￨O￨- sampling￨L￨NN￨O￨- yields￨L￨VBZ￨O￨- an￨L￨DT￨O￨- improvement￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sampled￨L￨VBN￨O￨A data￨L￨NNS￨O￨- but￨L￨CC￨O￨- is￨L￨VBZ￨O￨- strongly￨L￨RB￨O￨- limited￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- underestimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- density￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sampled￨L￨VBN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Uniform￨U￨NN￨O￨- node￨L￨NN￨O￨- sampling￨L￨NN￨O￨A indeed￨L￨RB￨O￨- maintains￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- density￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- contact￨L￨NN￨O￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- densities￨L￨NNS￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- structured￨L￨VBN￨O￨- in￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- classes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- school￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- recent￨L￨JJ￨O￨- sparse￨L￨JJ￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- SINDy￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- uses￨L￨VBZ￨O￨- sparse￨L￨JJ￨O￨- regression￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- Pareto￨U￨NNP￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- correctly￨L￨RB￨O￨A discover￨L￨VB￨O￨- parsimonious￨L￨JJ￨O￨- governing￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- combinatorially￨L￨RB￨O￨- large￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Schematic￨U￨JJ￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- generation￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- generation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- terms￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- relative￨L￨JJ￨O￨- Akaike￨U￨JJ￨MISC￨- information￨L￨NN￨O￨- criteria￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- AICc￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Section￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- shows￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- down-selected￨L￨VBN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- combinatorially￨L￨RB￨O￨- large￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- space￨L￨NN￨O￨- using￨L￨VBG￨O￨- SINDy￨U￨NNP￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- further￨L￨JJ￨O￨- sub-selected￨L￨JJ￨O￨- and￨L￨CC￨O￨- ranked￨L￨VBD￨O￨- using￨L￨VBG￨O￨- information￨L￨NN￨O￨- criteria￨L￨NNS￨O￨A .￨L￨.￨O￨- +As￨U￨IN￨O￨- outlined￨L￨VBN￨O￨- in￨L￨IN￨O￨- figure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- AIC￨U￨NNP￨ORGANIZATION￨- scores￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- correctly￨L￨RB￨O￨A infer￨L￨VB￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time-series￨L￨NNS￨O￨- dataset￨L￨VBP￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- combinatorially￨L￨RB￨O￨- large￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- manuscript￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Akaike￨U￨NNP￨O￨- information￨L￨NN￨O￨- criteria￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- AIC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- connected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- SINDy￨U￨NNP￨O￨- architecture￨L￨NN￨O￨- to￨L￨TO￨O￨- hierarchically￨L￨RB￨O￨- rank￨L￨VB￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Pareto￨U￨NNP￨O￨- front￨L￨NN￨O￨- for￨L￨IN￨O￨- automatic￨L￨JJ￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- informative￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Based￨U￨VBD￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- simulating￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- associated￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- cervical￨L￨JJ￨O￨- intraepithelial￨L￨JJ￨O￨- neoplasia￨L￨NN￨O￨- ,￨L￨,￨O￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- genital￨L￨JJ￨O￨- warts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- HPV￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- quadrivalent￨L￨NN￨O￨- and￨L￨CC￨O￨- bivalent￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- .￨L￨.￨O￨- +Kaufmann7￨U￨NN￨O￨- ,￨L￨,￨O￨- Yvonne￨U￨NNP￨PERSON￨- Deleré8￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Bernhard￨U￨NNP￨PERSON￨- Ultsch9￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ole￨U￨JJ￨O￨- Wichmann9￨U￨NN￨O￨- ,￨L￨,￨O￨- Alexander￨U￨NNP￨PERSON￨- Krämer10￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wolfgang￨U￨NNP￨PERSON￨- Greiner1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 15:18￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- papillomavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HPV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- cervical￨L￨JJ￨CAUSE_OF_DEATH￨- cancer￨L￨NN￨CAUSE_OF_DEATH￨A screening￨L￨NN￨O￨- programme￨L￨NN￨O￨- in￨L￨IN￨O￨- Germany￨U￨NNP￨COUNTRY￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Forecasting￨U￨NN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- subject￨L￨NN￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- forcingPaige￨L￨NNP￨O￨- B.￨U￨NNP￨O￨- Forecasting￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- using￨L￨VBG￨O￨- early￨L￨JJ￨O￨- warning￨L￨NN￨O￨- signals￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- EWS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- in￨L￨IN￨O￨- non-seasonal￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- proposed￨L￨VBD￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- new￨L￨JJ￨O￨- early￨L￨JJ￨O￨- warning￨L￨NN￨O￨- signals￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- wavelet￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assessed￨L￨VBD￨O￨- whether￨L￨IN￨O￨- EWS￨U￨NNP￨O￨- also￨L￨RB￨O￨- anticipate￨L￨VBP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨A in￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Large￨U￨JJ￨O￨- order￨L￨NN￨O￨- fluctuations￨L￨NNS￨O￨A ,￨L￨,￨O￨- switching￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Jason￨U￨NNP￨PERSON￨- Hindes1￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Ira￨U￨NNP￨O￨- B.￨U￨NNP￨O￨- Schwartz1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 10663￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksNonlinear￨L￨NN￨O￨- phenomenaStatistical￨L￨JJ￨O￨- physics￨L￨NN￨O￨- AbstractWe￨U￨NN￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- technique￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- large￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- and￨L￨CC￨O￨- switching￨L￨NN￨O￨- from￨L￨IN￨O￨- internal￨L￨JJ￨O￨- noise￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- switching￨L￨NN￨O￨- between￨L￨IN￨O￨- ordered￨L￨VBN￨O￨- states￨L￨NNS￨O￨- for￨L￨IN￨O￨- networks￨L￨NNS￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- mean-field￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- order-disorder￨L￨JJ￨O￨- kinetics￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- construct￨L￨VBP￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- probable￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- optimal￨L￨JJ￨O￨- path￨L￨NN￨O￨- of￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨A from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- ordered￨L￨VBN￨O￨- state￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- and￨L￨CC￨O￨- synthetic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- quantify￨L￨VBP￨O￨- how￨L￨WRB￨O￨- network￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- scaling￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- rainfall￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨A transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- this￨L￨DT￨O￨- condition￨L￨NN￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- to￨L￨TO￨O￨- lay￨L￨VB￨O￨- their￨L￨PRP$￨O￨- eggs￨L￨NNS￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- mosquito￨L￨NN￨O￨- to￨L￨TO￨O￨- come￨L￨VB￨O￨- into￨L￨IN￨O￨- contact￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨A transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- either￨L￨CC￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- vectors￨L￨NNS￨O￨- or￨L￨CC￨O￨- interrupt￨L￨VB￨O￨- the￨L￨DT￨O￨- human-vector￨L￨JJ￨O￨- contact￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- see￨L￨VB￨O￨- from￨L￨IN￨O￨- Figures￨U￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- rainfall￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- cosine￨L￨JJ￨O￨- function￨L￨NN￨O￨- dependence￨L￨NN￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- Stolwijk￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mosquitoes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Dengue￨U￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨A that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- human￨L￨JJ￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- bite￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- most￨L￨JJS￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- simulate￨L￨VBP￨O￨- curves￨L￨NNS￨O￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- these￨L￨DT￨O￨- approaches￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- outbreak￨L￨NN￨O￨- curves￨L￨NNS￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- ODA￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- an￨L￨DT￨O￨- overall￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- trend￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- until￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- quality￨L￨NN￨O￨- forecasting￨L￨NN￨O￨- is￨L￨VBZ￨O￨- achieved￨L￨VBN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- realistic￨L￨JJ￨O￨- averaged￨L￨VBD￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- describing￨L￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- regard￨L￨NN￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- curves￨L￨NNS￨O￨A ,￨L￨,￨O￨- several￨L￨JJ￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- pointed￨L￨VBN￨O￨- out￨L￨RP￨O￨- NumericCitation￨U￨NNP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- signals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- hindered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- shortage￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- enough￨L￨RB￨O￨- clearly-defined￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- signals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- authors￨L￨NNS￨O￨- including￨L￨VBG￨O￨- Buckeridge￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Jackson￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- algorithm￨L￨NN￨O￨- evaluation￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨A curve￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- shape￨L￨NN￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- mean￨L￨NN￨O￨- and￨L￨CC￨O￨- variance￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- outbreak￨L￨NN￨O￨A detection￨L￨NN￨O￨- algorithms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ODA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- Chen￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- review￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- designers￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- laboratory￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- opt￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- suitable￨L￨JJ￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- simpler￨L￨JJR￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- build￨L￨VB￨O￨- the￨L￨DT￨O￨- synthetic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨A curve￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- its￨L￨PRP$￨O￨- expected￨L￨JJ￨O￨- shape￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Lessons￨U￨NNPS￨MISC￨- from￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- decade￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- individual-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A :￨L￨:￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2006-2015￨L￨CD￨DURATION￨- )￨L￨-RRB-￨O￨- Lander￨U￨NNP￨O￨- Willem1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Frederik￨U￨NNP￨O￨- Verelst1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Joke￨U￨NNP￨O￨- Bilcke1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Niel￨U￨NNP￨PERSON￨- Hens1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Philippe￨U￨NNP￨PERSON￨- Beutels1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3BMC￨L￨NNP￨O￨- Infectious￨U￨JJ￨O￨- DiseasesBMC￨U￨NN￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 17:612￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Individual-based￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IBMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- useful￨L￨JJ￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- events￨L￨NNS￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- stochasticity￨L￨NN￨O￨- and/or￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- well￨L￨RB￨O￨- established￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- re￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- bioterrorism￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Individual￨U￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- level￨L￨NN￨O￨- is￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- documented￨L￨VBN￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- understood￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- elimination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- vaccine-preventable￨L￨JJ￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- polio￨L￨NNP￨O￨- ,￨L￨,￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- stochasticity￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extracted￨L￨VBD￨O￨- detailed￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- features￨L￨NNS￨O￨- from￨L￨IN￨O￨- papers￨L￨NNS￨O￨- on￨L￨IN￨O￨- established￨L￨JJ￨O￨- vaccine-preventable￨L￨JJ￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A based￨L￨VBN￨O￨- on￨L￨IN￨O￨- full-text￨L￨JJ￨O￨- screening￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- identified￨L￨VBD￨O￨- 698￨L￨CD￨NUMBER￨- papers￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- applied￨L￨VBD￨O￨- an￨L￨DT￨O￨- IBM￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- listed￨L￨VBN￨O￨- these￨L￨DT￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- reference￨L￨NN￨O￨- database￨L￨NN￨O￨- ,￨L￨,￨O￨- describing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- general￨L￨JJ￨TITLE￨- characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- interacting￨L￨VBG￨O￨- components￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- circles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- multiple￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- shaded￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- surrounding￨L￨VBG￨O￨- the￨L￨DT￨O￨- components￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- above-mentioned￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- also￨L￨RB￨O￨- face￨L￨VBP￨O￨- with￨L￨IN￨O￨- new￨L￨JJ￨O￨- opportunities￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- data-centric￨L￨JJ￨O￨- era￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- enabled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- confluence￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- various￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- analytical￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- in￨L￨IN￨O￨- data￨L￨NNS￨O￨- science￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- interacting￨L￨VBG￨O￨- and￨L￨CC￨O￨- coupling￨L￨NN￨O￨- relationships￨L￨NNS￨O￨- among￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- impact￨L￨NN￨O￨- factors￨L￨NNS￨O￨A have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- temporally￨L￨RB￨O￨- ,￨L￨,￨O￨- spatially￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- socially￨L￨RB￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- exhibiting￨L￨VBG￨O￨- systems￨L￨NNS￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- feedback￨L￨NN￨O￨- ,￨L￨,￨O￨- saturation￨L￨NN￨O￨- ,￨L￨,￨O￨- bifurcation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- chaos￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- make￨L￨VBP￨O￨- it￨L￨PRP￨O￨- hardly￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- utilize￨L￨VB￨O￨- the￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- comprehensive￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- forcing￨L￨VBG￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- snail￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- observed￨L￨VBN￨O￨- to￨L￨TO￨O￨- follow￨L￨VB￨O￨- seasonal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Later￨U￨RBR￨O￨- works￨L￨VBZ￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- played￨L￨VBN￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- water￨L￨NN￨O￨A sources￨L￨NNS￨O￨- and￨L￨CC￨O￨- individual￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- site-specific￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- features￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- local-scale￨L￨JJ￨O￨- heterogeneities￨L￨NNS￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- coupling￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- schistosomiasis￨L￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- emphasis￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- integration￨L￨NN￨O￨- of￨L￨IN￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- water￨L￨NN￨O￨A bodies￨L￨NNS￨O￨- may￨L￨MD￨O￨- represent￨L￨VB￨O￨- habitats￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- quality￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- snail￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- schistosomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- thus￨L￨RB￨O￨- be￨L￨VB￨O￨- relatively￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- snail￨L￨NN￨O￨- population￨L￨NN￨O￨- abundance￨L￨NN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- e.g￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- communities￨L￨NNS￨O￨- with￨L￨IN￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- several￨L￨JJ￨O￨- water￨L￨NN￨O￨A sources￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- risk￨L￨NN￨O￨- group￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- endowed￨L￨VBN￨O￨- with￨L￨IN￨O￨- differential￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- specific￨L￨JJ￨O￨- water-contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- schistosomiasis￨L￨NN￨O￨- transmission￨L￨NN￨O￨- also￨L￨RB￨O￨- requires￨L￨VBZ￨O￨- an￨L￨DT￨O￨- account￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- preferences￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- water￨L￨NN￨O￨A contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g￨L￨FW￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- were￨L￨VBD￨O￨- 214￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- clinical￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- 438,000￨L￨CD￨NUMBER￨- malaria-attributable￨L￨JJ￨O￨- deaths￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- occurred￨L￨VBD￨O￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- 88￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- deaths￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A a￨L￨DT￨O￨- leading￨L￨VBG￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- problem￨L￨NN￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- burden￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- geospatial￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- costing￨L￨VBG￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- optimization￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- budgeted￨L￨VBN￨O￨- and￨L￨CC￨O￨- projected￨L￨VBN￨O￨- funds￨L￨NNS￨O￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A intervention￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Allocative￨U￨JJ￨O￨- efficiency￨L￨NN￨O￨- gains￨L￨NNS￨O￨- could￨L￨MD￨O￨- avert￨L￨VB￨O￨- approximately￨L￨RB￨O￨- 84,000￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- or￨L￨CC￨O￨- 15.7￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Nigeria￨U￨NNP￨COUNTRY￨- over￨L￨IN￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Wilson1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 16:368￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- high￨L￨JJ￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- limited￨L￨JJ￨O￨- funding￨L￨NN￨O￨- means￨L￨VBZ￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- necessity￨L￨NN￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- allocative￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Importantly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- modulating￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- contact￨L￨NN￨O￨- structure￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- reversion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- strongest￨L￨JJS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- biologically￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- case￨L￨NN￨O￨- when￨L￨WRB￨O￨- fitness￨L￨NN￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- in￨L￨IN￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- are￨L￨VBP￨O￨- small￨L￨JJ￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- treatment￨L￨NN￨O￨- guidelines￨L￨NNS￨O￨- typically￨L￨RB￨O￨- occur￨L￨VBP￨O￨- much￨L￨RB￨O￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨A strain￨L￨NN￨O￨- has￨L￨VBZ￨O￨- fixed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- population￨L￨NN￨O￨- across￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- expect￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- crossing￨L￨VBG￨O￨- of￨L￨IN￨O￨- fitness￨L￨NN￨O￨- valleys￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- not￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- reversion￨L￨NN￨O￨- back￨L￨RB￨O￨- to￨L￨TO￨O￨- sensitivity￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- study￨L￨NN￨O￨- reveals￨L￨VBZ￨O￨- that￨L￨IN￨O￨- large￨L￨JJ￨O￨- fitness￨L￨NN￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- non-trivial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- reversion￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- once￨L￨RB￨DATE￨- treatment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stopped￨L￨VBN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- resistant￨L￨JJ￨O￨A strain￨L￨NN￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- fitness￨L￨NN￨O￨- deficit￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- impacts￨L￨NNS￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- manner￨L￨NN￨O￨- largely￨L￨RB￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- de￨L￨FW￨O￨- novo￨L￨FW￨O￨- emergence￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 40￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 42￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- wild-type￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- strains￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- simultaneously￨L￨RB￨O￨- spreading￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Published￨U￨VBN￨O￨- literature￨L￨NN￨O￨- in￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- categories￨L￨NNS￨O￨- are￨L￨VBP￨O￨- reviewed￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- identifying￨L￨VBG￨O￨- non-traditional￨L￨JJ￨O￨- but￨L￨CC￨O￨- critical￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- for￨L￨IN￨O￨- VL￨U￨NNP￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- resource￨L￨NN￨O￨- limited￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- Leishmaniasis￨U￨NNP￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- related￨L￨JJ￨O￨- vector￨L￨NN￨O￨A borne￨L￨VBD￨O￨A infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- identified￨L￨VBN￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- its￨L￨PRP$￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Challenges￨U￨NNS￨MISC￨- in￨L￨IN￨O￨- modeling￨L￨NN￨O￨- complexity￨L￨NN￨O￨- of￨L￨IN￨O￨- neglected￨L￨VBN￨O￨- tropical￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- visceral￨L￨JJ￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- resource￨L￨NN￨O￨- limited￨L￨JJ￨O￨- settingsSwati￨L￨NN￨O￨- DebRoy1￨U￨NN￨O￨- ,￨L￨,￨O￨- Olivia￨U￨JJ￨O￨- Prosper2￨U￨NN￨O￨- ,￨L￨,￨O￨- Austin￨U￨NNP￨CITY￨- Mishoe1￨U￨NNP￨O￨- and￨L￨CC￨O￨- Anuj￨U￨NNP￨PERSON￨- Mubayi3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 14:10￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Objectives￨U￨NNS￨O￨- Neglected￨U￨VBN￨O￨- tropical￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- NTD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- account￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- control￨L￨NN￨O￨- faces￨L￨VBZ￨O￨- several￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨A including￨L￨VBG￨O￨- diminishing￨L￨VBG￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- financial￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- for￨L￨IN￨O￨- those￨L￨DT￨O￨- distressed￨L￨JJ￨O￨- from￨L￨IN￨O￨- such￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- reviews￨L￨VBZ￨O￨- literature￨L￨NN￨O￨- on￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- collects￨L￨VBZ￨O￨- challenges￨L￨NNS￨O￨A and￨L￨CC￨O￨- successes￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- recommends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- MDA￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- elimination￨L￨NN￨O￨A of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- only￨L￨RB￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- approaching￨L￨VBG￨O￨- interruption￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- good￨L￨JJ￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- effective￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- re-introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- models￨L￨NNS￨O￨- range￨L￨VBP￨O￨- from￨L￨IN￨O￨- simple￨L￨JJ￨O￨- conceptual￨L￨JJ￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- distinguishing￨L￨VBG￨O￨- between￨L￨IN￨O￨- infection-versus￨L￨JJ￨O￨- vaccination-induced￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- inclusion￨L￨NN￨O￨A of￨L￨IN￨O￨- primary￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- failure￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- leaky￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- inclusion￨L￨NN￨O￨- of￨L￨IN￨O￨- age-dependent￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +Currently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- variable￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨A of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- has￨L￨VBZ￨O￨- had￨L￨VBN￨O￨- little￨L￨JJ￨O￨- attention￨L￨NN￨O￨- in￨L￨IN￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- cost-effectiveness￨L￨NN￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- annual￨L￨JJ￨SET￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨A of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- causes￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Importantly￨U￨RB￨O￨- ,￨L￨,￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨A of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- variable￨L￨JJ￨O￨- duration￨L￨NN￨O￨A of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- resistant￨L￨JJ￨O￨A and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- frog￨L￨NN￨O￨- species￨L￨NNS￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fungal￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- Batrachochytridium￨U￨NN￨O￨- dendrobatidis￨L￨VBZ￨O￨- upregulated￨L￨VBN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- experienced￨L￨VBD￨O￨- different￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outcomes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Characterizing￨U￨VBG￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- of￨L￨IN￨O￨- tolerant￨L￨JJ￨O￨- or￨L￨CC￨O￨- resistant￨L￨JJ￨O￨A vertebrate￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- fungal￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- identify￨L￨VB￨O￨- adaptive￨L￨JJ￨O￨- genes￨L￨NNS￨O￨- or￨L￨CC￨O￨- processes￨L￨NNS￨O￨- linked￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduced￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- or￨L￨CC￨O￨- occurrence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- can￨L￨MD￨O￨- then￨L￨RB￨O￨- inform￨L￨VB￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- species￨L￨NNS￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- species￨L￨NNS￨O￨- recently￨L￨RB￨DATE￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- insufficient￨L￨JJ￨O￨- time￨L￨NN￨O￨- has￨L￨VBZ￨O￨- elapsed￨L￨VBN￨O￨- for￨L￨IN￨O￨- selection￨L￨NN￨O￨- for￨L￨IN￨O￨- tolerance￨L￨NN￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- pathways￨L￨NNS￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- tolerant￨L￨JJ￨O￨- ,￨L￨,￨O￨- resistant￨L￨JJ￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- can￨L￨MD￨O￨- differ￨L￨VB￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- molecular￨L￨JJ￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +Few￨U￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- fungal￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- vertebrate￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- well￨L￨RB￨O￨- understood￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- these￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- often￨L￨RB￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- species￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Nevertheless￨U￨RB￨O￨- ,￨L￨,￨O￨- network￨L￨NN￨O￨- immunization￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- important￨L￨JJ￨O￨- in￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- for￨L￨IN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- links￨L￨NNS￨O￨A are￨L￨VBP￨O￨- evident￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- livestock￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- one￨L￨CD￨NUMBER￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- farm￨L￨NN￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- are￨L￨VBP￨O￨- connections￨L￨NNS￨O￨- by￨L￨IN￨O￨- transport￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- thus￨L￨RB￨O￨- three￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- costs￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- an￨L￨DT￨O￨- endeavor￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- itself￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- as￨L￨IN￨O￨- our￨L￨PRP$￨O￨- base￨L￨NN￨O￨- unit￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- gathering￨L￨VBG￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- cinfo￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- units￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- person￨L￨NN￨O￨- getting￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- cvacc￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- carry￨L￨VB￨O￨- out￨L￨RP￨O￨- a￨L￨DT￨O￨- targeted￨L￨VBN￨O￨A vaccination￨L￨NN￨O￨- campaign￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- would￨L￨MD￨O￨- first￨L￨RB￨ORDINAL￨- need￨L￨VB￨O￨- to￨L￨TO￨O￨- gather￨L￨VB￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- use￨L￨VB￨O￨- this￨L￨DT￨O￨- information￨L￨NN￨O￨- to￨L￨TO￨O￨- vaccinate￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- otherwise￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- strategy￨L￨NN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- works￨L￨VBZ￨O￨- by￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨A all￨L￨DT￨O￨- network￨L￨NN￨O￨- neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- person￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- premises￨L￨NNS￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- —￨L￨:￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- most￨L￨RBS￨O￨- active￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- being￨L￨VBG￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- exploit￨L￨VB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- targeted￨L￨VBN￨O￨A vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- non-rodent￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- cats￨L￨NNS￨O￨- and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- antibody-mediated￨L￨JJ￨O￨- immune￨L￨JJ￨O￨A responses￨L￨NNS￨O￨A to￨L￨TO￨O￨- persistent￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- appear￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- common￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- least￨L￨JJS￨O￨- twelve￨L￨CD￨NUMBER￨- known￨L￨JJ￨O￨- species￨L￨NNS￨O￨- or￨L￨CC￨O￨- subspecies￨L￨NNS￨O￨- of￨L￨IN￨O￨- Bartonella￨U￨NNP￨PERSON￨- bacteria￨L￨NNS￨O￨- are￨L￨VBP￨O￨- now￨L￨RB￨DATE￨- recognized￨L￨VBN￨O￨A zoonotic￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- others￨L￨NNS￨O￨- ,￨L￨,￨O￨- B.￨U￨NNP￨PERSON￨- Among￨U￨IN￨PERSON￨- Bartonella￨U￨NNP￨PERSON￨- spp.￨L￨NNP￨O￨- ,￨L￨,￨O￨- B.￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- B.￨U￨NNP￨O￨- antigens￨L￨NNS￨O￨- in￨L￨IN￨O￨- rodent￨L￨JJ￨O￨- serum￨L￨NN￨O￨- samples￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- but￨L￨CC￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- Bartonella￨U￨NNP￨PERSON￨- spp￨L￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- projected￨L￨VBN￨O￨A age-specific￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- demographic￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- POLYMOD￨U￨NN￨LOCATION￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- validated￨L￨VBN￨O￨- approximations￨L￨NNS￨O￨- to￨L￨TO￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- when￨L￨WRB￨O￨- directly￨L￨RB￨O￨- measured￨L￨VBN￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- POLYMOD￨U￨NN￨O￨- survey￨L￨NN￨O￨- collected￨L￨VBN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- contact￨L￨NN￨O￨- occurred￨L￨VBD￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- refined￨L￨JJ￨O￨- projection￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- household￨L￨NN￨O￨- structures￨L￨NNS￨O￨- ,￨L￨,￨O￨- labor-force￨L￨JJ￨O￨- participation￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- enrolment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- separately￨L￨RB￨O￨- projecting￨L￨VBG￨O￨- contacts￨L￨NNS￨O￨A in￨L￨IN￨O￨- different￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- tailor￨L￨VB￨O￨- the￨L￨DT￨O￨- POLYMOD￨U￨NN￨O￨- estimates￨L￨VBZ￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- setting￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- to￨L￨TO￨O￨- adjust￨L￨VB￨O￨- them￨L￨PRP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- age-profiles￨L￨NNS￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- country￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- eight￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- EU￨U￨NNP￨LOCATION￨- that￨L￨WDT￨O￨- contributed￨L￨VBD￨O￨- to￨L￨TO￨O￨- POLYMOD￨U￨NN￨O￨- ,￨L￨,￨O￨- inflating￨L￨VBG￨O￨- the￨L￨DT￨O￨- projected￨L￨VBN￨O￨A number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- younger￨L￨JJR￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- country￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- young￨L￨JJ￨O￨- age-profile￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- concurrently￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- projected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- elderly￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨A structure￨L￨NN￨O￨A of￨L￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- socioeconomic￨L￨JJ￨O￨- development￨L￨NN￨O￨- ,￨L￨,￨O￨- family￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- transition￨L￨NN￨O￨- differ￨L￨VBP￨O￨- substantially￨L￨RB￨O￨- and￨L￨CC￨O￨- contact￨L￨VB￨O￨- patterns￨L￨NNS￨O￨- concomitantly￨L￨RB￨O￨- vary￨L￨VBP￨O￨- across￨L￨IN￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- measured￨L￨VBD￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨A structure￨L￨NN￨O￨A of￨L￨IN￨O￨- ~￨L￨NN￨O￨- 100￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- contacts￨L￨NNS￨O￨- across￨L￨IN￨O￨- eight￨L￨CD￨NUMBER￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- using￨L￨VBG￨O￨- paper￨L￨NN￨O￨- diaries￨L￨NNS￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- POLYMOD￨U￨NN￨O￨- project￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- a￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- suggest￨L￨VBP￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- transmission￨L￨NN￨O￨- have￨L￨VBP￨O￨- emerged￨L￨VBN￨O￨- as￨L￨RB￨O￨- important￨L￨JJ￨O￨- tool￨L￨NN￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨- classification￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ICD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- ICD-10￨U￨NN￨MISC￨- code￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- process￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- phases￨L￨NNS￨O￨- :￨L￨:￨O￨- acute￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- period￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- B23￨U￨NN￨O￨- .0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Z20￨U￨NN￨O￨- .6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Z21￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- typical￨L￨JJ￨O￨- of￨L￨IN￨O￨- AIDS￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- B20￨U￨NN￨O￨- ~￨L￨NN￨O￨- B24￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- modify￨L￨VBP￨O￨- the￨L￨DT￨O￨- SEI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- patients￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- stage￨L￨NN￨O￨- were￨L￨VBD￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- apply￨L￨VB￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- time￨L￨NN￨O￨- dependent￨L￨JJ￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- Global￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Observatory￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- GHO￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- World￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- Organization￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- almost￨L￨RB￨O￨- 78￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨A people￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- about￨L￨IN￨O￨- 39￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- have￨L￨VBP￨O￨- died￨L￨VBN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- about￨L￨RB￨O￨- 35.0￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- were￨L￨VBD￨O￨- living￨L￨VBG￨O￨- with￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- and￨L￨CC￨O￨- 1.5￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- died￨L￨VBD￨O￨- of￨L￨IN￨O￨- AIDS-related￨U￨JJ￨O￨- illnesses￨L￨NNS￨O￨- worldwide￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- direct￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- adverse￨L￨JJ￨O￨- health￨L￨NN￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- toxins￨L￨NNS￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- issue￨L￨NN￨O￨- of￨L￨IN￨O￨- combating￨L￨VBG￨O￨- the￨L￨DT￨O￨- concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- AFs￨U￨NNS￨O￨- in￨L￨IN￨O￨- foods￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- difficult￨L￨JJ￨O￨- task￨L￨NN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- cloud￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainties￨L￨NNS￨O￨- which￨L￨WDT￨O￨- might￨L￨MD￨O￨- arise￨L￨VB￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- exposure￨L￨NN￨O￨- ,￨L￨,￨O￨- constrains￨L￨VBZ￨O￨- inprocuring￨L￨VBG￨O￨- representative￨L￨JJ￨TITLE￨- samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- food￨L￨NN￨O￨A from￨L￨IN￨O￨- subsistence￨L￨NN￨O￨- farmers￨L￨NNS￨O￨- ,￨L￨,￨O￨- multiple￨L￨JJ￨O￨- vulnerable￨L￨JJ￨O￨- crops￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- relevant￨L￨JJ￨O￨- confounding￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- mask￨L￨NN￨O￨- or￨L￨CC￨O￨- otherwise￨L￨RB￨O￨- obscure￨L￨JJ￨O￨- any￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- putative￨L￨JJ￨O￨- causative￨L￨JJ￨O￨- agent￨L￨NN￨O￨- within￨L￨IN￨O￨- food￨L￨NN￨O￨- supply￨L￨NN￨O￨- chain￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- AFs￨U￨NNS￨O￨- contamination￨L￨NN￨O￨A is￨L￨VBZ￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- Aspergillus￨U￨JJ￨O￨- species￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- ,￨L￨,￨O￨- farming￨L￨VBG￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- handling￨L￨VBG￨O￨- and￨L￨CC￨O￨- storage￨L￨NN￨O￨- practices￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- several￨L￨JJ￨O￨- other￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- toxins￨L￨NNS￨O￨- humans￨L￨NNS￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- make-up￨L￨NN￨O￨- ,￨L￨,￨O￨- drying￨L￨VBG￨O￨- or￨L￨CC￨O￨- evapo-transpiration￨L￨NN￨O￨- ,￨L￨,￨O￨- soil￨L￨NN￨O￨- nature￨L￨NN￨O￨- ,￨L￨,￨O￨- moisture￨L￨NN￨O￨- deficit￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- insect￨L￨JJ￨O￨- infestations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- numerous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- conducted￨L￨VBN￨O￨- showing￨L￨VBG￨O￨- toxicological￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- contamination￨L￨NN￨O￨A and￨L￨CC￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- AFs￨U￨NNS￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- mycotoxins￨L￨NNS￨O￨- ,￨L￨,￨O￨- aflatoxins￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- AFs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- principal￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- challenging￨L￨JJ￨O￨- in￨L￨IN￨O￨- foods￨L￨NNS￨O￨- and￨L￨CC￨O￨- animal￨L￨NN￨O￨- feeds￨L￨VBZ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- associated￨L￨VBN￨O￨- toxicity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- mutagenicity￨L￨NN￨O￨- ,￨L￨,￨O￨- carcinogenicity￨L￨NN￨O￨- and￨L￨CC￨O￨- teratogenicity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- heat￨L￨NN￨O￨- resistance￨L￨NN￨O￨- during￨L￨IN￨O￨- food￨L￨NN￨O￨A processing￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- probable￨L￨JJ￨O￨- intermediary￨L￨JJ￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- transmitted￨L￨VBD￨O￨- proto-HSV2￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- henceforth￨L￨NN￨O￨- HSV2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- anc-chimps￨L￨NNS￨O￨- to￨L￨TO￨O￨- modern￨L￨JJ￨O￨A humans￨L￨NNS￨O￨- involves￨L￨VBZ￨O￨- four￨L￨CD￨NUMBER￨- steps￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- acquisition￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- involves￨L￨VBZ￨O￨- collecting￨L￨VBG￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- fossil￨L￨NN￨O￨- records￨L￨NNS￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- intermediary￨L￨JJ￨O￨- hominins￨L￨NNS￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- geographical￨L￨JJ￨O￨- range￨L￨NN￨O￨- and￨L￨CC￨O￨- time-period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- tropical￨L￨JJ￨O￨- rainforest￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- network￨L￨NN￨O￨- generation￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- paths￨L￨NNS￨O￨- of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- from￨L￨IN￨O￨- anc-chimps￨L￨NNS￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- through￨L￨IN￨O￨- different￨L￨JJ￨O￨- hominins￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- created￨L￨VBN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- probabilistic￨L￨JJ￨O￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- involves￨L￨VBZ￨O￨- assigning￨L￨VBG￨O￨- weights￨L￨NNS￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- paths￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- network￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- optimal￨L￨JJ￨O￨- path￨L￨NN￨O￨- traversal￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- evaluates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- path￨L￨NN￨O￨- from￨L￨IN￨O￨- anc-chimps￨L￨NNS￨O￨- to￨L￨TO￨O￨- modern￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- weights￨L￨NNS￨O￨- assigned￨L￨VBN￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- hypothesise￨L￨VBP￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- combining￨L￨VBG￨O￨- fossil￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- when￨L￨WRB￨O￨- and￨L￨CC￨O￨- where￨L￨WRB￨O￨- different￨L￨JJ￨O￨- hominin￨L￨NN￨O￨- species￨L￨NNS￨O￨- were￨L￨VBD￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- geographical￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- modern￨L￨JJ￨O￨A chimpanzees￨L￨NNS￨O￨- and￨L￨CC￨O￨- bonobos￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- reconstructed￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- tropical￨L￨JJ￨O￨- rainforest￨L￨NN￨O￨- habitat￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- proxy￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- chimpanzee/bonobo￨L￨NN￨O￨- ancestor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- anc-chimps￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- it￨L￨PRP￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- statistically￨L￨RB￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- facilitated￨L￨VBD￨O￨- the￨L￨DT￨O￨- host-switch￨L￨NN￨O￨- of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- modern￨L￨JJ￨O￨- human￨L￨JJ￨O￨- lineage￨L￨NN￨O￨- defined￨L￨VBN￨O￨- here￨L￨RB￨O￨- as￨L￨IN￨O￨- beginning￨L￨VBG￨O￨- with￨L￨IN￨O￨- Homo￨U￨NN￨PERSON￨- erectus￨L￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- paths￨L￨NNS￨O￨A of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- from￨L￨IN￨O￨- anc-chimps￨L￨NNS￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- through￨L￨IN￨O￨- different￨L￨JJ￨O￨- hominins￨L￨NNS￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- directed￨L￨VBN￨O￨- acyclic￨L￨NN￨O￨- graph￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DAG￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- G￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- comprising￨L￨VBG￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- potential￨L￨JJ￨O￨- intermediary￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- connecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- species￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figs￨U￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- establish￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- probable￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- path￨L￨NN￨O￨- of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- from￨L￨IN￨O￨- anc-chimps￨L￨NNS￨O￨- to￨L￨TO￨O￨- modern￨L￨JJ￨O￨A humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- potential￨L￨JJ￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- intermediary￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- predicts￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- host-switch￨L￨NN￨O￨- of￨L￨IN￨O￨- HSV2￨U￨NN￨O￨- occurred￨L￨VBD￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- path￨L￨NN￨O￨A anc-chimps￨L￨NNS￨O￨- -￨L￨:￨O￨- >￨L￨JJR￨O￨- P.boisei￨U￨NN￨O￨- -￨L￨:￨O￨- >￨L￨JJR￨O￨- H.erectus￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- highlighted￨L￨VBN￨O￨- in￨L￨IN￨O￨- bold￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- has￨L￨VBZ￨O￨- tried￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- causative￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- for￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- successive￨L￨JJ￨O￨A years￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +Cases￨U￨NNS￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- with￨L￨IN￨O￨- classical￨L￨JJ￨O￨- presentation￨L￨NN￨O￨- and￨L￨CC￨O￨- having￨L￨VBG￨O￨- active￨L￨JJ￨O￨- oral￨L￨JJ￨O￨- lesions￨L￨NNS￨O￨- were￨L￨VBD￨O￨- selected￨L￨VBN￨O￨- during￨L￨IN￨O￨- monsoon￨L￨NN￨O￨- and￨L￨CC￨O￨- postmonsoon￨L￨NN￨O￨- session￨L￨NN￨O￨- between￨L￨IN￨O￨- July￨U￨NNP￨DATE￨- and￨L￨CC￨DATE￨- November￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- successive￨L￨JJ￨O￨A years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 2013￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2014￨L￨CD￨DATE￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- document￨L￨VB￨O￨- clinicoepidemiological￨L￨JJ￨O￨- profile￨L￨NN￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- and￨L￨CC￨O￨- molecular￨L￨JJ￨O￨A detection￨L￨NN￨O￨- of￨L￨IN￨O￨- circulating￨L￨VBG￨O￨- enteroviruses￨L￨NNS￨O￨- causing￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- Virological￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cases￨L￨NNS￨O￨A of￨L￨IN￨O￨- HFMD￨U￨NN￨ORGANIZATION￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- infrequently￨L￨RB￨O￨- done￨L￨VBN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- HFMD￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- enteroviral￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- caused￨L￨VBD￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨A by￨L￨IN￨O￨- enterovirus￨L￨NN￨O￨- 71￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- EV71￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- coxsackievirus￨L￨NN￨O￨- A16￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- CVA16￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨A techniques￨L￨NNS￨O￨- allow￨L￨VBP￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- shedding￨L￨VBG￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- predicting￨L￨VBG￨O￨- future￨L￨JJ￨DATE￨- trends￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Access￨U￨NN￨O￨- to￨L￨TO￨O￨- big￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- unanswered￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- enable￨L￨VBP￨O￨- novel￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- connect￨L￨VB￨O￨- within-host￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨A level￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- between-host￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Immunoepidemiological￨U￨JJ￨O￨- models￨L￨NNS￨O￨- factor￨L￨IN￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨A level￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Within-host￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨A level￨L￨NN￨O￨A study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- target￨L￨NN￨O￨- immune￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- —￨L￨:￨O￨- CD4￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- macrophages￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- dendritic￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- explicit￨L￨JJ￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨A mechanism￨L￨NN￨O￨- makes￨L￨VBZ￨O￨- process￨L￨NN￨O￨- models￨L￨NNS￨O￨- ideal￨L￨JJ￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- population-level￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- arise￨L￨VBP￨O￨- from￨L￨IN￨O￨- individual-level￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- ways￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- anticipate￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- details￨L￨NNS￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- today￨L￨NN￨DATE￨- feed￨L￨NN￨O￨- into￨L￨IN￨O￨- generating￨L￨VBG￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- tomorrow￨L￨NN￨DATE￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ABMs￨U￨NNS￨O￨- ;￨L￨:￨O￨- also￨L￨RB￨O￨- referred￨L￨VBN￨O￨A to￨L￨TO￨O￨- as￨L￨IN￨O￨- individual-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- modelled￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- state￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- plus￨L￨CC￨O￨- all￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- progresses￨L￨VBZ￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- rules￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- becoming￨L￨VBG￨O￨- increasingly￨L￨RB￨O￨A popular￨L￨JJ￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- drive￨L￨VBP￨O￨- the￨L￨DT￨O￨- host-to-host￨L￨JJ￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- within-host￨L￨NN￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- and￨L￨CC￨O￨- applied￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- these￨L￨DT￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- ,￨L￨,￨O￨- often￨L￨RB￨O￨- referred￨L￨VBN￨O￨A to￨L￨TO￨O￨- as￨L￨IN￨O￨- mechanistic￨L￨JJ￨O￨- or￨L￨CC￨O￨- process￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- increasingly￨L￨RB￨O￨- common￨L￨JJ￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ecology￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- in￨L￨IN￨O￨- veterinary￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- .￨L￨.￨O￨- +Early￨U￨RB￨O￨- epidemiological￨L￨JJ￨O￨- process￨L￨NN￨O￨- models￨L￨NNS￨O￨- typically￨L￨RB￨O￨- took￨L￨VBD￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨A models￨L￨NNS￨O￨A representing￨L￨VBG￨O￨- susceptible-infectious-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- susceptible-infectious-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 03￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- geo-computational￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- exploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- progression￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨A Wei-Chien-Benny￨U￨NNP￨O￨- Chin￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Tzai-Hung￨U￨JJ￨O￨- Wen1￨U￨NN￨O￨- ,￨L￨,￨O￨- Clive￨U￨NNP￨PERSON￨- E.￨U￨NNP￨PERSON￨- Sabel2￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- I-Hsiang￨U￨NNP￨O￨- Wang1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 12565￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Environmental￨U￨NNP￨O￨- social￨L￨JJ￨O￨- sciencesInfectious￨L￨JJ￨O￨- diseasesScientific￨L￨JJ￨O￨- data￨L￨NNS￨O￨- AbstractA￨U￨NN￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- linked￨L￨VBN￨O￨- events￨L￨NNS￨O￨- through￨L￨IN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- data￨L￨NN￨O￨- exploration￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- TrAcking￨U￨VBG￨O￨- Progression￨U￨NN￨O￨- In￨U￨IN￨O￨- Time￨U￨NNP￨O￨- And￨U￨CC￨O￨- Space￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- TaPiTaS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- diffusion￨L￨NN￨O￨A processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨- load￨L￨NN￨O￨- of￨L￨IN￨O￨- respiratory￨L￨JJ￨O￨- material￨L￨NN￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- with￨L￨IN￨O￨- MDR/XDR-TB￨U￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- differ￨L￨VB￨O￨- from￨L￨IN￨O￨- that￨L￨DT￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- drug￨L￨NN￨O￨- sensitivity￨L￨NN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- the￨L￨DT￨O￨- viability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- anti-TB￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- relatively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- uninfected￨L￨JJ￨O￨- ,￨L￨,￨O￨- latent￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- active￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- persons￨L￨NNS￨O￨- and￨L￨CC￨O￨- more￨L￨JJR￨O￨- detailed￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- subdivisions￨L￨NNS￨O￨- to￨L￨TO￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- strains￨L￨NNS￨O￨- :￨L￨:￨O￨- drug￨L￨NN￨O￨A sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- drug￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- allowing￨L￨VBG￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- different￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 3,5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Tuberculosis￨U￨NN￨CAUSE_OF_DEATH￨- remains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- main￨L￨JJ￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- multi-and￨L￨JJ￨O￨- extensively￨L￨RB￨O￨- drug￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- MDR￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- XDR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Mycobacterium￨U￨NN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨A (￨L￨-LRB-￨O￨- MbT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨A development￨L￨NN￨O￨- and￨L￨CC￨O￨- expansion￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- helpful￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- diagnosis￨L￨NN￨O￨- and￨L￨CC￨O￨- prognoses￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- treatment￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population-level￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- review￨L￨NN￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- an￨L￨DT￨O￨- approach￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- fitting￨L￨JJ￨O￨- by￨L￨IN￨O￨- logistic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- without￨L￨IN￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- detailed￨L￨JJ￨O￨A mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Article￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Control￨U￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- swine￨L￨NNS￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨A farms￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- modeling￨L￨NN￨O￨- assessmentCharlie￨L￨NN￨O￨- Cador1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Mathieu￨U￨NNP￨PERSON￨- Andraud1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Lander￨U￨NNP￨O￨- Willem2￨U￨NN￨O￨- and￨L￨CC￨O￨- Nicolas￨U￨NNP￨PERSON￨- Rose1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 48:58￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractSwine￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- viruses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- swIAVs￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- endemically￨L￨RB￨O￨- in￨L￨IN￨O￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨- farms￨L￨NNS￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- repeated￨L￨VBN￨O￨- swine￨L￨NNS￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- successive￨L￨JJ￨O￨- batches￨L￨NNS￨O￨- of￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- mostly￨L￨RB￨O￨- around￨L￨IN￨O￨- 8￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- specific￨L￨JJ￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨A farms￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- animals￨L￨NNS￨O￨- at￨L￨IN￨O￨- infection-time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- co-circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- subtypes￨L￨NNS￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- consecutive￨L￨JJ￨O￨- or￨L￨CC￨O￨- concomitant￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- evidenced￨L￨VBN￨O￨- as￨L￨IN￨O￨- factors￨L￨NNS￨O￨- favouring￨L￨VBG￨O￨- swIAV￨L￨NN￨O￨- persistence￨L￨NN￨O￨- within￨L￨IN￨O￨- herds￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- some￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- batch-to-batch￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- beneficial￨L￨JJ￨O￨- effect￨L￨NN￨O￨- in￨L￨IN￨O￨- breeding￨L￨VBG￨O￨- sows￨L￨VBZ￨O￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- swIAVs￨L￨NNS￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- subpopulation￨L￨NN￨O￨- ,￨L￨,￨O￨- none￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- achieved￨L￨VBD￨O￨- swIAVs￨L￨NNS￨O￨- fade-out￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨A herd￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- co-circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- swIAVs￨L￨NNS￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- farrow-to-finish￨L￨JJ￨O￨- pig￨L￨NN￨O￨A herd￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- reassortant￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- generation￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- co-infection￨L￨JJ￨O￨- events￨L￨NNS￨O￨- .￨L￨.￨O￨- +Zika￨U￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Flavivirus￨U￨NNP￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- dengue￨L￨VB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- primarily￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- bites￨L￨VBZ￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- female￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Aedes￨U￨NNP￨O￨- genus￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Lee￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Pietz￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- zika￨L￨NN￨O￨A transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- vector-host￨L￨JJ￨O￨- structure￨L￨NN￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- in￨L￨IN￨O￨- vector￨L￨NN￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- presented￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- zika￨L￨NN￨O￨A virus￨L￨NN￨O￨- with￨L￨IN￨O￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- Sun￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- developed￨L￨VBD￨O￨A a￨L￨DT￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2013￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- wave￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- H1N1￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- increased￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- short-term￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- waning￨L￨VBG￨O￨- after￨L￨IN￨O￨- jointly￨L￨RB￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- serological￨L￨JJ￨O￨A data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- widespread￨L￨JJ￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- serological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- many￨L￨JJ￨O￨- recent￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- serosurveillance￨L￨NN￨O￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- current￨L￨JJ￨DATE￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- thus￨L￨RB￨O￨- far￨L￨RB￨O￨- not￨L￨RB￨O￨- explicitly￨L￨RB￨O￨- represented￨L￨VBN￨O￨- individual￨L￨JJ￨O￨- antibody￨L￨NN￨O￨A titre￨L￨NN￨O￨- levels￨L￨NNS￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- correspondence￨L￨NN￨O￨- with￨L￨IN￨O￨- immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- coupling￨L￨NN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- serological￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- key￨L￨JJ￨O￨- biological￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- in￨L￨IN￨O￨- stratified￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- antibody￨L￨NN￨O￨A boosting￨L￨VBG￨O￨- and￨L￨CC￨O￨- protection￨L￨NN￨O￨- in￨L￨IN￨O￨- greater￨L￨JJR￨O￨- detail￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- antibody￨L￨NN￨O￨A boosting￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- antibody￨L￨NN￨O￨- titres￨L￨NNS￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- serological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- underestimation￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- because￨L￨RB￨O￨- low￨L￨JJ￨O￨- titres￨L￨NNS￨O￨- are￨L￨VBP￨O￨- ignored￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- an￨L￨DT￨O￨- age-structured￨L￨JJ￨O￨- multi-level￨L￨JJ￨O￨- susceptible-infected-recovered-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- all￨L￨DT￨O￨- antibody￨L￨NN￨O￨A titres￨L￨NNS￨O￨- were￨L￨VBD￨O￨- represented￨L￨VBN￨O￨- explicitly￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- here￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- titre￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- Methods￨U￨NNS￨O￨- and￨L￨CC￨O￨- Fig￨U￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨A in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- Francisco￨U￨NNP￨O￨- Herrerías-Azcué￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Tobias￨U￨NNP￨PERSON￨- Galla￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 13008￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsPopulation￨L￨NN￨O￨- dynamicsStatistical￨L￨JJ￨O￨- physics￨L￨NN￨O￨- AbstractModels￨U￨NNS￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- noise￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- cycles￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- population￨L￨NN￨O￨- averages￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptibilities￨L￨NNS￨O￨- and￨L￨CC￨O￨- infectivities￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- that￨L￨IN￨O￨- their￨L￨PRP$￨O￨- amplitude￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- higher-order￨L￨JJ￨O￨- moments￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- cycles￨L￨NNS￨O￨A ,￨L￨,￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- stochasticity￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- how￨L￨WRB￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptibilities￨L￨NNS￨O￨- and￨L￨CC￨O￨- propensities￨L￨NNS￨O￨- to￨L￨TO￨O￨- pass￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- affects￨L￨VBZ￨O￨- these￨L￨DT￨O￨- quasi-cycles￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- variant￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infective-recovered￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- both￨L￨DT￨O￨- agent-to-agent￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨A and￨L￨CC￨O￨- intrinsic￨L￨JJ￨O￨- noise￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- synchronisation￨L￨NN￨O￨- properties￨L￨NNS￨O￨- and￨L￨CC￨O￨- phase￨L￨NN￨O￨- lag￨L￨NN￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨A groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Counteracting￨U￨VBG￨O￨- structural￨L￨JJ￨O￨- errors￨L￨NNS￨O￨- in￨L￨IN￨O￨- ensemble￨L￨NN￨O￨- forecast￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- Sen￨U￨NNP￨O￨- Pei￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Jeffrey￨U￨NNP￨PERSON￨- Shaman1￨U￨NNP￨O￨- Nature￨U￨NNP￨O￨- Communicationsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 925￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Computational￨U￨JJ￨O￨- biology￨L￨NN￨O￨- and￨L￨CC￨O￨- bioinformaticsEpidemiologyInfectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- AbstractFor￨U￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecasts￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- forecast￨L￨NN￨O￨- inaccuracy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- partly￨L￨RB￨O￨- attributable￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- error￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- retrospective￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- historical￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- for￨L￨IN￨O￨- 95￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- overall￨L￨JJ￨O￨- forecast￨L￨NN￨O￨A accuracy￨L￨NN￨O￨- for￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- peak￨L￨NN￨O￨- timing￨L￨NN￨O￨- ,￨L￨,￨O￨- peak￨L￨NN￨O￨- intensity￨L￨NN￨O￨- and￨L￨CC￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- substantially￨L￨RB￨O￨- improved￨L￨VBN￨O￨- for￨L￨IN￨O￨- predicted￨L￨VBN￨O￨- lead￨L￨JJ￨O￨- times￨L￨NNS￨O￨- up￨L￨IN￨DURATION￨- to￨L￨TO￨DURATION￨- 10￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- quantification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- error￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- forecast￨L￨NN￨O￨A models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- needed￨L￨VBN￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- growth￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- corrected￨L￨VBN￨O￨- and￨L￨CC￨O￨- forecast￨L￨VBN￨O￨- skill￨L￨NN￨O￨- improved￨L￨VBN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- counteracting￨L￨VBG￨O￨- these￨L￨DT￨O￨- structural￨L￨JJ￨O￨- errors￨L￨NNS￨O￨- ,￨L￨,￨O￨- diagnosed￨L￨VBD￨O￨- using￨L￨VBG￨O￨- error￨L￨NN￨O￨- breeding￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- forecast￨L￨NN￨O￨A approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- dynamical￨L￨JJ￨O￨- error￨L￨NN￨O￨- correction￨L￨NN￨O￨- and￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- filtering￨L￨VBG￨O￨- techniques￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- error￨L￨NN￨O￨- growth￨L￨NN￨O￨- correction￨L￨NN￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- generalized￨L￨VBN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- forecast￨L￨NN￨O￨A accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- latter￨L￨JJ￨O￨- gives￨L￨VBZ￨O￨- an￨L￨DT￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- perfect￨L￨JJ￨O￨- vaccination.As￨L￨NNS￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- correspondence￨L￨NN￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Wilkinson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Sharkey￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A system￨L￨NN￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- equivalent￨L￨JJ￨O￨- non-Markovian￨L￨JJ￨MISC￨- pairwise￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- Poisson￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Wilkinson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Sharkey￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- contact￨L￨NN￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- Poisson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- generalised￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A equations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- unifying￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- representations￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- convergence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- monotone￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- follows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- here￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- StrictGreaterThan￨U￨NN￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- Kermack￨U￨NNP￨O￨- –￨L￨:￨O￨- McKendrick￨U￨NNP￨PERSON￨- model.KeywordsStochastic￨L￨NNP￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- Kermack￨U￨NNP￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- -341￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- KJS.Mathematics￨U￨NNPS￨O￨- Subject￨U￨NNP￨O￨- Classification92D30￨U￨NN￨O￨- 91D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionOne￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- earliest￨L￨JJS￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- comprehensively￨L￨RB￨O￨- analysed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Kermack￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1927￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +2.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- Karrer￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Newman￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Wilkinson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Sharkey￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- more￨L￨JJR￨O￨- general￨L￨JJ￨TITLE￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A system￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- underestimate￨L￨VB￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- StrictGreaterThan￨U￨NN￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- during￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Theorem￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- Corollary￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +SharkeyOpen￨U￨NNP￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1.2￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 3￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractWe￨U￨NN￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- stochastic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- it￨L￨PRP￨O￨- takes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- contact￨L￨VB￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighbours￨L￨NNS￨O￨- after￨L￨IN￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- correlated￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨- events￨L￨NNS￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- as￨L￨IN￨O￨- unknowns￨L￨NNS￨O￨- to￨L￨TO￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- sampled￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- MCMC￨U￨NN￨O￨- routine￨L￨NN￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- these￨L￨DT￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- exact￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- times￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- household￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- method￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- posteriors￨L￨NNS￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- compute￨L￨VBP￨O￨- show￨L￨VB￨O￨- good￨L￨JJ￨O￨- convergence￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- household￨L￨NN￨O￨A data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨A the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- dispersal￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Esteva￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Vargas￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- considering￨L￨VBG￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- variable￨L￨JJ￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Polwiang￨U￨NN￨PERSON￨- discussed￨L￨VBD￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨A and￨L￨CC￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- climate￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +So￨U￨RB￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- made￨L￨VBN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +used￨L￨VBN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- analysis￨L￨NN￨O￨- comparing￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- dengue￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- software￨L￨NN￨O￨- package￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- R￨U￨NN￨O￨- language￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- and￨L￨CC￨O￨- study￨L￨VB￨O￨- concepts￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- modern￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨- or￨L￨CC￨O￨- write￨L￨VB￨O￨- computer￨L￨NN￨O￨- code￨L￨NN￨O￨- .￨L￨.￨O￨- +New￨U￨NNP￨O￨- tools￨L￨NNS￨O￨- and￨L￨CC￨O￨- approaches￨L￨NNS￨O￨- are￨L￨VBP￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- reach￨L￨VB￨O￨- a￨L￨DT￨O￨- wider￨L￨JJR￨O￨- audience￨L￨NN￨O￨- and￨L￨CC￨O￨- allow￨L￨VB￨O￨- students￨L￨NNS￨O￨- to￨L￨TO￨O￨- learn￨L￨VB￨O￨- concepts￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- critical￨L￨JJ￨O￨- community￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- population-level￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- obstacles￨L￨NNS￨O￨- of￨L￨IN￨O￨- coding￨L￨VBG￨O￨- or￨L￨CC￨O￨- having￨L￨VBG￨O￨- to￨L￨TO￨O￨- formulate￨L￨VB￨O￨- and￨L￨CC￨O￨- analyze￨L￨VB￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- package￨L￨NN￨O￨A includes￨L￨VBZ￨O￨- documentation￨L￨NN￨O￨- and￨L￨CC￨O￨- material￨L￨NN￨O￨- to￨L￨TO￨O￨- serve￨L￨VB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- stand-alone￨L￨JJ￨O￨- tool￨L￨NN￨O￨- —￨L￨:￨O￨- supplemented￨L￨VBN￨O￨- as￨L￨IN￨O￨- needed￨L￨VBN￨O￨- with￨L￨IN￨O￨- provided￨L￨VBN￨O￨- references￨L￨NNS￨O￨- —￨L￨:￨O￨- for￨L￨IN￨O￨- students￨L￨NNS￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- an￨L￨DT￨O￨- introduction￨L￨NN￨O￨- to￨L￨TO￨O￨- important￨L￨JJ￨O￨- modern￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- concepts￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- textbooks￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- that￨L￨WDT￨O￨- teach￨L￨VBP￨O￨- a￨L￨DT￨O￨- model-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- exist￨L￨VBP￨O￨- ,￨L￨,￨O￨- almost￨L￨RB￨O￨- any￨L￨DT￨O￨- such￨L￨JJ￨O￨- teaching￨L￨NN￨O￨- material￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- students￨L￨NNS￨O￨A to￨L￨TO￨O￨- work￨L￨VB￨O￨- with￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- write￨L￨VB￨O￨- computer￨L￨NN￨O￨- code￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- package￨L￨NN￨O￨A is￨L￨VBZ￨O￨- built￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- modular￨L￨JJ￨O￨- way￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- student￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- seamlessly￨L￨RB￨O￨- continue￨L￨VB￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- journey￨L￨NN￨O￨- of￨L￨IN￨O￨- learning￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modeling￨L￨NN￨O￨- if￨L￨IN￨O￨- they￨L￨PRP￨O￨- choose￨L￨VBP￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- so￨L￨RB￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- characterize￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- and￨L￨CC￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨A events￨L￨NNS￨O￨- ,￨L￨,￨O￨- mediated￨L￨VBN￨O￨- by￨L￨IN￨O￨- transient￨L￨JJ￨O￨- heterosubtypic￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- following￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- integrate￨L￨VB￨O￨- environmental￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- on￨L￨IN￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- two-strain￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- heterosubtypic￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- new￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨A risk￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- expected￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨A declines￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- wake￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- does￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- early￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- pandemic￨L￨NN￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- preceded￨L￨VBN￨O￨- by￨L￨IN￨O￨- viral￨L￨JJ￨O￨- reassortment￨L￨NN￨O￨- in￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- co-infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- should￨L￨MD￨O￨- become￨L￨VB￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- increases￨L￨VBZ￨O￨- [￨L￨-LRB-￨O￨- 34￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 36￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- simulated￨L￨JJ￨O￨- thousands￨L￨NNS￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- virus￨L￨NN￨O￨- introductions￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- changing￨L￨VBG￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- emergence￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- Reff￨U￨NNP￨PERSON￨- upon￨L￨IN￨O￨- emergence￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- seasons￨L￨NNS￨O￨- unfold￨L￨VBP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- methods￨L￨NNS￨O￨- would￨L￨MD￨O￨- contribute￨L￨VB￨O￨- in￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- of￨L￨IN￨O￨- household￨L￨NN￨O￨A structures￨L￨NNS￨O￨- among￨L￨IN￨O￨- Indigenous￨U￨JJ￨O￨- communities￨L￨NNS￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- accurate￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- better￨L￨JJR￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- support￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- regarding￨L￨VBG￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- household￨L￨NN￨O￨A structures￨L￨NNS￨O￨- in￨L￨IN￨O￨- remote￨L￨JJ￨O￨- and￨L￨CC￨O￨- isolated￨L￨VBN￨O￨- communities￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- especially￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- them￨L￨PRP￨O￨- into￨L￨IN￨O￨- consideration￨L￨NN￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Household￨U￨NNP￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- ages￨L￨NNS￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨A resident￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- people￨L￨NNS￨O￨- per￨L￨IN￨O￨- room￨L￨NN￨O￨- ,￨L￨,￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- vary￨L￨VB￨O￨- across￨L￨IN￨O￨- subpopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- upon￨L￨IN￨O￨- fertility￨L￨NN￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- socioeconomic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- cultural￨L￨JJ￨O￨- norms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Transcriptional￨U￨JJ￨O￨- regulation￨L￨NN￨O￨- ,￨L￨,￨O￨- led￨L￨VBN￨O￨- by￨L￨IN￨O￨- transcription￨L￨NN￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- TFs￨U￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- regulation￨L￨NN￨O￨- proteins￨L￨NNS￨O￨- that￨L￨WDT￨O￨- link￨L￨VBP￨O￨- DNA￨U￨NN￨O￨- sequences￨L￨NNS￨O￨- in￨L￨IN￨O￨- specific￨L￨JJ￨O￨- promoter￨L￨NN￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- target￨L￨NN￨O￨- genes￨L￨NNS￨O￨A –￨L￨:￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- mechanism￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- activated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- organism￨L￨NN￨O￨- to￨L￨TO￨O￨- enhance￨L￨VB￨O￨- or￨L￨CC￨O￨- repress￨L￨VB￨O￨- gene￨L￨NN￨O￨- expression￨L￨NN￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- internal￨L￨JJ￨O￨- or￨L￨CC￨O￨- external￨L￨JJ￨O￨- stimuli￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- cacao￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Theobroma￨U￨NN￨O￨- cacao￨L￨NN￨O￨- L.￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- portion￨L￨NN￨O￨- of￨L￨IN￨O￨- WRKY￨U￨NN￨O￨- genes￨L￨NNS￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- identified￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- with￨L￨IN￨O￨- regards￨L￨VBZ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- expression￨L￨NN￨O￨- ,￨L￨,￨O￨- phylogeny￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- Malvaceae￨U￨NNP￨O￨- family￨L￨NN￨O￨- ,￨L￨,￨O￨- and/or￨L￨CC￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- marker￨L￨NN￨TITLE￨- assisted￨L￨VBN￨O￨- selection￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- no￨L￨DT￨O￨- exhaustive￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- TF￨U￨NN￨O￨- family￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- cacao￨L￨NN￨O￨- genome￨L￨NN￨O￨- data￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- WRKY￨U￨NN￨O￨- proteins￨L￨NNS￨O￨A contain￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- DNA￨U￨NN￨MISC￨- binding￨L￨NN￨O￨- domains￨L￨NNS￨O￨- of￨L￨IN￨O￨- 60￨L￨CD￨NUMBER￨- amino￨L￨NN￨O￨- acids￨L￨NNS￨O￨- containing￨L￨VBG￨O￨- the￨L￨DT￨O￨- conserved￨L￨VBN￨O￨- heptapeptide￨L￨NN￨O￨- WRKYGQK￨U￨NN￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- zinc-finger￨L￨JJ￨O￨- motif￨L￨NN￨O￨- C2H2￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- C-X4-5-C-X22-23-H-X-H￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- C2HC￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- C-X7-C-X23-24-H-X-C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- scheme￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- in￨L￨IN￨O￨- silico￨L￨JJ￨O￨- pipeline￨L￨NN￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Theobroma￨U￨NN￨O￨- cacao￨L￨NN￨O￨- WRKY￨U￨NN￨O￨- protein￨L￨NN￨O￨A set￨L￨NN￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- S1￨U￨NN￨O￨- Fig￨U￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- expression￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- WRKY￨U￨NN￨O￨- genes￨L￨NNS￨O￨A in￨L￨IN￨O￨- cacao￨L￨NN￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogenic￨L￨JJ￨O￨- fungus￨L￨NN￨O￨- M￨U￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Targeted￨U￨VBN￨O￨- Recovery￨U￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- Effective￨U￨JJ￨O￨- Strategy￨U￨NN￨O￨- against￨L￨IN￨O￨- Epidemic￨U￨NNP￨O￨- Spreading￨U￨NNP￨O￨- L.￨U￨NNP￨O￨- J.￨U￨NNP￨O￨- Herrmann1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 14356￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComplex￨L￨NNP￨O￨- networksPhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractWe￨U￨NN￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- targeted￨L￨VBN￨O￨A intervention￨L￨NN￨O￨- protocol￨L￨NN￨O￨- where￨L￨WRB￨O￨- recovery￨L￨NN￨O￨- is￨L￨VBZ￨O￨- restricted￨L￨JJ￨O￨- to￨L￨TO￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- least￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- neighbours￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- targeted￨L￨VBN￨O￨A recovery￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- standard￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- constituents￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- spontaneously￨L￨RB￨O￨- recover￨L￨VB￨O￨- after￨L￨IN￨O￨- being￨L￨VBG￨O￨- infected19￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- spatially￨L￨RB￨O￨A embedded￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- stays￨L￨NNS￨O￨- strongly￨L￨RB￨O￨- spatially￨L￨RB￨O￨- confined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- length￨L￨NN￨O￨- scale￨L￨NN￨O￨- undergoing￨L￨VBG￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- targeted￨L￨VBN￨O￨A recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- would￨L￨MD￨O￨- recover￨L￨VB￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- boundary￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- first￨L￨RB￨ORDINAL￨- .￨L￨.￨O￨- +Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equation￨L￨NN￨O￨- at￨L￨IN￨O￨- criticality￨L￨NN￨O￨A demonstrates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- nonsymmetric￨L￨JJ￨O￨- average￨L￨JJ￨O￨- avalanche￨L￨NN￨O￨- shapes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- experiments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- occur￨L￨VBP￨O￨- for￨L￨IN￨O￨- certain￨L￨JJ￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +Avalanching￨U￨VBG￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- disciplines￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- average￨L￨JJ￨O￨- avalanche￨L￨NN￨O￨- shapes￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- profiles￨L￨NNS￨O￨A of￨L￨IN￨O￨- avalanches￨L￨NNS￨O￨- of￨L￨IN￨O￨- fixed￨L￨VBN￨O￨- duration￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- Markov￨U￨NNP￨PERSON￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- an￨L￨DT￨O￨- equation￨L￨NN￨O￨- governing￨L￨VBG￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨A avalanche￨L￨NN￨O￨- shape￨L￨NN￨O￨- for￨L￨IN￨O￨- cascade￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rescaled￨L￨VBN￨O￨- average￨L￨JJ￨O￨A avalanche￨L￨NN￨O￨- shapes￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- collapse￨L￨NN￨O￨- onto￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- universal￨L￨JJ￨O￨- curve￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- developed￨L￨VBD￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- trajectory￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- DOTS￨U￨NNS￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- maintained￨L￨VBN￨O￨- or￨L￨CC￨O￨- if￨L￨IN￨O￨- new￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- 8.6￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨A new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- 1.3￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- 320,000￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- a￨L￨DT￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- incorporated￨L￨VBD￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨A and￨L￨CC￨O￨- chemoprophylaxis￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- modified￨L￨VBN￨O￨- predator￨L￨NN￨O￨- –￨L￨:￨O￨- prey￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- transmissible￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨- and￨L￨CC￨O￨- prey￨L￨NN￨O￨- species￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- analysed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- police￨L￨NN￨O￨- as￨L￨IN￨O￨- predators￨L￨NNS￨O￨- and￨L￨CC￨O￨- gang￨L￨NN￨O￨- members￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- recruitment￨L￨NN￨O￨- into￨L￨IN￨O￨- gangs￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- manner￨L￨NN￨O￨A reminiscent￨L￨JJ￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- details￨L￨NNS￨O￨A the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- gang￨L￨NN￨O￨- territories￨L￨NNS￨O￨- and￨L￨CC￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- between-gang￨L￨JJ￨O￨- violence￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- studied￨L￨VBN￨O￨- using￨L￨VBG￨O￨- Lotka￨U￨NNP￨LOCATION￨- –￨L￨:￨O￨- Volterra￨U￨NNP￨CITY￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- gang￨L￨NN￨O￨- violence￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- crimes￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- carried￨L￨VBN￨O￨A out￨L￨RP￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- gaps￨L￨NNS￨O￨- identified￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- National￨U￨NNP￨ORGANIZATION￨- Malaria￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- Program￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- NMCP￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- rational￨L￨JJ￨O￨- deployment￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- and￨L￨CC￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- makes￨L￨VBZ￨O￨- it￨L￨PRP￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- further￨L￨RB￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- usefulness￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- support￨L￨VB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- This￨U￨DT￨O￨- paper￨L￨NN￨O￨- will￨L￨MD￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A situation￨L￨NN￨O￨- in￨L￨IN￨O￨- Ghana￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- brief￨L￨JJ￨O￨- account￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Ghanaian￨U￨JJ￨NATIONALITY￨- context￨L￨NN￨O￨- towards￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- informed￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- elimination￨L￨NN￨O￨- programme￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨ORGANIZATION￨- Development￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- successive￨L￨JJ￨O￨- strategic￨L￨JJ￨O￨- plans￨L￨NNS￨O￨- of￨L￨IN￨O￨- action￨L￨NN￨O￨- ,￨L￨,￨O￨- intervention￨L￨NN￨O￨- policies￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- boost￨L￨NN￨O￨- in￨L￨IN￨O￨- financial￨L￨JJ￨O￨- support￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- years￨L￨NNS￨DURATION￨- in￨L￨IN￨O￨- Ghana￨U￨NNP￨COUNTRY￨- have￨L￨VBP￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- coverage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A morbidity￨L￨NN￨O￨- in￨L￨IN￨O￨- Ghana￨U￨NNP￨COUNTRY￨- remains￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- high￨L￨JJ￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- If￨U￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- collaboration￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- National￨U￨NNP￨ORGANIZATION￨- Malaria￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Ministry￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Ghana￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Service￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- could￨L￨MD￨O￨- guide￨L￨VB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨A alone￨L￨RB￨O￨- or￨L￨CC￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- settings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Estimates￨U￨NNS￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- trends￨L￨NNS￨O￨- are￨L￨VBP￨O￨- created￨L￨VBN￨O￨- by￨L￨IN￨O￨- statistically￨L￨RB￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- Estimation￨U￨NN￨O￨- and￨L￨CC￨O￨- Projection￨U￨NNP￨O￨- Package￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- EPP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- ‘￨L￨``￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- ’￨L￨''￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- sentinel￨L￨NN￨O￨A surveillance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ANC-SS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- prevalence￨L￨NN￨O￨- from￨L￨IN￨O￨- nationally￨L￨RB￨O￨- representative￨L￨JJ￨TITLE￨- household￨L￨NN￨O￨- surveys￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- national￨L￨JJ￨O￨- survey￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- for￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- settings￨L￨NNS￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- sites￨L￨NNS￨O￨- and￨L￨CC￨O￨- frequent￨L￨JJ￨O￨- sentinel￨L￨NN￨O￨A surveys￨L￨NNS￨O￨- ,￨L￨,￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- tend￨L￨VBP￨O￨- to￨L￨TO￨O￨- overwhelm￨L￨VB￨O￨- the￨L￨DT￨O￨- higher-quality￨L￨JJ￨O￨- national￨L￨JJ￨O￨- survey￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- trends￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- inconsistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- national￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- primary￨L￨JJ￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- are￨L￨VBP￨O￨- sentinel￨L￨JJ￨O￨A surveillance￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- among￨L￨IN￨O￨- pregnant￨L￨JJ￨O￨- women￨L￨NNS￨O￨- attending￨L￨VBG￨O￨- antenatal￨L￨JJ￨O￨- clinics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ANC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- linear￨L￨JJ￨O￨- mixed-effects￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- potentially￨L￨RB￨O￨- unbalanced￨L￨JJ￨O￨- repeated￨L￨VBN￨O￨- observations￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- when￨L￨WRB￨O￨- inferring￨L￨VBG￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- prevalence￨L￨NN￨O￨A trend￨L￨NN￨O￨- from￨L￨IN￨O￨- ANC-SS￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- assumption￨L￨NN￨O￨- underpinning￨L￨VBG￨O￨- this￨L￨DT￨O￨- estimation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- discrepancies￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- predictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- ANC-SS￨U￨NN￨O￨- prevalence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- error￨L￨NN￨O￨- expected￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- clinic￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +al￨L￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- and￨L￨CC￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- explains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- phenomena￨L￨NNS￨O￨- of￨L￨IN￨O￨- polarization￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- evolve￨L￨VBP￨O￨- under￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- implementing￨L￨VBG￨O￨- those￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- social￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- opinion￨L￨NN￨O￨A ’s￨L￨POS￨O￨- formation￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- compromise￨L￨NN￨O￨- and￨L￨CC￨O￨- persuasion￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- each￨L￨DT￨O￨- agent￨L￨NN￨O￨- may￨L￨MD￨O￨- change￨L￨VB￨O￨- its￨L￨PRP$￨O￨- decision￨L￨NN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- pressure￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- switching￨L￨VBG￨O￨- his￨L￨PRP$￨O￨- present￨L￨JJ￨DATE￨- choice￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- non-linearly￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- opposite￨L￨JJ￨O￨- opinion￨L￨NN￨O￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- are￨L￨VBP￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- studying￨L￨VBG￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- opinion￨L￨NN￨O￨A formation￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- favor￨L￨NN￨O￨- or￨L￨CC￨O￨- against￨L￨IN￨O￨- of￨L￨IN￨O￨- getting￨L￨VBG￨O￨- vaccinated￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- contribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- opinion￨L￨NN￨O￨A formation￨L￨NN￨O￨- on￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- the￨L￨DT￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- patch-level￨L￨JJ￨O￨- approach￨L￨NN￨O￨- conforms￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- desirable￨L￨JJ￨O￨- SEIR-type￨U￨JJ￨MISC￨- mechanistic￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- successful￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- unsuccessful￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- represented￨L￨VBN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- patch￨L￨NN￨O￨A level￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- aggregation￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- points￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- arbitrary￨L￨JJ￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- inevitably￨L￨RB￨O￨- degrades￨L￨VBZ￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- resolution￨L￨NN￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- individual-to-individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission-network-based￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- partial-likelihood￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- preserves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- point￨L￨NN￨O￨- nature￨L￨NN￨O￨- ’￨L￨''￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- but￨L￨CC￨O￨- fails￨L￨VBZ￨O￨- to￨L￨TO￨O￨- conform￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨A framework￨L￨NN￨O￨- by￨L￨IN￨O￨- completely￨L￨RB￨O￨- ignoring￨L￨VBG￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- class￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- growing￨L￨VBG￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- more￨L￨RBR￨O￨- precise￨L￨JJ￨O￨- spatio-temporal￨L￨JJ￨O￨- data￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- accompanied￨L￨VBN￨O￨- by￨L￨IN￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- statistically￨L￨RB￨O￨- sound￨L￨JJ￨O￨- mechanistic￨L￨JJ￨O￨A frameworks￨L￨NNS￨O￨- for￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- individual-to-individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Conventional￨U￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- SEIR￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- require￨L￨VBP￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- account￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- which￨L￨WDT￨O￨- specifies￨L￨VBZ￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- successful￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- in￨L￨IN￨O￨- class￨L￨NN￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- more￨L￨RBR￨O￨- challengingly￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- unsuccessful￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- who￨L￨WP￨O￨- has￨L￨VBZ￨O￨- remained￨L￨VBN￨O￨- susceptible￨L￨JJ￨O￨- in￨L￨IN￨O￨- class￨L￨NN￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 09￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Genomic￨U￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- characterisation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- among￨L￨IN￨O￨- blood￨L￨NN￨O￨- donors￨L￨NNS￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- Nuno￨U￨NNP￨O￨- R.￨U￨NNP￨O￨- Sabino2￨U￨NNP￨O￨- ,3￨L￨CD￨NUMBER￨- na2￨L￨NN￨O￨- &￨L￨CC￨O￨- NHLBI￨U￨NNP￨ORGANIZATION￨- Recipient￨U￨NNP￨O￨- Epidemiology￨U￨NNP￨O￨- and￨L￨CC￨O￨- Donor￨U￨NNP￨O￨- Evaluation￨U￨NN￨O￨- Study-III￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- REDS-III￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 15216￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Dengue￨U￨NNP￨O￨- virusPhylogeneticsViral￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- AbstractOutbreaks￨U￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- Dengue￨U￨NNP￨O￨- ,￨L￨,￨O￨- Zika￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Chikungunya￨U￨NNP￨LOCATION￨- viruses￨L￨NNS￨O￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- rapidly￨L￨RB￨O￨- in￨L￨IN￨O￨- immunologically￨L￨RB￨O￨- naïve￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- geographic￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- DENV￨U￨NN￨O￨- types￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- dramatically￨L￨RB￨O￨- increased￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨O￨- decades4￨L￨NN￨O￨- ,￨L￨,￨O￨- fueled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- main￨L￨JJ￨O￨- vector￨L￨NN￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨- mosquito￨L￨NN￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- ,￨L￨,￨O￨- international￨L￨JJ￨O￨- travel￨L￨NN￨O￨A and￨L￨CC￨O￨- trade￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- increasing￨L￨VBG￨O￨- urbanization￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- and￨L￨CC￨O￨- subtropics5￨L￨NN￨O￨- ,6￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- analysing￨L￨VBG￨O￨- 92￨L￨CD￨NUMBER￨- newly￨L￨RB￨O￨- generated￨L￨VBN￨O￨- viral￨L￨JJ￨O￨- genome￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- from￨L￨IN￨O￨- blood￨L￨NN￨O￨- donors￨L￨NNS￨O￨- and￨L￨CC￨O￨- recipients￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨- serotype￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Rio￨U￨NNP￨CITY￨- de￨L￨IN￨CITY￨- Janeiro￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Modelling￨U￨VBG￨O￨- analysis￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- viral￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- started￨L￨VBD￨O￨- in￨L￨IN￨O￨- early￨L￨JJ￨DATE￨- January￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- introductions￨L￨NNS￨O￨- ,￨L￨,￨O￨- most￨L￨RBS￨O￨- likely￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- northern￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- within-country￨L￨JJ￨O￨- air￨L￨NN￨O￨- travel￨L￨NN￨O￨A to￨L￨TO￨O￨- Rio￨U￨NNP￨CITY￨- de￨L￨IN￨CITY￨- Janeiro￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Brazil￨U￨NNP￨COUNTRY￨- has￨L￨VBZ￨O￨- reported￨L￨VBN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A cases￨L￨NNS￨O￨- worldwide￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- >￨L￨JJR￨O￨- 7.3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 20137￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- occurring￨L￨VBG￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- country8￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- BT￨U￨NNP￨O￨- tension￨L￨NN￨O￨- with￨L￨IN￨O￨- geographical￨L￨JJ￨O￨- and￨L￨CC￨O￨- socioeconomic￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- hypothesis￨L￨NN￨O￨- testing￨L￨NN￨O￨- ,￨L￨,￨O￨- criterion￨L￨NN￨O￨- χ2￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- factors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- entropy￨L￨NN￨O￨A of￨L￨IN￨O￨- random￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- and￨L￨CC￨O￨- total￨L￨JJ￨O￨- entropy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- indicators￨L￨NNS￨O￨- of￨L￨IN￨O￨- BT￨U￨NNP￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- growth￨L￨NN￨O￨- dynamic￨L￨NN￨O￨- were￨L￨VBD￨O￨- processed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- guidelines￨L￨NNS￨O￨A on￨L￨IN￨O￨- conducting￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨- monitoring￨L￨NN￨O￨- of￨L￨IN￨O￨- exotic￨L￨JJ￨O￨- ,￨L￨,￨O￨- very￨L￨RB￨O￨- dangerous￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- unknown￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- OIE￨U￨NNP￨O￨- Animal￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- Code￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- significance￨L￨NN￨O￨- set￨L￨VBN￨O￨- at￨L￨IN￨O￨- 5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- April￨U￨NNP￨DATE￨- )￨L￨-RRB-￨O￨- 2016￨L￨CD￨DATE￨- ,￨L￨,￨O￨- BT￨U￨NNP￨ORGANIZATION￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- registered￨L￨VBN￨O￨- in￨L￨IN￨O￨- 12￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- African￨U￨JJ￨NATIONALITY￨- continent￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- 3987￨L￨CD￨NUMBER￨- outbreaks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 28￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- of￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- 156993￨L￨CD￨NUMBER￨- outbreaks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- 5684￨L￨CD￨NUMBER￨- outbreaks￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- <￨L￨JJR￨O￨- 0.001￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- spread￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- .￨L￨.￨O￨- +Used￨U￨VBN￨O￨- coefficients￨L￨NNS￨O￨- similarly￨L￨RB￨O￨- show￨L￨VBP￨O￨- the￨L￨DT￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- BT￨U￨NNP￨O￨- stationarity￨L￨NN￨O￨- on￨L￨IN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- lethality￨L￨NN￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- small￨L￨JJ￨O￨- cattle￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- why￨L￨WRB￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨A our￨L￨PRP$￨O￨- epizootical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- BT￨U￨NNP￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- make￨L￨VB￨O￨- a￨L￨DT￨O￨- schema￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- situation￨L￨NN￨O￨- and￨L￨CC￨O￨- expected￨L￨VBN￨O￨- forecasts￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- Bobbie￨U￨NNP￨PERSON￨- is￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- Alex￨U￨NNP￨PERSON￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- earlier￨L￨RBR￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- serial￨L￨JJ￨O￨- partnership￨L￨NN￨O￨A than￨L￨IN￨O￨- a￨L￨DT￨O￨- concurrent￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- focused￨L￨VBN￨O￨- relationship￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Conversely￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- Charlie￨U￨NNP￨PERSON￨- is￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- Alex￨U￨NNP￨PERSON￨- becomes￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- earlier￨L￨RBR￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- concurrent￨L￨JJ￨O￨- partnership￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- forced￨L￨VBN￨O￨- by￨L￨IN￨O￨- partnership￨L￨NN￨O￨- timing￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- serial￨L￨NN￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- illustrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- by￨L￨IN￨O￨- halving￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- and￨L￨CC￨O￨- doubling￨L￨VBG￨O￨- the￨L￨DT￨O￨- partnership￨L￨NN￨O￨A duration￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- concurrent￨L￨JJ￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- concurrent￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- at￨L￨IN￨O￨- exactly￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- times￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- could￨L￨MD￨O￨- occur￨L￨VB￨O￨- in￨L￨IN￨O￨- either￨L￨CC￨O￨- partnership￨L￨NN￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- comparisons￨L￨NNS￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- change￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- concurrency￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- conflated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- interactions￨L￨NNS￨O￨- per￨L￨IN￨O￨- individual￨L￨NN￨O￨- or￨L￨CC￨O￨- per￨L￨IN￨O￨- partnership￨L￨NN￨O￨A .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV-specific￨U￨JJ￨O￨- antibodies￨L￨NNS￨O￨A in￨L￨IN￨O￨- tropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- ambiguous￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- cross-reactive￨L￨JJ￨O￨- antibodies￨L￨NNS￨O￨- elicited￨L￨VBN￨O￨- by￨L￨IN￨O￨- previous￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- antigenically￨L￨RB￨O￨- related￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- widespread￨L￨JJ￨O￨- DENV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- limiting￨L￨VBG￨O￨- accurate￨L￨JJ￨O￨- diagnostic￨L￨JJ￨O￨- testing￨L￨NN￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- using￨L￨VBG￨O￨- highly￨L￨RB￨O￨- specific￨L￨JJ￨O￨- neutralization￨L￨NN￨O￨- tests￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Uncertainty￨U￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- ZIKV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- exposed￨L￨VBN￨O￨- has￨L￨VBZ￨O￨- key￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- trajectory￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- American￨U￨JJ￨NATIONALITY￨- ZIKV￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- studies￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- etiology￨L￨NN￨O￨- and￨L￨CC￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV-associated￨U￨JJ￨O￨- congenital￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- have￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- high￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- clinically￨L￨RB￨O￨- suspected￨L￨VBN￨O￨- ZIKV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨A of￨L￨IN￨O￨- laboratory-confirmed￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- explore￨L￨VB￨O￨- its￨L￨PRP$￨O￨- etiologic￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- congenital￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- project￨L￨VB￨O￨- the￨L￨DT￨O￨- trajectory￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- ZIKV￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- specimens￨L￨NNS￨O￨- sampled￨L￨VBN￨O￨- before￨L￨RB￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- ZIKV￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- to￨L￨TO￨O￨- reconstruct￨L￨VB￨O￨A the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- in￨L￨IN￨O￨- Salvador￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- capital￨L￨NN￨O￨- of￨L￨IN￨O￨- Bahia￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- directly￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- pathogens￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- arthropod￨L￨NN￨O￨- transmitted￨L￨VBD￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨A species￨L￨NNS￨O￨A diversity￨L￨NN￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- interactions￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- interest￨L￨NN￨O￨- as￨L￨IN￨O￨- co-occurring￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- of￨L￨IN￨O￨- low-competency￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dilution￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- influence￨L￨VB￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- competent￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- amplifying￨L￨VBG￨O￨- hosts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- or￨L￨CC￨O￨- decreasing￨L￨VBG￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- an￨L￨DT￨O￨- assemblage￨L￨NN￨O￨- containing￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- pathogen￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- area￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dilution￨L￨NN￨O￨- effect￨L￨NN￨O￨- is￨L￨VBZ￨O￨- said￨L￨VBN￨O￨- to￨L￨TO￨O￨- occur￨L￨VB￨O￨- when￨L￨WRB￨O￨- increasing￨L￨VBG￨O￨- host￨L￨NN￨TITLE￨A species￨L￨NNS￨O￨A richness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- diversity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- metric￨L￨NN￨O￨- that￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- both￨L￨DT￨O￨- richness￨L￨NN￨O￨- and￨L￨CC￨O￨- relative￨L￨JJ￨O￨- abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- pathogen￨L￨NN￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- species￨L￨NNS￨O￨- that￨L￨WDT￨O￨- maintains￨L￨VBZ￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- readily￨L￨RB￨O￨- transmits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- opposite￨L￨JJ￨O￨- pattern￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ‘‘￨L￨``￨O￨- amplification￨L￨NN￨O￨- effect￨L￨NN￨O￨- ,￨L￨,￨O￨- ”￨L￨''￨O￨- occurs￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- increased￨L￨VBN￨O￨- host￨L￨NN￨TITLE￨A species￨L￨NNS￨O￨A richness/diversity￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- increased￨L￨VBN￨O￨- encounters￨L￨NNS￨O￨- between￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- concentration￨L￨NN￨O￨- influence￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- testing￨L￨VBG￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- null￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- IHNV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- fish￨L￨NN￨O￨- using￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- experimental￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- null￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- listed￨L￨VBN￨O￨- above￨L￨RB￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- manipulability￨L￨NN￨O￨- of￨L￨IN￨O￨- rainbow￨L￨NN￨O￨- trout￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- breed￨L￨VB￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen-free￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- captivity￨L￨NN￨O￨- ,￨L￨,￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- IHNV￨U￨NN￨O￨- viral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- fitness￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- interventions￨L￨NNS￨O￨- against￨L￨IN￨O￨- IHNV￨U￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- innate￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccine-induced￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A .￨L￨.￨O￨- +Heterogeneity￨U￨NN￨O￨- in￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- departure￨L￨NN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- null￨L￨JJ￨O￨A hypothesis￨L￨NN￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- present￨L￨JJ￨DATE￨- among￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- both￨L￨DT￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- shape￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- challenge￨L￨NN￨O￨- dose￨L￨NN￨O￨- and￨L￨CC￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- constants￨L￨NNS￨O￨A in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- diagnosed￨L￨VBN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- undiagnosed￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- focus￨L￨NN￨O￨- will￨L￨MD￨O￨- then￨L￨RB￨O￨- be￨L￨VB￨O￨- given￨L￨VBN￨O￨- to￨L￨TO￨O￨- determination￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- constants￨L￨NNS￨O￨A in￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- show￨L￨VB￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- constants￨L￨NNS￨O￨A depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Highly￨U￨RB￨O￨- specific￨L￨JJ￨O￨- ‘￨L￨``￨O￨- matching-allele￨L￨NN￨O￨- ’￨L￨''￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- parasites￨L￨NNS￨O￨A must￨L￨MD￨O￨- ‘￨L￨``￨O￨- match￨L￨VB￨O￨- ’￨L￨''￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- loci￨L￨NNS￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- ,￨L￨,￨O￨- commonly￨L￨RB￨O￨- generate￨L￨VBP￨O￨- coevolutionary￨L￨JJ￨O￨- ‘￨L￨``￨O￨- cycles￨L￨NNS￨O￨- ’￨L￨''￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- FSD￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- selection￨L￨NN￨O￨- favours￨L￨VBZ￨O￨- parasite￨L￨NN￨O￨- genotypes￨L￨NNS￨O￨- capable￨L￨JJ￨O￨- of￨L￨IN￨O￨- infecting￨L￨VBG￨O￨- common￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- genotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- generating￨L￨VBG￨O￨- negative￨L￨JJ￨O￨- frequency-dependent￨L￨JJ￨O￨- selection￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- ‘￨L￨``￨O￨- gene-for-gene￨L￨NN￨O￨- ’￨L￨''￨O￨- interactions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- specificity￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- parasites￨L￨NNS￨O￨A vary￨L￨VBP￨O￨- from￨L￨IN￨O￨- specialists￨L￨NNS￨O￨- to￨L￨TO￨O￨- generalists￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- often￨L￨RB￨O￨- produce￨L￨VBP￨O￨- ARD￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- directional￨L￨JJ￨O￨- selection￨L￨NN￨O￨- favours￨L￨VBZ￨O￨- increasing￨L￨VBG￨O￨- resistance￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- ranges￨L￨NNS￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- there￨L￨EX￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- transition￨L￨NN￨O￨- to￨L￨TO￨O￨- FSD￨U￨NNP￨ORGANIZATION￨- if￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- costs￨L￨NNS￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- defence￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Theory￨U￨NNP￨O￨- predicts￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- coevolution￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- parasites￨L￨NNS￨O￨A may￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- coevolutionary￨L￨JJ￨O￨- stable￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- co-ESS￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- static￨L￨JJ￨O￨- within-population￨L￨NN￨O￨- dimorphism￨L￨NN￨O￨- or￨L￨CC￨O￨- polymorphism￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- escalation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- arms￨L￨NNS￨O￨- race￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- ARD￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- fluctuating￨L￨VBG￨O￨- selection￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- FSD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Theoretical￨U￨JJ￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- primarily￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- specificity￨L￨NN￨O￨- between￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- parasites￨L￨NNS￨O￨A lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- fluctuating￨L￨VBG￨O￨- selection￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11,19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- using￨L￨VBG￨O￨- eco-evolutionary￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- for￨L￨IN￨O￨- varying￨L￨VBG￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- owing￨L￨VBG￨O￨- to￨L￨TO￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- defence￨L￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨A infectivity￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- human￨L￨JJ￨O￨A mobility￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- :￨L￨:￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- impedance￨L￨NN￨O￨- modelKankoé￨L￨NN￨O￨- Sallah1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Roch￨U￨NNP￨PERSON￨- Giorgi1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Linus￨U￨NNP￨PERSON￨- Bengtsson4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Xin￨U￨NNP￨PERSON￨- Lu4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Erik￨U￨NNP￨PERSON￨- Wetter5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Paul￨U￨NNP￨PERSON￨- Adrien8￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Stanislas￨U￨NNP￨PERSON￨- Rebaudet9￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Renaud￨U￨NNP￨PERSON￨- Piarroux10￨U￨NNP￨O￨- and￨L￨CC￨O￨- Jean￨U￨NNP￨PERSON￨- Gaudart1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 16:42￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- a￨L￨DT￨O￨- great￨L￨JJ￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨- in￨L￨IN￨O￨- contexts￨L￨NNS￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- scarcity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- his￨L￨PRP$￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- benefits￨L￨NNS￨O￨- tradeoff￨L￨NN￨O￨- between￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- virulence￨L￨NN￨O￨A were￨L￨VBD￨O￨- systematically￨L￨RB￨O￨- studied￨L￨VBN￨O￨- through￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- validated￨L￨VBD￨O￨- the￨L￨DT￨O￨- idea￨L￨NN￨O￨- that￨L￨IN￨O￨- non-vector-borne￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- relying￨L￨VBG￨O￨- on￨L￨IN￨O￨- direct￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- benign￨L￨JJ￨O￨- while￨L￨IN￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- mode￨L￨NN￨O￨- are￨L￨VBP￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- virulent￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Anderson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- May￨U￨NNP￨DATE￨- are￨L￨VBP￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- pioneers￨L￨NNS￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- mathematics￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- proposed￨L￨VBN￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- Ro￨U￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- pathogen￨L￨NN￨O￨- fitness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- written￨L￨VBN￨O￨- as￨L￨IN￨O￨- :￨L￨:￨O￨- #Mortality￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- virulence￨L￨NN￨O￨A for￨L￨IN￨O￨- its￨L￨PRP$￨O￨- simplicity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- would￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- virulence￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- will￨L￨MD￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- reduce￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- ’s￨L￨POS￨O￨- mobility￨L￨NN￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- theories￨L￨NNS￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- virulence￨L￨NN￨O￨A ,￨L￨,￨O￨- all￨L￨DT￨O￨- pathogens￨L￨NNS￨O￨- will￨L￨MD￨O￨- end￨L￨VB￨O￨- up￨L￨RP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- relationship￨L￨NN￨O￨- of￨L￨IN￨O￨- commensalism￨L￨NN￨O￨- or￨L￨CC￨O￨- mutualism￨L￨NN￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- being￨L￨VBG￨O￨- avirulent￨L￨JJ￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Ewald￨U￨NNP￨PERSON￨- was￨L￨VBD￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- firsts￨L￨NNS￨O￨- to￨L￨TO￨O￨- argue￨L￨VB￨O￨- that￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- and￨L￨CC￨O￨- virulence￨L￨NN￨O￨A α￨L￨NN￨O￨- are￨L￨VBP￨O￨- linked￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- branching￨L￨VBG￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tree￨L￨NN￨O￨- roughly￨L￨RB￨O￨- approximates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- event￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- an￨L￨DT￨O￨- implicit￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- of￨L￨IN￨O￨- nonparametric￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A methods￨L￨NNS￨O￨- using￨L￨VBG￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- subtree￨L￨JJ￨O￨- clusters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- ‘￨L￨``￨O￨- hotspots￨L￨NNS￨O￨- ’￨L￨''￨O￨- of￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model-based￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- parametric￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- clustering￨L￨NN￨O￨A method￨L￨NN￨O￨- substantially￨L￨RB￨O￨- outperforms￨L￨VBZ￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- nonparametric￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- recovering￨L￨VBG￨O￨- clusters￨L￨NNS￨O￨- of￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- differences￨L￨NNS￨O￨- are￨L￨VBP￨O￨- recapitulated￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- HIV-1￨U￨NN￨MISC￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Subtree￨U￨NN￨O￨- methods￨L￨NNS￨O￨- define￨L￨VBP￨O￨- clusters￨L￨NNS￨O￨A relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- ancestors￨L￨NNS￨O￨- of￨L￨IN￨O￨- sequences￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨- tree￨L￨NN￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- quantities￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- branch￨L￨NN￨O￨- length￨L￨NN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- descendants￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ancestral￨L￨JJ￨O￨- node￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- fundamentally￨L￨RB￨O￨- new￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- genetic￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- tree￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- observed￨L￨VBN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- nonparametric￨L￨JJ￨O￨- clustering￨L￨NN￨O￨A methods￨L￨NNS￨O￨- seem￨L￨VBP￨O￨- relatively￨L￨RB￨O￨- insensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Exploring￨U￨NNP￨O￨- Voluntary￨U￨NNP￨O￨- Vaccinating￨U￨NNP￨O￨- Behaviors￨U￨NNP￨O￨- using￨L￨VBG￨O￨- Evolutionary￨U￨JJ￨MISC￨- N-person￨U￨NN￨MISC￨- Threshold￨U￨NNP￨MISC￨- Games￨U￨NNPS￨MISC￨- Benyun￨U￨NNP￨MISC￨- Shi1￨U￨NN￨O￨- ,￨L￨,￨O￨- Weihao￨U￨NNP￨O￨- Wang2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Hongjun￨U￨NNP￨PERSON￨- Qiu1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Yu-Wang￨U￨NNP￨O￨- Chen3￨U￨NNP￨O￨- &￨L￨CC￨O￨- Shaoliang￨U￨NNP￨O￨- Peng1￨U￨NN￨O￨- ,4,5￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 16355￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- science￨L￨NN￨O￨- AbstractUnderstanding￨U￨NN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- voluntary￨L￨JJ￨O￨- vaccinating￨L￨VBG￨O￨A behaviors￨L￨NNS￨O￨- plays￨L￨VBZ￨O￨- essential￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- making￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- policies￨L￨NNS￨O￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- vaccinepreventable￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- consideration￨L￨NN￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- N-person￨U￨NN￨MISC￨- threshold￨L￨NN￨O￨- game￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- dynamically￨L￨RB￨O￨- adjust￨L￨VB￨O￨- their￨L￨PRP$￨O￨- vaccinating￨L￨VBG￨O￨A strategies￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- payoffs￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- nonlinearly￨L￨RB￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reached￨L￨VBN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- well-mixed￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- relationships￨L￨NNS￨O￨- at￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨A cost￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- relative￨L￨JJ￨O￨A costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Towards￨U￨IN￨MISC￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A elimination￨L￨NN￨O￨- in￨L￨IN￨O￨- Savannakhet￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Lao￨U￨NNP￨NATIONALITY￨- PDR￨U￨NNP￨O￨- :￨L￨:￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- driven￨L￨VBN￨O￨- strategy￨L￨NN￨O￨- designSai￨L￨NNP￨O￨- Thein￨U￨NNP￨O￨- Than￨U￨IN￨O￨- Tun1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Lorenz￨U￨NNP￨PERSON￨- von￨L￨NNP￨O￨- Seidlein1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Tiengkham￨U￨NNP￨O￨- Pongvongsa3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Mayfong￨U￨NNP￨O￨- Mayxay2￨U￨NNP￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Sompob￨U￨NNP￨O￨- Saralamba1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Shwe￨U￨NNP￨O￨- Sin￨U￨NNP￨O￨- Kyaw1￨U￨NN￨O￨- ,￨L￨,￨O￨- Phetsavanh￨U￨NNP￨O￨- Chanthavilay5￨U￨NNP￨O￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Olivier￨U￨NNP￨PERSON￨- Celhay1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Tran￨U￨NNP￨PERSON￨- Dang￨U￨NNP￨PERSON￨- Nguyen7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Thu￨U￨NNP￨O￨- Nguyen-Anh￨U￨NNP￨O￨- Tran7￨U￨NN￨O￨- ,￨L￨,￨O￨- Daniel￨U￨NNP￨PERSON￨- M.￨U￨NNP￨PERSON￨- White1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 16:483￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- Plasmodium￨U￨NN￨O￨- falciparum￨L￨NN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- has￨L￨VBZ￨O￨- decreased￨L￨VBN￨O￨- substantially￨L￨RB￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DATE￨- 15￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- against￨L￨IN￨O￨- anti-malarial￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- and￨L￨CC￨O￨- insecticides￨L￨NNS￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- decline￨L￨NN￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- continue￨L￨VB￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- interventions￨L￨NNS￨O￨A comprised￨L￨VBD￨O￨- universal￨L￨JJ￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- early￨L￨JJ￨O￨- diagnosis￨L￨NN￨O￨- and￨L￨CC￨O￨- adequate￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- improved￨L￨VBD￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- long-lasting￨L￨JJ￨O￨- insecticidal￨L￨JJ￨O￨- nets￨L￨NNS￨O￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- monthly￨L￨JJ￨SET￨- rounds￨L￨NNS￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- drug￨L￨NN￨O￨- administration￨L￨NN￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- RTS￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- vaccination￨L￨NN￨O￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- booster￨L￨NN￨O￨- dose￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- screening￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- imported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- modelling￨L￨NN￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sequential￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- five￨L￨CD￨NUMBER￨- available￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- integrated￨L￨VBN￨O￨- strategy￨L￨NN￨O￨- was￨L￨VBD￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- stop￨L￨VB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- 3-year￨L￨JJ￨DURATION￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- urgent￨L￨JJ￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- alternative￨L￨NN￨O￨- ,￨L￨,￨O￨- accelerated￨L￨VBD￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- like￨L￨IN￨O￨- Lao￨U￨NNP￨NATIONALITY￨- PDR￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- remaining￨L￨VBG￨O￨- endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- perform￨L￨VBP￨O￨- retrospective￨L￨JJ￨O￨- forecasting￨L￨NN￨O￨- over￨L￨IN￨O￨- 10￨L￨CD￨NUMBER￨- seasons￨L￨NNS￨O￨- for￨L￨IN￨O￨- 95￨L￨CD￨NUMBER￨- cities￨L￨NNS￨O￨- using￨L￨VBG￨O￨- 4￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨A :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- no￨L￨DT￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨- ;￨L￨:￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- optimization￨L￨NN￨O￨- and￨L￨CC￨O￨- forecast￨L￨NN￨O￨- with￨L￨IN￨O￨- local￨L￨JJ￨O￨- climatological￨L￨JJ￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- historical￨L￨JJ￨O￨- average￨L￨JJ￨O￨- AH￨U￨NN￨O￨- conditions￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- optimization￨L￨NN￨O￨- and￨L￨CC￨O￨- forecast￨L￨NN￨O￨- with￨L￨IN￨O￨- local￨L￨JJ￨O￨- observed￨L￨VBN￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- AH￨U￨FW￨O￨- as￨L￨IN￨O￨- observed￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- optimization￨L￨NN￨O￨- with￨L￨IN￨O￨- observed￨L￨VBN￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨- and￨L￨CC￨O￨- forecast￨L￨VBN￨O￨- with￨L￨IN￨O￨- climatological￨L￨JJ￨O￨- AH￨U￨NN￨O￨- forcing￨L￨VBG￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecast￨L￨NN￨O￨- over￨L￨IN￨O￨- larger￨L￨JJR￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- US￨U￨NNP￨ORGANIZATION￨- CDC￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Human￨U￨NNP￨ORGANIZATION￨- Services￨U￨NNPS￨ORGANIZATION￨- multi-state￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- subtropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- heretofore￨L￨RB￨O￨- adopted￨L￨VBN￨O￨- a￨L￨DT￨O￨- SIRS￨U￨NN￨O￨- form￨L￨NN￨O￨- without￨L￨IN￨O￨- AH￨U￨NNP￨O￨- forcing￨L￨VBG￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- systems￨L￨NNS￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-recovered-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- first￨L￨JJ￨ORDINAL￨- optimized￨L￨VBN￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨A using￨L￨VBG￨O￨- observational￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- US￨U￨NNP￨COUNTRY￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- municipal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- first￨L￨RB￨ORDINAL￨- developed￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- AH-forced￨U￨JJ￨O￨- SIRS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- state￨L￨NN￨O￨- geographic￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Modeling￨U￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨A of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- temperate￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reproduced￨L￨VBN￨O￨- when￨L￨WRB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- observed￨L￨VBN￨O￨- AH￨U￨NN￨O￨- conditions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- ITNs￨U￨NNS￨O￨- and￨L￨CC￨O￨- IRS￨U￨NNP￨ORGANIZATION￨- :￨L￨:￨O￨- larviciding￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- attractive￨L￨JJ￨O￨- toxic￨L￨JJ￨O￨- sugar￨L￨NN￨O￨- baits￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ATSBs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- insecticide￨L￨NN￨O￨A spraying￨L￨VBG￨O￨- of￨L￨IN￨O￨- male￨L￨JJ￨O￨- mating￨L￨NN￨O￨- swarms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- mosquito-proofed￨L￨JJ￨O￨- housing￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- spatial￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- repellents￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- personal￨L￨JJ￨O￨- protection￨L￨NN￨O￨- measures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- topical￨L￨JJ￨O￨- repellents￨L￨NNS￨O￨- ,￨L￨,￨O￨- insecticide-treated￨L￨JJ￨O￨- clothing￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- systemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- topical￨L￨JJ￨O￨- insecticide-treated￨L￨JJ￨O￨- cattle￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- odor-baited￨L￨JJ￨O￨- traps￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- space￨L￨NN￨O￨- spraying￨L￨VBG￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- package￨L￨NN￨O￨- of￨L￨IN￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A required￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- entomological￨L￨JJ￨O￨- inoculation￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- levels￨L￨NNS￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- local￨L￨JJ￨O￨- elimination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- African￨U￨JJ￨NATIONALITY￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- vectors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- Anopheles￨U￨NNP￨O￨- gambiae￨L￨NNS￨O￨- s.s￨L￨VBP￨O￨- .￨L￨.￨O￨- +Fortunately￨U￨RB￨O￨- ,￨L￨,￨O￨- field￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- promising￨L￨JJ￨O￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨A interventions￨L￨NNS￨O￨A that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- underutilized￨L￨VBN￨O￨- or￨L￨CC￨O￨- emerging￨L￨VBG￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- complement￨L￨VB￨O￨- ITNs￨U￨NNS￨O￨- and/or￨L￨CC￨O￨- IRS￨U￨NNP￨ORGANIZATION￨- by￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- resources￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- combining￨L￨VBG￨O￨- existing￨L￨VBG￨O￨- and￨L￨CC￨O￨- novel￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- in￨L￨IN￨O￨- synergistic￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- where￨L￨WRB￨O￨- ITNs￨U￨NNS￨O￨- and/or￨L￨CC￨O￨- IRS￨U￨NNP￨ORGANIZATION￨- are￨L￨VBP￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- but￨L￨CC￨O￨- where￨L￨WRB￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A persists￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Where￨U￨WRB￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- made￨L￨VBD￨O￨- various￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨A processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- draw￨L￨VB￨O￨- inferences￨L￨NNS￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- Bayesian￨U￨JJ￨O￨- approach￨L￨NN￨O￨- includes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- unobserved￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- times￨L￨NNS￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- quantifies￨L￨VBZ￨O￨- them￨L￨PRP￨O￨- along￨L￨RP￨O￨- with￨L￨IN￨O￨- all￨L￨DT￨O￨- other￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- fit￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- published￨L￨VBN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- transmission￨L￨NN￨O￨- experiments￨L￨NNS￨O￨A for￨L￨IN￨O￨- foot-and-mouth￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FMDV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- African￨U￨JJ￨NATIONALITY￨- swine￨L￨NNS￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ASFV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- our￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- periods￨L￨NNS￨O￨A of￨L￨IN￨O￨- inoculated￨L￨VBN￨O￨- and￨L￨CC￨O￨- contact-challenged￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- has￨L￨VBZ￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 01￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Bayesian￨U￨NNP￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- transmission￨L￨NN￨O￨- experiments￨L￨NNS￨O￨A Ben￨U￨NNP￨O￨- Hu1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jose￨U￨NNP￨PERSON￨- L.￨U￨NNP￨PERSON￨- Gonzales￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Simon￨U￨NNP￨PERSON￨- Gubbins￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 16774￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- MicrobiologyViral￨U￨NNP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- AbstractEpidemiological￨U￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- livestock￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- inferred￨L￨VBN￨O￨- from￨L￨IN￨O￨- transmission￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- .￨L￨.￨O￨- +Focusing￨U￨VBG￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- package￨L￨NN￨O￨A that￨L￨WDT￨O￨- offers￨L￨VBZ￨O￨- detailed￨L￨JJ￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- inference￨L￨NN￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- applies￨L￨VBZ￨O￨- evidence￨L￨NN￨O￨- synthesis￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- to￨L￨TO￨O￨- combine￨L￨VB￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- stratified￨L￨VBN￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- risk￨L￨NN￨O￨- status￨L￨NN￨O￨- and￨L￨CC￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- age-stratified￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- package￨L￨NN￨O￨A is￨L￨VBZ￨O￨- particularly￨L￨RB￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- modelling￨L￨NN￨O￨- and￨L￨CC￨O￨- evaluating￨L￨VBG￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- directly￨L￨RB￨O￨- transmissible￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- use￨L￨VBP￨O￨- proxy￨L￨NN￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- influenza-like-illness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- counts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- respiratory￨L￨JJ￨O￨- syncytial￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- RSV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- exception￨L￨NN￨O￨- here￨L￨RB￨O￨- is￨L￨VBZ￨O￨- amei￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- R￨U￨NN￨O￨- package￨L￨NN￨O￨A for￨L￨IN￨O￨- optimising￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- management￨L￨NN￨O￨- framework￨L￨NN￨O￨- while￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- package￨L￨NN￨O￨- mainly￨L￨RB￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- high￨L￨JJ￨O￨- quality￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- implementation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Susceptible￨U￨NNP￨MISC￨- Exposed￨U￨VBN￨MISC￨- Infectious￨U￨JJ￨MISC￨- Removed￨U￨VBN￨MISC￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- previously￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- later￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- cost/benefit￨L￨NN￨O￨- of￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- programme￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- Kingdom￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- adapted￨L￨VBD￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- it￨L￨PRP￨O￨- more￨L￨RBR￨O￨- generally￨L￨RB￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- previous￨L￨JJ￨O￨- research￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- lab￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- pH￨L￨NN￨COUNTRY￨- values￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- to10￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨A of￨L￨IN￨O￨- F.￨U￨NNP￨O￨- proliferatum￨L￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- pH￨L￨NN￨COUNTRY￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 10￨L￨CD￨NUMBER￨- had￨L￨VBD￨O￨- no￨L￨DT￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- but￨L￨CC￨O￨- affected￨L￨VBD￨O￨- fusaic￨L￨JJ￨O￨- acid￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- production￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- understanding￨L￨VBG￨O￨- secretomics￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- vital￨L￨JJ￨O￨- information￨L￨NN￨O￨- for￨L￨IN￨O￨- advances￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- extracellular￨L￨JJ￨O￨- proteins￨L￨NNS￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- pathogenicity￨L￨NN￨O￨- of￨L￨IN￨O￨- F￨U￨NN￨O￨- .￨L￨.￨O￨- +Numerous￨U￨JJ￨O￨- researches￨L￨VBZ￨O￨- were￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- pH￨L￨NN￨COUNTRY￨- signal￨L￨NN￨O￨- transduction￨L￨NN￨O￨- and￨L￨CC￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- pH￨L￨NN￨COUNTRY￨- regulation￨L￨NN￨O￨A and￨L￨CC￨O￨- fungal￨L￨JJ￨O￨- pathogenicity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- pathogenic￨L￨JJ￨O￨- microorganisms￨L￨NNS￨O￨- usually￨L￨RB￨O￨- secret￨L￨JJ￨O￨- proteins￨L￨NNS￨O￨A to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- their￨L￨PRP$￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- colonization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- disturbance￨L￨NN￨O￨- of￨L￨IN￨O￨- wooded￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- and￨L￨CC￨O￨- forests￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨A in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- white-footed￨L￨JJ￨O￨- mice￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- competent￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- ticks￨L￨NNS￨O￨- ;￨L￨:￨O￨- also￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- predation￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- ecologically￨L￨RB￨O￨- fragmented￨L￨JJ￨O￨- peri-urban￨L￨JJ￨O￨- built￨L￨VBN￨O￨- environment￨L￨NN￨O￨- areas￨L￨NNS￨O￨- will￨L￨MD￨O￨- increase￨L￨VB￨O￨- mouse￨L￨NN￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- note￨L￨VB￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- factors￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨A of￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- provider￨L￨NN￨O￨- 's￨L￨POS￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- non-specific￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- and￨L￨CC￨O￨- unrecognized￨L￨JJ￨O￨- tick￨L￨NN￨O￨- bites￨L￨VBZ￨O￨- may￨L￨MD￨O￨- delay￨L￨VB￨O￨- on-time￨L￨JJ￨O￨- diagnosis￨L￨NN￨O￨- of￨L￨IN￨O￨- LD￨U￨NN￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- chronic￨L￨JJ￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- PTLDS￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- factors￨L￨NNS￨O￨- may￨L￨MD￨O￨- influence￨L￨VB￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- LD￨U￨NN￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- USA￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- climate￨L￨NN￨O￨- ,￨L￨,￨O￨- prevention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- awareness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- and￨L￨CC￨O￨- recognition￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨A by￨L￨IN￨O￨- physicians￨L￨NNS￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- ticks￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- LD￨U￨NN￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- reservoir￨L￨NN￨O￨A hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- rodents￨L￨NNS￨O￨- and￨L￨CC￨O￨- tick￨L￨VB￨O￨- predators￨L￨NNS￨O￨- like￨L￨IN￨O￨- songbirds￨L￨NNS￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- in￨L￨IN￨O￨- Dutchess￨U￨NNP￨LOCATION￨- County￨U￨NNP￨LOCATION￨- located￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Hudson￨U￨NNP￨CITY￨- River￨U￨NNP￨TITLE￨- Valley￨U￨NNP￨CITY￨- of￨L￨IN￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- State￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- the￨L￨DT￨O￨- rise￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networking￨L￨NN￨O￨- sites￨L￨NNS￨O￨- like￨L￨IN￨O￨- Facebook￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- media￨L￨NNS￨O￨- like￨L￨IN￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- penetrated￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- lives￨L￨NNS￨O￨- from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- dimensions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- opinion￨L￨NN￨O￨A diffusion￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- more￨L￨RBR￨O￨- broadly￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- attracted￨L￨VBN￨O￨- the￨L￨DT￨O￨- attention￨L￨NN￨O￨- of￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- from￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- disciplines￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- memes￨L￨NNS￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- memes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- propagated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- people￨L￨NNS￨O￨- who￨L￨WP￨O￨- know￨L￨VBP￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- know￨L￨VB￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- in￨L￨IN￨O￨- opinion￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- initially￨L￨RB￨O￨- there￨L￨EX￨O￨- exist￨L￨VBP￨O￨- several￨L￨JJ￨O￨- different￨L￨JJ￨O￨- opinions￨L￨NNS￨O￨A distributed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- opinions￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- people￨L￨NNS￨O￨- are￨L￨VBP￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- their￨L￨PRP$￨O￨- neighbours￨L￨NNS￨O￨- and￨L￨CC￨O￨- update￨L￨VB￨O￨- their￨L￨PRP$￨O￨- opinions￨L￨NNS￨O￨A ,￨L￨,￨O￨- often￨L￨RB￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- majority￨L￨NN￨O￨- rule￨L￨NN￨O￨- or￨L￨CC￨O￨- imitation￨L￨NN￨O￨- .￨L￨.￨O￨- +Opinion￨U￨NN￨O￨- or￨L￨CC￨O￨- product￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- economics￨L￨NNS￨O￨- literature￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- dynamic￨L￨JJ￨O￨- behaviours￨L￨NNS￨O￨- are￨L￨VBP￨O￨- commonly￨L￨RB￨O￨- termed￨L￨VBN￨O￨- social￨L￨JJ￨O￨- learning￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- latter￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- involve￨L￨VBP￨O￨- bounded￨L￨VBN￨O￨- confidence￨L￨NN￨O￨- between￨L￨IN￨O￨- people￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- opinions￨L￨NNS￨O￨A of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- are￨L￨VBP￨O￨- too￨L￨RB￨O￨- far￨L￨RB￨O￨- apart￨L￨RB￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- influence￨L￨VB￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- its￨L￨PRP$￨O￨- simplest￨L￨JJS￨O￨- form￨L￨NN￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- βN￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- that￨L￨WDT￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- p￨L￨NN￨O￨- of￨L￨IN￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- through￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- multiplied￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- –￨L￨:￨O￨- density￨L￨NN￨O￨A function￨L￨NN￨O￨- that￨L￨WDT￨O￨- equals￨L￨VBZ￨O￨- cN/A￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- area￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- when￨L￨WRB￨O￨- linear￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- density-dependent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- c￨L￨NN￨O￨- when￨L￨WRB￨O￨- constant￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- frequency-dependent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- random￨L￨JJ￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- quickly￨L￨RB￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- expected￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- contact￨L￨NN￨O￨- –￨L￨:￨O￨- density￨L￨NN￨O￨A functions￨L￨NNS￨O￨- will￨L￨MD￨O￨- differently￨L￨RB￨O￨- affect￨L￨VB￨O￨- outbreak￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Sexually￨U￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- described￨L￨VBN￨O￨- using￨L￨VBG￨O￨- frequency-dependent￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- remain￨L￨VB￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- modelling￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- encountering￨L￨VBG￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- either￨L￨CC￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- frequency-dependent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- linearly￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- density-dependent￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨RBS￨O￨- importantly￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- functions￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- in￨L￨IN￨O￨- whether￨L￨IN￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- persist￨L￨VB￨O￨- below￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- density￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- comprehensive￨L￨JJ￨O￨- phylodynamic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- available￨L￨JJ￨O￨- West￨U￨JJ￨MISC￨- African￨U￨JJ￨NATIONALITY￨- EBOV￨U￨NN￨O￨- genomes￨L￨NNS￨O￨A also￨L￨RB￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- population￨L￨NN￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- explanatory￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- spatial￨L￨JJ￨O￨A analyses￨L￨NNS￨O￨- and￨L￨CC￨O￨- modelling￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- EBOV￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- have￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- population￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- influential￨L￨JJ￨O￨- factor￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- gravity￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- parametrized￨L￨VBN￨O￨- to￨L￨TO￨O￨- case-reporting￨L￨JJ￨O￨- data￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 30￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 32￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- how￨L￨WRB￨O￨- EBOV￨U￨NN￨O￨- molecular￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- virus￨L￨NN￨O￨- genomes￨L￨NNS￨O￨A ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- directly￨L￨RB￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- spatio-temporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Sierra￨U￨NNP￨COUNTRY￨- Leone￨U￨NNP￨COUNTRY￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Analogous￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- attracting￨L￨VBG￨O￨- force￨L￨NN￨O￨- between￨L￨IN￨O￨- physical￨L￨JJ￨O￨- masses￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- gravity￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- human￨L￨JJ￨O￨- movements￨L￨NNS￨O￨- as￨L￨IN￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- and￨L￨CC￨O￨- distance￨L￨NN￨O￨A between￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Measures￨U￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- macaques￨L￨NNS￨O￨- ’￨L￨POS￨O￨- network￨L￨NN￨O￨- centrality￨L￨NN￨O￨- —￨L￨:￨O￨- an￨L￨DT￨O￨- index￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- and￨L￨CC￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- social￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- potentially￨L￨RB￨O￨- their￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- —￨L￨:￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- show￨L￨VB￨O￨- clear￨L￨JJ￨O￨- and￨L￨CC￨O￨- consistent￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- time￨L￨NN￨O￨- spent￨L￨VBN￨O￨- in￨L￨IN￨O￨- close￨L￨JJ￨O￨- proximity￨L￨NN￨O￨A to￨L￨TO￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- tourists￨L￨NNS￨O￨- .￨L￨.￨O￨- +Disease￨U￨NN￨CAUSE_OF_DEATH￨- simulation￨L￨NN￨O￨- modelling￨L￨NN￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- while￨L￨IN￨O￨- higher-ranked￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- significantly￨L￨RB￨O￨- greater￨L￨JJR￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A within￨L￨IN￨O￨- the￨L￨DT￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- absolute￨L￨JJ￨O￨- terms￨L￨NNS￨O￨- there￨L￨RB￨O￨- was￨L￨VBD￨O￨- little￨L￨JJ￨O￨- difference￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- different￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- predicted￨L￨VBN￨O￨- to￨L￨TO￨O￨- cause￨L￨VB￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 704￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 717￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asImplications￨L￨NNS￨O￨- of￨L￨IN￨O￨- Tourist￨U￨NNP￨O￨- –￨L￨:￨O￨- Macaque￨U￨NNP￨O￨- Interactions￨U￨NNS￨O￨- for￨L￨IN￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- TransmissionAuthorsAuthors￨U￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsCharlotte￨L￨NN￨O￨- CarneStuart￨U￨NN￨MISC￨- SempleAnn￨U￨NNP￨MISC￨- MacLarnonBonaventura￨U￨NNP￨MISC￨- MajoloLaëtitia￨U￨NNP￨MISC￨- MaréchalOpen￨U￨NNP￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- ContributionFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 65￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1.1￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨MISC￨- AbstractDuring￨U￨VBG￨O￨- wildlife￨L￨NN￨O￨- tourism￨L￨NN￨O￨- ,￨L￨,￨O￨- proximity￨L￨NN￨O￨A or￨L￨CC￨O￨- actual￨L￨JJ￨O￨- contact￨L￨NN￨O￨- between￨L￨IN￨O￨- people￨L￨NNS￨O￨- and￨L￨CC￨O￨- animals￨L￨NNS￨O￨- may￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- anthropozoonotic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- simulation￨L￨NN￨O￨- modelling￨L￨NN￨O￨A and￨L￨CC￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- animal￨L￨NN￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- behaviour￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- such￨L￨JJ￨O￨- risks￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- site￨L￨NN￨O￨- in￨L￨IN￨O￨- Morocco￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- tourists￨L￨NNS￨O￨- come￨L￨VBP￨O￨- to￨L￨TO￨O￨- see￨L￨VB￨O￨- wild￨L￨JJ￨O￨- Barbary￨U￨NNP￨O￨- macaques￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Macaca￨U￨NNP￨O￨- sylvanus￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- observed￨L￨VBD￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- physical￨L￨JJ￨O￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- close￨L￨JJ￨O￨- proximity￨L￨NN￨O￨A between￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- macaques￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- during￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- periods￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- macaques￨L￨NNS￨O￨- were￨L￨VBD￨O￨- coughing￨L￨VBG￨O￨- and￨L￨CC￨O￨- sneezing￨L￨VBG￨O￨- heavily￨L￨RB￨O￨- ,￨L￨,￨O￨- highlighting￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- We￨U￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- proposed￨L￨VBD￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- for￨L￨IN￨O￨- those￨L￨DT￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- notified￨L￨VBN￨O￨- cases￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- tip￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- iceberg￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨- C￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- notified￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- varied￨L￨VBD￨O￨A between￨L￨IN￨O￨- 163,902￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 169,382￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- non-notified￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- varied￨L￨VBD￨O￨- between￨L￨IN￨O￨- 1,433,638￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 1,446,771￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- total￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- varied￨L￨VBD￨O￨- between￨L￨IN￨O￨- 1,597,540￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 1,616,153￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- incomplete￨L￨JJ￨O￨- notification￨L￨NN￨O￨- of￨L￨IN￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- non-notified￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- illustrated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A C￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- National￨U￨NNP￨O￨- or￨L￨CC￨O￨- local￨L￨JJ￨O￨- laws￨L￨NNS￨O￨- ,￨L￨,￨O￨- norms￨L￨NNS￨O￨- or￨L￨CC￨O￨- regulations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- sometimes￨L￨RB￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- countries￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- require￨L￨VBP￨O￨- medical￨L￨JJ￨O￨- providers￨L￨NNS￨O￨- to￨L￨TO￨O￨- report￨L￨VB￨O￨- notifiable￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨A authorities￨L￨NNS￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Estimating￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- under-reported￨L￨JJ￨O￨- age-dependent￨L￨JJ￨O￨- compulsorily￨L￨RB￨O￨- notification￨L￨NN￨O￨- databasesMarcos￨L￨NN￨O￨- Amaku1￨U￨NN￨O￨- ,￨L￨,￨O￨- Marcelo￨U￨NNP￨PERSON￨- Nascimento￨U￨NNP￨PERSON￨- Burattini1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Eleazar￨U￨NNP￨PERSON￨- Chaib1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Francisco￨U￨NNP￨PERSON￨- Antonio￨U￨NNP￨PERSON￨- Bezerra￨U￨NNP￨PERSON￨- Coutinho1￨U￨NN￨O￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- Greenhalgh3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Luis￨U￨NNP￨PERSON￨- Fernandez￨U￨NNP￨PERSON￨- Lopez1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Eduardo￨U￨NNP￨PERSON￨- Massad1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 14:23￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- practical￨L￨JJ￨O￨- yet￨L￨RB￨O￨- mathematically￨L￨RB￨O￨- rigorous￨L￨JJ￨O￨- and￨L￨CC￨O￨- computationally￨L￨RB￨O￨- efficient￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- that￨L￨WDT￨O￨- comprehensively￨L￨RB￨O￨- assimilate￨L￨VBP￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- uncertainty￨L￨NN￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- generate￨L￨VBP￨O￨A estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- ,￨L￨,￨O￨- behavior￨L￨NN￨O￨- changes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- test￨L￨NN￨O￨- hypotheses￨L￨NNS￨O￨- ,￨L￨,￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- evaluate￨L￨VB￨O￨- how￨L￨WRB￨O￨- behavior￨L￨NN￨O￨- changes￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- gain￨L￨NN￨O￨- insight￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- pathways￨L￨NNS￨O￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- optimize￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- generate￨L￨VBP￨O￨- short￨L￨JJ￨O￨- and￨L￨CC￨O￨- long-term￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- ,￨L￨,￨O￨- just￨L￨RB￨O￨- to￨L￨TO￨O￨- name￨L￨VB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Richards￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨A rate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- limitation￨L￨NN￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- deviation￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- S-shaped￨U￨JJ￨MISC￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- review￨L￨VBP￨O￨- and￨L￨CC￨O￨- illustrate￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- data￨L￨NNS￨O￨- assimilation￨L￨NN￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- connecting￨L￨VBG￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- data￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- progression￨L￨NN￨O￨- of￨L￨IN￨O￨- case￨L￨NN￨O￨- counts￨L￨VBZ￨O￨- relating￨L￨VBG￨O￨- to￨L￨TO￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨A or￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g￨L￨NN￨O￨- ,￨L￨,￨O￨- daily￨L￨JJ￨SET￨- incident￨L￨NN￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- growth￨L￨NN￨O￨A phase￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- denoting￨L￨VBG￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- deceleration￨L￨NN￨O￨- of￨L￨IN￨O￨- growth￨L￨NN￨O￨- ”￨L￨''￨O￨- parameter￨L￨NN￨O￨- varied￨L￨VBD￨O￨- between￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- GRM￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- Richards￨U￨NNP￨PERSON￨- growth￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- free￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- logistic-type￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Multinational￨U￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- asymmetry￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨- influence￨L￨NN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- Amy￨U￨NNP￨PERSON￨- Wesolowski1￨U￨NNP￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Elisabeth￨U￨NNP￨PERSON￨- zu￨L￨NNP￨O￨- Erbach-Schoenberg2￨U￨NN￨O￨- ,3￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Andrew￨U￨NNP￨PERSON￨- J.￨U￨NNP￨PERSON￨- Metcalf￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,10￨L￨CD￨NUMBER￨- na2￨L￨NN￨O￨- Nature￨U￨NNP￨O￨- Communicationsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2069￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Developing￨U￨VBG￨O￨- worldEcological￨L￨JJ￨O￨- epidemiologyEcological￨L￨JJ￨O￨- modellingEnvironmental￨L￨JJ￨O￨- social￨L￨JJ￨O￨- sciences￨L￨NNS￨O￨- AbstractSeasonal￨U￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨A mobility￨L￨NN￨O￨A is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- ubiquitous￨L￨JJ￨O￨- and￨L￨CC￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- seasonality￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- limited￨L￨VBN￨O￨- by￨L￨IN￨O￨- data￨L￨NNS￨O￨- availability￨L￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- travel￨L￨NN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨A mobility￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- neglected￨L￨VBN￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- :￨L￨:￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- seasonal9￨L￨JJ￨O￨- ,10,11,12￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- this￨L￨DT￨O￨- broader￨L￨JJR￨O￨- pattern￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- also￨L￨RB￨O￨- fluctuates￨L￨VBZ￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- year￨L￨NN￨DATE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- increased￨L￨VBN￨O￨- travel￨L￨NN￨O￨A from￨L￨IN￨O￨- rural￨L￨JJ￨O￨- to￨L￨TO￨O￨- urban￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- after￨L￨IN￨O￨- national￨L￨JJ￨O￨- holidays￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- seasonal￨L￨JJ￨O￨- travel￨L￨NN￨O￨A and￨L￨CC￨O￨- directional￨L￨JJ￨O￨- asymmetries￨L￨NNS￨O￨- in￨L￨IN￨O￨- Kenya￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- Namibia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Pakistan￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- spectrum￨L￨NN￨O￨- from￨L￨IN￨O￨- rural￨L￨JJ￨O￨- nomadic￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- to￨L￨TO￨O￨- highly￨L￨RB￨O￨- urbanized￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Estimating￨U￨VBG￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- which￨L￨WDT￨O￨- monitor￨L￨VBP￨O￨- respiratory￨L￨JJ￨O￨- healthcare￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- and￨L￨CC￨O￨- resource￨L￨NN￨O￨- use￨L￨VBP￨O￨- including￨L￨VBG￨O￨- general￨L￨JJ￨TITLE￨- practitioner￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- GP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- visits￨L￨NNS￨O￨- ,￨L￨,￨O￨- hospitalizations￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Wales￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- between￨L￨IN￨O￨- 7000￨L￨CD￨DATE￨- –￨L￨:￨O￨- 25,000￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- during￨L￨IN￨O￨- winter￨L￨NN￨DATE￨- periods￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- seen￨L￨VBN￨O￨- among￨L￨IN￨O￨- persons￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- 75￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- over￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- PHE￨U￨NNP￨ORGANIZATION￨- publish￨L￨VB￨O￨- weekly￨L￨JJ￨SET￨- surveillance￨L￨NN￨O￨- reports￨L￨NNS￨O￨- that￨L￨IN￨O￨- report￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza-like-illness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- GP￨U￨NN￨O￨- consultations￨L￨NNS￨O￨- ,￨L￨,￨O￨- respiratory￨L￨JJ￨O￨- hospitalizations￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- all-cause￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2014￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A ,￨L￨,￨O￨- geographical￨L￨JJ￨O￨- pilots￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- was￨L￨VBD￨O￨- offered￨L￨VBN￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- 4-to￨L￨JJ￨O￨- 11-year-old￨L￨JJ￨DURATION￨- children￨L￨NNS￨O￨- were￨L￨VBD￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- distinct￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- across￨L￨IN￨O￨- England￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- extension￨L￨NN￨O￨- is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- implemented￨L￨VBN￨O￨- by￨L￨IN￨O￨- Public￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- England￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- PHE￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- stages￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- 2-and￨L￨JJ￨O￨- 3-Citation￨L￨NN￨O￨- –￨L￨:￨O￨- 2014￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A season￨L￨NN￨O￨A .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- in￨L￨IN￨O￨- Zambia￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- globally￨L￨RB￨O￨- have￨L￨VBP￨O￨- discussed￨L￨VBN￨O￨- ECF-related￨U￨JJ￨MISC￨- issues￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- quantification/modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- economic￨L￨JJ￨O￨A impacts￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- confirmed￨L￨VBD￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- ECF￨U￨NN￨ORGANIZATION￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- survey￨L￨NN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- conducted￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 699￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- key￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- affecting￨L￨VBG￨O￨- traditional￨L￨JJ￨O￨- cattle￨L￨NNS￨O￨A farmers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- by￨L￨IN￨O￨- several￨L￨JJ￨O￨- donor-funded￨L￨JJ￨O￨- projects￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- ASVEZA￨U￨NNP￨O￨- program￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Belgian￨U￨JJ￨NATIONALITY￨- government￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- farmers￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Government￨U￨NN￨O￨- of￨L￨IN￨O￨- Zambia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- ECF￨U￨NNP￨ORGANIZATION￨- cases￨L￨NNS￨O￨- are￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Eastern￨U￨NNP￨MISC￨- province￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- endemic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- provinces￨L￨NNS￨O￨- of￨L￨IN￨O￨- Zambia￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- uttermost￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- importance￨L￨NN￨O￨- in￨L￨IN￨O￨- Eastern￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Central￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Southern￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- where￨L￨WRB￨O￨- it￨L￨PRP￨O￨- causes￨L￨VBZ￨O￨- severe￨L￨JJ￨O￨- direct￨L￨JJ￨O￨- and￨L￨CC￨O￨- indirect￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- losses￨L￨NNS￨O￨- among￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A farmers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +East￨U￨NNP￨LOCATION￨- Coast￨U￨NNP￨LOCATION￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ECF￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- cattle￨L￨NNS￨O￨A caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- protozoan￨L￨NN￨O￨- parasite￨L￨NN￨O￨- Theileria￨U￨FW￨O￨- parva￨L￨FW￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- transstadially￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- three-host￨L￨JJ￨O￨- tick￨L￨NN￨O￨- Rhipicephalus￨U￨JJ￨MISC￨- appendiculatus￨L￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effects￨L￨NNS￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- sense￨L￨NN￨O￨- expected￨L￨VBN￨O￨- :￨L￨:￨O￨- if￨L￨IN￨O￨- human￨L￨JJ￨O￨- weight￨L￨NN￨O￨A is￨L￨VBZ￨O￨- dynamic￨L￨JJ￨O￨- on￨L￨IN￨O￨- short￨L￨JJ￨O￨- timescales￨L￨NNS￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- quasi-equilibrium￨L￨NN￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- BMI￨U￨NNP￨O￨- distributions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- balance￨L￨NN￨O￨- between￨L￨IN￨O￨- drift￨L￨NN￨O￨- towards￨L￨IN￨O￨- the￨L￨DT￨O￨- center￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- diffusion￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- aggregate￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- multifactorial￨L￨JJ￨O￨- perturbations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- alternative￨L￨JJ￨O￨- explanations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- broadening￨L￨VBG￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- put￨L￨VBN￨O￨- forward￨L￨RB￨O￨- that￨L￨IN￨O￨- include￨L￨VBP￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- obesogenic￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- runaway￨L￨JJ￨O￨- train￨L￨NN￨CRIMINAL_CHARGE￨- ”￨L￨''￨O￨- theory￨L￨NN￨O￨- that￨L￨WDT￨O￨- BMI￨U￨NNP￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- right-skewed￨L￨JJ￨O￨- because￨L￨IN￨O￨- high-BMI￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- vicious￨L￨JJ￨O￨- self-reinforcing￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- weight￨L￨NN￨O￨A gain￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- data￨L￨NNS￨O￨- provides￨L￨VBZ￨O￨- strong￨L￨JJ￨O￨- indications￨L￨NNS￨O￨- that￨L￨WDT￨O￨- human￨L￨JJ￨O￨- BMI￨U￨NN￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- balance￨L￨NN￨O￨- between￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- drift￨L￨NN￨O￨A towards￨L￨IN￨O￨- a￨L￨DT￨O￨- natural￨L￨JJ￨O￨- set￨L￨NN￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- diffusion￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- random￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- diet￨L￨NN￨O￨- and￨L￨CC￨O￨- physical￨L￨JJ￨O￨- activity￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- data￨L￨NN￨O￨A set￨L￨NN￨O￨A of￨L￨IN￨O￨- BMI￨U￨NN￨O￨- measurements￨L￨NNS￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 750,000￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- receiving￨L￨VBG￨O￨- Chicago-area￨U￨JJ￨CITY￨- medical￨L￨JJ￨O￨- services￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- mechanistic￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- BMI￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- informed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- trends￨L￨NNS￨O￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- data￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- low-BMI￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- on￨L￨IN￨O￨- average￨L￨JJ￨O￨- increase￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- weight￨L￨NN￨O￨A year-over-year￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- high-BMI￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- decrease￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- weight￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increase/decrease￨L￨NN￨O￨- being￨L￨VBG￨O￨- approximately￨L￨RB￨O￨- linear￨L￨JJ￨O￨- in￨L￨IN￨O￨- BMI￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Mathematical￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- study￨L￨NN￨O￨- design￨L￨NN￨O￨A or￨L￨CC￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- reviewSereina￨L￨NNP￨O￨- A.￨U￨NN￨O￨- 2017Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- offer￨L￨VBP￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- informing￨L￨VBG￨O￨- design￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- to￨L￨TO￨O￨- what￨L￨WP￨O￨- extent￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- planning￨L￨NN￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- inform￨L￨VB￨O￨- study￨L￨NN￨O￨- design￨L￨NN￨O￨A for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- transmitted￨L￨VBD￨O￨- between￨L￨IN￨O￨- humans￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- animals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Eligible￨U￨JJ￨O￨- publications￨L￨NNS￨O￨- and￨L￨CC￨O￨- registered￨L￨VBN￨O￨- trials￨L￨NNS￨O￨- included￨L￨VBD￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- compartmental￨L￨JJ￨O￨- ,￨L￨,￨O￨- individual-based￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- Markov￨U￨NNP￨PERSON￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- were￨L￨VBD￨O￨- described￨L￨VBN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extracted￨L￨VBD￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- investigated￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- study￨L￨NN￨O￨- design￨L￨NN￨O￨A .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Dynamic￨U￨NNP￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Uzi￨U￨NNP￨O￨- Harush1￨U￨NNP￨O￨- &￨L￨CC￨O￨- Baruch￨U￨NNP￨O￨- Barzel1￨U￨NNP￨O￨- Nature￨U￨NNP￨O￨- Communicationsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2181￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksStatistical￨L￨JJ￨O￨- physics￨L￨NN￨O￨- AbstractAlthough￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- extensively￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- visualize￨L￨VB￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨- in￨L￨IN￨O￨- biological￨L￨JJ￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- technological￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- translating￨L￨VBG￨O￨- topology￨L￨NN￨O￨- into￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- flow￨L￨NN￨O￨- continues￨L￨VBZ￨O￨- to￨L￨TO￨O￨- challenge￨L￨VB￨O￨- us￨L￨PRP￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- similar￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- fundamentally￨L￨RB￨O￨- different￨L￨JJ￨O￨- flow￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- uncover￨L￨VB￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- actual￨L￨JJ￨O￨- flow￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- perturbative￨L￨JJ￨O￨- formalism￨L￨NN￨O￨- ,￨L￨,￨O￨- analytically￨L￨RB￨O￨- tracking￨L￨VBG￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- nodes/paths￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- flow￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- exposing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rules￨L￨NNS￨O￨- that￨L￨WDT￨O￨- link￨L￨VBP￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- diversity￨L￨NN￨O￨- of￨L￨IN￨O￨- flow￨L￨NN￨O￨A patterns￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- mapped￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- universal￨L￨JJ￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- topology￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- ultimately￨L￨RB￨O￨- allowing￨L￨VBG￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- main￨L￨JJ￨O￨- arteries￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨- .￨L￨.￨O￨- +Counter-intuitively￨U￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- formalism￨L￨NN￨O￨- predicts￨L￨VBZ￨O￨- a￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- frequently￨L￨RB￨O￨- encountered￨L￨VBN￨O￨- dynamics￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- flow￨L￨NN￨O￨A of￨L￨IN￨O￨- information￨L￨NN￨O￨- avoids￨L￨VBZ￨O￨- the￨L￨DT￨O￨- hubs￨L￨NNS￨O￨- ,￨L￨,￨O￨- favoring￨L￨VBG￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- peripheral￨L￨JJ￨O￨- pathways￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- striking￨L￨JJ￨O￨- disparity￨L￨NN￨O￨- between￨L￨IN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- information￨L￨NN￨O￨- flow￨L￨NN￨O￨A is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- determined￨L￨VBN￨O￨- solely￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- characterizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- nodes18￨L￨NN￨O￨- ,￨L￨,￨O￨- 23￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- genetic￨L￨JJ￨O￨- relatedness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- MRSA￨U￨NNP￨ORGANIZATION￨- isolates￨L￨NNS￨O￨A was￨L￨VBD￨O￨- determined￨L￨VBN￨O￨- using￨L￨VBG￨O￨- pulsed￨L￨JJ￨O￨- field￨L￨NN￨O￨- gel￨L￨NN￨O￨- electrophoresis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PFGE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- PFGE￨U￨NN￨O￨- banding￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- analysed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- The￨U￨DT￨O￨- MRSA￨U￨NNP￨ORGANIZATION￨- isolates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- spa-typed￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- using￨L￨VBG￨O￨- specific￨L￨JJ￨O￨- primers￨L￨NNS￨O￨- Table￨U￨NNP￨O￨- that￨L￨WDT￨O￨- targeted￨L￨VBD￨O￨- the￨L￨DT￨O￨- repetitive￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- region￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fc￨U￨NN￨MISC￨- binding￨L￨NN￨O￨- region￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- X￨U￨NN￨O￨- region￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- S.￨U￨NNP￨MISC￨- Nine￨U￨NNP￨NUMBER￨- representative￨L￨JJ￨TITLE￨- isolates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 71￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 100￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 131￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 133￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 134￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 143￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 165￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 183￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- randomly￨L￨RB￨O￨- selected￨L￨VBN￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- UPGMA￨U￨NNP￨ORGANIZATION￨- cluster￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spa-sequence￨L￨NN￨O￨- type￨L￨NN￨O￨- determination￨L￨NN￨O￨- using￨L￨VBG￨O￨- specific￨L￨JJ￨O￨- primers￨L￨NNS￨O￨- Table￨U￨NNP￨O￨- that￨L￨WDT￨O￨- targeted￨L￨VBD￨O￨- X￨U￨NN￨O￨- region￨L￨NN￨O￨- as￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- described￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Multilocus￨U￨JJ￨O￨- sequence￨L￨NN￨O￨- typing￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MLST￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- representative￨L￨JJ￨TITLE￨- MRSA￨U￨NNP￨O￨- isolates￨L￨NNS￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- nine￨L￨CD￨NUMBER￨- spa-typed￨L￨JJ￨O￨- MRSA￨U￨NNP￨ORGANIZATION￨- isolates￨L￨NNS￨O￨- targeting￨L￨VBG￨O￨- seven￨L￨CD￨NUMBER￨- housekeeping￨L￨JJ￨O￨- genes￨L￨NNS￨O￨- Table￨U￨NNP￨O￨- was￨L￨VBD￨O￨- PCR-amplified￨U￨JJ￨O￨- using￨L￨VBG￨O￨- specific￨L￨JJ￨O￨- primers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SCCmec-typing￨U￨NN￨O￨- and￨L￨CC￨O￨- CA-MRSA￨U￨NN￨O￨- and￨L￨CC￨O￨- HA-MRSA￨U￨NN￨O￨- designation￨L￨NN￨O￨- were￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- Using￨U￨VBG￨O￨- Specific￨U￨JJ￨O￨- Primer￨U￨NN￨O￨- pairs￨L￨NNS￨O￨- Table￨U￨NNP￨O￨- as￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- described￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- PCR￨U￨NN￨O￨- internal￨L￨JJ￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- targeting￨L￨VBG￨O￨A mecA￨L￨NNP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- assay￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- convergence￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- was￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- various￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A such￨L￨JJ￨O￨- as￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- childhood￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- borne￨L￨VBD￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- valuable￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- support￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A development￨L￨NN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- provided￨L￨VBD￨O￨- a￨L￨DT￨O￨- platform￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- discussion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- research￨L￨NN￨O￨- challenges￨L￨NNS￨O￨- and￨L￨CC￨O￨- achievements￨L￨NNS￨O￨- on￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨A behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- considered￨L￨VBD￨O￨- a￨L￨DT￨O￨- multipatch￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨A the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- movement￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- was￨L￨VBD￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨A behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assess￨L￨VBP￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- impact￨L￨VBP￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- AI￨U￨NN￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- CCS￨U￨NN￨ORGANIZATION￨- for￨L￨IN￨O￨- single￨L￨JJ￨O￨- and￨L￨CC￨O￨- co-infecting￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- CCS￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- market￨L￨NN￨O￨A turnover￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- R0￨U￨NN￨O￨- of￨L￨IN￨O￨- co-circulating￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- nature￨L￨NN￨O￨- and￨L￨CC￨O￨- rapid￨L￨JJ￨O￨- turnover￨L￨NN￨O￨A of￨L￨IN￨O￨- LBMs￨U￨NNS￨O￨- remain￨L￨VBP￨O￨- rare￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- detailed￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mechanisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- generate￨L￨VBP￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- restricted￨L￨JJ￨O￨- to￨L￨TO￨O￨- single￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- age‐acquired￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- age‐related￨L￨JJ￨O￨- structuring￨L￨NN￨O￨- observed￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- colony￨L￨NN￨O￨- ,￨L￨,￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- GIV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- maintained￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- breeding￨L￨VBG￨O￨A population￨L￨NN￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- herd￨L￨NN￨O￨- effect￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Figure￨U￨NNP￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- this￨L￨DT￨O￨- and￨L￨CC￨O￨- shows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- significantly￨L￨RB￨O￨- lower￨L￨JJR￨O￨- per‐susceptible￨L￨JJ￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- FOI￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- occupied￨L￨VBN￨O￨- by￨L￨IN￨O￨- breeding￨L￨VBG￨O￨A guillemots￨L￨NNS￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- occupied￨L￨VBN￨O￨- by￨L￨IN￨O￨- prebreeding￨L￨VBG￨O￨- guillemots￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- this￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- actively￨L￨RB￨O￨- ejecting￨L￨VBG￨O￨- prebreeding￨L￨JJ￨O￨- guillemots￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- aged￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- attempt￨L￨VBP￨O￨- to￨L￨TO￨O￨- enter￨L￨VB￨O￨- breeding￨L￨VBG￨O￨A areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- breeding￨L￨VBG￨O￨- site￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Guillemots￨U￨NNS￨O￨- with￨L￨IN￨O￨- very￨L￨RB￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- neutralizing￨L￨VBG￨O￨- antibody￨L￨NN￨O￨- against￨L￨IN￨O￨- GIV￨U￨NN￨O￨- ,￨L￨,￨O￨- suggestive￨L￨JJ￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- spend￨L￨VB￨O￨- less￨L￨JJR￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- breeding￨L￨VBG￨O￨A colony￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- are￨L￨VBP￨O￨- less￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- breed￨L￨VB￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- many￨L￨JJ￨O￨- prebreeding￨L￨JJ￨O￨- guillemots￨L￨NNS￨O￨- are￨L￨VBP￨O￨- present￨L￨JJ￨DATE￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- colony￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- breeding￨L￨VBG￨O￨A guillemots￨L￨NNS￨O￨- are￨L￨VBP￨O￨- incubating￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- eggs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- wild￨L￨JJ￨O￨- Mojave￨U￨NNP￨O￨- desert￨L￨NN￨O￨- tortoise￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Gopherus￨U￨NN￨O￨- agassizii￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- emerging￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- burrow￨L￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- base￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- creosote￨L￨NN￨O￨- shrub￨L￨NN￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- evidence￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- 2‐year‐long￨L￨JJ￨O￨- ,￨L￨,￨O￨- seminatural￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- experiment￨L￨NN￨O￨A conducted￨L￨VBN￨O￨- on￨L￨IN￨O￨- healthy￨L￨JJ￨O￨- ,￨L￨,￨O￨- previously￨L￨RB￨DATE￨- wild￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- antibody￨L￨NN￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- M.￨U￨NNP￨O￨- Because￨U￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progresses￨L￨VBZ￨O￨- slowly￨L￨RB￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- within￨L￨IN￨O￨- both￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- tortoises￨L￨NNS￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- evident￨L￨JJ￨O￨- in￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 276￨L￨CD￨NUMBER￨- tortoises￨L￨NNS￨O￨- without￨L￨IN￨O￨- signs￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- classified￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- seronegative￨L￨JJ￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- seronegative￨L￨JJ￨O￨- and￨L￨CC￨O￨- experimentally￨L￨RB￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- M.￨U￨NN￨O￨- Although￨U￨IN￨O￨- sensitive￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- tests￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- in￨L￨IN￨O￨- tortoises￨L￨NNS￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- exist￨L￨VB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- experiment￨L￨NN￨O￨A ,￨L￨,￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- animals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- likely￨L￨JJ￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- mycoplasma￨L￨NN￨O￨- at￨L￨IN￨O￨- some￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- lives￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- animals￨L￨NNS￨O￨- within￨L￨IN￨O￨- each￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- group￨L￨NN￨O￨- likely￨L￨JJ￨O￨- harbored￨L￨VBN￨O￨- low￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- M.￨U￨NN￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- quantify￨L￨VBP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- recrudescence￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Mycoplasma￨U￨NN￨O￨- agassizii￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- upper￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨A tract￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- URTD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- Mojave￨U￨NNP￨LOCATION￨- desert￨L￨NN￨O￨- tortoises￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Gopherus￨U￨NN￨O￨- agassizii￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- 20th￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- 40th￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- and￨L￨CC￨DATE￨- 60th￨L￨JJ￨DATE￨- days￨L￨NNS￨DATE￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨A case￨L￨NN￨O￨A was￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- box￨L￨NN￨O￨- plots￨L￨NNS￨O￨- of￨L￨IN￨O￨- MERS-CoV￨U￨NN￨O￨- incidences￨L￨NNS￨O￨- in￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- were￨L￨VBD￨O￨- computed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- variance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ANOVA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- control￨L￨NN￨O￨- intervention￨L￨NN￨O￨- was￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- MERS-CoV￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- immediately￨L￨RB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- confirmation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨A case￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- were￨L￨VBD￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 20th￨L￨JJ￨DATE￨- day￨L￨NN￨DATE￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- confirmation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- depicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- box￨L￨NN￨O￨- plots￨L￨NNS￨O￨- of￨L￨IN￨O￨- incidences￨L￨NNS￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- H￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- MERS-CoV￨U￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- intervention￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- 20th￨L￨JJ￨DATE￨- ,￨L￨,￨DATE￨- 40th￨L￨JJ￨DATE￨- ,￨L￨,￨DATE￨- and￨L￨CC￨DATE￨- 60th￨L￨JJ￨DATE￨- days￨L￨NNS￨DATE￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨A case￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- control￨L￨NN￨O￨- intervention￨L￨NN￨O￨- was￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- MERS-CoV￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- immediately￨L￨RB￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- confirmation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- index￨L￨NN￨O￨A case￨L￨NN￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- 10,000￨L￨CD￨NUMBER￨- stochastic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- computed￨L￨VBN￨O￨A by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨- with￨L￨IN￨O￨- initial￨L￨JJ￨O￨- values￨L￨NNS￨O￨- S￨U￨NN￨O￨- =￨L￨JJ￨O￨- 100,000￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- E￨U￨NN￨O￨- =￨L￨JJ￨O￨- 10￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- I￨U￨PRP￨O￨- =￨L￨JJ￨O￨- A￨U￨NN￨O￨- =￨L￨JJ￨O￨- H￨U￨NN￨O￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- β￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.085￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- l1￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- l2￨L￨NN￨O￨- =￨L￨JJ￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- κ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/6￨L￨CD￨NUMBER￨- .6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- ρ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.585￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.6403￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1/7￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- cascade￨L￨NN￨O￨A snapshot￨L￨NN￨O￨- consisting￨L￨VBG￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- infected/active￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- inference￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- a￨L￨DT￨O￨- cascade￨L￨NN￨O￨A that￨L￨WDT￨O￨- infects￨L￨VBZ￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- linear￨L￨JJ￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨O￨- node￨L￨NN￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- result￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- a￨L￨DT￨O￨- cascade￨L￨NN￨O￨- with￨L￨IN￨O￨- least￨L￨JJS￨O￨- difference￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- source￨L￨NN￨O￨A inference￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- tackled￨L￨VBN￨O￨- under￨L￨IN￨O￨- Independent￨U￨NNP￨ORGANIZATION￨- Cascade￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- IC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- and￨L￨CC￨O￨- topical￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨- interests￨L￨NNS￨O￨A ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- seasonal￨L￨JJ￨O￨- periodicity￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- summer￨L￨NN￨DATE￨- vacation￨L￨NN￨O￨- advertisements￨L￨NNS￨O￨- which￨L￨WDT￨O￨- spread￨L￨VBD￨O￨- more￨L￨RBR￨O￨- effectively￨L￨RB￨O￨- during￨L￨IN￨O￨- Spring￨U￨NN￨DATE￨- –￨L￨:￨O￨- Summer￨U￨NNP￨DATE￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- epidemic-based￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- analyzing￨L￨VBG￨O￨- such￨L￨JJ￨O￨- information￨L￨NN￨O￨- dissemination￨L￨NN￨O￨- processes￨L￨NNS￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- three￨L￨CD￨NUMBER￨- indicative￨L￨JJ￨O￨- operational￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- and￨L￨CC￨O￨- results￨L￨VBZ￨O￨- that￨L￨IN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation-based￨L￨JJ￨O￨- formalism￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- develop￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- framework￨L￨NN￨O￨- subject￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A modeling￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- between￨L￨IN￨O￨- information￨L￨NN￨O￨- propagation￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- associated￨L￨VBN￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- and￨L￨CC￨O￨- leveraging￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- that￨L￨WDT￨O￨- user￨L￨NN￨O￨- interests￨L￨NNS￨O￨- have￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Contrary￨U￨JJ￨O￨- to￨L￨TO￨O￨- previous￨L￨JJ￨O￨- works￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- user￨L￨NN￨O￨- interest￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- features￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- interest￨L￨NN￨O￨- periodicity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨A of￨L￨IN￨O￨- useful￨L￨JJ￨O￨- information￨L￨NN￨O￨- within￨L￨IN￨O￨- such￨L￨JJ￨O￨- complex￨L￨JJ￨O￨- wireless-social￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- social-wireless￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- generalized￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- other￨L￨JJ￨O￨- types￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- straightforwardly￨L￨RB￨O￨- considered.Motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- observations￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- proliferation￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- useful￨L￨JJ￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- generalized￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- useful￨L￨JJ￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected/informed￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- evolving￨L￨VBG￨O￨- user￨L￨NN￨O￨- interest￨L￨NN￨O￨- are￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- through￨L￨IN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- verified￨L￨VBN￨O￨- via￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨A cause￨L￨VBP￨O￨- significant￨L￨JJ￨O￨- threats￨L￨NNS￨O￨- to￨L￨TO￨O￨- honey￨L￨NN￨O￨- bees￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- bacteria￨L￨NNS￨O￨- ,￨L￨,￨O￨- microsporidia￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- arthropods￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- parasites￨L￨NNS￨O￨A include￨L￨VBP￨O￨- any￨L￨DT￨O￨- organism￨L￨NN￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Deformed￨U￨JJ￨O￨- Wing￨U￨NN￨O￨- Virus￨U￨NN￨O￨- that￨L￨WDT￨O￨- infects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- hemolymph￨L￨NN￨O￨- of￨L￨IN￨O￨- bees￨L￨NNS￨O￨- and￨L￨CC￨O￨- causes￨L￨VBZ￨O￨- deformed￨L￨VBN￨O￨- wings￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- Varroa￨U￨NNP￨O￨- destructor￨L￨NN￨O￨- mites￨L￨NNS￨O￨- that￨L￨WDT￨O￨- suck￨L￨VBP￨O￨- the￨L￨DT￨O￨- blood￨L￨NN￨O￨- of￨L￨IN￨O￨- bee￨L￨NN￨O￨- larvae￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- small￨L￨JJ￨O￨- hive￨L￨JJ￨O￨- beetles￨L￨NNS￨O￨- that￨L￨WDT￨O￨- parasitize￨L￨VBP￨O￨- the￨L￨DT￨O￨- honey￨L￨NN￨O￨- and￨L￨CC￨O￨- pollen￨L￨NN￨O￨- stores￨L￨NNS￨O￨- of￨L￨IN￨O￨- honey￨L￨NN￨O￨- bee￨L￨NN￨O￨- colonies￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ectoparasitic￨L￨JJ￨O￨- mite￨L￨JJ￨O￨- Varroa￨U￨NN￨O￨- destructor￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- it￨L￨PRP￨O￨- vectors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- cause￨L￨NN￨O￨A of￨L￨IN￨O￨- honey￨L￨NN￨O￨- bee￨L￨NN￨O￨- colony￨L￨NN￨O￨- losses￨L￨NNS￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- “￨L￨``￨O￨- parasite￨L￨NN￨O￨- ”￨L￨''￨O￨- to￨L￨TO￨O￨- broadly￨L￨RB￨O￨A refer￨L￨VB￨O￨- to￨L￨TO￨O￨- organisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- reduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- fitness￨L￨NN￨O￨- of￨L￨IN￨O￨- honey￨L￨NN￨O￨- bees￨L￨NNS￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- or￨L￨CC￨O￨- colony￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Why￨U￨WRB￨O￨- have￨L￨VBP￨O￨- honey￨L￨NN￨O￨- bee￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- management￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- had￨L￨VBD￨O￨- so￨L￨RB￨O￨- little￨L￨JJ￨O￨- success￨L￨NN￨O￨A ?￨L￨.￨O￨- +While￨U￨IN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- understanding￨L￨NN￨O￨- is￨L￨VBZ￨O￨- undesirable￨L￨JJ￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- scientific￨L￨JJ￨O￨- perspective￨L￨NN￨O￨A given￨L￨VBN￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- time-series￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- comprise￨L￨VBP￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- record￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- U.S.￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- troubling￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- perspective￨L￨NN￨O￨- in￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- leaves￨L￨VBZ￨O￨- in￨L￨IN￨O￨- limbo￨L￨NN￨O￨- the￨L￨DT￨O￨- question￨L￨NN￨O￨- of￨L￨IN￨O￨- what￨L￨WP￨O￨- potential￨L￨JJ￨O￨- visitors￨L￨NNS￨O￨- should￨L￨MD￨O￨- do￨L￨VB￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- visits￨L￨NNS￨O￨- −￨L￨VBP￨O￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- people￨L￨NNS￨O￨- by￨L￨IN￨O￨- necessity￨L￨NN￨O￨- must￨L￨MD￨O￨- revisit￨L￨VB￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- Ground￨U￨NN￨LOCATION￨- Zero￨U￨NNP￨LOCATION￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- or￨L￨CC￨O￨- weekly￨L￨JJ￨SET￨- basis￨L￨NN￨O￨- ,￨L￨,￨O￨- either￨L￨CC￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- work￨L￨VBP￨O￨- or￨L￨CC￨O￨- live￨L￨VBP￨O￨- there￨L￨RB￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- have￨L￨VBP￨O￨- family￨L￨NN￨O￨- there￨L￨RB￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Zika￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- notable￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- geographical￨L￨JJ￨O￨- resolution￨L￨NN￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- Ground￨U￨NN￨LOCATION￨- Zero￨U￨NNP￨LOCATION￨- areas￨L￨NNS￨O￨- were￨L￨VBD￨O￨- specified￨L￨VBN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- Wynwood￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NNP￨O￨- 1a￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Miami￨U￨NNP￨CITY￨- Beach￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Little￨U￨NNP￨LOCATION￨- River￨U￨NNP￨TITLE￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- separated￨L￨VBN￨O￨- from￨L￨IN￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- drive￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- Miami￨U￨NNP￨CITY￨- area￨L￨NN￨O￨A .￨L￨.￨O￨- +However￨U￨RB￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- report￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- incorporated￨L￨VBN￨O￨- this￨L￨DT￨O￨- visit-revisit￨L￨NN￨O￨- feature￨L￨NN￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- then￨L￨RB￨O￨- been￨L￨VBN￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- these￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- U.S.￨U￨NNP￨COUNTRY￨- Ground￨U￨NN￨LOCATION￨- Zero￨U￨NNP￨LOCATION￨- outbreaks￨L￨NNS￨O￨A .￨L￨.￨O￨- +Potential￨U￨JJ￨O￨- visitors￨L￨NNS￨O￨- to￨L￨TO￨O￨- Ground￨U￨NNP￨LOCATION￨- Zero￨U￨NNP￨LOCATION￨- at￨L￨IN￨O￨- timestep￨L￨NN￨O￨- t￨L￨NN￨O￨- enter￨L￨VBP￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨A p￨L￨NN￨O￨- and￨L￨CC￨O￨- leave￨L￨VB￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- p￨L￨NN￨O￨- Their￨U￨PRP$￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- individuals￨L￨NNS￨O￨- within￨L￨IN￨O￨- Ground￨U￨NN￨LOCATION￨- Zero￨U￨NNP￨LOCATION￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- q￨L￨NN￨O￨- of￨L￨IN￨O￨- getting￨L￨VBG￨O￨- bitten￨L￨NN￨O￨- and￨L￨CC￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- q￨L￨NN￨O￨- of￨L￨IN￨O￨- recovering￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- :￨L￨:￨O￨- Ground￨U￨NNP￨O￨- Zero￨U￨NNP￨NUMBER￨- (￨L￨-LRB-￨O￨- red￨L￨JJ￨O￨- shaded￨L￨JJ￨O￨- area￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- our￨L￨PRP$￨O￨- visit-revisit￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- extended￨L￨VBD￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- pair￨L￨NN￨O￨- formation￨L￨NN￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- at￨L￨IN￨O￨- most￨L￨JJS￨O￨- n￨L￨NN￨O￨- partners￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time.A￨L￨NN￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- In￨U￨IN￨O￨- epidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨A stages￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- predominantly￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨A approximation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- asymptomatically￨L￨RB￨O￨- exact￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- goes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity.KeywordsSI￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- Branching￨U￨VBG￨O￨- process￨L￨NN￨O￨- Basic￨U￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Dynamic￨U￨NNP￨O￨- network￨L￨NN￨O￨- Stochastic￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- Mathematics￨U￨NNP￨O￨- Subject￨U￨NNP￨O￨- Classification60J80￨U￨NNP￨O￨- 92D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSexually￨U￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- STIs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- ’s￨L￨POS￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- remaining￨L￨VBG￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- global￨L￨JJ￨O￨- threat￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infectious-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneously￨L￨RB￨O￨- mixing￨L￨VBG￨O￨- population￨L￨NN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- approximated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- branching￨L￨VBG￨O￨A process￨L￨NN￨O￨A approximation￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- partners￨L￨NNS￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- time￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unbounded￨L￨JJ￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- includes￨L￨VBZ￨O￨- as￨L￨IN￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- vaccinate￨L￨VBP￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- chosen￨L￨VBN￨O￨- uniformly￨L￨RB￨O￨- at￨L￨IN￨O￨- random￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- binomial￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- vaccinating￨L￨VBG￨O￨- households￨L￨NNS￨O￨A at￨L￨IN￨O￨- random￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- concentrated￨L￨VBN￨O￨- at￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Households-based￨U￨JJ￨O￨- vaccination￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- those￨L￨DT￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- households￨L￨NNS￨O￨A of￨L￨IN￨O￨- size￨L￨NN￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- every￨L￨DT￨O￨- household￨L￨NN￨O￨- size￨L￨NN￨O￨- n￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- specify￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- outline￨L￨VB￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨A outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- lastly￨L￨RB￨O￨- introduce￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- action￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- on￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- receive￨L￨VBP￨O￨- it￨L￨PRP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- initiated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- chosen￨L￨VBN￨O￨- uniformly￨L￨RB￨O￨A at￨L￨IN￨O￨- random￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- all￨L￨DT￨O￨- assumed￨L￨VBD￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- time￨L￨NN￨O￨- that￨L￨IN￨O￨- such￨L￨JJ￨O￨- data-driven￨L￨JJ￨O￨- modelling￨L￨NN￨O￨A involving￨L￨VBG￨O￨- contagion￨L￨NN￨O￨- both￨L￨CC￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- cities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- through￨L￨IN￨O￨- geographic￨L￨JJ￨O￨- proximity￨L￨NN￨O￨- or￨L￨CC￨O￨- media￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- country￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- basis￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- performed￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- at￨L￨IN￨O￨- analysing￨L￨VBG￨O￨A these￨L￨DT￨O￨- data￨L￨NNS￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- sheds￨L￨VBZ￨O￨- new￨L￨JJ￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- riots￨L￨NNS￨O￨- as￨L￨IN￨O￨- instances￨L￨NNS￨O￨- of￨L￨IN￨O￨- collective￨L￨JJ￨O￨- human￨L￨JJ￨O￨- behaviour4￨L￨NN￨O￨- ,5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- regular￨L￨JJ￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A on￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- data-driven￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- BelgiumGiancarlo￨U￨NNP￨O￨- De￨U￨NNP￨O￨- Luca1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Kim￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Kerckhove2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Pietro￨U￨NNP￨O￨- Coletti2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Chiara￨U￨NNP￨PERSON￨- Poletto1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Nathalie￨U￨NNP￨PERSON￨- Bossuyt3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Niel￨U￨NNP￨PERSON￨- Hens2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Vittoria￨U￨NNP￨PERSON￨- Colizza1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profileBMC￨L￨NN￨MISC￨- Infectious￨U￨JJ￨MISC￨- DiseasesBMC￨U￨NN￨MISC￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18:29￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- School￨U￨NNP￨O￨- closure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- option￨L￨NN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- often￨L￨RB￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- larger￨L￨JJR￨O￨- vulnerability￨L￨NN￨O￨- to￨L￨TO￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- limited￨L￨JJ￨O￨- prior￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- mix￨L￨VBP￨O￨- at￨L￨IN￨O￨- school￨L￨NN￨O￨A with￨L￨IN￨O￨- high￨L￨JJ￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- thus￨L￨RB￨O￨- representing￨L￨VBG￨O￨- key￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- age-specific￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- holiday-associated￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- affect￨L￨VBP￨O￨- seasonal￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- Changes￨U￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- establish￨L￨VBP￨O￨- contacts￨L￨NNS￨O￨- during￨L￨IN￨O￨- holidays￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- ingredient￨L￨NN￨O￨- explaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- mitigating￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- regular￨L￨JJ￨O￨- school￨L￨NN￨O￨A closure￨L￨NN￨O￨A .￨L￨.￨O￨- +Christmas￨U￨NNP￨DATE￨- holidays￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- largest￨L￨JJS￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- later￨L￨JJ￨O￨- school￨L￨NN￨O￨A breaks￨L￨NNS￨O￨- may￨L￨MD￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- stressing￨L￨VBG￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- calendar￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- process￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- one-class￨L￨JJ￨O￨- support￨L￨NN￨O￨- vector￨L￨NN￨O￨- machine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SVM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- determines￨L￨VBZ￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- flow￨L￨NN￨O￨A is￨L￨VBZ￨O￨- malicious￨L￨JJ￨O￨- or￨L￨CC￨O￨- normal￨L￨JJ￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- approach￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- two-stage￨L￨JJ￨O￨- process￨L￨NN￨O￨- for￨L￨IN￨O￨- detection￨L￨NN￨O￨A of￨L￨IN￨O￨- malicious￨L￨JJ￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- traffic￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- disparity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- node/edge￨L￨JJ￨O￨- turnover￨L￨NN￨O￨- ,￨L￨,￨O￨- highlighting￨L￨VBG￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- using￨L￨VBG￨O￨- lifetime-preserving￨L￨JJ￨O￨- reference￨L￨NN￨O￨A models￨L￨NNS￨O￨- when￨L￨WRB￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- edges￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- continuously￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- PT￨U￨NN￨O￨- implicitly￨L￨RB￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- edges￨L￨NNS￨O￨- and￨L￨CC￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- continuously￨L￨RB￨O￨A active￨L￨JJ￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- sampling￨L￨NN￨O￨- period￨L￨NN￨O￨- –￨L￨:￨O￨- an￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- hold￨L￨VB￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- PT￨U￨NN￨O￨- ,￨L￨,￨O￨- PTN￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- PTE￨U￨NN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- spreading￨L￨VBG￨O￨A dynamics￨L￨NNS￨O￨A on￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- synthetic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- edge￨L￨NN￨O￨- lifespans￨L￨NNS￨O￨- and￨L￨CC￨O￨- tunable￨L￨JJ￨O￨- burstiness￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- four￨L￨CD￨NUMBER￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- enter￨L￨VBP￨O￨- and￨L￨CC￨O￨- leave￨L￨VBP￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- dynamically￨L￨RB￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Lifetime-preserving￨U￨JJ￨O￨- reference￨L￨NN￨O￨A models￨L￨NNS￨O￨- for￨L￨IN￨O￨- characterizing￨L￨VBG￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Mingwu￨U￨NNP￨O￨- Li1￨U￨NN￨O￨- ,￨L￨,￨O￨- Vikyath￨U￨NN￨PERSON￨- D￨U￨NN￨PERSON￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- randomly￨L￨RB￨O￨- permuted￨L￨JJ￨O￨- times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PT￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- reference￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- probe￨L￨VB￨O￨- how￨L￨WRB￨O￨- temporal￨L￨JJ￨O￨- features￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Wu￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- na1￨L￨CD￨NUMBER￨- Nature￨U￨NNP￨O￨- Communicationsvolume￨U￨NNP￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 218￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksEpidemiologyInfectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- AbstractOver￨U￨VBP￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- few￨L￨JJ￨DURATION￨- decades￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- global￨L￨JJ￨O￨- metapopulation￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- built￨L￨VBN￨O￨- with￨L￨IN￨O￨- worldwide￨L￨JJ￨O￨- air-transportation￨L￨JJ￨O￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- how￨L￨WRB￨O￨- epidemics￨L￨NNS￨O￨- spread￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- origin￨L￨NN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- SARS￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Ebola￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- metapopulation￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- built￨L￨VBN￨O￨- with￨L￨IN￨O￨- worldwide￨L￨JJ￨O￨- air-transportation￨L￨JJ￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- WAN￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- global￨L￨JJ￨O￨A spread￨L￨NN￨O￨A of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza1￨L￨NN￨O￨- ,2,3,4￨L￨NN￨O￨- ,￨L￨,￨O￨- SARS5￨U￨NN￨O￨- ,6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- MERS-CoV7￨U￨NN￨O￨- ,￨L￨,￨O￨- Ebola8￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Zika9￨U￨NN￨O￨- ,10￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A/H1N1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- West￨U￨NNP￨MISC￨- African￨U￨NNP￨NATIONALITY￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Liberia.ResultsMajor￨U￨NNP￨O￨- assumptions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- frameworkThroughout￨L￨NN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- only￨L￨RB￨O￨- global￨L￨JJ￨O￨A spread￨L￨NN￨O￨A of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- relatively￨L￨RB￨O￨- fast￨L￨JJ￨O￨- timescales￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- population￨L￨NN￨O￨- peak￨L￨NN￨O￨- within￨L￨IN￨O￨- 300￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- establishment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- MERS￨U￨NNS￨O￨- ,￨L￨,￨O￨- Ebola￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- demographics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- births￨L￨NNS￨O￨- ,￨L￨,￨O￨- aging￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- negligible￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- metapopulation￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- cities￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- travel￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- WAN￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- WAN￨U￨NNP￨O￨- metapopulation￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- Methods￨U￨NNS￨O￨- for￨L￨IN￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- Ebola￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- to￨L￨TO￨O￨- show￨L￨VB￨O￨- that￨L￨IN￨O￨- key￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- robustly￨L￨RB￨O￨- estimated￨L￨VBN￨O￨- in￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- from￨L￨IN￨O￨- public￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨A spread￨L￨NN￨O￨A at￨L￨IN￨O￨- very￨L￨RB￨O￨- low￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- cost￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- Markovian￨U￨JJ￨MISC￨- transmission￨L￨NN￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨VBG￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- re-parametrised￨L￨JJ￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- pairwise-like￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- many￨L￨JJ￨O￨- well-known￨L￨JJ￨O￨- pairwise￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- regular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- is￨L￨VBZ￨O￨- exponentially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- or￨L￨CC￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- length.KeywordsEpidemics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- Non-Markovian￨U￨JJ￨MISC￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- Mean-field￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- Mathematics￨U￨NNP￨O￨- Subject￨U￨NNP￨O￨- Classification92D30￨U￨NN￨O￨- 37N25￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- IntroductionThe￨U￨NNP￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- and￨L￨CC￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- mature￨L￨JJ￨O￨- and￨L￨CC￨O￨- fruitful￨L￨JJ￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- possible￨L￨JJ￨O￨- states￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- pairwise￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- considering￨L￨VBG￨O￨- separately￨L￨RB￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- and￨L￨CC￨O￨- all￨L￨DT￨O￨- possible￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- become￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighbours￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- message￨L￨NN￨O￨A passing￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- MP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- formalism￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- living￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- patch￨L￨NN￨O￨- is￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dU￨L￨NNP￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- sigma￨L￨NN￨O￨A Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- dW￨L￨NN￨O￨- t￨L￨NN￨O￨- U￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- dt￨L￨NN￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- U￨U￨NNP￨O￨- U￨U￨NNP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- U￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- abundance￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- per-capita￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NNP￨PERSON￨- b￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- strength￨L￨NN￨O￨- of￨L￨IN￨O￨- intraspecific￨L￨JJ￨O￨- competition￨L￨NN￨O￨- ,￨L￨,￨O￨- Pow￨U￨NNP￨O￨- sigma￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infinitesimal￨L￨JJ￨O￨- variance￨L￨NN￨O￨- of￨L￨IN￨O￨- fluctuations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- per-capita￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- W￨U￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Brownian￨U￨JJ￨MISC￨- motion￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- long-term￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Rational￨U￨JJ￨MISC￨- Pow￨U￨NN￨MISC￨- sigma￨L￨NN￨O￨A 2￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- way￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- If￨U￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Rational￨U￨JJ￨O￨- Pow￨U￨NN￨O￨- sigma￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- U￨U￨NNP￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- u￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- U￨U￨NNP￨O￨- t￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- weakly￨L￨RB￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- unique￨L￨JJ￨O￨- invariant￨L￨JJ￨O￨- probability￨L￨NN￨O￨- measure￨L￨NN￨O￨- rho￨L￨NN￨O￨- on￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +which￨L￨WDT￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- sometimes￨L￨RB￨O￨- coupling￨L￨NN￨O￨- by￨L￨IN￨O￨- dispersal￨L￨NN￨O￨- can￨L￨MD￨O￨- make￨L￨VB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- persistent.KeywordsStochastic￨L￨JJ￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨A Density-dependence￨U￨NN￨MISC￨- Ergodicity￨U￨NNP￨MISC￨- Spatial￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- Lotka￨U￨NNP￨LOCATION￨- –￨L￨:￨O￨- Volterra￨U￨NNP￨CITY￨- model￨L￨NN￨TITLE￨- Lyapunov￨U￨NNP￨PERSON￨- exponent￨L￨NNP￨O￨- Habitat￨U￨NNP￨O￨- fragmentation￨L￨NN￨O￨- Stochastic￨U￨NNP￨O￨- environment￨L￨NN￨O￨- Dispersion￨U￨NNP￨O￨- A.￨U￨NNP￨O￨- Continuous-space￨U￨NNP￨O￨- discrete-time￨L￨JJ￨O￨- population￨L￨NN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- disperse￨L￨VBP￨O￨- and￨L￨CC￨O￨- experience￨L￨VBP￨O￨- uncorrelated￨L￨JJ￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- by￨L￨IN￨O￨- Hardin￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- density-dependent￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨A that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- dispersal￨L￨NN￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- complements￨L￨VBZ￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Evans￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨A sciences￨L￨NNS￨O￨- ,￨L￨,￨O￨- rumouring￨L￨VBG￨O￨- behaviour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- analysed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- collective￨L￨JJ￨O￨- sense-making￨L￨NN￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- understand￨L￨VB￨O￨- situations￨L￨NNS￨O￨- characterised￨L￨VBN￨O￨- by￨L￨IN￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- ,￨L￨,￨O￨- anxiety￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- official￨L￨JJ￨O￨- news￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rise￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨A media￨L￨NNS￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- even￨L￨RB￨O￨- better￨L￨JJR￨O￨- platform￨L￨NN￨O￨- for￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- rumours￨L￨NNS￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- Gaildraud￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- rumour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- informal￨L￨JJ￨O￨- noise￨L￨NN￨O￨- that￨L￨WDT￨O￨- exists￨L￨VBZ￨O￨- ,￨L￨,￨O￨- persists￨L￨VBZ￨O￨- ,￨L￨,￨O￨- becomes￨L￨VBZ￨O￨- evanescent￨L￨JJ￨O￨- and￨L￨CC￨O￨- disappears￨L￨VBZ￨O￨- as￨L￨RB￨O￨- fast￨L￨JJ￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- appeared￨L￨VBD￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- psychology￨L￨NN￨O￨- a￨L￨DT￨O￨- rumour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- declaration￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- plausible￨L￨JJ￨O￨- ,￨L￨,￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- news￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- widespread￨L￨JJ￨O￨A without￨L￨IN￨O￨- checking￨L￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- rumours￨L￨NNS￨O￨- could￨L￨MD￨O￨- only￨L￨RB￨O￨- be￨L￨VB￨O￨- by￨L￨IN￨O￨- word￨L￨NN￨O￨- of￨L￨IN￨O￨- mouth￨L￨NN￨O￨A .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- tested￨L￨VBN￨O￨- strains￨L￨NNS￨O￨- are￨L￨VBP￨O￨- included￨L￨VBN￨O￨- those￨L￨DT￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- circulated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- incoming￨L￨JJ￨O￨- season￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- tests￨L￨NNS￨O￨- yield￨L￨VBP￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- adult￨L￨JJ￨O￨- and￨L￨CC￨O￨- elderly￨L￨JJ￨O￨- population￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- a￨L￨DT￨O￨- joint￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- estimated￨L￨VBN￨O￨- age‐specific￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- and￨L￨CC￨O￨- reporting￨L￨VBG￨O￨- rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- derived￨L￨VBD￨O￨A an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- tested￨L￨VBN￨O￨- strain￨L￨NN￨O￨- coincides￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- circulating￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- season￨L￨NN￨O￨A ,￨L￨,￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- season￨L￨NN￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- that￨L￨IN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- summer￨L￨NN￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- negligible￨L￨JJ￨O￨- .￨L￨.￨O￨- +Historical￨U￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A activity￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- both￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- and￨L￨CC￨O￨- short-term￨L￨JJ￨O￨- predictability￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- use￨L￨VBP￨O￨- such￨L￨JJ￨O￨- autoregressive￨L￨JJ￨O￨- information￨L￨NN￨O￨- can￨L￨MD￨O￨- capture￨L￨VB￨O￨- and￨L￨CC￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- salient￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Santillana￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- ensemble￨L￨NN￨O￨- approach￨L￨NN￨O￨- combining￨L￨VBG￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- outperformed￨L￨VBD￨O￨- any￨L￨DT￨O￨- other￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- national￨L￨JJ￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨A predictions￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- original￨L￨JJ￨O￨- network￨L￨NN￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- Xia￨U￨NNP￨O￨- et￨L￨FW￨O￨- al24￨L￨FW￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Delhi￨U￨NNP￨CITY￨- using￨L￨VBG￨O￨- network￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- did￨L￨VBD￨O￨A not￨L￨RB￨O￨- take￨L￨VB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- attributes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- slum￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- larger￨L￨JJR￨O￨- family￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- daily￨L￨JJ￨SET￨- activity￨L￨NN￨O￨- schedules￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- is￨L￨VBZ￨O￨- about￨L￨IN￨O￨- 1000￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- per￨L￨IN￨O￨- square￨L￨NN￨O￨- mile￨L￨NN￨O￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- slums￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 100￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- higher￨L￨JJR￨O￨- .14￨L￨CD￨NUMBER￨- Larger￨U￨NN￨O￨- household￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- crowding￨L￨VBG￨O￨- make￨L￨VB￨O￨- it￨L￨PRP￨O￨- easier￨L￨JJR￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Baker￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨A al16￨L￨FW￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- among￨L￨IN￨O￨- children￨L￨NNS￨O￨- doubles￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- addition￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- adolescents￨L￨NNS￨O￨- or￨L￨CC￨O￨- adults￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- or￨L￨CC￨O￨- older￨L￨JJR￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- six-room￨L￨JJ￨O￨- house￨L￨NN￨O￨- .￨L￨.￨O￨- +Chen￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al4￨L￨FW￨O￨- used￨L￨VBN￨O￨- network￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- refined￨L￨VBN￨O￨A social￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- Delhi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- accounted￨L￨VBD￨O￨- for￨L￨IN￨O￨- slum￨L￨NN￨O￨- demographics￨L￨NNS￨O￨- and￨L￨CC￨O￨- slum￨L￨NN￨O￨- activities￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- study￨L￨VB￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- Delhi￨U￨NNP￨CITY￨- is￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- target￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- studying￨L￨VBG￨O￨- other￨L￨JJ￨O￨- slum￨L￨NN￨O￨- areas￨L￨NNS￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- outside￨L￨IN￨O￨- of￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨A types￨L￨NNS￨O￨- and￨L￨CC￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- examined￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- on￨L￨IN￨O￨- several￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- slum￨L￨NN￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- gender￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- Delhi￨U￨NNP￨CITY￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- original￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- network￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- refined￨L￨VBN￨O￨A (￨L￨-LRB-￨O￨- network￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +P.￨U￨NNP￨PERSON￨- Smith￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Roche￨U￨NNP￨O￨- :￨L￨:￨O￨- Grant￨U￨NNP￨O￨- Investigator￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- Consulting￨U￨NNP￨O￨- fee￨L￨NN￨O￨- C.￨U￨NNP￨PERSON￨- Chaiyakunapruk￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Roche￨U￨NNP￨O￨- :￨L￨:￨O￨- Grant￨U￨NNP￨O￨- Investigator￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- Consulting￨U￨NNP￨O￨- fee￨L￨NN￨O￨- and￨L￨CC￨O￨- Research￨U￨NN￨O￨- grant￨L￨NN￨O￨- K.￨U￨NNP￨PERSON￨- Kamauu￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Roche￨U￨NNP￨O￨- :￨L￨:￨O￨- Consultant￨U￨NN￨TITLE￨- and￨L￨CC￨O￨- Grant￨U￨NNP￨O￨- Investigator￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- Consulting￨U￨NNP￨O￨- fee￨L￨NN￨O￨- and￨L￨CC￨O￨- Research￨U￨NN￨O￨- support￨L￨NN￨O￨A R.￨U￨NNP￨PERSON￨- E.￨U￨NNP￨PERSON￨- Nelson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Roche￨U￨NNP￨O￨- :￨L￨:￨O￨- Consultant￨U￨NN￨TITLE￨- and￨L￨CC￨O￨- Grant￨U￨NNP￨O￨- Investigator￨U￨NNP￨TITLE￨- ,￨L￨,￨O￨- Consulting￨U￨NNP￨O￨- fee￨L￨NN￨O￨- ,￨L￨,￨O￨- Research￨U￨NNP￨O￨- grant￨L￨NN￨O￨- and￨L￨CC￨O￨- Research￨U￨NN￨O￨- support￨L￨NN￨O￨- M.￨U￨NN￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- were￨L￨VBD￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- rhinovirus￨L￨NN￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- not￨L￨RB￨O￨- previously￨L￨RB￨DATE￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- species￨L￨NNS￨O￨- other￨L￨JJ￨O￨- than￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- causative￨L￨JJ￨O￨- agent￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- chimpanzees￨L￨NNS￨O￨- by￨L￨IN￨O￨- directly￨L￨RB￨O￨- sampling￨L￨NN￨O￨- the￨L￨DT￨O￨- lesions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- dead￨L￨JJ￨O￨- animal￨L￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- noninvasive￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- from￨L￨IN￨O￨- feces￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- .￨L￨.￨O￨- +Anthroponotic￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- origin￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- respiratory￨L￨JJ￨O￨A viruses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- caused￨L￨VBN￨O￨- notable￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- chimpanzee￨L￨NN￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- –￨L￨:￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- molecular￨L￨JJ￨O￨- testing￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- postmortem￨L￨NN￨O￨- and￨L￨CC￨O￨- noninvasive￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- fecal￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- wild￨L￨JJ￨O￨- apes￨L￨NNS￨O￨- during￨L￨IN￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- implicated￨L￨VBN￨O￨- human￨L￨JJ￨O￨- paramyxoviruses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- family￨L￨NN￨O￨- Paramyxoviridae￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- anthroponotic￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- –￨L￨:￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Rhinovirus￨U￨NN￨O￨- C￨U￨NN￨O￨- causes￨L￨VBZ￨O￨- an￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- human￨L￨JJ￨O￨- upper￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨A tract￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- most￨L￨JJS￨O￨- acute￨L￨JJ￨O￨- exacerbations￨L￨NNS￨O￨- of￨L￨IN￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- rhinovirus￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- mildly￨L￨RB￨O￨- symptomatic￨L￨JJ￨O￨- ,￨L￨,￨O￨- rhinovirus￨L￨NN￨O￨- C￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- influenza-like￨L￨JJ￨O￨- respiratory￨L￨JJ￨O￨A symptoms￨L￨NNS￨O￨- and￨L￨CC￨O￨- acute￨L￨JJ￨O￨- exacerbations￨L￨NNS￨O￨- of￨L￨IN￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- origin￨L￨NN￨O￨A of￨L￨IN￨O￨- rhinovirus￨L￨NN￨O￨- C￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- protective￨L￨JJ￨O￨- allele￨L￨NN￨O￨- among￨L￨IN￨O￨- modern￨L￨JJ￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- thought￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- occurred￨L￨VBN￨O￨- ≈￨L￨SYM￨O￨- 8,000￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- ago￨L￨RB￨DATE￨- .￨L￨.￨O￨- +Network￨U￨NNP￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- suggested￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- useful￨L￨JJ￨O￨- tool￨L￨NN￨O￨- in￨L￨IN￨O￨- prioritizing￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- by￨L￨IN￨O￨- targeting￨L￨VBG￨O￨A the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- or￨L￨CC￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Network￨U￨NNP￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- demonstrated￨L￨VBN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- by￨L￨IN￨O￨- targeting￨L￨VBG￨O￨A those￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- or￨L￨CC￨O￨- locations￨L￨NNS￨O￨- most￨L￨RBS￨O￨- connected￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Extensive￨U￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- has￨L￨VBZ￨O￨- demonstrated￨L￨VBN￨O￨A the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- prophylactic￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- Hawaiian￨U￨JJ￨MISC￨- monk￨L￨NN￨TITLE￨- seals￨L￨NNS￨O￨- against￨L￨IN￨O￨- morbillivirus￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- monovalent￨L￨JJ￨O￨- recombinant￨L￨JJ￨O￨- CDV￨U￨NN￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- commercially￨L￨RB￨O￨- produced￨L￨VBN￨O￨- for￨L￨IN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- ferrets￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Purevax￨U￨NNP￨O￨- ,￨L￨,￨O￨- Merial￨U￨NNP￨ORGANIZATION￨- Inc.￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Duluth￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- GA￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- effective￨L￨JJ￨O￨- for￨L￨IN￨O￨- vaccinating￨L￨VBG￨O￨- other￨L￨JJ￨O￨- carnivores￨L￨NNS￨O￨- including￨L￨VBG￨O￨- seals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- option￨L￨NN￨O￨A for￨L￨IN￨O￨- protecting￨L￨VBG￨O￨- Hawaiian￨U￨JJ￨MISC￨- monk￨L￨NN￨TITLE￨- seals￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- morbillivirus￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- this￨L￨DT￨O￨- basis￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- influences￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- manpower￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- alarm￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- development￨L￨NN￨O￨- effort￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- team￨L￨NN￨O￨- size￨L￨NN￨O￨- are￨L￨VBP￨O￨- examined￨L￨VBN￨O￨- through￨L￨IN￨O￨- computer￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨- team￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- involves￨L￨VBZ￨O￨- six￨L￨CD￨NUMBER￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- G￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- function￨L￨NN￨O￨- f￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- alarm￨L￨NN￨O￨- threshold￨L￨NN￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- development￨L￨NN￨O￨- effort￨L￨NN￨O￨A W￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- manpower￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨- team￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- dependent￨L￨JJ￨O￨- upon￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- function￨L￨NN￨O￨- f￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- manpower￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- alarm￨L￨NN￨O￨- threshold￨L￨NN￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- effort￨L￨NN￨O￨A W￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- G.￨U￨NNP￨O￨- +An￨U￨DT￨O￨- optimal￨L￨JJ￨O￨A solution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- stands￨L￨VBZ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- choice￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- team￨L￨NN￨O￨- size￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- company￨L￨NN￨O￨- ’s￨L￨POS￨O￨- respective￨L￨JJ￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- that￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- team￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- tradeoff￨L￨NN￨O￨- first￨L￨RB￨ORDINAL￨- goes￨L￨VBZ￨O￨- sharply￨L￨RB￨O￨- down￨L￨RB￨O￨- then￨L￨RB￨O￨- goes￨L￨VBZ￨O￨- slowly￨L￨RB￨O￨- up￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- respective￨L￨JJ￨O￨- optimal￨L￨JJ￨O￨A team￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- 47￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 27￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 21￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Resource￨U￨NNP￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨- network￨L￨NN￨O￨- Jian￨U￨NNP￨O￨- Jiang1￨U￨NNP￨O￨- ,2￨L￨NNP￨O￨- &￨L￨CC￨O￨- Tianshou￨U￨NNP￨O￨- Zhou2￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 1629￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComplex￨L￨NNP￨O￨- networks￨L￨NNS￨O￨- AbstractWhile￨U￨NNP￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- resource￨L￨NN￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- factor￨L￨NN￨O￨- in￨L￨IN￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- contagions￨L￨NNS￨O￨- ,￨L￨,￨O￨- outbreaks￨L￨NNS￨O￨- may￨L￨MD￨O￨- occur￨L￨VB￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- reach￨L￨VBP￨O￨- a￨L￨DT￨O￨- finite￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- previous￨L￨JJ￨O￨- studies1￨L￨NN￨O￨- ,2,3,4,5,6,7,8,9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- was￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- single￨L￨JJ￨O￨- or￨L￨CC￨O￨- monoplex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- apparently￨L￨RB￨O￨- a￨L￨DT￨O￨- simplification￨L￨NN￨O￨- since￨L￨IN￨O￨- in￨L￨IN￨O￨- reality￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨A spread￨L￨VBN￨O￨A often￨L￨RB￨O￨- through￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- channels￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- different￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- travelling￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- airports￨L￨NNS￨O￨- ,￨L￨,￨O￨- train￨L￨NN￨CRIMINAL_CHARGE￨- ,￨L￨,￨O￨- bus￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- just￨L￨RB￨O￨- as￨L￨IN￨O￨- information￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- diffused￨L￨VBN￨O￨- through￨L￨IN￨O￨- different￨L￨JJ￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- mediums￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- Facebook￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨A spreading￨L￨NN￨O￨A processes￨L￨NNS￨O￨- may￨L￨MD￨O￨- simultaneously￨L￨RB￨O￨- occur￨L￨VB￨O￨- through￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- sexually￨L￨RB￨CAUSE_OF_DEATH￨- transmitted￨L￨JJ￨CAUSE_OF_DEATH￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- spread￨L￨VB￨O￨- both￨L￨CC￨O￨- in￨L￨IN￨O￨- homosexual￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- heterosexual￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +analyzed￨L￨VBN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- multilayer￨L￨JJ￨O￨A coupled￨L￨JJ￨O￨- network￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- classic￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model14￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- analyze￨L￨VBP￨O￨- a￨L￨DT￨O￨- mechanic￨L￨JJ￨TITLE￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- both￨L￨DT￨O￨- resource￨L￨NN￨O￨A factor￨L￨NN￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- assessment￨L￨NN￨O￨- and￨L￨CC￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- resilience￨L￨NN￨O￨A to￨L￨TO￨O￨- epidemics￨L￨NNS￨O￨- must￨L￨MD￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- identify￨L￨VBP￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- functionalities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- profile￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- maintained￨L￨VBN￨O￨- or￨L￨CC￨O￨- recover￨L￨VB￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- adverse￨L￨JJ￨O￨- events.Even￨L￨NN￨O￨- though￨L￨IN￨O￨- the￨L￨DT￨O￨- assessment￨L￨NN￨O￨- and￨L￨CC￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- adverse￨L￨JJ￨O￨- events￨L￨NNS￨O￨- resilience￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- subject￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- research32￨L￨NN￨O￨- ,33,35,36￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- integration￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- computational￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- threats￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- largely￨L￨RB￨O￨- unexplored27￨L￨JJ￨O￨- ,37,38￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Resilience￨U￨NN￨O￨- management￨L￨NN￨O￨A during￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- Emanuele￨U￨NNP￨PERSON￨- Massaro￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,2,3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Alexander￨U￨NNP￨PERSON￨- Ganin￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Nicola￨U￨NNP￨MISC￨- Perra5￨U￨NNP￨O￨- ,6,7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Igor￨U￨NNP￨PERSON￨- Linkov1￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Alessandro￨U￨NNP￨PERSON￨- Vespignani6￨U￨NNP￨O￨- ,7,8￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 1859￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Computational￨U￨NNP￨O￨- sciencePhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractAssessing￨U￨VBG￨O￨- and￨L￨CC￨O￨- managing￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- considering￨L￨VBG￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- exceedingly￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- and￨L￨CC￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- extremely￨L￨RB￨O￨- expensive￨L￨JJ￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- resilience￨L￨NN￨O￨A to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- structured￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- defining￨L￨VBG￨O￨- the￨L￨DT￨O￨- system-wide￨L￨JJ￨O￨- critical￨L￨JJ￨O￨- functionality￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- getting￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disruption￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- functionality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- deterioration￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- studying￨L￨VBG￨O￨- both￨L￨CC￨O￨- conceptual￨L￨JJ￨O￨- and￨L￨CC￨O￨- data-driven￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- integrated￨L￨JJ￨O￨- consideration￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- risks￨L￨NNS￨O￨- and￨L￨CC￨O￨- societal￨L￨JJ￨O￨- disruptions￨L￨NNS￨O￨- under￨L￨IN￨O￨- resilience￨L￨NN￨O￨A assessment￨L￨NN￨O￨- framework￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- insightful￨L￨JJ￨O￨- picture￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- might￨L￨MD￨O￨- impact￨L￨VB￨O￨- society￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- broaden￨L￨VB￨O￨- the￨L￨DT￨O￨- model-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- epidemic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- expanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- purview￨L￨NN￨O￨- by￨L￨IN￨O￨- including￨L￨VBG￨O￨- measures￨L￨NNS￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- resilience￨L￨NN￨O￨A ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- response￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- disturbances￨L￨NNS￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- aftermath￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- mitigation￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- recovery￨L￨NN￨O￨- and￨L￨CC￨O￨- retention￨L￨NN￨O￨- of￨L￨IN￨O￨- functionality28￨L￨NN￨O￨- ,29,30￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- he￨L￨PRP￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- cite￨L￨VB￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Darwin￨U￨NNP￨PERSON￨- itself￨L￨PRP￨O￨- ,￨L￨,￨O￨- Metchnikoff￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- student￨L￨NN￨TITLE￨- Charles￨U￨NNP￨PERSON￨- Nicolle￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- director￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Pasteur￨U￨NNP￨ORGANIZATION￨- Institute￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- Tunis￨U￨NNP￨CITY￨- for￨L￨IN￨O￨- 30￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- distinctive￨L￨JJ￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- '￨L￨``￨O￨- birth￨L￨NN￨O￨- ,￨L￨,￨O￨- life￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A '￨L￨POS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- notion￨L￨NN￨O￨- of￨L￨IN￨O￨- '￨L￨``￨O￨- mutation￨L￨NN￨O￨- '￨L￨''￨O￨- in￨L￨IN￨O￨- microorganisms￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- animal￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- can￨L￨MD￨O￨- act￨L￨VB￨O￨- as￨L￨IN￨O￨- '￨L￨``￨O￨- reservoirs￨L￨NNS￨O￨- '￨L￨''￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- idea￨L￨NN￨O￨- of￨L￨IN￨O￨- harnessing￨L￨VBG￨O￨- ecology￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- traced￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Pasteur￨U￨NNP￨O￨- and￨L￨CC￨O￨- Darwin￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨A biology￨L￨NN￨O￨- and￨L￨CC￨O￨- medical￨L￨JJ￨O￨- microbiology￨L￨NN￨O￨- have￨L￨VBP￨O￨- profoundly￨L￨RB￨O￨- changed￨L￨VBN￨O￨- ,￨L￨,￨O￨- both￨L￨DT￨O￨- theoretically￨L￨RB￨O￨- and￨L￨CC￨O￨- empirically￨L￨RB￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- then￨L￨RB￨O￨- .￨L￨.￨O￨- +Historian￨U￨NN￨TITLE￨- of￨L￨IN￨O￨- science￨L￨NN￨O￨- Andrew￨U￨NNP￨PERSON￨- Mendelsohn￨U￨NNP￨PERSON￨- even￨L￨RB￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- laboratories￨L￨NNS￨O￨- of￨L￨IN￨O￨- Pasteur￨U￨NNP￨O￨- and￨L￨CC￨O￨- Koch￨U￨NNP￨PERSON￨- as￨L￨IN￨O￨- '￨L￨``￨O￨- the￨L￨DT￨O￨- earliest￨L￨JJS￨O￨- place￨L￨NN￨O￨- of￨L￨IN￨O￨- sustained￨L￨JJ￨O￨- experimental￨L￨JJ￨O￨- cellular-level￨L￨NNS￨O￨- in￨L￨FW￨O￨- vitro￨L￨FW￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- phenomena￨L￨NNS￨O￨- understood￨L￨VBN￨O￨- as￨L￨IN￨O￨- biological￨L￨JJ￨O￨- variations￨L￨NNS￨O￨- and￨L￨CC￨O￨- evolutionary￨L￨JJ￨O￨A mechanisms￨L￨NNS￨O￨- '￨L￨POS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- Darwin￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- later￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- long￨L￨RB￨O￨- after￨L￨IN￨O￨- his￨L￨PRP$￨O￨- death￨L￨NN￨O￨- ,￨L￨,￨O￨- medical￨L￨JJ￨O￨A doctors￨L￨NNS￨O￨- in￨L￨IN￨O￨- Britain￨U￨NNP￨COUNTRY￨- brought￨L￨VBD￨O￨- his￨L￨PRP$￨O￨- ideas￨L￨NNS￨O￨- to￨L￨TO￨O￨- bear￨L￨VB￨O￨- on￨L￨IN￨O￨- issues￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- and￨L￨CC￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Evolutionary￨U￨JJ￨O￨- biology￨L￨NN￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- us￨L￨PRP￨O￨- understand￨L￨VB￨O￨- emerging￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- perhaps￨L￨RB￨O￨- already￨L￨RB￨O￨- foreseen￨L￨VBN￨O￨- by￨L￨IN￨O￨- Pasteur￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- test￨L￨VB￨O￨- our￨L￨PRP$￨O￨- hypothesis￨L￨NN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- remoteness￨L￨NN￨O￨- and￨L￨CC￨O￨- HSV-2￨U￨NN￨MISC￨- risk￨L￨NN￨O￨- in￨L￨IN￨O￨- Kaokoveld￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- ask￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- questions￨L￨NNS￨O￨- :￨L￨:￨O￨- At￨U￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- there￨L￨EX￨O￨- a￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- having￨L￨VBG￨O￨A a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- partners￨L￨NNS￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- ’s￨L￨POS￨O￨- residential￨L￨JJ￨O￨- region￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- partner￨L￨NN￨O￨- homophily￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- having￨L￨VBG￨O￨- HSV-2-specific￨U￨JJ￨O￨- antibodies￨L￨NNS￨O￨- ?￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- HSV-2￨U￨NN￨O￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- Kaokoveld￨U￨NNP￨LOCATION￨- NumericCitation￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- having￨L￨VBG￨O￨A a￨L￨DT￨O￨- high￨L￨JJ￨O￨- overall￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- women￨L￨NNS￨O￨- =￨L￨JJ￨O￨- 56￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- men￨L￨NNS￨O￨- =￨L￨JJ￨O￨- 29￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- HSV-2￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- heterogeneously￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- geographically￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- regions￨L￨NNS￨O￨- having￨L￨VBG￨O￨- significantly￨L￨RB￨O￨- higher￨L￨JJR￨O￨- prevalence￨L￨NN￨O￨- than￨L￨IN￨O￨- others￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- here￨L￨RB￨O￨- whether￨L￨IN￨O￨- these￨L￨DT￨O￨- high￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- regions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- functionally￨L￨RB￨O￨- remote￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- as￨L￨IN￨O￨- having￨L￨VBG￨O￨A higher￨L￨JJR￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- partner￨L￨NN￨O￨- selection￨L￨NN￨O￨- than￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- so￨L￨RB￨O￨- ,￨L￨,￨O￨- do￨L￨VBP￨O￨- these￨L￨DT￨O￨- functionally￨L￨RB￨O￨- remote￨L￨JJ￨O￨- regions￨L￨NNS￨O￨A have￨L￨VBP￨O￨- sexual￨L￨JJ￨O￨- network￨L￨NN￨O￨- structures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- densely￨L￨RB￨O￨- connected￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- foster￨L￨VBP￨O￨- accelerated￨L￨VBN￨O￨- STI￨U￨NNP￨O￨- transmission￨L￨NN￨O￨- ?￨L￨.￨O￨- +Apart￨U￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- fluctuating￨L￨VBG￨O￨- environmental￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨A thresholds￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- in￨L￨IN￨O￨- field￨L￨NN￨O￨- populations￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- scarcity￨L￨NN￨O￨- ,￨L￨,￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- replicated￨L￨VBN￨O￨- experimentation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- ecology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- environmental￨L￨JJ￨O￨- and￨L￨CC￨O￨- density-mediated￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- simply￨L￨RB￨O￨- by￨L￨IN￨O￨- high￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- density￨L￨NN￨O￨- enhancing￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- contacts￨L￨NNS￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- or￨L￨CC￨O￨- an￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- spore￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Through￨U￨IN￨O￨- epidemiological￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- we￨L￨PRP￨O￨- further￨L￨RB￨O￨- examine￨L￨VB￨O￨- how￨L￨WRB￨O￨- parameter￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨- can￨L￨MD￨O￨- influence￨L￨VB￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨A probability￨L￨NN￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- robustness￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨- threshold￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- experimental￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨A threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- experimental￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Daphnia￨U￨NNP￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- environmentally￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- fungal￨L￨JJ￨O￨- parasite￨L￨NN￨O￨- .￨L￨.￨O￨- +Central￨U￨NNP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- concept￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- to￨L￨TO￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- density￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- invasion￨L￨NN￨O￨- threshold￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- below￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unable￨L￨JJ￨O￨- to￨L￨TO￨O￨- invade￨L￨VB￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Accordingly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- accessed￨L￨VBD￨O￨- the￨L￨DT￨O￨- PCR￨U￨NN￨O￨- positivity￨L￨NN￨O￨- for￨L￨IN￨O￨- VACV￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- cows￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- domestic￨L￨JJ￨O￨- and￨L￨CC￨O￨- wild￨L￨JJ￨O￨- mammals￨L￨NNS￨O￨- from￨L￨IN￨O￨- areas￨L￨NNS￨O￨- with￨L￨IN￨O￨- or￨L￨CC￨O￨- without￨L￨IN￨O￨- official￨L￨JJ￨O￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- VACV￨U￨NN￨O￨- zoonotic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- west￨L￨NN￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- São￨U￨NNP￨LOCATION￨- Paulo￨U￨NNP￨LOCATION￨- State￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- VACV￨U￨NN￨ORGANIZATION￨- has￨L￨VBZ￨O￨- once￨L￨RB￨DATE￨- isolated￨L￨VBN￨O￨- from￨L￨IN￨O￨- peritoneum￨L￨NN￨O￨- and￨L￨CC￨O￨- testicles￨L￨NNS￨O￨- samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- Mus￨U￨NN￨O￨- musculus￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- VACV￨U￨NN￨O￨- DNA￨U￨NN￨O￨- was￨L￨VBD￨O￨- once￨L￨RB￨DATE￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- opossums￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Didelphis￨U￨NN￨O￨- albiventris￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- dogs￨L￨NNS￨O￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- VACV￨U￨NN￨ORGANIZATION￨- outbreaks￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- cows￨L￨NNS￨O￨- or￨L￨CC￨O￨- humans￨L￨NNS￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- species￨L￨NNS￨O￨- were￨L￨VBD￨O￨- established￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- Brazilian￨U￨JJ￨NATIONALITY￨- VACV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- positive￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- from￨L￨IN￨O￨- Anhembi￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- 0.7￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Bofete￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0.7￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- positivity￨L￨NN￨O￨- were￨L￨VBD￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- Torre￨U￨NNP￨PERSON￨- de￨L￨IN￨PERSON￨- Pedra￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- VACV￨U￨NN￨O￨- zoonotic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- were￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- reported￨L￨VBN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +VACV￨U￨NN￨O￨- DNA￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- also￨L￨RB￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- recipients￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨- samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- experimentally￨L￨RB￨O￨- infected￨L￨JJ￨O￨- cows￨L￨NNS￨O￨- and￨L￨CC￨O￨- mice￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- VACV￨U￨NN￨O￨- zoonotic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- VACV￨U￨NN￨O￨- DNA￨U￨NN￨O￨- was￨L￨VBD￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- blood￨L￨NN￨O￨A samples￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- milker￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- blood￨L￨NN￨O￨- of￨L￨IN￨O￨- her￨L￨PRP$￨O￨- two￨L￨CD￨NUMBER￨- daughters￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- engaged￨L￨VBN￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- exposure￨L￨NN￨O￨- activity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 05￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Epidemic￨U￨NNP￨O￨- spreading￨L￨VBG￨O￨- in￨L￨IN￨O￨- modular￨L￨JJ￨O￨A time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Matthieu￨U￨NNP￨O￨- Nadini1￨U￨NN￨O￨- ,6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kaiyuan￨U￨NNP￨PERSON￨- Sun2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Enrico￨U￨NNP￨PERSON￨- Ubaldi￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Michele￨U￨NNP￨PERSON￨- Starnini4￨U￨NNP￨O￨- ,5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Alessandro￨U￨NNP￨PERSON￨- Rizzo￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Nicola￨U￨NNP￨O￨- Perra7￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2352￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksPhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractWe￨U￨NN￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- modular￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- that￨L￨IN￨O￨- modular￨L￨JJ￨O￨A structures￨L￨NNS￨O￨- induce￨L￨VBP￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- without￨L￨IN￨O￨- communities￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- unfolding￨L￨VBG￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- conducted￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨A scale￨L￨NN￨O￨A separation￨L￨NN￨O￨- which￨L￨WDT￨O￨- effectively￨L￨RB￨O￨- neglects￨L￨VBZ￨O￨- all￨L￨DT￨O￨- such￨L￨JJ￨O￨- features￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- creation￨L￨NN￨O￨- or￨L￨CC￨O￨- renewal￨L￨NN￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- correlated￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- driving￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time-scale￨L￨JJ￨O￨- considered27￨L￨NN￨O￨- ,28￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- 2-layer￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmissions￨L￨NNS￨O￨- across￨L￨IN￨O￨- female￨L￨JJ￨O￨- sex￨L￨NN￨O￨A workers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- FSWs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- persons￨L￨NNS￨O￨- who￨L￨WP￨O￨- inject￨L￨VBP￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- (￨L￨-LRB-￨O￨- PWID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- through￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- behaviors￨L￨NNS￨O￨- :￨L￨:￨O￨- unprotected￨L￨JJ￨O￨- sex￨L￨NN￨O￨- and￨L￨CC￨O￨- needle-sharing￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- remains￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- how￨L￨WRB￨O￨- significant￨L￨JJ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- bridge￨L￨NN￨O￨A individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- who￨L￨WP￨O￨- connect￨L￨VBP￨O￨- multiple￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- targeting￨L￨VBG￨O￨- different￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- modes￨L￨NNS￨O￨- across￨L￨IN￨O￨- key￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Behavioral￨U￨JJ￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- unveiled￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- female￨L￨JJ￨O￨- sex￨L￨NN￨O￨A workers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- FSWs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- persons￨L￨NNS￨O￨- who￨L￨WP￨O￨- inject￨L￨VBP￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- (￨L￨-LRB-￨O￨- PWID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- could￨L￨MD￨O￨- facilitate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- populations6￨L￨NN￨O￨- ,7,8,9￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- studies￨L￨NNS￨O￨- demonstrated￨L￨VBD￨O￨- that￨L￨IN￨O￨- bridge￨L￨NN￨O￨A individuals￨L￨NNS￨O￨- played￨L￨VBD￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmissions￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- patients￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- just￨L￨RB￨O￨- smaller￨L￨JJR￨O￨- than￨L￨IN￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- foot￨L￨NN￨O￨A and￨L￨CC￨O￨- mouth￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- pediatric￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mumps￨L￨NNS￨O￨- virus￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- causative￨L￨JJ￨O￨- agent￨L￨NN￨O￨- of￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- enveloped￨L￨JJ￨O￨- RNA￨U￨NN￨O￨- virus￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- mumps￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- preventable￨L￨JJ￨O￨- by￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- doses￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mumps￨L￨NNS￨O￨- vaccine￨L￨NN￨O￨A in￨L￨IN￨O￨- many￨L￨JJ￨O￨- developed￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- nowadays￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- attenuated￨L￨VBN￨O￨- mumps￨L￨NNS￨O￨- virus￨L￨NN￨O￨A vaccine￨L￨NN￨O￨- was￨L￨VBD￨O￨- licensed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Namely￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- reproduce￨L￨VB￨O￨- molecular-level￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- seeding￨L￨FW￨O￨- ,￨L￨,￨O￨- aggregation￨L￨NN￨O￨A ,￨L￨,￨O￨- short-range￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- biological￨L￨JJ￨O￨- tissue￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- inter-regional￨L￨JJ￨O￨- macroscopic￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- long-range￨L￨JJ￨O￨- MP￨U￨NN￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- brain￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- integrative￨L￨JJ￨O￨- methodological￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- historical￨L￨JJ￨O￨- overview￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- aimed￨L￨VBN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- MP￨U￨NN￨O￨- seeding￨L￨NN￨O￨- ,￨L￨,￨O￨- aggregation￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- propagation￨L￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- section￨L￨NN￨O￨- offers￨L￨VBZ￨O￨- an￨L￨DT￨O￨- overview￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- prion￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- seeding￨L￨NN￨O￨- ,￨L￨,￨O￨- aggregation￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- short-range￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ODEs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Eigen￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- prototype￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- autocatalysis￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- Prusiner￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 23￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- intended￨L￨VBD￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- conversion￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- prion￨L￨NN￨O￨- protein￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- PrPC￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- agent￨L￨NN￨O￨- protein￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- usually￨L￨RB￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- PrPSc￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Fast￨U￨JJ￨O￨- and￨L￨CC￨O￨- accurate￨L￨JJ￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- source￨L￨NN￨O￨A in￨L￨IN￨O￨- large￨L￨JJ￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- Robert￨U￨NNP￨PERSON￨- Paluch1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Xiaoyan￨U￨NNP￨PERSON￨- Lu2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Krzysztof￨U￨NNP￨PERSON￨- Suchecki1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Bolesław￨U￨NNP￨PERSON￨- K.￨U￨NNP￨PERSON￨- Hołyst￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,4￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2508￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- scienceInformation￨L￨NN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- computation￨L￨NN￨O￨- AbstractSpread￨U￨NN￨O￨- over￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- ubiquitous￨L￨JJ￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- increasingly￨L￨RB￨O￨- wide￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- approach￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- observers￨L￨NNS￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- quality￨L￨NN￨O￨A information￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- spread￨L￨NN￨O￨- encounter￨L￨NN￨O￨- times￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- ignored￨L￨VBN￨O￨- and￨L￨CC￨O￨- potential￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- are￨L￨VBP￨O￨- selected￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- gradient￨L￨NN￨O￨- from￨L￨IN￨O￨- high￨L￨JJ￨O￨- quality￨L￨NN￨O￨- observers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Locating￨U￨VBG￨O￨- spread￨L￨NN￨O￨- sources￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- important￨L￨JJ￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Pinto￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Thiran￨U￨NNP￨O￨- and￨L￨CC￨O￨- Vetterli￨U￨NNP￨PERSON￨- introduced￨L￨VBD￨O￨- an￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PTVA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- act￨L￨VBP￨O￨- as￨L￨IN￨O￨- observers￨L￨NNS￨O￨- and￨L￨CC￨O￨- report￨L￨NN￨O￨- times￨L￨NNS￨O￨A at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- reached￨L￨VBD￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- had￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- research￨L￨NN￨O￨- questions￨L￨NNS￨O￨- :￨L￨:￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- daily￨L￨JJ￨SET￨- protozoal￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- children￨L￨NNS￨O￨- drinking￨L￨VBG￨O￨- from￨L￨IN￨O￨- contaminated￨L￨VBN￨O￨A tubewells￨L￨NNS￨O￨- ,￨L￨,￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- what￨L￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- associated￨L￨VBN￨O￨- child￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- does￨L￨VBZ￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- child￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- attributable￨L￨JJ￨O￨- to￨L￨TO￨O￨- protozoa￨L￨NN￨O￨- in￨L￨IN￨O￨- drinking￨L￨NN￨O￨- water￨L￨NN￨O￨- compare￨L￨VB￨O￨- to￨L￨TO￨O￨- actual￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- all-pathogen/all-pathway￨L￨JJ￨O￨- child￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- stated￨L￨VBN￨O￨- alternatively￨L￨RB￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- much￨L￨JJ￨O￨- child￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- morbidity￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- consumption￨L￨NN￨O￨- of￨L￨IN￨O￨- protozoa-contaminated￨L￨JJ￨O￨- drinking￨L￨NN￨O￨- water￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- cryptosporidiosis￨L￨NN￨O￨- or￨L￨CC￨O￨- giardiasis￨L￨NN￨O￨- from￨L￨IN￨O￨- drinking￨L￨NN￨O￨- water￨L￨NN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- diarrhea￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- 3,835￨L￨CD￨NUMBER￨- children￨L￨NNS￨O￨- in￨L￨IN￨O￨- study￨L￨NN￨O￨- communities￨L￨NNS￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- contaminated￨L￨VBN￨O￨A tubewell￨L￨NN￨O￨- drinking￨L￨NN￨O￨- water￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- quantitative￨L￨JJ￨O￨- microbial￨L￨JJ￨O￨- risk￨L￨NN￨O￨- assessment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- QMRA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- inputs￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- QMRA￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- published￨L￨VBN￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- population￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- sanitation￨L￨NN￨O￨- intervention￨L￨NN￨O￨- trial￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- measured￨L￨VBN￨O￨- protozoal￨L￨JJ￨O￨- concentrations￨L￨NNS￨O￨- in￨L￨IN￨O￨- tubewells￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- caretaker-reported￨L￨JJ￨O￨- 7-day￨L￨JJ￨DURATION￨- recall￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- period￨L￨NN￨O￨- prevalence￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- site-specific￨L￨JJ￨O￨- population￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- address￨L￨VB￨O￨- these￨L￨DT￨O￨- research￨L￨NN￨O￨- questions￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- diarrhea￨L￨NN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- from￨L￨IN￨O￨- ingestion￨L￨NN￨O￨- of￨L￨IN￨O￨- Cryptosporidium￨U￨NN￨O￨- and/or￨L￨CC￨O￨- Giardia￨U￨NN￨O￨- in￨L￨IN￨O￨- contaminated￨L￨VBN￨O￨A tubewell￨L￨NN￨O￨- drinking￨L￨NN￨O￨- water￨L￨NN￨O￨- was￨L￨VBD￨O￨- estimated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- QMRA￨U￨NN￨O￨- approach￨L￨NN￨O￨- coupled￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Mosquito￨U￨NNP￨O￨- community￨L￨NN￨O￨- influences￨L￨VBZ￨O￨- West￨U￨NNP￨LOCATION￨- Nile￨U￨NNP￨LOCATION￨- virus￨L￨NN￨O￨- seroprevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- birds￨L￨NNS￨O￨A :￨L￨:￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- spillover￨L￨NN￨O￨- into￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- Josué￨U￨NNP￨O￨- Martínez-de￨U￨NNP￨O￨- la￨L￨NNP￨O￨- Puente￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,4￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Martina￨U￨NNP￨PERSON￨- Ferraguti1￨U￨NNP￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Santiago￨U￨NNP￨CITY￨- Ruiz2￨U￨NN￨O￨- ,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- Roiz1￨U￨NNP￨PERSON￨- ,5￨L￨CD￨NUMBER￨- nAff5￨L￨NN￨O￨- ,￨L￨,￨O￨- Francisco￨U￨NNP￨PERSON￨- Llorente3￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Elisa￨U￨NNP￨PERSON￨- Pérez-Ramírez3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Miguel￨U￨NNP￨PERSON￨- Ángel￨U￨NNP￨PERSON￨- Jiménez-Clavero3￨U￨NN￨O￨- ,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ramón￨U￨NNP￨PERSON￨- Soriguer1￨U￨NN￨O￨- ,4￨L￨NN￨O￨- &￨L￨CC￨O￨- Jordi￨U￨NNP￨O￨- Figuerola1￨U￨NN￨O￨- ,4￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2599￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- BiodiversityEcological￨U￨NNP￨O￨- epidemiology￨L￨NN￨O￨- AbstractMosquito￨U￨NNP￨O￨- community￨L￨NN￨O￨- composition￨L￨NN￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- central￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨- vector-borne￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- sampled￨L￨VBD￨O￨- 2544￨L￨CD￨DATE￨- birds￨L￨NNS￨O￨A and￨L￨CC￨O￨- 340829￨L￨CD￨NUMBER￨- mosquitoes￨L￨NNS￨O￨- in￨L￨IN￨O￨- 45￨L￨CD￨NUMBER￨- localities￨L￨NNS￨O￨- ,￨L￨,￨O￨- analysed￨L￨VBN￨O￨- in￨L￨IN￨O￨- 15￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- containing￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- urban￨L￨JJ￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- rural￨L￨JJ￨O￨- and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- natural￨L￨JJ￨O￨- area￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- evaluated￨L￨VBD￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- community￨L￨NN￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- seroprevalence￨L￨NN￨O￨A of￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Nile￨U￨NNP￨LOCATION￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- WNV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- house￨L￨NN￨O￨- sparrows￨L￨NNS￨O￨- along￨L￨IN￨O￨- an￨L￨DT￨O￨- urbanisation￨L￨NN￨O￨- gradient￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- area￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +Human￨U￨JJ￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- was￨L￨VBD￨O￨- zero￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- localities￨L￨NNS￨O￨- where￨L￨WRB￨O￨- VNT-positive￨U￨JJ￨O￨- birds￨L￨NNS￨O￨A were￨L￨VBD￨O￨- captured￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- potentially￨L￨RB￨O￨- explains￨L￨VBZ￨O￨- the￨L￨DT￨O￨- low￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- WNV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Locating￨U￨VBG￨O￨- multiple￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- sources￨L￨NNS￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- varying￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- sparse￨L￨JJ￨O￨A observations￨L￨NNS￨O￨- Zhao-Long￨U￨NNP￨O￨- Hu1￨U￨NN￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Zhesi￨U￨NNP￨PERSON￨- Shen￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Shinan￨U￨JJ￨O￨- Cao3￨U￨NN￨O￨- ,￨L￨,￨O￨- Boris￨U￨NNP￨O￨- Podobnik4￨U￨NNP￨O￨- ,5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Huijie￨U￨NNP￨O￨- Yang6￨U￨NNP￨O￨- ,￨L￨,￨O￨- Wen-Xu￨U￨NNP￨O￨- Wang2￨U￨NNP￨O￨- ,6￨L￨NNP￨O￨- &￨L￨CC￨O￨- Ying-Cheng￨U￨NNP￨O￨- Lai7￨U￨NN￨O￨- ,8￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 2685￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksInformation￨L￨NN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- computation￨L￨NN￨O￨- AbstractData￨U￨NN￨O￨- based￨L￨VBN￨O￨- source￨L￨NN￨O￨- localization￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +Bridging￨U￨VBG￨O￨- structural￨L￨JJ￨O￨- observability￨L￨NN￨O￨- and￨L￨CC￨O￨- sparse￨L￨JJ￨O￨A signal￨L￨NN￨O￨- reconstruction￨L￨NN￨O￨- theories￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- locate￨L￨VB￨O￨- diffusion￨L￨NN￨O￨- sources￨L￨NNS￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- varying￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- solely￨L￨RB￨O￨- on￨L￨IN￨O￨- sparse￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- messenger￨L￨NN￨TITLE￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Choosing￨U￨VBG￨O￨- large￨L￨JJ￨O￨- degree￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- messengers￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- sparse￨L￨JJ￨O￨A observations￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- such￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- sufficient￨L￨JJ￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- sources￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- located￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- recent￨L￨JJ￨O￨- progress￨L￨NN￨O￨- ,￨L￨,￨O￨- locating￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- sources￨L￨NNS￨O￨A in￨L￨IN￨O￨- time￨L￨NN￨O￨- varying￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- outstanding￨L￨JJ￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +Counterintuitively￨U￨RB￨O￨- ,￨L￨,￨O￨- sources￨L￨NNS￨O￨A in￨L￨IN￨O￨- more￨L￨RBR￨O￨- rapidly￨L￨RB￨O￨- varying￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- identified￨L￨VBN￨O￨- more￨L￨RBR￨O￨- readily￨L￨RB￨O￨- with￨L￨IN￨O￨- fewer￨L￨JJR￨O￨- required￨L￨VBN￨O￨- messenger￨L￨NN￨TITLE￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- low-and￨L￨JJ￨O￨- middle-income￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- LMICs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- costs￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- considerable￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- impact￨L￨NN￨O￨- ,￨L￨,￨O￨- estimated￨L￨VBN￨O￨- at￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- gross￨L￨JJ￨O￨- domestic￨L￨JJ￨O￨- product￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GDP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- only￨L￨RB￨O￨- 0.04￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 0.13￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- GDP￨U￨NNP￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- in￨L￨IN￨O￨- high￨L￨JJ￨O￨- income￨L￨NN￨O￨A countries￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2016￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- predictive￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- using￨L￨VBG￨O￨- weather￨L￨NN￨O￨- predictions￨L￨NNS￨O￨- and￨L￨CC￨O￨- dengue￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- projections￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- validate￨L￨VB￨O￨- the￨L￨DT￨O￨- explanatory￨L￨JJ￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- features￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- specific￨L￨JJ￨O￨- application￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- regression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- using￨L￨VBG￨O￨- features￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨A population￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- ZIKV￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- has￨L￨VBZ￨O￨- spread￨L￨VBN￨O￨- to￨L￨TO￨O￨- many￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- South￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨A mosquito￨L￨NN￨O￨- species￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- vector￨L￨NN￨O￨- for￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Predictions￨U￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NNP￨O￨- cases￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- utilizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨A mosquitoes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- average￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- region￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- .￨L￨.￨O￨- +Notably￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vast￨L￨JJ￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- modelling￨L￨NN￨O￨- work￨L￨NN￨O￨- has￨L￨VBZ￨O￨- neglected￨L￨VBN￨O￨- the￨L￨DT￨O￨- microbial￨L￨JJ￨O￨- environment￨L￨NN￨O￨- :￨L￨:￨O￨- most￨L￨RBS￨O￨- mathematical￨L￨JJ￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A are￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- single￨L￨JJ￨O￨- or￨L￨CC￨O￨- sequential￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- broadly￨L￨RB￨O￨- simplified￨L￨VBN￨O￨- pathogen￨L￨NN￨O￨- ecology￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨A field￨L￨NN￨O￨- has￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- an￨L￨DT￨O￨- effort￨L￨NN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- realism￨L￨NN￨O￨- by￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- contact￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- ,￨L￨,￨O￨- age-related￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- cross￨L￨NN￨O￨- immunity￨L￨NN￨O￨- after￨L￨IN￨O￨- previous￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 19,21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modelling￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- tool￨L￨NN￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- many￨L￨JJ￨O￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- researchers￨L￨NNS￨O￨- to￨L￨TO￨O￨- probe￨L￨VB￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- intricacies￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- play￨L￨VB￨O￨- forward￨L￨RB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- to￨L￨TO￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- population-level￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- current￨L￨JJ￨DATE￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- or￨L￨CC￨O￨- severity￨L￨NN￨O￨- may￨L￨MD￨O￨- therefore￨L￨RB￨O￨- be￨L￨VB￨O￨- incomplete￨L￨JJ￨O￨- or￨L￨CC￨O￨- misguided￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- ignorance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨- change￨L￨NN￨O￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- aim￨L￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- dominant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- coming￨L￨VBG￨O￨- season￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- describing￨L￨VBG￨O￨- numerous￨L￨JJ￨O￨- cascading￨L￨VBG￨O￨- phenomena￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- neural￨L￨JJ￨O￨- firing￨L￨NN￨O￨- or￨L￨CC￨O￨- social￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- threshold￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- weighted￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- largely￨L￨RB￨O￨- overlooked￨L￨VBN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Threshold￨U￨NNP￨O￨- driven￨L￨VBN￨O￨- contagion￨L￨NN￨O￨- on￨L￨IN￨O￨- weighted￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- Samuel￨U￨NNP￨PERSON￨- Unicomb1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Gerardo￨U￨NNP￨PERSON￨- Iñiguez￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,3￨L￨CD￨NUMBER￨- &￨L￨CC￨O￨- Márton￨U￨NNP￨O￨- Karsai1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 3094￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- scienceNonlinear￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- AbstractWeighted￨U￨VBN￨O￨- networks￨L￨NNS￨O￨- capture￨L￨VBP￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- where￨L￨WRB￨O￨- interaction￨L￨NN￨O￨- strength￨L￨NN￨O￨- is￨L￨VBZ￨O￨- meaningful￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- cascade￨L￨NN￨O￨- emergence￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- non-monotonously￨L￨RB￨O￨- on￨L￨IN￨O￨- weight￨L￨NN￨O￨A heterogeneities￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- accelerate￨L￨VBP￨O￨- or￨L￨CC￨O￨- decelerate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- non-trivial￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- spaces￨L￨NNS￨O￨- for￨L￨IN￨O￨- various￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- weight￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- fill￨L￨VBP￨O￨- this￨L￨DT￨O￨- gap￨L￨NN￨O￨- by￨L￨IN￨O￨- studying￨L￨VBG￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- over￨L￨IN￨O￨- synthetic￨L￨JJ￨O￨- and￨L￨CC￨O￨- real￨L￨JJ￨O￨- weighted￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- and￨L￨CC￨O￨- analytical￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- fast￨L￨JJ￨O￨- and￨L￨CC￨O￨- bursty￨L￨JJ￨O￨- human￨L￨JJ￨O￨- communication￨L￨NN￨O￨A networks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- reported￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- animal￨L￨NN￨O￨- societies￨L￨NNS￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- very￨L￨RB￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- temporally￨L￨RB￨O￨- highly￨L￨RB￨O￨- resolved￨L￨VBN￨O￨- communication￨L￨NN￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- conducted￨L￨VBN￨O￨- over￨L￨RP￨O￨- long￨L￨RB￨O￨- enough￨L￨RB￨O￨- timescales￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- burstiness￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 16￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Instead￨U￨RB￨O￨- of￨L￨IN￨O￨- tracking￨L￨VBG￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- piece￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- or￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- probe￨L￨VBP￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- comparison￨L￨NN￨O￨- against￨L￨IN￨O￨- a￨L￨DT￨O￨- randomized￨L￨VBN￨O￨- reference￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- how￨L￨WRB￨O￨- spreading￨L￨VBG￨O￨A dynamics￨L￨NNS￨O￨A reflect￨L￨VBP￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Human￨U￨JJ￨O￨- communication￨L￨NN￨O￨A networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- intermittent￨L￨JJ￨O￨- ,￨L￨,￨O￨- unpredictable￨L￨JJ￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- between￨L￨IN￨O￨- successive￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- heavy-tailed￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- burstiness￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Temporal￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- thus￨L￨RB￨O￨- acknowledge￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- linked￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- available￨L￨JJ￨O￨- while￨L￨IN￨O￨- these￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- interact￨L￨VBP￨O￨- and￨L￨CC￨O￨- crucially￨L￨RB￨O￨- account￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- ordering￨L￨VBG￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨A ,￨L￨,￨O￨- making￨L￨VBG￨O￨- them￨L￨PRP￨O￨- particularly￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- spreading￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Honeybee￨U￨NNP￨O￨- trophallaxis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- an￨L￨DT￨O￨- excellent￨L￨JJ￨O￨- system￨L￨NN￨O￨- for￨L￨IN￨O￨- exploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- of￨L￨IN￨O￨- burstiness￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- nonhuman￨L￨JJ￨O￨- animal￨L￨NN￨O￨- society￨L￨NN￨O￨- ,￨L￨,￨O￨- permitting￨L￨VBG￨O￨- a￨L￨DT￨O￨- cross-species￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- human￨L￨JJ￨O￨- communication￨L￨NN￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- bubonic￨L￨JJ￨O￨- plague￨L￨VBP￨O￨A by￨L￨IN￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- ectoparasite￨L￨NN￨O￨- vector￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- human￨L￨JJ￨O￨- fleas￨L￨NNS￨O￨- or￨L￨CC￨O￨- body￨L￨NN￨O￨- lice￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- five￨L￨CD￨NUMBER￨- compartments￨L￨NNS￨O￨- for￨L￨IN￨O￨- humans￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- with￨L￨IN￨O￨- mild￨L￨JJ￨O￨- bacteremia￨L￨NN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- bacteremia￨L￨NN￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- dead￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- applied￨L￨VBD￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- nine￨L￨CD￨NUMBER￨- outbreaks￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- Second￨U￨JJ￨ORDINAL￨- Pandemic￨U￨NN￨MISC￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- plague￨L￨VBP￨O￨A in￨L￨IN￨O￨- European￨U￨JJ￨NATIONALITY￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- validate￨L￨VB￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- pneumonic￨L￨JJ￨O￨- and￨L￨CC￨O￨- rat-associated￨L￨JJ￨O￨- plague￨L￨VB￨O￨A epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- three￨L￨CD￨NUMBER￨- additional￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- curves￨L￨NNS￨O￨- from￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- with￨L￨IN￨O￨- known￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- routes￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- Third￨U￨NNP￨ORDINAL￨- Pandemic￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- plague￨L￨VBP￨O￨A during￨L￨IN￨O￨- the￨L￨DT￨O￨- Second￨U￨JJ￨ORDINAL￨- Pandemic￨U￨NN￨MISC￨- are￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- mainly￨L￨RB￨O￨- on￨L￨IN￨O￨- modeling￨L￨NN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- commensal￨L￨JJ￨O￨- rats￨L￨NNS￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 21￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infectious￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- plague￨L￨VB￨O￨A transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- human￨L￨JJ￨O￨- ectoparasite￨L￨NN￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- pneumonic￨L￨JJ￨O￨- and￨L￨CC￨O￨- rat￨L￨NN￨O￨- –￨L￨:￨O￨- flea￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- traits￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- resistance￨L￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- growth￨L￨NN￨O￨- respond￨L￨VBP￨O￨- similarly￨L￨RB￨O￨- to￨L￨TO￨O￨- temperature￨L￨NN￨O￨A changes￨L￨NNS￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- responses￨L￨NNS￨O￨- may￨L￨MD￨O￨- trade￨L￨VB￨O￨- off￨L￨RP￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- no￨L￨DT￨O￨- observed￨L￨VBN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- on￨L￨IN￨O￨- parasite￨L￨NN￨O￨- abundance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- change￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- temperature￨L￨NN￨O￨A can￨L￨MD￨O￨- have￨L￨VB￨O￨- differing￨L￨VBG￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- traits￨L￨NNS￨O￨- that￨L￨WDT￨O￨- together￨L￨RB￨O￨- determine￨L￨VBP￨O￨- outcomes￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- temperature￨L￨NN￨O￨A also￨L￨RB￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- traits￨L￨NNS￨O￨- that￨L￨WDT￨O￨- mediate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- survival￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- parasite￨L￨JJ￨O￨- development￨L￨NN￨O￨- rate￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- virulence￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- resistance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- tolerance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- parasites￨L￨NNS￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- traits￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- distinct￨L￨JJ￨O￨- temperature￨L￨NN￨O￨A responses￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- antagonistic￨L￨JJ￨O￨- and￨L￨CC￨O￨- synergistic￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- temperature￨L￨NN￨O￨- responses￨L￨NNS￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- traits￨L￨NNS￨O￨- that￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- net￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- changes￨L￨NNS￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Climate￨U￨NN￨O￨- change￨L￨NN￨O￨- –￨L￨:￨O￨- driven￨L￨VBN￨O￨- temperature￨L￨NN￨O￨A changes￨L￨NNS￨O￨- will￨L￨MD￨O￨- likely￨L￨RB￨O￨- impact￨L￨VB￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- parasite￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- both￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- traits￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- strongly￨L￨RB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- temperature￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- norovirus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- by￨L￨IN￨O￨- sampling￨L￨NN￨O￨- season￨L￨NN￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A ,￨L￨,￨O￨- R￨U￨NN￨O￨- e.￨L￨NNP￨O￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- when￨L￨WRB￨O￨- GII￨U￨NNP￨ORGANIZATION￨- .2￨L￨NN￨NUMBER￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 2015/16￨L￨CD￨NUMBER￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- GII￨U￨NN￨ORGANIZATION￨- .4￨L￨NN￨NUMBER￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- genotype￨L￨NN￨O￨- affecting￨L￨VBG￨O￨- infants￨L￨NNS￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- children￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 2016/17￨L￨CD￨NUMBER￨- seasons￨L￨NNS￨O￨- CI￨U￨NNP￨O￨- :￨L￨:￨O￨- confidence￨L￨NN￨O￨- interval￨L￨NN￨O￨- ;￨L￨:￨O￨- NA￨U￨NNP￨O￨- :￨L￨:￨O￨- not￨L￨RB￨O￨- applicable￨L￨JJ￨O￨- ;￨L￨:￨O￨- R￨U￨NN￨O￨- e￨L￨SYM￨O￨- :￨L￨:￨O￨- effective￨L￨JJ￨O￨A reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 2015/16￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- was￨L￨VBD￨O￨- higher￨L￨JJR￨O￨- at￨L￨IN￨O￨- 193￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- (￨L￨-LRB-￨O￨- 1,927￨L￨CD￨NUMBER￨- vs￨L￨CC￨O￨A 659￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 539￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- (￨L￨-LRB-￨O￨- 1,086￨L￨CD￨NUMBER￨- vs￨L￨CC￨O￨- 170￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 149￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- (￨L￨-LRB-￨O￨- 1,699￨L￨CD￨NUMBER￨- vs￨L￨CC￨O￨- 683￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- nursery￨L￨NN￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- kindergartens￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- elementary￨L￨JJ￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- attending￨L￨VBG￨O￨- schools￨L￨NNS￨O￨A or￨L￨CC￨O￨- nurseries￨L￨NNS￨O￨- were￨L￨VBD￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- norovirus￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Osaka￨U￨NNP￨LOCATION￨- prefecture￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1,5,15,19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- developed￨L￨VBD￨O￨- for￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- WNV￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- dengue￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- arboviral￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- exhibit￨L￨VB￨O￨- backward￨L￨RB￨O￨A bifurcation￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- violation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- threshold￨L￨NN￨O￨- condition￨L￨NN￨O￨- separating￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- endemicity￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- essential￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- microparasitic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- studied￨L￨VBN￨O￨- via￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- the￨L￨DT￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- or￨L￨CC￨O￨- compartments￨L￨NNS￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- defining￨L￨VBG￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- hosts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- latter￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- induced￨L￨VBD￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- death￨L￨NN￨O￨- rates￨L￨NNS￨O￨- among￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- particularly￨L￨RB￨O￨- important￨L￨JJ￨O￨- driving￨L￨VBG￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- of￨L￨IN￨O￨- backward￨L￨RB￨O￨A bifurcation￨L￨NN￨O￨- in￨L￨IN￨O￨- WNV￨U￨NNP￨O￨- ,￨L￨,￨O￨- dengue￨L￨NN￨O￨- ,￨L￨,￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- arboviral￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- host￨L￨NN￨TITLE￨- susceptible-exposed-infective-temporarily￨L￨JJ￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- SEIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- vector￨L￨NN￨O￨- SEI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- tune￨L￨VB￨O￨- it￨L￨PRP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- that￨L￨WDT￨O￨- complexity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- interactions￨L￨NNS￨O￨- and￨L￨CC￨O￨- parameters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- of￨L￨IN￨O￨- backward￨L￨RB￨O￨A bifurcation￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- case￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- defines￨L￨VBZ￨O￨- a￨L￨DT￨O￨- bifurcation￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- critical￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- when￨L￨WRB￨O￨- R0￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- stable￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- emerges￨L￨VBZ￨O￨- and￨L￨CC￨O￨- establishes￨L￨VBZ￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DFE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- emerges￨L￨VBZ￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- generalize￨L￨VB￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- different￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨- or￨L￨CC￨O￨- network￨L￨NN￨O￨- degree￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- in￨L￨IN￨O￨- those￨L￨DT￨O￨- papers￨L￨NNS￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- particular￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨A value￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- either￨L￨CC￨O￨- a￨L￨DT￨O￨- bipartite￨L￨JJ￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- random￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- here￨L￨RB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- arbitrary￨L￨JJ￨O￨- mixing￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- to￨L￨TO￨O￨- mixing￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- multi-type￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- process￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- converge￨L￨VB￨O￨- either￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- any￨L￨DT￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- situation￨L￨NN￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- in￨L￨IN￨O￨- either￨L￨CC￨O￨- group￨L￨NN￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- any￨L￨DT￨O￨- non-null￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- almost￨L￨RB￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- state￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨A the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- respective￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- levels￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- stable￨L￨JJ￨O￨- state￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- levels￨L￨NNS￨O￨- in￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- blue￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- sensitive￨L￨JJ￨O￨- group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- red￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨A level￨L￨NN￨O￨- m￨L￨NN￨O￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- would￨L￨MD￨O￨- imply￨L￨VB￨O￨- that￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨A between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- can￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- levels￨L￨NNS￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- community-associated￨L￨JJ￨O￨- methicillin-resistant￨L￨JJ￨O￨- Staphylococcus￨U￨FW￨MISC￨- aureus￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- MRSA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- targeting￨L￨VBG￨O￨- symptomatically￨L￨RB￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- asymptomatic￨L￨JJ￨O￨A carriers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- actually￨L￨RB￨O￨- incapable￨L￨JJ￨O￨- of￨L￨IN￨O￨- achieving￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- multiple￨L￨JJ￨O￨- control￨L￨NN￨O￨- types￨L￨NNS￨O￨- are￨L￨VBP￨O￨- implemented￨L￨VBN￨O￨- .￨L￨.￨O￨- +Neglecting￨U￨VBG￨O￨- asymptomatic￨L￨JJ￨O￨A carriers￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- significantly￨L￨RB￨O￨- overestimate￨L￨VB￨O￨- the￨L￨DT￨O￨- projected￨L￨VBN￨O￨- cumulative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- overestimate￨L￨VB￨O￨- the￨L￨DT￨O￨- population-level￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- contain￨L￨VB￨O￨- epidemics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- analysis￨L￨NN￨O￨- reveals￨L￨VBZ￨O￨- that￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- alter￨L￨VBP￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- asymptomatic￨L￨JJ￨O￨A carriers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- vulnerable￨L￨JJ￨O￨- to￨L￨TO￨O￨- being￨L￨VBG￨O￨- incorrectly￨L￨RB￨O￨- assessed￨L￨VBN￨O￨- by￨L￨IN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- inappropriate￨L￨JJ￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A carriers￨L￨NNS￨O￨- to￨L￨TO￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- both￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- asymptomatic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- make￨L￨VB￨O￨- comparisons￨L￨NNS￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- collapsed￨L￨VBD￨O￨- each￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- form￨L￨NN￨O￨- where￨L￨WRB￨O￨- hosts￨L￨NNS￨O￨- belong￨L￨VBP￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- asymptomatic￨L￨JJ￨O￨A carriers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- symptomatically￨L￨RB￨O￨- infectious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- prevalent￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- is￨L￨VBZ￨O￨- on-demand￨L￨JJ￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨DATE￨- may￨L￨MD￨DATE￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- near-linear￨L￨JJ￨O￨- product￨L￨NN￨O￨- adoption￨L￨NN￨O￨A rates￨L￨NNS￨O￨- ,￨L￨,￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- product￨L￨NN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- S-shaped￨U￨JJ￨MISC￨- curves￨L￨NNS￨O￨- predicted￨L￨VBN￨O￨- by￨L￨IN￨O￨- social￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- track￨L￨VBP￨O￨- the￨L￨DT￨O￨- adoption￨L￨NN￨O￨A through￨L￨IN￨O￨- 70￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- unique￨L￨JJ￨O￨- voucher￨L￨NN￨O￨- codes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 48￨L￨CD￨NUMBER￨- 000￨L￨CD￨NUMBER￨- codes￨L￨NNS￨O￨- in￨L￨IN￨O￨- Experiment￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- active￨L￨JJ￨O￨- information-seeking￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨- between￨L￨IN￨O￨- this￨L￨DT￨O￨- ODD￨U￨JJ￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- peer-to-peer￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- occur￨L￨VBP￨O￨- simultaneously￨L￨RB￨O￨- .￨L￨.￨O￨- +That￨U￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- once￨L￨RB￨DATE￨- product￨L￨NN￨O￨- adoption￨L￨NN￨O￨A is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- on-demand￨L￨JJ￨O￨- information￨L￨NN￨O￨- seeking￨L￨VBG￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- peer-to-peer￨L￨NNS￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- similarly￨L￨RB￨O￨- ranked￨L￨VBD￨O￨- list￨L￨NN￨O￨- through￨L￨IN￨O￨- search￨L￨NN￨O￨- engines￨L￨NNS￨O￨- and￨L￨CC￨O￨- Top￨U￨JJ￨O￨- 10￨L￨CD￨NUMBER￨- pages￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- disproportionately￨L￨RB￨O￨- rewards￨L￨VBZ￨O￨- products￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- top￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- list￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- may￨L￨MD￨O￨- see￨L￨VB￨O￨- winner-take-all￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- among￨L￨IN￨O￨- equivalent￨L￨JJ￨O￨- products￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- shaped￨L￨VBN￨O￨- by￨L￨IN￨O￨- search￨L￨NN￨O￨- engine￨L￨NN￨O￨- rankings￨L￨NNS￨O￨- as￨L￨IN￨O￨- interested￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- all￨L￨DT￨O￨- discover￨L￨VBP￨O￨- and￨L￨CC￨O￨- adopt￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- product￨L￨NN￨O￨- ,￨L￨,￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- equal￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- across￨L￨IN￨O￨- products￨L￨NNS￨O￨- when￨L￨WRB￨O￨- product￨L￨NN￨O￨- adoption￨L￨NN￨O￨A spreads￨L￨VBZ￨O￨- exclusively￨L￨RB￨O￨- along￨L￨IN￨O￨- social￨L￨JJ￨O￨- ties￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- product￨L￨NN￨O￨- adoption￨L￨NN￨O￨A processes￨L￨NNS￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- posting/searching￨L￨VBG￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- peer-to-peer￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- time-dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- drive￨L￨VBP￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- to￨L￨TO￨O￨- deploy￨L￨VB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulated￨L￨JJ￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- quantifying￨L￨VBG￨O￨- temporal￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- precision￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨A dying￨L￨VBG￨O￨- out￨L￨RP￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- CSA￨U￨NNP￨ORGANIZATION￨- integrates￨L￨VBZ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- outbreak￨L￨NN￨O￨A simulation￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- now￨L￨RB￨DATE￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- whether￨L￨IN￨O￨- instead￨L￨RB￨O￨- management￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- delayed￨L￨VBN￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- the￨L￨DT￨O￨- policy-maker￨L￨NN￨O￨- to￨L￨TO￨O￨- learn￨L￨VB￨O￨- more￨L￨JJR￨O￨- about￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- outbreak￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- farms￨L￨NNS￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- to￨L￨TO￨O￨- deploy￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- outbreak￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- governing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- a￨L￨DT￨O￨- policy-maker￨L￨NN￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨A for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- statuses￨L￨NNS￨O￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- farm￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- all￨L￨RB￨O￨- known￨L￨VBN￨O￨- ,￨L￨,￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- simply￨L￨RB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- statuses￨L￨NNS￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- optimising￨L￨VBG￨O￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- straightforward￨L￨JJ￨O￨- .￨L￨.￨O￨- +Should￨U￨MD￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- management￨L￨NN￨O￨- always￨L￨RB￨O￨- be￨L￨VB￨O￨- introduced￨L￨VBN￨O￨- immediately￨L￨RB￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- can￨L￨MD￨O￨- it￨L￨PRP￨O￨- instead￨L￨RB￨O￨- be￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- to￨L￨TO￨O￨- introduce￨L￨VB￨O￨- control￨L￨NN￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨A ?￨L￨.￨O￨- +Frailty￨U￨NNP￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- survival￨L￨NN￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- dependence￨L￨NN￨O￨- and￨L￨CC￨O￨- unobserved￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- multivariate￨L￨JJ￨O￨- time‐to‐event￨L￨JJ￨O￨- data￨L￨NNS￨O￨- explicitly￨L￨RB￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- questions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- event￨L￨NN￨O￨A times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Clayton￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1978￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Hougaard￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Duchateau￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Janssen￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- in￨L￨IN￨O￨- shared￨L￨JJ￨O￨A and￨L￨CC￨O￨- correlated￨L￨VBD￨O￨- frailty￨L￨NN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- or￨L￨CC￨O￨- time￨L￨NN￨O￨- invariant￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- implying￨L￨VBG￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- ‘￨L￨``￨O￨- frailty￨L￨NN￨O￨- ’￨L￨''￨O￨- level￨L￨NN￨O￨- during￨L￨IN￨O￨- their￨L￨PRP$￨O￨- entire￨L￨JJ￨O￨- life￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- rather￨L￨RB￨O￨- restrictive￨L￨JJ￨O￨- .￨L￨.￨O￨- +Multivariate￨U￨JJ￨O￨- frailty￨L￨NN￨O￨- models￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- univariate￨L￨JJ￨O￨- frailty￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- mutual￨L￨JJ￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- event￨L￨NN￨O￨A times￨L￨NNS￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- conditional￨L￨JJ￨O￨- proportional￨L￨JJ￨O￨- hazards￨L￨NNS￨O￨- given￨L￨VBN￨O￨- latent￨L￨JJ￨O￨- frailty￨L￨NN￨O￨- terms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- correlated￨L￨VBN￨O￨- frailty￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- extends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- shared￨L￨JJ￨O￨A frailty￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- flexible￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- structure￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- frailty￨L￨NN￨O￨- terms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Yashin￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- introduced￨L￨VBN￨O￨- time￨L￨NN￨O￨- varying￨L￨VBG￨O￨- shared￨L￨VBN￨O￨A frailties￨L￨NNS￨O￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- immunizing￨L￨VBG￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Grown￨U￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- mature￨L￨JJ￨O￨- field￨L￨NN￨O￨- that￨L￨WDT￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- enhance￨L￨VB￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- phylodynamics￨L￨NNS￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- inference￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- analytical￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- recover￨L￨VB￨O￨- evolutionary￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- mutations￨L￨NNS￨O￨A that￨L￨WDT￨O￨- accumulate￨L￨VBP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- genomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- rapidly￨L￨RB￨O￨- evolving￨L￨VBG￨O￨- pathogens￨L￨NNS￨O￨- during￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- mutations￨L￨NNS￨O￨A may￨L￨MD￨O￨- confer￨L￨VB￨O￨- phenotypic￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- viruses￨L￨NNS￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- different￨L￨JJ￨O￨- cell￨L￨NN￨O￨- types￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- evade￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- immune￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- transmit￨L￨VB￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- ,￨L￨,￨O￨- hosts￨L￨NNS￨O￨- or￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- mutations￨L￨NNS￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- molecular￨L￨JJ￨O￨- footprint￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- otherwise￨L￨RB￨O￨- not￨L￨RB￨O￨- directly￨L￨RB￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- simulation-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- date￨L￨NN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- occur￨L￨VB￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- mid-point￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- censored￨L￨VBN￨O￨- interval￨L￨NN￨O￨A once￨L￨RB￨DATE￨- participants￨L￨NNS￨O￨- start￨L￨VBP￨O￨- to￨L￨TO￨O￨- miss￨L￨VB￨O￨- their￨L￨PRP$￨O￨- scheduled￨L￨VBN￨O￨- test￨L￨NN￨O￨- dates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Imputation￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- date￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- censored￨L￨VBN￨O￨- interval￨L￨NN￨O￨A ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- straightforward￨L￨JJ￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- and￨L￨CC￨O￨- produces￨L￨VBZ￨O￨- estimates￨L￨NNS￨O￨- very￨L￨RB￨O￨- close￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- some￨L￨DT￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- mid-point￨L￨NN￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- interval￨L￨NN￨O￨A censoring￨L￨VBG￨O￨- assumption￨L￨NN￨O￨- is￨L￨VBZ￨O￨- satisfied￨L￨VBN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- popular￨L￨JJ￨O￨- ad￨L￨NN￨O￨- hoc￨L￨FW￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- impute￨L￨VB￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- date￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- mid-point￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- participant￨L￨NN￨O￨- ’s￨L￨POS￨O￨- censored￨L￨VBN￨O￨- interval￨L￨NN￨O￨A .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- aforementioned￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- considers￨L￨VBZ￨O￨- an￨L￨DT￨O￨- SEIQR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-infected-quarantined-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- imperfect￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- δ￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- p￨L￨NN￨O￨- ≤￨L￨CD￨NUMBER￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- efficacy￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- isand￨L￨VBD￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- properties￨L￨NNS￨O￨- :￨L￨:￨O￨- When￨U￨WRB￨O￨- R1￨U￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- holds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨A disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E0￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S0￨U￨NN￨O￨- ,￨L￨,￨O￨- 0,0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Λ￨U￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- δp￨L￨NN￨O￨- +￨L￨CC￨O￨- μ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 0,0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- δpΛ/μ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- δp￨L￨NN￨O￨- +￨L￨CC￨O￨- μ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- D￨U￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- R1￨U￨NN￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- holds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨A globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- persist￨L￨VB￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- ℝ￨U￨SYM￨O￨- +5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨A positive￨L￨JJ￨O￨- local￨L￨JJ￨O￨- solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- t￨L￨NN￨O￨- ∈￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- −￨L￨CD￨NUMBER￨- ω￨L￨NN￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- explosion￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- ℝ￨U￨SYM￨O￨- +5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨A positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨SYM￨O￨- ℝ￨U￨SYM￨O￨- +5￨L￨CD￨NUMBER￨- on￨L￨IN￨O￨- t￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- a.s￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- issues￨L￨NNS￨O￨- include￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨A takes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- complexity￨L￨NN￨O￨- increases￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- method￨L￨NN￨O￨- accuracy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- summary￨L￨NN￨O￨- statistic￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- accept/reject￨L￨JJ￨O￨- decision￨L￨NN￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- constructed￨L￨VBN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infectious-Removed￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A data￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Conventional￨U￨JJ￨O￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- estimation￨L￨NN￨O￨- ,￨L￨,￨O￨- require￨L￨VBP￨O￨- explicit￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A data￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- approach￨L￨NN￨O￨- R0￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- slope￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A data￨L￨NNS￨O￨A of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- estimate￨L￨VB￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨A the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Generally￨U￨RB￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- about￨L￨IN￨O￨- patients￨L￨NNS￨O￨- are￨L￨VBP￨O￨- reported￨L￨VBN￨O￨- by￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- practitioners￨L￨NNS￨O￨- via￨L￨IN￨O￨- passive￨L￨NN￨O￨- surveillance￨L￨NN￨O￨A systems￨L￨NNS￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- central￨L￨JJ￨O￨- database￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- trends￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- in￨L￨IN￨O￨- and￨L￨CC￨O￨- map￨L￨VB￨O￨- the￨L￨DT￨O￨- geographic￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- and￨L￨CC￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- via￨L￨IN￨O￨- sentinel￨L￨NN￨O￨- sites￨L￨NNS￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- inform￨L￨VB￨O￨- these￨L￨DT￨O￨- efforts￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Meanwhile￨U￨RB￨O￨- ,￨L￨,￨O￨- academic￨L￨JJ￨O￨- researchers￨L￨NNS￨O￨- —￨L￨:￨O￨- often￨L￨RB￨O￨- in￨L￨IN￨O￨- high-income￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- —￨L￨:￨O￨- are￨L￨VBP￨O￨- developing￨L￨VBG￨O￨- increasingly￨L￨RB￨O￨- sophisticated￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- collect￨L￨VB￨O￨- and￨L￨CC￨O￨- analyse￨L￨VB￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- spatial￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- using￨L￨VBG￨O￨- new￨L￨JJ￨O￨- Big￨U￨NNP￨O￨- Data￨U￨NNP￨O￨- sources￨L￨NNS￨O￨- ,￨L￨,￨O￨- mobile-Health￨L￨NN￨O￨- or￨L￨CC￨O￨- m-Health￨L￨NN￨MISC￨- approaches￨L￨NNS￨O￨A or￨L￨CC￨O￨- mechanistic￨L￨JJ￨O￨- and￨L￨CC￨O￨- statistical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- ongoing￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- to￨L￨TO￨O￨- implementation￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- promising￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- leverage￨L￨NN￨O￨- even￨L￨RB￨O￨- patchy￨L￨JJ￨O￨- and￨L￨CC￨O￨- low-quality￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- diverse￨L￨JJ￨O￨- new￨L￨JJ￨O￨- data￨L￨NNS￨O￨- streams￨L￨NNS￨O￨A that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- productively￨L￨RB￨O￨- harnessed￨L￨VBN￨O￨- to￨L￨TO￨O￨- strengthen￨L￨VB￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- resource￨L￨NN￨O￨- allocation￨L￨NN￨O￨- when￨L￨WRB￨O￨- integrated￨L￨VBN￨O￨- with￨L￨IN￨O￨- existing￨L￨VBG￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +New￨U￨NNP￨O￨- innovations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- transform￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨A and￨L￨CC￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- Big￨U￨NNP￨ORGANIZATION￨- Data￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- mobile￨L￨JJ￨TITLE￨- health￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- and￨L￨CC￨O￨- cutting￨L￨VBG￨O￨- edge￨L￨NN￨O￨- quantitative￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- offer￨L￨VBP￨O￨- hope￨L￨NN￨O￨- for￨L￨IN￨O￨- disrupting￨L￨VBG￨O￨- traditional￨L￨JJ￨O￨- health￨L￨NN￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- improving￨L￨VBG￨O￨- health￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- latent￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- take￨L￨VB￨O￨- up￨L￨RP￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨A bed￨L￨NN￨O￨- resources￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- meanwhile￨L￨RB￨O￨- ,￨L￨,￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- hospital￨L￨NN￨O￨- resources￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- first￨L￨JJ￨ORDINAL￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Shan￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Zhu￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- formula￨L￨NN￨O￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- where￨L￨WRB￨O￨- μ1￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- resources￨L￨NNS￨O￨- and￨L￨CC￨O￨- few￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- μ0￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- clinical￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨- bed-population￨L￨NN￨O￨- ratio￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nonnegative￨L￨JJ￨O￨- constant￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- combined￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- psychological￨L￨JJ￨O￨- effect￨L￨NN￨O￨- and￨L￨CC￨O￨- available￨L￨JJ￨O￨- hospital￨L￨NN￨O￨A resources￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- from￨L￨IN￨O￨- infected￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- βI￨L￨NN￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nonnegative￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- +￨L￨CC￨O￨- aI￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- measures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- inhibition￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- psychological￨L￨JJ￨O￨A effect￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- introduce￨L￨VB￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- function￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- hospital￨L￨NN￨O￨A resources￨L￨NNS￨O￨- in￨L￨IN￨O￨- spreading￨L￨NN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H7N9￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- established￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- function￨L￨NN￨O￨- reflected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨A bed-population￨L￨NN￨O￨- ratio￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- formulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- EvoEpiFlu￨U￨NNP￨O￨- were￨L￨VBD￨O￨- implemented￨L￨VBN￨O￨- :￨L￨:￨O￨- as￨L￨IN￨O￨- its￨L￨PRP$￨O￨- name￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- continuous￨L￨JJ￨O￨- ’￨L￨''￨O￨- version￨L￨NN￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨A change￨L￨NN￨O￨- information￨L￨NN￨O￨- continuously￨L￨RB￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- via￨L￨IN￨O￨- an￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- index￨L￨NN￨O￨- constructed￨L￨VBN￨O￨- from￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- amino￨L￨NN￨O￨- acid￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- epitope￨L￨NN￨O￨- sites￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- antigen￨L￨NN￨O￨- protein￨L￨NN￨O￨- HA￨U￨NN￨O￨- between￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- and￨L￨CC￨DATE￨- past￨L￨JJ￨DATE￨- strains￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- scale￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- estimated￨L￨VBN￨O￨- during￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- optimization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- process-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- EvoEpiFlu￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- evolutionary￨L￨JJ￨O￨A information￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- modified￨L￨VBN￨O￨- SIRS￨U￨NN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- Susceptible￨U￨NNP￨O￨- ,￨L￨,￨O￨- Infected￨U￨JJ￨O￨- ,￨L￨,￨O￨- Recovered￨U￨VBN￨O￨- and￨L￨CC￨O￨- Susceptible￨U￨JJ￨O￨- immune￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- absolute￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- for￨L￨IN￨O￨- subtype￨L￨NN￨O￨- H3N2￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨ORGANIZATION￨- States4￨U￨NN￨O￨- .￨L￨.￨O￨- +EvoEpiFlu￨U￨NNP￨O￨- makes￨L￨VBZ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨- information￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- antigenic￨L￨JJ￨O￨- change￨L￨NN￨O￨- based￨L￨VBN￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- sequences￨L￨NNS￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- H3N2￨U￨NN￨O￨- incidence￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- summer￨L￨NN￨DATE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- upcoming￨L￨VBG￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨A .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- sequences￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- ,￨L￨,￨O￨- EvoEpiFlu￨U￨NNP￨PERSON￨- produces￨L￨VBZ￨O￨- skillful￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- one￨L￨CD￨NUMBER￨- season￨L￨NN￨O￨A ahead￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- summer￨L￨NN￨DATE￨- with￨L￨IN￨O￨- data￨L￨NNS￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- June￨U￨NNP￨DATE￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- total￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- H3N2￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- upcoming￨L￨VBG￨O￨- season￨L￨NN￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- subtype￨L￨NN￨O￨- H3N2￨U￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- dominant4￨L￨NN￨O￨- .￨L￨.￨O￨- +Bottom￨U￨NN￨O￨- panel￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- H3N2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- -2018￨L￨CD￨NUMBER￨- season￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- cluster￨L￨NN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- EvoEpiFlu￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- yellow￨L￨JJ￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- report￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- variation￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- that￨L￨WDT￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- varied￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- producer￨L￨NN￨TITLE￨- specialization￨L￨NN￨O￨- and￨L￨CC￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- producers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- percolation￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- increased￨L￨VBN￨O￨- specialization￨L￨NN￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- significantly￨L￨RB￨O￨- diminished￨L￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- resilience￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- PEDv￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- three￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- facilitating￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- hog￨L￨NN￨O￨- industry￨L￨NN￨O￨- were￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- transfer￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- between￨L￨IN￨O￨- premises￨L￨NNS￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- deliveries￨L￨NNS￨O￨- of￨L￨IN￨O￨- contaminated￨L￨VBN￨O￨A feed￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- contaminated￨L￨VBN￨O￨- livestock￨L￨NN￨O￨- and￨L￨CC￨O￨- feed￨L￨NN￨O￨- transportation￨L￨NN￨O￨- equipment￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- investigate￨L￨VB￨O￨- percolation￨L￨NN￨O￨A in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- experimental￨L￨JJ￨O￨- results￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- numerically￨L￨RB￨O￨- assess￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- events￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- runs￨L￨VBZ￨O￨- scale￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- addition￨L￨NN￨O￨- of￨L￨IN￨O￨- producer￨L￨NN￨TITLE￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- address￨L￨VB￨O￨- this￨L￨DT￨O￨- question￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- /￨L￨:￨O￨- infective￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- computer￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- epidemiological￨L￨JJ￨O￨- events￨L￨NNS￨O￨- in￨L￨IN￨O￨- hog￨L￨NN￨O￨- production￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨A individual￨L￨NN￨O￨- may￨L￨MD￨O￨- spread￨L￨VB￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- recovered￨L￨JJ￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- reinfected￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- behaviour￨L￨NN￨O￨A and￨L￨CC￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- and￨L￨CC￨O￨- recommendations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- futureDale￨L￨NN￨O￨- Weston1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Katharina￨U￨NNP￨PERSON￨- Hauck2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Richard￨U￨NNP￨PERSON￨- Amlôt1BMC￨U￨NNP￨O￨- Public￨U￨NNP￨O￨- HealthBMC￨U￨NNP￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18:336￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- are￨L￨VBP￨O￨- contextualised￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- psychological￨L￨JJ￨O￨- literature￨L￨NN￨O￨- concerning￨L￨VBG￨O￨- health￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- behaviour￨L￨NN￨O￨- change￨L￨NN￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- recommendations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- in￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Given￨U￨VBN￨MISC￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- person￨L￨NN￨O￨- to￨L￨TO￨O￨- person￨L￨NN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- critically￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- that￨L￨IN￨O￨- human￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- appropriately￨L￨RB￨O￨- represented￨L￨VBN￨O￨- within￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- scale￨L￨NN￨O￨- scoping￨L￨VBG￨O￨- review￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- behaviour￨L￨NN￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- The￨U￨DT￨O￨- search￨L￨NN￨O￨- strategy￨L￨NN￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- terms￨L￨NNS￨O￨- relating￨L￨VBG￨O￨- to￨L￨TO￨O￨- behaviour￨L￨NN￨O￨A ,￨L￨,￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- fundamentally￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- greatly￨L￨RB￨O￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨- beliefs￨L￨NNS￨O￨- on￨L￨IN￨O￨- public￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- awareness￨L￨NN￨O￨- and￨L￨CC￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A for￨L￨IN￨O￨- driving￨L￨VBG￨O￨- the￨L￨DT￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- self-behavior.3￨L￨NN￨O￨- Risk￨U￨NN￨O￨- perception￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- awareness￨L￨NN￨O￨- or￨L￨CC￨O￨- belief￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- hazard￨L￨NN￨O￨- and/or￨L￨CC￨O￨- harm￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- shaping￨L￨VBG￨O￨- health-related￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- to￨L￨TO￨O￨- reducing￨L￨VBG￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- .4￨L￨CD￨NUMBER￨- Generally￨U￨RB￨O￨- ,￨L￨,￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨- is￨L￨VBZ￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- social￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- media￨L￨NNS￨O￨- release￨L￨NN￨O￨- by￨L￨IN￨O￨- health￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- ,￨L￨,￨O￨- observation￨L￨NN￨O￨- or￨L￨CC￨O￨- interaction￨L￨NN￨O￨- with￨L￨IN￨O￨- relation-specific￨L￨JJ￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- past￨L￨JJ￨DATE￨- experiences￨L￨NNS￨O￨- of￨L￨IN￨O￨- similar￨L￨JJ￨O￨- hazards￨L￨NNS￨O￨- ,￨L￨,￨O￨- habits￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- culture￨L￨NN￨O￨- .5￨L￨CD￨NUMBER￨- These￨U￨DT￨O￨- factors￨L￨NNS￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨- among￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- health-seeking￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .1￨L￨NN￨NUMBER￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- about￨L￨IN￨O￨- intervention￨L￨NN￨O￨- and￨L￨CC￨O￨- management￨L￨NN￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- to￨L￨TO￨O￨- what￨L￨WP￨O￨- extent￨L￨NN￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- scenarios￨L￨NNS￨O￨- of￨L￨IN￨O￨- with/without￨L￨NN￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- preventive/protective￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- age-specific￨L￨JJ￨O￨- network-driven￨L￨JJ￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A influences￨L￨VBZ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .2￨L￨NN￨NUMBER￨- To￨U￨TO￨O￨- control￨L￨VB￨O￨- respiratory￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- tracing￨L￨VBG￨O￨- ,￨L￨,￨O￨- isolation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- promotion￨L￨NN￨O￨- of￨L￨IN￨O￨- protective￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- suggested￨L￨VBN￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A and￨L￨CC￨O￨- behavior￨L￨NN￨O￨- across￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- .8,9￨L￨CD￨NUMBER￨- A￨U￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- people￨L￨NNS￨O￨- could￨L￨MD￨O￨- exchange￨L￨VB￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- risk-related￨L￨JJ￨O￨- events￨L￨NNS￨O￨- to￨L￨TO￨O￨- spur￨L￨VB￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- behavior￨L￨NN￨O￨- change￨L￨NN￨O￨- .10￨L￨CD￨NUMBER￨- Scherer￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Cho11￨U￨NN￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- individual￨L￨JJ￨O￨- perceptions￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- self-perception￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Funk￨U￨NNP￨O￨- et￨L￨FW￨O￨- al12￨L￨FW￨O￨- used￨L￨VBN￨O￨- SIR-based￨U￨JJ￨MISC￨- perceptual-influenza￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A on￨L￨IN￨O￨- behavioral￨L￨JJ￨O￨- change￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- reduction￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemiological￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- variances￨L￨NNS￨O￨- in￨L￨IN￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- by￨L￨IN￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- behavioral￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- intuitive￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- local￨L￨JJ￨O￨- structures26￨L￨NN￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- attention￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨- in￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A process￨L￨NN￨O￨A ,￨L￨,￨O￨- largely￨L￨RB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- particularities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- models￨L￨NNS￨O￨- typically￨L￨RB￨O￨- deployed￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- these￨L￨DT￨O￨- processes.In￨L￨NN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- classified￨L￨VBN￨O￨- to￨L￨TO￨O￨- two￨L￨CD￨NUMBER￨- broad￨L￨JJ￨O￨- categories12￨L￨NN￨O￨- ,27￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- incorporated￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- viewed￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- independent￨L￨JJ￨RELIGION￨- event￨L￨NN￨O￨- across￨L￨IN￨O￨- different￨L￨JJ￨O￨- pairs￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- its￨L￨PRP$￨O￨- neighbour￨L￨NN￨O￨- j￨L￨NN￨O￨- is￨L￨VBZ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- sociological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- viewed￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- interdependent￨L￨JJ￨O￨- event￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- its￨L￨PRP$￨O￨- neighbour￨L￨NN￨O￨- j￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- ’s￨L￨POS￨O￨- j￨L￨NN￨O￨- neighbours￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Yet￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- implication￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- premise￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- non-trivial￨L￨JJ￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- exposures￨L￨NNS￨O￨- can￨L￨MD￨O￨- interfere￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨A process￨L￨NN￨O￨A and￨L￨CC￨O￨- affect￨L￨VB￨O￨- key￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- simple￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- discussed￨L￨VBN￨O￨- below.Consider￨L￨NN￨O￨- the￨L￨DT￨O￨- toy￨L￨NN￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- Fig.￨U￨NN￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- can￨L￨MD￨O￨- switch￨L￨VB￨O￨- states￨L￨NNS￨O￨- irreversibly￨L￨RB￨O￨- from￨L￨IN￨O￨- ‘￨L￨``￨O￨- non-affected￨L￨JJ￨O￨- ’￨L￨''￨O￨- to￨L￨TO￨O￨- ‘￨L￨``￨O￨- affected￨L￨VBN￨O￨- ’￨L￨''￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- probability￨L￨NN￨O￨- p.￨L￨NN￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Modelling￨U￨NNP￨O￨- indirect￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- during￨L￨IN￨O￨- failure￨L￨NN￨O￨- spreading￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- project￨L￨NN￨O￨- activity￨L￨NN￨O￨- network￨L￨NN￨O￨- Christos￨U￨NNP￨PERSON￨- Ellinas￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 4373￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksStatistical￨L￨JJ￨O￨- physics￨L￨NNS￨O￨- AbstractSpreading￨U￨VBG￨O￨- broadly￨L￨RB￨O￨- refers￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- notion￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- entity￨L￨NN￨O￨- propagating￨L￨VBG￨O￨- throughout￨L￨IN￨O￨- a￨L￨DT￨O￨- networked￨L￨JJ￨O￨- system￨L￨NN￨O￨- via￨L￨IN￨O￨- its￨L￨PRP$￨O￨- interacting￨L￨VBG￨O￨- components￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- subsequent￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- effect￨L￨NN￨O￨- in￨L￨IN￨O￨- key￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- final￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- event￨L￨NN￨O￨A size￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- propagation￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- spreading￨L￨VBG￨O￨- event￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Role￨U￨NN￨O￨- of￨L￨IN￨O￨- monkeys￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sylvatic￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨A virus￨L￨NN￨O￨- in￨L￨IN￨O￨- Senegal￨U￨NNP￨COUNTRY￨- Benjamin￨U￨NNP￨O￨- M.￨U￨NNP￨O￨- Hanley3￨U￨NNP￨O￨- Nature￨U￨NNP￨O￨- Communicationsvolume￨U￨NNP￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 1046￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Ecological￨U￨NNP￨O￨- epidemiologyEpidemiologyViral￨L￨NNP￨O￨- infectionVirology￨L￨NNP￨O￨- AbstractArboviruses￨U￨NNPS￨O￨- spillover￨L￨JJR￨O￨- into￨L￨IN￨O￨- humans￨L￨NNS￨O￨- either￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- one-step￨L￨JJ￨O￨- jump￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- into￨L￨IN￨O￨- humans￨L￨NNS￨O￨- or￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- two-step￨L￨JJ￨O￨- jump￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- amplification￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- and￨L￨CC￨O￨- thence￨L￨RB￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +Infant￨U￨NN￨O￨- monkeys￨L￨NNS￨O￨- were￨L￨VBD￨O￨- positive￨L￨JJ￨O￨- for￨L￨IN￨O￨- CHIKV￨U￨NNP￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A was￨L￨VBD￨O￨- not￨L￨RB￨O￨- detected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- concurrent￨L￨JJ￨O￨- survey￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- was￨L￨VBD￨O￨- too￨L￨RB￨O￨- high￨L￨JJ￨O￨- for￨L￨IN￨O￨- monkeys￨L￨NNS￨O￨- alone￨L￨RB￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- continuous￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Over￨U￨IN￨O￨- 3￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- 737￨L￨CD￨NUMBER￨- monkeys￨L￨NNS￨O￨- were￨L￨VBD￨O￨- captured￨L￨VBN￨O￨- ,￨L￨,￨O￨- aged￨L￨VBN￨O￨- using￨L￨VBG￨O￨- anthropometry￨L￨NN￨O￨- and￨L￨CC￨O￨- dentition￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- tested￨L￨VBN￨O￨- for￨L￨IN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- CHIKV￨U￨NN￨O￨- by￨L￨IN￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- neutralizing￨L￨VBG￨O￨- antibodies￨L￨NNS￨O￨A .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- elucidate￨L￨VBP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- monkeys￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sylvatic￨L￨JJ￨O￨- ,￨L￨,￨O￨- enzootic￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨A virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- around￨L￨IN￨O￨- Kédougou￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Senegal￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- inference￨L￨NN￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- offspring￨L￨NN￨O￨- distribution￨L￨NN￨O￨- to￨L￨TO￨O￨- enable￨L￨VB￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨A from￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- phylogeny￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2011￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- jointly￨L￨RB￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- incidence￨L￨NN￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨- phylogeny￨L￨NN￨O￨A reduced￨L￨VBD￨O￨- uncertainties￨L￨NNS￨O￨- in￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- that￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨A could￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- either￨L￨RB￨O￨- from￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- phylogenetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- combining￨L￨VBG￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- should￨L￨MD￨O￨- provide￨L￨VB￨O￨- more￨L￨JJR￨O￨- accurate￨L￨JJ￨O￨- and￨L￨CC￨O￨- precise￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- precision￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- bias￨L￨NN￨O￨- of￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨A using￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +Besides￨U￨IN￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- pathogen￨L￨NN￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- playing￨L￨VBG￨O￨- an￨L￨DT￨O￨- increasingly￨L￨RB￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- epidemiological￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Volz￨U￨NNP￨PERSON￨- etal￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- scenarios￨L￨NNS￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- harbors￨L￨NNS￨O￨- substantial￨L￨JJ￨O￨- diversity￨L￨NN￨O￨A ,￨L￨,￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- which￨L￨WDT￨O￨- other￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- they￨L￨PRP￨O￨- infected￨L￨JJ￨O￨- —￨L￨:￨O￨- different￨L￨JJ￨O￨- lineages￨L￨NNS￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- been￨L￨VBN￨O￨- transmitted￨L￨VBN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- points￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- donor￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- genome￨L￨NN￨O￨- sequenced￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- donor￨L￨NN￨O￨- may￨L￨MD￨O￨- only￨L￨RB￨O￨- represent￨L￨VB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- lineage￨L￨NN￨O￨- captured￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- a￨L￨DT￨O￨- diagnostic￨L￨JJ￨O￨- sample￨L￨NN￨O￨- was￨L￨VBD￨O￨- taken￨L￨VBN￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- lineages￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- within￨L￨IN￨O￨- that￨L￨DT￨O￨- individual￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- early￨L￨JJ￨O￨- works￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- area￨L￨NN￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- genomes￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- pair￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- identical￨L￨JJ￨O￨- or￨L￨CC￨O￨- near-identical￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- genomic￨L￨JJ￨O￨A outbreak￨L￨NN￨O￨- investigations￨L￨NNS￨O￨- revealed￨L￨VBD￨O￨- the￨L￨DT￨O￨- complicating￨L￨JJ￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- introduced￨L￨VBN￨O￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- inferring￨L￨VBG￨O￨- person-to-person￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A events￨L￨NNS￨O￨A from￨L￨IN￨O￨- genomic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- consider￨L￨VBP￨O￨- within-host￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- simulation￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- ignored￨L￨VBN￨O￨- ,￨L￨,￨O￨- incorrect￨L￨JJ￨O￨- inferences￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- drawn￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A events￨L￨NNS￨O￨A that￨L￨WDT￨O￨- occurred￨L￨VBD￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- originally￨L￨RB￨O￨A used￨L￨VBD￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- tree￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- recently￨L￨RB￨DATE￨- showed￨L￨VBD￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- extend￨L￨VB￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- incorporate￨L￨VB￨O￨- other￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- view￨L￨NN￨O￨- of￨L￨IN￨O￨- discrepant￨L￨JJ￨O￨- reports￨L￨NNS￨O￨- of￨L￨IN￨O￨- lg￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- spVL￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- heritability￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- questioned￨L￨VBN￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- methods￨L￨NNS￨O￨A and￨L￨CC￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- various￨L￨JJ￨O￨- adaptations￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- overcome￨L￨VB￨O￨- potential￨L￨JJ￨O￨- pitfalls￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- false￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- assumptions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- neutral￨L￨JJ￨IDEOLOGY￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- ultrametricity￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- trees￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- imperfections￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- small￨L￨JJ￨O￨- data￨L￨NNS￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- cofactors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- measurement￨L￨NN￨O￨- error￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Phylogenetic￨U￨JJ￨O￨- comparative￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- measuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- so￨L￨RB￨O￨- called￨L￨VBN￨O￨- phylogenetic￨L￨JJ￨O￨- heritability￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- observed￨L￨VBN￨O￨- trait￨L￨NN￨O￨A values￨L￨NNS￨O￨- from￨L￨IN￨O￨- patients￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- (￨L￨-LRB-￨O￨- approximate￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- tree￨L￨NN￨O￨- inferred￨L￨VBD￨O￨- from￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- .￨L￨.￨O￨- +Two￨U￨CD￨NUMBER￨- families￨L￨NNS￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- heritability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- trait￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- its￨L￨PRP$￨O￨- genetic￨L￨JJ￨O￨- basis￨L￨NN￨O￨- :￨L￨:￨O￨- Resemblance￨U￨NNP￨O￨- estimators￨L￨NNS￨O￨- measuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- trait-similarity￨L￨NN￨O￨- within￨L￨IN￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission-related￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Results￨U￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compare￨L￨VBP￨O￨- these￨L￨DT￨O￨- estimators￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- report￨L￨VB￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- spVL￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- cohort￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- per￨L￨IN￨O￨- generation￨L￨NN￨O￨- given￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- entirely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- in￨L￨IN￨O￨- norovirus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- particular￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- of￨L￨IN￨O￨- noroviruses￨L￨NNS￨O￨- developed￨L￨VBN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- to￨L￨TO￨O￨- population￨L￨NN￨O￨- levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- a￨L￨DT￨O￨- remarkable￨L￨JJ￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- reproduction￨L￨NN￨O￨A numbers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Published￨U￨VBN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- norovirus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- demonstrate￨L￨VBP￨O￨- a￨L￨DT￨O￨- broad￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- relevant￨L￨JJ￨O￨- settings￨L￨NNS￨O￨A and￨L￨CC￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- local￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- settings￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- and￨L￨CC￨O￨- contrast￨L￨VB￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨A number￨L￨NN￨O￨- for￨L￨IN￨O￨- norovirus￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- High￨U￨NNP￨MISC￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- elementary￨L￨JJ￨O￨- schools￨L￨NNS￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- observational￨L￨JJ￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- Matsumoto￨U￨NNP￨CITY￨- City￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- JapanMitsuo￨U￨NNP￨O￨- Uchida1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Minoru￨U￨NNP￨PERSON￨- Kaneko1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Yoshihiko￨U￨NNP￨PERSON￨- Hidaka2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hiroshi￨U￨NNP￨PERSON￨- Yamamoto3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Takayuki￨U￨NNP￨PERSON￨- Honda4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Shouhei￨U￨NNP￨O￨- Takeuchi5￨U￨NNP￨O￨- ,￨L￨,￨O￨- Masaya￨U￨NNP￨PERSON￨- Saito6￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Shigeyuki￨U￨NNP￨MISC￨- Kawa1BMC￨U￨NNP￨MISC￨- Infectious￨U￨JJ￨MISC￨- DiseasesBMC￨U￨NN￨MISC￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 18:128￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- results￨L￨NNS￨O￨- were￨L￨VBD￨O￨- combined￨L￨VBN￨O￨- and￨L￨CC￨O￨- associations￨L￨NNS￨O￨- among￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨A measures￨L￨NNS￨O￨A including￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- mask￨L￨NN￨O￨- wearing￨L￨VBG￨O￨- ,￨L￨,￨O￨- hand￨L￨NN￨O￨- washing￨L￨VBG￨O￨- ,￨L￨,￨O￨- water￨L￨NN￨O￨- gargling￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- level￨L￨NN￨O￨- were￨L￨VBD￨O￨- evaluated￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- significant￨L￨JJ￨O￨- negative￨L￨JJ￨O￨- association￨L￨NN￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- between￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- school￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- between￨L￨IN￨O￨- other￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨A measures￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- .￨L￨.￨O￨- +2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- prevented￨L￨VBN￨O￨- by￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨A measures￨L￨NNS￨O￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- wearing￨L￨VBG￨O￨- a￨L￨DT￨O￨- mask￨L￨NN￨O￨- ,￨L￨,￨O￨- gargling￨L￨VBG￨O￨- with￨L￨IN￨O￨- water￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hand￨L￨NN￨O￨- washing￨L￨VBG￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 2015￨L￨CD￨DATE￨- season￨L￨NN￨O￨- evaluated￨L￨VBD￨O￨A the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- diagnosed￨L￨VBN￨O￨- patients￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- school￨L￨NN￨O￨- and￨L￨CC￨O￨- calculated￨L￨VBN￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- schoolchildren￨L￨NNS￨O￨- .￨L￨.￨O￨- +Overall￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aimed￨L￨VBD￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- generation￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨A tools￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- adapted￨L￨VBN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- epidemiological￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- of￨L￨IN￨O￨- central￨L￨JJ￨O￨- importance￨L￨NN￨O￨- to￨L￨TO￨O￨- HIV-1￨U￨NN￨MISC￨- prevention￨L￨NN￨O￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- the￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- sequence￨L￨NN￨O￨- availability￨L￨NN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- resource-poor￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- fundamentally￨L￨RB￨O￨- from￨L￨IN￨O￨- well￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- concentrated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- wealthy￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- viral￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨A tools￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proven￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- to￨L￨TO￨O￨- date￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- these￨L￨DT￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- generated￨L￨VBD￨O￨- corresponding￨L￨JJ￨O￨- viral￨L￨JJ￨O￨A sequence￨L￨NN￨O￨- datasets￨L￨NNS￨O￨- comprising￨L￨VBG￨O￨- simulated￨L￨JJ￨O￨- pol￨L￨NN￨O￨- ,￨L￨,￨O￨- gag￨L￨NN￨O￨- and￨L￨CC￨O￨- env￨L￨NN￨O￨- genes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- as￨L￨RB￨O￨- full￨L￨JJ￨O￨- genome￨L￨NN￨O￨- sequences￨L￨NNS￨O￨- for￨L￨IN￨O￨- brevity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- basic￨L￨JJ￨O￨- individual-level￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- those￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- sequenced￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Available￨U￨JJ￨O￨- viral￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨A techniques￨L￨NNS￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- of￨L￨IN￨O￨- concentrated￨L￨JJ￨O￨- HIV-1￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Phylogenetics￨U￨NNPS￨O￨- And￨U￨CC￨O￨- Networks￨U￨NNP￨O￨- for￨L￨IN￨O￨- Generalized￨U￨NNP￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- Epidemics￨U￨NNS￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- (￨L￨-LRB-￨O￨- PANGEA-HIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- consortium￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- viral￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- across￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- their￨L￨PRP$￨O￨- viral￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨A relationship￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- marker￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- HIV-1￨U￨NN￨MISC￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Estimating￨U￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨- introduction￨L￨NN￨O￨- and￨L￨CC￨O￨- secondary￨L￨JJ￨O￨- autochthonous￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- Eduardo￨U￨NNP￨LOCATION￨- Massad1￨U￨NN￨O￨- ,2,3,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Marcos￨U￨NNP￨PERSON￨- Amaku￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Francisco￨U￨NNP￨PERSON￨- Antonio￨U￨NNP￨PERSON￨- Bezerra￨U￨NNP￨PERSON￨- Coutinho1￨U￨NN￨O￨- ,￨L￨,￨O￨- Claudio￨U￨NNP￨PERSON￨- José￨U￨NNP￨PERSON￨- Struchiner5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marcelo￨U￨NNP￨PERSON￨- Nascimento￨U￨NNP￨PERSON￨- Burattini1￨U￨NNP￨O￨- ,6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kamran￨U￨NNP￨PERSON￨- Khan7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jing￨U￨NNP￨PERSON￨- Liu-Helmersson8￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Joacim￨U￨NNP￨O￨- Rocklöv8￨U￨NNP￨O￨- ,￨L￨,￨O￨- Moritz￨U￨NNP￨PERSON￨- U.￨U￨NNP￨PERSON￨- G.￨U￨NNP￨PERSON￨- Kraemer9￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Annelies￨U￨NNP￨O￨- Wilder-Smith8￨U￨NN￨O￨- ,10,11￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 4629￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Experimental￨U￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- diseaseInfectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- AbstractGiven￨U￨VBP￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- air￨L￨NN￨O￨- travel￨L￨NN￨O￨- ,￨L￨,￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- even￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- viremia￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- dengue￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- exported￨L￨VBN￨O￨- to￨L￨TO￨O￨- dengue￨L￨VB￨O￨- naïve￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- within￨L￨IN￨O￨- 24￨L￨CD￨DURATION￨- hours￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- applied￨L￨VBD￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue-viremic￨L￨JJ￨O￨- air￨L￨NN￨O￨- passengers￨L￨NNS￨O￨- from￨L￨IN￨O￨- 16￨L￨CD￨NUMBER￨- dengue-endemic￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- to￨L￨TO￨O￨- 27￨L￨CD￨NUMBER￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- exporting￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- travel￨L￨NN￨O￨- volume￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- viremic￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- models￨L￨NNS￨O￨- estimate￨L￨VBP￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- from￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 167￨L￨CD￨NUMBER￨- air￨L￨NN￨O￨- passengers￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- dengue-viremic￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- of￨L￨IN￨O￨- travel￨L￨NN￨O￨- from￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A endemic￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 27￨L￨CD￨NUMBER￨- receiving￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- set￨L￨VBD￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A virus￨L￨NN￨O￨- introductions￨L￨NNS￨O￨- via￨L￨IN￨O￨- travelers￨L￨NNS￨O￨- into￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- autochthonous￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- .￨L￨.￨O￨- +Methodology￨U￨NNP￨O￨- Article￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Heterogeneous￨U￨JJ￨O￨- computing￨L￨NN￨O￨- for￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- fitting￨L￨JJ￨O￨- and￨L￨CC￨O￨- simulationThomas￨L￨NNP￨O￨- Kovac￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Tom￨U￨NNP￨PERSON￨- Haber￨U￨NNP￨PERSON￨- †￨L￨SYM￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Frank￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Reeth2￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Niel￨U￨NN￨PERSON￨- Hens1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- †￨L￨NN￨O￨- Contributed￨U￨VBD￨O￨- equallyBMC￨L￨NN￨O￨- BioinformaticsBMC￨U￨NN￨O￨- series￨L￨NN￨O￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- 19:101￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Over￨U￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- years￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- substantial￨L￨JJ￨O￨- effort￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- put￨L￨VBN￨O￨- into￨L￨IN￨O￨- enhancing￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- arsenal￨L￨NN￨O￨- in￨L￨IN￨O￨- fighting￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- from￨L￨IN￨O￨- both￨L￨DT￨O￨- technological￨L￨JJ￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- perspectives￨L￨NNS￨O￨- with￨L￨IN￨O￨- scientists￨L￨NNS￨O￨A from￨L￨IN￨O￨- different￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- teaming￨L￨VBG￨O￨- up￨L￨RP￨O￨- for￨L￨IN￨O￨- rapid￨L￨JJ￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- potentially￨L￨RB￨O￨- urgent￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- particles￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- PSO￨U￨NNP￨ORGANIZATION￨- algorithm￨L￨NN￨O￨- are￨L￨VBP￨O￨- candidate￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- finding￨L￨VBG￨O￨- the￨L￨DT￨O￨- right￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- matter￨L￨NN￨O￨- of￨L￨IN￨O￨- optimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- function￨L￨NN￨O￨- which￨L￨WDT￨O￨- quantifies￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- well￨L￨RB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- focusses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- computational￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A and￨L￨CC￨O￨- applies￨L￨VBZ￨O￨- commonly￨L￨RB￨O￨- available￨L￨JJ￨O￨- graphics￨L￨NNS￨O￨- processing￨L￨VBG￨O￨- units￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- GPUs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- asynchronous￨L￨JJ￨O￨- particle￨L￨NN￨O￨- swarm￨L￨NN￨O￨- optimization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PSO￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- implementation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- where￨L￨WRB￨O￨- batches￨L￨NNS￨O￨- of￨L￨IN￨O￨- particles￨L￨NNS￨O￨A are￨L￨VBP￨O￨- sent￨L￨VBN￨O￨- asynchronously￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- CPU￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- GPU￨U￨NNP￨ORGANIZATION￨- for￨L￨IN￨O￨- evaluation￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- efficient￨L￨JJ￨O￨- GPU￨U￨NNP￨ORGANIZATION￨- implementation￨L￨NN￨O￨A for￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- a￨L￨DT￨O￨- small-scale￨L￨JJ￨O￨- ODE￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- usceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- nfected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- ecovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- discussed￨L￨VBN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- article￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- innovative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- extend￨L￨VB￨O￨- agent-based￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A by￨L￨IN￨O￨- capturing￨L￨VBG￨O￨- behavioral￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- decision-making￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- risky￨L￨JJ￨O￨- context￨L￨NN￨O￨- using￨L￨VBG￨O￨- machine￨L￨NN￨O￨- learning￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- .￨L￨.￨O￨- +Yet￨U￨RB￨O￨- ,￨L￨,￨O￨- current￨L￨JJ￨DATE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨A rarely￨L￨RB￨O￨- consider￨L￨VBP￨O￨- simulating￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- protective￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- illustrate￨L￨VBP￨O￨- it￨L￨PRP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Kumasi￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Ghana￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- spatial￨L￨JJ￨O￨A and￨L￨CC￨O￨- social￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- affect￨L￨VBP￨O￨- intelligent￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- corresponding￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidents￨L￨NNS￨O￨- .￨L￨.￨O￨- +Hand￨U￨VB￨O￨- ,￨L￨,￨O￨- foot￨L￨NN￨O￨- and￨L￨CC￨O￨- mouth￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- HFMD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- paediatric￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- which￨L￨WDT￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- usually￨L￨RB￨O￨- self-limiting￨L￨JJ￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- central￨L￨JJ￨O￨- nervous￨L￨JJ￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CNS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- death￨L￨NN￨O￨- .1￨L￨NN￨NUMBER￨- 2￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- viruses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- cause￨L￨VBP￨O￨- HFMD￨U￨NN￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- widespread￨L￨JJ￨O￨- in￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- each￨L￨DT￨SET￨- year￨L￨NN￨SET￨- .3￨L￨NN￨NUMBER￨- Citation￨U￨NNP￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- 29￨L￨CD￨NUMBER￨- children￨L￨NNS￨O￨- died4￨L￨NN￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- harbinger￨L￨NN￨O￨- of￨L￨IN￨O￨- fatal￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- continued￨L￨VBN￨O￨- to￨L￨TO￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 170￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 98￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .6￨L￨CD￨NUMBER￨- These￨U￨DT￨O￨- fatal￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- have￨L￨VBP￨O￨- influenced￨L￨VBN￨O￨- the￨L￨DT￨O￨- perceived￨L￨VBN￨O￨- severity￨L￨NN￨O￨A of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- and￨L￨CC￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- demand￨L￨NN￨O￨- for￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,7￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- recent￨L￨JJ￨O￨- phase￨L￨NN￨O￨- III￨U￨CD￨NUMBER￨- vaccine￨L￨NN￨O￨- trials￨L￨NNS￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ,8￨L￨CD￨NUMBER￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- through￨L￨IN￨O￨- Bayesian￨U￨JJ￨MISC￨- methods￨L￨NNS￨O￨- which￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- flexible￨L￨JJ￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- integrate￨L￨VB￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- severity￨L￨NN￨O￨A indices￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza11￨L￨NN￨O￨- 12￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- .13￨L￨CD￨NUMBER￨- To￨U￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- across￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- mortality￨L￨NN￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- against￨L￨IN￨O￨- it￨L￨PRP￨O￨- ,7￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- conducted￨L￨VBD￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- across￨L￨IN￨O￨- East￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Southeast￨U￨NNP￨O￨- Asia14￨U￨NNP￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- severity￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- usually￨L￨RB￨O￨- mild￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- where￨L￨WRB￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- vastly￨L￨RB￨O￨- exceed￨L￨VBP￨O￨- severe￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- efforts￨L￨NNS￨O￨- to￨L￨TO￨O￨- track￨L￨VB￨O￨- all￨L￨DT￨O￨- HFMD￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- indices￨L￨NNS￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- severity￨L￨NN￨O￨A are￨L￨VBP￨O￨- impractical￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- .9￨L￨CD￨NUMBER￨- With￨U￨IN￨O￨- the￨L￨DT￨O￨- exception￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- jurisdictions￨L￨NNS￨O￨- ,￨L￨,￨O￨- much￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- subpopulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- catchment￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- health￨L￨NN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- sentinel￨L￨NN￨O￨- clinics￨L￨NNS￨O￨- or￨L￨CC￨O￨- from￨L￨IN￨O￨- passive￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- using￨L￨VBG￨O￨- symptomatic￨L￨JJ￨O￨- case￨L￨NN￨O￨- notifications￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- ref￨L￨NN￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Obtaining￨U￨VBG￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- comprehensive￨L￨JJ￨O￨- picture￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- synthesising￨L￨VBG￨O￨- available￨L￨JJ￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- studies￨L￨NNS￨O￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- severity￨L￨NN￨O￨A levels￨L￨NNS￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- serological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- estimate￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- notification￨L￨NN￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- provide￨L￨VBP￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- clinically￨L￨RB￨O￨- identified￨L￨VBN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- hospital￨L￨NN￨O￨- records￨L￨NNS￨O￨- that￨L￨WDT￨O￨- showcase￨L￨NN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- more￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- expressions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- CNS￨U￨NN￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- death￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- sCFR￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- computed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- poor￨L￨JJ￨O￨- reflection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- severity￨L￨NN￨O￨A and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- sensitive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- notification￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- antibody￨L￨NN￨O￨- titers￨L￨NNS￨O￨- against￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- HAI￨U￨NN￨O￨- assays￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- over￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- seasons￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- in￨L￨IN￨O￨- Singapore￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- supplementary￨L￨JJ￨O￨- real-time￨L￨JJ￨O￨- polymerase￨L￨NN￨O￨- chain￨L￨NN￨O￨- reaction￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- RT-PCR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- from￨L￨IN￨O￨- various￨L￨JJ￨O￨- subpopulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- synthesized￨L￨VBD￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- RT-PCR￨U￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- repeated￨L￨VBN￨O￨- serological￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A evolution￨L￨NN￨O￨A of￨L￨IN￨O￨- HAI￨U￨NNP￨O￨- titers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- immediate￨L￨JJ￨O￨- aftermath￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- restriction￨L￨NN￨O￨- of￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- 4-fold￨L￨JJ￨O￨- rise￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- data￨L￨NN￨O￨- set￨L￨NN￨O￨- provided￨L￨VBN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨A evolution￨L￨NN￨O￨A of￨L￨IN￨O￨- titers￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- immediate￨L￨JJ￨O￨- aftermath￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- times￨L￨NNS￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- samples￨L￨NNS￨O￨- were￨L￨VBD￨O￨- taken￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- May￨U￨NNP￨DATE￨- –￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1B￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- temperature￨L￨NN￨O￨- forcing￨L￨VBG￨O￨- improves￨L￨VBZ￨O￨- forecast￨L￨NN￨O￨A accuracy￨L￨NN￨O￨- for￨L￨IN￨O￨- total￨L￨JJ￨O￨- human￨L￨JJ￨O￨- case￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨DATE￨- week￨L￨NN￨DATE￨- of￨L￨IN￨O￨- peak￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- abundance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- abundance￨L￨NN￨O￨- for￨L￨IN￨O￨- much￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- WNV￨U￨NN￨O￨- season￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- predicted￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- forecast￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- system￨L￨NN￨O￨- accurately￨L￨RB￨O￨- forecast￨L￨VBD￨O￨A mosquito￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨DATE￨- week￨L￨NN￨DATE￨- of￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- peak￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- accurately￨L￨RB￨O￨- predicted￨L￨VBD￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- WNV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- up￨L￨IN￨DURATION￨- to￨L￨TO￨DURATION￨- 9￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- reported￨L￨VBD￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨SET￨- week￨L￨NN￨SET￨- ,￨L￨,￨O￨- observations￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- WNV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 300￨L￨CD￨NUMBER￨- mosquitoes￨L￨NNS￨O￨- were￨L￨VBD￨O￨- sampled￨L￨VBN￨O￨- ,￨L￨,￨O￨- mosquito￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- assimilated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- EAKF￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- forecast￨L￨NN￨O￨A was￨L￨VBD￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- integrating￨L￨VBG￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ensemble￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- season￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- accurate￨L￨JJ￨O￨- and￨L￨CC￨O￨- reliable￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- WNV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- parsimonious￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- WNV￨U￨NN￨O￨- among￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨A and￨L￨CC￨O￨- birds￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- spillover￨L￨NN￨O￨- to￨L￨TO￨O￨- humans￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- such￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- proven￨L￨VBN￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- discriminating￨L￨VBG￨O￨- writing￨L￨VBG￨O￨- styles￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- robustness￨L￨NN￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- topological￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- usually￨L￨RB￨O￨- provide￨L￨VBP￨O￨- no￨L￨DT￨O￨- better￨L￨JJR￨O￨- results￨L￨NNS￨O￨- than￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- based￨L￨VBN￨O￨- e.g.￨L￨FW￨O￨- in￨L￨IN￨O￨- n-grams￨L￨JJ￨O￨- models￨L￨NNS￨O￨- when￨L￨WRB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- text￨L￨NN￨O￨A characterization￨L￨NN￨O￨- .￨L￨.￨O￨- +Traditional￨U￨JJ￨O￨- techniques￨L￨NNS￨O￨- use￨L￨VBP￨O￨- text￨L￨NN￨O￨A analytics￨L￨NNS￨O￨- and￨L￨CC￨O￨- natural￨L￨JJ￨O￨- language￨L￨NN￨O￨- processing￨L￨NN￨O￨- concepts￨L￨NNS￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- authors￨L￨NNS￨O￨- ’￨L￨POS￨O￨- writing￨L￨VBG￨O￨- styles￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paradigm￨L￨NN￨O￨- ,￨L￨,￨O￨- documents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- co-occurrence￨L￨NN￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- formed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- authors￨L￨NNS￨O￨A ’￨L￨POS￨O￨- fingerprints￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- classification￨L￨NN￨O￨- process￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- study￨L￨NN￨O￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- integrative￨L￨JJ￨O￨- ,￨L￨,￨O￨- joint￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- numerous￨L￨JJ￨O￨- suggested￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- triggers￨L￨VBZ￨O￨- ,￨L￨,￨O￨- comparing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- importance￨L￨NN￨O￨- and￨L￨CC￨O￨- possible￨L￨JJ￨O￨- cooperation￨L￨NN￨O￨- in￨L￨IN￨O￨- triggering￨L￨VBG￨O￨- pan-US￨L￨JJ￨O￨- waves￨L￨NNS￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Computational￨U￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- factors￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A began￨L￨VBD￨O￨- with￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- Susceptible-Infected-Resistant￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- traces￨L￨NNS￨O￨- its￨L￨PRP$￨O￨- origins￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨DATE￨- beginning￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- informative￨L￨JJ￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- predictors￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- initiation￨L￨NN￨O￨- of￨L￨IN￨O￨- pan-US￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A waves￨L￨NNS￨O￨- .￨L￨.￨O￨- +Initially￨U￨RB￨O￨- a￨L￨DT￨O￨- purely￨L￨RB￨O￨A theoretical￨L￨JJ￨O￨- tool￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- SIR-style￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- subsequently￨L￨RB￨O￨- enhanced￨L￨VBN￨O￨- with￨L￨IN￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- geographic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- application￨L￨NN￨O￨- to￨L￨TO￨O￨- specific￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distances￨L￨NNS￨O￨- between￨L￨IN￨O￨- them￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- likely￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- initiating￨L￨VBG￨O￨- each￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- wave￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- coevolution￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- and￨L￨CC￨O￨- awareness￨L￨NN￨O￨A ,￨L￨,￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- estimators￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- multiplex￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- disclose￨L￨VB￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- overlapping￨L￨VBG￨O￨- awareness￨L￨NN￨O￨A on￨L￨IN￨O￨- suicidal￨L￨JJ￨O￨- ideation￨L￨NN￨O￨- spreading￨L￨NN￨O￨- among￨L￨IN￨O￨- disordered￨L￨VBN￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- introduce￨L￨VB￨O￨- a￨L￨DT￨O￨- data-driven￨L￨JJ￨O￨- approach￨L￨NN￨O￨- by￨L￨IN￨O￨- integrating￨L￨VBG￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- modelling￨L￨NN￨O￨- approach￨L￨NN￨O￨- unveils￨L￨VBZ￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- distress￨L￨NN￨O￨- and￨L￨CC￨O￨- mental￨L￨JJ￨O￨- disorders￨L￨NNS￨O￨- propagation￨L￨NN￨O￨- and￨L￨CC￨O￨- suicidal￨L￨JJ￨O￨- ideation￨L￨NN￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- shedding￨L￨VBG￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- awareness￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- for￨L￨IN￨O￨- suicide￨L￨NN￨CAUSE_OF_DEATH￨- prevention￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Quantifying￨U￨VBG￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- distress￨L￨NN￨O￨- and￨L￨CC￨O￨- mental￨L￨JJ￨O￨- disorders￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- Marialisa￨U￨NNP￨O￨- Scatà1￨U￨NNP￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Alessandro￨U￨NNP￨PERSON￨- Di￨U￨NNP￨PERSON￨- Stefano1￨U￨NN￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Aurelio￨U￨NNP￨ORGANIZATION￨- La￨U￨NNP￨ORGANIZATION￨- Corte1￨U￨NNP￨ORGANIZATION￨- na1￨L￨NN￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Pietro￨U￨NNP￨ORGANIZATION￨- Liò2￨U￨NNP￨O￨- na1￨L￨NN￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 5005￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksPsychiatric￨L￨JJ￨O￨- disorders￨L￨NNS￨O￨- AbstractHeterogeneity￨U￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- beings￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- think￨L￨VB￨O￨- and￨L￨CC￨O￨- react￨L￨VB￨O￨- differently￨L￨RB￨O￨- to￨L￨TO￨O￨- social￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- .￨L￨.￨O￨- +Awareness￨U￨NN￨O￨- and￨L￨CC￨O￨- homophily￨L￨RB￨O￨- drive￨L￨VB￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- weigh￨L￨VB￨O￨- interactions￨L￨NNS￨O￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- multiplex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- influencing￨L￨VBG￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- Kermack￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- incorporated￨L￨VBD￨O￨- the￨L￨DT￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- Ross￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- proposed￨L￨VBD￨O￨- new￨L￨JJ￨O￨- and￨L￨CC￨O￨- modern￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- later￨L￨RB￨O￨- became￨L￨VBD￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- basic￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A modeling￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- serve￨L￨VB￨O￨- this￨L￨DT￨O￨- purpose￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- exploited￨L￨VBN￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- progression￨L￨NN￨O￨- ,￨L￨,￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- trend￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- tailor￨L￨NN￨TITLE￨- related￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- modeling￨L￨NN￨O￨A framework￨L￨NN￨O￨- still￨L￨RB￨O￨- plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- mosquito-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Modelers￨U￨NNS￨O￨- are￨L￨VBP￨O￨- obligated￨L￨VBN￨O￨- to￨L￨TO￨O￨- comprehend￨L￨VB￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- frameworks￨L￨NNS￨O￨A but￨L￨CC￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- behind￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Infectious￨U￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A modeling￨L￨NN￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- interdisciplinary￨L￨JJ￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +What￨U￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- of￨L￨IN￨O￨- notable￨L￨JJ￨O￨- popularity￨L￨NN￨O￨- in￨L￨IN￨O￨- big￨L￨JJ￨O￨- data￨L￨NNS￨O￨- analytics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- online￨L￨JJ￨O￨A search￨L￨NN￨O￨- queries￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 11-12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- mainly￨L￨RB￨O￨- using￨L￨VBG￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Trends￨U￨NNPS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- popular￨L￨JJ￨O￨- open￨L￨JJ￨O￨- tool￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- widely￨L￨RB￨O￨- integrated￨L￨VBN￨O￨- in￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- research￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- ,￨L￨,￨O￨- mainly￨L￨RB￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- health-related￨L￨JJ￨O￨- topics￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Google￨U￨NNP￨ORGANIZATION￨- Trends￨U￨NNPS￨ORGANIZATION￨- data￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- previously￨L￨RB￨DATE￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- valid￨L￨JJ￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- subject￨L￨NN￨O￨- has￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- the￨L￨DT￨O￨- tool￨L￨NN￨O￨- ’s￨L￨POS￨O￨- contribution￨L￨NN￨O￨- to￨L￨TO￨O￨- forecasting￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 45-46￨L￨CD￨DATE￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- online￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- provided￨L￨VBN￨O￨- careful￨L￨JJ￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- examined￨L￨VBN￨O￨- terms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- online￨L￨NN￨O￨A queries￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- “￨L￨``￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- ”￨L￨''￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- were￨L￨VBD￨O￨- analyzed￨L￨VBN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- nowcasting￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ie￨L￨FW￨O￨- ,￨L￨,￨O￨- forecasting￨L￨VBG￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- )￨L￨-RRB-￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- using￨L￨VBG￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Trends￨U￨NNPS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- if￨L￨IN￨O￨- nowcasting￨L￨JJ￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- using￨L￨VBG￨O￨- online￨L￨JJ￨O￨A search￨L￨NN￨O￨- traffic￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- further￨L￨JJ￨O￨- elaborate￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Pearson￨U￨NNP￨PERSON￨- correlations￨L￨NNS￨O￨- for￨L￨IN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Trends￨U￨NNPS￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨A “￨L￨``￨O￨- asthma￨L￨NN￨CAUSE_OF_DEATH￨- ”￨L￨''￨O￨- between￨L￨IN￨O￨- each￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- were￨L￨VBD￨O￨- calculated￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- variation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- prospects￨L￨NNS￨O￨- for￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- control￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- the￨L￨DT￨O￨- abundance￨L￨NN￨O￨- of￨L￨IN￨O￨- farms￨L￨NNS￨O￨- with￨L￨IN￨O￨- ,￨L￨,￨O￨- initially￨L￨RB￨O￨- ,￨L￨,￨O￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- frequencies￨L￨NNS￨O￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- longer￨L￨JJR￨O￨- the￨L￨DT￨O￨- breeding￨L￨VBG￨O￨- program￨L￨NN￨O￨- may￨L￨MD￨O￨- need￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- sustained￨L￨VBN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- R0￨U￨NN￨O￨- to￨L￨TO￨O￨- below￨L￨IN￨O￨- unity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- correspondingly￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- higher￨L￨JJR￨O￨- the￨L￨DT￨O￨- population-level￨L￨JJ￨O￨- minimum￨L￨NN￨O￨- ARR￨U￨NN￨O￨- allele￨L￨NN￨O￨A frequency￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- objective￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- compliance￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- long￨L￨RB￨O￨- the￨L￨DT￨O￨- ram￨L￨NN￨O￨- selection￨L￨NN￨O￨- program￨L￨NN￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- maintained￨L￨VBN￨O￨- to￨L￨TO￨O￨- reach￨L￨VB￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- ARR￨U￨NN￨O￨- allele￨L￨NN￨O￨A frequency￨L￨NN￨O￨- and￨L￨CC￨O￨- achieve￨L￨VB￨O￨- scrapie￨L￨NN￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ARR￨U￨NN￨ORGANIZATION￨- allele￨L￨NN￨O￨A for￨L￨IN￨O￨- which￨L￨WDT￨O￨- this￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- is￨L￨VBZ￨O￨- attained￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- minimum￨L￨JJ￨O￨- ARR￨U￨NN￨O￨- allele￨L￨NN￨O￨- frequency￨L￨NN￨O￨- for￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- control￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- concept￨L￨NN￨O￨- analogous￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- translate￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- within-flock￨L￨NN￨O￨- genotype￨L￨NN￨O￨- frequencies￨L￨NNS￨O￨A into￨L￨IN￨O￨- a￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- within-flock￨L￨NN￨O￨- R0￨U￨NN￨O￨- values￨L￨NNS￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- turn￨L￨NN￨O￨- serves￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- between-flock￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- calculation￨L￨NN￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- for￨L￨IN￨O￨- scrapie￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- quantification￨L￨NN￨O￨A of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- important￨L￨JJ￨O￨- between-flock￨L￨NN￨O￨- heterogeneities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Centre￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Mathematical￨U￨JJ￨O￨- Modelling￨U￨NN￨O￨- of￨L￨IN￨O￨- Infectious￨U￨JJ￨O￨- Diseases￨U￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- CMMID￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- London￨U￨NNP￨ORGANIZATION￨- School￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Hygiene￨U￨NNP￨ORGANIZATION￨- &￨L￨CC￨ORGANIZATION￨- Tropical￨U￨NNP￨ORGANIZATION￨- Medicine￨U￨NNP￨ORGANIZATION￨- produced￨L￨VBD￨O￨- weekly￨L￨JJ￨SET￨- situation￨L￨NN￨O￨- reports￨L￨NNS￨O￨- presenting￨L￨VBG￨O￨- updates￨L￨NNS￨O￨- of￨L￨IN￨O￨- publicly￨L￨RB￨O￨- available￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- fits￨L￨NNS￨O￨- and￨L￨CC￨O￨- forecasts￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- experienced￨L￨VBN￨O￨- by￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- λ￨L￨NN￨O￨- =￨L￨JJ￨O￨- βI/N￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- I￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- β￨L￨VB￨O￨- the￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A rate￨L￨NN￨O￨A which￨L￨WDT￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- W￨U￨NNP￨O￨- denotes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Wiener￨U￨NNP￨O￨- process￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- σ￨L￨IN￨O￨- the￨L￨DT￨O￨- volatility￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- log-transform￨L￨NN￨O￨- ensures￨L￨VBZ￨O￨- positivity￨L￨NN￨O￨- of￨L￨IN￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨A change￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- different￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- modelled￨L￨VBD￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- used￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- trajectories￨L￨NNS￨O￨- generated￨L￨VBN￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Challenge￨U￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- forecasts￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- cases￨L￨NNS￨O￨- at￨L￨IN￨O￨- upcoming￨L￨JJ￨O￨- time￨L￨NN￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- forecasts￨L￨NNS￨O￨A in￨L￨IN￨O￨- these￨L￨DT￨O￨- situation￨L￨NN￨O￨- reports￨L￨NNS￨O￨- were￨L￨VBD￨O￨- produced￨L￨VBN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- semi-mechanistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- estimated￨L￨VBD￨O￨- waning￨L￨VBG￨O￨- immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- severe￨L￨JJ￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A as￨L￨IN￨O￨- 1.41￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- after￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- calculated￨L￨VBD￨O￨- the￨L￨DT￨O￨- age-specific￨L￨JJ￨O￨- residual￨L￨JJ￨O￨- protection￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- persons￨L￨NNS￨O￨- 40￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 69￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- by￨L￨IN￨O￨- multiplying￨L￨VBG￨O￨- that￨L￨DT￨O￨- percentage￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- years￨L￨NNS￨DURATION￨- from￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- subtracting￨L￨VBG￨O￨- it￨L￨PRP￨O￨- from￨L￨IN￨O￨- 100￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- starting￨L￨VBG￨O￨- protection￨L￨NN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- researchers￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- optimistic￨L￨JJ￨O￨- about￨L￨IN￨O￨- residual￨L￨JJ￨O￨- vaccine-induced￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- assumed￨L￨VBD￨O￨- a￨L￨DT￨O￨- case-fatality￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CFR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- nonimmune￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- a￨L￨DT￨O￨- CFR￨U￨NN￨O￨- of￨L￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- –￨L￨:￨O￨- 70￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- reemerging￨L￨VBG￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Sydney￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- New￨U￨NNP￨LOCATION￨- South￨U￨NNP￨LOCATION￨- Wales￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- large￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- histories￨L￨NNS￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- estimates￨L￨VBZ￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ’s￨L￨POS￨O￨- immunologic￨L￨JJ￨O￨- status￨L￨NN￨O￨- .￨L￨.￨O￨- +Characteristics￨U￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- ,￨L￨,￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- NY￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- USA￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Sydney￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- New￨U￨NNP￨LOCATION￨- South￨U￨NNP￨LOCATION￨- Wales￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Australia￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- New￨U￨NNP￨STATE_OR_PROVINCE￨- York￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- healthy￨L￨JJ￨O￨- population￨L￨NN￨O￨- 40￨L￨CD￨NUMBER￨A –￨L￨:￨O￨- 69￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- vaccinated￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- severity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- H1N1￨U￨NN￨O￨- 2009￨L￨CD￨DATE￨- pandemic￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- assessed￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- dimensionless￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- representing￨L￨VBG￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibility￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- inversely￨L￨RB￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- affinity￨L￨NN￨O￨- epitopes￨L￨NNS￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- individual￨L￨JJ￨O￨- presents￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- viral￨L￨JJ￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- qualitatively￨L￨RB￨O￨- reproduce￨L￨VB￨O￨- some￨L￨DT￨O￨- known￨L￨JJ￨O￨- trends￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +Incorporating￨U￨VBG￨O￨- such￨L￨JJ￨O￨- individual-level￨L￨JJ￨O￨- immunological￨L￨JJ￨O￨- information￨L￨NN￨O￨- into￨L￨IN￨O￨- population-level￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨A or￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- heterogeneities￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- recently￨L￨RB￨DATE￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- for￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- predict￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨- using￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- 61￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- ethnicities￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- for￨L￨IN￨O￨- 81￨L￨CD￨NUMBER￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 85￨L￨CD￨NUMBER￨A Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- genome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- hence￨L￨RB￨O￨- proteome￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- sequence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- prior￨L￨JJ￨O￨- belief￨L￨NN￨O￨- ascribed￨L￨VBN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- equal￨L￨JJ￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- measure￨L￨NN￨O￨- forms￨L￨VBZ￨O￨- the￨L￨DT￨O￨- sole￨L￨JJ￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- Bayesian￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- selection￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- ranking￨L￨NN￨O￨- of￨L￨IN￨O￨- competing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- evidence￨L￨NN￨O￨A identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- unbiased￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- evidence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- which￨L￨WDT￨O￨- converges￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- evidence￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- samples￨L￨NNS￨O￨- N￨U￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- electronic￨L￨JJ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- appendix￨L￨NN￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- expression￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- deviance￨L￨NN￨O￨- information￨L￨NN￨O￨- criterion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DIC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- approximate￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨A selection￨L￨NN￨O￨A method￨L￨NN￨O￨- which￨L￨WDT￨O￨- tries￨L￨VBZ￨O￨- to￨L￨TO￨O￨- explicitly￨L￨RB￨O￨- balance￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- complexity￨L￨NN￨O￨- with￨L￨IN￨O￨- fit￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- calculates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- evidence￨L￨NN￨O￨A by￨L￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- generating￨L￨VBG￨O￨- samples￨L￨NNS￨O￨- from￨L￨IN￨O￨- K￨U￨NNP￨O￨- separate￨L￨JJ￨O￨- MCMC￨U￨NN￨O￨- chains￨L￨NNS￨O￨- at￨L￨IN￨O￨- different￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- temperatures￨L￨NNS￨O￨- ϕ1￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- ϕ2￨L￨NN￨O￨- >￨L￨JJR￨O￨- …￨L￨:￨O￨- >￨L￨JJR￨O￨- ϕ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- ‘￨L￨``￨O￨- observed￨L￨VBN￨O￨A data￨L￨NNS￨O￨A likelihood￨L￨NN￨O￨- ’￨L￨''￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- |￨L￨CD￨NUMBER￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- observed￨L￨VBN￨O￨- data￨L￨NNS￨O￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- latent￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- x￨L￨CC￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- θ￨L￨VBP￨O￨- .￨L￨.￨O￨- +Sasaki￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- his￨L￨PRP$￨O￨- collaborators￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- used￨L￨VBD￨O￨- an￨L￨DT￨O￨- intra-host￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- –￨L￨:￨O￨- antibodies￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- or￨L￨CC￨O￨- continuous￨L￨JJ￨O￨- one-dimensional￨L￨JJ￨O￨- strain￨L￨NN￨O￨- space￨L￨NN￨O￨A to￨L￨TO￨O￨- study￨L￨VB￨O￨- antigenic￨L￨JJ￨O￨- drift￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- virus￨L￨NN￨O￨- co-evolution￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- suggested￨L￨VBD￨O￨- an￨L￨DT￨O￨- elegant￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- within-host￨L￨JJ￨O￨- RNA￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- evolution￨L￨NN￨O￨- where￨L￨WRB￨O￨- virus￨L￨NN￨O￨- types￨L￨NNS￨O￨- were￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- distributed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- one-dimensional￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- space￨L￨NN￨O￨A according￨L￨VBG￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- fitness￨L￨NN￨O￨- .￨L￨.￨O￨- +Probably￨U￨RB￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- direction￨L￨NN￨O￨- was￨L￨VBD￨O￨- done￨L￨VBN￨O￨- by￨L￨IN￨O￨- Pease￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- formulated￨L￨VBD￨O￨- a￨L￨DT￨O￨- simplistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- inter-host￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- evolution￨L￨NN￨O￨A to￨L￨TO￨O￨- study￨L￨VB￨O￨- evolutionary￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +Western￨U￨JJ￨O￨- Fence￨U￨NN￨O￨- Lizards￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- Sceloporus￨U￨NN￨MISC￨- occidentalis￨L￨NN￨MISC￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- with￨L￨IN￨O￨- Plasmodium￨U￨NN￨O￨- mexicanum￨L￨NN￨O￨- ,￨L￨,￨O￨- displayed￨L￨VBD￨O￨- a￨L￨DT￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- hemoglobin￨L￨NN￨O￨- concentration￨L￨NN￨O￨- and￨L￨CC￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- oxygen￨L￨NN￨O￨- consumption￨L￨NN￨O￨- following￨L￨VBG￨O￨- physical￨L￨JJ￨O￨A exertion￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- uninfected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- evidencing￨L￨VBG￨O￨- similar￨L￨JJ￨O￨- increased￨L￨VBN￨O￨- reliance￨L￨NN￨O￨- on￨L￨IN￨O￨- anaerobic￨L￨JJ￨O￨- metabolism￨L￨NN￨O￨- and￨L￨CC￨O￨- greater￨L￨JJR￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- energy￨L￨NN￨O￨- should￨L￨MD￨O￨- become￨L￨VB￨O￨- limiting￨L￨VBG￨O￨- primarily￨L￨RB￨O￨- in￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- protective￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- activity￨L￨NN￨O￨A and￨L￨CC￨O￨- pathogenesis￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- less￨L￨RBR￨O￨- so￨L￨RB￨O￨- of￨L￨IN￨O￨- tolerant￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- trade-offs￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- therefore￨L￨RB￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- be￨L￨VB￨O￨- apparent￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- wild￨L￨JJ￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- metabolic￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- expected￨L￨VBN￨O￨- to￨L￨TO￨O￨- impair￨L￨VB￨O￨- the￨L￨DT￨O￨- physical￨L￨JJ￨O￨- activity￨L￨NN￨O￨A of￨L￨IN￨O￨- Plasmodium-infected￨U￨JJ￨MISC￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- accordingly￨L￨RB￨O￨- ,￨L￨,￨O￨- classical￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- include￨L￨VBP￨O￨- muscle￨L￨NN￨O￨- aches￨L￨NNS￨O￨- ,￨L￨,￨O￨- contractures￨L￨NNS￨O￨- ,￨L￨,￨O￨- fatigue￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- weakness￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- no￨L￨DT￨O￨- association￨L￨NN￨O￨- between￨L￨IN￨O￨- Plasmodium￨U￨NN￨LOCATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- status￨L￨NN￨O￨- and￨L￨CC￨O￨- sprint￨L￨NN￨O￨- speed￨L￨NN￨O￨- in￨L￨IN￨O￨- western￨L￨JJ￨O￨A fence￨L￨NN￨O￨- lizards￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- locomotor￨L￨NN￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- Spiny￨U￨NNP￨O￨- lizards￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Sceloporus￨U￨NN￨O￨- jarrovii￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- natural￨L￨JJ￨O￨- Plasmodium￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- were￨L￨VBD￨O￨- found￨L￨VBN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- reduced￨L￨VBN￨O￨- stamina￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- western￨L￨JJ￨O￨A fence￨L￨NN￨O￨- and￨L￨CC￨O￨- rainbow￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Agama￨U￨NN￨O￨- agama￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- lizards￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- assumptions￨L￨NNS￨O￨- Y1￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- Y6￨U￨NN￨O￨- lead￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- represents￨L￨VBZ￨O￨A the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- ξ￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- without￨L￨IN￨O￨- successful￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- prenatally￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- ϕ￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- waning￨L￨VBG￨O￨- vaccine￨L￨NN￨O￨- induced￨L￨VBD￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- characteristic￨L￨NN￨O￨- of￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- epidemiological￨L￨JJ￨O￨- subclasses￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- latent￨L￨JJ￨O￨- L￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- acutely￨L￨RB￨O￨- infected￨L￨JJ￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- chronic￨L￨JJ￨O￨- carrier￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- C￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBN￨O￨- with￨L￨IN￨O￨- permanent￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- acute￨L￨JJ￨O￨- and￨L￨CC￨O￨- chronic￨L￨JJ￨O￨- carrier￨L￨NN￨O￨- infected￨L￨JJ￨O￨- subclasses￨L￨NNS￨O￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- acute￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- chronic￨L￨JJ￨O￨- carrier￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- epidemiological￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- and￨L￨CC￨O￨- retrieve￨L￨VB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- section￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- name￨L￨VB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- shall￨L￨MD￨O￨- return￨L￨VB￨O￨- :￨L￨:￨O￨- Historically￨U￨NNP￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- settlements￨L￨NNS￨O￨- followed￨L￨VBD￨O￨- the￨L￨DT￨O￨- river￨L￨NN￨TITLE￨- networks￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- water￨L￨NN￨O￨- resources￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- River￨U￨NN￨TITLE￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- home￨L￨NN￨O￨- to￨L￨TO￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- provide￨L￨VB￨O￨- hierarchical￨L￨JJ￨O￨- habitat￨L￨NN￨O￨- features￨L￨NNS￨O￨A for￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- freshwater￨L￨NN￨O￨- fish￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- stream￨L￨NN￨O￨- ecology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- pathways￨L￨NNS￨O￨- to￨L￨TO￨O￨- life-threatening￨L￨JJ￨O￨- waterborne￨L￨JJ￨O￨- human￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- zoonoses￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- passed￨L￨VBN￨O￨- between￨L￨IN￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- humans￨L￨NNS￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- angle￨L￨NN￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- such￨L￨JJ￨O￨- features￨L￨NNS￨O￨A could￨L￨MD￨O￨- be￨L￨VB￨O￨- looked￨L￨VBN￨O￨- at￨L￨IN￨O￨- is￨L￨VBZ￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- linkages￨L￨NNS￨O￨- among￨L￨IN￨O￨- macroecological￨L￨JJ￨O￨- ‘￨L￨``￨O￨- laws￨L￨NNS￨O￨- ’￨L￨''￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- scaling￨L￨VBG￨O￨- theory￨L￨NN￨O￨- offers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- powerful￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- way￨L￨NN￨O￨- for￨L￨IN￨O￨- coherent￨L￨JJ￨O￨- ,￨L￨,￨O￨- unified￨L￨JJ￨O￨- descriptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- species￨L￨NNS￨O￨- ’￨L￨POS￨O￨- numbers￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- abundance￨L￨NN￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- remarkable￨L￨JJ￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- some￨L￨DT￨O￨- emerging￨L￨VBG￨O￨- features￨L￨NNS￨O￨A ,￨L￨,￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- ’￨L￨POS￨O￨- persistence￨L￨NN￨O￨- times￨L￨NNS￨O￨- at￨L￨IN￨O￨- observation￨L￨NN￨O￨- sites￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- controlled￨L￨VBN￨O￨- more￨L￨RBR￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- landscape￨L￨NN￨O￨- where￨L￨WRB￨O￨- interactions￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- than￨L￨IN￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- features￨L￨NNS￨O￨- specific￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- ecosystem￨L￨NN￨O￨- .￨L￨.￨O￨- +River￨U￨NNP￨TITLE￨- networks￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- also￨L￨RB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- meta-ecosystems￨L￨NNS￨O￨- that￨L￨WDT￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- metabolism￨L￨NN￨O￨- of￨L￨IN￨O￨- terrestrial￨L￨JJ￨O￨- organic￨L￨JJ￨O￨- carbon￨L￨NN￨O￨- in￨L￨IN￨O￨- freshwater￨L￨NN￨O￨- ecosystems￨L￨NNS￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- carbon￨L￨NN￨O￨- cycle￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- nutrients￨L￨NNS￨O￨- removed￨L￨VBN￨O￨- from￨L￨IN￨O￨- streams￨L￨NNS￨O￨- and￨L￨CC￨O￨- reservoirs￨L￨NNS￨O￨- ,￨L￨,￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- stream￨L￨NN￨O￨- ecology￨L￨NN￨O￨A therein￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Within￨U￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- ecohydrological￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- river￨L￨NN￨TITLE￨- network￨L￨NN￨O￨A structures￨L￨NNS￨O￨A and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- embedded￨L￨JJ￨O￨- hydrologic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- play￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- are￨L￨VBP￨O￨- strong￨L￨JJ￨O￨- ,￨L￨,￨O￨- chance￨L￨NN￨O￨- may￨L￨MD￨O￨- allow￨L￨VB￨O￨- some￨L￨DT￨O￨- virus￨L￨NN￨O￨- strains￨L￨NNS￨O￨- to￨L￨TO￨O￨- replicate￨L￨VB￨O￨- and￨L￨CC￨O￨- survive￨L￨VB￨O￨- while￨L￨IN￨O￨- others￨L￨NNS￨O￨- go￨L￨VBP￨O￨- extinct￨L￨JJ￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- drift￨L￨NN￨O￨A that￨L￨IN￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- "￨L￨``￨O￨- replicative￨L￨JJ￨O￨- drift￨L￨NN￨O￨- .￨L￨.￨O￨- "￨L￨''￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- generated￨L￨VBD￨O￨- quantitative￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- hypotheses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- HPAIVs￨U￨NNS￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨A hosts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- unlikely￨L￨JJ￨O￨- owing￨L￨NN￨O￨- to￨L￨TO￨O￨- unobserved￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- suppress￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- highly￨L￨RB￨O￨- pathogenic￨L￨JJ￨O￨- phenotypes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- testing￨L￨VBG￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- that￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- bird￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- HPAIV￨U￨NN￨O￨- poultry￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- self‐sustaining￨L￨VBG￨O￨- and￨L￨CC￨O￨- require￨L￨VB￨O￨- viral￨L￨JJ￨O￨- input￨L￨NN￨O￨- from￨L￨IN￨O￨- wild￨L￨JJ￨O￨- birds￨L￨NNS￨O￨- by￨L￨IN￨O￨- testing￨L￨VBG￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- that￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- domestic￨L￨JJ￨O￨- bird￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- reassortment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fully￨L￨RB￨O￨- Eurasian￨U￨JJ￨MISC￨- H5N8￨U￨NN￨O￨- with￨L￨IN￨O￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- LPAIVs￨U￨NNS￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- the￨L￨DT￨O￨- EA/NA￨U￨NN￨O￨- H5N2￨U￨NN￨O￨- provided￨L￨VBD￨O￨- a￨L￨DT￨O￨- fitness￨L￨NN￨O￨- advantage￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- reassortant￨L￨NN￨O￨- AIV￨U￨NN￨O￨- by￨L￨IN￨O￨- testing￨L￨VBG￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- that￨L￨WDT￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- EA/NA￨U￨NN￨O￨- H5N2￨U￨NN￨O￨- >￨L￨JJR￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- EA￨U￨NN￨ORGANIZATION￨- H5N8￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- North￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- wild￨L￨JJ￨O￨- bird￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- isolates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- tips￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨- tree￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- annotated￨L￨JJ￨O￨- with￨L￨IN￨O￨- strain￨L￨NN￨O￨- name￨L￨NN￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- IRD￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- sample￨L￨NN￨O￨- collection￨L￨NN￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- type￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- wild￨L￨JJ￨O￨A bird￨L￨NN￨O￨- or￨L￨CC￨O￨- poultry/domestic￨L￨JJ￨O￨- bird￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- state￨L￨NN￨O￨- or￨L￨CC￨O￨- province￨L￨NN￨O￨- of￨L￨IN￨O￨- collection￨L￨NN￨O￨- ,￨L￨,￨O￨- viral￨L￨JJ￨O￨- subtype￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- HA￨U￨NNP￨O￨- and￨L￨CC￨O￨- Neuraminidase￨U￨NNP￨MISC￨- [￨L￨-LRB-￨O￨- N￨U￨NNP￨O￨- ]￨L￨-RRB-￨O￨- combination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sequence￨L￨NN￨O￨- accession￨L￨NN￨O￨- identifier￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- S1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- modeled￨L￨VBD￨O￨- the￨L￨DT￨O￨- phylodynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- clade￨L￨NN￨O￨- 2.3.4.4￨L￨CD￨NUMBER￨- HA￨U￨NNP￨O￨- ,￨L￨,￨O￨- PB2￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- M￨U￨NN￨O￨- segments￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- multitype￨L￨JJ￨O￨- birth￨L￨NN￨O￨- –￨L￨:￨O￨- death￨L￨NN￨O￨- process￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- time‐rooted￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨A tree￨L￨NN￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- make￨L￨VB￨O￨- inference￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- segment￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- sampling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- viral￨L￨JJ￨O￨- migration￨L￨NN￨O￨- between￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- types￨L￨NNS￨O￨- using￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- nested￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- analysis￨L￨NN￨O￨- used￨L￨VBD￨O￨- all￨L￨DT￨O￨- isolated￨L￨VBN￨O￨- sequences￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- HA￨U￨NNP￨O￨- ,￨L￨,￨O￨- PB2￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- M￨U￨NN￨O￨- segments￨L￨NNS￨O￨- ,￨L￨,￨O￨- separately￨L￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- among￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- types￨L￨NNS￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- wild￨L￨JJ￨O￨A bird￨L￨NN￨O￨- or￨L￨CC￨O￨- poultry/domestic￨L￨JJ￨O￨- bird￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- once￨L￨RB￨DATE￨- sampled￨L￨VBN￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- virus￨L￨NN￨O￨- was￨L￨VBD￨O￨- removed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- because￨L￨IN￨O￨- wild￨L￨JJ￨O￨A bird￨L￨NN￨O￨- sampling￨L￨NN￨O￨- was￨L￨VBD￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- mortality￨L￨NN￨O￨- event￨L￨NN￨O￨- or￨L￨CC￨O￨- hunter￨L￨NN￨TITLE￨- harvest￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- operations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- high￨L￨JJ￨O￨- biosecurity￨L￨NN￨O￨- and￨L￨CC￨O￨- depopulation￨L￨NN￨O￨- once￨L￨RB￨DATE￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- detected￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- isolate￨L￨NN￨O￨- was￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨A the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- meningitis￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- nine￨L￨CD￨NUMBER￨- African￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- by￨L￨IN￨O￨- adopting￨L￨VBG￨O￨- some￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- wavelet￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- studies￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- “￨L￨``￨O￨- international￨L￨JJ￨O￨- cooperation￨L￨NN￨O￨- in￨L￨IN￨O￨- Public￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- and￨L￨CC￨O￨- cross￨L￨VB￨O￨- disciplines￨L￨NNS￨O￨- studies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- recommended￨L￨VBN￨O￨- to￨L￨TO￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- this￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- ”￨L￨''￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- meningococcal￨L￨JJ￨O￨- meningitis￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- cellular￨L￨JJ￨O￨- automata￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- was￨L￨VBD￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- five￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- asymptomatic￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- with￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨A ,￨L￨,￨O￨- carriers￨L￨NNS￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- died￨L￨VBD￨O￨- classes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- bacterial￨L￨JJ￨O￨- meningitis￨L￨NN￨CAUSE_OF_DEATH￨- becomes￨L￨VBZ￨O￨- worse￨L￨JJR￨O￨- when￨L￨WRB￨O￨- symptoms￨L￨NNS￨O￨A are￨L￨VBP￨O￨- not￨L￨RB￨O￨- detected￨L￨VBN￨O￨- early￨L￨RB￨O￨- enough￨L￨RB￨O￨- ;￨L￨:￨O￨- even￨L￨RB￨O￨- with￨L￨IN￨O￨- proper￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- could￨L￨MD￨O￨- die￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Those￨U￨DT￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- people￨L￨NNS￨O￨- tend￨L￨VBP￨O￨- to￨L￨TO￨O￨- mix￨L￨VB￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- own￨L￨JJ￨O￨- age￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- assortative￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- intergenerational￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- mixing￨L￨VBG￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- vary￨L￨VB￨O￨- between￨L￨IN￨O￨- settings￨L￨NNS￨O￨A ,￨L￨,￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- household￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- others￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Variation￨U￨NN￨O￨- in￨L￨IN￨O￨- Wolbachia￨U￨JJ￨LOCATION￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- Aedes￨U￨NNS￨O￨- mosquitoes￨L￨NNS￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- invasiveness￨L￨NN￨O￨- and￨L￨CC￨O￨- vectorial￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- Jessica￨U￨NNP￨PERSON￨- G.￨U￨NNP￨PERSON￨- Studies￨U￨NNS￨PERSON￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- certain￨L￨JJ￨O￨- Wolbachia￨U￨JJ￨O￨- strains￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- wMel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- reduce￨L￨VB￨O￨- replication￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- laboratory￨L￨NN￨O￨- ,￨L￨,￨O￨- prompting￨L￨VBG￨O￨- the￨L￨DT￨O￨- release￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- carrying￨L￨VBG￨O￨- the￨L￨DT￨O￨- bacterium￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- vectorial￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- realistically￨L￨RB￨O￨- assessed￨L￨VBN￨O￨- in￨L￨IN￨O￨- relation￨L￨NN￨O￨- to￨L￨TO￨O￨- native￨L￨JJ￨O￨- non-carriers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- applied￨L￨VBD￨O￨- a￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- developed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- back-calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨A Chinese￨U￨JJ￨NATIONALITY￨- workers￨L￨NNS￨O￨- in￨L￨IN￨O￨- Angola￨U￨NNP￨COUNTRY￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- extent￨L￨NN￨O￨- of￨L￨IN￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- 11￨L￨CD￨NUMBER￨- unvaccinated￨L￨JJ￨O￨A Chinese￨U￨JJ￨NATIONALITY￨- workers￨L￨NNS￨O￨- acquired￨L￨VBD￨O￨- yellow￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- many￨L￨JJ￨O￨- more￨L￨JJR￨O￨- Chinese￨U￨JJ￨NATIONALITY￨- workers￨L￨NNS￨O￨- in￨L￨IN￨O￨- Angola￨U￨NNP￨COUNTRY￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- vaccinated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Estimating￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨A Chinese￨U￨JJ￨NATIONALITY￨- workers￨L￨NNS￨O￨- against￨L￨IN￨O￨- yellow￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- AngolaA￨U￨NNP￨O￨- .￨L￨.￨O￨- +Eleven￨U￨CD￨NUMBER￨- unvaccinated￨L￨JJ￨O￨A Chinese￨U￨JJ￨NATIONALITY￨- nationals￨L￨NNS￨O￨- working￨L￨VBG￨O￨- in￨L￨IN￨O￨- Angola￨U￨NNP￨COUNTRY￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- imported￨L￨VBN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- presenting￨L￨VBG￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- importation￨L￨NN￨O￨- of￨L￨IN￨O￨- yellow￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- into￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- models￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- none￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 259,000￨L￨CD￨NUMBER￨- Chinese￨U￨NNP￨NATIONALITY￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- vaccinated￨L￨VBN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- yellow￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- mandated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- International￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- Regulations￨U￨NNPS￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- inequality￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- preventive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- in￨L￨IN￨O￨- rural￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- deforestation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- geographical￨L￨JJ￨O￨A diversity￨L￨NN￨O￨- allow￨L￨VBP￨O￨- the￨L￨DT￨O￨- circulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- array￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- in￨L￨IN￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- 30￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 32￨L￨CD￨NUMBER￨- departments￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- program￨L￨NN￨O￨- gathers￨L￨VBZ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- country￨L￨NN￨O￨A ,￨L￨,￨O￨- continually￨L￨RB￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ’s￨L￨POS￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- producing￨L￨VBG￨O￨- regional￨L￨JJ￨O￨- indicators￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Closer￨U￨JJR￨O￨- examination￨L￨NN￨O￨- of￨L￨IN￨O￨- TL￨U￨NN￨O￨- behavior￨L￨NN￨O￨- by￨L￨IN￨O￨- geographical￨L￨JJ￨O￨A region￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- Amazon￨U￨NNP￨LOCATION￨- region￨L￨NN￨O￨- exhibits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- observed￨L￨VBN￨O￨- periods￨L￨NNS￨O￨- .￨L￨.￨O￨- +Standardized￨U￨JJ￨O￨- Incidence￨U￨NN￨O￨- Ratios￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- calculated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Colombia￨U￨NNP￨COUNTRY￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨A considered￨L￨VBN￨O￨- using￨L￨VBG￨O￨- Empirical￨U￨NNP￨O￨- Bayes￨U￨NNP￨PERSON￨- smoothing￨L￨VBG￨O￨- method￨L￨NN￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- Clayton￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Kaldor￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- efficient￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- computational￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- pairwise￨L￨JJ￨O￨- calculations￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- ,￨L￨,￨O￨- whereby￨L￨WRB￨O￨- the￨L￨DT￨O￨- distances￨L￨NNS￨O￨- between￨L￨IN￨O￨- every￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- farms￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- calculated￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- kernel￨L￨NN￨O￨A must￨L￨MD￨O￨- be￨L￨VB￨O￨- evaluated￨L￨VBN￨O￨- for￨L￨IN￨O￨- those￨L￨DT￨O￨- distances￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- estimation￨L￨NN￨O￨- process￨L￨NN￨O￨- formulates￨L￨VBZ￨O￨- an￨L￨DT￨O￨- equation￨L￨NN￨O￨- that￨L￨WDT￨O￨- approximates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expected￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- kernel￨L￨NN￨O￨- evaluations￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- average￨L￨JJ￨O￨- grid￨L￨NN￨O￨A cell￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- expressed￨L￨VBN￨O￨- as￨L￨IN￨O￨- farms￨L￨NNS￨O￨- per￨L￨IN￨O￨- cell￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- subsequently￨L￨RB￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- θ￨L￨NN￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- fewest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- kernel￨L￨NN￨O￨- calls￨L￨NNS￨O￨- are￨L￨VBP￨O￨- predicted￨L￨VBN￨O￨- .￨L￨.￨O￨- +Keeling￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Rohani￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- introduced￨L￨VBD￨O￨- another￨L￨DT￨O￨- technique￨L￨NN￨O￨- ,￨L￨,￨O￨- hereafter￨L￨RB￨O￨- denoted￨L￨VBN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- entry￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- pattern￨L￨NN￨O￨- landscape￨L￨NN￨O￨- of￨L￨IN￨O￨- farm￨L￨NN￨O￨- locations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- overlaid￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- grid￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- split￨L￨VBN￨O￨- up￨L￨RB￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- steps￨L￨NNS￨O￨- :￨L￨:￨O￨- Does￨U￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- possibly￨L￨RB￨O￨- enter￨L￨VB￨O￨- the￨L￨DT￨O￨- grid￨L￨NN￨O￨- cell￨L￨NN￨O￨- ?￨L￨.￨O￨- +From￨U￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- farm￨L￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- red￨L￨JJ￨O￨- star￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- cell￨L￨NN￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- evaluated￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- entire￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- grid￨L￨NN￨O￨A cells￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- occasionally￨L￨RB￨O￨- evaluated￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- green￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Secondly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- grid￨L￨NN￨O￨A size￨L￨NN￨O￨- estimation￨L￨NN￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- determining￨L￨VBG￨O￨- a￨L￨DT￨O￨- grid￨L￨NN￨O￨- size￨L￨NN￨O￨- configuration￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- conditional￨L￨JJ￨O￨- subsample￨L￨NN￨O￨- and￨L￨CC￨O￨- conditional￨L￨JJ￨O￨- entry￨L￨NN￨O￨- algorithms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- ensures￨L￨VBZ￨O￨- fast￨L￨JJ￨O￨- computation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- its￨L￨PRP$￨O￨- performance￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- conclusions￨L￨NNS￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- implications￨L￨NNS￨O￨- drawn￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- many￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- depicting￨L￨VBG￨O￨- nosocomial￨L￨JJ￨O￨- MRSA￨U￨NNP￨O￨- transmission￨L￨NN￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- settings￨L￨NNS￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- mitigate￨L￨VB￨O￨- such￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- first￨L￨RB￨ORDINAL￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- delineate￨L￨VB￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sylvatic￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨A vectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- CHIKV￨U￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- shape￨L￨VBP￨O￨- these￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- association￨L￨NN￨O￨- of￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- presence￨L￨NN￨O￨- with￨L￨IN￨O￨- key￨L￨JJ￨O￨- drivers￨L￨NNS￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- spillover￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- mosquito￨L￨NN￨O￨- and￨L￨CC￨O￨- CHIKV￨U￨NN￨O￨- abundance￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Ecological￨U￨NNP￨MISC￨- niche￨L￨NN￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- Aedes￨U￨NNP￨O￨- mosquito￨L￨NN￨O￨A vectors￨L￨NNS￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- southeastern￨L￨JJ￨O￨- SenegalRebecca￨U￨NN￨O￨- Richman1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Diawo￨U￨NNP￨O￨- Diallo3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Mawlouth￨U￨NNP￨O￨- Diallo3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Amadou￨U￨NNP￨PERSON￨- A.￨U￨NNP￨O￨- 2018Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Chikungunya￨U￨NNP￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- originated￨L￨VBD￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- sylvatic￨L￨JJ￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- non-human￨L￨JJ￨O￨- animal￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- mosquitoes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- forests￨L￨NNS￨O￨- of￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- therefore￨L￨RB￨O￨- modeled￨L￨VBD￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- CHIKV￨U￨NN￨O￨- mosquito￨L￨NN￨O￨A vectors￨L￨NNS￨O￨- over￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- sequential￨L￨JJ￨O￨- rainy￨L￨JJ￨O￨- seasons￨L￨NNS￨O￨- in￨L￨IN￨O￨- Kédougou￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Senegal￨U￨NNP￨COUNTRY￨- using￨L￨VBG￨O￨- Maxent￨U￨NNP￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Mosquito￨U￨NNP￨O￨- data￨L￨NNS￨O￨- were￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- in￨L￨IN￨O￨- fifty￨L￨CD￨NUMBER￨- sites￨L￨NNS￨O￨- distributed￨L￨VBN￨O￨- in￨L￨IN￨O￨- five￨L￨CD￨NUMBER￨- land￨L￨NN￨O￨A cover￨L￨NN￨O￨- classes￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- area￨L￨NN￨O￨- .￨L￨.￨O￨- +Genetic￨U￨JJ￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- pairs￨L￨NNS￨O￨- in￨L￨IN￨O￨- large￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- sequence￨L￨NN￨O￨- databases￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- and￨L￨CC￨O￨- scalable￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- characterizing￨L￨VBG￨O￨- transmission￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- genetic￨L￨JJ￨O￨- clustering￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- unreliable￨L￨JJ￨O￨- proxy￨L￨NN￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- inferences￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- clusters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- biased￨L￨VBN￨O￨- by￨L￨IN￨O￨- correlations￨L￨NNS￨O￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- sampling￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +HIV￨U￨NN￨CAUSE_OF_DEATH￨- genetic￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- routine￨L￨JJ￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- testing￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- few￨L￨JJ￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- widely￨L￨RB￨O￨- available￨L￨JJ￨O￨- observational￨L￨JJ￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- directly￨L￨RB￨O￨- informative￨L￨JJ￨O￨- about￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨A patterns￨L￨NNS￨O￨A and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- See￨U￨VB￨O￨- the￨L￨DT￨O￨- The￨U￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PHIs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- com￨L￨NN￨O￨- bat￨L￨NN￨O￨- human￨L￨JJ￨O￨- immunodeficiency￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- pre-exposure￨L￨JJ￨O￨- prophylaxis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PrEP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- antiretroviral￨L￨JJ￨O￨- medications￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ARVs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- unknown￨L￨JJ￨O￨- variability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- longer￨L￨JJR￨O￨- evolutionary￨L￨JJ￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- populations￨L￨NNS￨O￨- or￨L￨CC￨O￨- risk￨L￨NN￨O￨A groups￨L￨NNS￨O￨- with￨L￨IN￨O￨- higher￨L￨JJR￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- will￨L￨MD￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- paraphyletic￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- with￨L￨IN￨O￨- populations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- primarily￨L￨RB￨O￨- recipients￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨A is￨L￨VBZ￨O￨- highly￨L￨RB￨O￨- variable￨L￨JJ￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- between￨L￨IN￨O￨- risk￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- geographically￨L￨RB￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Simulating￨U￨VBG￨O￨- SIR￨U￨NN￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- weighted￨L￨JJ￨O￨- shortest￨L￨JJS￨O￨A paths￨L￨NNS￨O￨- Dijana￨U￨NNP￨PERSON￨- Tolić1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Kaj-Kolja￨U￨NNP￨O￨- Kleineberg2￨U￨NNP￨O￨- &￨L￨CC￨O￨- Nino￨U￨NNP￨O￨- Antulov-Fantulin2￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 6562￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- science￨L￨NN￨O￨- AbstractWe￨U￨NN￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- SIR￨U￨NN￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- weighted￨L￨JJ￨O￨- shortest￨L￨JJS￨O￨- paths￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- different￨L￨JJ￨O￨- approximations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- neglecting￨L￨VBG￨O￨- dynamical￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- statistical￨L￨JJ￨O￨- independence￨L￨NN￨O￨- at￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- neighbourhood￨L￨NN￨O￨- ,￨L￨,￨O￨- pair￨L￨NN￨O￨- or￨L￨CC￨O￨- node￨L￨NN￨O￨- level￨L￨NN￨O￨- in￨L￨IN￨O￨- mean￨L￨JJ￨O￨- field￨L￨NN￨O￨- approximations11￨L￨NN￨O￨- ,12,13,14,15,16￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- neglecting￨L￨VBG￨O￨- loops￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- with￨L￨IN￨O￨- message￨L￨NN￨O￨- passing￨L￨NN￨O￨- or￨L￨CC￨O￨- belief￨L￨NN￨O￨- propagation￨L￨NN￨O￨A techniques17￨L￨NN￨O￨- ,18,19￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- neglecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- by￨L￨IN￨O￨- mapping￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- percolation￨L￨NN￨O￨- process20￨L￨NN￨O￨- ,21,22￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- run￨L￨NN￨O￨- using￨L￨VBG￨O￨- popular￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨- inference￨L￨NN￨O￨- tools￨L￨NNS￨O￨- like￨L￨IN￨O￨- MrBayes￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- BEAST￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- take￨L￨VB￨O￨- days￨L￨NNS￨DURATION￨- or￨L￨CC￨O￨- weeks￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- CPU￨U￨NNP￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- approximate￨L￨JJ￨O￨- a￨L￨DT￨O￨- posterior￨L￨JJ￨O￨A distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- realistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2014￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- update￨L￨VB￨O￨- a￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨A tree￨L￨NN￨O￨- with￨L￨IN￨O￨- new￨L￨JJ￨O￨- sequences￨L￨NNS￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- such￨L￨JJ￨O￨- tool￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- for￨L￨IN￨O￨- Bayesian￨U￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨- inference￨L￨NN￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- each￨L￨DT￨O￨- generation￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- particles￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- a￨L￨DT￨O￨- posterior￨L￨JJ￨O￨A sample￨L￨NN￨O￨- of￨L￨IN￨O￨- trees￨L￨NNS￨O￨- on￨L￨IN￨O￨- sequences￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- updated￨L￨VBN￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- sample￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- posterior￨L￨NN￨O￨- on￨L￨IN￨O￨- sequences￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- Bayesian￨U￨JJ￨MISC￨- inference￨L￨NN￨O￨- treat￨L￨VB￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- set￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨- entity￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- entirety￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- that￨L￨WDT￨O￨- computation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- posterior￨L￨JJ￨O￨A probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- begins￨L￨VBZ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- each￨L￨DT￨O￨- particle￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- sequence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- taxon￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- attached￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- tree￨L￨NN￨O￨- using￨L￨VBG￨O￨- proposal￨L￨NN￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- weight￨L￨NN￨O￨- is￨L￨VBZ￨O￨- computed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- particles￨L￨NNS￨O￨A are￨L￨VBP￨O￨- resampled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- weights￨L￨NNS￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- supplementary￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- targeting￨L￨VBG￨O￨- fully￨L￨RB￨O￨- susceptible￨L￨JJ￨O￨- adult￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- deemed￨L￨VBN￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- herd￨L￨NN￨O￨A immunity￨L￨NN￨O￨A and￨L￨CC￨O￨- avoid￨L￨VB￨O￨- another￨L￨DT￨O￨- major￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- that￨L￨DT￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- probabilistically￨L￨RB￨O￨- decline￨L￨VB￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- burden￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- sufficiently￨L￨RB￨O￨- elevating￨L￨VBG￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- level￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- recognized￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- essential￨L￨JJ￨O￨- step￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- rubella￨L￨NN￨O￨A and￨L￨CC￨O￨- CRS￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- medically￨L￨RB￨O￨- and￨L￨CC￨O￨- economically￨L￨RB￨O￨- justify￨L￨VB￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- pitfall￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- against￨L￨IN￨O￨- rubella￨L￨NN￨O￨A is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- sufficiently￨L￨RB￨O￨- immunized￨L￨VBN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- allows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- push￨L￨NN￨O￨- forward￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- at￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- cover￨L￨VB￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- status￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- enough￨L￨JJ￨O￨- doses￨L￨NNS￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- herd￨L￨NN￨O￨A immunity￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- practice￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- to￨L￨TO￨O￨- randomly￨L￨RB￨O￨- distribute￨L￨VB￨O￨- as￨L￨RB￨O￨- many￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- rubella￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- elevated￨L￨JJ￨O￨- to￨L￨TO￨O￨- women￨L￨NNS￨O￨- at￨L￨IN￨O￨- childbearing￨L￨JJ￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- insufficient￨L￨JJ￨O￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- can￨L￨MD￨O￨- controversially￨L￨RB￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- fetus￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Applying￨U￨VBG￨O￨- MUOD￨U￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- roughly￨L￨RB￨O￨- 400￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- Google￨U￨NNP￨ORGANIZATION￨- +￨L￨CC￨O￨- users￨L￨NNS￨O￨A ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- allowed￨L￨VBN￨O￨- identifying￨L￨VBG￨O￨- and￨L￨CC￨O￨- discriminating￨L￨VBG￨O￨- automatically￨L￨RB￨O￨- sets￨L￨NNS￨O￨- of￨L￨IN￨O￨- outlier￨L￨NN￨O￨- users￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- present￨L￨JJ￨DATE￨- features￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- definitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨- users￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- capacity￨L￨NN￨O￨- to￨L￨TO￨O￨- attract￨L￨VB￨O￨- engagement￨L￨NN￨O￨- ,￨L￨,￨O￨- capacity￨L￨NN￨O￨- to￨L￨TO￨O￨- attract￨L￨VB￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- followers￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- high￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- capacity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- report￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- unsupervised￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- Massive￨U￨JJ￨O￨- Unsupervised￨U￨JJ￨O￨- Outlier￨U￨NNP￨O￨- Detection￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- MUOD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- outliers￨L￨NNS￨O￨- detection￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- providing￨L￨VBG￨O￨- support￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨- users￨L￨NNS￨O￨A .￨L￨.￨O￨- +This￨U￨DT￨O￨- allows￨L￨VBZ￨O￨- classifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- outlier￨L￨NN￨O￨- users￨L￨NNS￨O￨A in￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- different￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨- users￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 03￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Unsupervised￨U￨NNP￨O￨- Scalable￨U￨NNP￨O￨- Statistical￨U￨NNP￨O￨- Method￨U￨NNP￨O￨- for￨L￨IN￨O￨- Identifying￨U￨NNP￨O￨- Influential￨U￨NNP￨O￨- Users￨U￨NNP￨O￨- in￨L￨IN￨O￨- Online￨U￨NNP￨O￨- Social￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- A.￨U￨NNP￨O￨- Sguera5￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 6955￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComputational￨L￨NNP￨O￨- scienceComputer￨L￨NN￨O￨- scienceStatistics￨L￨NNS￨O￨- AbstractBillions￨U￨NNS￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨A interact￨L￨VBP￨O￨- intensively￨L￨RB￨O￨- every￨L￨DT￨SET￨- day￨L￨NN￨SET￨- via￨L￨IN￨O￨- Online￨U￨NNP￨O￨- Social￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- OSNs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Facebook￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Twitter￨U￨NNP￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- Google￨U￨NNP￨ORGANIZATION￨- +￨L￨CC￨O￨- .￨L￨.￨O￨- +Consider￨U￨VB￨O￨- a￨L￨DT￨O￨- physical￨L￨JJ￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- exactly￨L￨RB￨O￨- N￨U￨NN￨O￨- possible￨L￨JJ￨O￨- configurations￨L￨NNS￨O￨- and￨L￨CC￨O￨- let￨L￨VB￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- configuration￨L￨NN￨O￨A i￨L￨FW￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t.￨L￨NN￨O￨- To￨U￨TO￨O￨- formulate￨L￨VB￨O￨- the￨L￨DT￨O￨- master￨L￨JJ￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- know￨L￨VB￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- transition￨L￨NN￨O￨- p￨L￨NN￨O￨- from￨L￨IN￨O￨- configuration￨L￨NN￨O￨- i￨L￨FW￨O￨- to￨L￨TO￨O￨- configuration￨L￨NN￨O￨- j.￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- monographs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- details￨L￨NNS￨O￨- .￨L￨.￨O￨- )￨L￨-RRB-￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- treat￨L￨VBP￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- p￨L￨NN￨O￨- may￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t.￨L￨NN￨O￨- Note￨U￨VBP￨O￨- that￨L￨IN￨O￨- even￨L￨RB￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- master￨L￨NN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- then￨L￨RB￨O￨- linear￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- interest￨L￨NN￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- intimately￨L￨RB￨O￨- connected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- Markov￨U￨NNP￨PERSON￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- finite￨L￨JJ￨O￨- configuration￨L￨NN￨O￨A spaces￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨O￨- process￨L￨NN￨O￨- is￨L￨VBZ￨O￨- uniquely￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- configurations￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- transition￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- probabilities￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- configuration￨L￨NN￨O￨A i￨L￨FW￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- given￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- configuration￨L￨NN￨O￨- j￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- τ￨L￨NN￨O￨- <￨L￨JJR￨O￨- t.￨L￨CD￨NUMBER￨- +These￨U￨DT￨O￨- different￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- applications￨L￨NNS￨O￨- are￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- lattice￨L￨NN￨O￨- structure￨L￨NN￨O￨- as￨L￨IN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- network￨L￨NN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- ties￨L￨NNS￨O￨A are￨L￨VBP￨O￨- regular￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- exhaustively￨L￨RB￨O￨- complete￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- maximally￨L￨RB￨O￨- complete￨L￨JJ￨O￨- structure￨L￨NN￨O￨- as￨L￨IN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- idealized￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- free￨L￨JJ￨IDEOLOGY￨- association￨L￨NN￨IDEOLOGY￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- connect￨L￨VB￨O￨- to￨L￨TO￨O￨- all￨L￨DT￨O￨- other￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- C￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Erdõs-Rényi￨U￨NN￨O￨- generation￨L￨NN￨O￨- structure￨L￨NN￨O￨- with￨L￨IN￨O￨- every￨L￨DT￨O￨- possible￨L￨JJ￨O￨- tie￨L￨NN￨O￨- existing￨L￨VBG￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- 0.25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ties￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- graph￨L￨NN￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨DURATION￨- quarter￨L￨NN￨DURATION￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- panel￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- B￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- an￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- empirically￨L￨RB￨O￨- observed￨L￨VBN￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- primates￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- Pan￨U￨NN￨O￨- troglodytes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Instead￨U￨RB￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- basic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- fitting￨L￨JJ￨O￨- network￨L￨NN￨O￨- arrangement￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- ideal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- maximally￨L￨RB￨O￨- complete￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- uniform￨L￨JJ￨O￨- ties￨L￨NNS￨O￨A to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- effectively￨L￨RB￨O￨- free￨L￨JJ￨IDEOLOGY￨- association￨L￨NN￨IDEOLOGY￨- among￨L￨IN￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- 1B￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- shown￨L￨VBN￨O￨- through￨L￨IN￨O￨- early￨L￨JJ￨O￨- critiques￨L￨NNS￨O￨- of￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- recently￨L￨RB￨DATE￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- resurgence￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- studies￨L￨NNS￨O￨- ,￨L￨,￨O￨- interactions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- random￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- instead￨L￨RB￨O￨- structured￨L￨VBN￨O￨- along￨L￨IN￨O￨- social￨L￨JJ￨O￨- ties￨L￨NNS￨O￨A between￨L￨IN￨O￨- specific￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- affiliative￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- mating￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- social￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Effective￨U￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- models￨L￨NNS￨O￨- take￨L￨VBP￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- and￨L￨CC￨O￨- predict￨L￨VBP￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- idealized￨L￨JJ￨O￨- population￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- Fisher￨U￨NNP￨PERSON￨- –￨L￨:￨O￨- Wright￨U￨NNP￨PERSON￨- populations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- groups￨L￨NNS￨O￨- are￨L￨VBP￨O￨- of￨L￨IN￨O￨- finite￨L￨JJ￨O￨- and￨L￨CC￨O￨- fixed￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨A ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- mate￨L￨VBP￨O￨- randomly￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- generations￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- overlap￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- specific￨L￨JJ￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- sizes￨L￨NNS￨O￨A and￨L￨CC￨O￨- outbreak￨L￨NN￨O￨- durations￨L￨NNS￨O￨- for￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- per￨L￨FW￨O￨- contact￨L￨NN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Clearly￨U￨RB￨O￨- ,￨L￨,￨O￨- X￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- remains￨L￨VBZ￨O￨- within￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- ]￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- starts￨L￨VBZ￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- interval.The￨L￨NN￨O￨- asymptotic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondarily￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Equality￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- gamma￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- beta￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- characterized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- if￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- le￨L￨DT￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- Equality￨U￨NN￨O￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- X￨U￨NN￨O￨- fulfilling￨L￨VBG￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- measurable￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- sigma￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- term￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- X￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- left￨L￨VBD￨O￨- Add￨U￨VB￨O￨- N￨U￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- right￨L￨NN￨O￨- X￨U￨NN￨O￨- beta￨L￨NN￨O￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- fulfil￨L￨VB￨O￨- some￨L￨DT￨O￨- technical￨L￨JJ￨O￨- condition￨L￨NN￨O￨A like￨L￨IN￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- Lipschitz￨U￨NNP￨PERSON￨- condition￨L￨NN￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- growth￨L￨NN￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- derived￨L￨VBN￨O￨- properties￨L￨NNS￨O￨- for￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- decision￨L￨NN￨O￨A problem￨L￨NN￨O￨- of￨L￨IN￨O￨- choosing￨L￨VBG￨O￨- the￨L￨DT￨O￨- cost-optimal￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- intensity.KeywordsContagion￨L￨NN￨O￨- Asymptotic￨U￨JJ￨O￨- properties￨L￨NNS￨O￨- Markov￨U￨NNP￨PERSON￨- processes￨L￨VBZ￨O￨- Disease￨U￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- This￨U￨DT￨O￨- research￨L￨NN￨O￨- was￨L￨VBD￨O￨- funded￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Austrian￨U￨JJ￨NATIONALITY￨- Science￨U￨NNP￨MISC￨- Fund￨U￨NNP￨MISC￨- FWF￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Project￨U￨NNP￨O￨- P￨U￨NN￨O￨- 24125-N13.1￨L￨NN￨O￨- IntroductionIn￨U￨NN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simplest￨L￨JJS￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Basically￨U￨RB￨O￨- a￨L￨DT￨O￨- decision￨L￨NN￨O￨- maker￨L￨NN￨O￨- may￨L￨MD￨O￨- try￨L￨VB￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- paramters￨L￨NNS￨O￨- beta￨L￨NN￨O￨- and￨L￨CC￨O￨- gamma￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- fulfilled￨L￨VBN￨O￨- .1.2￨L￨CD￨NUMBER￨- Diffusion-type￨U￨JJ￨O￨- SIS￨U￨NN￨O￨- modelsWhile￨L￨NN￨O￨- many￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- in￨L￨IN￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- Diekmann￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Note￨U￨VB￨O￨- that￨L￨IN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- N￨U￨NNP￨O￨- Add￨U￨VB￨O￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- Y￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- it￨L￨PRP￨O￨- suffices￨L￨VBZ￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- replacing￨L￨VBG￨O￨- Y￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- Add￨U￨VB￨O￨- N￨U￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- X￨U￨NN￨O￨- t￨L￨NN￨O￨- whenever￨L￨WRB￨O￨- necessary￨L￨JJ￨O￨A .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- paradox￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- parameter￨L￨NN￨O￨- spaces￨L￨NNS￨O￨- Hengcong￨U￨JJ￨O￨- Liu1￨U￨NN￨O￨- ,￨L￨,￨O￨- Muhua￨U￨NNP￨PERSON￨- Zheng1￨U￨NNP￨O￨- &￨L￨CC￨O￨- Zonghua￨U￨NNP￨O￨- Liu1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 7517￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- science￨L￨NN￨O￨- AbstractIt￨U￨NN￨O￨- is￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- revealed￨L￨VBN￨O￨- from￨L￨IN￨O￨- amounts￨L￨NNS￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- recurrent￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- of￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- loop￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- surprisingly￨L￨RB￨O￨- find￨L￨VBP￨O￨- a￨L￨DT￨O￨- paradox￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- loop￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- rate￨L￨NN￨O￨- increment￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transient￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- contradictory￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- spaces￨L￨NNS￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- long￨L￨RB￨O￨- enough￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- here￨L￨RB￨O￨- study￨L￨VB￨O￨- this￨L￨DT￨O￨- phenomenon￨L￨NN￨O￨- directly￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- find￨L￨VB￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- loop￨L￨NN￨O￨A ,￨L￨,￨O￨- implying￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- hysteresis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- nature￨L￨NN￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- case￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transient￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- loop￨L￨NN￨O￨A will￨L￨MD￨O￨- increase￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- but￨L￨CC￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- .￨L￨.￨O￨- +That￨U￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- rate￨L￨NN￨O￨- increment￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- hysteresis￨L￨NN￨O￨- loop￨L￨NN￨O￨A will￨L￨MD￨O￨- decrease￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- but￨L￨CC￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- reachability￨L￨NN￨O￨- of￨L￨IN￨O￨- contagion￨L￨NN￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- contact￨L￨NN￨O￨A networks￨L￨NNS￨O￨A :￨L￨:￨O￨- how￨L￨WRB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- latency￨L￨NN￨O￨- can￨L￨MD￨O￨- exploit￨L￨VB￨O￨- the￨L￨DT￨O￨- rhythm￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- behaviorEwan￨L￨NN￨O￨- Colman1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Kristen￨U￨NNP￨PERSON￨- Spies1￨U￨NNP￨O￨- and￨L￨CC￨O￨- Shweta￨U￨NNP￨O￨- Bansal1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 18:219￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Peer￨U￨NNP￨O￨- Review￨U￨NNP￨O￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- symptoms￨L￨NNS￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- influence￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- withdraw￨L￨VB￨O￨- from￨L￨IN￨O￨- social￨L￨JJ￨O￨- activity￨L￨NN￨O￨- limiting￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- that￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- should￨L￨MD￨O￨- consider￨L￨VB￨O￨- contact￨L￨NN￨O￨- periodicity￨L￨NN￨O￨- in￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- suggest￨L￨VBP￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- that￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- optimize￨L￨VB￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- synchronization￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- maximum￨L￨NN￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- results￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- the￨L￨DT￨O￨- generation￨L￨NN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- synchronized￨L￨VBN￨O￨- with￨L￨IN￨O￨- human￨L￨JJ￨O￨- circadian￨L￨JJ￨O￨- rhythms￨L￨NNS￨O￨- of￨L￨IN￨O￨- 24￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- minimum￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- when￨L￨WRB￨O￨- latent￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- phase￨L￨NN￨O￨- with￨L￨IN￨O￨- circadian￨L￨JJ￨O￨- rhythms￨L￨NNS￨O￨- by￨L￨IN￨O￨- 12￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨A that￨L￨WDT￨O￨- incorporate￨L￨VBP￨O￨- behavioral￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- that￨L￨WDT￨O￨- effectively￨L￨RB￨O￨- shorten￨L￨VB￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +Initial￨U￨JJ￨O￨- analyses￨L￨NNS￨O￨- and￨L￨CC￨O￨- forecasts￨L￨NNS￨O￨- were￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- case￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- January￨U￨NNP￨DATE￨- 23￨L￨CD￨DATE￨- to￨L￨TO￨O￨- March￨U￨NNP￨DATE￨- 29￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2015￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- week￨L￨NN￨DURATION￨A 13￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- year￨L￨NN￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- term￨L￨VBP￨O￨- the￨L￨DT￨DATE￨- Week￨U￨NN￨DATE￨- 13￨L￨CD￨NUMBER￨- report￨L￨NN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- forecasts￨L￨NNS￨O￨- was￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- through￨L￨IN￨O￨- April￨U￨NNP￨DATE￨- 26￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2015￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- week￨L￨NN￨DURATION￨- 17￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- termed￨L￨VBN￨O￨- the￨L￨DT￨DATE￨- Week￨U￨NN￨DATE￨- 17￨L￨CD￨NUMBER￨- report￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aims￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- analysis￨L￨NN￨O￨- were￨L￨VBD￨O￨- 2-fold￨L￨JJ￨O￨- :￨L￨:￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A susceptibility￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- expected￨L￨JJ￨O￨- future￨L￨JJ￨DATE￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Lola￨U￨NNP￨CITY￨- prefecture￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- color￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- subprefecture￨L￨NN￨O￨- coincides￨L￨VBZ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- up￨L￨IN￨DURATION￨- to￨L￨TO￨DURATION￨- week￨L￨NN￨DURATION￨A 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Comparing￨U￨VBG￨O￨- TOL￨U￨NN￨O￨- to￨L￨TO￨O￨- conventional￨L￨JJ￨O￨- treatment￨L￨NN￨O￨A ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- load￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ROL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- ,￨L￨,￨O￨- acute￨L￨JJ￨O￨- and￨L￨CC￨O￨- chronic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- ROL￨U￨NN￨O￨- always￨L￨RB￨O￨- outperforms￨L￨VBZ￨O￨- TOL￨U￨NN￨O￨- even￨L￨RB￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- that￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- resistance￨L￨NN￨O￨- can￨L￨MD￨O￨- emerge￨L￨VB￨O￨- against￨L￨IN￨O￨- ROL￨U￨NNP￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- for￨L￨IN￨O￨- chronic￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-induced￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- increases￨L￨NNS￨O￨- for￨L￨IN￨O￨- low￨L￨JJ￨O￨- treatment￨L￨NN￨O￨A coverage￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- carriers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- TOL￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- effective￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- may￨L￨MD￨O￨- even￨L￨RB￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- resistance￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- long￨L￨JJ￨O￨- run￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- problematic￨L￨JJ￨O￨- epidemiologically￨L￨RB￨O￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- the￨L￨DT￨O￨- zoonotic￨L￨JJ￨O￨- parasites￨L￨NNS￨O￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- modes￨L￨NNS￨O￨- ,￨L￨,￨O￨- Trypanosoma￨U￨NNP￨PERSON￨- cruzi￨L￨NNP￨O￨- (￨L￨-LRB-￨O￨- Kinetoplastida￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- Trypanosomatidae￨U￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- protozoan￨L￨NN￨O￨- parasite￨L￨NN￨O￨A which￨L￨WDT￨O￨- causes￨L￨VBZ￨O￨- Chagas￨U￨NNP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- ecology￨L￨NN￨O￨- that￨L￨WDT￨O￨- challenges￨L￨VBZ￨O￨- transmission￨L￨NN￨O￨- modelling￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- zoonotic￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- multi-host￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- or￨L￨CC￨O￨- parasites￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- whose￨L￨WP$￨O￨- various￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- may￨L￨MD￨O￨- differ￨L￨VB￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- contribution￨L￨NN￨O￨- to￨L￨TO￨O￨- parasite￨L￨NN￨O￨A transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- over￨L￨IN￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- ecology￨L￨NN￨O￨- of￨L￨IN￨O￨- multi-host￨L￨JJ￨O￨- parasite￨L￨NN￨O￨A spread￨L￨VBN￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- potential￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- by￨L￨IN￨O￨- developing￨L￨VBG￨O￨- the￨L￨DT￨O￨- ‘￨L￨``￨O￨- ecomultiplex￨L￨NN￨O￨- ’￨L￨''￨O￨- framework￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- short￨L￨JJ￨O￨- for￨L￨IN￨O￨- ecological￨L￨JJ￨O￨- multiplex￨L￨JJ￨O￨- framework￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Figure￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Secondly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ecomultiplex￨L￨JJ￨O￨- framework￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- metabolic￨L￨JJ￨O￨- theory￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- species￨L￨NNS￨O￨- frequencies￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨- parasite￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- contribution￨L￨NN￨O￨- to￨L￨TO￨O￨- parasite￨L￨NN￨O￨A transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- ’￨L￨POS￨O￨- abundance￨L￨NN￨O￨- ,￨L￨,￨O￨- exposure￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- predict￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- an￨L￨DT￨O￨- adaptive￨L￨JJ￨O￨- antiviral￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- with￨L￨IN￨O￨- properly￨L￨RB￨O￨- timed￨L￨VBN￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- drug￨L￨NN￨O￨A usage￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- chemoprophylaxis￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- ways￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- keep￨L￨VB￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- low￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- a￨L￨DT￨O￨- drug￨L￨NN￨O￨A resistant￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- strain￨L￨NN￨O￨- is￨L￨VBZ￨O￨- as￨L￨IN￨O￨- transmissible￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- non-resistant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- fitness￨L￨NN￨O￨- penalty￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- socially￨L￨RB￨O￨- suboptimal￨L￨JJ￨O￨- Nash￨U￨NNP￨PERSON￨- equilibrium￨L￨NN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- where￨L￨WRB￨O￨- both￨L￨DT￨O￨- players￨L￨NNS￨O￨- use￨L￨VBP￨O￨- antiviral￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- socially￨L￨RB￨O￨- optimal￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- is￨L￨VBZ￨O￨- actually￨L￨RB￨O￨- for￨L￨IN￨O￨- both￨L￨DT￨O￨- players￨L￨NNS￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- previous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- isolation￨L￨NN￨O￨- from￨L￨IN￨O￨- other￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- conditions￨L￨NNS￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- decisions￨L￨NNS￨O￨- about￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- drug￨L￨NN￨O￨- use￨L￨NN￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- can￨L￨MD￨O￨- affect￨L￨VB￨O￨- other￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- calls￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- tools￨L￨NNS￨O￨- like￨L￨IN￨O￨- game￨L￨NN￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- certain￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- make￨L￨VB￨O￨- sense￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- to￨L￨TO￨O￨- cooperate￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Prisoner￨U￨NNP￨O￨- 's￨L￨POS￨O￨- Dilemma￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- by￨L￨IN￨O￨- both￨L￨DT￨O￨- treating￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- level￨L￨NN￨O￨- and￨L￨CC￨O￨- thereby￨L￨RB￨O￨- avoiding￨L￨VBG￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- drug￨L￨NN￨O￨A resistance￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- may￨L￨MD￨O￨- defect￨L￨NN￨O￨- by￨L￨IN￨O￨- adopting￨L￨VBG￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- treatment￨L￨NN￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- drug￨L￨NN￨O￨A resistant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- is￨L￨VBZ￨O￨- created￨L￨VBN￨O￨- and￨L￨CC￨O￨- spread￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- preventative￨L￨JJ￨O￨- measure￨L￨NN￨O￨- against￨L￨IN￨O￨- mumps￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- doses￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mumps￨L￨NNS￨O￨- vaccine￨L￨NN￨O￨A ,￨L￨,￨O￨- invented￨L￨VBN￨O￨- by￨L￨IN￨O￨- American￨U￨JJ￨NATIONALITY￨- microbiologist￨L￨NN￨TITLE￨- Maurice￨U￨NNP￨PERSON￨- Hilleman￨U￨NNP￨PERSON￨- at￨L￨IN￨O￨- Merck￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- fluctuate￨L￨VBP￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- seasonal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- incident￨L￨NN￨O￨A rate￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- whooping￨L￨JJ￨O￨- cough￨L￨NN￨O￨- ,￨L￨,￨O￨- polio￨L￨NNP￨O￨- ,￨L￨,￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- chickenpox￨L￨NN￨O￨- ,￨L￨,￨O￨- mumps￨L￨NNS￨O￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- Bjϕ￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- American￨U￨NNP￨ORGANIZATION￨- Academy￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Pediatrics￨U￨NNP￨ORGANIZATION￨- recommends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- routine￨L￨JJ￨O￨- administration￨L￨NN￨O￨- of￨L￨IN￨O￨- MMR￨U￨NN￨ORGANIZATION￨- vaccine￨L￨NN￨O￨- at￨L￨IN￨O￨- ages￨L￨NNS￨O￨A 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 40￨L￨CD￨PERCENT￨- percent￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- persons￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- mumps￨L￨NNS￨O￨- virus￨L￨NN￨O￨A do￨L￨VBP￨O￨- not￨L￨RB￨O￨- show￨L￨VB￨O￨- symptoms￨L￨NNS￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- and￨L￨CC￨O￨- spread￨L￨VBN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- without￨L￨IN￨O￨- knowing￨L￨VBG￨O￨- it￨L￨PRP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Mumps￨U￨NNP￨O￨- vaccination￨L￨NN￨O￨A is￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- universally￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- developed￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- nowadays￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- investigates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- absolute￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A and￨L￨CC￨O￨- inhomogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- improve￨L￨VB￨O￨- our￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- :￨L￨:￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- now-casting￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- predict￨L￨VBP￨O￨- future￨L￨JJ￨DATE￨- incidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- forecasting￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- contains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- materials￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- analysis￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- and￨L￨CC￨O￨- absolute￨L￨JJ￨O￨- humidity￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- “￨L￨``￨O￨- transmission￨L￨NN￨O￨- ”￨L￨''￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- how￨L￨WRB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- spreads￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- alternatives￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- observation￨L￨NN￨O￨- ”￨L￨''￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- connects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- notifications￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- Bayesian￨U￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- more￨L￨RBR￨O￨- generally￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- selecting￨L￨VBG￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- predictive￨L￨JJ￨O￨A skill￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- by￨L￨IN￨O￨- “￨L￨``￨O￨- predictive￨L￨JJ￨O￨- skill￨L￨NN￨O￨- ”￨L￨''￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- “￨L￨``￨O￨- future￨L￨JJ￨DATE￨- ”￨L￨''￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- forecast￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- conditional￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- already￨L￨RB￨O￨- observed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Building￨U￨NN￨O￨- on￨L￨IN￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- with￨L￨IN￨O￨- mechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨- filter￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- lab-confirmed￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- observed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Victorian￨U￨JJ￨ORGANIZATION￨- Department￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Human￨U￨NNP￨ORGANIZATION￨- Services￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Australia￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- which￨L￨WDT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- suitable￨L￨JJ￨O￨- for￨L￨IN￨O￨- now-casting￨L￨JJ￨O￨- and￨L￨CC￨O￨- forecasting￨L￨NN￨O￨A .￨L￨.￨O￨- +An￨U￨DT￨O￨- alternative￨L￨JJ￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- restrain￨L￨VB￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- inhomogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mixing￨L￨VBG￨O￨A of￨L￨IN￨O￨- real￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- divide￨L￨VBP￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- presented￨L￨VBD￨O￨- into￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- broad￨L￨JJ￨O￨- classes￨L￨NNS￨O￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- static￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨A network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- configuration￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ”￨L￨''￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- mass￨L￨NN￨O￨- action￨L￨NN￨O￨- mixing￨L￨VBG￨O￨- ,￨L￨,￨O￨- vector-borne￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mass-action￨L￨NN￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- network￨L￨NN￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- dynamic￨L￨JJ￨O￨- partnership￨L￨NN￨O￨- changes￨L￨NNS￨O￨- preferential￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- begin￨L￨VBP￨O￨- by￨L￨IN￨O￨- revisiting￨L￨VBG￨O￨- existing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- mass-action￨L￨NN￨O￨- mixing￨L￨VBG￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨- network￨L￨NN￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- another￨L￨DT￨O￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- .￨L￨.￨O￨- +Unfortunately￨U￨RB￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- existing￨L￨VBG￨O￨A mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- through￨L￨IN￨O￨- networks￨L￨NNS￨O￨- require￨L￨VBP￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- expand￨L￨VBP￨O￨- on￨L￨IN￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- with￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- advances￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- incorporate￨L￨VBP￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- suite￨L￨NN￨O￨- of￨L￨IN￨O￨- empirically-derived￨L￨JJ￨O￨- ,￨L￨,￨O￨- unimodal￨L￨JJ￨O￨- thermal￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- known￨L￨VBN￨O￨- transmission-relevant￨L￨JJ￨O￨- mosquito￨L￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- traits￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- temperature￨L￨NN￨O￨A mean￨L￨NN￨O￨- and￨L￨CC￨O￨- variation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- constant￨L￨JJ￨O￨- temperatures￨L￨NNS￨O￨- or￨L￨CC￨O￨- daily￨L￨JJ￨SET￨- temperature￨L￨NN￨O￨- variation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- framework￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- temperature￨L￨NN￨O￨- regimes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiologically-relevant￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- peak￨L￨NN￨O￨- incidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- vectorial￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- directly￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- field-relevant￨L￨JJ￨O￨- temperature￨L￨NN￨O￨A regimes￨L￨NNS￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- across￨L￨IN￨O￨- temperature￨L￨NN￨O￨- means￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 38￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- ranges￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- from￨L￨IN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- predicted￨L￨VBN￨O￨- suitable￨L￨JJ￨O￨- range￨L￨NN￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- included￨L￨VBD￨O￨- seasonal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- temperature￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examined￨L￨VBD￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- varied￨L￨VBD￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- temperature￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- began￨L￨VBD￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- temperature￨L￨NN￨O￨- regimes￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- set￨L￨VBD￨O￨- T￨U￨NN￨O￨- =￨L￨JJ￨O￨- 40.0￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- ,￨L￨,￨O￨- T￨U￨NN￨O￨- =￨L￨JJ￨O￨- 25.0￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- T￨U￨NN￨O￨- =￨L￨JJ￨O￨- 10.0￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- temperature￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- default￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Appendix￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- varied￨L￨VBD￨O￨- the￨L￨DT￨O￨- temperature￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- from￨L￨IN￨O￨- 10.0￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- to￨L￨TO￨O￨- 40.0￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- in￨L￨IN￨O￨- increments￨L￨NNS￨O￨- of￨L￨IN￨O￨- 0.1￨L￨CD￨NUMBER￨- °C￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- How￨U￨WRB￨O￨- do￨L￨VBP￨O￨- temperature￨L￨NN￨O￨A mean￨L￨NN￨O￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- range￨L￨NN￨O￨- interact￨L￨VBP￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ?￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- bats￨L￨NNS￨O￨- were￨L￨VBD￨O￨- indeed￨L￨RB￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- and￨L￨CC￨O￨- unique￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- of￨L￨IN￨O￨- filoviruses￨L￨NNS￨O￨- as￨L￨IN￨O￨- EBOV￨U￨NN￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- outbreaks￨L￨NNS￨O￨- might￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- primarily￨L￨RB￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- direct￨L￨JJ￨O￨A human-bat￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- by￨L￨IN￨O￨- other￨L￨JJ￨O￨- means￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- infected￨L￨JJ￨O￨- primate￨L￨JJ￨O￨- carcasses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- bushmeat￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- bat￨L￨NN￨O￨- feces￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- Predictive￨U￨NNP￨O￨- Spatial￨U￨NNP￨O￨- Distribution￨U￨NN￨O￨- Framework￨U￨NN￨O￨- for￨L￨IN￨O￨- Filovirus-Infected￨U￨NNP￨O￨- Bats￨U￨NNP￨O￨- Graziano￨U￨NNP￨O￨- Fiorillo1￨U￨NN￨O￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Paolo￨U￨NNP￨PERSON￨- Bocchini￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- na1￨L￨NN￨O￨- &￨L￨CC￨O￨- Javier￨U￨NNP￨O￨- Buceta2￨U￨NNP￨O￨- ,3￨L￨CD￨NUMBER￨- na1￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 7970￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsEcological￨L￨JJ￨O￨- epidemiologyViral￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- AbstractTools￨U￨NNS￨O￨- with￨L￨IN￨O￨- predictive￨L￨JJ￨O￨A capabilities￨L￨NNS￨O￨- in￨L￨IN￨O￨- regards￨L￨VBZ￨O￨- of￨L￨IN￨O￨- filovirus￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- mainly￨L￨RB￨O￨- anthropocentric￨L￨JJ￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- disregarded￨L￨VBN￨O￨- the￨L￨DT￨O￨- ecological￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- contribute￨L￨VBP￨O￨- to￨L￨TO￨O￨- shift￨L￨VB￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- paradigm￨L￨NN￨O￨- by￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- putative￨L￨JJ￨O￨- main￨L￨JJ￨O￨- zoonotic￨L￨JJ￨O￨- niche￨L￨NN￨O￨- of￨L￨IN￨O￨- filoviruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- bats￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- link￨L￨NN￨O￨- to￨L￨TO￨O￨- environmental￨L￨JJ￨O￨A drivers￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- implement￨L￨VBP￨O￨- a￨L￨DT￨O￨- regression￨L￨NN￨O￨- analysis￨L￨NN￨O￨- using￨L￨VBG￨O￨- factual￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- correlate￨L￨VB￨O￨- environmental￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- bats￨L￨NNS￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- outbreaks￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨A exposure￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- to￨L￨TO￨O￨- bats￨L￨NNS￨O￨- in￨L￨IN￨O￨- Africa9￨U￨NN￨O￨- .￨L￨.￨O￨- +Case￨U￨NN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- classroom￨L￨NN￨O￨- teaching￨L￨NN￨O￨- to￨L￨TO￨O￨- introduce￨L￨VB￨O￨- students￨L￨NNS￨O￨- to￨L￨TO￨O￨- key￨L￨JJ￨O￨A epidemiological￨L￨JJ￨O￨A concepts￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- serial￨L￨NN￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Participation￨U￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- real-time￨L￨JJ￨O￨- simulated￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- analysing￨L￨VBG￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- data￨L￨NNS￨O￨- reinforces￨L￨VBZ￨O￨- and￨L￨CC￨O￨- affords￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- important￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨A while￨L￨IN￨O￨- gaining￨L￨VBG￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- these￨L￨DT￨O￨- ,￨L￨,￨O￨- initial￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- include￨L￨VBP￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- onward￨L￨RB￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- R0￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- understanding￨L￨VBG￨O￨- key￨L￨JJ￨O￨A epidemiological￨L￨JJ￨O￨A features￨L￨NNS￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- possible￨L￨JJ￨O￨- control￨L￨NN￨O￨- policies￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- approach￨L￨NN￨O￨- involved￨L￨VBD￨O￨- real-time￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- among￨L￨IN￨O￨- participants￨L￨NNS￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- ranged￨L￨VBD￨O￨- from￨L￨IN￨O￨- university￨L￨NN￨O￨- undergraduate￨L￨JJ￨O￨- students￨L￨NNS￨O￨- to￨L￨TO￨O￨- academic￨L￨JJ￨O￨- professors￨L￨NNS￨O￨- ,￨L￨,￨O￨- attending￨L￨VBG￨O￨- an￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- training￨L￨NN￨O￨- course￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- few￨L￨JJ￨O￨- training￨L￨NN￨O￨- modules￨L￨NNS￨O￨- that￨L￨WDT￨O￨- explicitly￨L￨RB￨O￨- use￨L￨VBP￨O￨- real-time￨L￨JJ￨O￨- simulated￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- participants￨L￨NNS￨O￨A themselves￨L￨PRP￨O￨- comprise￨L￨VBP￨O￨- the￨L￨DT￨O￨- dataset￨L￨NN￨O￨- they￨L￨PRP￨O￨- subsequently￨L￨RB￨O￨- analyse￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- recent￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨A and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- underscores￨L￨VBZ￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- better￨L￨JJR￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- forecasting.Methods￨L￨NNS￨O￨- :￨L￨:￨O￨- To￨U￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- suitability￨L￨NN￨O￨- of￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- forecasting￨L￨NN￨O￨- emerging￨L￨VBG￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Defense￨U￨NNP￨ORGANIZATION￨- Advanced￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- Projects￨U￨NNP￨ORGANIZATION￨- Agency￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- DARPA￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2015￨L￨CD￨DATE￨- DARPA￨U￨NNP￨O￨- Chikungunya￨U￨NNP￨O￨- Challenge￨U￨NNP￨O￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- need￨L￨NN￨O￨A to￨L￨TO￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- quality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- accurately￨L￨RB￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics.KeywordsChikungunyaForecastingMorphological￨L￨JJ￨O￨- modelsMechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- BackgroundMathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨DURATION￨- than￨L￨IN￨DURATION￨- a￨L￨DT￨DURATION￨- century￨L￨NN￨DURATION￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Forecasting￨U￨NN￨O￨- approaches￨L￨NNS￨O￨- vary￨L￨VBP￨O￨- substantially￨L￨RB￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- method￨L￨NN￨O￨- and￨L￨CC￨O￨- complexity￨L￨NN￨O￨A ;￨L￨:￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- use￨L￨NN￨O￨- human￨L￨JJ￨O￨- judgment￨L￨NN￨O￨- or￨L￨CC￨O￨- prediction￨L￨NN￨O￨- markets￨L￨NNS￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- use￨L￨NN￨O￨- purely￨L￨RB￨O￨- statistical￨L￨JJ￨O￨- or￨L￨CC￨O￨- machine￨L￨NN￨O￨- learning￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- others￨L￨NNS￨O￨- rely￨L￨VBP￨O￨- upon￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- varying￨L￨VBG￨O￨- complexity￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- only￨L￨RB￨O￨- recently￨L￨RB￨DATE￨- have￨L￨VB￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- systems￨L￨NNS￨O￨- begun￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- designed￨L￨VBN￨O￨- specifically￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- task￨L￨NN￨O￨- of￨L￨IN￨O￨- providing￨L￨VBG￨O￨- regularly￨L￨RB￨O￨- updated￨L￨VBN￨O￨- quantitative￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- analogous￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- available￨L￨JJ￨O￨- for￨L￨IN￨O￨- weather￨L￨NN￨O￨- prediction￨L￨NN￨O￨- .￨L￨.￨O￨- +Challenge￨U￨NN￨O￨- participants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 38￨L￨CD￨NUMBER￨- during￨L￨IN￨O￨- final￨L￨JJ￨O￨- evaluation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- provided￨L￨VBD￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨A epidemics￨L￨NNS￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- six-month￨L￨JJ￨DURATION￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- September￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2014￨L￨CD￨DATE￨- to￨L￨TO￨O￨- February￨U￨NNP￨DATE￨- 16￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2015￨L￨CD￨DATE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- evaluated￨L￨VBN￨O￨- by￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- reported￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Pan￨U￨NNP￨ORGANIZATION￨- American￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- PAHO￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- resistance￨L￨NN￨O￨- breakdown￨L￨NN￨O￨- or￨L￨CC￨O￨- high￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- erosion￨L￨NN￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- cultivars￨L￨NNS￨O￨- becoming￨L￨VBG￨O￨- ineffective￨L￨JJ￨O￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- their￨L￨PRP$￨O￨- durability￨L￨NN￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- chemicals￨L￨NNS￨O￨- ,￨L￨,￨O￨- agronomic￨L￨JJ￨O￨- practices￨L￨NNS￨O￨A ,￨L￨,￨O￨- varying￨L￨VBG￨O￨- crop￨L￨NN￨O￨- diversity￨L￨NN￨O￨- either￨L￨CC￨O￨- temporally￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- crop￨L￨NN￨O￨- rotations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- spatially￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- pyramiding￨L￨VBG￨O￨- ,￨L￨,￨O￨- mixtures￨L￨NNS￨O￨- ,￨L￨,￨O￨- mosaics￨L￨NNS￨O￨- of￨L￨IN￨O￨- fields￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- or￨L￨CC￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- cultural￨L￨JJ￨O￨- practices￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- for￨L￨IN￨O￨- landscape‐scale￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- in￨L￨IN￨O￨- spite￨L￨NN￨O￨- of￨L￨IN￨O￨- considerable￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- from￨L￨IN￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- landscape￨L￨NN￨O￨A organization￨L￨NN￨O￨- can￨L￨MD￨O￨- affect￨L￨VB￨O￨- pathogen￨L￨NN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- impede￨L￨VB￨O￨- adaptation￨L￨NN￨O￨- to￨L￨TO￨O￨- host￨L￨NN￨TITLE￨- resistance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨A crop￨L￨NN￨O￨- cultivars￨L￨NNS￨O￨- against￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- typically￨L￨RB￨O￨- reduces￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- associated￨L￨VBN￨O￨- yield￨L￨NN￨O￨- losses￨L￨NNS￨O￨- in￨L￨IN￨O￨- agricultural￨L￨JJ￨O￨- production￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- either￨L￨DT￨O￨- qualitative￨L￨JJ￨O￨- or￨L￨CC￨O￨- quantitative￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- –￨L￨:￨O￨- pathogen￨L￨NN￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- towards￨L￨IN￨O￨- increased￨L￨VBN￨O￨- infectivity￨L￨NN￨O￨- or￨L￨CC￨O￨- aggressiveness￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- resistant￨L￨JJ￨O￨A host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- penalized￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- fitness￨L￨NN￨O￨- cost￨L￨NN￨O￨- on￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- such￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- ,￨L￨,￨O￨- new￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- may￨L￨MD￨O￨- quickly￨L￨RB￨O￨- emerge￨L￨VB￨O￨- in￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- total￨L￨JJ￨O￨- breakdown￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- resistance￨L￨NN￨O￨A gene￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- susceptible-latent-breakingout-quarantine-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SLBQRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- preserves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- at￨L￨IN￨O￨- all￨L￨DT￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- domain￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- continuous￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- structure￨L￨NN￨O￨- preserving￨L￨NN￨O￨- numerical￨L￨JJ￨O￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- motivation￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- the￨L￨DT￨O￨- reliable￨L￨JJ￨O￨- positivity￨L￨NN￨O￨- preserving￨L￨VBG￨O￨- numerical￨L￨JJ￨O￨- schemes￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨A network￨L￨NN￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- of￨L￨IN￨O￨- reliability￨L￨NN￨O￨- ,￨L￨,￨O￨- efficiency￨L￨NN￨O￨- and￨L￨CC￨O￨- capability￨L￨NN￨O￨- of￨L￨IN￨O￨- preserving￨L￨VBG￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- NSFD￨U￨NN￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- SLBQRS￨U￨NNP￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- numerical￨L￨JJ￨O￨- scheme￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- justify￨L￨VB￨O￨- negative￨L￨JJ￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- because￨L￨IN￨O￨- negative￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- meaningless￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effort￨L￨NN￨O￨A available￨L￨JJ￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- quantity￨L￨NN￨O￨- of￨L￨IN￨O￨- operational￨L￨JJ￨O￨- equipment￨L￨NN￨O￨- or￨L￨CC￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- healthcare￨L￨NN￨O￨- personnel￨L￨NNS￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- space￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- H￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- surface￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- initially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- bivariate￨L￨JJ￨O￨- Gaussian￨U￨JJ￨MISC￨- density￨L￨NN￨O￨- function￨L￨NN￨O￨- with￨L￨IN￨O￨- mean￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- epicenter￨L￨NN￨O￨- x0￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- represent￨L￨VB￨O￨- a￨L￨DT￨O￨- central￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- point￨L￨NN￨O￨- or￨L￨CC￨O￨- medical￨L￨JJ￨O￨- facility￨L￨NN￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- originates￨L￨VBZ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- variance-covariance￨L￨NN￨O￨- matrix￨L￨NN￨O￨- I.￨U￨NN￨O￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- analogous￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- person￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- immunized￨L￨VBN￨O￨- at￨L￨IN￨O￨- location￨L￨NN￨O￨- x￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- where￨L￨WRB￨O￨- local￨L￨JJ￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- smoothing￨L￨VBG￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- kernel￨L￨NN￨O￨- K￨U￨NN￨O￨- with￨L￨IN￨O￨- parameter￨L￨NN￨O￨- α￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- effort￨L￨NN￨O￨- ,￨L￨,￨O￨- H￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- below￨L￨IN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- parameterized￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- values￨L￨NNS￨O￨- :￨L￨:￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- τ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- δ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ρ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- intensity￨L￨NN￨O￨- ε￨L￨NN￨O￨- =￨L￨JJ￨O￨- 20￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨A scale￨L￨NN￨O￨- α￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Supplementary￨U￨NNP￨O￨- Information￨U￨NNP￨O￨- for￨L￨IN￨O￨- sensitivity￨L￨NN￨O￨- of￨L￨IN￨O￨- results￨L￨NNS￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- illustrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- distribution￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- promptness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- response￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- employed￨L￨VBN￨O￨A a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- combined￨L￨VBN￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- vaccines￨L￨NNS￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- .￨L￨.￨O￨- +Dias￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- has￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- an￨L￨DT￨O￨- adaptation￨L￨NN￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- also￨L￨RB￨O￨- seen￨L￨VBN￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- attempts￨L￨NNS￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- in￨L￨IN￨O￨- cattle￨L￨NNS￨O￨- herds￨L￨NNS￨O￨- using￨L￨VBG￨O￨- IBM￨U￨NNP￨ORGANIZATION￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- describe￨L￨VBP￨O￨- expressive￨L￨JJ￨O￨- developments￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- modelling￨L￨NN￨O￨A of￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- brucellosis￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- less￨L￨JJR￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- IBM￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- such￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- other￨L￨JJ￨O￨- works￨L￨NNS￨O￨- that￨L￨WDT￨O￨- use￨L￨VBP￨O￨- IBM￨U￨NNP￨ORGANIZATION￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- brucellosis￨L￨NN￨O￨- as￨L￨IN￨O￨- seen￨L￨VBN￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- outside-host￨L￨JJ￨O￨- bacterial￨L￨JJ￨O￨- competition￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨A and￨L￨CC￨O￨- phage-resistant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- phage￨L￨NN￨O￨- resistance￨L￨NN￨O￨- determines￨L￨VBZ￨O￨- phage￨L￨NN￨O￨- therapy￨L￨NN￨O￨- outcome￨L￨NN￨O￨- from￨L￨IN￨O￨- stable￨L￨JJ￨O￨- coexistence￨L￨NN￨O￨- to￨L￨TO￨O￨- local￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- extinction￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- sources￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- PPR￨U￨NNP￨ORGANIZATION￨- virus￨L￨NN￨O￨- are￨L￨VBP￨O￨- sick￨L￨JJ￨O￨- small￨L￨JJ￨O￨- ruminant￨L￨NN￨O￨- animals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- release￨L￨VBP￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- with￨L￨IN￨O￨- nasal￨L￨JJ￨O￨- and￨L￨CC￨O￨- teary￨L￨JJ￨O￨- outflows￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- with￨L￨IN￨O￨- feces￨L￨NNS￨O￨- ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨DATE￨- 1st￨L￨JJ￨DATE￨- day￨L￨NN￨DATE￨- of￨L￨IN￨O￨- febrile￨L￨JJ￨O￨- state￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- manifestation￨L￨NN￨O￨- of￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- signs￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- 2-3￨L￨CD￨NUMBER￨- days￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- their￨L￨PRP$￨O￨- appearance￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- PPR￨U￨NNP￨ORGANIZATION￨- occurrence￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- were￨L￨VBD￨O￨- obliged￨L￨VBN￨O￨- to￨L￨TO￨O￨- determinate￨L￨VB￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- of￨L￨IN￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- different￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- consequences￨L￨NNS￨O￨- depending￨L￨VBG￨O￨A on￨L￨IN￨O￨- various￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- that￨L￨WDT￨O￨- PPR￨U￨NNP￨ORGANIZATION￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- appearance￨L￨NN￨O￨A may￨L￨MD￨O￨- vary￨L￨VB￨O￨- from￨L￨IN￨O￨- area￨L￨NN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- region￨L￨NN￨O￨- predisposition￨L￨NN￨O￨- or￨L￨CC￨O￨- existing￨L￨VBG￨O￨- factors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- Geo-information￨U￨JJ￨MISC￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- QuickMAP￨U￨NN￨O￨- has￨L￨VBZ￨O￨- processed￨L￨VBN￨O￨- clustering￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- outbreaks￨L￨NNS￨O￨- incidence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- cases/or￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- focus￨L￨NN￨O￨A of￨L￨IN￨O￨- PPR￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- mapping￨L￨NN￨O￨- .￨L￨.￨O￨- +Peste￨U￨NNP￨O￨- des￨L￨NNP￨O￨- petits￨L￨VBZ￨O￨- ruminants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- PPR￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- highly￨L￨RB￨O￨- contagious￨L￨JJ￨O￨- ,￨L￨,￨O￨- emergent￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transboundary￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- affects￨L￨VBZ￨O￨- goats￨L￨NNS￨O￨- and￨L￨CC￨O￨- sheep￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Specific￨U￨JJ￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- resulting￨L￨VBG￨O￨- case￨L￨NN￨O￨- counts￨L￨NNS￨O￨- are￨L￨VBP￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- factors￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨A strain￨L￨NN￨O￨- of￨L￨IN￨O￨- EVD￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- specific￨L￨JJ￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- either￨L￨RB￨O￨- reduce￨L￨VB￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aid￨L￨NN￨O￨- included￨L￨VBD￨O￨- health￨L￨NN￨O￨A care￨L￨NN￨O￨A resources￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- affected￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- altered￨L￨VBD￨O￨- individual￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- quickly￨L￨RB￨O￨- contained￨L￨VBD￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- limited￨L￨VBD￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- immensely￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- evident￨L￨JJ￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- early￨L￨JJ￨O￨- Ebola￨U￨NN￨MISC￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- Sudan￨U￨NNP￨COUNTRY￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- a￨L￨DT￨O￨- reflection￨L￨NN￨O￨- of￨L￨IN￨O￨- preparedness￨L￨NN￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨A care￨L￨NN￨O￨A providers￨L￨NNS￨O￨- and￨L￨CC￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- public￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Report￨U￨NNP￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- WHO￨U￨WP￨O￨- /￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Unlike￨U￨IN￨O￨- previous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- simply￨L￨RB￨O￨- reduce￨L￨VB￨O￨A various￨L￨JJ￨O￨- rates￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- education￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- different￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- group￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- protocols￨L￨NNS￨O￨A are￨L￨VBP￨O￨- not￨L￨RB￨O￨- followed￨L￨VBN￨O￨- ,￨L￨,￨O￨- hospital￨L￨NN￨O￨- settings￨L￨NNS￨O￨- can￨L￨MD￨O￨- produce￨L￨VB￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- during￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- outbreaks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- ZVL￨U￨NN￨O￨- is￨L￨VBZ￨O￨- curable￨L￨JJ￨O￨- using￨L￨VBG￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- miltefosine￨L￨NN￨O￨- ,￨L￨,￨O￨- paromomycin￨L￨NN￨O￨- and￨L￨CC￨O￨- liposomal￨L￨JJ￨O￨- amphotericin￨L￨NN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- basic￨L￨JJ￨O￨- anti-ZVL￨L￨JJ￨O￨- preventive￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- personal￨L￨JJ￨O￨- protection￨L￨NN￨O￨- against￨L￨IN￨O￨- sandfly￨L￨JJ￨O￨- bites￨L￨VBZ￨O￨- and￨L￨CC￨O￨- sandfly-reduction￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- spraying￨L￨VBG￨O￨- anti-sandfly￨L￨JJ￨O￨- insecticides￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- animal￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨A habitats￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- remain￨L￨VBP￨O￨- perhaps￨L￨RB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- combating￨L￨VBG￨O￨- ZVL￨U￨NNP￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- insight￨L￨NN￨O￨- into￨L￨IN￨O￨- ZVL￨U￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- and/or￨L￨CC￨O￨- reservoir￨L￨NN￨O￨A populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Carvalho￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- references￨L￨NNS￨O￨- therein￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +proposed￨L￨VBN￨O￨- mechanistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- ZVL￨U￨NN￨O￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- animal￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨A populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- theoretical￨L￨JJ￨O￨- extensions￨L￨NNS￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨A rates￨L￨NNS￨O￨A beyond￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- in￨L￨IN￨O￨- ODEs￨U￨NNS￨O￨- have￨L￨VBP￨O￨- only￨L￨RB￨O￨- started￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- developed￨L￨VBN￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- constant￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- rates￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- exponentially￨L￨RB￨O￨- distributed￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- are￨L￨VBP￨O￨- epidemiologically￨L￨RB￨O￨- unrealistic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Next￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- an￨L￨DT￨O￨- alternative￨L￨JJ￨O￨- probability￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- spent￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- class￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- forms￨L￨NNS￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨A rates￨L￨NNS￨O￨A in￨L￨IN￨O￨- ODE￨U￨NNP￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- dog￨L￨NN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- vector￨L￨NN￨O￨- transmitting￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- ;￨L￨:￨O￨- Those￨U￨DT￨O￨- three￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- humans￨L￨NNS￨O￨A ,￨L￨,￨O￨- dogs￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- constants￨L￨NNS￨O￨- ;￨L￨:￨O￨- Both￨U￨CC￨O￨- human￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- indexed￨L￨VBN￨O￨- as￨L￨IN￨O￨- h￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- dog￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- indexed￨L￨VBN￨O￨- as￨L￨IN￨O￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- categories￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- and￨L￨CC￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- but￨L￨CC￨O￨- without￨L￨IN￨O￨- noticeable￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- l￨L￨NN￨O￨- and￨L￨CC￨O￨- l￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- latent￨L￨JJ￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- clinically￨L￨RB￨O￨- ill￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- y￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- immunes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- z￨L￨SYM￨O￨- and￨L￨CC￨O￨- z￨L￨SYM￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- must￨L￨MD￨O￨- add￨L￨VB￨O￨- an￨L￨DT￨O￨- entrance￨L￨NN￨O￨- term￨L￨NN￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- natality￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- choose￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-induced￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- humans￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- clinically￨L￨RB￨O￨- ill￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- maintain￨L￨VB￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- latent￨L￨JJ￨O￨- humans￨L￨NNS￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- humans￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Zoonotic￨U￨JJ￨O￨- Visceral￨U￨JJ￨O￨- Leishmaniasis￨U￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- major￨L￨JJ￨O￨- human￨L￨JJ￨O￨A and￨L￨CC￨O￨- veterinary￨L￨JJ￨O￨- medical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- that￨L￨WDT￨O￨- involves￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- interplay￨L￨NN￨O￨- between￨L￨IN￨O￨- trypanosomatids￨L￨NNS￨O￨- protozoan￨L￨NN￨O￨- from￨L￨IN￨O￨- Leishmania￨U￨NN￨LOCATION￨- complex￨L￨NN￨O￨- ,￨L￨,￨O￨- arthropod￨L￨NN￨O￨- vectors￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- the￨L￨DT￨O￨- female￨L￨JJ￨O￨- sandfly￨L￨JJ￨O￨- Lutzomyia￨U￨NN￨O￨- longipalpis￨L￨NN￨O￨- and￨L￨CC￨O￨- Lutzomyia￨U￨NN￨PERSON￨- cruzi￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- environmental￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- vector￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- small￨L￨JJ￨O￨- companion￨L￨NN￨TITLE￨- animal￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dog￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- reservoir￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- new￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- we￨L￨PRP￨O￨- updated￨L￨VBD￨O￨A most￨L￨JJS￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- calculated￨L￨VBN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- value￨L￨NN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- sensitivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- an￨L￨DT￨O￨- infinitesimal￨L￨JJ￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- varies￨L￨VBZ￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- infected￨L￨JJ￨O￨- flies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- bite￨L￨VB￨O￨- on￨L￨IN￨O￨- any￨L￨DT￨O￨- category￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨A population￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- cell￨L￨NN￨O￨- in￨L￨IN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- Since￨U￨IN￨O￨- our￨L￨PRP$￨O￨- goal￨L￨NN￨O￨- concerns￨L￨VBZ￨O￨- the￨L￨DT￨O￨- minimization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨A people￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vicinity￨L￨NN￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimization￨L￨NN￨O￨- criterion￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- cell￨L￨NN￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- it￨L￨PRP￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- objective￨L￨NN￨O￨- functionwhere￨L￨NN￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- severity￨L￨NN￨O￨- weights￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- controls￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- travel-blocking￨L￨JJ￨O￨- vicinity￨L￨NN￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- restrict￨L￨VB￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨A people￨L￨NNS￨O￨A coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- and￨L￨CC￨O￨- aiming￨L￨VBG￨O￨- to￨L￨TO￨O￨- reach￨L￨VB￨O￨- the￨L￨DT￨O￨- cell￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- travel-blocking￨L￨JJ￨O￨- vicinity￨L￨NN￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- approach￨L￨NN￨O￨- will￨L￨MD￨O￨- show￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- blocker￨L￨NN￨TITLE￨- control￨L￨NN￨O￨- on￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- contacts￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- people￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- cell￨L￨NN￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨A people￨L￨NNS￨O￨A coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- cell￨L￨NN￨O￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- cells￨L￨NNS￨O￨- from￨L￨IN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- multi-cells￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- vicinity￨L￨NN￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A strategy￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- here￨L￨RB￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- represent￨L￨VB￨O￨- good￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- for￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- studies￨L￨NNS￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- results￨L￨NNS￨O￨- were￨L￨VBD￨O￨- calculated￨L￨VBN￨O￨- across￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- health￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- :￨L￨:￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- hospitalization￨L￨NN￨O￨- ,￨L￨,￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- ICU￨U￨NN￨O￨- admission￨L￨NN￨O￨- ,￨L￨,￨O￨- peak￨L￨JJ￨O￨- demand￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- acute-care￨L￨JJ￨O￨- hospital￨L￨NN￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- peak￨L￨NN￨O￨- ICU￨U￨NN￨O￨- demand￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- capacity￨L￨NN￨O￨- and￨L￨CC￨O￨- total￨L￨JJ￨O￨- deaths￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- recognizing￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- distribution￨L￨NN￨O￨- could￨L￨MD￨O￨- prioritize￨L￨VB￨O￨- high-risk￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- interest￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- geographical￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- accommodate￨L￨VB￨O￨- surges￨L￨VBZ￨O￨- in￨L￨IN￨O￨- patient￨L￨NN￨O￨- demand￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- would￨L￨MD￨O￨- therefore￨L￨RB￨O￨- benefit￨L￨VB￨O￨- from￨L￨IN￨O￨- early￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- hospital-resource￨L￨JJ￨O￨- adequacy￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- InFluNet￨U￨NNP￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- developed￨L￨VBD￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨- —￨L￨:￨O￨- we￨L￨PRP￨O￨- project￨L￨VBP￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- second-wave￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- burden￨L￨NN￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- location￨L￨NN￨O￨- under￨L￨IN￨O￨- various￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- severity￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- method￨L￨NN￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- :￨L￨:￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- susceptibility￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infectivity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- σ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- mean￨L￨VB￨O￨A number￨L￨NN￨O￨A of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- either￨L￨DT￨O￨- symptomatically￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- IC/N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- asymptomatically￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- IA/N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infected￨L￨JJ￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- cost-effective￨L￨JJ￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- containing￨L￨VBG￨O￨- pandemic￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- mitigating￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- associated￨L￨VBN￨O￨- burdens￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- effects￨L￨NNS￨O￨- are￨L￨VBP￨O￨- especially￨L￨RB￨O￨- influential￨L￨JJ￨O￨- for￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- relatively￨L￨RB￨O￨- long￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- populations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- few￨L￨JJ￨O￨- but￨L￨CC￨O￨- long￨L￨JJ￨O￨- lasting￨L￨JJ￨O￨- partnerships￨L￨NNS￨O￨A .￨L￨.￨O￨- +If￨U￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- form￨L￨NN￨O￨- long￨L￨RB￨O￨- lasting￨L￨JJ￨O￨- partnerships￨L￨NNS￨O￨A and￨L￨CC￨O￨- have￨L￨VBP￨O￨- repeated￨L￨VBN￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- individual￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- spreads￨L￨VBZ￨O￨- via￨L￨IN￨O￨- those￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- partnerships￨L￨NNS￨O￨A are￨L￨VBP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- order￨L￨NN￨O￨- of￨L￨IN￨O￨- magnitude￨L￨NN￨O￨- ,￨L￨,￨O￨- partnership￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- interacts￨L￨VBZ￨O￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- itself￨L￨PRP￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- such￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- pair￨L￨NN￨O￨A formation￨L￨NN￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- first￨L￨RB￨ORDINAL￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- by￨L￨IN￨O￨- Dietz￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Hadeler￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- partnerships￨L￨NNS￨O￨A are￨L￨VBP￨O￨- monogamous￨L￨JJ￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- susceptibles￨L￨NNS￨O￨- are￨L￨VBP￨O￨- protected￨L￨VBN￨O￨- from￨L￨IN￨O￨- becoming￨L￨VBG￨O￨- infected￨L￨JJ￨O￨- as￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- partnership￨L￨NN￨O￨- lasts￨L￨VBZ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A among￨L￨IN￨O￨- foxes￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- inspired￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- rabies￨L￨NNP￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- on￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨- and￨L￨CC￨O￨- designing￨L￨VBG￨O￨- useful￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- pioneer￨L￨NN￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- Anderson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jackson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- May￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Smith￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1981￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- subclasses￨L￨NNS￨O￨- of￨L￨IN￨O￨- fox￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- epidemiological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A in￨L￨IN￨O￨- fox￨L￨NN￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +Clayton￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Duke-Sylvester￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Gross￨U￨NNP￨O￨- ,￨L￨,￨O￨- Lenhart￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Real￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Ding￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Gross￨U￨NNP￨O￨- ,￨L￨,￨O￨- Langston￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Lenhart￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Real￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- SEIRS￨U￨NNP￨ORGANIZATION￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A in￨L￨IN￨O￨- raccoons￨L￨NNS￨O￨- .￨L￨.￨O￨- +Rabies￨U￨NN￨O￨- virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- present￨L￨JJ￨DATE￨- among￨L￨IN￨O￨- various￨L￨JJ￨O￨- mammal￨L￨NN￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- red￨L￨JJ￨O￨- fox￨L￨NN￨O￨- and￨L￨CC￨O￨- raccoon￨L￨NN￨O￨- dog￨L￨NN￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- raccoon￨L￨NN￨O￨- ,￨L￨,￨O￨- red￨L￨JJ￨O￨- fox￨L￨NN￨O￨- ,￨L￨,￨O￨- skunk￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- insectivorous￨L￨JJ￨O￨- bats￨L￨NNS￨O￨- in￨L￨IN￨O￨- North￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- domestic￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨A ,￨L￨,￨O￨- insectivorous￨L￨JJ￨O￨- and￨L￨CC￨O￨- vampire￨L￨NN￨O￨- bats￨L￨NNS￨O￨- in￨L￨IN￨O￨- South￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- dogs￨L￨NNS￨O￨- ,￨L￨,￨O￨- bat￨L￨NN￨O￨- ,￨L￨,￨O￨- Chinese￨U￨JJ￨NATIONALITY￨- ferret￨L￨VBP￨O￨- badger￨L￨NN￨O￨- ,￨L￨,￨O￨- raccoon￨L￨NN￨O￨- dog￨L￨NN￨O￨- ,￨L￨,￨O￨- rat￨L￨NN￨O￨- ,￨L￨,￨O￨- fox￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- wolf￨L￨NN￨O￨- in￨L￨IN￨O￨- Asia￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Dimitrov￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hallam￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Rupprecht￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Turmelle￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- McCracken￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- presented￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- rabies￨L￨NNP￨O￨A virus￨L￨NN￨O￨- in￨L￨IN￨O￨- bats￨L￨NNS￨O￨- and￨L￨CC￨O￨- George￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Especially￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- work￨L￨NN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rates￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- time￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- spreading￨L￨VBG￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +And￨U￨CC￨O￨- this￨L￨DT￨O￨- invites￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- follow￨L￨VB￨O￨- the￨L￨DT￨O￨- precious￨L￨JJ￨O￨- works￨L￨NNS￨O￨- and￨L￨CC￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- combining￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- ,￨L￨,￨O￨- influence￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- with￨L￨IN￨O￨- both￨L￨DT￨O￨- individual￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- and￨L￨CC￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- increased￨L￨VBD￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- correlation￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- infectivity￨L￨NN￨O￨- availed￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- individual￨L￨JJ￨O￨- degree￨L￨NN￨O￨- ,￨L￨,￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- increasing￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- increment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- findings￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- closely￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A and￨L￨CC￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Environmental￨U￨JJ￨O￨- variability￨L￨NN￨O￨- is￨L￨VBZ￨O￨- especially￨L￨RB￨O￨- important￨L￨JJ￨O￨- in￨L￨IN￨O￨- modeling￨L￨NN￨O￨- zoonotic￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- vector-borne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- waterborne￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Ebola￨U￨NNP￨O￨- ,￨L￨,￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Stochastic￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- variability￨L￨NN￨O￨A in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- births￨L￨NNS￨O￨- ,￨L￨,￨O￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- impacts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- outcome￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- sections￨L￨NNS￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- stochastic￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- formulated￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible-Infectious-Recovered￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Ross￨U￨NNP￨PERSON￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A host-vector￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- additional￨L￨JJ￨O￨- examples￨L￨NNS￨O￨A and￨L￨CC￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- consult￨L￨VB￨O￨- the￨L￨DT￨O￨- textbooks￨L￨NNS￨O￨- and￨L￨CC￨O￨- papers￨L￨NNS￨O￨- listed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- references￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- well-known￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- illustration￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- host-vector￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- can￨L￨MD￨O￨- play￨L￨VB￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- helping￨L￨VBG￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- possible￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A by￨L￨IN￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- determining￨L￨VBG￨O￨- threshold￨L￨NN￨O￨- quantities￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- survival￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- elaborate￨L￨VB￨O￨- on￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- ways￨L￨NNS￨O￨- of￨L￨IN￨O￨- finding￨L￨VBG￨O￨- for￨L￨IN￨O￨- ODE￨U￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- bearing￨L￨VBG￨O￨- in￨L￨IN￨O￨- mind￨L￨NN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- meaning￨L￨NN￨O￨- of￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- how￨L￨WRB￨O￨- this￨L￨DT￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- guide￨L￨VB￨O￨- control￨L￨NN￨O￨A strategies￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemiological￨L￨JJ￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- infected￨L￨JJ￨O￨A individual￨L￨JJ￨O￨A introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- has￨L￨VBZ￨O￨- acquired￨L￨VBN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- healthy￨L￨JJ￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- acquire￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Sections￨U￨NNS￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- apply￨L￨VB￨O￨- these￨L￨DT￨O￨- ideas￨L￨NNS￨O￨A to￨L￨TO￨O￨- models￨L￨NNS￨O￨- specific￨L￨JJ￨O￨- for￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Nile￨U￨NNP￨LOCATION￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- birds￨L￨NNS￨O￨- ,￨L￨,￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- anthrax￨L￨NN￨O￨- in￨L￨IN￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- numerical￨L￨JJ￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- references￨L￨NNS￨O￨A given￨L￨VBN￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- proofs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- detailed￨L￨VBN￨O￨- here￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Model-based￨U￨JJ￨MISC￨- assessments￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- done￨L￨VBN￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- outbreaks￨L￨NNS￨O￨- :￨L￨:￨O￨- this￨L￨DT￨O￨- was￨L￨VBD￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- for￨L￨IN￨O￨- MERS-CoV￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Middle￨U￨NNP￨LOCATION￨- East￨U￨NNP￨LOCATION￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A in￨L￨IN￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- [￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- chikungunya￨L￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Americas￨U￨NNPS￨LOCATION￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2017￨L￨CD￨DATE￨- ZIKV￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- Guadeloupe￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- Martinique￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Saint-Martin￨U￨NNP￨PERSON￨- was￨L￨VBD￨O￨- collected￨L￨VBN￨O￨- by￨L￨IN￨O￨- local￨L￨JJ￨O￨- sentinel￨L￨NN￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- practitioners￨L￨NNS￨O￨- and￨L￨CC￨O￨- reported￨L￨VBD￨O￨- weekly￨L￨JJ￨SET￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- health￨L￨NN￨O￨A authorities￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- hierarchical￨L￨JJ￨O￨A statistical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- and￨L￨CC￨O￨- extract￨L￨VB￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- historical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- distributions￨L￨NNS￨O￨- for￨L￨IN￨O￨- required￨L￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Griffiths￨U￨NNP￨PERSON￨- phases￨L￨NNS￨O￨- in￨L￨IN￨O￨- infinite-dimensional￨L￨JJ￨O￨- ,￨L￨,￨O￨- non-hierarchical￨L￨JJ￨O￨- modular￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- Wesley￨U￨NNP￨PERSON￨- Cota￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Géza￨U￨NNP￨O￨- Ódor￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Silvio￨U￨NNP￨PERSON￨- C.￨U￨NNP￨PERSON￨- Ferreira￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 9144￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksPhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractGriffiths￨U￨NNP￨O￨- phases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- GPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneities￨L￨NNS￨O￨- on￨L￨IN￨O￨- modular￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- ,￨L￨,￨O￨- rid￨L￨JJ￨O￨- of￨L￨IN￨O￨- fine￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- tuning￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- activity￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- evolving￨L￨VBG￨O￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- random￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- highly￨L￨RB￨O￨- modular￨L￨JJ￨O￨A structure￨L￨NN￨O￨- and￨L￨CC￨O￨- organized￨L￨VBN￨O￨- non-hierarchically￨L￨RB￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- consequence￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- extended￨L￨JJ￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- regions￨L￨NNS￨O￨- with￨L￨IN￨O￨- continuously￨L￨RB￨O￨- changing￨L￨VBG￨O￨- dynamical￨L￨JJ￨O￨- exponents￨L￨NNS￨O￨- for￨L￨IN￨O￨- single￨L￨JJ￨O￨- network￨L￨NN￨O￨- realizations￨L￨NNS￨O￨- ,￨L￨,￨O￨- preserved￨L￨VBN￨O￨- after￨L￨IN￨O￨- finite￨L￨JJ￨O￨A size￨L￨NN￨O￨- analyses￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- GP￨U￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- conjectured￨L￨VBD￨O￨- requirement￨L￨NN￨O￨- for￨L￨IN￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- modular￨L￨JJ￨O￨A structures￨L￨NNS￨O￨- was￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- modules￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- hierarchically￨L￨RB￨O￨- organized￨L￨VBN￨O￨- and￨L￨CC￨O￨- possess￨L￨VBP￨O￨- finite￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- .￨L￨.￨O￨- +Subsequent￨U￨JJ￨O￨- development￨L￨NN￨O￨- has￨L￨VBZ￨O￨- largely￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- Bayesian￨U￨JJ￨MISC￨- approaches￨L￨NNS￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- prior￨L￨RB￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- piecewise￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- techniques￨L￨NNS￨O￨- are￨L￨VBP￨O￨- derivatives￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- skyline￨L￨NN￨O￨- coalescent￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- piecewise￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- nonparametric￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- its￨L￨PRP$￨O￨- logarithm￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- Brownian￨U￨JJ￨MISC￨- motion￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Genealogies￨U￨NNS￨O￨- often￨L￨RB￨O￨- provide￨L￨VBP￨O￨- very￨L￨RB￨O￨- little￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A near￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- sample￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- exponentially￨L￨RB￨O￨- increasing￨L￨VBG￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Below￨U￨IN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- prior￨L￨JJ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- autoregressive￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- effective￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- study￨L￨NN￨O￨- illustrated￨L￨VBD￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨- theory￨L￨NN￨O￨- in￨L￨IN￨O￨- establishing￨L￨VBG￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- educational￨L￨JJ￨O￨- campaign￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- persons￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- cutting￨L￨VBG￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- indirect￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- via￨L￨IN￨O￨- free-living￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- present￨L￨JJ￨DATE￨- symptoms￨L￨NNS￨O￨- and￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- present￨L￨VBP￨DATE￨- symptoms￨L￨NNS￨O￨- but￨L￨CC￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- hospital￨L￨NN￨O￨- and￨L￨CC￨O￨- hospitalized￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- present￨L￨VBP￨DATE￨- symptoms￨L￨NNS￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- admitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- hospital￨L￨NN￨O￨- could￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- HFMD￨U￨NN￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Thailand￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- roles￨L￨NNS￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- contaminated￨L￨VBN￨O￨- environments￨L￨NNS￨O￨- were￨L￨VBD￨O￨- investigated￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨A results￨L￨NNS￨O￨A show￨L￨VBP￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- factors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- delay￨L￨VB￨O￨- and￨L￨CC￨O￨- prevent￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Thailand￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- HFMD￨U￨NN￨O￨- models￨L￨NNS￨O￨- only￨L￨RB￨O￨- analysed￨L￨VBD￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- hand-washing￨L￨NN￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨A contact￨L￨NN￨O￨A rate￨L￨NN￨O￨- and￨L￨CC￨O￨- school￨L￨NN￨O￨- closure￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +applied￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- without￨L￨IN￨O￨- hospitalized￨L￨VBN￨O￨A but￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- hospitalized￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- with￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +HFMD￨U￨NN￨O￨- spreads￨L￨NNS￨O￨- mainly￨L￨RB￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- under￨L￨IN￨O￨- five￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨DURATION￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- these￨L￨DT￨O￨- viruses￨L￨NNS￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Three￨U￨CD￨NUMBER￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- simulated￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- are￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- :￨L￨:￨O￨- daily￨L￨JJ￨SET￨- snapshots￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- black￨L￨JJ￨O￨- line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- weekly￨L￨JJ￨SET￨- aggregated￨L￨JJ￨O￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- with￨L￨IN￨O￨- no￨L￨DT￨O￨- reporting￨L￨NN￨O￨A error￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- perfect￨L￨JJ￨O￨- reporting￨L￨NN￨O￨- ,￨L￨,￨O￨- blue￨L￨JJ￨O￨- line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- weekly￨L￨JJ￨SET￨- aggregated￨L￨JJ￨O￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- with￨L￨IN￨O￨- reporting￨L￨VBG￨O￨- error￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- imperfect￨L￨JJ￨O￨- reporting￨L￨NN￨O￨- ,￨L￨,￨O￨- red￨L￨JJ￨O￨- line￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- top￨L￨JJ￨O￨- panel￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- calculated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- :￨L￨:￨O￨- daily￨L￨JJ￨SET￨- snapshots￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- black￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- weekly￨L￨JJ￨SET￨A case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- blue￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- monthly￨L￨JJ￨SET￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- red￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Estimates￨U￨NNS￨O￨- for￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- reporting￨L￨VBG￨O￨A efficacy￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- USA￨U￨NNP￨COUNTRY￨- are￨L￨VBP￨O￨- around￨L￨IN￨O￨- 45￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- NumericCitation￨U￨NN￨O￨- In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- raw￨L￨JJ￨O￨- weekly￨L￨JJ￨SET￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- bottom￨L￨JJ￨O￨- row￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- aggregated￨L￨VBN￨O￨- into￨L￨IN￨O￨- bi-weekly￨L￨JJ￨SET￨- and￨L￨CC￨O￨- four-weekly￨L￨JJ￨DURATION￨- reports￨L￨NNS￨O￨- .￨L￨.￨O￨- +Transmission￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- birth￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- with￨L￨IN￨O￨- average￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 106￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- importation￨L￨NN￨O￨- rate￨L￨NN￨O￨- ζ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- case￨L￨NN￨O￨- per￨L￨IN￨O￨- week￨L￨NN￨DURATION￨A ,￨L￨,￨O￨- mean￨L￨VB￨O￨- life￨L￨NN￨O￨- expectancy￨L￨NN￨O￨- of￨L￨IN￨O￨- 70￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- mean￨L￨VB￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- 1￨L￨CD￨DURATION￨- week￨L￨NN￨DURATION￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- case￨L￨NN￨O￨- aggregation￨L￨NN￨O￨- and￨L￨CC￨O￨- reporting￨L￨VBG￨O￨A error￨L￨NN￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- mismatch￨L￨NN￨O￨- between￨L￨IN￨O￨- snapshots￨L￨NNS￨O￨- and￨L￨CC￨O￨- imperfect￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- interacting￨L￨VBG￨O￨- factors￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- —￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- chickenpox￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A may￨L￨MD￨O￨- impact￨L￨VB￨O￨- shingles￨L￨NNS￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- epidemiology￨L￨NN￨O￨- —￨L￨:￨O￨- complements￨L￨VBZ￨O￨- conventional￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- offers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- controlled￨L￨JJ￨O￨- study￨L￨NN￨O￨- using￨L￨VBG￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- exogenous￨L￨JJ￨O￨- VZV-CMI￨U￨NN￨O￨- boosting￨L￨VBG￨O￨A has￨L￨VBZ￨O￨- sparked￨L￨VBN￨O￨- a￨L￨DT￨O￨- debate￨L￨NN￨O￨- about￨L￨IN￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- chickenpox￨L￨NN￨O￨- vaccine￨L￨NN￨O￨- will￨L￨MD￨O￨- limit￨L￨VB￨O￨- the￨L￨DT￨O￨- boosting￨L￨VBG￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- to￨L￨TO￨O￨- shingles￨L￨NNS￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- to-date￨L￨NN￨O￨- is￨L￨VBZ￨O￨- largely￨L￨RB￨O￨- inconclusive￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- studies￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- shingles￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- increasing￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- recent￨L￨JJ￨DURATION￨- decades￨L￨NNS￨DURATION￨- prior￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- chickenpox￨L￨NN￨O￨- vaccination￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- previous￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- studies￨L￨NNS￨O￨A of￨L￨IN￨O￨- shingles￨L￨NNS￨O￨- and￨L￨CC￨O￨- chickenpox￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- conducted￨L￨VBN￨O￨- using￨L￨VBG￨O￨- aggregate￨L￨JJ￨O￨- population-level￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- antigenic￨L￨JJ￨O￨- drift￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- immunity￨L￨NN￨O￨- generates￨L￨VBZ￨O￨- virus￨L￨NN￨O￨- strains￨L￨NNS￨O￨A that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- covered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- requires￨L￨VBZ￨O￨- frequent￨L￨JJ￨O￨- reformulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- drifted￨L￨VBN￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- relative￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- strains￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- cross-immunity￨L￨NN￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extend￨L￨VBP￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- antigenically￨L￨RB￨O￨- distinct￨L￨JJ￨O￨- co-circulating￨L￨JJ￨O￨- strains￨L￨NNS￨O￨A and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- which￨L￨WDT￨O￨- targets￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- trivalent￨L￨JJ￨O￨- inactivated￨L￨VBN￨O￨- vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TIV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- primarily￨L￨RB￨O￨- induces￨L￨VBZ￨O￨- humoral￨L￨JJ￨O￨- strain-specific￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- directed￨L￨VBN￨O￨- against￨L￨IN￨O￨- HA￨U￨NNP￨O￨- and￨L￨CC￨O￨- NA￨U￨NNP￨O￨- included￨L￨VBD￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- and￨L￨CC￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- generate￨L￨VB￨O￨- broad￨L￨JJ￨O￨- cross-immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- mismatched￨L￨JJ￨O￨- strains￨L￨NNS￨O￨A .￨L￨.￨O￨- +Cases￨U￨NNS￨O￨- analyzed￨L￨VBD￨O￨- just￨L￨RB￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- that￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- 42￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- were￨L￨VBD￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- strains￨L￨NNS￨O￨A antigenically￨L￨RB￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- strain￨L￨NN￨O￨- included￨L￨VBD￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- season￨L￨NN￨O￨- ’s￨L￨POS￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Opinions￨U￨NNS￨O￨- ,￨L￨,￨O￨- behaviours￨L￨NNS￨O￨- ,￨L￨,￨O￨- knowledge￨L￨NN￨O￨- or￨L￨CC￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- represented￨L￨VBN￨O￨- as￨L￨IN￨O￨- concepts￨L￨NNS￨O￨A that￨L￨WDT￨O￨- spread￨L￨VBP￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- chance￨L￨NN￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- the￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- they￨L￨PRP￨O￨- encounter￨L￨VBP￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- concepts￨L￨NNS￨O￨A has￨L￨VBZ￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- real-world￨L￨JJ￨O￨- environments￨L￨NNS￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- multiple￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨A active￨L￨JJ￨O￨- simultaneously￨L￨RB￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- concept￨L￨NN￨O￨- interaction￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- concept￨L￨NN￨O￨- ’s￨L￨POS￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- .￨L￨.￨O￨- +Existing￨U￨VBG￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨- spread￨L￨NN￨O￨- typically￨L￨RB￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- concept￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- that￨L￨DT￨O￨- concepts￨L￨NNS￨O￨A block￨L￨VBP￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨- ,￨L￨,￨O￨- preventing￨L￨VBG￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- from￨L￨IN￨O￨- activating￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- that￨L￨IN￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- most￨L￨JJS￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- influence￨L￨NN￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- select￨L￨VB￨O￨- seed￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- concept￨L￨NN￨O￨A we￨L￨PRP￨O￨- wish￨L￨VBP￨O￨- to￨L￨TO￨O￨- maximise￨L￨VB￨O￨- .￨L￨.￨O￨- +Climate￨U￨NN￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- temperature￨L￨NN￨O￨- and￨L￨CC￨O￨- precipitation￨L￨NN￨O￨- significantly￨L￨RB￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- life￨L￨NN￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A mosquitoes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- thus￨L￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- factors￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- included￨L￨VBN￨O￨- in￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- two-patch￨L￨JJ￨O￨- dengue￨L￨NN￨O￨A transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- seasonality￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- patch-specific￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- Aedes￨U￨NNS￨O￨- mosquitoes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- found￨L￨VBN￨O￨- on￨L￨IN￨O￨- Jeju￨U￨NNP￨LOCATION￨- Island￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- humid￨L￨JJ￨O￨- subtropical￨L￨JJ￨O￨- climate￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- warmer￨L￨JJR￨O￨- than￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- in￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- inflow￨L￨NN￨O￨- of￨L￨IN￨O￨- travelers￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- island￨L￨NN￨O￨A has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- increased￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- autochthonous￨L￨JJ￨O￨- dengue￨L￨NN￨O￨- transmission￨L￨NN￨O￨- on￨L￨IN￨O￨- Jeju￨U￨NNP￨LOCATION￨- Island￨U￨NNP￨LOCATION￨- is￨L￨VBZ￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- Korea￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- susceptible-exposed-infectious-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- dengue￨L￨JJ￨O￨A strains￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- mosquitoes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Chen￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Hsieh￨U￨NNP￨PERSON￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- temperature￨L￨NN￨O￨- variation￨L￨NN￨O￨- on￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single-strain￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Assuming￨U￨VBG￨O￨- that￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- routine￨L￨JJ￨O￨- RCV￨U￨NN￨O￨- coverage￨L￨NN￨O￨A rates￨L￨NNS￨O￨- will￨L￨MD￨O￨- reflect￨L￨VB￨O￨- current￨L￨JJ￨DATE￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- India￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- RCV￨U￨NNP￨O￨- coverage￨L￨NN￨O￨- rates￨L￨NNS￨O￨- will￨L￨MD￨O￨- likely￨L￨RB￨O￨- range￨L￨VB￨O￨- between￨L￨IN￨O￨- 53￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- 96￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- across￨L￨IN￨O￨- Indian￨U￨JJ￨NATIONALITY￨- states￨L￨NNS￨O￨- ’￨L￨POS￨O￨- rural￨L￨JJ￨O￨- and￨L￨CC￨O￨- urban￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- areas￨L￨NNS￨O￨- with￨L￨IN￨O￨- coverage￨L￨NN￨O￨- below￨L￨IN￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- long-and￨L￨JJ￨O￨- short-term￨L￨JJ￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- examining￨L￨VBG￨O￨- childhood￨L￨NN￨O￨- immunisation￨L￨NN￨O￨- programmes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- suggested￨L￨VBN￨O￨- that￨L￨IN￨O￨- 80￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- RCV￨U￨NN￨O￨- coverage￨L￨NN￨O￨A is￨L￨VBZ￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- long-term￨L￨JJ￨O￨- increases￨L￨NNS￨O￨- in￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- incidence￨L￨NN￨O￨- post-RCV￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- across￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- contexts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- short-term￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- annual￨L￨JJ￨SET￨- )￨L￨-RRB-￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- post-RCV￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- CRS￨U￨NNP￨O￨- in￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨JJ￨O￨- year￨L￨NN￨DURATION￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Greece￨U￨NNP￨COUNTRY￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- Costa￨U￨NNP￨COUNTRY￨- Rica￨U￨NNP￨COUNTRY￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- 1998￨L￨CD￨DATE￨- –￨L￨:￨O￨- 99￨L￨CD￨NUMBER￨- rubella￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- both￨L￨DT￨O￨- these￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- followed￨L￨VBD￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- low￨L￨JJ￨O￨- coverage￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- RCV￨U￨NN￨O￨- introduction￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulated￨L￨JJ￨O￨- rubella￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨- across￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- vaccination￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- CRS￨U￨NNP￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- of￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- to￨L￨TO￨O￨- mosquito￨L￨NN￨O￨- bites￨L￨VBZ￨O￨A was￨L￨VBD￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- factors￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- proximity￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- aquatic￨L￨JJ￨O￨- habitats￨L￨NNS￨O￨- of￨L￨IN￨O￨- immature￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- house￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- insecticide￨L￨NN￨O￨- use￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- movements￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- forth￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- individual￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- biting￨L￨VBG￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- mosquito￨L￨NN￨O￨- bites￨L￨VBZ￨O￨A some￨L￨DT￨O￨- hosts￨L￨NNS￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- others￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- human￨L￨JJ￨O￨- sex￨L￨NN￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- pregnancy￨L￨NN￨O￨- ,￨L￨,￨O￨- defensive￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- blood￨L￨NN￨O￨- type￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- odors￨L￨NNS￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- others￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- compartmental-type￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- generally￨L￨RB￨O￨- assumed￨L￨VBD￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- mixing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- bites￨L￨VBZ￨O￨A of￨L￨IN￨O￨- humans￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- can￨L￨MD￨O￨- bite￨L￨VB￨O￨- any￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- equal￨L￨JJ￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- heterogeneity￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨A dynamics￨L￨NNS￨O￨A have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- addressed￨L￨VBN￨O￨- using￨L￨VBG￨O￨- meta-population￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- virus￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨A and/or￨L￨CC￨O￨- cost￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Each￨U￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- four￨L￨CD￨NUMBER￨- sets￨L￨NNS￨O￨A match￨L￨VBP￨O￨- the￨L￨DT￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- edges￨L￨NNS￨O￨- ,￨L￨,￨O￨- node￨L￨NN￨O￨- attributes￨L￨NNS￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- GWESP￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- geometrically￨L￨RB￨O￨- weighted￨L￨JJ￨O￨- edgewise￨L￨NN￨O￨- shared￨L￨VBD￨O￨- partner￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- statistic￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- triangles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- networks￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Faux￨U￨NNP￨ORGANIZATION￨- Magnolia￨U￨NNP￨ORGANIZATION￨- network￨L￨NN￨O￨- matches￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Add￨U￨VB￨O￨- Health￨U￨NNP￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨A ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- triangles￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- ERGM￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- candidate￨L￨NN￨TITLE￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- gives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- observing￨L￨VBG￨O￨A an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- α￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- process￨L￨NN￨O￨- with￨L￨IN￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- x￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Networks￨U￨NNP￨O￨- drawn￨L￨VBN￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- have￨L￨VBP￨O￨- values￨L￨NNS￨O￨A of￨L￨IN￨O￨- these￨L￨DT￨O￨- statistics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- closely￨L￨RB￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- observed￨L￨VBN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- otherwise￨L￨RB￨O￨- random￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- sets￨L￨NNS￨O￨A are￨L￨VBP￨O￨- generated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- GWESP￨U￨NN￨MISC￨- statistic￨L￨NN￨O￨- ,￨L￨,￨O￨- 0.25￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 0.5￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- Bayesian￨U￨JJ￨O￨- fitting￨L￨JJ￨O￨- models￨L￨NNS￨O￨- explore￨L￨VBP￨O￨- an￨L￨DT￨O￨- approach￨L￨NN￨O￨- that￨L￨WDT￨O￨- matches￨L￨VBZ￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- various￨L￨JJ￨O￨- simplifications￨L￨NNS￨O￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- explore￨L￨VBP￨O￨- simpler￨L￨JJR￨O￨- methods￨L￨NNS￨O￨- of￨L￨IN￨O￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- observation￨L￨NN￨O￨A process￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- relatively￨L￨RB￨O￨- simple￨L￨JJ￨O￨- MCMC￨U￨NN￨ORGANIZATION￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- incorporate￨L￨VBP￨O￨- stochasticity￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- observation￨L￨NN￨O￨A ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- variable￨L￨JJ￨O￨- generation-interval￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- not￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- known￨L￨VBN￨O￨- when￨L￨WRB￨O￨- fitting￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- relatively￨L￨RB￨O￨- straightforward￨L￨JJ￨O￨- to￨L￨TO￨O￨- relax￨L￨VB￨O￨- this￨L￨DT￨O￨- assumption￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- by￨L￨IN￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- finer￨L￨JJR￨TITLE￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- reporting￨L￨VBG￨O￨- interval￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- in￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- but￨L￨CC￨O￨- fitting￨L￨JJ￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- we￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- explore￨L￨VB￨O￨- these￨L￨DT￨O￨- questions￨L￨NNS￨O￨- here￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- generated￨L￨VBD￨O￨- test￨L￨NN￨O￨- data￨L￨NNS￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- process￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- discrete-time￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- observation￨L￨NN￨O￨A process￨L￨NN￨O￨- to￨L￨TO￨O￨- account￨L￨VB￨O￨- for￨L￨IN￨O￨- incomplete￨L￨JJ￨O￨- reporting￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- then￨L￨RB￨O￨- fit￨L￨VBP￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- simulations￨L￨NNS￨O￨- using￨L￨VBG￨O￨- Bayesian￨U￨JJ￨MISC￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- model￨L￨VBP￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- true￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- latent￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- unobserved￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- variable￨L￨NN￨O￨A .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Under￨U￨IN￨O￨- a￨L￨DT￨O￨- favorable￨L￨JJ￨O￨- scenario￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- is￨L￨VBZ￨O￨- cost-saving￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- negative￨L￨JJ￨O￨- incremental￨L￨JJ￨O￨- cost-effective￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- ;￨L￨:￨O￨- ICER￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- costs￨L￨VBZ￨O￨- up￨L￨RP￨O￨- to￨L￨TO￨O￨- US$￨U￨$￨MONEY￨- 6￨L￨CD￨MONEY￨- per￨L￨IN￨O￨- individual￨L￨NN￨O￨- without￨L￨IN￨O￨- herd￨L￨NN￨O￨A immunity￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- US$￨U￨$￨MONEY￨- 4￨L￨CD￨MONEY￨- per￨L￨IN￨O￨- individual￨L￨NN￨O￨- with￨L￨IN￨O￨- 8￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- herd￨L￨NN￨O￨- immunity￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Using￨U￨VBG￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- ZIKV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- Colombian￨U￨JJ￨NATIONALITY￨- population￨L￨NN￨O￨- setting￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- conducted￨L￨VBD￨O￨- cost-effectiveness￨L￨NN￨O￨- analysis￨L￨NN￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- without￨L￨IN￨O￨- pre-existing￨L￨JJ￨O￨- herd￨L￨NN￨O￨A immunity￨L￨NN￨O￨A .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Cost-effectiveness￨U￨NN￨MISC￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- Zika￨U￨NNP￨PERSON￨- vaccine￨L￨NN￨O￨- candidate￨L￨NN￨TITLE￨A :￨L￨:￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- for￨L￨IN￨O￨- ColombiaAffan￨U￨NNP￨O￨- Shoukat1￨U￨NN￨O￨- ,￨L￨,￨O￨- Thomas￨U￨NNP￨PERSON￨- Vilches2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Seyed￨U￨NNP￨O￨- M￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- elevated￨L￨JJ￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- arises￨L￨VBZ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- with￨L￨IN￨O￨- either￨L￨CC￨O￨- reproduction￨L￨NN￨O￨- later￨L￨RB￨O￨- in￨L￨IN￨O￨- life￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- a0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- z￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- juveniles￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- reproduce￨L￨VB￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- maturation￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- g0￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- z￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a0￨L￨NN￨O￨- and￨L￨CC￨O￨- g0￨L￨NN￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- reproduction￨L￨NN￨O￨- and￨L￨CC￨O￨- maturation￨L￨NN￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- when￨L￨WRB￨O￨- juvenile￨L￨JJ￨O￨- and￨L￨CC￨O￨- adult￨L￨JJ￨O￨A susceptibility￨L￨NN￨O￨- are￨L￨VBP￨O￨- equal￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨A is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- high￨L￨JJ￨O￨- when￨L￨WRB￨O￨- hosts￨L￨NNS￨O￨- have￨L￨VBP￨O￨- short￨L￨JJ￨O￨- or￨L￨CC￨O￨- long￨L￨JJ￨O￨- lifespans￨L￨NNS￨O￨- and￨L￨CC￨O￨- low￨L￨JJ￨O￨- or￨L￨CC￨O￨- high￨L￨JJ￨O￨- probabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- reaching￨L￨VBG￨O￨- maturity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- low￨L￨JJ￨O￨- in￨L￨IN￨O￨- between￨L￨IN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- and￨L￨CC￨O￨- mode￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- a￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- what￨L￨WP￨O￨- drives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- hosts￨L￨NNS￨O￨- trade-off￨L￨NN￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- with￨L￨IN￨O￨- maturation￨L￨NN￨O￨- or￨L￨CC￨O￨- reproduction￨L￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- adult￨L￨JJ￨O￨A stage￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- growth￨L￨NN￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- important￨L￨JJ￨O￨- during￨L￨IN￨O￨- juvenile￨L￨JJ￨O￨- than￨L￨IN￨O￨- during￨L￨IN￨O￨- adult￨L￨JJ￨O￨A stages￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- trade-off￨L￨NN￨O￨- only￨L￨RB￨O￨- occurs￨L￨VBZ￨O￨- between￨L￨IN￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- maturation/adult￨L￨NN￨O￨- reproduction￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- explore￨L￨VBP￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- elevated￨L￨JJ￨O￨- juvenile￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- well-mixed￨L￨JJ￨O￨- ,￨L￨,￨O￨- asexual￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- where￨L￨WRB￨O￨- adult￨L￨JJ￨O￨A susceptibility￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- held￨L￨VBN￨O￨- constant￨L￨JJ￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- far￨L￨RB￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨A could￨L￨MD￨O￨- help￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- make￨L￨VBP￨O￨- judgements￨L￨NNS￨O￨- about￨L￨IN￨O￨- policy￨L￨NN￨O￨- ,￨L￨,￨O￨- infer￨L￨VBP￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- side￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- lies￨L￨VBZ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- track￨L￨VBP￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- towards￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- providing￨L￨VBG￨O￨- early￨L￨JJ￨O￨- warnings￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- even￨L￨RB￨O￨- away￨L￨RB￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- of￨L￨IN￨O￨- evaluating￨L￨VBG￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- external￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- aimed￨L￨VBN￨O￨- at￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- Wiggins￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- written￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨A field￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- overdot￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- derivative￨L￨JJ￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- phase￨L￨NN￨O￨- space￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- θ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- explain￨L￨VB￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- challenges￨L￨NNS￨O￨- in￨L￨IN￨O￨- further￨L￨JJ￨O￨- developing￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- make￨L￨VB￨O￨- reference￨L￨NN￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- elements￨L￨NNS￨O￨- of￨L￨IN￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- 's￨L￨POS￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- arises￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- case￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvalues￨L￨NNS￨O￨A of￨L￨IN￨O￨- F￨U￨NN￨O￨- are￨L￨VBP￨O￨- continuous￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- θ￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- none￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- eigenvalues￨L￨NNS￨O￨- have￨L￨VBP￨O￨- zero￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- potentially￨L￨RB￨O￨- robust￨L￨JJ￨O￨- basis￨L￨NN￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- slowing￨L￨VBG￨O￨- down￨L￨RB￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- 's￨L￨POS￨O￨- dynamics￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- approached￨L￨VBN￨O￨- .￨L￨.￨O￨- +Where￨U￨WRB￨O￨- livestock￨L￨NN￨O￨A share￨L￨NN￨O￨- grazing￨L￨NN￨O￨- land￨L￨NN￨O￨- with￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- border￨L￨NN￨O￨- of￨L￨IN￨O￨- conservation￨L￨NN￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- parasite￨L￨JJ￨O￨- species￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- both￨L￨CC￨O￨- wild￨L￨JJ￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨- in￨L￨IN￨O￨- livestock￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- parasites￨L￨NNS￨O￨- in￨L￨IN￨O￨- wildlife￨L￨NN￨O￨- through￨L￨IN￨O￨- spillover￨L￨NN￨O￨- between￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- arid￨L￨JJ￨O￨- and￨L￨CC￨O￨- semi‐arid￨L￨JJ￨O￨- ecosystems￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- this￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- rainfall￨L￨NNS￨O￨- limits￨L￨VBZ￨O￨- the￨L￨DT￨O￨- survival￨L￨NN￨O￨- and￨L￨CC￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- free‐living￨L￨VBG￨O￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- worms￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- also￨L￨RB￨O￨- driving￨L￨VBG￨O￨- seasonal￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- potential￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨A diversity￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- migration￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- concentration￨L￨NN￨O￨- of￨L￨IN￨O￨- grazers￨L￨NNS￨O￨- around￨L￨IN￨O￨- seasonally￨L￨RB￨O￨- scarce￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- parasite￨L￨NN￨O￨- infects￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- six￨L￨CD￨NUMBER￨- species￨L￨NNS￨O￨- of￨L￨IN￨O￨- wild￨L￨JJ￨O￨- and￨L￨CC￨O￨- domestic￨L￨JJ￨O￨- ungulate￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- area￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- of￨L￨IN￨O￨- livestock￨L￨NN￨O￨A locally￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Gastrointestinal￨U￨JJ￨O￨- nematodes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- worms￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- determinant￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- production￨L￨NN￨O￨- and￨L￨CC￨O￨- fitness￨L￨NN￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- ungulate￨L￨JJ￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- domestic￨L￨JJ￨O￨A populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Predictive￨U￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- offer￨L￨VBP￨O￨A a￨L￨DT￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- effective￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- use￨L￨NN￨O￨- is￨L￨VBZ￨O￨- growing￨L￨VBG￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Meanwhile￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- the￨L￨DT￨O￨- surveillance￨L￨NN￨O￨- was￨L￨VBD￨O￨- initially￨L￨RB￨O￨- mainly￨L￨RB￨O￨- focused￨L￨VBN￨O￨- on￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- already￨L￨RB￨O￨- detected￨L￨VBN￨O￨- as￨L￨IN￨O￨- infected￨L￨VBN￨O￨- in￨L￨IN￨O￨- Corsica￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- areas￨L￨NNS￨O￨- surrounding￨L￨VBG￨O￨- positive￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- sampled￨L￨VBN￨O￨- host￨L￨NN￨TITLE￨- genera￨L￨NN￨O￨- and￨L￨CC￨O￨- sampled￨L￨VBN￨O￨- municipalities￨L￨NNS￨O￨- were￨L￨VBD￨O￨- later￨L￨RB￨O￨- significantly￨L￨RB￨O￨- increased￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- lower￨L￨JJR￨O￨- panel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- aim￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨JJR￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- X.￨U￨NNP￨MISC￨- fastidiosa￨L￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- highly￨L￨RB￨O￨- diverse￨L￨JJ￨O￨- plant￨L￨NN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- Corsica￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- large￨L￨JJ￨O￨- wild￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- hidden￨L￨JJ￨O￨A compartment/infection￨L￨NN￨O￨- reservoir￨L￨NN￨O￨- hypothesis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- plausible￨L￨JJ￨O￨- a￨L￨DT￨O￨- priori￨L￨FW￨O￨- and￨L￨CC￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- tested￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- multi‐host￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- settled￨L￨VBN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- environments￨L￨NNS￨O￨- mixing￨L￨VBG￨O￨- cultivated￨L￨VBN￨O￨- ,￨L￨,￨O￨- urban￨L￨JJ￨O￨- and￨L￨CC￨O￨- wild￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- unravelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- that￨L￨WDT￨O￨- underlies￨L￨VBZ￨O￨- observations￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- complicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- hidden￨L￨JJ￨O￨A compartment￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- hosts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- observable￨L￨JJ￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- play￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- reservoir￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- have￨L￨VBP￨O￨- an￨L￨DT￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- observations￨L￨NNS￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- observable￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- .￨L￨.￨O￨- +fastidiosa￨L￨NN￨O￨- to￨L￨TO￨O￨- invade￨L￨VB￨O￨- new￨L￨JJ￨O￨- environments￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- facilitated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- numerous￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- varying￨L￨VBG￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨- range￨L￨NN￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- preference￨L￨NN￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- multi‐host￨L￨JJ￨O￨- nature￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- difficulty￨L￨NN￨O￨- in￨L￨IN￨O￨- observing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- or￨L￨CC￨O￨- symptoms￨L￨NNS￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- other￨L￨JJ￨O￨- disorders￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- water￨L￨NN￨O￨- stress￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- framework￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete‐time￨L￨JJ￨O￨- Susceptible￨U￨NNP￨O￨- –￨L￨:￨O￨- Infected￨U￨JJ￨O￨- –￨L￨:￨O￨- Removed￨U￨VBN￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- hidden￨L￨JJ￨O￨A compartment￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- surveillance/control￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- and￨L￨CC￨O￨- results￨L￨VBZ￨O￨- A￨U￨DT￨O￨- stochastic￨L￨JJ￨O￨- lattice-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- couples￨L￨VBZ￨O￨- a￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- dispersal￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- susceptible-exposed-infected-recovered￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- environments￨L￨NNS￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- factors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- determinants￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A ,￨L￨,￨O￨- including￨L￨VBG￨O￨- climate￨L￨NN￨O￨- suitability￨L￨NN￨O￨- ,￨L￨,￨O￨- life￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- and￨L￨CC￨O￨- vectors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- mosquito￨L￨NN￨O￨- population￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Simple￨U￨JJ￨O￨- ,￨L￨,￨O￨- lumped-population￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A prevalence￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- insufficient￨L￨JJ￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- environmental￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- applicability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- capturing￨L￨VBG￨O￨- the￨L￨DT￨O￨- climate-driven￨L￨JJ￨O￨- hydrologic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- demographic￨L￨JJ￨O￨- variability￨L￨NN￨O￨- on￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- A￨U￨DT￨O￨- stochastic￨L￨JJ￨O￨- lattice-based￨L￨JJ￨O￨- integrated￨L￨VBN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- put￨L￨VBN￨O￨- forward￨L￨RB￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Identifying￨U￨VBG￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- gained￨L￨VBN￨O￨- great￨L￨JJ￨O￨- attention￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- research￨L￨NN￨O￨- community￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A is￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- its￨L￨PRP$￨O￨- position￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- proposed￨L￨VBN￨O￨- K-shell￨U￨NN￨MISC￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- ClusterRank￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- ranking￨L￨NN￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨A .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- contagion￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- rich￨L￨JJ￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- ,￨L￨,￨O￨- discontinuous￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hybrid￨L￨NN￨O￨- phase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- ,￨L￨,￨O￨- criticality￨L￨NN￨O￨- ,￨L￨,￨O￨- tricriticality￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- double￨L￨JJ￨O￨- transitions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- a￨L￨DT￨O￨- double￨L￨JJ￨O￨A phase￨L￨NN￨O￨- transition￨L￨NN￨O￨- showing￨L￨VBG￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- transition￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- following￨L￨VBG￨O￨- discontinuous￨L￨JJ￨O￨- transition￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- adopted￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- double￨L￨JJ￨O￨- transition￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- intermediate￨L￨JJ￨O￨- phase￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- following￨L￨VBG￨O￨- simple￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A become￨L￨VBP￨O￨- adopted￨L￨VBN￨O￨- but￨L￨CC￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- complex￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- remain￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- diagram￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- complex￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A .￨L￨.￨O￨- +With￨U￨IN￨O￨- this￨L￨DT￨O￨- probability￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- simple￨L￨JJ￨O￨- contagion￨L￨NN￨O￨A get￨L￨VB￨O￨- adopted￨L￨VBN￨O￨- and￨L￨CC￨O￨- trigger￨L￨VB￨O￨- a￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- manuscript￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A in￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- information￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- interactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- meta-paths￨L￨NNS￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Information￨U￨NNP￨O￨- Spread￨U￨NNP￨O￨- and￨L￨CC￨O￨- Topic￨U￨NNP￨O￨- Diffusion￨U￨NNP￨O￨- in￨L￨IN￨O￨- Heterogeneous￨U￨JJ￨O￨- Information￨U￨NN￨O￨- Networks￨U￨NNP￨O￨- Soheila￨U￨NNP￨O￨- Molaei1￨U￨NN￨O￨- ,￨L￨,￨O￨- Sama￨U￨FW￨PERSON￨- Babaei1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Mostafa￨U￨NNP￨PERSON￨- Salehi￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,2￨L￨NN￨O￨- &￨L￨CC￨O￨- Mahdi￨U￨NNP￨TITLE￨- Jalili3￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 9549￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Computer￨U￨NNP￨O￨- scienceInformation￨L￨NN￨O￨- technologyScientific￨L￨JJ￨O￨- data￨L￨NNS￨O￨- AbstractDiffusion￨U￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- largely￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- mainly￨L￨RB￨O￨- addressed￨L￨VBN￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨A in￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- where￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- consist￨L￨VBP￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨A types￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- edges￨L￨NNS￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- natural￨L￨JJ￨O￨- and￨L￨CC￨O￨- vaccine-derived￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- distinguished￨L￨VBN￨O￨- ,￨L￨,￨O￨- interpreting￨L￨VBG￨O￨- serological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- accounting￨L￨NN￨O￨- for￨L￨IN￨O￨- historical￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- achieved￨L￨VBN￨O￨- both￨L￨CC￨O￨- through￨L￨IN￨O￨- routine￨L￨JJ￨O￨- services￨L￨NNS￨O￨- and￨L￨CC￨O￨- SIAs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- we￨L￨PRP￨O￨- illustrate￨L￨VBP￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- coverage￨L￨NN￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- of￨L￨IN￨O￨- poor￨L￨JJ￨O￨- quality￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- misrepresent￨L￨VB￨O￨- population￨L￨NN￨O￨A immunity￨L￨NN￨O￨A because￨L￨IN￨O￨- most￨L￨JJS￨O￨- countries￨L￨NNS￨O￨- lack￨L￨VBP￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- under￨L￨IN￨O￨- field￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- an￨L￨DT￨O￨- average￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- effectiveness￨L￨NN￨O￨- ,￨L￨,￨O￨- may￨L￨MD￨O￨- overestimate￨L￨VB￨O￨- population￨L￨NN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- countries￨L￨NNS￨O￨- with￨L￨IN￨O￨- weak￨L￨JJ￨O￨- cold￨L￨JJ￨O￨- chain￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- analytic￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- population￨L￨NN￨O￨A immunity￨L￨NN￨O￨A profiles￨L￨NNS￨O￨- from￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- methods￨L￨NNS￨O￨- necessarily￨L￨RB￨O￨- rely￨L￨VBP￨O￨- on￨L￨IN￨O￨- indirect￨L￨JJ￨O￨- inference￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- rather￨L￨RB￨O￨- than￨L￨IN￨O￨- direct￨L￨JJ￨O￨- measurement￨L￨NN￨O￨- .￨L￨.￨O￨- +Depending￨U￨VBG￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- design￨L￨NN￨O￨- ,￨L￨,￨O￨- serological￨L￨JJ￨O￨- surveys￨L￨NNS￨O￨- can￨L￨MD￨O￨- reveal￨L￨VB￨O￨- “￨L￨``￨O￨- immunity￨L￨NN￨O￨A gaps￨L￨NNS￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- ie￨L￨FW￨O￨- ,￨L￨,￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- or￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- expected￨L￨VBN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- below￨L￨IN￨O￨- some￨L￨DT￨O￨- operational￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- identifying￨L￨VBG￨O￨- areas￨L￨NNS￨O￨- for￨L￨IN￨O￨- additional￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Elimination￨U￨NN￨O￨- efforts￨L￨NNS￨O￨- include￨L￨VBP￨O￨- attaining￨L￨NN￨O￨- and￨L￨CC￨O￨- sustaining￨L￨VBG￨O￨- high￨L￨JJ￨O￨- coverage￨L￨NN￨O￨A with￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- dose￨L￨NN￨O￨- of￨L￨IN￨O￨- MCV￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- scaling￨L￨VBG￨O￨- up￨L￨IN￨O￨- of￨L￨IN￨O￨- routine￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- dose￨L￨NN￨O￨- of￨L￨IN￨O￨- MCV￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- RCVs￨U￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- supplemental￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- [￨L￨-LRB-￨O￨- SIAs￨U￨NNS￨O￨- ]￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- campaigns￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- MCV￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- RCV￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- Measles￨U￨NNP￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- these￨L￨DT￨O￨- travellers￨L￨NNS￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- after￨L￨IN￨O￨- its￨L￨PRP$￨O￨- introduction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Δ￨U￨NN￨O￨- =￨L￨JJ￨O￨- 52￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- bywhere￨L￨JJ￨O￨- σ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potentially￨L￨RB￨O￨- infective￨L￨JJ￨O￨- contact￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- arrived￨L￨VBD￨O￨- at￨L￨IN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- t0￨L￨NN￨O￨- and￨L￨CC￨O￨- remains￨L￨VBZ￨O￨- infective￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- 1weeks￨L￨NNS￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨A rate￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disease-induced￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- θ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- t0￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Heaviside￨U￨NNP￨O￨- step￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +Many￨U￨JJ￨O￨- countries￨L￨NNS￨O￨- where￨L￨WRB￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- controlled￨L￨VBN￨O￨- in￨L￨IN￨O￨- past￨L￨JJ￨DATE￨- decades￨L￨NNS￨DURATION￨- are￨L￨VBP￨O￨- reporting￨L￨VBG￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- exotic￨L￨JJ￨O￨- and￨L￨CC￨O￨- frequently￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- spread￨L￨VBN￨O￨- by￨L￨IN￨O￨- infected￨L￨JJ￨O￨- travellers/immigrants￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- recent￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A spreading￨L￨VBG￨O￨- by￨L￨IN￨O￨- travellers￨L￨NNS￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- Zika￨U￨NN￨O￨- virus￨L￨NN￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Latin￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- imported￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- French￨U￨JJ￨NATIONALITY￨- Polynesia￨U￨NN￨O￨- by￨L￨IN￨O￨- infected￨L￨JJ￨O￨- travellers￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Situations￨U￨NNS￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- relatively￨L￨RB￨O￨A small￨L￨JJ￨O￨A number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- travel￨L￨VBP￨O￨- to￨L￨TO￨O￨- previously￨L￨RB￨DATE￨- disease-free￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- critical￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- below￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- b￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- p￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- β1￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨A infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- EV71￨U￨NN￨O￨- ;￨L￨:￨O￨- β2￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- CVA16￨U￨NN￨O￨- ;￨L￨:￨O￨- μ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- α￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- per-capita￨L￨JJ￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- progression￨L￨NN￨O￨- from￨L￨IN￨O￨- latent￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- q￨L￨JJ￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- EV71￨U￨NN￨O￨- from￨L￨IN￨O￨- latent￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- accordingly￨L￨RB￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- q￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- CVA16￨U￨NN￨O￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- human￨L￨JJ￨O￨- enteroviruses￨L￨NNS￨O￨- serotypes￨L￨NNS￨O￨- from￨L￨IN￨O￨- latent￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- d1￨L￨NN￨O￨- ,￨L￨,￨O￨- d2￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- induced￨L￨VBD￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- I1￨U￨NN￨O￨- ,￨L￨,￨O￨- I2￨U￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- γ1￨L￨NN￨O￨- ,￨L￨,￨O￨- γ2￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- I1￨U￨NN￨O￨- ,￨L￨,￨O￨- I2￨U￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- ω￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- η1￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- η2￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- controls￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- vaccination￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- individuals￨L￨NNS￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨A coefficient￨L￨NN￨O￨A β￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- byIt￨L￨NN￨O￨- is￨L￨VBZ￨O￨- clear￨L￨JJ￨O￨- thatwhich￨L￨NN￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- have￨L￨VBP￨O￨- contributed￨L￨VBN￨O￨- to￨L￨TO￨O￨- decrease￨L￨VB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- R0￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibria￨L￨NNS￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A of￨L￨IN￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- the￨L￨DT￨O￨- Lyapunov￨U￨NN￨MISC￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨A bounded￨L￨VBN￨O￨- feasible￨L￨JJ￨O￨- region￨L￨NN￨O￨- :￨L￨:￨O￨- Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- I￨U￨PRP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- may￨L￨MD￨O￨- reduce￨L￨VB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equivalent￨L￨JJ￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- with￨L￨IN￨O￨- Λ￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- b￨L￨NN￨O￨- +￨L￨CC￨O￨- pbη1￨L￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- +￨L￨CC￨O￨- η1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- positively￨L￨RB￨O￨- invariant￨L￨JJ￨O￨- setIn￨L￨NN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- discuss￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +Directly￨U￨RB￨O￨- calculating￨L￨VBG￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A P0￨U￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S0￨U￨NN￨O￨- ,￨L￨,￨O￨- E0￨U￨NN￨O￨- ,￨L￨,￨O￨- I0￨U￨NN￨O￨- ,￨L￨,￨O￨- T0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- S0￨U￨NN￨O￨- =￨L￨JJ￨O￨- Λ￨U￨NN￨O￨- /￨L￨:￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ω￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- E0￨U￨NN￨O￨- =￨L￨JJ￨O￨- I0￨U￨NN￨O￨- =￨L￨JJ￨O￨- T0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A of￨L￨IN￨O￨- collective￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- local￨L￨JJ￨O￨- perturbations￨L￨NNS￨O￨- trigger￨L￨VBP￨O￨- global￨L￨JJ￨O￨- activity￨L￨NN￨O￨- cascades￨L￨NNS￨O￨- that￨L￨WDT￨O￨- propagate￨L￨VB￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- linear￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Mišić￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,￨L￨,￨O￨- 2015￨L￨CD￨DATE￨- ;￨L￨:￨O￨- O￨U￨NN￨O￨- ’￨L￨''￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- diffusion￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- statistical￨L￨JJ￨O￨- associations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- functional￨L￨JJ￨O￨A connectivity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- distributed￨L￨VBN￨O￨- areas￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Goñi￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,￨L￨,￨O￨- 2013￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- functional￨L￨JJ￨O￨- brain￨L￨NN￨O￨- networks￨L￨NNS￨O￨- into￨L￨IN￨O￨- coherent￨L￨JJ￨O￨- modules￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- R￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- biological￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨- develops￨L￨VBZ￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- cascade￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- two￨L￨CD￨NUMBER￨- signals￨L￨NNS￨O￨A synergistically￨L￨RB￨O￨- spread￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- how￨L￨WRB￨O￨- two￨L￨CD￨NUMBER￨- signals￨L￨NNS￨O￨- ,￨L￨,￨O￨- endowed￨L￨JJ￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- content￨L￨NN￨O￨- ,￨L￨,￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- ultimately￨L￨RB￨O￨- integrate￨L￨VB￨O￨- with￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- report￨L￨NN￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- integration￨L￨NN￨O￨- of￨L￨IN￨O￨- neural￨L￨JJ￨O￨- signals￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- mesoscale￨L￨NN￨O￨- Drosophila￨U￨FW￨O￨- connectome￨L￨FW￨O￨- ,￨L￨,￨O￨- previously￨L￨RB￨DATE￨- reconstructed￨L￨VBN￨O￨- from￨L￨IN￨O￨- 12,995￨L￨CD￨NUMBER￨- images￨L￨NNS￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- neurons￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +IBMs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- well-suited￨L￨JJ￨O￨- for￨L￨IN￨O￨- creating￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨- and￨L￨CC￨O￨- studying￨L￨VBG￨O￨- intervention￨L￨NN￨O￨- impact￨L￨NN￨O￨- because￨L￨IN￨O￨- they￨L￨PRP￨O￨- allow￨L￨VBP￨O￨- for￨L￨IN￨O￨- attributes￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- added￨L￨VBN￨O￨- to￨L￨TO￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- environments￨L￨NNS￨O￨- without￨L￨IN￨O￨- exponentially￨L￨RB￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- items￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- compartments￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- tracked￨L￨VBN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- making￨L￨VBG￨O￨- the￨L￨DT￨O￨- code￨L￨NN￨O￨- and￨L￨CC￨O￨- documentation￨L￨NN￨O￨- openly￨L￨RB￨O￨- available￨L￨JJ￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- team￨L￨NN￨O￨- hopes￨L￨VBZ￨O￨- to￨L￨TO￨O￨- enable￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- researchers￨L￨NNS￨O￨- ,￨L￨,￨O￨- policy-makers￨L￨NNS￨O￨- ,￨L￨,￨O￨- implementers￨L￨NNS￨O￨- and￨L￨CC￨O￨- funders￨L￨NNS￨O￨- to￨L￨TO￨O￨- access￨L￨NN￨O￨- modeling￨L￨NN￨O￨- software￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- staffing￨L￨NN￨O￨- more￨L￨RBR￨O￨- commonly￨L￨RB￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- academic￨L￨JJ￨O￨- and￨L￨CC￨O￨- similar￨L￨JJ￨O￨- organizations￨L￨NNS￨O￨- .￨L￨.￨O￨- +IBMs￨U￨NNS￨O￨- ,￨L￨,￨O￨- also￨L￨RB￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- or￨L￨CC￨O￨- micro-simulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- use￨L￨VBP￨O￨- computer￨L￨NN￨O￨- simulation￨L￨NN￨O￨- to￨L￨TO￨O￨- track￨L￨VB￨O￨- interacting￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- environment￨L￨NN￨O￨- to￨L￨TO￨O￨- better￨L￨RBR￨O￨- understand￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- summarize￨L￨VBP￨O￨- the￨L￨DT￨O￨- decade-long￨L￨JJ￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- freely￨L￨RB￨O￨- available￨L￨JJ￨O￨A individual-based￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- EMOD￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- expanded￨L￨VBN￨O￨- beyond￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- other￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- share￨L￨VBP￨O￨- a￨L￨DT￨O￨- common￨L￨JJ￨O￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- gives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- flexibility￨L￨NN￨O￨- to￨L￨TO￨O￨- add￨L￨VB￨O￨- demographic￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- and￨L￨CC￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- flexibility￨L￨NN￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- transmission￨L￨NN￨O￨- might￨L￨MD￨O￨- occur￨L￨VB￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- still￨L￨RB￨O￨- preserving￨L￨VBG￨O￨- SEIRS￨U￨NNP￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- internal￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- .￨L￨.￨O￨- +falciparum￨L￨NN￨O￨A prevalence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- strains￨L￨NNS￨O￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- artemisinin-resistance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- k13￨L￨NN￨O￨- mutation￨L￨NN￨O￨- plus￨L￨CC￨O￨- a￨L￨DT￨O￨- slow￨L￨JJ￨O￨- clearing￨L￨NN￨O￨- phenotype￨L￨NN￨O￨- ,￨L￨,￨O￨- henceforth￨L￨NN￨O￨- ‘￨L￨``￨O￨- mutants￨L￨NNS￨O￨- ’￨L￨POS￨O￨- )￨L￨-RRB-￨O￨- until￨L￨IN￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨ORGANIZATION￨- criteria￨L￨NNS￨O￨- of￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨- partial￨L￨JJ￨O￨- artemisinin￨L￨NN￨O￨- resistance￨L￨NN￨O￨- is￨L￨VBZ￨O￨- met￨L￨VBN￨O￨- .￨L￨.￨O￨- +falciparum￨L￨NN￨O￨A prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- exposure-acquired￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- time-to-emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- artemisinin￨L￨NN￨O￨- resistance￨L￨NN￨O￨- .￨L￨.￨O￨- +I.￨U￨NN￨O￨- Fowkes1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 17:279￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Artemisinin-resistant￨U￨JJ￨O￨- Plasmodium￨U￨NN￨O￨- falciparum￨L￨NN￨O￨A has￨L￨VBZ￨O￨- emerged￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Greater￨U￨NNP￨LOCATION￨- Mekong￨U￨NNP￨LOCATION￨- Subregion￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- relatively￨L￨RB￨O￨- low￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- has￨L￨VBZ￨O￨- yet￨L￨RB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- immense￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- to￨L￨TO￨O￨- systematically￨L￨RB￨O￨- investigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- disparities￨L￨NNS￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- ,￨L￨,￨O￨- overall￨L￨JJ￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- via￨L￨IN￨O￨- metrics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- inoculation￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- vectorial￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- forth￨L￨RB￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- epidemiology￨L￨NN￨O￨A of￨L￨IN￨O￨- CL￨U￨NN￨O￨- is￨L￨VBZ￨O￨- complex￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- intraand￨L￨JJ￨O￨- inter-specific￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- ,￨L￨,￨O￨- reservoir￨L￨NN￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- sandfly￨L￨RB￨O￨- vectors￨L￨NNS￨O￨- ,￨L￨,￨O￨- clinical￨L￨JJ￨O￨- manifestations￨L￨NNS￨O￨- and￨L￨CC￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- therapy￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- multiple￨L￨JJ￨O￨- circulating￨L￨VBG￨O￨- Leishmania￨U￨NNP￨O￨- species￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- geographical￨L￨JJ￨O￨- area￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- 20￨L￨CD￨NUMBER￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- was￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- per￨L￨IN￨O￨- year￨L￨NN￨DURATION￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Madrid￨U￨NNP￨CITY￨- autonomous￨L￨JJ￨O￨A community￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- around￨L￨RB￨O￨- 0.5￨L￨CD￨NUMBER￨- per￨L￨IN￨O￨- 100,000￨L￨CD￨NUMBER￨- inhabitants￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Leishmaniasis￨U￨NN￨CAUSE_OF_DEATH￨- epidemiology￨L￨NN￨O￨A in￨L￨IN￨O￨- Colombia￨U￨NNP￨COUNTRY￨- :￨L￨:￨O￨- Colombia￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- America￨U￨NNP￨COUNTRY￨- region￨L￨NN￨O￨- with￨L￨IN￨O￨- highest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- supplement￨L￨VB￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨A with￨L￨IN￨O￨- more￨L￨JJR￨O￨- up-to-date￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- methods￨L￨NNS￨O￨- to￨L￨TO￨O￨- nowcast￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- provide￨L￨VBP￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- incidence￨L￨NN￨O￨- during￨L￨IN￨O￨- more￨L￨RBR￨O￨- recent￨L￨JJ￨DURATION￨- weeks￨L￨NNS￨DURATION￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- available￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- forecast￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- using￨L￨VBG￨O￨- online￨L￨JJ￨O￨- search￨L￨NN￨O￨- trends￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- twitter￨L￨NN￨O￨- feeds￨L￨VBZ￨O￨- [￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- access￨L￨NN￨O￨- logs￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza-related￨L￨JJ￨O￨- webpages￨L￨NNS￨O￨- at￨L￨IN￨O￨- Wikipedia￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- online￨L￨JJ￨O￨- news￨L￨NN￨O￨- and￨L￨CC￨O￨- informal￨L￨JJ￨O￨- reports￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- electronic￨L￨JJ￨O￨- health￨L￨NN￨O￨- records￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- also￨L￨RB￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- methods￨L￨NNS￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- model-inference￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- average￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- statistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- super-ensemble￨L￨NN￨O￨- of￨L￨IN￨O￨- eight￨L￨CD￨NUMBER￨- statistical￨L￨JJ￨O￨- and￨L￨CC￨O￨- mechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- —￨L￨:￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2017￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- point￨L￨NN￨O￨- and￨L￨CC￨O￨- probabilistic￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨A in￨L￨IN￨O￨- real￨L￨JJ￨O￨- time￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- FluSight￨U￨NN￨O￨- competition￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compare￨L￨VBP￨O￨- and￨L￨CC￨O￨- report￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- seven￨L￨CD￨NUMBER￨- targets￨L￨NNS￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- evaluated￨L￨VBN￨O￨- using￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- measures￨L￨NNS￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- logarithmic￨L￨JJ￨O￨- scoring￨L￨VBG￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- probabilistic￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- absolute￨L￨JJ￨O￨- error￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- point￨L￨NN￨O￨- forecasts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2014￨L￨CD￨DATE￨- season￨L￨NN￨O￨- ,￨L￨,￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- 's￨L￨POS￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- Division￨U￨NNP￨MISC￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- coordinating￨L￨VBG￨O￨- with￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- groups￨L￨NNS￨O￨- to￨L￨TO￨O￨- assemble￨L￨VB￨O￨- real-time￨L￨JJ￨O￨- weekly￨L￨JJ￨SET￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecasts￨L￨NNS￨O￨A at￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨ORGANIZATION￨- National￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Human￨U￨NNP￨ORGANIZATION￨- Services￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- HHS￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- regional￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- measure￨L￨VBP￨O￨- the￨L￨DT￨O￨- improvement￨L￨NN￨O￨- in￨L￨IN￨O￨- forecast￨L￨NN￨O￨- accuracy￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- nowcasts￨L￨NNS￨O￨- as￨L￨IN￨O￨- supplements￨L￨NNS￨O￨- to￨L￨TO￨O￨- near￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- ILI￨U￨NN￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- simulated￨L￨JJ￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- real-time￨L￨JJ￨O￨- decision-making￨L￨NN￨O￨- by￨L￨IN￨O￨- fitting￨L￨NN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- confirmed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- herd-level￨L￨NN￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- at￨L￨IN￨O￨- weekly￨L￨JJ￨SET￨- intervals￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- historical￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- foot-and-mouth￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- FMD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- economically￨L￨RB￨O￨- important￨L￨JJ￨O￨- livestock￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- forward￨L￨RB￨O￨A simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- culling￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- management￨L￨NN￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- total￨L￨JJ￨O￨- culls￨L￨NNS￨O￨- so￨L￨RB￨O￨- as￨L￨IN￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- disease-freedom￨L￨NN￨O￨- .￨L￨.￨O￨- +Recent￨U￨JJ￨O￨- research￨L￨NN￨O￨- has￨L￨VBZ￨O￨- outlined￨L￨VBN￨O￨- frameworks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- combine￨L￨VBP￨O￨- Bayesian￨U￨JJ￨MISC￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- generating￨L￨VBG￨O￨- real-time￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- severity￨L￨NN￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- aiming￨L￨VBG￨O￨- to￨L￨TO￨O￨- assimilate￨L￨VB￨O￨- available￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- into￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- estimates￨L￨NNS￨O￨A as￨L￨IN￨O￨- rapidly￨L￨RB￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Forward￨U￨RB￨O￨- simulations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- therefore￨L￨RB￨O￨- conditional￨L￨JJ￨O￨- upon￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨A state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- inferred￨L￨VBN￨O￨- ,￨L￨,￨O￨- undetected￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- having￨L￨VBG￨O￨- enacted￨L￨VBN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- controls￨L￨NNS￨O￨- until￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- question￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- become￨L￨VBP￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- improve￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- manner￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unfolding￨L￨VBG￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- estimates￨L￨NNS￨O￨A of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- of￨L￨IN￨O￨- where￨L￨WRB￨O￨- likely￨L￨JJ￨O￨- new￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- located￨L￨JJ￨O￨- ,￨L￨,￨O￨- via￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- but￨L￨CC￨O￨- undetected￨L￨JJ￨O￨- farms￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- repeated￨L￨VBD￨O￨- these￨L￨DT￨O￨- forward￨L￨RB￨O￨A simulations￨L￨NNS￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- point￨L￨NN￨O￨- using￨L￨VBG￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- fitted￨L￨VBD￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- thereby￨L￨RB￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- we￨L￨PRP￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- done￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨DATE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- we￨L￨PRP￨O￨- could￨L￨MD￨O￨- have￨L￨VB￨O￨- done￨L￨VBN￨O￨- in￨L￨IN￨O￨- retrospect￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- distinct￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- variations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- vector￨L￨NN￨O￨A abundance￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- running￨L￨VBG￨O￨- computer￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- CA￨U￨NNP￨STATE_OR_PROVINCE￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- each￨L￨DT￨O￨- cell￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- CA￨U￨NNP￨STATE_OR_PROVINCE￨- lattice￨L￨NN￨O￨A is￨L￨VBZ￨O￨- occupied￨L￨VBN￨O￨- by￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- individual￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- cell￨L￨NN￨O￨- there￨L￨EX￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- an￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- S-individual￨U￨JJ￨MISC￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- P￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- v￨L￨LS￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- eight￨L￨CD￨NUMBER￨- surrounding￨L￨VBG￨O￨- neighbors￨L￨NNS￨O￨A and￨L￨CC￨O￨- η￨L￨NN￨O￨- is￨L￨VBZ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- I-neighbors￨U￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- vectors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- CA￨U￨NNP￨STATE_OR_PROVINCE￨- lattice￨L￨NN￨O￨A is￨L￨VBZ￨O￨- V￨U￨NN￨O￨- =￨L￨JJ￨O￨- ∑￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- surveillance￨L￨NN￨O￨- systems￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- ultimate￨L￨JJ￨O￨- elimination￨L￨NN￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- contrast￨L￨NN￨O￨- to￨L￨TO￨O￨- merely￨L￨RB￨O￨- marginal￨L￨JJ￨O￨- declines￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- philanthropic￨L￨JJ￨O￨- funders￨L￨NNS￨O￨- ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- others￨L￨NNS￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- better￨L￨RBR￨O￨- armed￨L￨VBN￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- justify￨L￨VB￨O￨- and￨L￨CC￨O￨- target￨L￨VB￨O￨- efforts￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- longest￨L￨JJS￨O￨- last￨L￨JJ￨O￨- mile￨L￨NN￨O￨- ,￨L￨,￨O￨- ”￨L￨''￨O￨- especially￨L￨RB￨O￨- if￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- tipping￨L￨JJ￨O￨- point￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- crossed￨L￨VBN￨O￨- and￨L￨CC￨O￨- all￨L￨PDT￨O￨- that￨L￨DT￨O￨- remains￨L￨VBZ￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- sustain￨L￨VB￨O￨- the￨L￨DT￨O￨- gains￨L￨NNS￨O￨- already￨L￨RB￨O￨- achieved￨L￨VBN￨O￨- and￨L￨CC￨O￨- allow￨L￨VB￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- run￨L￨VB￨O￨- its￨L￨PRP$￨O￨- course￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- has￨L￨VBZ￨O￨- already￨L￨RB￨O￨- been￨L￨VBN￨O￨- crossed￨L￨VBN￨O￨- ,￨L￨,￨O￨- elimination￨L￨NN￨O￨A only￨L￨RB￨O￨- requires￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- policy￨L￨NN￨O￨- be￨L￨VB￨O￨- maintained￨L￨VBN￨O￨- while￨L￨IN￨O￨- transient￨L￨JJ￨O￨- chains￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- are￨L￨VBP￨O￨- allowed￨L￨VBN￨O￨- to￨L￨TO￨O￨- peter￨L￨VB￨O￨- out￨L￨RP￨O￨- ;￨L￨:￨O￨- alternatively￨L￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- is￨L￨VBZ￨O￨- near￨L￨IN￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- yet￨L￨RB￨O￨- crossed￨L￨VBN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- increases￨L￨VBZ￨O￨- in￨L￨IN￨O￨- effort￨L￨NN￨O￨- or￨L￨CC￨O￨- pulse￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- supplementary￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- push￨L￨VB￨O￨- the￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- process￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- tipping￨L￨JJ￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- not￨L￨RB￨O￨- all￨L￨DT￨O￨- switching￨L￨NN￨O￨- among￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- states￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- preceded￨L￨VBN￨O￨- by￨L￨IN￨O￨- leading￨L￨VBG￨O￨- indicators￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transcritical￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨- that￨L￨WDT￨O￨- occurs￨L￨VBZ￨O￨- in￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- elimination￨L￨NN￨O￨A does￨L￨VBZ￨O￨- ,￨L￨,￨O￨- implying￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- case￨L￨NN￨O￨- reports￨L￨NNS￨O￨- will￨L￨MD￨O￨- contain￨L￨VB￨O￨- statistical￨L￨JJ￨O￨- signatures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- elimination￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- leading￨L￨VBG￨O￨- indicators￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- critical￨L￨JJ￨O￨- slowing￨L￨VBG￨O￨- down￨L￨RP￨O￨- may￨L￨MD￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- means￨L￨NN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- how￨L￨WRB￨O￨- successful￨L￨JJ￨O￨- elimination￨L￨NN￨O￨A efforts￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- by￨L￨IN￨O￨- indicating￨L￨VBG￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- tipping￨L￨JJ￨O￨- point￨L￨NN￨O￨- has￨L￨VBZ￨O￨- already￨L￨RB￨O￨- been￨L￨VBN￨O￨- crossed￨L￨VBN￨O￨- or￨L￨CC￨O￨- is￨L￨VBZ￨O￨- close￨L￨RB￨O￨- at￨L￨IN￨O￨- hand￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- endemism￨L￨NN￨O￨- and￨L￨CC￨O￨- disease-free￨L￨JJ￨O￨- status￨L￨NN￨O￨- are￨L￨VBP￨O￨- alternative￨L￨JJ￨O￨- states￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- threshold￨L￨NN￨O￨- acting￨L￨VBG￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- tipping￨L￨JJ￨O￨- point￨L￨NN￨O￨A between￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- question￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- maximize￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨A leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- successful￨L￨JJ￨O￨- promotion￨L￨NN￨O￨- campaign.Up￨L￨NN￨O￨- to￨L￨TO￨O￨- now￨L￨RB￨DATE￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- were￨L￨VBD￨O￨- proposed￨L￨VBN￨O￨- for￨L￨IN￨O￨- ranking￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- identifying￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- spreading￨L￨NN￨O￨- ability￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 09￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Identification￨U￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- using￨L￨VBG￨O￨- HybridRank￨U￨NNP￨O￨- algorithm￨L￨NN￨O￨- Sara￨U￨NNP￨O￨- Ahajjam1￨U￨NNP￨O￨- &￨L￨CC￨O￨- Hassan￨U￨NNP￨O￨- Badir1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 11932￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Computer￨U￨NNP￨O￨- scienceEngineering￨L￨VBG￨O￨- AbstractIdentifying￨U￨VBG￨O￨- the￨L￨DT￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- who￨L￨WP￨O￨- is￨L￨VBZ￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- processes￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- maximization￨L￨NN￨O￨- through￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- paper￨L￨NN￨O￨- of￨L￨IN￨O￨- Lü￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 6￨L￨CD￨NUMBER￨- reviewed￨L￨VBN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- art￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- proposed￨L￨VBN￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- approaches￨L￨NNS￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- vital￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- HybridRank￨U￨NNP￨O￨- algorithm￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- hybrid￨L￨NN￨O￨- centrality￨L￨NN￨O￨- measure￨L￨NN￨O￨- for￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- influential￨L￨JJ￨O￨A spreaders￨L￨NNS￨O￨A using￨L￨VBG￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Kitsak￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 7￨L￨CD￨NUMBER￨- put￨L￨VBD￨O￨- forward￨L￨RB￨O￨- a￨L￨DT￨O￨- fast￨L￨JJ￨O￨- node￨L￨NN￨O￨- ranking￨L￨NN￨O￨A method￨L￨NN￨O￨- called￨L￨VBN￨O￨- k-shell￨L￨JJ￨O￨- decomposition￨L￨NN￨O￨- for￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- develop￨L￨VB￨O￨- a￨L￨DT￨O￨- computational￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- global￨L￨JJ￨O￨- mass￨L￨NN￨O￨- gatherings￨L￨NNS￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- modelling￨L￨NN￨O￨- study￨L￨NN￨O￨- provided￨L￨VBD￨O￨- important￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- support￨L￨NN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- decision￨L￨NN￨O￨- making￨L￨VBG￨O￨- during￨L￨IN￨O￨- school￨L￨NN￨O￨A outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- school-based￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- programme￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- among￨L￨IN￨O￨- school￨L￨NN￨O￨A children￨L￨NNS￨O￨- in￨L￨IN￨O￨- Shenzhen￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- school-based￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- intervention￨L￨NN￨O￨- .￨L￨.￨O￨- +Panel￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- e￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- f￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- simulation￨L￨NN￨O￨- results￨L￨VBZ￨O￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- threshold￨L￨NN￨O￨- set￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 10￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- cases￨L￨NNS￨O￨- per￨L￨IN￨O￨- week￨L￨NN￨DURATION￨- per￨L￨IN￨O￨- school￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recently￨L￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- presentation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- patient￨L￨NN￨O￨A infectious￨L￨JJ￨O￨- with￨L￨IN￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- ED￨U￨NNP￨O￨- in￨L￨IN￨O￨- Dallas￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Texas￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- resulted￨L￨VBD￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 180￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- hospital￨L￨NN￨O￨- personnel￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- were￨L￨VBD￨O￨- in￨L￨IN￨O￨- close￨L￨JJ￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- this￨L￨DT￨O￨- patient￨L￨NN￨O￨- or￨L￨CC￨O￨- with￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- nurses￨L￨NNS￨O￨- who￨L￨WP￨O￨- became￨L￨VBD￨O￨- infected￨L￨JJ￨O￨- after￨L￨IN￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- patient￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- implemented￨L￨VBN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- observed￨L￨VBD￨O￨- 293,181￨L￨CD￨NUMBER￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- 4,732￨L￨CD￨NUMBER￨- patient￨L￨NN￨O￨A and￨L￨CC￨O￨- 85￨L￨CD￨NUMBER￨- staff￨L￨NN￨O￨- participants￨L￨NNS￨O￨- during￨L￨IN￨O￨- 81￨L￨CD￨NUMBER￨- shifts￨L￨NNS￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- year￨L￨NN￨DURATION￨- (￨L￨-LRB-￨O￨- July￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2009￨L￨CD￨DATE￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- June￨U￨NNP￨DATE￨- 30￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- objectives￨L￨NNS￨O￨- were￨L￨VBD￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risks￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- contacts￨L￨NNS￨O￨A and￨L￨CC￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- individual￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- differential￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- the￨L￨DT￨O￨- social-contact￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- individual￨L￨JJ￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ED￨U￨NNP￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- 12-hour￨L￨JJ￨DURATION￨- shift￨L￨NN￨O￨A .￨L￨.￨O￨- +Susceptible￨U￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- time-and￨L￨JJ￨O￨- age-dependent￨L￨JJ￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- λ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- i￨L￨FW￨O￨- denote￨L￨FW￨O￨- time￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- age￨L￨NN￨O￨A ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 89￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- age￨L￨NN￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- /￨L￨:￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- j￨L￨NN￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- C￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- matrix￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- i￨L￨FW￨O￨- with￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- j￨L￨NN￨O￨- ;￨L￨:￨O￨- finally￨L￨RB￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- hypothesis￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- age-independent￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- proportionality￨L￨NN￨O￨- factor￨L￨NN￨O￨- driving￨L￨VBG￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- contacts￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- where￨L￨WRB￨O￨- This￨U￨DT￨O￨- simple￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- accounts￨L￨NNS￨O￨- for￨L￨IN￨O￨- linear￨L￨JJ￨O￨- temporal￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- below￨L￨IN￨O￨- 3￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨A and￨L￨CC￨O￨- aims￨L￨VBZ￨O￨- at￨L￨IN￨O￨- illustrating￨L￨VBG￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- increased￨L￨VBN￨O￨- attendance￨L￨NN￨O￨- at￨L￨IN￨O￨- day-care￨L￨NN￨O￨- centers￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- hypothesized￨L￨VBN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- varicella￨L￨NN￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- young￨L￨JJ￨O￨- ages￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- ascribable￨L￨JJ￨O￨- to￨L￨TO￨O￨- increased￨L￨VBN￨O￨- social￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- age￨L￨NN￨O￨A groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- possibly￨L￨RB￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- earlier￨L￨JJR￨O￨- inclusion￨L￨NN￨O￨- in￨L￨IN￨O￨- nurseries￨L￨NNS￨O￨- or￨L￨CC￨O￨- day-care￨L￨JJ￨O￨- centers￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- model￨L￨NN￨TITLE￨- M1￨U￨NN￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨A i￨L￨FW￨O￨- with￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- j￨L￨NN￨O￨- is￨L￨VBZ￨O￨- computed￨L￨VBN￨O￨- as￨L￨IN￨O￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Where￨U￨WRB￨O￨- measles￨L￨VBZ￨O￨A is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- extinct￨L￨JJ￨O￨- ,￨L￨,￨O￨- yet￨L￨RB￨O￨- susceptibility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- sufficiently￨L￨RB￨O￨- high￨L￨JJ￨O￨- ,￨L￨,￨O￨- generally￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- accumulation￨L￨NN￨O￨- of￨L￨IN￨O￨- unvaccinated￨L￨JJ￨O￨- births￨L￨NNS￨O￨- ,￨L￨,￨O￨- outbreak￨L￨NN￨O￨- risk￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- shaped￨L￨VBN￨O￨- by￨L￨IN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- human￨L￨JJ￨O￨- travel￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- characterise￨L￨VB￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- anticipate￨L￨VB￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A spatial￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- existing￨L￨VBG￨O￨- data-streams￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- attempt￨L￨VBP￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2013￨L￨CD￨DATE￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- our￨L￨PRP$￨O￨- prediction￨L￨NN￨O￨- by￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- estimated￨L￨VBN￨O￨- spatial￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- risk￨L￨NN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- observed￨L￨VBN￨O￨- via￨L￨IN￨O￨- available￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +Settings￨U￨NNS￨O￨- with￨L￨IN￨O￨- sufficiently￨L￨RB￨O￨- detailed￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- pre-vaccination￨L￨JJ￨O￨- allow￨L￨VBP￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- another￨L￨DT￨O￨- important￨L￨JJ￨O￨- variable￨L￨NN￨O￨- for￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- connectivity￨L￨NN￨O￨- underpinning￨L￨VBG￨O￨- re-introduction￨L￨NN￨O￨- events￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Pakistan￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- country￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- >￨L￨JJR￨O￨- 185￨L￨CD￨NUMBER￨- million￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- mobile￨L￨JJ￨TITLE￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- birth￨L￨NN￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- 31￨L￨CD￨NUMBER￨- births￨L￨NNS￨O￨- per￨L￨IN￨O￨- 1000￨L￨CD￨DATE￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- substantial￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Supplementary￨U￨NNP￨O￨- Information￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- health￨L￨NN￨O￨- system￨L￨NN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- vaccination￨L￨NN￨O￨A coverage￨L￨NN￨O￨A and￨L￨CC￨O￨- incidence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- quality￨L￨NN￨O￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- the￨L￨DT￨O￨- landscape￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- remains￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨A can￨L￨MD￨O￨- provide￨L￨VB￨O￨- broad￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- arbovirus￨L￨NN￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- cross-sectional￨L￨JJ￨O￨- serosurveys￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- measure￨L￨VB￨O￨- contemporary￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- characterising￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- detail￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- cohort-based￨L￨JJ￨O￨- seroepidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- in￨L￨IN￨O￨- island￨L￨NN￨O￨- settings￨L￨NNS￨O￨- where￨L￨WRB￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infrequent￨L￨JJ￨O￨- and￨L￨CC￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- tested￨L￨VBD￨O￨- the￨L￨DT￨O￨- paired￨L￨JJ￨O￨- samples￨L￨NNS￨O￨A for￨L￨IN￨O￨- anti-DENV￨L￨JJ￨O￨- IgG￨U￨NN￨O￨- antibodies￨L￨NNS￨O￨- using￨L￨VBG￨O￨- ELISA￨U￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- recombinant￨L￨JJ￨O￨- antigen-based￨L￨JJ￨O￨- microsphere￨L￨NN￨O￨- immunoassay￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MIA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- combined￨L￨VBN￨O￨- these￨L￨DT￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- possible￨L￨JJ￨O￨- explanations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨A caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- DENV-3￨U￨NN￨MISC￨- occurred￨L￨VBD￨O￨- in￨L￨IN￨O￨- Fiji￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 25,000￨L￨CD￨NUMBER￨- suspected￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- reported￨L￨VBD￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NNP￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- /￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- followed￨L￨VBD￨O￨- up￨L￨RP￨O￨- participants￨L￨NNS￨O￨- from￨L￨IN￨O￨- this￨L￨DT￨O￨- survey￨L￨NN￨O￨- in￨L￨IN￨O￨- Central￨U￨NNP￨ORGANIZATION￨- Division￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- paired￨L￨JJ￨O￨- pre-and￨L￨JJ￨O￨- post-outbreak￨L￨JJ￨O￨- serological￨L￨JJ￨O￨- samples￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Materials￨U￨NNPS￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Compared￨U￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- baseline￨L￨NN￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- 314,437￨L￨CD￨NUMBER￨- fewer￨L￨JJR￨O￨- cases￨L￨NNS￨O￨- occurred￨L￨VBD￨O￨- when￨L￨WRB￨O￨- we￨L￨PRP￨O￨- simulated￨L￨JJ￨O￨- vector￨L￨NN￨O￨A control￨L￨NN￨O￨A only￨L￨RB￨O￨- in￨L￨IN￨O￨- 301￨L￨CD￨NUMBER￨- municipalities￨L￨NNS￨O￨- that￨L￨WDT￨O￨- had￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- reported￨L￨VBN￨O￨- DENV￨U￨NN￨O￨- ,￨L￨,￨O￨- illustrating￨L￨VBG￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- previous￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- ,￨L￨,￨O￨- data-driven￨L￨JJ￨O￨- ,￨L￨,￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- CHIKV￨U￨NN￨O￨- mitigation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- previous￨L￨JJ￨O￨- DENV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +van￨L￨NN￨O￨- Panhuis￨U￨NNP￨O￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,7￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 12201￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Computational￨U￨NNP￨O￨- modelsInfectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- AbstractNew￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- emerge￨L￨VB￨O￨- any￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- illustrated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- chikungunya￨L￨NN￨O￨- virus￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- CHIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ZIKV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- Latin￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- explored￨L￨VBD￨O￨- using￨L￨VBG￨O￨- data￨L￨NNS￨O￨- about￨L￨IN￨O￨- previous￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DENV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- CHIKV￨U￨NNP￨O￨- mitigation￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- vector￨L￨NN￨O￨A control￨L￨NN￨O￨A in￨L￨IN￨O￨- all￨L￨DT￨O￨- 521￨L￨CD￨NUMBER￨- municipalities￨L￨NNS￨O￨- with￨L￨IN￨O￨- mosquito￨L￨NN￨O￨- populations￨L￨NNS￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- 402,940￨L￨CD￨NUMBER￨- fewer￨L￨JJR￨O￨- clinical￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- CHIKV￨U￨NN￨ORGANIZATION￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- baseline￨L￨NN￨O￨- scenario￨L￨NN￨O￨- without￨L￨IN￨O￨- intervention￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- temporal-network￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- three￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- measured￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- component￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- events￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- lifetime￨L￨NN￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- temporal-network￨L￨JJ￨O￨- percolation￨L￨NN￨O￨- has￨L￨VBZ￨O￨- strong￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- to￨L￨TO￨O￨- directed￨L￨VBN￨O￨- percolation.Weighted￨L￨JJ￨O￨- event￨L￨NN￨O￨- graphs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- static￨L￨JJ￨O￨- ,￨L￨,￨O￨- weighted￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- directed￨L￨VBD￨O￨- acyclic￨L￨JJ￨O￨- graphs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- DAGs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- encapsulate￨L￨VBP￨O￨- the￨L￨DT￨O￨- complete￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- δt-constrained￨L￨JJ￨O￨- time-respecting￨L￨JJ￨O￨- paths￨L￨NNS￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- δt￨L￨NN￨O￨- simultaneously￨L￨RB￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Mapping￨U￨NN￨O￨- temporal-network￨L￨NN￨O￨- percolation￨L￨NN￨O￨A to￨L￨TO￨O￨- weighted￨L￨JJ￨O￨- ,￨L￨,￨O￨- static￨L￨JJ￨O￨- event￨L￨NN￨O￨- graphs￨L￨NNS￨O￨- Mikko￨U￨NNP￨PERSON￨- Kivelä1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jordan￨U￨NNP￨CITY￨- Cambe2￨U￨NNP￨O￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jari￨U￨NNP￨PERSON￨- Saramäki1￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Márton￨U￨NNP￨O￨- Karsai2￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 12357￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- sciencePhase￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- and￨L￨CC￨O￨- critical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- AbstractThe￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- diffusion-like￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- on￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- correlations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- very￨L￨RB￨O￨- low￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- δt￨L￨NN￨O￨- ,￨L￨,￨O￨- network-wide￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unlikely￨L￨JJ￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- percolate￨L￨VB￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- value￨L￨NN￨O￨- δt￨L￨NN￨O￨- may￨L￨MD￨O￨- provide￨L￨VB￨O￨- the￨L￨DT￨O￨- pathways￨L￨NNS￨O￨- for￨L￨IN￨O￨- infecting￨L￨VBG￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network.Therefore￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- limit￨L￨NN￨O￨- δt￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- percolation￨L￨NN￨O￨A problem￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- connectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- paths￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- follow￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- another￨L￨DT￨O￨- within￨L￨IN￨O￨- δt￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- event￨L￨NN￨O￨- graph￨L￨NN￨O￨- as￨L￨IN￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- computational￨L￨JJ￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal-network￨L￨JJ￨O￨- percolation￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- this￨L￨DT￨O￨- representation￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- percolation￨L￨NN￨O￨- in￨L￨IN￨O￨- artificial￨L￨JJ￨O￨- and￨L￨CC￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- percolation￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- event￨L￨NN￨O￨- graphs￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- simulated￨L￨JJ￨O￨- and￨L￨CC￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- rationale￨L￨NN￨O￨- for￨L￨IN￨O￨- ABM￨U￨NNP￨O￨- use￨L￨VBP￨O￨- over￨L￨IN￨O￨- other￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨A centres￨L￨NNS￨O￨- around￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- points￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- represent￨L￨VB￨O￨- increased￨L￨VBN￨O￨- stochasticity￨L￨NN￨O￨- in￨L￨IN￨O￨- low-transmission￨L￨JJ￨O￨- settings￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- high-resolution￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- heterogeneities￨L￨NNS￨O￨- in￨L￨IN￨O￨- drug￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- efficacies￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- individual￨L￨JJ￨O￨- patient￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Agent-based￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A :￨L￨:￨O￨- a￨L￨DT￨O￨- systematic￨L￨JJ￨O￨- reviewNeal￨L￨NNP￨O￨- R.￨U￨NNP￨O￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- modellers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- increasingly￨L￨RB￨O￨- adopting￨L￨VBG￨O￨- agent-based￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- model￨L￨VBP￨O￨- hosts￨L￨NNS￨O￨- ,￨L￨,￨O￨- vectors￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- their￨L￨PRP$￨O￨- interactions￨L￨NNS￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- 90￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- was￨L￨VBD￨O￨- performed￨L￨VBN￨O￨- ,￨L￨,￨O￨- characterizing￨L￨VBG￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ABMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- relevant￨L￨JJ￨O￨- to￨L￨TO￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- approaches￨L￨NNS￨O￨- provides￨L￨VBZ￨O￨- avenues￨L￨NNS￨O￨- for￨L￨IN￨O￨- further￨L￨JJ￨O￨- exploration￨L￨NN￨O￨- of￨L￨IN￨O￨- agent-based￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- for￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- costs￨L￨NNS￨O￨- of￨L￨IN￨O￨- eradication￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- essential￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- PPRV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- small￨L￨JJ￨O￨A ruminant￨L￨NN￨O￨- populations￨L￨NNS￨O￨- acting￨L￨VBG￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- reservoir￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- targeted￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- within￨L￨IN￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- minimal￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- immunized￨L￨VBN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- viral￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- global￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- heavily￨L￨RB￨O￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- immunization￨L￨NN￨O￨- of￨L￨IN￨O￨- small￨L￨JJ￨O￨- ruminant￨L￨NN￨O￨- populations￨L￨NNS￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- organization￨L￨NN￨O￨- of￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨A ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- efficacious￨L￨JJ￨O￨- attenuated￨L￨VBN￨O￨- live￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- producing￨L￨VBG￨O￨- lifelong￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- against￨L￨IN￨O￨- all￨L￨DT￨O￨- PPRV￨U￨NN￨ORGANIZATION￨- serotypes￨L￨NNS￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- administration￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- campaigns￨L￨NNS￨O￨A are￨L￨VBP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- costly￨L￨JJ￨O￨- and￨L￨CC￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- implement￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- ’s￨L￨POS￨O￨- thermolability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- accessibility￨L￨NN￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- small￨L￨JJ￨O￨- ruminant￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- precise￨L￨JJ￨O￨- census￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- national￨L￨JJ￨O￨- animal￨L￨NN￨O￨- identification￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- fitting￨L￨JJ￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- PPRV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- survey￨L￨NN￨O￨- results￨L￨VBZ￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- PPRV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- Ethiopian￨U￨JJ￨NATIONALITY￨- small￨L￨JJ￨O￨A ruminant￨L￨NN￨O￨- village￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- coverage￨L￨NN￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- elimination￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- simulated￨L￨JJ￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- PPRV￨U￨NN￨O￨- between￨L￨IN￨O￨- small￨L￨JJ￨O￨A ruminants￨L￨NNS￨O￨- —￨L￨:￨O￨- sheep￨L￨NN￨O￨- and￨L￨CC￨O￨- goats￨L￨NNS￨O￨- —￨L￨:￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- Ethiopian￨U￨JJ￨NATIONALITY￨- villages￨L￨NNS￨O￨- .￨L￨.￨O￨- +Beyond￨U￨IN￨O￨- evolutionary￨L￨JJ￨O￨A parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- invasion￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- invading￨L￨VBG￨O￨- and￨L￨CC￨O￨- invaded￨L￨VBD￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- face￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- complexity￨L￨NN￨O￨A ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- offer￨L￨VBP￨O￨- valuable￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- synthesize￨L￨VB￨O￨- information￨L￨NN￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- observed￨L￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- test￨L￨VB￨O￨- different￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- key￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Wallinga￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Teunis￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- generic￨L￨JJ￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- requires￨L￨VBZ￨O￨- only￨L￨RB￨O￨- case￨L￨NN￨O￨- incidence￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- serial￨L￨NN￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨A of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨- case￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- R￨U￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- key￨L￨JJ￨O￨- factor￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- huge￨L￨JJ￨O￨- complexity￨L￨NN￨O￨A is￨L￨VBZ￨O￨- non-stationarity￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- meaning￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- evolve￨L￨VBP￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Model-based￨U￨JJ￨MISC￨- analyses￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨A and￨L￨CC￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- knowledge￨L￨NN￨O￨- gaps￨L￨NNS￨O￨- exist￨L￨VBP￨O￨- that￨L￨DT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- difficult￨L￨JJ￨O￨- or￨L￨CC￨O￨- impossible￨L￨JJ￨O￨- to￨L￨TO￨O￨- test￨L￨NN￨O￨- using￨L￨VBG￨O￨- animal￨L￨NN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- long-term￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- through￨L￨IN￨O￨- and￨L￨CC￨O￨- across￨L￨IN￨O￨- many￨L￨JJ￨O￨- seasons￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- serological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- can￨L￨MD￨O￨- vary￨L￨VB￨O￨- substantially￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- criteria￨L￨NNS￨O￨- used￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- produce￨L￨VBP￨O￨- estimates￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- vastly￨L￨RB￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- antibodies￨L￨NNS￨O￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- completely￨L￨RB￨O￨A understood￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Assumptions￨U￨NNS￨O￨- around￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- can￨L￨MD￨O￨- propagate￨L￨VB￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- modelling￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- we￨L￨PRP￨O￨- understand￨L￨VBP￨O￨- and￨L￨CC￨O￨- characterise￨L￨VBP￨O￨- epidemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- estimating￨L￨VBG￨O￨A the￨L￨DT￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- seasonal￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- when￨L￨WRB￨O￨- calculating￨L￨VBG￨O￨- optimal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- policy￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- such￨L￨JJ￨O￨- ,￨L￨,￨O￨- careful￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- high-quality￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- estimating￨L￨VBG￨O￨A both￨L￨CC￨O￨- population￨L￨NN￨O￨- susceptibility￨L￨NN￨O￨- and￨L￨CC￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- critical￨L￨JJ￨O￨- to￨L￨TO￨O￨- inform￨L￨VB￨O￨- present￨L￨JJ￨DATE￨- and￨L￨CC￨O￨- future￨L￨JJ￨DATE￨- modeling￨L￨NN￨O￨- efforts￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- few￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- completely￨L￨RB￨O￨A susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- estimates￨L￨NNS￨O￨- are￨L￨VBP￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- genes￨L￨NNS￨O￨A showed￨L￨VBD￨O￨- increased￨L￨VBN￨O￨- expression￨L￨NN￨O￨- between￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- 4￨L￨CD￨NUMBER￨- dpi￨L￨NNS￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- genotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- stronger￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- two￨L￨CD￨NUMBER￨- pectate￨L￨NN￨O￨- lyases￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- hydrolase￨L￨NN￨O￨- were￨L￨VBD￨O￨- expressed￨L￨VBN￨O￨- higher￨L￨JJR￨O￨- at￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- dpi￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- acetyltransferase￨L￨NN￨O￨- activity￨L￨NN￨O￨- was￨L￨VBD￨O￨- highly￨L￨RB￨O￨- enriched￨L￨VBN￨O￨- at￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- dpi￨L￨NNS￨O￨- .￨L￨.￨O￨- +Genes￨U￨NNS￨O￨- with￨L￨IN￨O￨- unique￨L￨JJ￨O￨- ,￨L￨,￨O￨- high￨L￨JJ￨O￨- up-regulation￨L￨NN￨O￨- by￨L￨IN￨O￨- Fg￨U￨NN￨O￨- in￨L￨IN￨O￨- Wuhan￨U￨NNP￨CITY￨- 1￨L￨CD￨NUMBER￨- were￨L￨VBD￨O￨- mostly￨L￨RB￨O￨- transiently￨L￨RB￨O￨- expressed￨L￨VBN￨O￨- at￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- dpi￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- many￨L￨JJ￨O￨- defense-associated￨L￨JJ￨O￨- genes￨L￨NNS￨O￨A were￨L￨VBD￨O￨- up-regulated￨L￨VBN￨O￨- at￨L￨IN￨O￨- both￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 4￨L￨CD￨NUMBER￨- dpi￨L￨NNS￨O￨- in￨L￨IN￨O￨- Nyubai￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- unique￨L￨JJ￨O￨- genes￨L￨NNS￨O￨- up-regulated￨L￨VBN￨O￨- in￨L￨IN￨O￨- HC374￨U￨NN￨O￨- were￨L￨VBD￨O￨- detected￨L￨VBN￨O￨- at￨L￨IN￨O￨- 4￨L￨CD￨NUMBER￨- dpi￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- analyzed￨L￨VBD￨O￨- transcriptomics￨L￨NNS￨O￨- data￨L￨NNS￨O￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- wheat￨L￨NN￨O￨- genotypes￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Nyubai￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- Wuhan￨U￨NNP￨ORGANIZATION￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- HC374￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Shaw￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 4￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- post￨L￨JJ￨O￨- inoculation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- dpi￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- Fg￨U￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- RNA-seq￨U￨JJ￨MISC￨- technology￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- susceptible￨L￨JJ￨O￨- genotype￨L￨NN￨O￨- Shaw￨U￨NNP￨PERSON￨- exhibited￨L￨VBD￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- pathogen￨L￨NN￨O￨A DEGs￨U￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- 2270￨L￨CD￨NUMBER￨- DEGs￨U￨NNS￨O￨- associating￨L￨VBG￨O￨- with￨L￨IN￨O￨- FHB￨U￨NN￨O￨- susceptibility￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- A￨U￨DT￨O￨- total￨L￨NN￨O￨- of￨L￨IN￨O￨- 37,772￨L￨CD￨NUMBER￨- differentially￨L￨RB￨O￨- expressed￨L￨VBN￨O￨- genes￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- DEGs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- ,￨L￨,￨O￨- 28,961￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- wheat￨L￨NN￨O￨- and￨L￨CC￨O￨- 8811￨L￨CD￨DATE￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- to￨L￨TO￨O￨- guide￨L￨VB￨O￨- strategic￨L￨JJ￨O￨- thinking￨L￨VBG￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- zones￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- targeted￨L￨VBN￨O￨- for￨L￨IN￨O￨- elimination￨L￨NN￨O￨A ,￨L￨,￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- maintained￨L￨VBN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- areas￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- elimination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- technically￨L￨RB￨O￨- possible￨L￨JJ￨O￨- in￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- areas￨L￨NNS￨O￨- being￨L￨VBG￨O￨- considered￨L￨VBN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- but￨L￨CC￨O￨- resources￨L￨NNS￨O￨- to￨L￨TO￨O￨- intensify￨L￨VB￨O￨- control￨L￨NN￨O￨- programs￨L￨NNS￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- elimination￨L￨NN￨O￨- are￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- targeting￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- area￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Targeting￨U￨NN￨O￨- isolated￨L￨VBD￨O￨- islands￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- elimination￨L￨NN￨O￨A may￨L￨MD￨O￨- also￨L￨RB￨O￨- have￨L￨VB￨O￨- value￨L￨NN￨O￨- as￨L￨IN￨O￨- tests￨L￨NNS￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- technologies￨L￨NNS￨O￨- or￨L￨CC￨O￨- systems￨L￨NNS￨O￨- ;￨L￨:￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- whether￨L￨IN￨O￨- targeting￨L￨VBG￨O￨- low￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- areas￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- strategy￨L￨NN￨O￨- than￨L￨IN￨O￨- focusing￨L￨VBG￨O￨- those￨L￨DT￨O￨- resources￨L￨NNS￨O￨- on￨L￨IN￨O￨- eliminating￨L￨VBG￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- higher￨L￨JJR￨O￨- transmission￨L￨NN￨O￨- areas￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- when￨L￨WRB￨O￨- these￨L￨DT￨O￨- lower￨L￨JJR￨O￨- transmission￨L￨NN￨O￨- areas￨L￨NNS￨O￨- face￨L￨VBP￨O￨- risks￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- importation￨L￨NN￨O￨- from￨L￨IN￨O￨- neighbouring￨L￨VBG￨O￨- higher￨L￨JJR￨O￨- transmission￨L￨NN￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- sites￨L￨NNS￨O￨- are￨L￨VBP￨O￨- additionally￨L￨RB￨O￨- characterised￨L￨VBN￨O￨- by￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- at￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- annual￨L￨JJ￨SET￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- burden￨L￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- vulnerability￨L￨NN￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- required￨L￨VBN￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- intensified￨L￨VBN￨O￨- control￨L￨NN￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- T.￨U￨FW￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- potential￨L￨NN￨O￨- and￨L￨CC￨O￨- T￨U￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- intensified￨L￨VBN￨O￨- measures￨L￨NNS￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- achieve￨L￨VB￨O￨- elimination￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- and/or￨L￨CC￨O￨- financial￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- these￨L￨DT￨O￨- additional￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- measures￨L￨NNS￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- areas￨L￨NNS￨O￨- simultaneously￨L￨RB￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- that￨L￨IN￨O￨- overall￨L￨JJ￨O￨- elimination￨L￨NN￨O￨A can￨L￨MD￨O￨- only￨L￨RB￨O￨- be￨L￨VB￨O￨- achieved￨L￨VBN￨O￨- by￨L￨IN￨O￨- intensified￨L￨VBN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- area￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- case￨L￨NN￨O￨- until￨L￨IN￨O￨- local￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- interrupted￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- wish￨L￨VBP￨O￨- to￨L￨TO￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- hypothetical￨L￨JJ￨O￨- issue￨L￨NN￨O￨- :￨L￨:￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- product￨L￨NN￨O￨- for￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- particular￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- serotype￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- aforementioned￨L￨JJ￨O￨- antibody-dependent￨L￨JJ￨O￨- enhancement￨L￨NN￨O￨- does￨L￨VBZ￨O￨- occur￨L￨VB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- there￨L￨EX￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- coverage￨L￨NN￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- particular￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- while￨L￨IN￨O￨- simultaneously￨L￨RB￨O￨- contributing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- serotypes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- antibody￨L￨NN￨O￨- enhancement.Our￨L￨NN￨O￨- conceptual￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- formulation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- guided￨L￨VBN￨O￨- by￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A endemic￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- recent￨L￨JJ￨O￨- immunological￨L￨JJ￨O￨- cross-reactivity￨L￨NN￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- confirmed￨L￨VBN￨O￨- that￨L￨IN￨O￨- convalescent￨L￨JJ￨O￨- plasma￨L￨NN￨O￨- following￨L￨VBG￨O￨- dengue￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- enhance￨L￨VB￨O￨- Zika￨U￨NN￨PERSON￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- global￨L￨JJ￨O￨- efforts￨L￨NNS￨O￨- of￨L￨IN￨O￨- developing￨L￨VBG￨O￨- dengue￨L￨JJ￨O￨- and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- vaccines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- intensified￨L￨VBN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- examine￨L￨VB￨O￨- whether￨L￨IN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- may￨L￨MD￨O￨- affect￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- another￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- antibody-dependent￨L￨JJ￨O￨- enhancement￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Through￨U￨IN￨O￨- a￨L￨DT￨O￨- conceptual￨L￨JJ￨O￨- co-infection￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- parametrized￨L￨VBN￨O￨- by￨L￨IN￨O￨- reported￨L￨VBN￨O￨- dengue￨L￨NN￨O￨A and￨L￨CC￨O￨- Zika￨U￨NN￨PERSON￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- immunological￨L￨JJ￨O￨- cross-reactivity￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- evaluate￨L￨VBP￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- on￨L￨IN￨O￨- Zika￨U￨NN￨PERSON￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- season￨L￨NN￨O￨- when￨L￨WRB￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- particular￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨- serotype￨L￨NN￨O￨- is￨L￨VBZ￨O￨- involved￨L￨VBN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- appropriately￨L￨RB￨O￨- designed￨L￨VBN￨O￨- and￨L￨CC￨O￨- optimized￨L￨VBN￨O￨- dengue￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- help￨L￨VB￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- spread￨L￨NN￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- ,￨L￨,￨O￨- counter-intuitively￨L￨RB￨O￨- ,￨L￨,￨O￨- reduce￨L￨VB￨O￨- Zika￨U￨NN￨PERSON￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- identify￨L￨VBP￨O￨- optimal￨L￨JJ￨O￨- dengue￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- coverages￨L￨NNS￨O￨- for￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- dengue￨L￨NN￨O￨- and￨L￨CC￨O￨- simultaneously￨L￨RB￨O￨- reducing￨L￨VBG￨O￨- Zika￨U￨NNP￨PERSON￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- coverages￨L￨NNS￨O￨- exceeding￨L￨VBG￨O￨- which￨L￨WDT￨O￨- dengue￨L￨VBP￨O￨- vaccination￨L￨NN￨O￨- will￨L￨MD￨O￨- increase￨L￨VB￨O￨- Zika￨U￨NNP￨PERSON￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 03￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Mechanistic￨U￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- popularity￨L￨NN￨O￨- prediction￨L￨NN￨O￨- Sijuan￨U￨NNP￨O￨- Ma1￨U￨NN￨O￨- ,￨L￨,￨O￨- Ling￨U￨NNP￨PERSON￨- Feng￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- &￨L￨CC￨O￨- Choy-Heng￨U￨NNP￨O￨- Lai1￨U￨NN￨O￨- ,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 13126￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- scienceInformation￨L￨NN￨O￨- technologyInformation￨L￨NN￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- computation￨L￨NN￨O￨- AbstractOnline￨U￨NNP￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A are￨L￨VBP￨O￨- becoming￨L￨VBG￨O￨- major￨L￨JJ￨O￨- platforms￨L￨NNS￨O￨- for￨L￨IN￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- exchange￨L￨VB￨O￨- opinions￨L￨NNS￨O￨- and￨L￨CC￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A have￨L￨VBP￨O￨- higher￨L￨JJR￨O￨- order￨L￨NN￨O￨- correlations￨L￨NNS￨O￨- among￨L￨IN￨O￨- node￨L￨NN￨O￨- degrees￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- for￨L￨IN￨O￨- directed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- like￨L￨IN￨O￨- Twitter￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- spreading￨L￨VBG￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- previous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- users￨L￨NNS￨O￨- ’￨L￨POS￨O￨- limited￨L￨JJ￨O￨- attention￨L￨NN￨O￨- and￨L￨CC￨O￨- heterogeneous￨L￨JJ￨O￨- interests￨L￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- retweet￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- empirical￨L￨JJ￨O￨A Twitter￨U￨NNP￨ORGANIZATION￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- both￨L￨CC￨O￨- non-trivial￨L￨JJ￨O￨- correlations￨L￨NNS￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- structures￨L￨NNS￨O￨- and￨L￨CC￨O￨- non-standard￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- for￨L￨IN￨O￨- viral￨L￨JJ￨O￨- tweets￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- overload￨L￨NN￨O￨- for￨L￨IN￨O￨- retweeting￨L￨VBG￨O￨- behaviors￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- in￨L￨IN￨O￨- line￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- ,￨L￨,￨O￨- Infectious￨U￨JJ￨O￨- and￨L￨CC￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- sublinear￨L￨JJ￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- epidemiological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- consider￨L￨VBP￨O￨- discrete￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- states￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- “￨L￨``￨O￨- susceptible￨L￨JJ￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- “￨L￨``￨O￨- infected￨L￨JJ￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- recovered￨L￨VBN￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reduce￨L￨VB￨O￨- bias/increase￨L￨NN￨O￨- precision￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- state-specific￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- opposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- multi-state￨L￨JJ￨O￨- CMR￨U￨NN￨O￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- accounting￨L￨VBG￨O￨- for￨L￨IN￨O￨- several￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- gradually￨L￨RB￨O￨- increased￨L￨VBD￨O￨- uncertainty￨L￨NN￨O￨A by￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- assigning￨L￨VBG￨O￨- each￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- equal￨L￨JJ￨O￨- amount￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NN￨O￨- set￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- “￨L￨``￨O￨- homogeneity￨L￨NN￨O￨- ”￨L￨''￨O￨- scenario￨L￨NN￨O￨- ,￨L￨,￨O￨- Figure￨U￨NNP￨O￨- 1A￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- homogeneity￨L￨NN￨O￨- scenario￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- gradually￨L￨RB￨O￨- increased￨L￨VBD￨O￨- uncertainty￨L￨NN￨O￨A by￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- assigning￨L￨VBG￨O￨- each￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- equal￨L￨JJ￨O￨- amount￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- simulated￨L￨JJ￨O￨- data￨L￨NN￨O￨- set￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- evaluated￨L￨VBD￨O￨- how￨L￨WRB￨O￨- increasing￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- U￨U￨NNP￨O￨- individuals￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- affected￨L￨VBN￨O￨- bias￨L￨NN￨O￨- and￨L￨CC￨O￨- precision￨L￨NN￨O￨- of￨L￨IN￨O￨- eco-epidemiological￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- purpose￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- simulations￨L￨NNS￨O￨- and￨L￨CC￨O￨- focused￨L￨VBD￨O￨- on￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- partial￨L￨JJ￨O￨- observation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- some￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- detected￨L￨VBN￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- sampled￨L￨VBN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- field￨L￨NN￨O￨- session￨L￨NN￨O￨- and￨L￨CC￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- are￨L￨VBP￨O￨- assigned￨L￨VBN￨O￨- an￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- “￨L￨``￨O￨- U￨U￨NNP￨O￨- ”￨L￨''￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- occasion￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- the￨L￨DT￨O￨- ubiquity￨L￨NN￨O￨- and￨L￨CC￨O￨- negative￨L￨JJ￨O￨- fitness￨L￨NN￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- organisms￨L￨NNS￨O￨- gaining￨L￨VBG￨O￨- fitness￨L￨NN￨O￨- benefits￨L￨NNS￨O￨- from￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- exploitation￨L￨NN￨O￨- ,￨L￨,￨O￨- microbial￨L￨JJ￨O￨A symbionts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- protection￨L￨NN￨O￨- greatly￨L￨RB￨O￨- benefit￨L￨VBP￨O￨- hosts￨L￨NNS￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- line￨L￨NN￨O￨- of￨L￨IN￨O￨- defense￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- mutualisms￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- coadapted￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- species￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- protection￨L￨NN￨O￨- for￨L￨IN￨O￨- host￨L￨NN￨TITLE￨A ,￨L￨,￨O￨- within‐host￨L￨JJ￨O￨- colonization￨L￨NN￨O￨- for￨L￨IN￨O￨- bacterium￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- greatest￨L￨JJS￨O￨- in￨L￨IN￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- coevolved￨L￨VBN￨O￨- host‐defensive￨L￨JJ￨O￨- bacterium￨L￨NN￨O￨- populations￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- evolutionary￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- widespread￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- defensive￨L￨JJ￨O￨- mutualisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- little￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- how￨L￨WRB￨O￨- these￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- arise￨L￨VBP￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- coadapted￨L￨VBN￨O￨- and￨L￨CC￨O￨- shaped￨L￨VBN￨O￨- by￨L￨IN￨O￨- reciprocal￨L￨JJ￨O￨- selection￨L￨NN￨O￨- between￨L￨IN￨O￨- host￨L￨NN￨TITLE￨A and￨L￨CC￨O￨- microbe￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- microbial￨L￨JJ￨O￨A symbionts￨L￨NNS￨O￨- can￨L￨MD￨O￨- determine￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- susceptibility￨L￨NN￨O￨- to￨L￨TO￨O￨- parasites￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- through￨L￨IN￨O￨- defensive￨L￨JJ￨O￨- mutualism￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- times￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- originating￨L￨VBG￨O￨A from￨L￨IN￨O￨- a￨L￨DT￨O￨- source￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- nearest￨L￨JJS￨O￨- neighbour￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- GENs￨U￨NNS￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- utility￨L￨NN￨O￨- in￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Dynamics￨U￨NNP￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- can￨L￨MD￨O￨- likewise￨L￨RB￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- pairwise￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- between￨L￨IN￨O￨- an￨L￨DT￨O￨- origin￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- destination￨L￨NN￨O￨- node￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- sources￨L￨NNS￨O￨- and￨L￨CC￨O￨- sinks￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- node￨L￨NN￨O￨- given￨L￨VBN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- originating￨L￨VBG￨O￨A at￨L￨IN￨O￨- another￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- centrality￨L￨NN￨O￨A of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- measured￨L￨VBN￨O￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- ways￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- PageRank￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- betweenness￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- or￨L￨CC￨O￨- random￨L￨JJ￨O￨- walk￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- centralities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- GENs￨U￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- identify￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- centrality￨L￨NN￨O￨A using￨L￨VBG￨O￨- the￨L￨DT￨O￨- pairwise￨L￨JJ￨O￨- importance￨L￨NN￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- global￨L￨JJ￨O￨- centralities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- highly￨L￨RB￨O￨- correlated￨L￨VBN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- common￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- is￨L￨VBZ￨O￨- valuable￨L￨JJ￨O￨- for￨L￨IN￨O￨- correlating￨L￨VBG￨O￨- dose￨L￨NN￨O￨A and￨L￨CC￨O￨- response￨L￨NN￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- after￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- has￨L￨VBZ￨O￨- occurred￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- a￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- biological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- dose￨L￨NN￨O￨- ,￨L￨,￨O￨- dictate￨L￨VBP￨O￨- individual￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- correlative￨L￨JJ￨O￨- descriptions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- predictive￨L￨JJ￨O￨- capacity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Current￨U￨JJ￨DATE￨- dose￨L￨NN￨O￨A –￨L￨:￨O￨- response￨L￨NN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- such￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- typically￨L￨RB￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- single￨L￨JJ￨O￨- hit￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- ingested￨L￨VBN￨O￨- pathogen￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- cause￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- independent￨L￨JJ￨RELIGION￨- action￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- any￨L￨DT￨O￨- particular￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- is￨L￨VBZ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- ingested￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Logically￨U￨RB￨O￨- building￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- understanding￨L￨NN￨O￨- that￨L￨WDT￨O￨- listeriosis￨L￨VBZ￨O￨- is￨L￨VBZ￨O￨- dose-dependent￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- quantification￨L￨NN￨O￨- of￨L￨IN￨O￨- dose￨L￨NN￨O￨A –￨L￨:￨O￨- response￨L￨NN￨O￨- relationships￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- via￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- supported￨L￨VBN￨O￨- by￨L￨IN￨O￨- animal￨L￨NN￨O￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g￨L￨FW￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨A ,￨L￨,￨O￨- drawing￨L￨VBG￨O￨- from￨L￨IN￨O￨- ‘￨L￨``￨O￨- humanized￨L￨JJ￨O￨- ’￨L￨''￨O￨- transgenic￨L￨JJ￨O￨- murine￨L￨JJ￨O￨- models￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- guinea￨L￨NN￨COUNTRY￨- pigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- rabbits￨L￨NNS￨O￨- ,￨L￨,￨O￨- scientific￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- explored￨L￨VBN￨O￨- the￨L￨DT￨O￨- intracellular￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- its￨L￨PRP$￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- cross￨L￨VB￨O￨- the￨L￨DT￨O￨- intestinal￨L￨JJ￨O￨- wall￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +compared￨L￨VBN￨O￨- six￨L￨CD￨NUMBER￨- dose￨L￨NN￨O￨A –￨L￨:￨O￨- response￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- illustrating￨L￨VBG￨O￨- vast￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- respective￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- when￨L￨WRB￨O￨- extrapolating￨L￨VBG￨O￨- from￨L￨IN￨O￨- high￨L￨JJ￨O￨- to￨L￨TO￨O￨- low￨L￨JJ￨O￨- doses￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- screening￨L￨NN￨O￨A and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- HCV￨U￨NN￨O￨- birth￨L￨NN￨O￨- cohort￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 1975￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- maximize￨L￨VB￨O￨- population￨L￨NN￨O￨- health￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- next￨L￨JJ￨DURATION￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- payer￨L￨NN￨O￨- ’s￨L￨POS￨O￨- perspective￨L￨NN￨O￨- under￨L￨IN￨O￨- spending￨L￨NN￨O￨- budget￨L￨NN￨O￨- constraints￨L￨NNS￨O￨- .￨L￨.￨O￨- +HCV￨U￨NN￨O￨- screening￨L￨NN￨O￨A can￨L￨MD￨O￨- help￨L￨VB￨O￨- identify￨L￨VB￨O￨- HCV-infected￨U￨JJ￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- potential￨L￨JJ￨O￨- liver￨L￨NN￨O￨- damage￨L￨NN￨O￨- and￨L￨CC￨O￨- consequently￨L￨RB￨O￨- allow￨L￨VBP￨O￨- efficient￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- improving￨L￨VBG￨O￨- population￨L￨NN￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- lowering￨L￨VBG￨O￨- HCV-related￨U￨JJ￨MISC￨- morbidity￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- project￨L￨VB￨O￨- the￨L￨DT￨O￨- societal￨L￨JJ￨O￨- benefit￨L￨NN￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- discounted￨L￨JJ￨O￨- quality-adjusted￨L￨JJ￨O￨- life-years￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- QALYs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- targeted￨L￨VBN￨O￨- US￨U￨NNP￨COUNTRY￨- age￨L￨NN￨O￨- cohorts￨L￨NNS￨O￨- with￨L￨IN￨O￨- given￨L￨VBN￨O￨- budget￨L￨NN￨O￨- limits￨L￨NNS￨O￨- and￨L￨CC￨O￨- optimized￨L￨VBN￨O￨- screening￨L￨NN￨O￨A and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- implementation￨L￨NN￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Centers￨U￨NNPS￨ORGANIZATION￨- for￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨ORGANIZATION￨- Preventive￨U￨NNP￨ORGANIZATION￨- Services￨U￨NNPS￨ORGANIZATION￨- Task￨U￨NNP￨ORGANIZATION￨- Force￨U￨NNP￨ORGANIZATION￨- both￨L￨CC￨O￨- shifted￨L￨VBD￨O￨- their￨L￨PRP$￨O￨- stances￨L￨NNS￨O￨- on￨L￨IN￨O￨- HCV￨U￨NN￨O￨- screening￨L￨NN￨O￨A ,￨L￨,￨O￨- recommending￨L￨VBG￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- providers￨L￨NNS￨O￨- to￨L￨TO￨O￨- offer￨L￨VB￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- new￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- people￨L￨NNS￨O￨- born￨L￨VBN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- age￨L￨NN￨O￨- cohorts￨L￨NNS￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- approximately￨L￨RB￨O￨- 75￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- HCV￨U￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- 73￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- HCV-associated￨U￨JJ￨O￨- mortality￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- decision￨L￨NN￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- chronic￨L￨JJ￨O￨- HCV￨U￨NN￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- that￨L￨WDT￨O￨- mimics￨L￨VBZ￨O￨- HCV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- progression￨L￨NN￨O￨- ,￨L￨,￨O￨- screening￨L￨NN￨O￨A ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- lessons￨L￨NNS￨O￨- that￨L￨WDT￨O￨- underpins￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- modeling￨L￨NN￨O￨- rinderpest￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- distinguishing￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- vs.￨L￨CC￨O￨- This￨U￨DT￨O￨- observation￨L￨NN￨O￨- may￨L￨MD￨O￨- seem￨L￨VB￨O￨- self-evident￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- consideration￨L￨NN￨O￨- of￨L￨IN￨O￨- past￨L￨NN￨DATE￨A analyses￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- demonstrates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- inappropriately￨L￨RB￨O￨- aggregated￨L￨VBD￨O￨- geography￨L￨NN￨O￨- can￨L￨MD￨O￨- mask￨L￨NN￨O￨- vital￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- mitigation￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- of￨L￨IN￨O￨- older￨L￨JJR￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- relatively￨L￨RB￨O￨- uncontrolled￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- includes￨L￨VBZ￨O￨- rinderpest￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression￨L￨NN￨O￨A ,￨L￨,￨O￨- geographic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- perform￨L￨VB￨O￨- historically￨L￨RB￨O￨- successful￨L￨JJ￨O￨- mitigations￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- culling￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- reduction￨L￨NN￨O￨- .￨L￨.￨O￨- +Past￨U￨JJ￨DATE￨- and￨L￨CC￨O￨- potential￨L￨JJ￨O￨- rinderpest￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- single￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- entities￨L￨NNS￨O￨- amenable￨L￨JJ￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- reasonably￨L￨RB￨O￨- well-defined￨L￨JJ￨O￨- presentation￨L￨NN￨O￨- and￨L￨CC￨O￨- progression￨L￨NN￨O￨A of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- biological￨L￨JJ￨O￨- features￨L￨NNS￨O￨- support￨L￨VBP￨O￨- modeling￨L￨NN￨O￨- rinderpest￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- entity￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- Shim￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- approved￨L￨VBN￨O￨- dengue￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- program￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Philippines￨U￨NNPS￨COUNTRY￨- and￨L￨CC￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- with￨L￨IN￨O￨- appropriated￨L￨VBN￨O￨- pricing￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- burden￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Philippines￨U￨NNPS￨COUNTRY￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- potential￨L￨NN￨O￨- to￨L￨TO￨O￨- confer￨L￨VB￨O￨- the￨L￨DT￨O￨- excellent￨L￨JJ￨O￨- value￨L￨NN￨O￨- were￨L￨VBD￨O￨- possible￨L￨JJ￨O￨- .￨L￨.￨O￨- +Esteva￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Vargus￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-recovery￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- human￨L￨JJ￨O￨- and￨L￨CC￨O￨- vector￨L￨NN￨O￨- populations￨L￨NNS￨O￨- while￨L￨IN￨O￨- Chanprasopchai￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Pongsumpun￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Tang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- dengue￨L￨JJ￨O￨A hemorrhagic￨L￨JJ￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- included￨L￨VBD￨O￨- an￨L￨DT￨O￨- age￨L￨NN￨O￨- structure￨L￨NN￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- tetravalent￨L￨JJ￨O￨- dengue￨L￨NN￨O￨A vaccine￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Dengvaxia￨U￨NN￨O￨- ™￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- countries￨L￨NNS￨O￨- at￨L￨IN￨O￨- danger￨L￨NN￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- dengue￨L￨JJ￨O￨A viruses￨L￨NNS￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- are￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- discuss￨L￨VBP￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- directed￨L￨VBN￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- proposing￨L￨VBG￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- ranking￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- named￨L￨VBN￨O￨- ClusterRank￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- is￨L￨VBZ￨O￨- effective￨L￨JJ￨O￨- but￨L￨CC￨O￨- mainly￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- local￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- lacking￨L￨VBG￨O￨- global￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- hybrid￨L￨JJ￨O￨- degree￨L￨NN￨O￨- centrality￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- HC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- weighted￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- this￨L￨DT￨O￨- theory￨L￨NN￨O￨- improves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- extent￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- ignores￨L￨VBZ￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- use￨L￨NN￨O￨- generalizing￨L￨VBG￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- shortest￨L￨JJS￨O￨- paths￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- node￨L￨NN￨O￨- centrality￨L￨NN￨O￨A in￨L￨IN￨O￨- weighted￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- has￨L￨VBZ￨O￨- certain￨L￨JJ￨O￨- accuracy￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- mainly￨L￨RB￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- local￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- comprehensiveness￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- semi-local￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measure￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- tradeoff￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- low-relevant￨L￨JJ￨O￨- degree￨L￨NN￨O￨- centrality￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- time-consuming￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- betweenness￨L￨NN￨O￨- or￨L￨CC￨O￨- closeness￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- new￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- centrality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EffC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- rank￨L￨VB￨O￨- the￨L￨DT￨O￨- spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- influential￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨A .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- predicts￨L￨VBZ￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- VT￨U￨NN￨STATE_OR_PROVINCE￨- serotypes￨L￨NNS￨O￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- within￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- PCV￨U￨NN￨O￨- introduction￨L￨NN￨O￨- in￨L￨IN￨O￨- RV￨U￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- near-complete￨L￨JJ￨O￨- replacement￨L￨NN￨O￨- by￨L￨IN￨O￨- NVT￨U￨NN￨O￨- serotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- resulting￨L￨VBG￨O￨- in￨L￨IN￨O￨- little￨L￨JJ￨O￨- or￨L￨CC￨O￨- no￨L￨DT￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- carriage￨L￨NN￨O￨A prevalence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- A￨U￨NNP￨O￨- &￨L￨CC￨O￨- B￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- children￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- >￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- adults￨L￨NNS￨O￨- .￨L￨.￨O￨- +Pre-PCV￨U￨JJ￨O￨- carriage￨L￨NN￨O￨A estimates￨L￨VBZ￨O￨- across￨L￨IN￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- for￨L￨IN￨O￨- VT￨U￨NN￨STATE_OR_PROVINCE￨- (￨L￨-LRB-￨O￨- left￨L￨JJ￨O￨- panel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- NVT￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- right￨L￨JJ￨O￨- panel￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- survey￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- plain￨L￨JJ￨O￨- vertical￨L￨JJ￨O￨- lines￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- meta-regression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- dotted￨L￨VBN￨O￨- vertical￨L￨JJ￨O￨- lines￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- estimates￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- estimates￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- manuscript￨L￨NN￨O￨- we￨L￨PRP￨O￨- explored￨L￨VBD￨O￨- the￨L￨DT￨O￨- differential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- carriage￨L￨NN￨O￨A and￨L￨CC￨O￨- invasive￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- catch-up￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- targeting￨L￨VBG￨O￨- various￨L￨JJ￨O￨- age￨L￨NN￨O￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- explored￨L￨VBD￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- introduction￨L￨NN￨O￨- delay￨L￨NN￨O￨- .￨L￨.￨O￨- +Legend￨U￨NNP￨O￨- :￨L￨:￨O￨- Predicted￨U￨VBD￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- VT￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- NVT￨U￨NNP￨O￨- and￨L￨CC￨O￨- overall￨L￨JJ￨O￨- carriage￨L￨NN￨O￨A in￨L￨IN￨O￨- <￨L￨JJR￨O￨- 5￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- olds￨L￨NNS￨O￨- without￨L￨IN￨O￨- a￨L￨DT￨O￨- catch-up￨L￨NN￨O￨- campaign￨L￨NN￨O￨- .￨L￨.￨O￨- +B￨U￨NN￨O￨- :￨L￨:￨O￨- Predicted￨U￨VBN￨O￨- trends￨L￨NNS￨O￨- in￨L￨IN￨O￨- VT￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- NVT￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- overall￨L￨JJ￨O￨- carriage￨L￨NN￨O￨A in￨L￨IN￨O￨- ≥￨L￨CD￨NUMBER￨- 5￨L￨CD￨DURATION￨- year￨L￨NN￨DURATION￨- olds￨L￨NNS￨O￨- in￨L￨IN￨O￨- RV￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- spatial￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- kernel￨L￨NN￨O￨- quantifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- hazard￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- likelihood￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- per￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- unit￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- analysis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨DURATION￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- posed￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- premises￨L￨NNS￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- premises￨L￨NNS￨O￨- located￨L￨VBN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- distance￨L￨NN￨O￨- away￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Minnesota￨U￨NNP￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- Iowa￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- was￨L￨VBD￨O￨- severe￨L￨JJ￨O￨- :￨L￨:￨O￨- 180￨L￨CD￨NUMBER￨- commercial￨L￨JJ￨O￨- premises￨L￨NNS￨O￨A were￨L￨VBD￨O￨- infected￨L￨VBN￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- with￨L￨IN￨O￨- devastating￨L￨VBG￨O￨- consequences￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spatial￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- H5N2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- analyzed￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- kernel￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- turkey￨L￨NN￨COUNTRY￨- premises￨L￨NNS￨O￨A had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- Eurasian￨U￨JJ￨MISC￨- HPAI￨U￨NN￨MISC￨- H5N8￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- IAV￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- frequently￨L￨RB￨O￨- recorded￨L￨VBN￨O￨- in￨L￨IN￨O￨- swine￨L￨NNS￨O￨- herds￨L￨NNS￨O￨- with￨L￨IN￨O￨- risks￨L￨NNS￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- still￨L￨RB￨O￨- gaps￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- regarding￨L￨VBG￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- IAV￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- limited￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- studies￨L￨NNS￨O￨- conducted￨L￨VBN￨O￨- on￨L￨IN￨O￨- IAV￨U￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- pig￨L￨NN￨O￨- farm￨L￨NN￨O￨A level￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Their￨U￨PRP$￨O￨- findings￨L￨NNS￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- as￨L￨RB￨O￨- long￨L￨JJ￨O￨- as￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- inflow￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- farm￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- persists￨L￨VBZ￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- small￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- IAV￨U￨NN￨O￨- in￨L￨IN￨O￨- swine￨L￨NNS￨O￨- that￨L￨WDT￨O￨- showed￨L￨VBD￨O￨- a￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- finishing￨L￨VBG￨O￨- herd￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- seroprevalence￨L￨NN￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- between￨L￨IN￨O￨- farrow-to-finish￨L￨JJ￨O￨- farm￨L￨NN￨O￨A herd￨L￨NN￨O￨- size￨L￨NN￨O￨- and￨L￨CC￨O￨- seroprevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- factors￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A including￨L￨VBG￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- immunity￨L￨NN￨O￨- levels￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- work￨L￨NN￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- maternally￨L￨RB￨O￨- derived￨L￨VBN￨O￨- immunity￨L￨NN￨O￨- on￨L￨IN￨O￨- IAV￨U￨NN￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- farrow-to-finish￨L￨JJ￨O￨- farm￨L￨NN￨O￨A .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Quantifying￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- groups￨L￨NNS￨O￨A and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- inequalities￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modelJames￨L￨NNS￨O￨- D.￨U￨NNP￨O￨- Methods￨U￨NNS￨O￨- To￨U￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- on￨L￨IN￨O￨- inequalities￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- subsequent￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- integrates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- calibrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- epidemiologic￨L￨JJ￨O￨- and￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- suggests￨L￨VBZ￨O￨- realistic￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- key￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- contributing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- —￨L￨:￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- —￨L￨:￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- social￨L￨JJ￨O￨- groups￨L￨NNS￨O￨A can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- twice￨L￨RB￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- high-risk￨L￨JJ￨O￨- population￨L￨NN￨O￨- group￨L￨NN￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- low-risk￨L￨JJ￨O￨- population￨L￨NN￨O￨- group￨L￨NN￨O￨- .￨L￨.￨O￨- +Importantly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- contrary￨L￨JJ￨O￨- to￨L￨TO￨O￨- social￨L￨JJ￨O￨- policy￨L￨NN￨O￨- intentions￨L￨NNS￨O￨- ,￨L￨,￨O￨- promoting￨L￨VBG￨O￨- an￨L￨DT￨O￨- equal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- uptake￨L￨NN￨O￨A across￨L￨IN￨O￨- population￨L￨NN￨O￨- groups￨L￨NNS￨O￨- may￨L￨MD￨O￨- magnify￨L￨VB￨O￨- inequalities￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +Vaccination￨U￨NN￨O￨- amplified￨L￨VBD￨O￨- this￨L￨DT￨O￨- inequality￨L￨NN￨O￨- further￨L￨RB￨O￨- :￨L￨:￨O￨- equal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- uptake￨L￨NN￨O￨A across￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- population￨L￨NN￨O￨- groups￨L￨NNS￨O￨- led￨L￨VBD￨O￨- to￨L￨TO￨O￨- up￨L￨RB￨O￨- to￨L￨TO￨O￨- seven￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- high-risk￨L￨JJ￨O￨- group￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- likely￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- among￨L￨IN￨O￨- laboratories￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- only￨L￨RB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- birth￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- date￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- sample￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- optimal￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- distinguishing￨L￨VBG￨O￨- between￨L￨IN￨O￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- negatives￨L￨NNS￨O￨- tests￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- unknown￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- correlation￨L￨NN￨O￨- in￨L￨IN￨O￨- CDV￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- wolves￨L￨NNS￨O￨- and￨L￨CC￨O￨- grizzly￨L￨JJ￨O￨- bears￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- GYE￨U￨NNP￨O￨- using￨L￨VBG￨O￨- serological￨L￨JJ￨O￨- data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DATE￨- 30￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨A .￨L￨.￨O￨- +During￨U￨IN￨O￨- these￨L￨DT￨O￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- coyotes￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Canis￨U￨NN￨MISC￨- latrans￨L￨NNS￨MISC￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- cougars￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Puma￨U￨NNP￨ORGANIZATION￨- concolor￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- CDV￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- comparable￨L￨JJ￨O￨- information￨L￨NN￨O￨- is￨L￨VBZ￨O￨- lacking￨L￨VBG￨O￨A for￨L￨IN￨O￨- bear￨L￨NN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- GYE￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- CDV￨U￨NN￨O￨- exposure￨L￨NN￨O￨- in￨L￨IN￨O￨- bears￨L￨NNS￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- correlated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨A of￨L￨IN￨O￨- distemper￨L￨NN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- wolves￨L￨NNS￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- often￨L￨RB￨O￨- consist￨L￨VBP￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- systems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- parameter￨L￨NN￨O￨- settings/perturbations￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- multiple￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- and￨L￨CC￨O￨- boundary￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- recent￨L￨JJ￨O￨- work￨L￨NN￨O￨- points￨L￨VBZ￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- ensemble￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- inadequate￨L￨JJ￨O￨- to￨L￨TO￨O￨- correctly￨L￨RB￨O￨- separate￨L￨VB￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- and￨L￨CC￨O￨- model￨L￨NN￨TITLE￨- structural￨L￨JJ￨O￨- uncertainty￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- study￨L￨NN￨O￨- using￨L￨VBG￨O￨- large￨L￨JJ￨O￨- climate￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ensembles￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- perturbation￨L￨NN￨O￨- approach￨L￨NN￨O￨- involved￨L￨VBD￨O￨- defining￨L￨VBG￨O￨- a￨L￨DT￨O￨- prior￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A from￨L￨IN￨O￨- expert￨L￨JJ￨O￨- opinion￨L￨NN￨O￨- or￨L￨CC￨O￨- field￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- applying￨L￨VBG￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- performance￨L￨NN￨O￨- criterion￨L￨NN￨O￨- to￨L￨TO￨O￨- reject￨L￨VB￨O￨- some￨L￨DT￨O￨- parameter￨L￨NN￨O￨- combinations￨L￨NNS￨O￨- a￨L￨DT￨O￨- posteriori￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- system￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- climate￨L￨NN￨O￨- information￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- drive￨L￨VB￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- observed￨L￨VBN￨O￨- clinical￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- highland￨L￨NN￨O￨- tea￨L￨NN￨O￨- plantation￨L￨NN￨O￨- location￨L￨NN￨O￨- in￨L￨IN￨O￨- East￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- weather￨L￨NN￨O￨- prediction￨L￨NN￨O￨- and￨L￨CC￨O￨- climate￨L￨NN￨O￨- projection￨L￨NN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- cascade￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨A ,￨L￨,￨O￨- with￨L￨IN￨O￨- errors￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- and￨L￨CC￨O￨- boundary￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- system￨L￨NN￨O￨- itself￨L￨PRP￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- uncertainty￨L￨NN￨O￨A with￨L￨IN￨O￨- regard￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- setting￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- evaluated￨L￨VBN￨O￨- by￨L￨IN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- susceptibility￨L￨NN￨O￨- index￨L￨NN￨O￨A S￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- giant￨L￨JJ￨O￨- component￨L￨NN￨O￨- σ￨L￨NN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- well-known￨L￨JJ￨O￨- existing￨L￨VBG￨O￨- metrics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Jaccard￨U￨NNP￨PERSON￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- Bridgeness￨U￨NNP￨MISC￨- index￨L￨NN￨O￨- ,￨L￨,￨O￨- Betweenness￨U￨NN￨O￨- centrality￨L￨NN￨O￨- and￨L￨CC￨O￨- Reachability￨U￨NN￨MISC￨- index￨L￨NN￨O￨- in￨L￨IN￨O￨- nine￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Identifying￨U￨NNP￨O￨- critical￨L￨JJ￨O￨- edges￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- En-Yu￨U￨JJ￨O￨- Yu1￨U￨NN￨O￨- ,￨L￨,￨O￨- Duan-Bing￨U￨JJ￨O￨- Chen1￨U￨NN￨O￨- ,2￨L￨NN￨O￨- &￨L￨CC￨O￨- Jun-Yan￨U￨NN￨MISC￨- Zhao3￨U￨NN￨MISC￨- Scientific￨U￨NNP￨MISC￨- Reportsvolume￨U￨NNP￨MISC￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 14469￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨NN￨O￨- networksInformation￨L￨NN￨O￨- technology￨L￨NN￨O￨- AbstractThe￨U￨NNP￨O￨- critical￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- extraordinary￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- which￨L￨WDT￨O￨- play￨L￨VBP￨O￨- more￨L￨JJR￨O￨- significant￨L￨JJ￨O￨- role￨L￨NN￨O￨- than￨L￨IN￨O￨- other￨L￨JJ￨O￨- edges￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- function￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- critical￨L￨JJ￨O￨- edges￨L￨NNS￨O￨A in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- attracted￨L￨VBN￨O￨- much￨L￨JJ￨O￨- attention￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- theoretical￨L￨JJ￨O￨- significance￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- applications￨L￨NNS￨O￨- .￨L￨.￨O￨- +Experimental￨U￨JJ￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- method￨L￨NN￨O￨- outperforms￨L￨VBZ￨O￨- these￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- critical￨L￨JJ￨O￨- edges￨L￨NNS￨O￨A both￨L￨CC￨O￨- in￨L￨IN￨O￨- network￨L￨NN￨O￨- connectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- spreading￨L￨VBG￨O￨- dynamic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- disseminate￨L￨VB￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- edge￨L￨NN￨O￨- ranking￨L￨JJ￨O￨- algorithm￨L￨NN￨O￨- BCCMOD￨U￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- cliques￨L￨NNS￨O￨- and￨L￨CC￨O￨- paths￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨A in￨L￨IN￨O￨- this￨L￨DT￨O￨- report￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- average￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- expect￨L￨VBP￨O￨- that￨L￨IN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- less￨L￨JJR￨O￨- vaccinated￨L￨VBN￨O￨A populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- European￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- more￨L￨RBR￨O￨- vaccinated￨L￨VBN￨O￨- populations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- strains￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- better￨L￨RBR￨O￨- targeted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- recent￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- from￨L￨IN￨O￨- test-negative￨L￨JJ￨O￨- design￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TND￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2010￨L￨CD￨DATE￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2017￨L￨CD￨DATE￨- show￨L￨NN￨O￨- lower￨L￨JJR￨O￨A VE￨U￨NN￨O￨- against￨L￨IN￨O￨- H3N2￨U￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- both￨L￨DT￨O￨- H1N1￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- A1￨U￨NN￨O￨- and￨L￨CC￨O￨- Figure￨U￨NN￨O￨- A2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Vaccines￨U￨NNS￨O￨- might￨L￨MD￨O￨- also￨L￨RB￨O￨- distinguish￨L￨VB￨O￨- between￨L￨IN￨O￨- strains￨L￨NNS￨O￨A defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- other￨L￨JJ￨O￨- phylogenetic￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- lineages￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- A4￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- clades￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A/H3N2￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Table￨U￨NNP￨O￨- A5￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- ,￨L￨,￨O￨- seasonal￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨A coverage￨L￨NN￨O￨- averaged￨L￨VBD￨O￨- 43.4￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- ranged￨L￨VBD￨O￨- from￨L￨IN￨O￨- 32.6￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- to￨L￨TO￨O￨- 46.1￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2009￨L￨CD￨DATE￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2015￨L￨CD￨DATE￨- seasons￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- within-host￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- evolutionary￨L￨JJ￨O￨- problem￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- different￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- virus￨L￨NN￨O￨- compete￨L￨VB￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- a￨L￨DT￨O￨- limited￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- cells￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- variant￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- virions￨L￨NNS￨O￨- each￨L￨DT￨O￨- variant￨L￨JJ￨O￨- produces￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- chance￨L￨NN￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- virions￨L￨NNS￨O￨- successfully￨L￨RB￨O￨- infect￨L￨VB￨O￨- further￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- cells￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- possibility￨L￨NN￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- variant￨L￨JJ￨O￨- coexistence￨L￨NN￨O￨- is￨L￨VBZ￨O￨- if￨L￨IN￨O￨- cells￨L￨NNS￨O￨A infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- produce￨L￨VBP￨O￨- more￨L￨JJR￨O￨- virions￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- virions￨L￨NNS￨O￨- ,￨L￨,￨O￨- than￨L￨IN￨O￨- singly￨L￨RB￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Ló￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Díaz-Muñ￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- variants￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- A￨U￨NN￨O￨- and￨L￨CC￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- infect￨L￨VB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- cells￨L￨NNS￨O￨A inside￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Issues￨U￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- banking￨L￨VBG￨O￨- efficiency￨L￨NN￨O￨A have￨L￨VBP￨O￨- long￨L￨RB￨O￨- been￨L￨VBN￨O￨- emphasized￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- wherein￨L￨WRB￨O￨- financial￨L￨JJ￨O￨- ratio￨L￨NN￨O￨- analysis￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- data￨L￨NNS￨O￨- envelopment￨L￨NN￨O￨- analysis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DEA￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- semi-nonparametric￨L￨JJ￨O￨- envelopment￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- StoNED￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- frontier￨L￨NN￨O￨- analysis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SFA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- production￨L￨NN￨O￨- or￨L￨CC￨O￨- cost￨L￨NN￨O￨- frontier￨L￨NN￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- productivity￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- production￨L￨NN￨O￨- systems￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- multiple￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- structure￨L￨NN￨O￨- ;￨L￨:￨O￨- these￨L￨DT￨O￨- include￨L￨VBP￨O￨- new￨L￨JJ￨O￨- energy￨L￨NN￨O￨- enterprises￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- iron￨L￨NN￨O￨- and￨L￨CC￨O￨- steel￨L￨NN￨O￨- industry￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- service￨L￨NN￨O￨- industry￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- commercial￨L￨JJ￨O￨- banks￨L￨NNS￨O￨- and￨L￨CC￨O￨- supply￨L￨NN￨O￨- chains￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- many￨L￨JJ￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- assessed￨L￨VBN￨O￨- banking￨L￨NN￨O￨- performance￨L￨NN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- undesirable￨L￨JJ￨O￨- outputs￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- non-performing￨L￨JJ￨O￨- loans￨L￨NNS￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Huang￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- super￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Khodabakhshi￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- ;￨L￨:￨O￨- Webb￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- UK￨U￨NNP￨COUNTRY￨- retail￨L￨JJ￨O￨- Banks￨U￨NNS￨O￨- ;￨L￨:￨O￨- Puri￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +Infection￨U￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- serotype￨L￨NN￨O￨A is￨L￨VBZ￨O￨- immunizing￨L￨VBG￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- can￨L￨MD￨O￨- get￨L￨VB￨O￨- HFMD￨U￨JJ￨O￨- multiple￨L￨JJ￨O￨- times￨L￨NNS￨O￨- if￨L￨IN￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- serotypes￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +EV-A71￨U￨NN￨O￨- has￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- focus￨L￨NN￨O￨- of￨L￨IN￨O￨- ongoing￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- development￨L￨NN￨O￨- ;￨L￨:￨O￨- monovalent￨L￨JJ￨O￨- vaccines￨L￨NNS￨O￨- against￨L￨IN￨O￨- this￨L￨DT￨O￨- serotype￨L￨NN￨O￨A do￨L￨VBP￨O￨- not￨L￨RB￨O￨- protect￨L￨VB￨O￨- against￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- CV-A16￨U￨NN￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- first￨L￨RB￨ORDINAL￨- reported￨L￨VBN￨O￨A cases￨L￨NNS￨O￨A of￨L￨IN￨O￨- HFMD￨U￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- CV-A16￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- EV-A71￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨A >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- management￨L￨NN￨O￨- is￨L￨VBZ￨O￨- optimized￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- value￨L￨NN￨O￨- increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- parasites￨L￨NNS￨O￨- per￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- treatments￨L￨NNS￨O￨- decrease￨L￨VBP￨O￨- at￨L￨IN￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- when￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨A >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- management￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- optimized￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- value￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- improvement￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- expenditures￨L￨NNS￨O￨- or￨L￨CC￨O￨- losses￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- sea￨L￨NN￨O￨- lice￨L￨NN￨O￨- in￨L￨IN￨O￨- salmon￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- value￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- expenditures￨L￨NNS￨O￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- losses￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- 0.065￨L￨CD￨MONEY￨- €￨L￨$￨MONEY￨- /￨L￨:￨O￨- unit￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨A /￨L￨:￨O￨- kg￨L￨NN￨O￨- production￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- at￨L￨IN￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- the￨L￨DT￨O￨- economic￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨A .￨L￨.￨O￨- +Genetic￨U￨JJ￨O￨- improvement￨L￨NN￨O￨- of￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- text￨L￨NN￨O￨A lowers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- loss-expenditure￨L￨JJ￨O￨- frontier￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨A illness￨L￨NN￨CAUSE_OF_DEATH￨- given￨L￨VBN￨O￨- HEV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- thought￨L￨VBN￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- with￨L￨IN￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- about￨L￨RB￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- adults￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- genotypes￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- 2￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- death￨L￨NN￨O￨- given￨L￨VBN￨O￨- symptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- estimated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- approximately￨L￨RB￨O￨- 2￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- for￨L￨IN￨O￨- non-pregnant￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- pregnant￨L￨JJ￨O￨- women￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- vaccine￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- >￨L￨JJR￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- efficacy￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- three￨L￨CD￨NUMBER￨- dose￨L￨NN￨O￨- schedule￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 6￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- clinical￨L￨JJ￨O￨- trial￨L￨NN￨O￨- involving￨L￨VBG￨O￨- 109,959￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- HEV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- setting￨L￨NN￨O￨- ,￨L￨,￨O￨- primarily￨L￨RB￨O￨- with￨L￨IN￨O￨- genotype￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- both￨L￨DT￨O￨- pre-emptive￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- prior￨L￨JJ￨O￨- to￨L￨TO￨O￨- HEV￨U￨NN￨O￨- cases￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- reactive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- once￨L￨RB￨DATE￨- HEV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- already￨L￨RB￨O￨- underway￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- selecting￨L￨VBG￨O￨A different￨L￨JJ￨O￨- target￨L￨NN￨O￨- groups￨L￨NNS￨O￨- to￨L￨TO￨O￨- receive￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- do￨L￨VB￨O￨- this￨L￨DT￨O￨- we￨L￨PRP￨O￨- fitted￨L￨VBD￨O￨- dynamic￨L￨JJ￨O￨A transmission￨L￨NN￨O￨A models￨L￨NNS￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- large￨L￨JJ￨O￨- HEV￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- IDP￨U￨NNP￨O￨- camps￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- general￨L￨JJ￨TITLE￨- and￨L￨CC￨O￨- simple￨L￨JJ￨O￨- relationships￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨A of￨L￨IN￨O￨- virus￨L￨NN￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- annual￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- train￨L￨VB￨O￨- them￨L￨PRP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- analytic￨L￨JJ￨O￨A predictions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- ,￨L￨,￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- most￨L￨RBS￨O￨- recent￨L￨JJ￨O￨- common￨L￨JJ￨O￨- ancestor￨L￨NN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- cross-immunity￨L￨NN￨O￨- distance￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- either￨L￨RB￨O￨- infected￨L￨JJ￨O￨- or￨L￨CC￨O￨- recovered￨L￨VBN￨O￨A ,￨L￨,￨O￨- as￨L￨IN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- normalization￨L￨NN￨O￨- condition￨L￨NN￨O￨- The￨U￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- mutations￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- rare￨L￨JJ￨O￨- ,￨L￨,￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- below￨L￨IN￨O￨- in￨L￨IN￨O￨- subsection￨L￨NN￨O￨- Mutation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- analytic￨L￨JJ￨O￨A approach￨L￨NN￨O￨- combining￨L￨VBG￨O￨- a￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- framework￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- theory￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- multivariable￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- regression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- comparing￨L￨VBG￨O￨- VL￨U￨NNP￨O￨- to￨L￨TO￨O￨- recent￨L￨JJ￨O￨- asymptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- rK39￨L￨NN￨O￨- ELISA￨U￨NN￨O￨- positivity￨L￨NN￨O￨A and￨L￨CC￨O￨- LST￨U￨NN￨O￨- negativity￨L￨NN￨O￨- at￨L￨IN￨O￨- baseline￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- living￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- household￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- case￨L￨NN￨O￨- was￨L￨VBD￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- significantly￨L￨RB￨O￨- increased￨L￨VBN￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- symptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- OR￨U￨NN￨STATE_OR_PROVINCE￨- =￨L￨JJ￨O￨- 2.85￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- 1.45￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5.61￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.003￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NNP￨O￨- was￨L￨VBD￨O￨- substantially￨L￨RB￨O￨- higher￨L￨JJR￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- living￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- household￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- previous￨L￨JJ￨O￨- case￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- OR￨U￨NN￨STATE_OR_PROVINCE￨- =￨L￨JJ￨O￨- 6.37￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- 3.30￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12.28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- <￨L￨JJR￨O￨- 0.0001￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- decreased￨L￨VBD￨O￨- relatively￨L￨RB￨O￨- quickly￨L￨RB￨O￨- with￨L￨IN￨O￨- distance￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- OR￨U￨NN￨STATE_OR_PROVINCE￨- =￨L￨JJ￨O￨- 1.85￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- 0.95￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3.60￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0.07￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- household￨L￨NN￨O￨- without￨L￨IN￨O￨- VL￨U￨NNP￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 50m￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- rK39￨L￨NN￨O￨- ELISA￨U￨NN￨O￨- positivity￨L￨NN￨O￨A and￨L￨CC￨O￨- LST￨U￨NN￨O￨- positivity￨L￨NN￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- strongly￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- proximity￨L￨NN￨O￨- to￨L￨TO￨O￨- previous￨L￨JJ￨O￨- VL￨U￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Associations￨U￨NNS￨O￨- between￨L￨IN￨O￨- VL￨U￨NNP￨O￨- risk￨L￨NN￨O￨- and￨L￨CC￨O￨- asymptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- as￨L￨IN￨O￨- measured￨L￨VBN￨O￨- by￨L￨IN￨O￨- rK39￨L￨NN￨O￨- ELISA￨U￨NN￨O￨- positivity￨L￨NN￨O￨A or￨L￨CC￨O￨- LST￨U￨NN￨O￨- positivity￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- distance￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- VL￨U￨NNP￨O￨- case￨L￨NN￨O￨- were￨L￨VBD￨O￨- assessed￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- odds￨L￨NNS￨O￨- ratios￨L￨NNS￨O￨- of￨L￨IN￨O￨- having￨L￨VBG￨O￨- VL￨U￨NNP￨O￨- or￨L￨CC￨O￨- being￨L￨VBG￨O￨- rK39￨L￨NN￨O￨- ELISA/LST-positive￨U￨JJ￨O￨- if￨L￨IN￨O￨- living￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- household￨L￨NN￨O￨- as￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- household￨L￨NN￨O￨- but￨L￨CC￨O￨- <￨L￨JJR￨O￨- 50m￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- closest￨L￨JJS￨O￨- previous￨L￨JJ￨O￨- VL￨U￨NNP￨O￨- case￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- living￨L￨VBG￨O￨- >￨L￨JJR￨O￨- 50m￨L￨CD￨NUMBER￨- from￨L￨IN￨O￨- them￨L￨PRP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨O￨- xenodiagnosis￨L￨NN￨O￨- experiments￨L￨NNS￨O￨- ,￨L￨,￨O￨- asymptomatic￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- high￨L￨JJ￨O￨- anti-leishmanial￨L￨JJ￨O￨- antibody￨L￨NN￨O￨- titres￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- agglutination￨L￨NN￨O￨- test￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DAT￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- rK39￨L￨NN￨O￨- enzyme-linked￨L￨JJ￨O￨- immunosorbent￨L￨JJ￨O￨- assay￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ELISA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- symptoms￨L￨NNS￨O￨- or￨L￨CC￨O￨- prior￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- VL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- failed￨L￨VBD￨O￨- to￨L￨TO￨O￨- infect￨L￨VB￨O￨- sandflies￨L￨NNS￨O￨- fed￨L￨VBN￨O￨- upon￨L￨IN￨O￨- them￨L￨PRP￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- VL￨U￨NN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- post￨L￨NN￨O￨- kala-azar￨L￨JJ￨O￨- dermal￨L￨JJ￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- PKDL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- cases￨L￨NNS￨O￨- infected￨L￨JJ￨O￨- sandflies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- mechanisms￨L￨NNS￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- temperature￨L￨NN￨O￨A is￨L￨VBZ￨O￨- hypothesized￨L￨VBN￨O￨- to￨L￨TO￨O￨- influence￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- STEC￨U￨NN￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- affecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- spent￨L￨VBD￨O￨- engaged￨L￨VBN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- grazing￨L￨NN￨O￨- vs.￨L￨CC￨O￨- We￨U￨PRP￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- ,￨L￨,￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- ABM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- STEC￨U￨NN￨ORGANIZATION￨- among￨L￨IN￨O￨- grazing￨L￨NN￨O￨- cattle￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- mechanisms￨L￨NNS￨O￨- underlying￨L￨VBG￨O￨- seasonality￨L￨NN￨O￨- in￨L￨IN￨O￨- STEC￨U￨NNP￨O￨- incidence￨L￨NN￨O￨- in￨L￨IN￨O￨- grazing￨L￨NN￨O￨- cattle￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- ABM￨U￨NNP￨MISC￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- STEC￨U￨NN￨ORGANIZATION￨- that￨L￨WDT￨O￨- incorporates￨L￨VBZ￨O￨- varying￨L￨VBG￨O￨- mechanisms￨L￨NNS￨O￨- linking￨L￨VBG￨O￨- temperature￨L￨NN￨O￨A and￨L￨CC￨O￨- STEC￨U￨NN￨ORGANIZATION￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Proposed￨U￨VBN￨O￨- mechanisms￨L￨NNS￨O￨- include￨L￨VBP￨O￨- enhanced￨L￨VBN￨O￨- transmission￨L￨NN￨O￨- mediated￨L￨VBN￨O￨- by￨L￨IN￨O￨- water￨L￨NN￨O￨- and￨L￨CC￨O￨- flies￨L￨VBZ￨O￨- at￨L￨IN￨O￨- higher￨L￨JJR￨O￨- temperature￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- increased￨L￨VBD￨O￨- susceptibility￨L￨NN￨O￨- linked￨L￨VBN￨O￨- to￨L￨TO￨O￨- hormonal￨L￨JJ￨O￨- fluctuations￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- day￨L￨NN￨DURATION￨- length￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- how￨L￨WRB￨O￨- temperature￨L￨NN￨O￨A fluctuation￨L￨NN￨O￨- caused￨L￨VBD￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- STEC￨U￨NN￨ORGANIZATION￨- incidence￨L￨NN￨O￨- among￨L￨IN￨O￨- grazing￨L￨NN￨O￨- cattle￨L￨NNS￨O￨- by￨L￨IN￨O￨- influencing￨L￨VBG￨O￨- diurnal￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- global￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨A of￨L￨IN￨O￨- trachoma￨L￨NN￨O￨- continues￨L￨VBZ￨O￨- to￨L￨TO￨O￨- decline￨L￨VB￨O￨- it￨L￨PRP￨O￨- becomes￨L￨VBZ￨O￨- increasingly￨L￨RB￨O￨- challenging￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- and￨L￨CC￨O￨- confirm￨L￨VB￨O￨- TF￨U￨NN￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- training￨L￨NN￨O￨- graders￨L￨NNS￨O￨- becomes￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- expensive￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- sero-surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- trachoma￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- currently￨L￨RB￨DATE￨- being￨L￨VBG￨O￨- evaluated￨L￨VBN￨O￨- as￨L￨IN￨O￨- more￨L￨JJR￨O￨- long-term￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- low-level￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- re-emergence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- PCR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- simulated￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨A data￨L￨NNS￨O￨A within￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- community￨L￨NN￨O￨- of￨L￨IN￨O￨- 3,000￨L￨CD￨NUMBER￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1/3rd￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- were￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- aged￨L￨JJ￨O￨- 1-9￨L￨CD￨NUMBER￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- TF￨U￨NN￨O￨- and￨L￨CC￨O￨- PCR￨U￨NN￨O￨- positive￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- a￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- validated￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- structure￨L￨NN￨O￨- that￨L￨WDT￨O￨- was￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- parsimonious￨L￨JJ￨O￨- and￨L￨CC￨O￨- appropriate￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- when￨L￨WRB￨O￨- fitting￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- cross-section￨L￨NN￨O￨- of￨L￨IN￨O￨- age-specific￨L￨JJ￨O￨- PCR￨U￨NN￨O￨- and￨L￨CC￨O￨- TF￨U￨NN￨O￨- prevalence￨L￨NN￨O￨A data￨L￨NNS￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- evaluate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- TF￨U￨NN￨O￨- and￨L￨CC￨O￨- PCR￨U￨NN￨O￨- positive￨L￨JJ￨O￨A individuals￨L￨NNS￨O￨- changes￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- intervention￨L￨NN￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- during￨L￨IN￨O￨- re-emergence￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- if￨L￨IN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- how￨L￨WRB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- impacts￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- detecting￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- used￨L￨VBD￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- prevalence￨L￨NN￨O￨A data￨L￨NNS￨O￨A at￨L￨IN￨O￨- different￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- PCR￨U￨NN￨O￨- and￨L￨CC￨O￨- TF￨U￨NN￨O￨- positive￨L￨JJ￨O￨- at￨L￨IN￨O￨- any￨L￨DT￨O￨- point￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Mathematical￨U￨JJ￨MISC￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- vancomycin-resistant￨L￨JJ￨O￨- enterococci￨L￨NN￨O￨- transmission￨L￨NN￨O￨- during￨L￨IN￨O￨- passive￨L￨NN￨O￨- surveillance￨L￨NN￨O￨A and￨L￨CC￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- with￨L￨IN￨O￨- contact￨L￨NN￨O￨- isolation￨L￨NN￨O￨- highlights￨L￨VBZ￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- and￨L￨CC￨O￨- address￨L￨VB￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- acquisitionAgnes￨L￨NNS￨O￨- Loo￨U￨NNP￨O￨- Yee￨U￨NNP￨O￨- Cheah1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Allen￨U￨NNP￨PERSON￨- C.￨U￨NNP￨O￨- 2018Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Clinical￨U￨JJ￨MISC￨- studies￨L￨NNS￨O￨- and￨L￨CC￨O￨- mathematical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- with￨L￨IN￨O￨- contact￨L￨NN￨O￨- isolation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- reduced￨L￨VBN￨O￨- vancomycin-resistant￨L￨JJ￨O￨- enterococci￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- VRE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- prevalence￨L￨NN￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- passive￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- .￨L￨.￨O￨- +Models￨U￨NNS￨O￨- using￨L￨VBG￨O￨- pre-and￨L￨JJ￨O￨- post-intervention￨L￨JJ￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- imperfect￨L￨JJ￨O￨- observation￨L￨NN￨O￨- and￨L￨CC￨O￨- serial￨L￨NN￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- VRE￨U￨NN￨O￨- transmission￨L￨NN￨O￨- events￨L￨NNS￨O￨- can￨L￨MD￨O￨- better￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨A and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- contact￨L￨NN￨O￨- isolation￨L￨NN￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- not￨L￨RB￨O￨- been￨L￨VBN￨O￨- performed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- surveillance￨L￨NN￨O￨A data￨L￨NNS￨O￨- collected￨L￨VBN￨O￨- pre-and￨L￨JJ￨O￨- post-implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- active￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- with￨L￨IN￨O￨- contact￨L￨NN￨O￨- isolation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- haematology-oncology￨L￨JJ￨O￨- ward￨L￨NN￨O￨- .￨L￨.￨O￨- +During￨U￨IN￨O￨- its￨L￨PRP$￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- real‐time￨L￨JJ￨O￨- publication￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- data￨L￨NNS￨O￨- stream￨L￨NN￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- accurate￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- outbreak￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 13￨L￨CD￨NUMBER￨- Nsoesie￨U￨NN￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- used￨L￨VBN￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- to￨L￨TO￨O￨- forecast￨L￨VB￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- peak￨L￨NN￨O￨- timing￨L￨NN￨O￨- in￨L￨IN￨O￨- Seattle￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Washington￨U￨NNP￨STATE_OR_PROVINCE￨- ,￨L￨,￨O￨- 5‐6￨L￨CD￨NUMBER￨- weeks￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- .14￨L￨CD￨NUMBER￨- Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- Shaman￨U￨NN￨O￨- and￨L￨CC￨O￨- Karspeck￨U￨NN￨PERSON￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- real‐time￨L￨JJ￨O￨- seasonal￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecast￨L￨NN￨O￨- for￨L￨IN￨O￨- New￨U￨NNP￨CITY￨- York￨U￨NNP￨CITY￨- City￨U￨NNP￨CITY￨- using￨L￨VBG￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- generated￨L￨VBD￨O￨- skillful￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- peak￨L￨NN￨O￨- timing￨L￨NN￨O￨- 7￨L￨CD￨DURATION￨- weeks￨L￨NNS￨DURATION￨- before￨L￨IN￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- peak￨L￨NN￨O￨- .15￨L￨CD￨NUMBER￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- GFT￨U￨NNP￨ORGANIZATION￨- had￨L￨VBD￨O￨- well‐documented￨L￨VBN￨O￨- limitations￨L￨NNS￨O￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- A/H1N1￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic9￨L￨NN￨O￨- ,￨L￨,￨O￨- 16￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- inflated￨L￨VBD￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- A/H3N2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ‐￨L￨SYM￨O￨- 13￨L￨CD￨NUMBER￨- season￨L￨NN￨O￨- .9￨L￨CD￨NUMBER￨- Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- several￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- new￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- using￨L￨VBG￨O￨- online￨L￨JJ￨O￨- search￨L￨NN￨O￨- queries￨L￨NNS￨O￨- ,12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 17￨L￨CD￨NUMBER￨- tweets￨L￨NNS￨O￨- ,18￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 19￨L￨CD￨NUMBER￨- Wikipedia￨U￨NNP￨ORGANIZATION￨- access￨L￨NN￨O￨- logs￨L￨NNS￨O￨- ,20￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 21￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- other￨L￨JJ￨O￨- public￨L￨JJ￨O￨- generated￨L￨VBN￨O￨- content￨L￨NN￨O￨- ;￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 23￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- was￨L￨VBD￨O￨- only￨L￨RB￨O￨- available￨L￨JJ￨O￨- at￨L￨IN￨O￨- national￨L￨JJ￨O￨- and￨L￨CC￨O￨- regional￨L￨JJ￨O￨- geographic￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- forecast￨L￨NN￨O￨- of￨L￨IN￨O￨- more￨L￨JJR￨O￨- local￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- activity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- these￨L￨DT￨O￨- issues￨L￨NNS￨O￨- by￨L￨IN￨O￨- testing￨L￨VBG￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- forecast￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- using￨L￨VBG￨O￨- 6￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- state￨L￨NN￨O￨- and￨L￨CC￨O￨- county￨L￨NN￨O￨- departments￨L￨NNS￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- in￨L￨IN￨O￨- Arizona￨U￨NNP￨STATE_OR_PROVINCE￨- and￨L￨CC￨O￨- Indiana￨U￨NNP￨STATE_OR_PROVINCE￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- thus￨L￨RB￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- forecast￨L￨NN￨O￨A accuracy￨L￨NN￨O￨- and￨L￨CC￨O￨- utility￨L￨NN￨O￨- when￨L￨WRB￨O￨- incorporating￨L￨VBG￨O￨- different￨L￨JJ￨O￨- local￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- types￨L￨NNS￨O￨- .￨L￨.￨O￨- +Little￨U￨JJ￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- despite￨L￨IN￨O￨- a￨L￨DT￨O￨- renewed￨L￨VBN￨O￨- research￨L￨NN￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- tropical￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨- over￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- increased￨L￨VBN￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- sequence￨L￨NN￨O￨- data￨L￨NNS￨O￨- .16￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 17￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 18￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 19￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 20￨L￨CD￨NUMBER￨- To￨U￨TO￨O￨- date￨L￨NN￨O￨- ,￨L￨,￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- tropical￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- concentrated￨L￨VBN￨O￨- on￨L￨IN￨O￨- whether￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- annual￨L￨JJ￨SET￨- seasonality21￨L￨NN￨O￨- ,￨L￨,￨O￨- 22￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 23￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 24￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 26￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 27￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 29￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- viruses￨L￨NNS￨O￨- show￨L￨VBP￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- year‐round￨L￨JJ￨O￨- persistence￨L￨NN￨O￨- .30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 31￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 32￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 33￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 34￨L￨CD￨NUMBER￨- A￨U￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- question￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- received￨L￨VBN￨O￨- less￨L￨JJR￨O￨- attention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- syndromic￨L￨JJ￨O￨- influenza‐like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- surveillance￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- peaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- troughs￨L￨NNS￨O￨- as￨L￨IN￨O￨- molecular￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- these￨L￨DT￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Indeed￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- by￨L￨IN￨O￨- several￨L￨JJ￨O￨- research￨L￨NN￨O￨- groups￨L￨NNS￨O￨- for￨L￨IN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- 's￨L￨POS￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- prediction￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Flu￨U￨NNP￨CAUSE_OF_DEATH￨- Trends￨U￨VBZ￨O￨- .7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 10￨L￨CD￨NUMBER￨- Critiques￨U￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- algorithm￨L￨NN￨O￨- included￨L￨VBD￨O￨- its￨L￨PRP$￨O￨- reliance￨L￨NN￨O￨- on￨L￨IN￨O￨- Internet￨U￨NN￨MISC￨- search￨L￨NN￨O￨- behavior￨L￨NN￨O￨- remaining￨L￨VBG￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- overfitting￨L￨JJ￨O￨- effect￨L￨NN￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- given￨L￨VBN￨O￨- too￨L￨RB￨O￨- much￨L￨JJ￨O￨- weight￨L￨NN￨O￨- to￨L￨TO￨O￨- associations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- training￨L￨NN￨O￨- data￨L￨NNS￨O￨- sets￨L￨VBZ￨O￨- only￨L￨RB￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- specific￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- incorrect￨L￨JJ￨O￨- forecasts￨L￨NNS￨O￨- .9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- challenge￨L￨NN￨O￨- in￨L￨IN￨O￨- big‐data￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- surveillance￨L￨NN￨O￨A is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- narrow￨L￨VB￨O￨- the￨L￨DT￨O￨- gap￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- point￨L￨NN￨O￨- describing￨L￨VBG￨O￨- it￨L￨PRP￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- a￨L￨DT￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- generate￨L￨VB￨O￨- large￨L￨JJ￨O￨- data￨L￨NNS￨O￨- sets￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- points￨L￨NNS￨O￨- are￨L￨VBP￨O￨- grounded￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- antibody￨L￨NN￨O￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- symptoms￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- reasons￨L￨NNS￨O￨- for￨L￨IN￨O￨- disagreement￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- literature￨L￨NN￨O￨- as￨L￨IN￨O￨- some￨L￨DT￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- claim￨L￨VBP￨O￨- support￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- transmission￨L￨NN￨O￨- season21￨L￨NN￨O￨- ,￨L￨,￨O￨- 26￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 29￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 39￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 40￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 42￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 47￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 48￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 49￨L￨CD￨NUMBER￨- while￨L￨IN￨O￨- others￨L￨NNS￨O￨- show￨L￨VBP￨O￨- mixed￨L￨JJ￨O￨- or￨L￨CC￨O￨- no￨L￨DT￨O￨- evidence￨L￨NN￨O￨- .22￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 27￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 46￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 50￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 51￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 52￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 53￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 54￨L￨CD￨NUMBER￨- Among￨U￨IN￨O￨- these￨L￨DT￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- weakly￨L￨RB￨O￨- supported￨L￨VBN￨O￨- results￨L￨NNS￨O￨- are￨L￨VBP￨O￨- being￨L￨VBG￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- policy￨L￨NN￨O￨- to￨L￨TO￨O￨- advocate￨L￨VB￨O￨- for￨L￨IN￨O￨- particular￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- timings￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- incorrectly￨L￨RB￨O￨- identified￨L￨VBN￨O￨- seasonal￨L￨JJ￨O￨- signals￨L￨NNS￨O￨- .29￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 49￨L￨CD￨NUMBER￨- For￨U￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A virus￨L￨NN￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- studies￨L￨NNS￨O￨- with￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- data27￨L￨NN￨O￨- ,￨L￨,￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 55￨L￨CD￨NUMBER￨- have￨L￨VBP￨O￨- generally￨L￨RB￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- annual￨L￨JJ￨SET￨- seasonal￨L￨JJ￨O￨- signals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- supported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- shows￨L￨VBZ￨O￨- an￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- progressing￨L￨VBG￨O￨- from￨L￨IN￨O￨- tropical￨L￨JJ￨O￨A to￨L￨TO￨O￨- temperate￨L￨VB￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .30￨L￨CD￨NUMBER￨- A￨U￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- example￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- study￨L￨NN￨O￨- published￨L￨VBN￨O￨- using￨L￨VBG￨O￨- sentinel￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- in￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transition￨L￨NN￨O￨- from￨L￨IN￨O￨- large￨L￨JJ￨O￨- wintertime￨L￨NN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- peaks￨L￨VBZ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- north￨L￨NN￨O￨- to￨L￨TO￨O￨- smaller￨L￨JJR￨O￨- less￨L￨RBR￨O￨- predictable￨L￨JJ￨O￨- peaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- subtropics￨L￨NNS￨O￨- .63￨L￨CD￨NUMBER￨- Beyond￨U￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- examples￨L￨NNS￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- links￨L￨NNS￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- hard￨L￨JJ￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- paucity￨L￨NN￨O￨- of￨L￨IN￨O￨- long‐term￨L￨JJ￨O￨- consistent￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- tropical￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- temperate￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- agencies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- rely￨L￨VB￨O￨- on￨L￨IN￨O￨- ILI￨U￨NN￨O￨- reporting￨L￨VBG￨O￨- to￨L￨TO￨O￨- signal￨L￨VB￨O￨- the￨L￨DT￨O￨- onset￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- ,1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 35￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 36￨L￨CD￨NUMBER￨- but￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- known￨L￨VBN￨O￨- whether￨L￨IN￨O￨- ILI￨U￨NNP￨O￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- correlate￨L￨VBP￨O￨- in￨L￨IN￨O￨- tropical￨L￨JJ￨O￨A countries￨L￨NNS￨O￨- .37￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 38￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- looking￨L￨VBG￨O￨- at￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and/or￨L￨CC￨O￨- respiratory￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- tropics￨L￨NNS￨O￨- have￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- drawbacks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- recommended￨L￨VBD￨O￨- that￨L￨IN￨O￨- populations￨L￨NNS￨O￨- at￨L￨IN￨O￨- higher￨L￨JJR￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- hospitalizations￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- vaccinated￨L￨VBN￨O￨- .1￨L￨CD￨NUMBER￨- Healthy￨U￨JJ￨O￨- school‐going￨L￨JJ￨O￨- children￨L￨NNS￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- excluded￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- defined￨L￨VBN￨O￨- vulnerable￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- contracting￨L￨VBG￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- increased￨L￨VBN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- frequent￨L￨JJ￨O￨- close￨L￨JJ￨O￨- contact￨L￨NN￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- .2￨L￨NN￨NUMBER￨- School‐based￨U￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A vaccination￨L￨NN￨O￨A programs￨L￨NNS￨O￨- have￨L￨VBP￨O￨- therefore￨L￨RB￨O￨- been￨L￨VBN￨O￨- recommended￨L￨VBN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- settings￨L￨NNS￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- existing￨L￨VBG￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- programs￨L￨NNS￨O￨- but￨L￨CC￨O￨- remain￨L￨VBP￨O￨- rare￨L￨JJ￨O￨- globally￨L￨RB￨O￨- .3￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- free￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- vaccination￨L￨NN￨O￨- policy￨L￨NN￨O￨- was￨L￨VBD￨O￨- launched￨L￨VBN￨O￨- in￨L￨IN￨O￨- primary￨L￨JJ￨O￨- ,￨L￨,￨O￨- secondary￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- schoolchildren￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- 6‐18￨L￨CD￨NUMBER￨- years￨L￨NNS￨DURATION￨- old￨L￨JJ￨O￨- .5￨L￨CD￨NUMBER￨- Temporary￨U￨JJ￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- POVs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- established￨L￨VBN￨O￨- at￨L￨IN￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- students￨L￨NNS￨O￨- with￨L￨IN￨O￨- their￨L￨PRP$￨O￨- parent￨L￨NN￨O￨- 's￨L￨POS￨O￨- written￨L￨VBN￨O￨- consent￨L￨NN￨O￨- are￨L￨VBP￨O￨- organized￨L￨VBN￨O￨- to￨L￨TO￨O￨- receive￨L￨VB￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- there￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- judging￨L￨VBG￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- intensities￨L￨NNS￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- with￨L￨IN￨O￨- vs￨L￨CC￨O￨A without￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- averted￨L￨VBN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- medically￨L￨RB￨O￨- attended￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- outpatient￨L￨NN￨O￨- and￨L￨CC￨O￨- emergency￨L￨NN￨O￨- attended￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- ‐￨L￨SYM￨O￨- 2016￨L￨CD￨DATE￨- seasons￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- estimated￨L￨VBN￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- vs￨L￨CC￨O￨A without￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- equals￨L￨VBZ￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- averted￨L￨VBN￨O￨- by￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Beijing￨U￨NNP￨CITY￨- among￨L￨IN￨O￨- children￨L￨NNS￨O￨- aged￨L￨JJ￨O￨- 5‐14￨L￨CD￨NUMBER￨- years￨L￨NNS￨DURATION￨- using￨L￨VBG￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Next￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- were￨L￨VBD￨O￨- again￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A infections￨L￨NNS￨CAUSE_OF_DEATH￨- without￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Evaluating￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- for￨L￨IN￨O￨- Usutu￨U￨NN￨MISC￨- virus￨L￨NN￨O￨- circulation￨L￨NN￨O￨- in￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- :￨L￨:￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨A niche￨L￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- modelsYanchao￨L￨NN￨O￨- Cheng1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Nils￨U￨NNP￨PERSON￨- Benjamin￨U￨NNP￨PERSON￨- Tjaden1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Anja￨U￨NNP￨PERSON￨- Jaeschke1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Renke￨U￨NNP￨PERSON￨- Lühken2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Ute￨U￨NNP￨O￨- Ziegler3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Stephanie￨U￨NNP￨PERSON￨- Margarete￨U￨NNP￨PERSON￨- Thomas1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Carl￨U￨NNP￨PERSON￨- Beierkuhnlein1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 17:35￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Usutu￨U￨NNP￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- USUV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- mosquito-borne￨L￨JJ￨O￨- flavivirus￨L￨NN￨O￨- ,￨L￨,￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- of￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Europe￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- host￨L￨NN￨TITLE￨- range￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- implemented￨L￨VBD￨O￨- a￨L￨DT￨O￨- parallel￨L￨JJ￨O￨- approach￨L￨NN￨O￨- incorporating￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- commonly￨L￨RB￨O￨- applied￨L￨VBN￨O￨- modelling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Maxent￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- correlation-based￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨A niche￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- mechanistic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- susceptible-exposed-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- environmental￨L￨JJ￨O￨A niche￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- depicts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- situation￨L￨NN￨O￨- better￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- with￨L￨IN￨O￨- USUV￨U￨NN￨ORGANIZATION￨- still￨L￨RB￨O￨- being￨L￨VBG￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- invasive￨L￨JJ￨O￨- stage￨L￨NN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- chance￨L￨NN￨O￨- for￨L￨IN￨O￨- under-estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- environmental￨L￨JJ￨O￨A niche￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- was￨L￨VBD￨O￨- run￨L￨VBN￨O￨- with￨L￨IN￨O￨- long-term￨L￨JJ￨O￨- bio-climatic￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- source￨L￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- climatic￨L￨JJ￨O￨- suitability￨L￨NN￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- models￨L￨NNS￨O￨- show￨L￨VBP￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨A for￨L￨IN￨O￨- USUV￨U￨NN￨O￨- in￨L￨IN￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- France￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Pannonian￨U￨NNP￨LOCATION￨- Basin￨U￨NNP￨LOCATION￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- northern￨L￨JJ￨O￨- Italy￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- assimilation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- also￨L￨RB￨O￨- as￨L￨IN￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- point￨L￨NN￨O￨- processors￨L￨NNS￨O￨- ,￨L￨,￨O￨- Kalman￨U￨NNP￨PERSON￨- filters￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- linear￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- regression￨L￨NN￨O￨A method￨L￨NN￨O￨- meant￨L￨VBN￨O￨- to￨L￨TO￨O￨- solve￨L￨VB￨O￨- inverse￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- estimating￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- often￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- context￨L￨NN￨O￨- of￨L￨IN￨O￨- solving￨L￨VBG￨O￨- a￨L￨DT￨O￨- forward￨L￨RB￨O￨- problem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- issuing￨L￨VBG￨O￨- a￨L￨DT￨O￨- forecast￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- was￨L￨VBD￨O￨- initially￨L￨RB￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- contexts￨L￨NNS￨O￨- of￨L￨IN￨O￨- space￨L￨NN￨O￨- travel￨L￨NN￨O￨- by￨L￨IN￨O￨- Kalman￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Brownian￨U￨NNP￨MISC￨- motion￨L￨NN￨O￨- by￨L￨IN￨O￨- Thiele￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Cases￨U￨NNS￨O￨- were￨L￨VBD￨O￨- mostly￨L￨RB￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- urban￨L￨JJ￨O￨- prefectures￨L￨NNS￨O￨- with￨L￨IN￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- curves￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- one￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Tokyo￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- adjacent￨L￨JJ￨O￨A areas￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- Osaka￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- areas￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- Osaka￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- identified￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- metapopulation￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- spatiotemporal￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- over￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- patches￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- line￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- total￨L￨NN￨O￨A of￨L￨IN￨O￨- 47￨L￨CD￨NUMBER￨- prefectures￨L￨NNS￨O￨- in￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Top￨U￨JJ￨O￨- :￨L￨:￨O￨- Weekly￨U￨NNP￨SET￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- notified￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- Kanto￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Tokyo￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- adjacent￨L￨JJ￨O￨A prefectures￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Kansai￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- Osaka￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- adjacent￨L￨JJ￨O￨- prefectures￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Among￨U￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨NN￨O￨A of￨L￨IN￨O￨- 16,730￨L￨CD￨NUMBER￨- notified￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- 4,116￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 24.6￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- 3,600￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 21.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- reported￨L￨VBN￨O￨- from￨L￨IN￨O￨- Tokyo￨U￨NNP￨CITY￨- and￨L￨CC￨O￨- Osaka￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- largest￨L￨JJS￨O￨- prefectures￨L￨NNS￨O￨- in￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2013￨L￨CD￨DATE￨- rubella￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- Japan￨U￨NNP￨COUNTRY￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- mostly￨L￨RB￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- urban￨L￨JJ￨O￨- areas￨L￨NNS￨O￨A .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- who￨L￨WP￨O￨- interacts￨L￨VBZ￨O￨- with￨L￨IN￨O￨- whom￨L￨WP￨O￨- ,￨L￨,￨O￨- one￨L￨PRP￨NUMBER￨- can￨L￨MD￨O￨- comprehensively￨L￨RB￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- topological￨L￨JJ￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- systems20.Non-Poissonian￨L￨JJ￨O￨- bursty￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- constituents￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- strongly￨L￨RB￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- taking￨L￨VBG￨O￨- place￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- system21￨L￨NN￨O￨- ,22,23,24,25,26,27,28,29,30,31,32￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Correlated￨U￨JJ￨O￨- bursts￨L￨NNS￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A slow￨L￨VB￨O￨- down￨L￨RP￨O￨- spreading￨L￨VBG￨O￨- Takayuki￨U￨NNP￨PERSON￨- Hiraoka￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- &￨L￨CC￨O￨- Hang-Hyun￨U￨NNP￨PERSON￨- Jo￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 15321￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- networksComputational￨L￨JJ￨O￨- science￨L￨NN￨O￨- AbstractSpreading￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- place￨L￨NN￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- temporal￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- between￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- show￨L￨VBP￨O￨- non-Poissonian￨L￨JJ￨MISC￨- bursty￨L￨JJ￨O￨- nature￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- those￨L￨DT￨O￨- effects￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- two-step￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- probabilistic￨L￨JJ￨O￨- SI￨U￨NN￨O￨- dynamics￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- inhomogeneous￨L￨JJ￨O￨A and￨L￨CC￨O￨- correlated￨L￨VBD￨O￨- IETs￨U￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- correlated￨L￨VBD￨O￨- bursts￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- non-Poissonian￨L￨JJ￨MISC￨- temporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- fully￨L￨RB￨O￨- understood￨L￨VBN￨O￨- both￨L￨CC￨O￨- by￨L￨IN￨O￨- inhomogeneous￨L￨JJ￨O￨A interevent￨L￨JJ￨O￨- times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IETs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- IETs18￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨A is￨L￨VBZ￨O￨- constant￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- ∀￨L￨NN￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- classes￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨A the￨L￨DT￨O￨- global￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- Zika￨U￨NNP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- available￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- approximated￨L￨VBD￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- is￨L￨VBZ￨O￨- transmitted￨L￨VBN￨O￨- via￨L￨IN￨O￨- both￨L￨CC￨O￨- mosquitoes￨L￨NNS￨O￨- and￨L￨CC￨O￨- sexual￨L￨JJ￨O￨A contact￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- transmissibility￨L￨NN￨O￨- is￨L￨VBZ￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- β￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- used￨L￨VBN￨O￨- here￨L￨RB￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- helps￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- observing￨L￨VBG￨O￨- a￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- consequently￨L￨RB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- city￨L￨NN￨O￨A of￨L￨IN￨O￨- Rio￨U￨NNP￨CITY￨- de￨L￨IN￨CITY￨- Janeiro￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- individual-level￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- measured￨L￨VBN￨O￨- in￨L￨IN￨O￨- appropriate￨L￨JJ￨O￨- animal￨L￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- carefully￨L￨RB￨O￨- designed￨L￨VBN￨O￨- trials￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- subsequent￨L￨JJ￨O￨- population-level￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- predicted￨L￨VBN￨O￨- using￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- intervention￨L￨NN￨O￨A feasibility￨L￨NN￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- relates￨L￨VBZ￨O￨- to￨L￨TO￨O￨- costs￨L￨NNS￨O￨- and￨L￨CC￨O￨- logistics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- recently￨L￨RB￨DATE￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- computational￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- computing￨L￨VBG￨O￨- Dynamic￨U￨NNP￨O￨- Optimal￨U￨JJ￨O￨- Control￨U￨NN￨O￨- Policies￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- DOCPs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- year-to-year￨L￨JJ￨O￨- relative￨L￨JJ￨O￨- investment￨L￨NN￨O￨- in￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- prevention￨L￨NN￨O￨A strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- minimize￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- incident￨L￨NN￨O￨- cases￨L￨NNS￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- represented￨L￨VBD￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- MSM￨U￨NNP￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Fig￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Table￨U￨NNP￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- encompassing￨L￨VBG￨O￨- 9￨L￨CD￨NUMBER￨- states￨L￨NNS￨O￨- dividing￨L￨VBG￨O￨- individuals￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- virally￨L￨RB￨O￨- suppressed￨L￨VBD￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- treatment￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- T￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- protected￨L￨VBD￨O￨- susceptible￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- susceptibility￨L￨NN￨O￨- intervention￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- P￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- DOCPs￨U￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- robust￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- assumptions￨L￨NNS￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- allocation￨L￨NN￨O￨- of￨L￨IN￨O￨- resources￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- assumptions￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- deployment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- intervention￨L￨NN￨O￨A rather￨L￨RB￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- biological￨L￨JJ￨O￨- and￨L￨CC￨O￨- behavioral￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- system￨L￨NN￨O￨- alone￨L￨RB￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- most￨L￨RBS￨O￨- data-driven￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- time-varying￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- attempt￨L￨VBP￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- characteristic￨L￨JJ￨O￨- time￨L￨NN￨O￨- scale￨L￨NN￨O￨- in￨L￨IN￨O￨- isolation￨L￨NN￨O￨- —￨L￨:￨O￨- typically￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- short-time￨L￨JJ￨O￨- memory￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- or￨L￨CC￨O￨- with￨L￨IN￨O￨- long-time￨L￨JJ￨O￨- abrupt￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- external￨L￨JJ￨O￨- or￨L￨CC￨O￨- systemic￨L￨JJ￨O￨- events￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Change￨U￨NNP￨O￨- points￨L￨NNS￨O￨- ,￨L￨,￨O￨- memory￨L￨NN￨O￨A and￨L￨CC￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- Tiago￨U￨NNP￨O￨- P.￨U￨NNP￨O￨- Peixoto1￨U￨NNP￨O￨- ,2￨L￨NNP￨O￨- &￨L￨CC￨O￨- Laetitia￨U￨NNP￨O￨- Gauvin2￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 15511￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComplex￨L￨NNP￨O￨- networksComputational￨L￨NNP￨O￨- science￨L￨NN￨O￨- AbstractDynamic￨U￨JJ￨O￨- networks￨L￨NNS￨O￨- exhibit￨L￨VBP￨O￨- temporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- that￨L￨WDT￨O￨- vary￨L￨VBP￨O￨- across￨L￨IN￨O￨- different￨L￨JJ￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- potentially￨L￨RB￨O￨- affect￨L￨VB￨O￨- processes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- take￨L￨VBP￨O￨- place￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- do￨L￨VBP￨O￨- so￨L￨RB￨O￨- by￨L￨IN￨O￨- developing￨L￨VBG￨O￨- an￨L￨DT￨O￨- arbitrary-order￨L￨NN￨O￨- mixed￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- change￨L￨NN￨O￨- points￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- nonparametric￨L￨JJ￨O￨- Bayesian￨U￨JJ￨MISC￨- formulation￨L￨NN￨O￨- that￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- order￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- position￨L￨NN￨O￨- of￨L￨IN￨O￨- change￨L￨NN￨O￨- points￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- from￨L￨IN￨O￨- data￨L￨NNS￨O￨- without￨L￨IN￨O￨- overfitting￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- unified￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨- both￨L￨CC￨O￨- aspects￨L￨NNS￨O￨- simultaneously￨L￨RB￨O￨- ,￨L￨,￨O￨- detecting￨L￨VBG￨O￨- short￨L￨JJ￨O￨- and￨L￨CC￨O￨- long-time￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨A networks￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- sPop￨L￨NN￨O￨- packages￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- a￨L￨DT￨O￨- flexible￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨A and￨L￨CC￨O￨- development￨L￨NN￨O￨- categories￨L￨NNS￨O￨- ,￨L￨,￨O￨- include￨L￨VBP￨O￨- both￨L￨CC￨O￨- deterministic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- offer￨L￨NN￨O￨- high-speed￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- parameter￨L￨NN￨O￨- inference￨L￨NN￨O￨- .￨L￨.￨O￨- +Incorporating￨U￨VBG￨O￨- age￨L￨NN￨O￨A dependency￨L￨NN￨O￨- in￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- challenging￨L￨VBG￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- keep￨L￨VB￨O￨- track￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- previously￨L￨RB￨DATE￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- ILI￨U￨NN￨O￨- +￨L￨CC￨O￨- proxy￨L￨NN￨O￨A provides￨L￨VBZ￨O￨- an￨L￨DT￨O￨- estimate￨L￨NN￨O￨- that￨L￨WDT￨O￨- correlates￨L￨VBZ￨O￨- linearly￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- hospitalizations￨L￨NNS￨O￨- for￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- pdm09￨L￨NN￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- ;￨L￨:￨O￨- some￨L￨DT￨O￨- have￨L￨VBP￨O￨- argued￨L￨VBN￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- metric￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨RBR￨O￨- linear￨L￨JJ￨O￨- correlate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- than￨L￨IN￨O￨- ILI￨U￨NN￨O￨- rates￨L￨NNS￨O￨- alone￨L￨RB￨O￨- or￨L￨CC￨O￨- laboratory￨L￨NN￨O￨- detection￨L￨NN￨O￨- rates￨L￨NNS￨O￨- alone￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- multiplied￨L￨VBD￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- ILI￨U￨NN￨O￨- rates￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨O￨- virus￨L￨NN￨O￨- detection￨L￨NN￨O￨- rates￨L￨NNS￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- a￨L￨DT￨O￨- proxy￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- hereafter￨L￨RB￨O￨- ILI￨U￨NNP￨O￨- +￨L￨CC￨O￨- proxy￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- each￨L￨DT￨SET￨- week￨L￨NN￨SET￨- (￨L￨-LRB-￨O￨- Figure￨U￨NN￨O￨- ,￨L￨,￨O￨- panel￨L￨NN￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- reviewed￨L￨VBD￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- influenza-like￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- activity￨L￨NN￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- school￨L￨NN￨O￨- closures￨L￨NNS￨O￨A on￨L￨IN￨O￨- community￨L￨NN￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +One￨U￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interventions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- by￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- health￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- school￨L￨NN￨O￨- closures￨L￨NNS￨O￨A ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A B￨U￨NN￨O￨- ,￨L￨,￨O￨- Yamagata￨U￨NNP￨LOCATION￨- lineage￨L￨NN￨O￨- ,￨L￨,￨O￨- occurred￨L￨VBD￨O￨- in￨L￨IN￨O￨- Hong￨U￨NNP￨CITY￨- Kong￨U￨NNP￨CITY￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- 2016-2017￨L￨CD￨DURATION￨- epizootiological￨L￨JJ￨O￨- inspection￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- RF￨U￨NN￨O￨- revealed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- emergence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨A remained￨L￨VBD￨O￨- critical￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨- incurred￨L￨VBN￨O￨- LSD￨U￨NN￨O￨- stated￨L￨VBN￨O￨- as￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- problems￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- RF￨U￨NN￨MISC￨- NumericCitation￨U￨NN￨MISC￨- .￨L￨.￨O￨- +SBV￨U￨NN￨ORGANIZATION￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- territory￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- RF￨U￨NN￨O￨- appeared￨L￨VBD￨O￨A only￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- season￨L￨NN￨O￨- after￨L￨IN￨O￨- its￨L￨PRP$￨O￨- first￨L￨JJ￨ORDINAL￨- appearance￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- asymptomatic￨L￨JJ￨O￨- in￨L￨IN￨O￨- adult￨L￨JJ￨O￨- ruminants￨L￨NNS￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- milk￨L￨NN￨O￨- drop￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- diarrhea￨L￨NN￨O￨- ,￨L￨,￨O￨- congenital￨L￨JJ￨O￨- malformations￨L￨NNS￨O￨- in￨L￨IN￨O￨- newborn￨L￨JJ￨O￨- and￨L￨CC￨O￨- abortions￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- SBV￨U￨NN￨ORGANIZATION￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- RF￨U￨NN￨O￨- were￨L￨VBD￨O￨- 36.78￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- ,￨L￨,￨O￨- indicating￨L￨VBG￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- and￨L￨CC￨O￨- seriousness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨A NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Office￨U￨NNP￨ORGANIZATION￨- International￨U￨NNP￨ORGANIZATION￨- des￨L￨NNP￨ORGANIZATION￨- Epizootics￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- OIE￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Rosselkhoznadzor￨U￨NNP￨MISC￨- include￨L￨VBP￨O￨- ASF￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- BT￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- other￨L￨JJ￨O￨- nosocomial￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Schmallenberg￨U￨NN￨O￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SBV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Lumpy￨U￨JJ￨O￨- skin￨L￨NN￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- LSD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- past￨L￨JJ￨DURATION￨- 10￨L￨CD￨DURATION￨A years￨L￨NNS￨DURATION￨A (￨L￨-LRB-￨O￨- until￨L￨IN￨O￨- February￨U￨NNP￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨DATE￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- RF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- 1.209￨L￨CD￨NUMBER￨- LSD￨U￨NN￨O￨- outbreaks￨L￨NNS￨O￨- had￨L￨VBD￨O￨- been￨L￨VBN￨O￨- reported￨L￨VBN￨O￨- globally￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- total￨L￨JJ￨O￨A population￨L￨NN￨O￨- of￨L￨IN￨O￨- 20.548￨L￨CD￨NUMBER￨- animals￨L￨NNS￨O￨- at￨L￨IN￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- visibility￨L￨NN￨O￨- into￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- vaccine￨L￨NN￨O￨- inventory￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- tracking￨L￨VBG￨O￨- inventory￨L￨NN￨O￨- levels￨L￨NNS￨O￨- geographically￨L￨RB￨O￨A and￨L￨CC￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- allocation￨L￨NN￨O￨- decisions￨L￨NNS￨O￨- can￨L￨MD￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- visibility￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- vaccine￨L￨NN￨O￨- supply￨L￨NN￨O￨- chain￨L￨NN￨O￨- caused￨L￨VBD￨O￨- some￨L￨DT￨O￨- areas￨L￨NNS￨O￨- to￨L￨TO￨O￨- end￨L￨VB￨O￨- the￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- season￨L￨NN￨O￨- with￨L￨IN￨O￨- excess￨L￨JJ￨O￨- inventory￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- leftover￨L￨JJR￨O￨- vaccine￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- other￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- especially￨L￨RB￨O￨- those￨L￨DT￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- uptake￨L￨NN￨O￨A rates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- experienced￨L￨JJ￨O￨- unmet￨L￨JJ￨O￨- demand￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- ,￨L￨,￨O￨- states￨L￨NNS￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- good￨L￨JJ￨O￨- visibility￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- uptake￨L￨NN￨O￨- rates￨L￨NNS￨O￨- and￨L￨CC￨O￨- vaccine￨L￨NN￨O￨- inventory￨L￨NN￨O￨- levels￨L￨NNS￨O￨- geographically￨L￨RB￨O￨A .￨L￨.￨O￨- +As￨U￨IN￨O￨- new￨L￨JJ￨O￨- batches￨L￨NNS￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨A became￨L￨VBD￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- were￨L￨VBD￨O￨- allocated￨L￨VBN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- state￨L￨NN￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- ’s￨L￨POS￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- population-based￨L￨JJ￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- pro-rata￨L￨JJ￨O￨- ”￨L￨''￨O￨- allocation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Compelling￨U￨JJ￨O￨- genetic￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- suggests￨L￨VBZ￨O￨- domestic￨L￨JJ￨O￨A cats￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- haemoplasmas￨L￨NNS￨O￨- in￨L￨IN￨O￨- wild￨L￨JJ￨O￨- felids￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- high￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- among￨L￨IN￨O￨- some￨L￨DT￨O￨- wild￨L￨JJ￨O￨- felids￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- suggest￨L￨VB￨O￨- persistent￨L￨JJ￨O￨- onward￨L￨RB￨O￨- transmission￨L￨NN￨O￨- following￨L￨VBG￨O￨- spillover￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- widely￨L￨RB￨O￨- acknowledged￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- known￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- multiple￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- species￨L￨NNS￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- infecting￨L￨VBG￨O￨- domestic￨L￨JJ￨O￨A dogs￨L￨NNS￨O￨- and￨L￨CC￨O￨- cats￨L￨NNS￨O￨- infect￨L￨VBP￨O￨- other￨L￨JJ￨O￨- mammalian￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- evaluates￨L￨VBZ￨O￨- spillover￨L￨NN￨O￨- of￨L￨IN￨O￨- CMhm￨U￨NN￨O￨- in￨L￨IN￨O￨- domestic￨L￨JJ￨O￨A and￨L￨CC￨O￨- wild￨L￨JJ￨O￨- felids￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- and￨L￨CC￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- onward￨L￨RB￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- analyze￨L￨VBP￨O￨- field￨L￨NN￨O￨- surveys￨L￨NNS￨O￨- of￨L￨IN￨O￨- sympatric￨L￨JJ￨O￨- domestic￨L￨JJ￨O￨A cats￨L￨NNS￨O￨- ,￨L￨,￨O￨- bobcats￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- pumas￨L￨NNS￨O￨- from￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- sites￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- United￨U￨NNP￨COUNTRY￨- States￨U￨NNPS￨COUNTRY￨- in￨L￨IN￨O￨- conjunction￨L￨NN￨O￨- with￨L￨IN￨O￨- global￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- CMhm￨U￨NN￨O￨- in￨L￨IN￨O￨- felids￨L￨NNS￨O￨- .￨L￨.￨O￨- +CMhm￨U￨NN￨O￨- DNA￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- isolated￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- saliva￨L￨NN￨O￨- of￨L￨IN￨O￨- domestic￨L￨JJ￨O￨A cats￨L￨NNS￨O￨- and￨L￨CC￨O￨- vampire￨L￨NN￨O￨- bats￨L￨NNS￨O￨- ,￨L￨,￨O￨- implicating￨L￨VBG￨O￨- social￨L￨JJ￨O￨- grooming￨L￨NN￨O￨- and￨L￨CC￨O￨- aggression￨L￨NN￨O￨- as￨L￨IN￨O￨- possible￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- of￨L￨IN￨O￨- direct￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- the￨L￨DT￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- –￨L￨:￨O￨- including￨L￨VBG￨O￨- diversified￨L￨JJ￨O￨- testing￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- treatment￨L￨NN￨O￨- as￨L￨IN￨O￨- prevention￨L￨NN￨O￨A ,￨L￨,￨O￨- PrEP￨U￨NN￨O￨- and￨L￨CC￨O￨- harm￨L￨NN￨O￨- reduction￨L￨NN￨O￨- –￨L￨:￨O￨- have￨L￨VBP￨O￨- multiplied￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- application￨L￨NN￨O￨- across￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- is￨L￨VBZ￨O￨- uneven￨L￨JJ￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- settings￨L￨NNS￨O￨- ,￨L￨,￨O￨- far￨L￨RB￨O￨- lower￨L￨JJR￨O￨- than￨L￨IN￨O￨- needed￨L￨VBN￨O￨- to￨L￨TO￨O￨- impact￨L￨NN￨O￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- PrEP￨U￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- toolkit￨L￨NN￨O￨- is￨L￨VBZ￨O￨- most￨L￨RBS￨O￨- accurately￨L￨RB￨O￨- captured￨L￨VBN￨O￨- in￨L￨IN￨O￨- New￨U￨NNP￨LOCATION￨- South￨U￨NNP￨LOCATION￨- Wales￨U￨NNP￨LOCATION￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- observed￨L￨VBD￨O￨- a￨L￨DT￨O￨- 35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- state‐wide￨L￨JJ￨O￨- new￨L￨JJ￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- diagnoses￨L￨NNS￨O￨- in￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- following￨L￨VBG￨O￨- rapid￨L￨JJ￨O￨- scale‐up￨L￨NN￨O￨- of￨L￨IN￨O￨- PrEP￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- EPIC￨U￨NN￨O￨- trial￨L￨NN￨O￨A ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- seroconversions￨L￨NNS￨O￨- amongst￨L￨IN￨O￨- 3927￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- follow‐up￨L￨JJ￨O￨- amongst￨L￨IN￨O￨- trial￨L￨NN￨O￨- participants￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +MRC￨U￨NNP￨ORGANIZATION￨- Clinical￨U￨JJ￨ORGANIZATION￨- Trials￨U￨NNS￨ORGANIZATION￨- Unit￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- University￨U￨NNP￨ORGANIZATION￨- College￨U￨NNP￨ORGANIZATION￨- London￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- London￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- UK￨U￨NNP￨COUNTRY￨- Within￨U￨IN￨O￨- and￨L￨CC￨O￨- beyond￨L￨IN￨O￨- Europe￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- PrEP￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- undoubtedly￨L￨RB￨O￨- contributing￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- decline￨L￨NN￨O￨A in￨L￨IN￨O￨- new￨L￨JJ￨O￨- diagnoses￨L￨NNS￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- gay￨L￨JJ￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- benefit￨L￨NN￨O￨- is￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- precisely￨L￨RB￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impressive￨L￨JJ￨O￨- decline￨L￨NN￨O￨- seen￨L￨VBN￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- city￨L￨NN￨O￨- clinics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- universal￨L￨JJ￨O￨- .￨L￨.￨O￨- +European￨U￨JJ￨NATIONALITY￨- Centre￨U￨NNP￨O￨- for￨L￨IN￨O￨- Disease￨U￨NNP￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- ECDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Stockholm￨U￨NNP￨CITY￨- ,￨L￨,￨O￨- Sweden￨U￨NNP￨COUNTRY￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- increasing￨L￨VBG￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- European￨U￨JJ￨NATIONALITY￨- region￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- whole￨L￨JJ￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- large￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- differences￨L￨NNS￨O￨- between￨L￨IN￨O￨- Western￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Central￨U￨NNP￨O￨- and￨L￨CC￨O￨- Eastern￨U￨NNP￨LOCATION￨- Europe￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conducted￨L￨VBD￨O￨- active￨L￨JJ￨O￨- ,￨L￨,￨O￨- national￨L￨JJ￨O￨- ,￨L￨,￨O￨- laboratory-based￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- for￨L￨IN￨O￨- invasive￨L￨JJ￨O￨- pneumococcal￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- IPD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- serotyping￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- testing￨L￨NN￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- A￨U￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- decision￨L￨NN￨O￨- support￨L￨NN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- informatics￨L￨NNS￨O￨- supporting￨L￨VBG￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- areas￨L￨NNS￨O￨- for￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaksRachel￨L￨NN￨O￨- Beard1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Elizabeth￨U￨NNP￨PERSON￨- Wentz3￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Matthew￨U￨NNP￨PERSON￨- Scotch1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 17:38￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Zoonotic￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- account￨L￨VBP￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- substantial￨L￨JJ￨O￨- portion￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- and￨L￨CC￨O￨- burden￨L￨NN￨O￨- on￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- programs￨L￨NNS￨O￨- to￨L￨TO￨O￨- maintain￨L￨VB￨O￨- surveillance￨L￨NN￨O￨- and￨L￨CC￨O￨- preventative￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- decision￨L￨NN￨O￨- support￨L￨NN￨O￨- systems￨L￨NNS￨O￨- developed￨L￨VBD￨O￨- to￨L￨TO￨O￨- assist￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- officials￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- zoonotic￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Spatial￨U￨JJ￨O￨- decision￨L￨NN￨O￨A support￨L￨NN￨O￨- tools￨L￨NNS￨O￨- can￨L￨MD￨O￨- equip￨L￨VB￨O￨- heath￨L￨NN￨O￨- care￨L￨NN￨O￨- officials￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- analytics￨L￨NNS￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- modeling￨L￨NN￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- visual￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- to￨L￨TO￨O￨- effectively￨L￨RB￨O￨- make￨L￨VB￨O￨- decisions￨L￨NNS￨O￨- and￨L￨CC￨O￨- policy￨L￨NN￨O￨- recommendations￨L￨NNS￨O￨- to￨L￨TO￨O￨- improve￨L￨VB￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- facilitate￨L￨VB￨O￨- data￨L￨NNS￨O￨- collection￨L￨NN￨O￨- ,￨L￨,￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- decision-making￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- decision￨L￨NN￨O￨A support￨L￨NN￨O￨- systems￨L￨NNS￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DATE￨- 10￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- has￨L￨VBZ￨O￨- increased￨L￨VBN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- The￨U￨DT￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- ,￨L￨,￨O￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- modeling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨- of￨L￨IN￨O￨- recent￨L￨JJ￨O￨- SDSS￨U￨NNS￨ORGANIZATION￨- that￨L￨WDT￨O￨- target￨L￨VBP￨O￨- zoonotic￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- were￨L￨VBD￨O￨- described￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- urban￨L￨JJ￨O￨A tourists￨L￨NNS￨O￨- '￨L￨POS￨O￨- satisfaction￨L￨NN￨O￨- may￨L￨MD￨O￨- produce￨L￨VB￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- effect￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- channels￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- pure￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- technology￨L￨NN￨O￨- spillover￨L￨NN￨O￨- effect￨L￨NN￨O￨- —￨L￨:￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- tourists￨L￨NNS￨O￨- ’￨L￨POS￨O￨- experiences￨L￨NNS￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨- tourism￨L￨NN￨O￨- attractions￨L￨NNS￨O￨- ,￨L￨,￨O￨- urban￨L￨JJ￨O￨- tourism￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- will￨L￨MD￨O￨- travel￨L￨VB￨O￨- to￨L￨TO￨O￨- cities￨L￨NNS￨O￨- with￨L￨IN￨O￨- similar￨L￨JJ￨O￨- attractions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- produced￨L￨VBN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- and￨L￨CC￨O￨- emulate￨L￨VB￨O￨- them￨L￨PRP￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- traffic￨L￨NN￨O￨- overflow￨L￨NN￨O￨- effect￨L￨NN￨O￨- —￨L￨:￨O￨- the￨L￨DT￨O￨- convenience￨L￨NN￨O￨- of￨L￨IN￨O￨- transportation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- factor￨L￨NN￨O￨- for￨L￨IN￨O￨- tourists￨L￨NNS￨O￨- ’￨L￨POS￨O￨- travel￨L￨NN￨O￨- frequency￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- also￨L￨RB￨O￨- probes￨L￨NNS￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- intra-regional￨L￨JJ￨O￨- spillover￨L￨JJ￨O￨- effect￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨A tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- urban￨L￨JJ￨O￨- GDP￨U￨NN￨O￨- income￨L￨NN￨O￨- and￨L￨CC￨O￨- urban￨L￨JJ￨O￨- living￨L￨NN￨O￨- standards￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- might￨L￨MD￨O￨- sheds￨L￨VB￨O￨- new￨L￨JJ￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- facilitate￨L￨VB￨O￨- greater￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Tourism￨U￨NNP￨O￨- industry￨L￨NN￨O￨- market￨L￨NN￨O￨- rules￨L￨NNS￨O￨- .￨L￨.￨O￨- +Before￨U￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨A tourists￨L￨NNS￨O￨- ’￨L￨POS￨O￨- satisfaction￨L￨NN￨O￨- on￨L￨IN￨O￨- urban￨L￨JJ￨O￨- economic￨L￨JJ￨O￨- GDP￨U￨NN￨O￨- income￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- must￨L￨MD￨O￨- first￨L￨RB￨ORDINAL￨- figure￨L￨VB￨O￨- out￨L￨RP￨O￨- how￨L￨WRB￨O￨- urban￨L￨JJ￨O￨- tourists￨L￨NNS￨O￨- '￨L￨POS￨O￨- satisfaction￨L￨NN￨O￨- directly￨L￨RB￨O￨- affects￨L￨VBZ￨O￨- intra-regional￨L￨JJ￨O￨- GDP￨U￨NN￨O￨- income￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- spillover￨L￨NN￨O￨- effect￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- effect￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- extent￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- ’s￨L￨POS￨O￨- potential￨L￨JJ￨O￨- innovation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨A tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- urban￨L￨JJ￨O￨- macro-economy￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- perspective￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- dimension￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- say￨L￨VB￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- panel￨L￨NN￨O￨- Durbin￨U￨NNP￨PERSON￨- econometric￨L￨JJ￨O￨- regression￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- taking￨L￨VBG￨O￨- urban￨L￨JJ￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- independent￨L￨JJ￨RELIGION￨- variable￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- factors￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- with￨L￨IN￨O￨- tourist￨L￨NN￨O￨- attractions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨A of￨L￨IN￨O￨- tourists￨L￨NNS￨O￨- ’￨L￨POS￨O￨- host-guest￨L￨JJ￨O￨- contact￨L￨NN￨O￨- preference￨L￨NN￨O￨- on￨L￨IN￨O￨- perceived￨L￨VBN￨O￨- destination￨L￨NN￨O￨- image￨L￨NN￨O￨- and￨L￨CC￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- of￨L￨IN￨O￨- China￨U￨NNP￨COUNTRY￨- ’s￨L￨POS￨O￨- historical￨L￨JJ￨O￨- and￨L￨CC￨O￨- cultural￨L￨JJ￨O￨- Cities￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- City￨U￨NNP￨O￨- features￨L￨VBZ￨O￨- influence￨L￨VB￨O￨- the￨L￨DT￨O￨- satisfaction￨L￨NN￨O￨- of￨L￨IN￨O￨- Urban￨U￨NNP￨O￨- Visitors￨U￨NNPS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Research￨U￨NN￨O￨- on￨L￨IN￨O￨- tourist￨L￨NN￨O￨- satisfaction￨L￨NN￨O￨- in￨L￨IN￨O￨- Smart￨U￨JJ￨O￨- tourism￨L￨NN￨O￨- scenic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- Satisfaction￨U￨NN￨ORGANIZATION￨- Evaluation￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Tourist￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Influence￨U￨NN￨ORGANIZATION￨- Factors￨U￨NNS￨ORGANIZATION￨- Analysis￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- Rural￨U￨JJ￨O￨- Tourism￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Mimicking￨U￨VBG￨O￨- methods￨L￨NNS￨O￨- from￨L￨IN￨O￨- non-STIs￨L￨JJ￨MISC￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- researchers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- utilised￨L￨VBN￨O￨- deterministic￨L￨JJ￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ODE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- simplify￨L￨VB￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- while￨L￨IN￨O￨- other￨L￨JJ￨O￨- have￨L￨VBP￨O￨- adopted￨L￨VBN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- ,￨L￨,￨O￨- subdividing￨L￨VBG￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- characteristics￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- :￨L￨:￨O￨- age￨L￨NN￨O￨- and￨L￨CC￨O￨- sexual￨L￨JJ￨O￨A activity￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- or￨L￨CC￨O￨- previous￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- experience￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨A behaviour￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- strongly￨L￨RB￨O￨- upon￨L￨IN￨O￨- several￨L￨JJ￨O￨- compounding￨L￨VBG￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- sex￨L￨NN￨O￨- ,￨L￨,￨O￨- sexual￨L￨JJ￨O￨- preference￨L￨NN￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- cultural￨L￨JJ￨O￨- norms￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨- partners￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- trends￨L￨NNS￨O￨- across￨L￨IN￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- extreme￨L￨JJ￨O￨- heterogeneity￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- sexual￨L￨JJ￨O￨A partners￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- partnership￨L￨NN￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- scale-free￨L￨JJ￨O￨- sexual￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- ;￨L￨:￨O￨- furthermore￨L￨RB￨O￨- ,￨L￨,￨O￨- trends￨L￨NNS￨O￨- shift￨L￨NN￨O￨- across￨L￨IN￨O￨- time￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- heterogeneity￨L￨NN￨O￨- reported￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Natsal-3￨U￨NN￨MISC￨- survey￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- captured￨L￨VBN￨O￨- by￨L￨IN￨O￨- parsimonious￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- annual￨L￨JJ￨SET￨- rates￨L￨NNS￨O￨- —￨L￨:￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- mixture￨L￨NN￨O￨- of￨L￨IN￨O￨- Poisson￨U￨NNP￨PERSON￨- distributions￨L￨NNS￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Natsal-3￨U￨NN￨O￨- survey￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- -12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- distributions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- partnerships￨L￨NNS￨O￨- that￨L￨WDT￨O￨- involve￨L￨VBP￨O￨- unprotected￨L￨JJ￨O￨- sex￨L￨NN￨O￨A and￨L￨CC￨O￨- can￨L￨MD￨O￨- therefore￨L￨RB￨O￨- allow￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- STIs￨U￨NNS￨O￨- .￨L￨.￨O￨- +Experimentally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- exploring￨L￨VBG￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- centrality￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- k-core￨L￨NN￨O￨- measure￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- with￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- accuracy￨L￨NN￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- information￨L￨NN￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- access￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- graph￨L￨NN￨O￨A and￨L￨CC￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- compute￨L￨VBP￨O￨- the￨L￨DT￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- graph￨L￨NN￨O￨A exploration￨L￨NN￨O￨- sampling￨L￨NN￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- accurately￨L￨RB￨O￨- identifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- influential￨L￨JJ￨O￨- spreaders￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- any￨L￨DT￨O￨- prior￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- apart￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- collected￨L￨VBN￨O￨- samples/subgraphs￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conduct￨L￨VBP￨O￨- extensive￨L￨JJ￨O￨- experiments￨L￨NNS￨O￨- in￨L￨IN￨O￨- eight￨L￨CD￨NUMBER￨- real￨L￨JJ￨O￨A world￨L￨NN￨O￨A networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- simulating￨L￨VBG￨O￨- the￨L￨DT￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- serve￨L￨VBP￨O￨- as￨L￨IN￨O￨- ground￨L￨NN￨O￨- truth￨L￨NN￨O￨- identifiers￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- spreading￨L￨VBG￨O￨- efficiency￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- Rank￨U￨NNP￨O￨- Degree￨U￨NNP￨O￨- graph￨L￨NN￨O￨A sampling￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Pre-emptive￨U￨JJ￨MISC￨- spectral￨L￨JJ￨O￨- graph￨L￨NN￨O￨- protection￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- on￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨A social￨L￨JJ￨O￨- networksArie￨L￨NNP￨O￨- Wahyu￨U￨NNP￨O￨- Wijayanto1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- and￨L￨CC￨O￨- Tsuyoshi￨U￨NNP￨PERSON￨- Murata1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 3:5￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractConstructing￨U￨NNP￨O￨- effective￨L￨JJ￨O￨- and￨L￨CC￨O￨- scalable￨L￨JJ￨O￨- protection￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- over￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenging￨L￨JJ￨O￨- issue￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- address￨L￨VBP￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- suppressing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- multiplex￨L￨JJ￨O￨A social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- allocating￨L￨VBG￨O￨- protection￨L￨NN￨O￨- resources￨L￨NNS￨O￨- throughout￨L￨IN￨O￨- different￨L￨JJ￨O￨- layers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- a￨L￨DT￨O￨- multiplex￨L￨JJ￨O￨A graph￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- k￨L￨NN￨O￨- budget￨L￨NN￨O￨- of￨L￨IN￨O￨- protection￨L￨NN￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- survived￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- maximized￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- MultiplexShield￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- employs￨L￨VBZ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- graph￨L￨NN￨O￨- spectral￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- degree￨L￨NN￨O￨- centrality￨L￨NN￨O￨- and￨L￨CC￨O￨- layer-wise￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- pre-emptively￨L￨RB￨O￨- select￨L￨JJ￨O￨- k￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- for￨L￨IN￨O￨- protection￨L￨NN￨O￨A .￨L￨.￨O￨- +Multiplex￨U￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- multiplelayers￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- appear￨L￨VBP￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- layers￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- resulting￨L￨VBG￨O￨- age-structured￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- ;￨L￨:￨O￨- readers￨L￨NNS￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- additional￨L￨JJ￨O￨- detail￨L￨NN￨O￨- are￨L￨VBP￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- S1￨U￨NN￨O￨- Appendix￨U￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- ∘￨L￨SYM￨O￨- indicates￨L￨VBZ￨O￨A the￨L￨DT￨O￨- Hadamard￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- element-wise￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- product￨L￨NN￨O￨- ;￨L￨:￨O￨- ×￨L￨SYM￨O￨- indicates￨L￨VBZ￨O￨- matrix￨L￨NN￨O￨- multiplication￨L￨NN￨O￨- ;￨L￨:￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- matrix￨L￨NN￨O￨- :￨L￨:￨O￨- f￨L￨LS￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- occur￨L￨VBP￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- children￨L￨NNS￨O￨- ;￨L￨:￨O￨- similarly￨L￨RB￨O￨- f￨L￨FW￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- occur￨L￨VBP￨O￨- with￨L￨IN￨O￨- adults￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- f￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- f￨L￨FW￨O￨- ;￨L￨:￨O￨- f￨L￨LS￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- adult￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- occur￨L￨VBP￨O￨- with￨L￨IN￨O￨- children￨L￨NNS￨O￨- ;￨L￨:￨O￨- f￨L￨LS￨O￨- =￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- f￨L￨SYM￨O￨- indicates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- adult￨L￨NN￨O￨- ’s￨L￨POS￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- that￨L￨WDT￨O￨- occur￨L￨VBP￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- adults￨L￨NNS￨O￨- ;￨L￨:￨O￨- ω￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- aging￨L￨NN￨O￨- rate￨L￨NN￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- children￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- carries￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- meaning￨L￨NN￨O￨- with￨L￨IN￨O￨- c1￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Specifically￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- investigates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- particle￨L￨NN￨O￨- filtering￨L￨VBG￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- —￨L￨:￨O￨- adhering￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- Susceptible￨U￨JJ￨O￨- —￨L￨:￨O￨- Exposure￨U￨NN￨O￨- —￨L￨:￨O￨- Infectious￨U￨JJ￨O￨- —￨L￨:￨O￨- Recovered￨U￨VBN￨O￨- )￨L￨-RRB-￨O￨- structure￨L￨NN￨O￨- —￨L￨:￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A to￨L￨TO￨O￨- recurrently￨L￨RB￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- anticipate￨L￨VB￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- outbreak￨L￨NN￨O￨- transitions￨L￨NNS￨O￨- in￨L￨IN￨O￨- pre-vaccination￨L￨JJ￨O￨- era￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- seeks￨L￨VBZ￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- more￨L￨JJR￨O￨- accurate￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A dynamics￨L￨NNS￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- a￨L￨DT￨O￨- computational￨L￨JJ￨O￨- statistics￨L￨NNS￨O￨- technique￨L￨NN￨O￨- that￨L￨WDT￨O￨- combines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- insights￨L￨NNS￨O￨- from￨L￨IN￨O￨- ongoing￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- although￨L￨IN￨O￨- noisy￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- empirical￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- although￨L￨IN￨O￨- fraught￨L￨JJ￨O￨- by￨L￨IN￨O￨- systematic￨L￨JJ￨O￨- errors￨L￨NNS￨O￨- ,￨L￨,￨O￨- omissions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- divergence￨L￨NN￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- while￨L￨IN￨O￨- mitigating￨L￨VBG￨O￨- important￨L￨JJ￨O￨- weaknesses￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- .￨L￨.￨O￨- +Similar￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- of￨L￨IN￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- aggregate￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- age￨L￨NN￨O￨A group￨L￨NN￨O￨A across￨L￨IN￨O￨- the￨L￨DT￨O￨- timeframe￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- pyramid￨L￨NN￨O￨- of￨L￨IN￨O￨- Saskatchewan￨U￨NNP￨STATE_OR_PROVINCE￨- NumericCitation￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- employed￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- equals￨L￨VBZ￨O￨- N￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- project￨L￨NN￨O￨- employs￨L￨VBZ￨O￨- a￨L￨DT￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨A SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- component￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- state-equation￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- particle￨L￨NN￨O￨- filtering￨L￨VBG￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Caswell1￨U￨NN￨O￨- are￨L￨VBP￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- absorbing￨L￨VBG￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨A in￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- demographic￨L￨JJ￨O￨- and￨L￨CC￨O￨- ecological￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Caswell￨U￨NNP￨PERSON￨- .2￨L￨NN￨NUMBER￨- The￨U￨DT￨O￨- reader￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- alerted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- perturbation￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- long‐standing￨L￨VBG￨O￨- problem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- survey￨L￨NN￨O￨- by￨L￨IN￨O￨- Avrachenkov￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- approach￨L￨NN￨O￨- suggested￨L￨VBN￨O￨- by￨L￨IN￨O￨- Caswell1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- aligned￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- perturbed￨L￨VBN￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- other￨L￨JJ￨O￨- works￨L￨NNS￨O￨- .4￨L￨RB￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- essentially￨L￨RB￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- bounding￨L￨VBG￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- stationary￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- functional￨L￨JJ￨O￨- space￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- one‐step￨L￨JJ￨O￨- transition￨L￨NN￨O￨- probability￨L￨NN￨O￨- matrix￨L￨NN￨O￨- P￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete‐time￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- is￨L￨VBZ￨O￨- replaced￨L￨VBN￨O￨- by￨L￨IN￨O￨- another￨L￨DT￨O￨- one‐step￨L￨JJ￨O￨- transition￨L￨NN￨O￨- probability￨L￨NN￨O￨- matrix￨L￨NN￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- papers￨L￨NNS￨O￨- by￨L￨IN￨O￨- Li￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 6￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Seneta￨U￨NN￨O￨- .8￨L￨NN￨NUMBER￨- For￨U￨IN￨O￨- CTMCs￨U￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- steady‐state￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- measured￨L￨VBN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- infinitesimal￨L￨JJ￨O￨- generator￨L￨NN￨O￨- Q￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- perturbed￨L￨VBN￨O￨- to￨L￨TO￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- ϵ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- sufficiently￨L￨RB￨O￨- small￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- number￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- matrix￨L￨NN￨O￨- Q￨U￨NNP￨O￨- ∗￨L￨CD￨NUMBER￨- satisfies￨L￨NNS￨O￨- certain￨L￨JJ￨O￨- weak￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- section￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Altman￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 9￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- papers￨L￨NNS￨O￨- by￨L￨IN￨O￨- Altman￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,9￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Heidergott￨U￨NNP￨LOCATION￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- 10￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- representative￨L￨JJ￨TITLE￨- contributions￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- denumerable￨L￨JJ￨O￨- and￨L￨CC￨O￨- finite￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨- with￨L￨IN￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- queueing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- setting￨L￨NN￨O￨- of￨L￨IN￨O￨- perturbed￨L￨VBN￨O￨- QBD￨U￨NN￨O￨- processes￨L￨NNS￨O￨- analyzed￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- by￨L￨IN￨O￨- Li￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Liu28￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- excellent￨L￨JJ￨O￨- work￨L￨NN￨O￨- where￨L￨WRB￨O￨- censoring￨L￨VBG￨O￨- techniques￨L￨NNS￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- integral￨L￨JJ￨O￨- functionals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- discuss￨L￨VB￨O￨- infinitesimal￨L￨JJ￨O￨- sensitivity￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- perturbed￨L￨VBN￨O￨- structured￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨A and￨L￨CC￨O￨- Markovian￨U￨JJ￨O￨- arrival￨L￨NN￨O￨- streams￨L￨NNS￨O￨- ;￨L￨:￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- related￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- see￨L￨VB￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Dendievel￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ,29￨L￨CD￨NUMBER￨- where￨L￨WRB￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- perturbed￨L￨VBN￨O￨- stationary￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- QBD￨U￨NN￨O￨- process￨L￨NN￨O￨- are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- by￨L￨IN￨O￨- restricting￨L￨VBG￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- two￨L￨CD￨NUMBER￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- states￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- transmission￨L￨NN￨O￨- pathways￨L￨NNS￨O￨- of￨L￨IN￨O￨- diarrhea￨L￨NN￨O￨- using￨L￨VBG￨O￨- symptoms￨L￨NNS￨O￨- occurrence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- individual￨L￨JJ￨O￨- households￨L￨NNS￨O￨A consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- family￨L￨NN￨O￨- members￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- children￨L￨NNS￨O￨- and￨L￨CC￨O￨- adults￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- subject￨L￨NN￨O￨- to￨L￨TO￨O￨- waterborne￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- contamination￨L￨NN￨O￨- and￨L￨CC￨O￨- possibly￨L￨RB￨O￨- also￨L￨RB￨O￨- other￨L￨JJ￨O￨- risks￨L￨NNS￨O￨- effecting￨L￨VBG￨O￨- baseline￨L￨NN￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- see￨L￨VBP￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- additionally￨L￨RB￨O￨- compounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- surveillance￨L￨NN￨O￨- programs￨L￨NNS￨O￨- operate￨L￨VBP￨O￨- with￨L￨IN￨O￨- limited￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- diarrhea￨L￨NN￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- limited￨L￨VBN￨O￨- to￨L￨TO￨O￨- demographics￨L￨NNS￨O￨- ,￨L￨,￨O￨- reported￨L￨VBD￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- diarrhea￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- possibly￨L￨RB￨O￨- some￨L￨DT￨O￨- outcome￨L￨NN￨O￨- measures￨L￨NNS￨O￨- on￨L￨IN￨O￨- households￨L￨NNS￨O￨A or￨L￨CC￨O￨- individuals￨L￨NNS￨O￨- testing￨L￨VBG￨O￨- positive￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- observational￨L￨JJ￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- to￨L￨TO￨O￨- first￨L￨RB￨ORDINAL￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- household-level￨L￨JJ￨O￨- occurrence￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- parametric￨L￨JJ￨O￨- resampling￨L￨NN￨O￨- technique￨L￨NN￨O￨- akin￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- synthetic￨L￨JJ￨O￨- likelihood￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- approximate￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- occurrence￨L￨NN￨O￨- across￨L￨IN￨O￨- households￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- count￨L￨NN￨TITLE￨- data￨L￨NNS￨O￨- X1￨U￨NN￨O￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- X￨U￨NN￨O￨- represents￨L￨VBZ￨O￨- household￨L￨NN￨O￨- level￨L￨NN￨O￨- diarrhea￨L￨NN￨O￨- cases￨L￨NNS￨O￨- among￨L￨IN￨O￨- adults￨L￨NNS￨O￨A and￨L￨CC￨O￨- juveniles￨L￨NNS￨O￨- under￨L￨IN￨O￨- and￨L￨CC￨O￨- contaminated￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- clean￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- V￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- environments￨L￨NNS￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- the￨L￨DT￨O￨- generative￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- observed￨L￨VBN￨O￨- likelihood￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- numerically￨L￨RB￨O￨- solved￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- three￨L￨CD￨NUMBER￨- steady-state￨L￨JJ￨O￨- quantities￨L￨NNS￨O￨- :￨L￨:￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- ,￨L￨,￨O￨- PrEP￨U￨NN￨O￨- coverage￨L￨NN￨O￨A per￨L￨IN￨O￨- risk￨L￨NN￨O￨- group￨L￨NN￨O￨- and￨L￨CC￨O￨- population￨L￨NN￨O￨- level￨L￨NN￨O￨- ART￨U￨NN￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- in￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- prevalence￨L￨NN￨O￨- for￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- PrEP￨U￨NN￨O￨- uptake￨L￨NN￨O￨A and￨L￨CC￨O￨- determined￨L￨VBD￨O￨- which￨L￨WDT￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- PrEP￨U￨NN￨O￨- uptake￨L￨NN￨O￨- ,￨L￨,￨O￨- effectiveness￨L￨NN￨O￨- and￨L￨CC￨O￨- duration￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- elimination￨L￨NN￨O￨- .￨L￨.￨O￨- +Daily￨U￨NNP￨SET￨- or￨L￨CC￨O￨- intermittent￨L￨JJ￨O￨- PrEP￨U￨NN￨O￨- uptake￨L￨NN￨O￨A was￨L￨VBD￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- effective￨L￨JJ￨O￨- in￨L￨IN￨O￨- preventing￨L￨VBG￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- among￨L￨IN￨O￨- MSM￨U￨NNP￨ORGANIZATION￨- in￨L￨IN￨O￨- trials￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- cohort￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- clinical￨L￨JJ￨O￨- practice￨L￨NN￨O￨- studies￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- assumed￨L￨VBD￨O￨- universal￨L￨JJ￨O￨- ART￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- daily￨L￨JJ￨SET￨A PrEP￨U￨NN￨O￨- use￨L￨NN￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- 's￨L￨POS￨O￨- risk￨L￨NN￨O￨- behavior￨L￨NN￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- analytical￨L￨JJ￨O￨A modeling￨L￨NN￨O￨- achieve￨L￨VB￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- traditional￨L￨JJ￨O￨- analytical￨L￨JJ￨O￨- WSN￨U￨NNP￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- compartmentalization￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- health￨L￨NN￨O￨- status￨L￨NN￨O￨- ,￨L￨,￨O￨- agent￨L￨NN￨O￨- modeling￨L￨NN￨O￨- would￨L￨MD￨O￨- enable￨L￨VB￨O￨- the￨L￨DT￨O￨- building￨L￨NN￨O￨- of￨L￨IN￨O￨- agent￨L￨NN￨O￨- simulators￨L￨NNS￨O￨- with￨L￨IN￨O￨- more￨L￨JJR￨O￨- spatial￨L￨JJ￨O￨- capabilities￨L￨NNS￨O￨- using￨L￨VBG￨O￨- simple￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- formalized￨L￨VBN￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- achieving￨L￨VBG￨O￨- the￨L￨DT￨O￨- productive￨L￨JJ￨O￨- and￨L￨CC￨O￨- supplementary￨L￨JJ￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- agent-based￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- to￨L￨TO￨O￨- analytical￨L￨JJ￨O￨A modeling￨L￨NN￨O￨- methods￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- equation-based￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- analytical￨L￨JJ￨O￨A )￨L￨-RRB-￨O￨- approach￨L￨NN￨O￨- we￨L￨PRP￨O￨- adopt￨L￨VBP￨O￨- a￨L￨DT￨O￨- method￨L￨NN￨O￨- gleaned￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- extant￨L￨JJ￨O￨- literature￨L￨NN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- referred￨L￨VBD￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- Epidemic￨U￨JJ￨O￨- Modeling￨U￨NN￨O￨- and￨L￨CC￨O￨- Analysis￨U￨NN￨O￨- of￨L￨IN￨O￨- Cyber￨U￨NNP￨O￨- Dynamical￨U￨NNP￨O￨- Systems￨U￨NNPS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- because￨L￨IN￨O￨- agent￨L￨NN￨O￨A modeling￨L￨NN￨O￨- employs￨L￨VBZ￨O￨- simple￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- that￨L￨WDT￨O￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- complex￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- phenomenon￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- agent￨L￨NN￨O￨A modeling￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- based￨L￨VBN￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- IBMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- complementarily￨L￨RB￨O￨- add￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- equation-based￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- .￨L￨.￨O￨- +ABC￨U￨NNP￨ORGANIZATION￨- then￨L￨RB￨O￨- offers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- alternative￨L￨NN￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- for￨L￨IN￨O￨- fitting￨L￨JJ￨O￨A complex￨L￨NN￨O￨- individual-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- include￨L￨VB￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- sparse￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- parameter￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- fitted￨L￨JJ￨O￨- models￨L￨NNS￨O￨- must￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- estimated￨L￨VBN￨O￨- if￨L￨IN￨O￨- robust￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- data￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- challenging￨L￨VBG￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- noisy￨L￨JJ￨O￨A and￨L￨CC￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- modelled￨L￨VBN￨O￨- by￨L￨IN￨O￨- simple￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- such￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- approximate￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- computation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- valid￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- fitting￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- data￨L￨NNS￨O￨- sources￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- fitting￨L￨JJ￨O￨A using￨L￨VBG￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- phylogenetic￨L￨JJ￨O￨- data￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- review￨L￨NN￨O￨- we￨L￨PRP￨O￨- assess￨L￨VBP￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- global￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A spread￨L￨NN￨O￨A in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- highlight￨L￨VB￨O￨- common￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- and￨L￨CC￨O￨- good￨L￨JJ￨O￨- practice￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- identify￨L￨VB￨O￨- any￨L￨DT￨O￨- gaps￨L￨NNS￨O￨- for￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- research￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- type￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- input￨L￨NN￨O￨- data￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- parametrise￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- validation￨L￨NN￨O￨A data￨L￨NNS￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- model￨L￨NN￨TITLE￨- accuracy￨L￨NN￨O￨- and￨L￨CC￨O￨- judge￨L￨NN￨TITLE￨- quality￨L￨NN￨O￨- .￨L￨.￨O￨- +Directed￨U￨NNP￨O￨- by￨L￨IN￨O￨- this￨L￨DT￨O￨- view￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨A what￨L￨WP￨O￨- modelling￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- potential￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- what￨L￨WP￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- parametrise￨L￨VB￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Validation￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- multi-component￨L￨JJ￨O￨- process￨L￨NN￨O￨- involving￨L￨VBG￨O￨- :￨L￨:￨O￨- conceptual￨L￨JJ￨O￨- validation￨L￨NN￨O￨A ,￨L￨,￨O￨- logical￨L￨JJ￨O￨- validation￨L￨NN￨O￨- ,￨L￨,￨O￨- experimental￨L￨JJ￨O￨- validation￨L￨NN￨O￨- ,￨L￨,￨O￨- operational￨L￨JJ￨O￨- validation￨L￨NN￨O￨- and￨L￨CC￨O￨- validation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- validation￨L￨NN￨O￨A of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- models￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- discussed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Meslé￨U￨NNP￨LOCATION￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- although￨L￨IN￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- explored￨L￨VBN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- metapopulation￨L￨NN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- previous‐generation￨L￨JJ￨O￨- antimicrobials￨L￨NNS￨O￨- become￨L￨VBP￨O￨- clinically￨L￨RB￨O￨- ineffective￨L￨JJ￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- or￨L￨CC￨O￨- habitats￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- local￨L￨JJ￨O￨- competitive￨L￨JJ￨O￨A displacement￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial‐sensitive￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- by￨L￨IN￨O￨- antimicrobial‐resistant￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- common￨L￨JJ￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- competitive￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- among￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- strains￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- intricately￨L￨RB￨O￨- linked￨L￨VBN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- interactions￨L￨NNS￨O￨- with￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- decoupling￨L￨VBG￨O￨- local￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- from￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- selection￨L￨NN￨O￨- regimes￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- hope￨L￨VBP￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- managing￨L￨VBG￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- over￨L￨IN￨O￨- space￨L￨NN￨O￨- that￨L￨WDT￨O￨- apply￨L￨VBP￨O￨- across￨L￨IN￨O￨- systems￨L￨NNS￨O￨- when￨L￨WRB￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- governing￨L￨VBG￨O￨- local￨L￨JJ￨O￨- competitive￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- between￨L￨IN￨O￨- antimicrobial‐resistant￨L￨JJ￨O￨- and￨L￨CC￨O￨- antimicrobial‐susceptible￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- genetics￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- often￨L￨RB￨O￨- differ￨L￨VBP￨O￨- considerably￨L￨RB￨O￨- from￨L￨IN￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- herbivorous￨L￨JJ￨O￨- pests￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- question￨L￨NN￨O￨- in￨L￨IN￨O￨- both￨L￨DT￨O￨- domains￨L￨NNS￨O￨- concerns￨L￨VBZ￨O￨- a￨L￨DT￨O￨- balancing￨L￨NN￨O￨- act￨L￨NN￨O￨- :￨L￨:￨O￨- How￨U￨WRB￨O￨- can￨L￨MD￨O￨- the￨L￨DT￨O￨- migratory￨L￨JJ￨O￨- and￨L￨CC￨O￨- competitive￨L￨JJ￨O￨A potential￨L￨NN￨O￨- of￨L￨IN￨O￨- antimicrobial‐sensitive￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- be￨L￨VB￨O￨- leveraged￨L￨VBN￨O￨- to￨L￨TO￨O￨- mitigate￨L￨VB￨O￨- the￨L￨DT￨O￨- strong￨L￨JJ￨O￨- selective￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- anthropogenic￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- antimicrobial￨L￨JJ￨O￨- use￨L￨NN￨O￨- or￨L￨CC￨O￨- agricultural￨L￨JJ￨O￨- toxins￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ?￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- that￨L￨IN￨O￨- antimicrobial‐sensitive￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- occupying￨L￨VBG￨O￨- sites￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- antimicrobial￨L￨JJ￨O￨- are￨L￨VBP￨O￨- displaced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- antimicrobial‐resistant￨L￨JJ￨O￨- strain￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨A strain￨L￨NN￨O￨- 's￨L￨POS￨O￨- colonization￨L￨NN￨O￨- rate￨L￨NN￨O￨- c￨L￨NN￨O￨- of￨L￨IN￨O￨- empty￨L￨JJ￨O￨- patches￨L￨NNS￨O￨- .￨L￨.￨O￨- +Study￨U￨NNP￨O￨- protocol￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Study￨U￨NNP￨MISC￨- protocol￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- iMPaCT￨L￨NN￨O￨- project￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- longitudinal￨L￨JJ￨O￨- cohort￨L￨NN￨O￨- study￨L￨NN￨O￨- assessing￨L￨VBG￨O￨- psychological￨L￨JJ￨O￨- determinants￨L￨NNS￨O￨- ,￨L￨,￨O￨- sexual￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- chlamydia￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- re￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- heterosexual￨L￨JJ￨O￨- STI￨U￨NN￨O￨- clinic￨L￨NN￨O￨- visitorsDaphne￨L￨NNP￨O￨- A.￨U￨NNP￨O￨- 2018Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Chlamydia￨U￨NN￨O￨- trachomatis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- chlamydia￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- commonly￨L￨RB￨O￨- reported￨L￨VBN￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- STI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Netherlands￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- severe￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- longitudinal￨L￨JJ￨O￨- cohort￨L￨NN￨O￨- study￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- conducted￨L￨VBN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- between￨L￨IN￨O￨- psychological￨L￨JJ￨O￨- and￨L￨CC￨O￨- behavioural￨L￨JJ￨O￨- determinants￨L￨NNS￨O￨- and￨L￨CC￨O￨- chlamydia￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- re￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- among￨L￨IN￨O￨- heterosexual￨L￨JJ￨O￨- STI￨U￨NN￨O￨- clinic￨L￨NN￨O￨- visitors￨L￨NNS￨O￨- aged￨L￨VBN￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 24￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- makes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- incorporation￨L￨NN￨O￨- of￨L￨IN￨O￨- psychological￨L￨JJ￨O￨- determinants￨L￨NNS￨O￨- and￨L￨CC￨O￨- behaviour￨L￨NN￨O￨- change￨L￨NN￨O￨- in￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- on￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨A transmission￨L￨NN￨O￨- especially￨L￨RB￨O￨- important￨L￨JJ￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- unaware￨L￨JJ￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- preventive￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- or￨L￨CC￨O￨- health-care￨L￨NN￨O￨- seeking￨L￨VBG￨O￨- behaviour￨L￨NN￨O￨- mostly￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- psychological￨L￨JJ￨O￨A determinants￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- risk￨L￨NN￨O￨- perception￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Mathematical￨U￨JJ￨MISC￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- life￨L￨NN￨O￨- cycle￨L￨NN￨O￨- of￨L￨IN￨O￨- taenia-cysticercosis￨L￨NN￨O￨- :￨L￨:￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- chemotherapy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Part￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Marco￨U￨NNP￨O￨- V.￨U￨NNP￨O￨- 2018Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Taenia￨U￨NNP￨O￨- solium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- aetiological￨L￨JJ￨O￨- agent￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- taeniasis￨L￨NN￨O￨- ,￨L￨,￨O￨- pig￨L￨NN￨O￨A cysticercosis￨L￨NN￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨- neurocysticercosis￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- serious￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- problems￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- adult￨L￨JJ￨O￨- worms￨L￨NNS￨O￨- tends￨L￨VBZ￨O￨A to￨L￨TO￨O￨- rapidly￨L￨RB￨O￨- stabilize￨L￨VB￨O￨- in￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- parasite￨L￨NN￨O￨- per￨L￨IN￨O￨- individual￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- taeniasis￨L￨NN￨O￨- ,￨L￨,￨O￨- pig￨L￨NN￨O￨A and￨L￨CC￨O￨- human￨L￨JJ￨O￨- cysticercosis￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- A￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- taeniasis-cysticercosis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- assortativity￨L￨NN￨O￨- between￨L￨IN￨O￨- networks￨L￨NNS￨O￨- was￨L￨VBD￨O￨- defined￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- results￨L￨NNS￨O￨- were￨L￨VBD￨O￨- demonstrated￨L￨VBN￨O￨- :￨L￨:￨O￨- assortative￨L￨JJ￨O￨A connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- networks￨L￨NNS￨O￨- lowered￨L￨VBD￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- hop￨L￨NN￨O￨- length￨L￨NN￨O￨- and￨L￨CC￨O￨- enhanced￨L￨VBN￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- ,￨L￨,￨O￨- whereas￨L￨IN￨O￨- disassortative￨L￨JJ￨O￨- connections￨L￨NNS￨O￨- between￨L￨IN￨O￨- networks￨L￨NNS￨O￨- distributed￨L￨VBN￨O￨- the￨L￨DT￨O￨- communication￨L￨NN￨O￨- loads￨L￨NNS￨O￨- of￨L￨IN￨O￨- internetwork￨L￨NN￨O￨- links￨L￨NNS￨O￨- and￨L￨CC￨O￨- enhanced￨L￨VBD￨O￨- robustness￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- single￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- indicated￨L￨VBD￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- decrease￨L￨NN￨O￨- in￨L￨IN￨O￨- assortativity￨L￨NN￨O￨- provided￨L￨VBN￨O￨- low￨L￨JJ￨O￨- hop￨L￨NN￨O￨- length￨L￨NN￨O￨- ,￨L￨,￨O￨- high￨L￨JJ￨O￨- information￨L￨NN￨O￨A diffusion￨L￨NN￨O￨A efficiency￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- communication￨L￨NN￨O￨- load￨L￨NN￨O￨- on￨L￨IN￨O￨- edges￨L￨NNS￨O￨- .￨L￨.￨O￨- +Nodes￨U￨NNS￨O￨- of￨L￨IN￨O￨- similar￨L￨JJ￨O￨- degree￨L￨NN￨O￨- tend￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- exhibit￨L￨VBP￨O￨- high￨L￨JJ￨O￨- assortativity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- termed￨L￨VBN￨O￨- as￨L￨IN￨O￨- assortative￨L￨JJ￨O￨A mixing￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- carefully￨L￨RB￨O￨- adjust￨L￨VB￨O￨- assortativity￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- degree￨L￨NN￨O￨A distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- involved￨L￨JJ￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- possessed￨L￨VBD￨O￨- the￨L￨DT￨O￨- desired￨L￨VBN￨O￨- degree￨L￨NN￨O￨A of￨L￨IN￨O￨- assortativity￨L￨NN￨O￨- .￨L￨.￨O￨- +Compartmental￨U￨JJ￨O￨- models￨L￨NNS￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- or￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- area￨L￨NN￨O￨- of￨L￨IN￨O￨- phylodynamic￨L￨JJ￨O￨A inference￨L￨NN￨O￨- ,￨L￨,￨O￨- non-parametric￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- skyline￨L￨NN￨O￨- coalescent￨L￨NN￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- sampling-birth-death￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- are￨L￨VBP￨O￨- more￨L￨RBR￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- flexible￨L￨JJ￨O￨- framework￨L￨NN￨O￨- enables￨L￨VBZ￨O￨- phylodynamic￨L￨JJ￨O￨A inference￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- published￨L￨VBN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- variants￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- non-genetic￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +Phylogeographic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- migration￨L￨NN￨O￨A rates￨L￨NNS￨O￨- between￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- demes￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- within￨L￨IN￨O￨- this￨L￨DT￨O￨- modeling￨L￨NN￨O￨- framework￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- phylogeographic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- time-varying￨L￨JJ￨O￨- or￨L￨CC￨O￨- state-dependent￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- or￨L￨CC￨O￨- migration￨L￨NN￨O￨- rates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- easily￨L￨RB￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +Parameters￨U￨NNS￨O￨- estimated￨L￨VBN￨O￨- by￨L￨IN￨O￨- fitting￨L￨JJ￨O￨- mechanistic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- surveillance￨L￨NN￨O￨A and￨L￨CC￨O￨- forecasting￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- quantification￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- edges￨L￨NNS￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- removal￨L￨NN￨O￨- strategy￨L￨NN￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- outperforms￨L￨VBZ￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- those￨L￨DT￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- also￨L￨RB￨O￨- preserves￨L￨VBZ￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- connectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- proposal￨L￨NN￨O￨- concentrates￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- ,￨L￨,￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- link￨L￨NN￨O￨A and￨L￨CC￨O￨- thus￨L￨RB￨O￨- enabling￨L￨VBG￨O￨- containment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- removal￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- emphasized￨L￨VBN￨O￨- that￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- make￨L￨VBP￨O￨- use￨L￨NN￨O￨- only￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- to￨L￨TO￨O￨- decide￨L￨VB￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- edges￨L￨NNS￨O￨A have￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- removed￨L￨VBN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- or￨L￨CC￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- are￨L￨VBP￨O￨- ignored￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- determination￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- link￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- importance￨L￨NN￨O￨- requires￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- cope￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- propagation￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨A only￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- participation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- link￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- How￨U￨WRB￨O￨- Physical￨U￨JJ￨O￨- Proximity￨U￨NNP￨O￨- Shapes￨U￨NNP￨O￨- Complex￨U￨JJ￨O￨- Social￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- Arkadiusz￨U￨NNP￨O￨- Stopczynski1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Alex￨U￨NNP￨PERSON￨- ‘￨L￨``￨PERSON￨- Sandy￨U￨NNP￨PERSON￨- ’￨L￨''￨O￨- Pentland2￨U￨NNP￨O￨- &￨L￨CC￨O￨- Sune￨U￨NNP￨PERSON￨- Lehmann￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 17722￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsComputational￨L￨NNP￨O￨- science￨L￨NN￨O￨- AbstractSocial￨U￨NNP￨O￨- interactions￨L￨NNS￨O￨- among￨L￨IN￨O￨- humans￨L￨NNS￨O￨- create￨L￨VBP￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- –￨L￨:￨O￨- despite￨L￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- increase￨L￨NN￨O￨- of￨L￨IN￨O￨- online￨L￨NN￨O￨- communication￨L￨NN￨O￨- –￨L￨:￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- mediated￨L￨VBN￨O￨- through￨L￨IN￨O￨- physical￨L￨JJ￨O￨- proximity￨L￨NN￨O￨A remain￨L￨VBP￨O￨- a￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- way￨L￨NN￨O￨- for￨L￨IN￨O￨- people￨L￨NNS￨O￨- to￨L￨TO￨O￨- connect￨L￨VB￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- networks￨L￨NNS￨O￨- arise￨L￨VBP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- underlying￨L￨VBG￨O￨- behavioral￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- quantitatively￨L￨RB￨O￨- measure￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proximity￨L￨NN￨O￨A network￨L￨NN￨O￨- –￨L￨:￨O￨- short-range￨L￨JJ￨O￨- versus￨L￨CC￨O￨- long-range￨L￨JJ￨O￨- –￨L￨:￨O￨- impacts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Bulletin￨U￨NNP￨O￨- of￨L￨IN￨O￨- Mathematical￨U￨NNP￨O￨- Biology￨U￨NNP￨O￨- pp￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asThe￨L￨NNP￨O￨- Final￨U￨NNP￨O￨- Size￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Serious￨U￨JJ￨O￨- EpidemicAuthorsAuthors￨U￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsFred￨L￨JJ￨O￨- BrauerOpen￨U￨NN￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 38￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨MISC￨- AbstractIn￨U￨NNP￨MISC￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- serious￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- behavioral￨L￨JJ￨O￨- response￨L￨NN￨O￨- that￨L￨WDT￨O￨- decreases￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- considerably￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- taking￨L￨VBG￨O￨- this￨L￨DT￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- may￨L￨MD￨O￨- lead￨L￨VB￨O￨- to￨L￨TO￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- much￨L￨RB￨O￨- smaller￨L￨JJR￨O￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- than￨L￨IN￨O￨- estimates￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- take￨L￨VB￨O￨- this￨L￨DT￨O￨- into￨L￨IN￨O￨- account.KeywordsEpidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- Final￨U￨JJ￨O￨- size￨L￨NN￨O￨- relations￨L￨NNS￨O￨- Behavioral￨U￨JJ￨O￨- response￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionIt￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- standard￨L￨JJ￨O￨- practice￨L￨NN￨O￨- in￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- to￨L￨TO￨O￨- formulate￨L￨VB￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- observed￨L￨VBN￨O￨- early￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- fit￨L￨VB￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨A and￨L￨CC￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- management￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- suggestions￨L￨NNS￨O￨- include￨L￨VBP￨O￨- metapopulation￨L￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- including￨L￨VBG￨O￨- cross-coupling￨L￨JJ￨O￨- and￨L￨CC￨O￨- mobility￨L￨NN￨O￨- ,￨L￨,￨O￨- clustering￨L￨NN￨O￨- in￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- dynamic￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- ,￨L￨,￨O￨- agent-based￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- infectivity￨L￨NN￨O￨- and￨L￨CC￨O￨- susceptibility￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- reactive￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- early￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Further￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- quarantine￨L￨NN￨O￨- could￨L￨MD￨O￨- do￨L￨VB￨O￨- nothing￨L￨NN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- travel￨L￨NN￨O￨- of￨L￨IN￨O￨- rats￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- did￨L￨VBD￨O￨- little￨L￨JJ￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- .2￨L￨NN￨NUMBER￨- A￨U￨DT￨O￨- Variable-Contact-Rate￨U￨NNP￨O￨- Epidemic￨U￨NNP￨O￨- ModelAnother￨U￨NNP￨O￨- direction￨L￨NN￨O￨- that￨L￨WDT￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- well￨L￨RB￨O￨- worth￨L￨JJ￨O￨- further￨L￨JJ￨O￨- exploration￨L￨NN￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- decreasing￨L￨VBG￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A outbreak￨L￨NN￨O￨A .￨L￨.￨O￨- +There￨U￨EX￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- mechanism￨L￨NN￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨A rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- mechanisms￨L￨NNS￨O￨- from￨L￨IN￨O￨- incidence￨L￨NN￨O￨- data.A￨L￨NN￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- situations￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- slower￨L￨JJR￨O￨- than￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- possible￨L￨JJ￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- pointed￨L￨VBN￨O￨- out￨L￨RP￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- 2015￨L￨CD￨DATE￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- general￨L￨JJ￨TITLE￨- growth￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- where￨L￨WRB￨O￨- C￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- occurring￨L￨VBG￨O￨- up￨L￨RP￨O￨- to￨L￨TO￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- p￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- deceleration￨L￨NN￨O￨- of￨L￨IN￨O￨- growth￨L￨NN￨O￨- ”￨L￨''￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- exponential￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- if￨L￨IN￨O￨- Equality￨U￨NN￨O￨- p￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- but￨L￨CC￨O￨- solutions￨L￨NNS￨O￨- with￨L￨IN￨O￨- polynomial￨L￨JJ￨O￨- growth￨L￨NN￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨PERSON￨- StrictLessThan￨U￨NNP￨PERSON￨- 0￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- influence￨L￨NN￨O￨- points￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- reasons￨L￨NNS￨O￨- for￨L￨IN￨O￨- persistent￨L￨JJ￨O￨- cultural￨L￨JJ￨O￨A diversity￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- less￨L￨JJR￨O￨- clarity￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- interplay￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- cultural￨L￨JJ￨O￨- influence￨L￨NN￨O￨- with￨L￨IN￨O￨- fundamental￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- micro-level￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 25￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 996￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 1023￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asBetween￨L￨NN￨O￨- Monoculture￨U￨NN￨O￨- and￨L￨CC￨O￨- Cultural￨U￨JJ￨O￨- Polarization￨U￨NN￨O￨- :￨L￨:￨O￨- Agent-based￨U￨JJ￨MISC￨- Models￨U￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Interplay￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Social￨U￨NNP￨ORGANIZATION￨- Influence￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- Cultural￨U￨JJ￨O￨- DiversityAuthorsAuthors￨U￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsAndreas￨L￨NNS￨O￨- FlacheOpen￨U￨NNP￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 464￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨MISC￨- AbstractSocial￨U￨NNP￨MISC￨- influence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- social￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- .￨L￨.￨O￨- +I￨U￨PRP￨O￨- give￨L￨VBP￨O￨- a￨L￨DT￨O￨- brief￨L￨JJ￨O￨- overview￨L￨NN￨O￨- illustrating￨L￨VBG￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- agent-based￨L￨JJ￨O￨- modelers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- decades￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- conditions￨L￨NNS￨O￨- and￨L￨CC￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- cultural￨L￨JJ￨O￨A diversity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- agent-based￨L￨JJ￨O￨- computational￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- unraveling￨L￨VBG￨O￨- the￨L￨DT￨O￨- complex￨L￨JJ￨O￨- interplay￨L￨NN￨O￨A between￨L￨IN￨O￨- simple￨L￨JJ￨O￨- first￨L￨JJ￨ORDINAL￨- principles￨L￨NNS￨O￨- of￨L￨IN￨O￨- interpersonal￨L￨JJ￨O￨- social￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- and￨L￨CC￨O￨- emergent￨L￨JJ￨O￨- societal￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Very￨U￨RB￨O￨- often￨L￨RB￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- social￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- ,￨L￨,￨O￨- influence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- assimilative￨L￨JJ￨O￨- in￨L￨IN￨O￨- that￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- more￨L￨RBR￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- others￨L￨NNS￨O￨- they￨L￨PRP￨O￨- interact￨L￨VBP￨O￨- with￨L￨IN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- below-threshold￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- initiated￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- approximation￨L￨NN￨O￨A via￨L￨IN￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- works￨L￨VBZ￨O￨- well￨L￨RB￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- above-threshold￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- initiated￨L￨VBN￨O￨- at￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- methods￨L￨NNS￨O￨- from￨L￨IN￨O￨- Hamiltonian￨U￨JJ￨IDEOLOGY￨- statistical￨L￨JJ￨O￨- mechanics￨L￨NNS￨O￨- yield￨L￨VBP￨O￨- correct￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- as￨L￨IN￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- widely-used￨L￨JJ￨O￨- Ornstein-Uhlenbeck￨U￨NNP￨MISC￨- diffusion￨L￨NN￨O￨- approximation￨L￨NN￨O￨- gives￨L￨VBZ￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- poor￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- may￨L￨MD￨O￨- retain￨L￨VB￨O￨- some￨L￨DT￨O￨- value￨L￨NN￨O￨- for￨L￨IN￨O￨- qualitative￨L￨JJ￨O￨- comparisons￨L￨NNS￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iv￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- detailed￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- approximation￨L￨NN￨O￨- can￨L￨MD￨O￨- give￨L￨VB￨O￨- good￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- in￨L￨IN￨O￨- certain￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- provide￨L￨VB￨O￨- correct￨L￨JJ￨O￨- large￨L￨JJ￨O￨- population￨L￨NN￨O￨- asymptotic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- relied￨L￨VBN￨O￨- upon￨L￨IN￨O￨- without￨L￨IN￨O￨- some￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- external￨L￨JJ￨O￨- validation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- eg￨L￨FW￨O￨- simulation￨L￨NN￨O￨- studies￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +KeywordsStochastic￨U￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- Large￨U￨JJ￨O￨- deviations￨L￨NNS￨O￨- Endemic￨U￨JJ￨O￨- fade-out￨L￨NN￨O￨- Persistence￨U￨NN￨O￨- time￨L￨NN￨O￨- Mathematics￨U￨NNP￨O￨- Subject￨U￨NNP￨O￨- Classification￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- 92D30￨L￨NN￨O￨- 60J28￨L￨CD￨NUMBER￨- Download￨U￨VB￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- article￨L￨NN￨O￨- textNotesAcknowledgmentsElliott￨L￨NN￨O￨- Tjia￨U￨NN￨O￨- was￨L￨VBD￨O￨- supported￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- studentship￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Engineering￨U￨NNP￨O￨- and￨L￨CC￨O￨- Physical￨U￨NNP￨ORGANIZATION￨- Sciences￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- Council￨U￨NNP￨ORGANIZATION￨- .￨L￨.￨O￨- +J￨U￨NNP￨O￨- Appl￨U￨NNP￨O￨- Probab￨U￨NNP￨O￨- 53:203￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 215MathSciNetCrossRefGoogle￨L￨JJ￨O￨- ScholarBritton￨U￨NN￨O￨- T￨U￨NN￨O￨- ,￨L￨,￨O￨- Neal￨U￨NNP￨PERSON￨- P￨U￨NN￨PERSON￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- extinction￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS-household-epidemic￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +J￨U￨NNP￨O￨- Math￨U￨NNP￨O￨- Biol￨U￨NNP￨O￨- 41:559￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 580MathSciNetCrossRefGoogle￨L￨NN￨O￨- ScholarAndersson￨U￨NN￨O￨- H￨U￨NN￨O￨- ,￨L￨,￨O￨- Djehiche￨U￨NN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1998￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- threshold￨L￨NN￨O￨- limit￨L￨NN￨O￨- theorem￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨A logistic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +J￨U￨NNP￨O￨- Appl￨U￨NNP￨O￨- Probab￨U￨NNP￨O￨- 35:662￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 670MathSciNetCrossRefGoogle￨L￨JJ￨O￨- ScholarAsaf￨U￨NN￨O￨- M￨U￨NN￨O￨- ,￨L￨,￨O￨- Meerson￨U￨NN￨PERSON￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- Extinction￨U￨NN￨O￨- of￨L￨IN￨O￨- metastable￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- important￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨A and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- illustrated￨L￨VBN￨O￨- by￨L￨IN￨O￨- some￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- examples.KeywordsPermanence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinctionLyapunov￨L￨NN￨O￨- functionalStochastic￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- theoremStrong￨L￨NN￨O￨- number￨L￨NN￨O￨- theorem￨L￨NN￨O￨- of￨L￨IN￨O￨- martingale￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionAs￨U￨NNPS￨O￨- we￨L￨PRP￨O￨- all￨L￨DT￨O￨- know￨L￨VBP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- Lotka￨U￨NNP￨LOCATION￨- –￨L￨:￨O￨- Volterra￨U￨NNP￨CITY￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- well￨L￨RB￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- competition￨L￨NN￨O￨- among￨L￨IN￨O￨- different￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- field￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- ecology￨L￨NN￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- on￨L￨IN￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- separately￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- condition￨L￨NN￨O￨- to￨L￨TO￨O￨- maintain￨L￨VB￨O￨- permanence￨L￨NN￨O￨A and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- proper￨L￨JJ￨O￨- Lyapunov￨U￨NNP￨O￨- functional￨L￨JJ￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- comparison￨L￨NN￨O￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- strong￨L￨JJ￨O￨- law￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- for￨L￨IN￨O￨- martingales￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- several￨L￨JJ￨O￨- important￨L￨JJ￨O￨- inequalities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Permanence￨U￨NN￨MISC￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- high-dimensional￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- resource￨L￨NN￨O￨- competition￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- noiseLi￨L￨NN￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- Xiaoqiang￨U￨NNP￨PERSON￨- Wang2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Qimin￨U￨NNP￨O￨- Zhang1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:441￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- kind￨L￨NN￨O￨- of￨L￨IN￨O￨- resource￨L￨NN￨O￨- competition￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- noises￨L￨NNS￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- Tillman￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- scholars￨L￨NNS￨O￨- also￨L￨RB￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- method￨L￨NN￨O￨- that￨L￨WDT￨O￨- predicted￨L￨VBD￨O￨- the￨L￨DT￨O￨- final￨L￨JJ￨O￨- competition￨L￨NN￨O￨A results￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- resource￨L￨NN￨O￨- requirement￨L￨NN￨O￨- among￨L￨IN￨O￨- competing￨L￨VBG￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Mathematical￨U￨JJ￨MISC￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- education￨L￨NN￨O￨A on￨L￨IN￨O￨- tungiasis￨L￨NN￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- neglected￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- many￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- communitiesRachel￨L￨NNP￨O￨- A.￨U￨NN￨O￨- Orwa4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:426￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- formulate￨L￨VBP￨O￨- and￨L￨CC￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- jigger￨L￨NN￨TITLE￨- infestation￨L￨NN￨O￨- incorporating￨L￨VBG￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- education￨L￨NN￨O￨- using￨L￨VBG￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- computational￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- established￨L￨VBD￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- stabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨A equilibria￨L￨NNS￨O￨- points￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- E￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- breaks￨L￨VBZ￨O￨- out￨L￨RP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- results￨L￨VBZ￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨- or￨L￨CC￨O￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- eventually￨L￨RB￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- c-Jun￨L￨NN￨O￨- N-terminal￨U￨JJ￨O￨- kinases￨L￨NNS￨O￨- differentially￨L￨RB￨O￨- regulate￨L￨VBP￨O￨- TNFand￨U￨NN￨MISC￨- TLRs-mediated￨U￨JJ￨MISC￨- necroptosis￨L￨NN￨O￨- through￨L￨IN￨O￨- their￨L￨PRP$￨O￨- kinase-dependent￨L￨JJ￨O￨- and￨L￨CC￨O￨- -￨L￨:￨O￨- independent￨L￨JJ￨RELIGION￨- activities￨L￨NNS￨O￨- Mengtao￨U￨NNP￨O￨- Cao1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Fei￨U￨NNP￨O￨- Chen1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- ,￨L￨,￨O￨- Ni￨U￨NN￨MISC￨- Xie1￨U￨NN￨O￨- ,￨L￨,￨O￨- Meng-Yao￨U￨NNP￨O￨- Cao3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Pengfei￨U￨NNP￨PERSON￨- Chen1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Qi￨U￨NNP￨O￨- Lou1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yanli￨U￨NNP￨PERSON￨- Zhao1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Chen￨U￨NNP￨PERSON￨- He4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Shuyuan￨U￨NNP￨PERSON￨- Zhang5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Xinyang￨U￨NNP￨CITY￨- Song6￨U￨NNP￨O￨- ,￨L￨,￨O￨- Yu￨U￨NNP￨PERSON￨- Sun￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- Weimin￨U￨NNP￨PERSON￨- Zhu7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Lisha￨U￨NNP￨PERSON￨- Mou1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Shaodong￨U￨NNP￨PERSON￨- Luan5￨U￨NNP￨PERSON￨- &￨L￨CC￨O￨- Hanchao￨U￨NNP￨O￨- Gao1￨U￨NN￨O￨- ,5￨L￨CD￨NUMBER￨- na1￨L￨NN￨O￨- Cell￨U￨NN￨O￨- Death￨U￨NNP￨O￨- &￨L￨CC￨O￨- Diseasevolume￨U￨NNP￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 1140￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- Cell￨U￨NN￨O￨- death￨L￨NN￨O￨- and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- responseNecroptosis￨L￨NN￨O￨- AbstractTumor￨U￨NN￨O￨- necrosis￨L￨NN￨O￨- factor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TNF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Toll-like￨U￨JJ￨MISC￨- receptor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TLR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- 3/TLR4￨L￨NN￨O￨- activation￨L￨NN￨O￨- trigger￨L￨NN￨O￨- necroptotic￨L￨JJ￨O￨- cell￨L￨NN￨O￨A death￨L￨NN￨O￨- through￨L￨IN￨O￨- downstream￨L￨JJ￨O￨- signaling￨L￨NN￨O￨- complex￨L￨NN￨O￨- containing￨L￨VBG￨O￨- receptor-interacting￨L￨JJ￨O￨- protein￨L￨NN￨O￨- kinase￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- RIPK1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- RIPK3￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- pseudokinase￨L￨NN￨O￨- mixed￨L￨JJ￨O￨- lineage￨L￨NN￨O￨- kinase-domain-like￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- MLKL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Meanwhile￨U￨RB￨O￨- ,￨L￨,￨O￨- blocking￨L￨VBG￨O￨- the￨L￨DT￨O￨- kinase￨L￨NN￨O￨- activity￨L￨NN￨O￨- of￨L￨IN￨O￨- JNK￨U￨NN￨O￨- dramatically￨L￨RB￨O￨- reduced￨L￨VBD￨O￨- TNF￨U￨NN￨O￨- and￨L￨CC￨O￨- TLRs-induced￨U￨JJ￨O￨- necroptotic￨L￨JJ￨O￨- cell￨L￨NN￨O￨A death￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 267￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asEpidemiological￨L￨JJ￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- waning￨L￨VBG￨O￨- immunization￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨A populationAuthorsAuthors￨L￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsEwa￨L￨NNP￨MISC￨- GrelaMichael￨U￨NNP￨MISC￨- StichAmit￨U￨NNP￨MISC￨- K￨U￨NNP￨MISC￨- ChattopadhyayOpen￨U￨NNP￨MISC￨- AccessRegular￨U￨NNP￨MISC￨- ArticleFirst￨U￨NNP￨MISC￨- Online￨U￨NNP￨MISC￨- :￨L￨:￨O￨- 01￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 50￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- Abstract￨U￨JJ￨O￨- This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- SIRV￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- study￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- containing￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- 4-tiered￨L￨JJ￨O￨- population￨L￨NN￨O￨- compartment￨L￨NN￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBD￨O￨- agents￨L￨NNS￨O￨- .￨L￨.￨O￨- +J.￨U￨NNP￨O￨- B￨U￨NNP￨O￨- 88￨L￨CD￨NUMBER￨A ,￨L￨,￨O￨- 326￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2015￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ADSCrossRefGoogle￨U￨NN￨O￨- Scholar8￨U￨NN￨O￨- .￨L￨.￨O￨- +Nunes￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- N.R.￨U￨NNP￨PERSON￨- Bernardino￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- J.M.￨U￨NNP￨PERSON￨- Pacheco￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- M.C.￨U￨NNP￨PERSON￨- Gomes￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- J.￨U￨NNP￨O￨- 233￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 553￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2005￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- CrossRefGoogle￨U￨NNP￨O￨- Scholar6￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 1215￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1230￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asEfficient￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- hbox￨L￨NN￨O￨- Pow￨U￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- M￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- schemes￨L￨NNS￨O￨- for￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- kinetic￨L￨JJ￨O￨- modelsAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsAndrew￨L￨NN￨O￨- GolightlyTheodore￨U￨NN￨O￨- KypraiosOpen￨U￨NN￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 748￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractFitting￨U￨VBG￨O￨- stochastic￨L￨JJ￨O￨- kinetic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- Markov￨U￨NNP￨PERSON￨- jump￨L￨NN￨O￨A processes￨L￨NNS￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- Bayesian￨U￨JJ￨MISC￨- paradigm￨L￨NN￨O￨- is￨L￨VBZ￨O￨- complicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- intractability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- observed-data￨L￨JJ￨O￨- likelihood￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- method￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- recently￨L￨RB￨DATE￨- proposed￨L￨VBN￨O￨- constructs￨L￨NNS￨O￨- for￨L￨IN￨O￨- sampling￨L￨NN￨O￨- conditioned￨L￨VBN￨O￨- jump￨L￨NN￨O￨A processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- inference￨L￨NN￨O￨- schemes￨L￨NNS￨O￨- typically￨L￨RB￨O￨- require￨L￨VBP￨O￨- fewer￨L￨JJR￨O￨- state￨L￨NN￨O￨- particles￨L￨NNS￨O￨- than￨L￨IN￨O￨- when￨L￨WRB￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- bootstrap￨L￨NN￨O￨- filter￨L￨NN￨O￨- .￨L￨.￨O￨- +Computing￨U￨NNP￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- weights￨L￨NNS￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- hbox￨L￨NN￨O￨- Pow￨U￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- M￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- requires￨L￨VBZ￨O￨- running￨L￨VBG￨O￨- a￨L￨DT￨O￨- particle￨L￨NN￨O￨A filter￨L￨NN￨O￨- over￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- states￨L￨NNS￨O￨- to￨L￨TO￨O￨- unbiasedly￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- the￨L￨DT￨O￨- intractable￨L￨JJ￨O￨- observed-data￨L￨JJ￨O￨- likelihood￨L￨NN￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- time￨L￨NN￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- rejuvenation￨L￨NN￨O￨- step￨L￨NN￨O￨- is￨L￨VBZ￨O￨- key￨L￨JJ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- recently￨L￨RB￨DATE￨- proposed￨L￨VBN￨O￨- Mul￨U￨NN￨O￨- hbox￨L￨NN￨O￨- Pow￨U￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- M￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- algorithm￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- pseudo-marginal￨L￨JJ￨O￨- analogue￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- idealised￨L￨JJ￨O￨- scheme￨L￨NN￨O￨A known￨L￨VBN￨O￨- as￨L￨IN￨O￨- iterated￨L￨JJ￨O￨- batch￨L￨NN￨O￨- importance￨L￨NN￨O￨- sampling￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- an￨L￨DT￨O￨- auxiliary￨L￨JJ￨O￨- particle￨L￨NN￨O￨A filter￨L￨NN￨O￨- inside￨L￨IN￨O￨- the￨L￨DT￨O￨- Mul￨U￨NN￨O￨- hbox￨L￨NN￨O￨- Pow￨U￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- M￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- scheme￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- known￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- N￨U￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- expected￨L￨VBN￨O￨- persistence￨L￨NN￨O￨- time￨L￨NN￨O￨- tau￨L￨NN￨O￨A for￨L￨IN￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- endemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- satisfies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- sim￨L￨NN￨O￨- to￨L￨TO￨O￨- denote￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- ratio￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- sides￨L￨NNS￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- C￨U￨NN￨O￨- are￨L￨VBP￨O￨- constants￨L￨NNS￨O￨- whose￨L￨WP$￨O￨- values￨L￨NNS￨O￨- depend￨L￨VBP￨O￨- upon￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- upon￨L￨IN￨O￨- N.￨U￨NNP￨O￨- For￨U￨IN￨O￨- multidimensional￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- most￨L￨RBS￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- only￨L￨RB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- establish￨L￨VB￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- cruder￨L￨JJR￨O￨- form￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Limit￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- N￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- log￨L￨NN￨O￨- tau￨L￨NN￨O￨- N￨U￨NN￨O￨- -￨L￨:￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- leading-order￨L￨NN￨O￨- constant￨L￨NN￨O￨- A￨U￨NN￨O￨- via￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2016￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- extended￨L￨VBD￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- Andersson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Djehiche￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 1998￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- classic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- allow￨L￨VB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- quite￨L￨RB￨O￨- general￨L￨JJ￨TITLE￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- applying￨L￨VBG￨O￨- a￨L￨DT￨O￨- result￨L￨NN￨O￨- on￨L￨IN￨O￨- insensitivity￨L￨NN￨O￨- in￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- from￨L￨IN￨O￨- Zachary￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- finding￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- leading-order￨L￨NN￨O￨- constant￨L￨NN￨O￨A A￨U￨NN￨O￨- takes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- value￨L￨NN￨O￨- regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- distribution￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- provided￨L￨VBN￨O￨- only￨L￨RB￨O￨- that￨L￨IN￨O￨- its￨L￨PRP$￨O￨- mean￨L￨NN￨O￨- is￨L￨VBZ￨O￨- held￨L￨VBN￨O￨- constant￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- prefactor￨L￨NN￨O￨- constant￨L￨JJ￨O￨- C￨U￨NN￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- appropriately￨L￨RB￨O￨- modified.A￨L￨NN￨O￨- different￨L￨JJ￨O￨- extension￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- Andersson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Djehiche￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 1998￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- established￨L￨VBN￨O￨- in￨L￨IN￨O￨- Clancy￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- may￨L￨MD￨O￨- alternatively￨L￨RB￨O￨- be￨L￨VB￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- describing￨L￨VBG￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨VBG￨O￨- through￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- directed￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- annealed￨L￨JJ￨O￨- network￨L￨NN￨O￨- approximation.KeywordsStochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- Large￨U￨JJ￨O￨- deviations￨L￨NNS￨O￨- Endemic￨U￨JJ￨O￨- fade-out￨L￨NN￨O￨- Stochastic￨U￨NNP￨O￨- networks￨L￨NNS￨O￨- Superspreaders￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionFor￨U￨NNP￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- long-term￨L￨JJ￨O￨- quasi-stable￨L￨JJ￨O￨- endemicity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- variable￨L￨NN￨O￨- of￨L￨IN￨O￨- particular￨L￨JJ￨O￨- interest￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨A time￨L￨NN￨O￨- until￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- heterogeneity￨L￨NN￨O￨- in￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptibility￨L￨NN￨O￨- or￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectiousness￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- formula￨L￨NN￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- leading-order￨L￨NN￨O￨- constant￨L￨NN￨O￨- A￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- relationship￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Limit￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- N￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- log￨L￨NN￨O￨- tau￨L￨NN￨O￨A N￨U￨NN￨O￨- -￨L￨:￨O￨- A￨U￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Rumor￨U￨NN￨MISC￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- complex￨L￨NN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- hesitating￨L￨VBG￨O￨- mechanismXiongding￨L￨NN￨O￨- Liu1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2View￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Tao￨U￨NNP￨O￨- Li1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Mi￨U￨NNP￨O￨- Tian3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:391￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨NN￨O￨A ,￨L￨,￨O￨- controlling￨L￨VBG￨O￨- and￨L￨CC￨O￨- killing￨L￨VBG￨O￨- rumor￨L￨NN￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- importance￨L￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- dramatic￨L￨JJ￨O￨- importance￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- plays￨L￨VBZ￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- managing￨L￨NN￨O￨- and￨L￨CC￨O￨- controlling￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor.Rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- complex￨L￨NN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- attracted￨L￨VBN￨O￨- an￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- attention￨L￨NN￨O￨- from￨L￨IN￨O￨- researchers￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- direct￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- rumor￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- comprehensively￨L￨RB￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨NN￨O￨A in￨L￨IN￨O￨- detail￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- corresponding￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- formulate￨L￨VB￨O￨- the￨L￨DT￨O￨- characteristics￨L￨NNS￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +presented￨L￨VBN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨VBG￨O￨A model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- demographics￨L￨NNS￨O￨- on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Ibeas4￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2018:390￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- multicontroller￨L￨JJ￨O￨- structure￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIADR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-symptomatic￨L￨JJ￨O￨- infectious-asymptomatic￨L￨JJ￨O￨- infectious-dead￨L￨NN￨O￨- lying￨L￨VBG￨O￨- bodies￨L￨NNS￨O￨- recovered￨L￨VBN￨O￨- by￨L￨IN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- immune￨L￨JJ￨O￨- ,￨L￨,￨O￨- subpopulations￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- controls￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- feedback￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- subpopulation￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- antiviral￨L￨JJ￨O￨A treatment￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- symptomatic￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- subpopulation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨- removal￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- lying￨L￨VBG￨O￨- bodies￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- supervisory￨L￨JJ￨O￨- loss￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- cost￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- function￨L￨NN￨O￨- incorporates￨L￨VBZ￨O￨- several￨L￨JJ￨O￨- additive￨L￨JJ￨O￨- weighted￨L￨JJ￨O￨- terms￨L￨NNS￨O￨- including￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- loss￨L￨NN￨O￨- function￨L￨NN￨O￨- evolution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- antiviral￨L￨JJ￨O￨A treatment￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- bodies￨L￨NNS￨O￨- removal￨L￨NN￨O￨- efforts.KeywordsEpidemicsVaccinationTreatmentImpulsive￨L￨JJ￨O￨- controlsRemovalSupervisionSwitching￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionRelevant￨U￨JJ￨O￨- attention￨L￨NN￨O￨- is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- paid￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DATE￨- two￨L￨CD￨DATE￨- decades￨L￨NNS￨DATE￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- integro-differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- difference￨L￨NN￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- boundedness￨L￨NN￨O￨- ,￨L￨,￨O￨- oscillatory￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- positivity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stability￨L￨NN￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- injection￨L￨NN￨O￨- of￨L￨IN￨O￨- some￨L￨DT￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- feedback￨L￨NN￨O￨- regular￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- impulsive￨L￨JJ￨O￨A control￨L￨NN￨O￨- laws￨L￨NNS￨O￨- are￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- in￨L￨IN￨O￨- proposed￨L￨VBN￨O￨- true-mass￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- uncertainties￨L￨NNS￨O￨- and￨L￨CC￨O￨- eventual￨L￨JJ￨O￨- delays￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- supervised￨L￨JJ￨O￨- multicontroller￨L￨NN￨O￨- scheme￨L￨NN￨O￨A consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- parallel￨L￨JJ￨O￨- disposal￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- alternative￨L￨JJ￨O￨- controller￨L￨NN￨TITLE￨- parameterizations￨L￨NNS￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- switching￨L￨NN￨O￨- scheme￨L￨NN￨O￨- that￨L￨WDT￨O￨- chooses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- active￨L￨JJ￨O￨- controller￨L￨NN￨TITLE￨- through￨L￨IN￨O￨- consecutive￨L￨JJ￨O￨- time￨L￨NN￨O￨- intervals￨L￨NNS￨O￨- via￨L￨IN￨O￨- a￨L￨DT￨O￨- supervisory￨L￨JJ￨O￨- decision￨L￨NN￨O￨- scheme￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- A￨U￨NN￨O￨- switched￨L￨VBD￨O￨- multicontroller￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIADR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- monitored￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- and￨L￨CC￨O￨- supervised￨L￨JJ￨O￨- transients￨L￨NNS￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨A costsM￨L￨NN￨O￨- .￨L￨.￨O￨- +Transmission￨U￨NNP￨O￨- tree￨L￨NN￨O￨- reconstruction￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- specify￨L￨VB￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- individual￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- locations￨L￨NNS￨O￨A to￨L￨TO￨O￨- overall￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- characterise￨L￨VBP￨O￨- heterogeneous￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- within￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- identify￨L￨VB￨O￨- transmission￨L￨NN￨O￨- routes￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- a￨L￨DT￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- concept￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- implement￨L￨VBP￨O￨- the￨L￨DT￨O￨- within-host￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- introduced￨L￨VBN￨O￨- with￨L￨IN￨O￨- TransPhylo￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- distinct￨L￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨A genetic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- outbreaker￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- demonstrate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- even￨L￨RB￨O￨- complex￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- results￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- successfully￨L￨RB￨O￨- included￨L￨VBN￨O￨- with￨L￨IN￨O￨- minimal￨L￨JJ￨O￨- effort￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- R￨U￨NN￨O￨- package￨L￨NN￨O￨- re-implements￨L￨NNS￨O￨- and￨L￨CC￨O￨- extends￨L￨VBZ￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- introduced￨L￨VBN￨O￨- with￨L￨IN￨O￨- outbreaker￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- most￨L￨RBS￨O￨- importantly￨L￨RB￨O￨- also￨L￨RB￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- modular￨L￨JJ￨O￨- platform￨L￨NN￨O￨- allowing￨L￨VBG￨O￨- users￨L￨NNS￨O￨- to￨L￨TO￨O￨- specify￨L￨VB￨O￨- custom￨L￨NN￨O￨- models￨L￨NNS￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- optimised￨L￨JJ￨O￨- inferential￨L￨JJ￨O￨- framework￨L￨NN￨O￨- .￨L￨.￨O￨- +2018Published￨L￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Reconstructing￨U￨VBG￨O￨- individual￨L￨JJ￨O￨- transmission￨L￨NN￨O￨A events￨L￨NNS￨O￨A in￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- valuable￨L￨JJ￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- help￨L￨NN￨O￨- inform￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- policy￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- establish￨L￨VBP￨O￨- faculty￨L￨NN￨O￨- hiring￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- mechanism￨L￨NN￨O￨- that￨L￨WDT￨O￨- drives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- persistent￨L￨JJ￨O￨- epistemic￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- elite￨L￨NN￨O￨- institutions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- lower￨L￨JJR￨O￨- bound￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- structural￨L￨JJ￨O￨- inequality￨L￨NN￨O￨- in￨L￨IN￨O￨- shaping￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- ideas￨L￨NNS￨O￨A in￨L￨IN￨O￨- science.KeywordsSocial￨L￨JJ￨O￨- inequalitySociology￨L￨NN￨O￨- of￨L￨IN￨O￨- scienceComputational￨L￨JJ￨O￨- social￨L￨JJ￨O￨- scienceFaculty￨L￨NN￨O￨- hiring￨L￨VBG￨O￨- networksInformation￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionA￨U￨NN￨O￨- core￨L￨NN￨O￨- principle￨L￨NN￨O￨- of￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- progress￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- free￨L￨JJ￨O￨- exchange￨L￨NN￨O￨- of￨L￨IN￨O￨- ideas￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- enables￨L￨VBZ￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- ideas￨L￨NNS￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- scientific￨L￨JJ￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +Having￨U￨VBG￨O￨- established￨L￨VBN￨O￨- such￨L￨PDT￨O￨- a￨L￨DT￨O￨- mechanism￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- then￨L￨RB￨O￨- analyze￨L￨VBP￨O￨- its￨L￨PRP$￨O￨- potential￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- using￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- generic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- ideas￨L￨NNS￨O￨A and￨L￨CC￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- where￨L￨WRB￨O￨- an￨L￨DT￨O￨- idea￨L￨NN￨O￨- originates￨L￨VBZ￨O￨- on￨L￨IN￨O￨- its￨L￨PRP$￨O￨- longterm￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- across￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Analyzing￨U￨VBG￨O￨- five￨L￨CD￨NUMBER￨- popular￨L￨JJ￨O￨- research￨L￨NN￨O￨- topics￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- empirically￨L￨RB￨O￨- that￨L￨IN￨O￨- faculty￨L￨NN￨O￨- hiring￨L￨NN￨O￨- can￨L￨MD￨O￨- and￨L￨CC￨O￨- does￨L￨VBZ￨O￨- facilitate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- ideas￨L￨NNS￨O￨A in￨L￨IN￨O￨- science￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- faculty￨L￨NN￨O￨- hiring￨L￨VBG￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- embody￨L￨VBP￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- researcher￨L￨NN￨TITLE￨- transitions￨L￨NNS￨O￨- from￨L￨IN￨O￨- doctoral￨L￨JJ￨O￨- to￨L￨TO￨O￨- faculty￨L￨NN￨O￨- institutions￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- shaping￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- ideas￨L￨NNS￨O￨A in￨L￨IN￨O￨- computer￨L￨NN￨O￨- science￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- where￨L￨WRB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- an￨L￨DT￨O￨- idea￨L￨NN￨O￨- originates￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Past￨U￨JJ￨DATE￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- scholarly￨L￨JJ￨O￨- productivity￨L￨NN￨O￨- show￨L￨NN￨O￨- dramatic￨L￨JJ￨O￨- epistemic￨L￨JJ￨O￨- inequality￨L￨NN￨O￨- :￨L￨:￨O￨- scientists￨L￨NNS￨O￨- at￨L￨IN￨O￨- elite￨L￨NN￨O￨- institutions￨L￨NNS￨O￨- produce￨L￨VBP￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- articles￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- play￨L￨VBP￨O￨- an￨L￨DT￨O￨- outsized￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- setting￨L￨VBG￨O￨- the￨L￨DT￨O￨- pace￨L￨NN￨O￨- and￨L￨CC￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- scientific￨L￨JJ￨O￨A achievement￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- receive￨L￨VB￨O￨- the￨L￨DT￨O￨- majority￨L￨NN￨O￨- of￨L￨IN￨O￨- both￨L￨DT￨O￨- professional￨L￨JJ￨O￨- awards￨L￨NNS￨O￨- and￨L￨CC￨O￨- recognition￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- few￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- the￨L￨DT￨O￨- endangered￨L￨VBN￨O￨- species.Assume￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Allee￨U￨NN￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- African￨U￨JJ￨NATIONALITY￨- wild￨L￨JJ￨O￨- dog￨L￨NN￨O￨- species￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- x￨L￨CC￨O￨- Tuple￨U￨NNP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- x￨L￨NN￨O￨- Mul￨U￨NN￨O￨- biggl￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- biggr￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- biggl￨L￨NN￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- biggr￨L￨NN￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- K￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- x￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Allee￨U￨NNP￨O￨- effect￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- mating￨L￨VBG￨O￨- restrictions￨L￨NNS￨O￨- .￨L￨.￨O￨- +So￨U￨IN￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- African￨U￨JJ￨NATIONALITY￨- wild￨L￨JJ￨O￨- dog￨L￨NN￨O￨- impulsive￨L￨JJ￨O￨A feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Allee￨U￨NN￨O￨- effect￨L￨NN￨O￨- and￨L￨CC￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- y￨L￨NNP￨O￨- Tuple￨U￨NNP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- A￨U￨NN￨MISC￨- Lycaon￨U￨NN￨MISC￨- pictus￨L￨NN￨O￨- impulsive￨L￨JJ￨O￨A state￨L￨NN￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Allee￨U￨NN￨O￨- effect￨L￨NN￨O￨- and￨L￨CC￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- delayYaning￨L￨VBG￨O￨- Li1￨U￨NN￨O￨- ,￨L￨,￨O￨- Huidong￨U￨NNP￨O￨- Cheng1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- and￨L￨CC￨O￨- Yanhui￨U￨NN￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2018:367￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractAllee￨U￨NNP￨O￨- effect￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- sparse￨L￨JJ￨O￨- effect￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- active￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 26￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- 6th-order￨L￨JJ￨O￨- approximation￨L￨NN￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- various￨L￨JJ￨O￨- Equality￨U￨NNP￨O￨- h￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- 0.90000000000000002￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- h￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- h￨L￨NN￨O￨- Mul￨U￨NN￨O￨- mbox￨L￨NN￨O￨- Mul￨U￨NN￨O￨- o￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- m￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- l￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NN￨O￨- h￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- 1.1000000000000001￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- in￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Figure￨U￨NNP￨O￨- 11￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- optimum￨L￨NN￨O￨- and￨L￨CC￨O￨- minimum￨L￨NN￨O￨A values￨L￨NNS￨O￨- of￨L￨IN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Figure￨U￨NN￨O￨- 12￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- optimum￨L￨NN￨O￨- and￨L￨CC￨O￨- minimum￨L￨NN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- F￨U￨NN￨O￨- t￨L￨NN￨O￨- Figure￨U￨NN￨O￨- 13￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- optimum￨L￨NN￨O￨- and￨L￨CC￨O￨- minimum￨L￨NN￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- G￨U￨NN￨O￨- t￨L￨NN￨O￨- By￨U￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- figures￨L￨NNS￨O￨- note￨L￨VBP￨O￨- the￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- HAM￨U￨NN￨O￨- .￨L￨.￨O￨- +,￨L￨,￨O￨- and￨L￨CC￨O￨- fixing￨L￨VBG￨O￨- Equality￨U￨NN￨O￨- s￨L￨NNS￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ith-order￨L￨NN￨O￨- deformation￨L￨NN￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- and￨L￨CC￨O￨- Then￨U￨RB￨O￨- the￨L￨DT￨O￨- ith-order￨L￨NN￨O￨- deformation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- i￨L￨FW￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- or￨L￨CC￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- becomes￨L￨VBZ￨O￨- 6￨L￨CD￨NUMBER￨- Numerical￨U￨JJ￨O￨- resultsConsider￨L￨NN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- values￨L￨NNS￨O￨A for￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- Mathematica￨U￨NNP￨O￨- software￨L￨NN￨O￨- to￨L￨TO￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- sixth-order￨L￨NN￨O￨- expansions￨L￨NNS￨O￨- for￨L￨IN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- F￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- G￨U￨NN￨O￨- t￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 7￨L￨CD￨NUMBER￨- DiscussionWe￨U￨NN￨O￨- have￨L￨VBP￨O￨- found￨L￨VBN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- containing￨L￨VBG￨O￨- h￨L￨NN￨O￨- by￨L￨IN￨O￨- showing￨L￨VBG￨O￨- an￨L￨DT￨O￨- easy￨L￨JJ￨O￨- technique￨L￨NN￨O￨- for￨L￨IN￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- adjustment￨L￨NN￨O￨- of￨L￨IN￨O￨- curves￨L￨NNS￨O￨- ensuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- convergence￨L￨NN￨O￨- of￨L￨IN￨O￨- solution￨L￨NN￨O￨- series￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- recommended￨L￨VBN￨O￨- by￨L￨IN￨O￨- Liao￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Schematic￨U￨JJ￨O￨- figure￨L￨NN￨O￨A of￨L￨IN￨O￨- EIAV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Parameter￨U￨NN￨O￨- meanings￨L￨NNS￨O￨- of￨L￨IN￨O￨- EIAV￨U￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- Parameters￨U￨NNS￨O￨- and￨L￨CC￨O￨- variables￨L￨NNS￨O￨- meaningDependent￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- E￨U￨NN￨O￨- susceptible￨L￨JJ￨O￨- F￨U￨NN￨O￨- infected￨L￨JJ￨O￨- G￨U￨NN￨O￨- VirusParameters￨U￨NNS￨O￨- and￨L￨CC￨O￨- constantsΛrecruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- β￨L￨VBP￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- μ￨L￨NN￨O￨- decay￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- a￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- production￨L￨NN￨O￨- ψ￨L￨NN￨O￨- clearance￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- α￨L￨NN￨O￨- virus￨L￨NN￨O￨- cleared￨L￨VBN￨O￨- by￨L￨IN￨O￨- neutralizing￨L￨VBG￨O￨- antibodies￨L￨NNS￨O￨- ω￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ρ￨L￨VBP￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- cell￨L￨NN￨O￨- killing￨L￨NN￨O￨- by￨L￨IN￨O￨- CTLS￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- Mathematical￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- EIAV￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- 4.1￨L￨CD￨NUMBER￨- Boundedness￨U￨NN￨O￨- and￨L￨CC￨O￨- positivity￨L￨NN￨O￨- Theorem￨U￨NNP￨O￨- 4.1￨L￨CD￨NUMBER￨- Let￨U￨VB￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- –￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- residual￨L￨JJ￨O￨A functions￨L￨NNS￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 24￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 25￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 26￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Following￨U￨VBG￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- square￨L￨JJ￨O￨- residual￨L￨JJ￨O￨- error￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- sixth-order￨L￨NN￨O￨- approximation￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 28￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 29￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- h￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- h￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- h￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- Mul￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- E￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- F￨U￨NN￨O￨- h￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- G￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- minimal￨L￨JJ￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- .￨L￨.￨O￨- +Tipsri￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Chinviriyasit￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- bifurcating￨L￨VBG￨O￨- periodic￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- and￨L￨CC￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence.In￨L￨NN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- net￨L￨JJ￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- acquired￨L￨VBN￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- encounters￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- noted￨L￨VBN￨O￨- that￨L￨IN￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- monitors￨L￨VBZ￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- variables￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- nonnegative.The￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- GreaterThan￨U￨NNP￨O￨- Equality￨U￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- theta￨L￨IN￨O￨A phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- theta￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Banach￨U￨NNP￨O￨- space￨L￨NN￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- mapping￨L￨VBG￨O￨- the￨L￨DT￨O￨- interval￨L￨NN￨O￨- into￨L￨IN￨O￨- It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- fundamental￨L￨JJ￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- functional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- that￨L￨WDT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- solution￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- satisfying￨L￨VBG￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2016a￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- derive￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- error￨L￨NN￨O￨- bounds￨L￨NNS￨O￨A by￨L￨IN￨O￨- making￨L￨VBG￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- periodicity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨JJ￨O￨- value￨L￨NN￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- recourse￨L￨NN￨O￨- function￨L￨NN￨O￨- Q￨U￨NNP￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- convex￨L￨NN￨O￨- approximation￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Q￨U￨NNP￨O￨- hat￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- intuition￨L￨NN￨O￨- behind￨L￨IN￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- by￨L￨IN￨O￨- imposing￨L￨VBG￨O￨- restrictions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- higher-order￨L￨JJ￨O￨- derivatives￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- pdf￨L￨NN￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- exclude￨L￨VB￨O￨- the￨L￨DT￨O￨- piecewise￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- pdf￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- have￨L￨VBP￨O￨- jump￨L￨NN￨O￨- discontinuities.To￨L￨NN￨O￨- obtain￨L￨VB￨O￨- these￨L￨DT￨O￨- error￨L￨NN￨O￨- bounds￨L￨VBZ￨O￨A we￨L￨PRP￨O￨- improve￨L￨VB￨O￨- the￨L￨DT￨O￨- existing￨L￨VBG￨O￨- bounds￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- expectation￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- by￨L￨IN￨O￨- Romeijnders￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +van￨L￨NN￨PERSON￨- der￨L￨FW￨PERSON￨- Vlerk￨U￨FW￨PERSON￨- passed￨L￨VBN￨O￨- away￨L￨RB￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- writing￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .1￨L￨CD￨NUMBER￨- IntroductionConsider￨U￨NNP￨O￨- the￨L￨DT￨O￨- two-stage￨L￨JJ￨O￨- recourse￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- random￨L￨JJ￨O￨- right-hand￨L￨JJ￨O￨- side￨L￨NN￨O￨- eta￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- recourse￨L￨NN￨O￨- function￨L￨NN￨O￨- Q￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- tender￨L￨NN￨O￨- variables￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- z￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- R￨U￨NNP￨O￨- mathbb￨L￨NN￨O￨A m￨L￨NN￨O￨- as￨L￨IN￨O￨- Q￨U￨NNP￨O￨- z￨L￨SYM￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- function￨L￨NN￨O￨- v￨L￨LS￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- Mul￨U￨NN￨O￨- s￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- R￨U￨NNP￨O￨- mathbb￨L￨NN￨O￨- m￨L￨NN￨O￨- as￨L￨IN￨O￨- v￨L￨LS￨O￨- s￨L￨PRP￨O￨- This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- describes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- two-stage￨L￨JJ￨O￨- decision￨L￨NN￨O￨- problem￨L￨NN￨O￨- under￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- bounds￨L￨VBZ￨O￨A on￨L￨IN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨JJ￨O￨- -1￨L￨CD￨NUMBER￨- Q￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Vert￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- hat￨L￨NN￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- deriving￨L￨VBG￨O￨- total￨L￨JJ￨O￨- variation￨L￨NN￨O￨- bounds￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- expectation￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- Math￨U￨NNP￨O￨- Program￨U￨NNP￨O￨- 157:3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 46￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2016b￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- them￨L￨PRP￨O￨- to￨L￨TO￨O￨- derive￨L￨VB￨O￨- error￨L￨NN￨O￨- bounds￨L￨NNS￨O￨A for￨L￨IN￨O￨- convex￨L￨NN￨O￨- approximations￨L￨NNS￨O￨- of￨L￨IN￨O￨- simple￨L￨JJ￨O￨- integer￨L￨NN￨O￨- recourse￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +AMR￨U￨NNP￨ORGANIZATION￨- determinants￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- to￨L￨TO￨O￨- survive￨L￨VB￨O￨A in￨L￨IN￨O￨- environments￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- sludge￨L￨NN￨O￨- and￨L￨CC￨O￨- wastewater￨L￨NN￨O￨- treatment￨L￨NN￨O￨- systems￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- thus￨L￨RB￨O￨- allowing￨L￨VBG￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- and￨L￨CC￨O￨- accelerating￨L￨VBG￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- AMR.Mathematical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- important￨L￨JJ￨O￨- decision￨L￨NN￨O￨- support￨L￨NN￨O￨- tools￨L￨NNS￨O￨- in￨L￨IN￨O￨- medicine￨L￨NN￨O￨- and￨L￨CC￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- published￨L￨VBD￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- on￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨A models￨L￨NNS￨O￨A on￨L￨IN￨O￨- AMR￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- concluded￨L￨VBD￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- was￨L￨VBD￨O￨- still￨L￨RB￨O￨- a￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- major￨L￨JJ￨O￨- improvements￨L￨NNS￨O￨- of￨L￨IN￨O￨- AMR￨U￨NNP￨ORGANIZATION￨- models￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- regarding￨L￨VBG￨O￨- implementing￨L￨VBG￨O￨- important￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- including￨L￨VBG￨O￨- resistance￨L￨NN￨O￨- mechanisms￨L￨NNS￨O￨- and￨L￨CC￨O￨- inter-species￨L￨NNS￨O￨- cooperation￨L￨NN￨O￨- .￨L￨.￨O￨- +Objective￨U￨NN￨O￨- The￨U￨DT￨O￨- objective￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- systematic￨L￨JJ￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- published￨L￨VBN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- AMR￨U￨NNP￨ORGANIZATION￨- development￨L￨NN￨O￨A and￨L￨CC￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- a￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- antimicrobial￨L￨JJ￨O￨- resistance￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- restricts￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- useful￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨A models￨L￨NNS￨O￨A .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- Many￨U￨JJ￨O￨- mathematical￨L￨JJ￨O￨A models￨L￨NNS￨O￨A of￨L￨IN￨O￨- AMR￨U￨NNP￨ORGANIZATION￨- development￨L￨NN￨O￨- and￨L￨CC￨O￨- spread￨L￨VBN￨O￨- exist￨L￨VBP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- quarantine￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- alpha￨L￨NN￨O￨- mu￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- alpha￨L￨NN￨O￨- mu￨L￨NN￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- sigma￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- sigma￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- quarantined￨L￨VBN￨O￨A individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Parameters￨U￨NNPS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- meanings￨L￨NNS￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ParameterDescription￨U￨NN￨O￨- A￨U￨NN￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- β￨L￨NN￨O￨- The￨U￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- μ￨L￨NN￨O￨- The￨U￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- populations￨L￨NNS￨O￨- c￨L￨NN￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- recovers￨L￨VBZ￨O￨- and￨L￨CC￨O￨- comes￨L￨VBZ￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- ε￨L￨NN￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- some￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- people￨L￨NNS￨O￨- become￨L￨VBP￨O￨- infective￨L￨JJ￨O￨- α￨L￨NN￨O￨- The￨U￨DT￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- quarantined￨L￨VBN￨O￨A population￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- sigma￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- quarantined￨L￨VBN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- population￨L￨NN￨O￨- sigma￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- quarantined￨L￨VBN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- population￨L￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- population￨L￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- quarantined￨L￨VBN￨O￨- populationWith￨L￨NN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- they￨L￨PRP￨O￨- NumericCitation￨U￨NN￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- also￨L￨RB￨O￨- estimated￨L￨VBD￨O￨- the￨L￨DT￨O￨- domain￨L￨NN￨O￨- of￨L￨IN￨O￨- attraction￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +After￨U￨IN￨O￨- that￨L￨DT￨O￨- ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- Hopf￨U￨NN￨PERSON￨- bifurcation￨L￨NN￨O￨A are￨L￨VBP￨O￨- derived￨L￨VBN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- stated￨L￨VBN￨O￨A in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- evolve￨L￨VBP￨O￨- by￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- there￨L￨EX￨O￨- appear￨L￨VBP￨O￨- some￨L￨DT￨O￨- symptoms￨L￨NNS￨O￨- needing￨L￨VBG￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- namely￨L￨RB￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- demonstrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- dwSSA￨L￨NN￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- systems￨L￨NNS￨O￨- —￨L￨:￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infectious￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBD￨O￨- –￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- yeast￨L￨NN￨O￨- polarization￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- —￨L￨:￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- its￨L￨PRP$￨O￨- computational￨L￨JJ￨O￨- efficiency￨L￨NN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- dwSSA.KeywordsStochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- Rare￨U￨JJ￨O￨- event￨L￨NN￨O￨A probability￨L￨NN￨O￨- estimation￨L￨NN￨O￨- SSA￨U￨NNP￨ORGANIZATION￨- dwSSA￨L￨NNP￨O￨- Gillespie￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨- Importance￨U￨NN￨O￨- sampling￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionWhen￨U￨NNP￨PERSON￨- Gillespie￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- 1976￨L￨CD￨DATE￨- ,￨L￨,￨O￨- 1977￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- introduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SSA￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- its￨L￨PRP$￨O￨- use￨L￨NN￨O￨- was￨L￨VBD￨O￨- deemed￨L￨VBN￨O￨- purely￨L￨RB￨O￨- academic￨L￨JJ￨O￨- as￨L￨IN￨O￨- computers￨L￨NNS￨O￨- were￨L￨VBD￨O￨- not￨L￨RB￨O￨- powerful￨L￨JJ￨O￨- enough￨L￨JJ￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- SSA￨U￨NNP￨ORGANIZATION￨- simulations￨L￨NNS￨O￨- except￨L￨IN￨O￨- for￨L￨IN￨O￨- toy￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +in￨L￨IN￨O￨- J￨U￨NNP￨O￨- Chem￨U￨NNP￨MISC￨- Phys￨U￨NNP￨MISC￨- 134:044110￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2011￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- called￨L￨VBN￨O￨- dwSSA￨L￨NNP￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- significantly￨L￨RB￨O￨- improves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- convergence￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- rare￨L￨JJ￨O￨A event￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- conventional￨L￨JJ￨O￨- multilevel￨L￨JJ￨O￨- cross-entropy￨L￨JJ￨O￨- method￨L￨NN￨O￨- in￨L￨IN￨O￨- dwSSA￨L￨NN￨O￨- is￨L￨VBZ￨O￨- either￨L￨CC￨O￨- unable￨L￨JJ￨O￨- to￨L￨TO￨O￨- converge￨L￨VB￨O￨- or￨L￨CC￨O￨- converges￨L￨VBZ￨O￨- very￨L￨RB￨O￨- slowly￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- dwSSA￨L￨NN￨O￨- +￨L￨CC￨O￨- +￨L￨CC￨O￨- that￨L￨WDT￨O￨- contains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- and￨L￨CC￨O￨- improved￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- computing￨L￨VBG￨O￨- optimal￨L￨JJ￨O￨- importance￨L￨NN￨O￨- sampling￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unable￨L￨JJ￨O￨- to￨L￨TO￨O￨- reach￨L￨VB￨O￨- the￨L￨DT￨O￨- rare￨L￨JJ￨O￨A event￨L￨NN￨O￨- with￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- speed￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- wSSA￨L￨NN￨O￨- bias￨L￨NN￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- IS￨U￨VBZ￨O￨- parameters￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- recorded￨L￨VBN￨O￨- at￨L￨IN￨O￨- each￨L￨DT￨O￨- reaction￨L￨NN￨O￨- selection￨L￨NN￨O￨- step￨L￨NN￨O￨- and￨L￨CC￨O￨- used￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- end￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- an￨L￨DT￨O￨- unbiased￨L￨JJ￨O￨- estimate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rare￨L￨JJ￨O￨A event￨L￨NN￨O￨- probability￨L￨NN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- we￨L￨PRP￨O￨- apply￨L￨VBP￨O￨- transmission￨L￨NN￨O￨- centrality￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- weak￨L￨JJ￨O￨- ties￨L￨NNS￨O￨- in￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- large￨L￨JJ￨O￨- empirical￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- metric￨L￨JJ￨O￨- outperforms￨L￨VBZ￨O￨- other￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- links￨L￨NNS￨O￨- that￨L￨WDT￨O￨- drive￨L￨VBP￨O￨- spreading￨L￨VBG￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network.KeywordsSocial￨L￨JJ￨O￨- networksLink￨L￨NN￨O￨- centrality￨L￨NN￨O￨- measuresDiffusion￨L￨NN￨O￨- processesWeak￨L￨NN￨O￨- tie￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionThe￨U￨NNP￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- commonly￨L￨RB￨O￨- measured￨L￨VBN￨O￨- through￨L￨IN￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨O￨- Access￨U￨NN￨O￨- Link￨U￨NN￨O￨- transmission￨L￨NN￨O￨- centrality￨L￨NN￨O￨A in￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networksQian￨L￨NN￨O￨- Zhang1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Márton￨U￨NNP￨O￨- Karsai1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Alessandro￨U￨NNP￨PERSON￨- Vespignani1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:33￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractUnderstanding￨U￨VBG￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmitting￨L￨VBG￨O￨- information￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- ways￨L￨NNS￨O￨- to￨L￨TO￨O￨- hinder￨L￨VB￨O￨- or￨L￨CC￨O￨- postpone￨L￨VB￨O￨- ongoing￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- contrary￨L￨NN￨O￨- ,￨L￨,￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- global￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- betweenness￨L￨NN￨O￨- and￨L￨CC￨O￨- closeness￨L￨NN￨O￨- centrality￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Katz￨U￨NNP￨PERSON￨- centrality￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- k-shell￨L￨JJ￨O￨- index￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- subgraph￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- induced￨L￨VBD￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- may￨L￨MD￨O￨- better￨L￨RB￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- or￨L￨CC￨O￨- link￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- measure￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- centrality￨L￨NN￨O￨A ,￨L￨,￨O￨- that￨L￨WDT￨O￨- captures￨L￨VBZ￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- by￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- whom￨L￨WP￨O￨- they￨L￨PRP￨O￨- transfer￨L￨VBP￨O￨- information￨L￨NN￨O￨- during￨L￨IN￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- measures￨L￨NNS￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- provide￨L￨VB￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- links￨L￨NNS￨O￨A play￨L￨VBP￨O￨- global￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Basic￨U￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- hybrid￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- modelShujing￨L￨NN￨O￨- Gao1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yunbo￨U￨NNP￨O￨- Tu1￨U￨NN￨O￨- and￨L￨CC￨O￨- Jialin￨U￨NN￨PERSON￨- Wang1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2018:310￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- hybrid￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-periodic￨L￨JJ￨O￨- pulses￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- environmental￨L￨JJ￨O￨- period￨L￨NN￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +52:224￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 234￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- established￨L￨JJ￨O￨- model.KeywordsHybrid￨L￨NN￨O￨- systemBasic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- numberNext￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- operator￨L￨NN￨TITLE￨A 1￨L￨CD￨NUMBER￨- IntroductionThe￨U￨NNP￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- measure￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- many￨L￨JJ￨O￨- secondary￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- will￨L￨MD￨O￨- become￨L￨VB￨O￨- infected￨L￨JJ￨O￨- if￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- initial￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- infected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- naïve￨L￨JJ￨O￨- population￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spectral￨L￨JJ￨O￨- radius￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- operator￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Xiao￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- gave￨L￨VBD￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- impulsive￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- pulses￨L￨NNS￨O￨- on￨L￨IN￨O￨- both￨L￨DT￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- uninfected￨L￨JJ￨O￨- compartments￨L￨NNS￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- List￨U￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- functions￨L￨NNS￨O￨- Parameters￨U￨NNS￨O￨- and￨L￨CC￨O￨- functions￨L￨NNS￨O￨- Meaning￨U￨VBG￨O￨- Values￨U￨NNS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Susceptible￨U￨JJ￨O￨- computers￨L￨NNS￨O￨A at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NN￨O￨- S￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- 20￨L￨CD￨NUMBER￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Infected￨U￨JJ￨O￨- computers￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 15￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Recovered￨U￨VBN￨O￨- computers￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- 10￨L￨CD￨NUMBER￨- f￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Rate￨U￨NNP￨O￨- of￨L￨IN￨O￨- external￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- false￨L￨JJ￨O￨- lambda￨L￨NN￨O￨- Rate￨U￨NN￨O￨- of￨L￨IN￨O￨- infecting￨L￨VBG￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- computer￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 0.001￨L￨CD￨NUMBER￨- varepsilon￨L￨NN￨O￨- Rate￨U￨NN￨O￨- of￨L￨IN￨O￨- recovery￨L￨NN￨O￨- for￨L￨IN￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- varepsilon￨L￨NN￨O￨- 0.10000000000000001￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- Rate￨U￨NN￨O￨- of￨L￨IN￨O￨- removing￨L￨VBG￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- Equality￨U￨NN￨O￨- d￨L￨NN￨O￨- 0.10000000000000001￨L￨CD￨NUMBER￨- Main￨U￨NNP￨O￨- ideaLet￨L￨NNP￨O￨- L￨U￨NNP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- operators￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨ORGANIZATION￨- g￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨O￨- text￨L￨NN￨O￨- Pow￨U￨NN￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- text￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- constant￨L￨JJ￨O￨- values￨L￨NNS￨O￨- c￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- c￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VB￨O￨- Equality￨U￨NN￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- c￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Now￨U￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- homotopy￨L￨JJ￨O￨- maps￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- q￨L￨NN￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- u￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- m￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- i￨L￨FW￨ORGANIZATION￨- Mul￨U￨FW￨ORGANIZATION￨- c￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- C￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- n￨L￨NN￨O￨- o￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- embedding￨L￨NN￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- hbar￨L￨NN￨O￨- Mul￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ne￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- convergence￨L￨NN￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- auxiliary￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- ,￨L￨,￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- linear￨L￨JJ￨O￨- operators￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- finally￨L￨RB￨O￨- N￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- operators￨L￨NNS￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- According￨U￨VBG￨O￨- to￨L￨TO￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- zero-order￨L￨NN￨O￨- deformation￨L￨NN￨O￨- ,￨L￨,￨O￨- equations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Now￨U￨RB￨DATE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- write￨L￨VB￨O￨- the￨L￨DT￨O￨- Taylor￨U￨NNP￨PERSON￨- series￨L￨NN￨O￨- for￨L￨IN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- q￨L￨VB￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- For￨U￨IN￨O￨- more￨L￨JJR￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- vectors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- Mul￨U￨NN￨O￨- displaystyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- Mul￨U￨NN￨O￨- displaystyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- tilde￨L￨VBP￨O￨- Mul￨U￨NN￨O￨- displaystyle￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- tilde￨L￨NN￨O￨- Differentiating￨U￨VBG￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +and￨L￨CC￨O￨- putting￨L￨VBG￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- q￨L￨VBD￨O￨- 0￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- mth-order￨L￨NN￨O￨- deformation￨L￨NN￨O￨- equations￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- L￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨PERSON￨- left￨L￨VBD￨O￨- Mul￨U￨NNP￨PERSON￨- right￨L￨RB￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- chi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- -￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- g￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- hbar￨L￨NN￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NNP￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Mul￨U￨NN￨PERSON￨- begin￨L￨VBP￨O￨- Mul￨U￨NN￨ORGANIZATION￨- g￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨O￨- e￨L￨SYM￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- By￨U￨IN￨O￨- putting￨L￨VBG￨O￨- false￨L￨JJ￨O￨- and￨L￨CC￨O￨- applying￨L￨VBG￨O￨- the￨L￨DT￨O￨- inverse￨L￨JJ￨O￨- operators￨L￨NNS￨O￨A Pow￨U￨VBP￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- -1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Pow￨U￨NN￨O￨- L￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- R￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- g￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨O￨- e￨L￨SYM￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- chi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- -￨L￨:￨O￨- 1￨L￨CD￨DATE￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- hbar￨L￨NN￨O￨- Integral￨U￨JJ￨O￨- Pow￨U￨NN￨O￨- limits￨L￨NNS￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mth-order￨L￨NN￨O￨- approximate￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- as￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- displaystyle￨L￨NN￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Sum￨U￨NN￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- j￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Numerical￨U￨JJ￨O￨- illustrationIn￨L￨NN￨O￨- this￨L￨DT￨O￨- section￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- HAM￨U￨NN￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- .￨L￨.￨O￨- +Several￨U￨JJ￨O￨- hbar￨L￨SYM￨O￨- -￨L￨:￨O￨- curves￨L￨NNS￨O￨- are￨L￨VBP￨O￨- plotted￨L￨VBN￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- convergence￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- residual￨L￨JJ￨O￨- errors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- theses￨L￨DT￨O￨- regions.KeywordsSusceptible￨L￨NN￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBD￨O￨- model￨L￨NN￨TITLE￨- Modified￨U￨VBN￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- Computer￨U￨NN￨O￨- virus￨L￨NN￨O￨- Homotopy￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- method￨L￨NN￨O￨- hbar￨L￨SYM￨O￨- -￨L￨:￨O￨- Curve￨U￨NN￨O￨- IntroductionIn￨U￨NN￨O￨- recent￨L￨JJ￨DURATION￨- decades￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- computer￨L￨NN￨O￨- systems￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- great￨L￨JJ￨O￨- changes￨L￨NNS￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- of￨L￨IN￨O￨- life￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 211￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 222￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asSolving￨L￨VBG￨O￨- a￨L￨DT￨O￨- modified￨L￨VBN￨O￨- nonlinear￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨A viruses￨L￨NNS￨O￨- by￨L￨IN￨O￨- homotopy￨L￨NN￨O￨- analysis￨L￨NN￨O￨- methodAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsSamad￨L￨NNP￨O￨- NoeiaghdamMuhammad￨U￨NNP￨MISC￨- SulemanHüseyin￨U￨NNP￨MISC￨- BudakOpen￨U￨NNP￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- PaperFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 215￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨MISC￨- AbstractThe￨U￨NNP￨MISC￨- susceptible￨L￨JJ￨O￨- –￨L￨:￨O￨- infected￨L￨JJ￨O￨- –￨L￨:￨O￨- recovered￨L￨VBD￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- homotopy￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HAM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- numerical￨L￨JJ￨O￨- example￨L￨NN￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- illustrate￨L￨VB￨O￨- the￨L￨DT￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨A process￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- improvements￨L￨NNS￨O￨- after￨L￨IN￨O￨- taking￨L￨VBG￨O￨- corresponding￨L￨JJ￨O￨- measures.KeywordsSIR￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- Oversaturated￨U￨JJ￨O￨- conditions￨L￨NNS￨O￨- Congestion￨U￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- Congestion￨U￨NN￨O￨- propagation￨L￨NN￨O￨- rate￨L￨NN￨O￨- Gray￨U￨NNP￨O￨- system￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- Communicated￨U￨VBN￨O￨- by￨L￨IN￨O￨- Xuesong￨U￨NNP￨PERSON￨- Zhou￨U￨NNP￨PERSON￨- .1￨L￨CD￨NUMBER￨- IntroductionCongestion￨U￨NNP￨O￨- ,￨L￨,￨O￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- urban￨L￨JJ￨O￨- transit￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- becoming￨L￨VBG￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- concerns￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transportation￨L￨NN￨O￨- system￨L￨NN￨O￨- agencies￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- oversaturated￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- gray￨L￨JJ￨O￨- system￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- introduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨A rate￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- joint￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- six￨L￨CD￨NUMBER￨- influential￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- passenger￨L￨NN￨O￨- flow￨L￨NN￨O￨- ,￨L￨,￨O￨- train￨L￨NN￨CRIMINAL_CHARGE￨- headway￨L￨NN￨O￨- ,￨L￨,￨O￨- passenger￨L￨NN￨O￨- transfer￨L￨NN￨O￨- convenience￨L￨NN￨O￨- ,￨L￨,￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- congestion￨L￨NN￨O￨- occurring￨L￨VBG￨O￨- ,￨L￨,￨O￨- initial￨L￨JJ￨O￨- congested￨L￨JJ￨O￨- station￨L￨NN￨O￨- and￨L￨CC￨O￨- station￨L￨NN￨O￨- capacity￨L￨NN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- research￨L￨NN￨O￨- ,￨L￨,￨O￨- Zang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- calculate￨L￨VB￨O￨- the￨L￨DT￨O￨- boundary￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- congestion￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- traffic￨L￨NN￨O￨- flow￨L￨NN￨O￨A theory￨L￨NN￨O￨- .￨L￨.￨O￨- +Stephen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- described￨L￨VBD￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- oversaturated￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- in￨L￨IN￨O￨- rail￨L￨NN￨O￨- transit￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- combustion￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- he￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨A is￨L￨VBZ￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- ripple￨L￨NN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨A is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- calculating￨L￨VBG￨O￨- congestion￨L￨NN￨O￨- propagation￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- constructed￨L￨VBN￨O￨- .￨L￨.￨O￨- +And￨U￨CC￨O￨- references￨L￨NNS￨O￨A [￨L￨-LRB-￨O￨- 56￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 58￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- thought￨L￨VBD￨O￨- the￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- transformation.In￨L￨NN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- stochastic￨L￨JJ￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- disturbance￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- build￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Brownian￨U￨JJ￨MISC￨- motion￨L￨NN￨O￨- with￨L￨IN￨O￨- intensity￨L￨NN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- sigma￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Figure￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- process￨L￨NN￨O￨- diagram￨L￨NN￨O￨- for￨L￨IN￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- By￨U￨IN￨O￨- using￨L￨VBG￨O￨- LaSalle￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- invariance￨L￨NN￨O￨- principle￨L￨NN￨O￨- and￨L￨CC￨O￨- Lyapunov￨U￨NNP￨PERSON￨- direct￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Equality￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- Lambda￨U￨NNP￨ORGANIZATION￨- beta￨L￨NN￨O￨- Pow￨U￨NN￨O￨- mu￨L￨NN￨O￨A Add￨U￨VB￨O￨- alpha￨L￨NN￨O￨- Add￨U￨VB￨O￨- r￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- r￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- -1￨L￨CD￨NUMBER￨- was￨L￨VBD￨O￨- established￨L￨VBN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable.As￨L￨NNPS￨O￨- we￨L￨PRP￨O￨- all￨L￨DT￨O￨- know￨L￨VBP￨O￨- ,￨L￨,￨O￨- real￨L￨JJ￨O￨- life￨L￨NN￨O￨- is￨L￨VBZ￨O￨- filled￨L￨VBN￨O￨- with￨L￨IN￨O￨- randomness￨L￨NN￨O￨- and￨L￨CC￨O￨- unpredictability￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- both￨L￨DT￨O￨- transfer￨L￨NN￨O￨A from￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- transfer￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- proposed￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Λ￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transfer￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mortality￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- loss￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- return￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Extinction￨U￨NN￨MISC￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- transfer￨L￨NN￨O￨A from￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- to￨L￨TO￨O￨- susceptibleYi￨L￨NN￨O￨- Song1￨U￨NN￨O￨- ,￨L￨,￨O￨- Anqi￨U￨JJ￨O￨- Miao1￨U￨NN￨O￨- ,￨L￨,￨O￨- Tongqian￨U￨JJ￨O￨- Zhang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Xinzeng￨U￨NN￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Jianxin￨U￨NNP￨PERSON￨- Liu3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:293￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- stochastic￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- transfer￨L￨NN￨O￨- from￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- discussed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Stochastic￨U￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- better￨L￨RB￨O￨- conform￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- situation￨L￨NN￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- many￨L￨JJ￨O￨- scholars￨L￨NNS￨O￨- have￨L￨VBP￨O￨- done￨L￨VBN￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- randomness￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- references￨L￨NNS￨O￨A [￨L￨-LRB-￨O￨- 28￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 38￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- effect￨L￨NN￨O￨- in￨L￨IN￨O￨- population￨L￨NN￨O￨- dynamical￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- references￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 39￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 42￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- set￨L￨VBD￨O￨- up￨L￨RP￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- algorithms￨L￨NNS￨O￨- a￨L￨DT￨O￨- selection￨L￨NN￨O￨A threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- that￨L￨WDT￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- structural￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- graph￨L￨NN￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- improves￨L￨VBZ￨O￨- significantly￨L￨RB￨O￨- the￨L￨DT￨O￨- selection￨L￨NN￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- seed￨L￨NN￨O￨- set￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- multi-hops￨L￨JJ￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- select￨L￨VB￨O￨- most￨L￨RBS￨O￨- influential￨L￨JJ￨O￨- users￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- distinct￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- measure￨L￨VBP￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- selected￨L￨VBN￨O￨- seed￨L￨NN￨O￨A set￨L￨NN￨O￨- performed￨L￨VBN￨O￨- by￨L￨IN￨O￨- our￨L￨PRP$￨O￨- algorithms￨L￨NNS￨O￨- and￨L￨CC￨O￨- existing￨L￨VBG￨O￨- approaches￨L￨NNS￨O￨- on￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- diffusion￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- screening￨L￨NN￨O￨- assay￨L￨NN￨O￨- for￨L￨IN￨O￨- Selective￨U￨JJ￨O￨- Dimerizing￨U￨VBG￨O￨- Glucocorticoid￨U￨NN￨O￨- Receptor￨U￨NN￨O￨- Agonists￨U￨NNS￨O￨- and￨L￨CC￨O￨- Modulators￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- SEDIGRAM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- effective￨L￨JJ￨O￨- against￨L￨IN￨O￨- acute￨L￨JJ￨O￨- inflammation￨L￨NN￨O￨- Jolien￨U￨NN￨O￨- Souffriau1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Melanie￨U￨NNP￨PERSON￨- Eggermont1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Sara￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Ryckeghem1￨U￨NN￨PERSON￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kelly￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Looveren1￨U￨NN￨PERSON￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Lise￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Wyngene1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Evelien￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Hamme3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marnik￨U￨NNP￨O￨- Vuylsteke4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Rudi￨U￨NNP￨PERSON￨- Beyaert￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Karolien￨U￨NNP￨O￨- De￨U￨NNP￨O￨- Bosscher5￨U￨NNP￨O￨- ,6￨L￨NNP￨O￨- &￨L￨CC￨O￨- Claude￨U￨NNP￨O￨- Libert1￨U￨NNP￨O￨- ,2￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 12894￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Acute￨U￨JJ￨O￨- inflammationSepsis￨L￨NN￨O￨- AbstractIt￨U￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- suggested￨L￨VBN￨O￨- that￨L￨IN￨O￨- glucocorticoid￨L￨NN￨O￨- receptor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- agonists￨L￨NNS￨O￨- that￨L￨WDT￨O￨- promote￨L￨VBP￨O￨- GR￨U￨NN￨O￨- homodimerization￨L￨NN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- standard￨L￨JJ￨O￨- glucocorticoids￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Dexamethasone￨U￨NN￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- effective￨L￨JJ￨O￨- anti-inflammatory￨L￨JJ￨O￨- molecules￨L￨NNS￨O￨- against￨L￨IN￨O￨- acute￨L￨JJ￨O￨- and￨L￨CC￨O￨- life-threatening￨L￨JJ￨O￨- inflammatory￨L￨JJ￨O￨A conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- principle￨L￨NN￨O￨- experiment￨L￨NN￨O￨A ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- seven￨L￨CD￨NUMBER￨- candidate￨L￨NN￨TITLE￨- compounds￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- identified￨L￨VBD￨O￨- two￨L￨CD￨NUMBER￨- potentially￨L￨RB￨O￨- interesting￨L￨JJ￨O￨- compounds￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Cortivazol￨U￨NN￨O￨- and￨L￨CC￨O￨- AZD2906￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- strong￨L￨JJ￨O￨- protection￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- mouse￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- aggressive￨L￨JJ￨O￨- TNF-induced￨U￨JJ￨O￨- lethal￨L￨JJ￨O￨- inflammation￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- screening￨L￨JJ￨O￨- pipeline￨L￨NN￨O￨- for￨L￨IN￨O￨- SEDIGRAM￨U￨NNP￨O￨- may￨L￨MD￨O￨- assist￨L￨VB￨O￨- the￨L￨DT￨O￨- search￨L￨NN￨O￨- for￨L￨IN￨O￨- compounds￨L￨NNS￨O￨- that￨L￨WDT￨O￨- promote￨L￨VBP￨O￨- GR￨U￨NN￨O￨- dimerization￨L￨NN￨O￨- and￨L￨CC￨O￨- limit￨L￨NN￨O￨- overwhelming￨L￨JJ￨O￨- acute￨L￨JJ￨O￨- inflammatory￨L￨JJ￨O￨A responses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Both￨U￨DT￨O￨- issues￨L￨NNS￨O￨- are￨L￨VBP￨O￨- being￨L￨VBG￨O￨- addressed￨L￨VBN￨O￨- by￨L￨IN￨O￨- searching￨L￨VBG￨O￨- for￨L￨IN￨O￨- new￨L￨JJ￨O￨- molecules￨L￨NNS￨O￨- with￨L￨IN￨O￨- enhanced￨L￨VBN￨O￨- GC￨U￨NN￨O￨- therapeutic￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- and￨L￨CC￨O￨- fewer￨L￨JJR￨O￨A or￨L￨CC￨O￨- less￨L￨RBR￨O￨- severe￨L￨JJ￨O￨- side￨L￨NN￨O￨- effects.GCs￨L￨NNS￨O￨- are￨L￨VBP￨O￨- lipophilic￨L￨JJ￨O￨- ,￨L￨,￨O￨- so￨L￨IN￨O￨- they￨L￨PRP￨O￨- penetrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- cell￨L￨NN￨O￨- membrane￨L￨NN￨O￨- and￨L￨CC￨O￨- bind￨L￨VBP￨O￨- the￨L￨DT￨O￨- GC￨U￨NN￨O￨- receptor￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- analysis￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- universal￨L￨JJ￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- TL￨U￨NN￨O￨- and￨L￨CC￨O￨- δ15N￨L￨NN￨O￨- that￨L￨WDT￨O￨- permits￨L￨VBZ￨O￨- a￨L￨DT￨O￨- robust￨L￨JJ￨O￨- prognostic￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- configuration￨L￨NN￨O￨- of￨L￨IN￨O￨- food￨L￨NN￨O￨A webs￨L￨NNS￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- all￨L￨DT￨O￨- system￨L￨NN￨O￨- components￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reliably￨L￨RB￨O￨- analysed￨L￨VBN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- saturated￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- rate￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨JJ￨O￨- eta￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨NNP￨ORGANIZATION￨- V￨U￨NNP￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- eta￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- lose￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- join￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- become￨L￨VBP￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- crashing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- half￨L￨NN￨O￨- saturation￨L￨NN￨O￨- constant￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- saturation￨L￨NN￨O￨- constant￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Having￨U￨VBG￨O￨- this￨L￨DT￨O￨- idea￨L￨NN￨O￨- in￨L￨IN￨O￨- mind￨L￨NN￨O￨- and￨L￨CC￨O￨- considering￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- may￨L￨MD￨O￨- use￨L￨VB￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- worth￨L￨JJ￨O￨- investigating￨L￨VBG￨O￨- the￨L￨DT￨O￨- Hopf￨U￨NNP￨O￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨JJ￨O￨- eta￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- V￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- eta￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- computers.The￨L￨NN￨O￨- organization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Stability￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcationBy￨L￨NNP￨O￨- direct￨L￨JJ￨O￨- computation￨L￨NN￨O￨- we￨L￨PRP￨O￨- get￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨A delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- viral￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equation￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- 3￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- with￨L￨IN￨O￨- For￨U￨IN￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +Combining￨U￨VBG￨O￨- the￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- predation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- eco-epidemiological￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- prey￨L￨NN￨O￨- refuge￨L￨NN￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- prey￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- change￨L￨NN￨O￨- of￨L￨IN￨O￨- variables￨L￨NNS￨O￨- Mul￨U￨NNP￨O￨- Phi￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- bigl￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- rewriting￨L￨VBG￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 3￨L￨CD￨NUMBER￨- EquilibriaAll￨U￨NN￨ORGANIZATION￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Y￨U￨NN￨O￨- c￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- alpha￨L￨NN￨O￨A Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 3.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- trivial￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Theorem￨U￨NNP￨O￨- 4.1￨L￨CD￨NUMBER￨- Supposing￨U￨VBG￨O￨- that￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- B￨U￨NN￨O￨- underline￨L￨VBP￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- B￨U￨NN￨O￨- overline￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictLessThan￨U￨NN￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- underline￨L￨VBP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- gamma￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- dfrac￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- K￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨PERSON￨- K￨U￨NN￨PERSON￨- Pow￨U￨NN￨PERSON￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- K￨U￨NNP￨O￨- K￨U￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- dfrac￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- K￨U￨NNP￨O￨- alpha￨L￨NN￨O￨A -1￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- K￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨PERSON￨- StrictLessThan￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- K￨U￨NNP￨PERSON￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- K￨U￨NNP￨O￨- alpha￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- c￨L￨NN￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- e￨L￨SYM￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- alpha￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- .￨L￨.￨O￨- +Theorem￨U￨NNP￨O￨- 4.2￨L￨CD￨NUMBER￨- Assuming￨U￨VBG￨O￨- that￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- B￨U￨NN￨O￨- underline￨L￨VBP￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- B￨U￨NN￨O￨- overline￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NN￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- overline￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- K￨U￨NNP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨A -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- K￨U￨NNP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- alpha￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- alpha￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 4.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- negative￨L￨JJ￨O￨- real￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- A￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- iff￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 4.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Inequality￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 4.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- term￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 4.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- inequality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- equivalent￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- cases￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- inequality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- always￨L￨RB￨O￨- holds￨L￨VBZ￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- biggl￨L￨NN￨O￨- Mul￨U￨NN￨O￨- biggr￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- c￨L￨NN￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- e￨L￨SYM￨O￨- -1￨L￨CD￨NUMBER￨- If￨U￨IN￨O￨- StrictLessThan￨U￨JJ￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- varphi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- tilde￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Y￨U￨NN￨O￨- tilde￨L￨NN￨O￨- has￨L￨VBZ￨O￨- its￨L￨PRP$￨O￨- ecological￨L￨JJ￨O￨- meanings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Additionally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- spatio-temporal￨L￨JJ￨O￨- realizations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- process￨L￨NN￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- instructive￨L￨JJ￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- its￨L￨PRP$￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- and￨L￨CC￨O￨- exploring￨L￨VBG￨O￨- how￨L￨WRB￨O￨- different￨L￨JJ￨O￨- influences￨L￨NNS￨O￨- affect￨L￨VBP￨O￨- its￨L￨PRP$￨O￨- speed￨L￨NN￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- evolution.KeywordsAgent-based￨L￨JJ￨O￨- modelDiffusion￨L￨NN￨O￨- processSpreading￨L￨NN￨O￨- processStochastic￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- algorithmHuman￨L￨NN￨O￨- mobility￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionModeling￨U￨NN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- behavior￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- topic￨L￨NN￨O￨- of￨L￨IN￨O￨- great￨L￨JJ￨O￨- relevance￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- and￨L￨CC￨O￨- understanding￨L￨VBG￨O￨- many￨L￨JJ￨O￨- real-world￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- migration￨L￨NN￨O￨- and￨L￨CC￨O￨- traffic￨L￨NN￨O￨- flows￨L￨VBZ￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- processes￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- and￨L￨CC￨O￨- interaction￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- innovations￨L￨NNS￨O￨A [￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Human￨U￨JJ￨MISC￨- mobility￨L￨NN￨O￨A and￨L￨CC￨O￨- innovation￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- ancient￨L￨JJ￨O￨- times￨L￨NNS￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- approachNataša￨L￨NN￨O￨- Djurdjevac￨U￨NN￨O￨- Conrad1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Luzie￨U￨NN￨O￨- Helfmann1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Johannes￨U￨NNP￨PERSON￨- Zonker1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Stefanie￨U￨NNP￨PERSON￨- Winkelmann1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Christof￨U￨NNP￨PERSON￨- Schütte1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 7:24￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractHuman￨U￨NNP￨O￨- mobility￨L￨NN￨O￨- always￨L￨RB￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- great￨L￨JJ￨O￨- influence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- cultural￨L￨JJ￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- technological￨L￨JJ￨O￨- ideas￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- innovations￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- ancient￨L￨JJ￨O￨- world￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- human￨L￨JJ￨O￨- movements￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- model￨L￨NN￨TITLE￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- of￨L￨IN￨O￨- innovations￨L￨NNS￨O￨A on￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- network￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- changing￨L￨VBG￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- agents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- changing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- positions￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- spreading￨L￨VBG￨O￨A processes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- happened￨L￨VBD￨O￨- in￨L￨IN￨O￨- ancient￨L￨JJ￨O￨- times￨L￨NNS￨O￨- faces￨L￨VBZ￨O￨- the￨L￨DT￨O￨- additional￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- that￨L￨WDT￨O￨- available￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- limited￨L￨JJ￨O￨- and￨L￨CC￨O￨- sparse￨L￨JJ￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- structuring￨L￨VBG￨O￨- information￨L￨NN￨O￨- overload￨L￨NN￨O￨- issues￨L￨NNS￨O￨- which￨L￨WDT￨O￨- extends￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨- factors￨L￨NNS￨O￨- and￨L￨CC￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- overload￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- decision-making￨L￨JJ￨O￨- process.KeywordsInformation￨L￨NN￨O￨- processing￨L￨NN￨O￨- Information￨U￨NN￨O￨- management￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- Information￨U￨NN￨O￨- overload￨L￨NN￨O￨- Literature￨U￨NN￨O￨- review￨L￨NN￨O￨- Bibliometric￨U￨JJ￨MISC￨- literature￨L￨NN￨O￨A analysis￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionInformation￨U￨NN￨O￨- overload￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- decisive￨L￨JJ￨O￨- factor￨L￨NN￨O￨- driving￨L￨VBG￨O￨- negative￨L￨JJ￨O￨- “￨L￨``￨O￨- work￨L￨NN￨O￨- environments￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- that￨L￨IN￨O￨- ]￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- killing￨L￨VBG￨O￨- productivity￨L￨NN￨O￨- ,￨L￨,￨O￨- dampening￨L￨VBG￨O￨- creativity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- making￨L￨VBG￨O￨- us￨L￨PRP￨O￨- unhappy￨L￨JJ￨O￨- ”￨L￨''￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Business￨U￨NNP￨ORGANIZATION￨- Research￨U￨NNP￨ORGANIZATION￨- pp￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 44￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asInformation￨L￨NN￨O￨- overload￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- age￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- from￨L￨IN￨O￨- business￨L￨NN￨O￨- administration￨L￨NN￨O￨A ,￨L￨,￨O￨- business￨L￨NN￨O￨- psychology￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- related￨L￨JJ￨O￨- disciplines￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- bibliometric￨L￨JJ￨O￨- approach￨L￨NN￨O￨- and￨L￨CC￨O￨- framework￨L￨NN￨O￨- developmentAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsPeter￨L￨NNP￨O￨- Gordon￨U￨NNP￨O￨- RoetzelOpen￨U￨NNP￨O￨- AccessOriginal￨U￨NNP￨O￨- ResearchFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1.8￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- AbstractIn￨U￨VBP￨O￨- the￨L￨DT￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- age￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- overload￨L￨NN￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- media￨L￨NNS￨O￨- ,￨L￨,￨O￨- virtual￨L￨JJ￨O￨- collaboration￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rises￨L￨VBZ￨O￨- rapidly￨L￨RB￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- of￨L￨IN￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- business￨L￨NN￨O￨- administration￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- subjects￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨DATE￨- last￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- reveals￨L￨VBZ￨O￨- research￨L￨NN￨O￨- directions￨L￨NNS￨O￨- and￨L￨CC￨O￨- bridges￨L￨NNS￨O￨- of￨L￨IN￨O￨- literature￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wide￨L￨JJ￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- fields￨L￨NNS￨O￨- of￨L￨IN￨O￨- business￨L￨NN￨O￨- administration￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- accounting￨L￨NN￨O￨- ,￨L￨,￨O￨- finance￨L￨NN￨O￨- ,￨L￨,￨O￨- health￨L￨NN￨O￨- management￨L￨NN￨O￨- ,￨L￨,￨O￨- human￨L￨JJ￨O￨- resources￨L￨NNS￨O￨- ,￨L￨,￨O￨- innovation￨L￨NN￨O￨- management￨L￨NN￨O￨- ,￨L￨,￨O￨- international￨L￨JJ￨O￨- management￨L￨NN￨O￨- ,￨L￨,￨O￨- information￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- marketing￨L￨NN￨O￨- ,￨L￨,￨O￨- manufacturing￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- organizational￨L￨JJ￨O￨- science￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- review￨L￨NN￨O￨- article￨L￨NN￨O￨- analyzes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- overload￨L￨NN￨O￨- literature￨L￨NN￨O￨- in￨L￨IN￨O￨- business￨L￨NN￨O￨- administration￨L￨NN￨O￨A and￨L￨CC￨O￨- related￨L￨JJ￨O￨- interdisciplinary￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- and￨L￨CC￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- comprehensive￨L￨JJ￨O￨- and￨L￨CC￨O￨- overarching￨L￨JJ￨O￨- overview￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- bibliometric￨L￨JJ￨O￨- literature￨L￨NN￨O￨- analysis￨L￨NN￨O￨- combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- snowball￨L￨NN￨O￨- sampling￨L￨NN￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- review￨L￨NN￨O￨- article￨L￨NN￨O￨- identifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- research￨L￨NN￨O￨- streams￨L￨NNS￨O￨- to￨L￨TO￨O￨- capture￨L￨VB￨O￨- the￨L￨DT￨O￨- pulse￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨A overload-related￨L￨JJ￨O￨- research￨L￨NN￨O￨- and￨L￨CC￨O￨- suggest￨L￨VBP￨O￨- new￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- addressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- future￨L￨NN￨DATE￨- and￨L￨CC￨O￨- identifies￨L￨VBZ￨O￨- concrete￨L￨JJ￨O￨- open￨L￨JJ￨O￨- gaps￨L￨NNS￨O￨- for￨L￨IN￨O￨- further￨L￨JJ￨O￨- research￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- illustrate￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- empirically￨L￨RB￨O￨- ,￨L￨,￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- Gaussian￨U￨JJ￨MISC￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- application￨L￨NN￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modelling.KeywordsABC￨L￨NN￨O￨- Markov￨U￨NNP￨PERSON￨- chain￨L￨NN￨O￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- Sequential￨U￨NNP￨ORGANIZATION￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- Slice￨U￨VB￨ORGANIZATION￨- sampling￨L￨NN￨O￨- Infectious￨U￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- modelling￨L￨NN￨O￨- Electronic￨U￨JJ￨O￨- supplementary￨L￨JJ￨O￨- materialThe￨L￨NN￨O￨- online￨L￨NN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- doi￨L￨FW￨O￨- :￨L￨:￨O￨- 10.1007￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- s11222-017-9764-4￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- contains￨L￨VBZ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- authorized￨L￨VBN￨O￨- users￨L￨NNS￨O￨- .1￨L￨CD￨NUMBER￨- IntroductionApproximate￨U￨NNP￨O￨- Bayesian￨U￨NNP￨O￨- computation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- family￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- approximate￨L￨JJ￨O￨- inference￨L￨NN￨O￨A ,￨L￨,￨O￨- used￨L￨VBN￨O￨- when￨L￨WRB￨O￨- likelihoods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- impossible￨L￨JJ￨O￨- or￨L￨CC￨O￨- impractical￨L￨JJ￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- numerically￨L￨RB￨O￨- but￨L￨CC￨O￨- simulating￨L￨VBG￨O￨- datasets￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- is￨L￨VBZ￨O￨- straightforward￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- parameter￨L￨NN￨O￨- value￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rare￨L￨JJ￨O￨A event￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- roughly￨L￨RB￨O￨- consistent￨L￨JJ￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- observations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- rare￨L￨JJ￨O￨A event￨L￨NN￨O￨- probability￨L￨NN￨O￨- estimator￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- estimate￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- pseudo-marginal￨L￨JJ￨O￨- Metropolis￨U￨NNP￨O￨- –￨L￨:￨O￨- Hastings￨U￨NNP￨PERSON￨- algorithm￨L￨NN￨O￨- for￨L￨IN￨O￨- parameter￨L￨NN￨O￨- inference￨L￨NN￨O￨- .￨L￨.￨O￨- +EverittTheodore￨U￨NNP￨MISC￨- KypraiosOpen￨U￨NNP￨MISC￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 3.8￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨MISC￨- AbstractApproximate￨U￨NNP￨MISC￨- Bayesian￨U￨NNP￨MISC￨- computation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- ABC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- methods￨L￨NNS￨O￨- permit￨L￨VBP￨O￨- approximate￨L￨JJ￨O￨- inference￨L￨NN￨O￨A for￨L￨IN￨O￨- intractable￨L￨JJ￨O￨- likelihoods￨L￨NNS￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 891￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 904￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asA￨L￨NN￨O￨- network￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- online￨L￨JJ￨O￨- community￨L￨NN￨O￨- commissioning￨L￨VBG￨O￨- dataAuthorsAuthors￨L￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsClement￨L￨NNP￨O￨- LeeAndrew￨U￨NNP￨O￨- GarbettDarren￨U￨NNP￨O￨- J.￨U￨NNP￨O￨- WilkinsonOpen￨U￨NNP￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 02￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 5.9￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- AbstractA￨U￨NN￨O￨- statistical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- preferential￨L￨JJ￨O￨- attachment￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- generated￨L￨VBN￨O￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- sequentially￨L￨RB￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- simple￨L￨JJ￨O￨- rules￨L￨NNS￨O￨- ,￨L￨,￨O￨- usually￨L￨RB￨O￨- describes￨L￨VBZ￨O￨- real-life￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- better￨L￨RBR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- assuming￨L￨VBG￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Bernoulli￨U￨NNP￨MISC￨- random￨L￨JJ￨O￨- graph￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- any￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- being￨L￨VBG￨O￨- connected￨L￨VBN￨O￨- ,￨L￨,￨O￨- does￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- online￨L￨JJ￨O￨- commissioning￨L￨VBG￨O￨- data.KeywordsStochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- MCMC￨U￨NNP￨O￨- Random￨U￨NNP￨O￨- graphs￨L￨NNS￨O￨- Preferential￨U￨JJ￨O￨- attachment￨L￨NN￨O￨- Community￨U￨NN￨O￨- commissioning￨L￨VBG￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSocial￨U￨NNP￨ORGANIZATION￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- popular￨L￨JJ￨O￨- research￨L￨NN￨O￨- topic￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DURATION￨- couple￨L￨NN￨DURATION￨- of￨L￨IN￨DURATION￨- decades￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- thanks￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- unprecedentedly￨L￨RB￨O￨- large￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- internet￨L￨NN￨O￨- data￨L￨NNS￨O￨- available￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- power￨L￨NN￨O￨- of￨L￨IN￨O￨- computers￨L￨NNS￨O￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- details￨L￨NNS￨O￨- ties￨L￨NNS￨O￨- between￨L￨IN￨O￨- people￨L￨NNS￨O￨- or￨L￨CC￨O￨- objects￨L￨NNS￨O￨- all￨L￨DT￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- though￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- degrees￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- flexibly￨L￨RB￨O￨- modelled￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- completely￨L￨RB￨O￨- independent￨L￨JJ￨RELIGION￨- as￨L￨IN￨O￨- they￨L￨PRP￨O￨- have￨L￨VBP￨O￨- to￨L￨TO￨O￨- sum￨L￨VB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- even￨L￨RB￨O￨- integer.One￨L￨JJ￨O￨- prominent￨L￨JJ￨O￨- feature￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨A life￨L￨NN￨O￨A is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- scale-free￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- follows￨L￨VBZ￨O￨- a￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- approximately￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Albert￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- stress￨L￨VBP￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- retain￨L￨VB￨O￨- the￨L￨DT￨O￨- demographic￨L￨JJ￨O￨- noise￨L￨NN￨O￨- derived￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- emphasise￨L￨VB￨O￨- this￨L￨DT￨O￨- point￨L￨NN￨O￨- by￨L￨IN￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- direction￨L￨NN￨O￨- of￨L￨IN￨O￨- selection￨L￨NN￨O￨A compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- prediction￨L￨NN￨O￨- made￨L￨VBN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- deterministic￨L￨JJ￨O￨- model.KeywordsStochastic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- Population￨U￨NNP￨O￨- genetics￨L￨NNS￨O￨- Time-scale￨U￨JJ￨MISC￨- separation￨L￨NN￨O￨- Effective￨U￨JJ￨O￨- models￨L￨NNS￨O￨- Noise-induced￨U￨JJ￨MISC￨- selection￨L￨NN￨O￨- Population￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionIn￨U￨NN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- articles￨L￨NNS￨O￨- on￨L￨IN￨O￨- biological￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- published￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Journal￨U￨NNP￨O￨- of￨L￨IN￨O￨- Statistical￨U￨NNP￨O￨- Physics￨U￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- natural￨L￨JJ￨O￨- to￨L￨TO￨O￨- ask￨L￨VB￨O￨- what￨L￨WP￨O￨- expertise￨L￨NN￨O￨- and￨L￨CC￨O￨- insights￨L￨NNS￨O￨- statistical￨L￨JJ￨O￨- physicists￨L￨NNS￨O￨- can￨L￨MD￨O￨- bring￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- what￨L￨WP￨O￨- way￨L￨NN￨O￨- might￨L￨MD￨O￨- their￨L￨PRP$￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- subject￨L￨JJ￨O￨- differ￨L￨VBP￨O￨- from￨L￨IN￨O￨- biologists￨L￨NNS￨O￨- .￨L￨.￨O￨- +That￨U￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- start￨L￨VB￨O￨- with￨L￨IN￨O￨- genes￨L￨NNS￨O￨- as￨L￨IN￨O￨- basic￨L￨JJ￨O￨- constituents￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- type￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- allele￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- location￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- carrying￨L￨VBG￨O￨- the￨L￨DT￨O￨- gene￨L￨NN￨O￨- is￨L￨VBZ￨O￨- located￨L￨VBN￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- island￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sex￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- carrying￨L￨VBG￨O￨- the￨L￨DT￨O￨- gene￨L￨NN￨O￨- ,￨L￨,￨O￨- etc.Secondly￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨A description￨L￨NN￨O￨- contains￨L￨VBZ￨O￨- too￨L￨RB￨O￨- much￨L￨JJ￨O￨- detail￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- irrelevant￨L￨JJ￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- macroscale￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mesoscale￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- some￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- element￨L￨NN￨O￨- is￨L￨VBZ￨O￨- retained￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- derive￨L￨VB￨O￨- a￨L￨DT￨O￨- reduced￨L￨VBN￨O￨- or￨L￨CC￨O￨- effective￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- contains￨L￨VBZ￨O￨- parameters￨L￨NNS￨O￨- which￨L￨WDT￨O￨- depend￨L￨VBP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- description￨L￨NN￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- encapsulate￨L￨VB￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- microscopic￨L￨JJ￨O￨- description.Thirdly￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- generic￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- include￨L￨VBP￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- haploid￨L￨NN￨O￨- Moran￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨A number￨L￨NN￨O￨- of￨L￨IN￨O￨- islands￨L￨NNS￨O￨- with￨L￨IN￨O￨- selection￨L￨NN￨O￨- and￨L￨CC￨O￨- mutation￨L￨NN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- Lotka￨U￨NNP￨LOCATION￨- –￨L￨:￨O￨- Volterra￨U￨NNP￨CITY￨- competition￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- islands￨L￨NNS￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- Lotka￨U￨NNP￨LOCATION￨- –￨L￨:￨O￨- Volterra￨U￨NNP￨CITY￨- competition￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- derivation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Hardy￨U￨NNP￨O￨- –￨L￨:￨O￨- Weinberg￨U￨NNP￨PERSON￨- approximation￨L￨NN￨O￨- from￨L￨IN￨O￨- first￨L￨JJ￨ORDINAL￨- principles￨L￨NNS￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- best￨L￨JJS￨O￨- not￨L￨RB￨O￨- to￨L￨TO￨O￨- apply￨L￨VB￨O￨- treatment￨L￨NN￨O￨- immediately￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- to￨L￨TO￨O￨- wait￨L￨VB￨O￨- and￨L￨CC￨O￨- see￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progresses￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- partly￨L￨RB￨O￨- because￨L￨IN￨O￨- learning￨L￨NN￨O￨- may￨L￨MD￨O￨- occur￨L￨VB￨O￨- over￨L￨IN￨O￨- time￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- and￨L￨CC￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategies.The￨L￨NNP￨O￨- real￨L￨JJ￨O￨- options￨L￨NNS￨O￨A approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- actions￨L￨NNS￨O￨- for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- it￨L￨PRP￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- convenient￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- couple￨L￨NN￨O￨- uncertainty￨L￨NN￨O￨- with￨L￨IN￨O￨- economic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- presented￨L￨VBN￨O￨- here￨L￨RB￨O￨- have￨L￨VBP￨O￨- important￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- way￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- real￨L￨JJ￨O￨- options￨L￨NNS￨O￨A approach￨L￨NN￨O￨- is￨L￨VBZ￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- optimal￨L￨JJ￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- given￨L￨VBN￨O￨- uncertainty￨L￨NN￨O￨- in￨L￨IN￨O￨- future￨L￨JJ￨DATE￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- progression.KeywordsReal￨L￨NN￨O￨- options￨L￨NNS￨O￨- Logistic￨U￨NNP￨O￨- SDE￨U￨NNP￨O￨- Disease￨U￨NNP￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- Stochastic￨U￨NNP￨O￨- epidemics￨L￨NNS￨O￨- Optimal￨U￨JJ￨O￨- timing￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionInvasive￨U￨NNP￨O￨- pests￨L￨NNS￨O￨- and￨L￨CC￨O￨- pathogens￨L￨NNS￨O￨- are￨L￨VBP￨O￨- increasing￨L￨VBG￨O￨- worldwide￨L￨RB￨O￨- ,￨L￨,￨O￨- posing￨L￨VBG￨O￨- a￨L￨DT￨O￨- threat￨L￨NN￨O￨- to￨L￨TO￨O￨- agriculture￨L￨NN￨O￨- and￨L￨CC￨O￨- forestry￨L￨NN￨O￨- production￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +A.￨U￨NN￨O￨- GilliganOpen￨U￨NNP￨O￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 3￨L￨CD￨NUMBER￨- Shares￨U￨NNP￨O￨- 1k￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨MISC￨- AbstractThe￨U￨NNP￨MISC￨- real￨L￨JJ￨O￨- options￨L￨NNS￨O￨A approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- within￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- economics￨L￨NNS￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- timing￨L￨NN￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- to￨L￨TO￨O￨- minimise￨L￨VB￨O￨- the￨L￨DT￨O￨- impacts￨L￨NNS￨O￨- of￨L￨IN￨O￨- invasive￨L￨JJ￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- pests￨L￨NNS￨O￨- and￨L￨CC￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- used￨L￨VBN￨O￨- does￨L￨VBZ￨O￨- not￨L￨RB￨O￨- appropriately￨L￨RB￨O￨- capture￨L￨VB￨O￨- uncertainty￨L￨NN￨O￨A in￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- excessive￨L￨JJ￨O￨- delay￨L￨NN￨O￨- before￨L￨IN￨O￨- treatment￨L￨NN￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- option￨L￨NN￨O￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- realised￨L￨VBN￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- error￨L￨NN￨O￨- analysis￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- residuals￨L￨NNS￨O￨- witnesses￨L￨NNS￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- convergence￨L￨NN￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- EPA￨U￨NNP￨ORGANIZATION￨- is￨L￨VBZ￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- globally￨L￨RB￨O￨- convergent￨L￨JJ￨O￨- non-standard￨L￨JJ￨O￨- finite￨L￨JJ￨O￨- difference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NSFD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- larger￨L￨JJR￨O￨- time￨L￨NN￨O￨- steps.KeywordsNonlinear￨L￨JJ￨O￨- modelEvolutionary￨L￨JJ￨O￨- computingPadé￨L￨NN￨O￨- approximationOptimization￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionA￨U￨NN￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- malicious￨L￨JJ￨O￨- code￨L￨NN￨O￨- which￨L￨WDT￨O￨- executes￨L￨VBZ￨O￨- harmful￨L￨JJ￨O￨- and￨L￨CC￨O￨- unauthorized￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- like￨L￨IN￨O￨- erasing￨L￨VBG￨O￨- necessary￨L￨JJ￨O￨- files￨L￨NNS￨O￨- ,￨L￨,￨O￨- accessing￨L￨VBG￨O￨- confidential￨L￨JJ￨O￨- data￨L￨NNS￨O￨- and￨L￨CC￨O￨- personal￨L￨JJ￨O￨- information￨L￨NN￨O￨- like￨L￨IN￨O￨- passwords￨L￨NNS￨O￨- ,￨L￨,￨O￨- account￨L￨VBP￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- contact￨L￨NN￨O￨- lists￨L￨NNS￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- involve￨L￨VBP￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- susceptible-infected-recovered-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- susceptible-exposed-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SEIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- SEIQS￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- quarantined￨L￨VBN￨O￨- class￨L￨NN￨O￨- included￨L￨VBD￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- SEIRS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- SEIQRS￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- SEIRS-V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- vaccinated￨L￨VBN￨O￨- subpopulation￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on.Mathematical￨L￨JJ￨O￨- tool-based￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨A analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- essential￨L￨JJ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- investigations￨L￨NNS￨O￨- for￨L￨IN￨O￨- acquiring￨L￨VBG￨O￨- better￨L￨JJR￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- evolution￨L￨NN￨O￨- ,￨L￨,￨O￨- impact￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- deriving￨L￨VBG￨O￨- mechanisms￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Numerical￨U￨JJ￨MISC￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A in￨L￨IN￨O￨- computer￨L￨NN￨O￨- networks￨L￨NNS￨O￨- :￨L￨:￨O￨- an￨L￨DT￨O￨- innovative￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- Padé￨U￨NN￨O￨- approximation￨L￨NN￨O￨- schemeJavaid￨L￨NN￨O￨- Ali1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Muhammad￨U￨NNP￨PERSON￨- Saeed1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Muhammad￨U￨NNP￨PERSON￨- Rafiq2￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Shaukat￨U￨NNP￨O￨- Iqbal3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:214￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- work￨L￨NN￨O￨- proposes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- mesh￨L￨NN￨O￨- free￨L￨JJ￨O￨- evolutionary￨L￨JJ￨O￨- Padé￨U￨NN￨O￨- approximation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- EPA￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- framework￨L￨NN￨O￨- for￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨- closed￨L￨JJ￨O￨- form￨L￨NN￨O￨- numerical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- computer￨L￨NN￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- computational￨L￨JJ￨O￨- architecture￨L￨NN￨O￨- of￨L￨IN￨O￨- EPA￨U￨NNP￨ORGANIZATION￨- scheme￨L￨NN￨O￨- assimilates￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Padé￨U￨NN￨O￨- approximation￨L￨NN￨O￨A to￨L￨TO￨O￨- transform￨L￨VB￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- nonlinear￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- equivalent￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +Differential￨U￨JJ￨O￨- evolution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- closed￨L￨JJ￨O￨A form￨L￨NN￨O￨A numerical￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- developed￨L￨VBN￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- CDRs-based￨U￨JJ￨MISC￨- indicators￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- spatial￨L￨JJ￨O￨- activities￨L￨NNS￨O￨- and￨L￨CC￨O￨- interactions￨L￨NNS￨O￨- hold￨L￨VBP￨O￨- promise￨L￨NN￨O￨- for￨L￨IN￨O￨- gaining￨L￨VBG￨O￨- insight￨L￨NN￨O￨- of￨L￨IN￨O￨- contagion￨L￨NN￨O￨- heterogeneity￨L￨NN￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- for￨L￨IN￨O￨- developing￨L￨VBG￨O￨- mitigation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- decision-making￨L￨JJ￨O￨- during￨L￨IN￨O￨- country-level￨L￨JJ￨O￨- epidemics.KeywordsSpatial￨L￨JJ￨O￨- networksMobile￨L￨NN￨O￨- phone￨L￨NN￨O￨A dataHuman￨L￨NNP￨O￨- mobilityEpidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionEpidemic￨U￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- represent￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- healthcare￨L￨NN￨O￨- challenge￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- represent￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- suffering￨L￨NN￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- A￨U￨DT￨O￨- comparison￨L￨NN￨O￨- of￨L￨IN￨O￨- spatial-based￨L￨JJ￨O￨- targeted￨L￨VBN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- mitigation￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- using￨L￨VBG￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨A dataStefania￨L￨NNP￨O￨- Rubrichi1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Zbigniew￨U￨NNP￨PERSON￨- Smoreda1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Mirco￨U￨NNP￨PERSON￨- Musolesi2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:17￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractEpidemic￨U￨NNP￨O￨- outbreaks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- healthcare￨L￨NN￨O￨- challenge￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- developing￨L￨VBG￨O￨- countries￨L￨NNS￨O￨- where￨L￨WRB￨O￨- they￨L￨PRP￨O￨- represent￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- major￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- of￨L￨IN￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- employing￨L￨VBG￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- meta-population￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨A Call￨U￨VB￨O￨- Detail￨U￨NNP￨O￨- Records￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- CDRs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- mobility￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- may￨L￨MD￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- hypothetical￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approaches￨L￨NNS￨O￨- presented￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- provide￨L￨VB￨O￨- further￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- that￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- phone￨L￨NN￨O￨A data￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- effectively￨L￨RB￨O￨- exploited￨L￨VBN￨O￨- to￨L￨TO￨O￨- facilitate￨L￨VB￨O￨- our￨L￨PRP$￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- spatial￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- relationship￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ’￨L￨POS￨O￨- contagion￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- different￨L￨JJ￨O￨- existing￨L￨VBG￨O￨- measures￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨A dimension￨L￨NN￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- and￨L￨CC￨O￨- interactions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- analyse￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- relevance￨L￨NN￨O￨- in￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- risk￨L￨NN￨O￨- sub-population￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- candidates￨L￨NNS￨O￨- for￨L￨IN￨O￨- isolation￨L￨NN￨O￨- countermeasures￨L￨NNS￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- PreliminariesTo￨U￨NN￨O￨- make￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- be￨L￨VB￨O￨- biologically￨L￨RB￨O￨- significant￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- list￨L￨VBP￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Assumption￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- theta￨L￨IN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- theta￨L￨IN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- xi￨L￨VB￨O￨A a￨L￨DT￨O￨- are￨L￨VBP￨O￨- non-negative￨L￨JJ￨O￨- and￨L￨CC￨O￨- belong￨L￨VBP￨O￨- to￨L￨TO￨O￨- with￨L￨IN￨O￨- respective￨L￨JJ￨O￨- essential￨L￨JJ￨O￨- upper￨L￨JJ￨O￨- bound￨L￨VBN￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- beta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- beta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- beta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- beta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- theta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- theta￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨ORGANIZATION￨- bar￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- xi￨L￨NN￨O￨- in￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- xi￨L￨VB￨O￨- a￨L￨DT￨O￨- are￨L￨VBP￨O￨- Lipschitz￨U￨NNP￨PERSON￨- continuous￨L￨JJ￨O￨- on￨L￨IN￨O￨- R￨U￨NN￨O￨- with￨L￨IN￨O￨- coefficients￨L￨NNS￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- xi￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- GreaterThan￨U￨NNP￨O￨- Abs￨U￨NNS￨O￨- Add￨U￨VBP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- theta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨MISC￨- Abs￨U￨NNS￨MISC￨- Add￨U￨VBP￨MISC￨- theta￨L￨IN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- xi￨L￨NN￨O￨- a￨L￨DT￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨O￨- theta￨L￨IN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- StrictGreaterThan￨U￨NNP￨O￨- a￨L￨DT￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- Lyapunov￨U￨NNP￨O￨- functionals￨L￨NNS￨O￨- and￨L￨CC￨O￨- LaSalle￨U￨NNP￨O￨- ’s￨L￨POS￨O￨- invariance￨L￨NN￨O￨- principle￨L￨NN￨O￨- and￨L￨CC￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable.KeywordsAge-structured￨L￨JJ￨O￨- modelSaturating￨L￨NN￨O￨- incidenceAsymptotic￨L￨JJ￨O￨- smoothnessLyapunov￨L￨NN￨O￨- functionalGlobal￨L￨NN￨O￨- stability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionHepatitis￨U￨NN￨O￨- B￨U￨NN￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- contagious￨L￨JJ￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- hard￨L￨JJ￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- its￨L￨PRP$￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +□￨L￨SYM￨O￨- Proposition￨U￨NN￨O￨- 2.2￨L￨CD￨NUMBER￨- If￨U￨IN￨O￨- Mul￨U￨NN￨O￨- X￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- X￨U￨NN￨O￨- mathcal￨L￨JJ￨O￨A and￨L￨CC￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- constant￨L￨JJ￨O￨- GreaterThan￨U￨NNP￨O￨- M￨U￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Lambda￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- statements￨L￨NNS￨O￨- hold￨L￨VBP￨O￨- for￨L￨IN￨O￨- GreaterThan￨U￨NNP￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- LessThan￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- LessThan￨U￨NNP￨PERSON￨- i￨L￨FW￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- gamma￨L￨NN￨O￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- both￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- follow￨L￨VBP￨O￨- the￨L￨DT￨O￨- Susceptible-Infective-Recovered￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- survive￨L￨VB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- evolve￨L￨VB￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- timescale￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- closely￨L￨RB￨O￨- matched￨L￨VBN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A on￨L￨IN￨O￨- which￨L￨WDT￨O￨- it￨L￨PRP￨O￨- depends.KeywordsSIR￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- Epidemics￨U￨NNS￨O￨- Superinfection￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- Branching￨U￨VBG￨O￨- processes￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSuperinfections￨U￨NNS￨ORGANIZATION￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- global￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- morbidity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- epidemiological￨L￨JJ￨O￨- language￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- correspond￨L￨VBP￨O￨- to￨L￨TO￨O￨- coupled￨L￨VBN￨O￨- Susceptible-Infective-Susceptible￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemics￨L￨NNS￨O￨- ;￨L￨:￨O￨- empty￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- sites￨L￨NNS￨O￨- are￨L￨VBP￨O￨- interpreted￨L￨VBN￨O￨- as￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- who￨L￨WP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- primary￨L￨JJ￨O￨A (￨L￨-LRB-￨O￨- host￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- secondary￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- parasite￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 171￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 1122￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1135￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asA￨L￨NN￨O￨- Re-entrant￨U￨JJ￨O￨- Phase￨U￨NN￨O￨- Transition￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Survival￨U￨NN￨O￨- of￨L￨IN￨O￨- Secondary￨U￨JJ￨O￨- Infections￨U￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- NetworksAuthorsAuthors￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- affiliationsSam￨L￨NNP￨MISC￨- MoorePeter￨U￨NNP￨MISC￨- MörtersTim￨U￨NNP￨MISC￨- RogersOpen￨U￨NNP￨MISC￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 275￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨O￨- AbstractWe￨U￨NNP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- secondary￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- currently￨L￨RB￨DATE￨- carrying￨L￨VBG￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- primary￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- secondary￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- of￨L￨IN￨O￨- large￨L￨JJ￨O￨- sparse￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- mapped￨L￨VBN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- branching￨L￨VBG￨O￨- process￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- time-sensitive￨L￨JJ￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- primary￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Multiscale￨U￨NNP￨O￨- unfolding￨L￨VBG￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- by￨L￨IN￨O￨- geometric￨L￨JJ￨O￨A renormalization￨L￨NN￨O￨- Guillermo￨U￨NNP￨PERSON￨- García-Pérez1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Marián￨U￨NNP￨PERSON￨- Boguñá￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨PERSON￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- &￨L￨CC￨O￨- M.￨U￨NNP￨O￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- small-world￨L￨JJ￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- complicates￨L￨VBZ￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- renormalization￨L￨NN￨O￨- group￨L￨NN￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- correlations￨L￨NNS￨O￨- between￨L￨IN￨O￨- coexisting￨L￨VBG￨O￨- scales￨L￨NNS￨O￨- .￨L￨.￨O￨- +ADSArticle￨U￨NN￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Scholar4.Song￨U￨NNP￨O￨- ,￨L￨,￨O￨- C.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Havlin￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- S.￨U￨NNP￨O￨- Nature￨U￨NNP￨O￨- 433￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 392￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 395￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2005￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +99￨L￨CD￨NUMBER￨A ,￨L￨,￨O￨- 038701￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +While￨U￨IN￨O￨- this￨L￨DT￨O￨- in￨L￨IN￨O￨- no￨L￨DT￨O￨- way￨L￨NN￨O￨- excludes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- prospect￨L￨NN￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- MSMs￨U￨NNS￨MISC￨- provide￨L￨VBP￨O￨- good￨L￨JJ￨O￨- justifications￨L￨NNS￨O￨- for￨L￨IN￨O￨- policy￨L￨NN￨O￨A decisions￨L￨NNS￨O￨- ,￨L￨,￨O￨- my￨L￨PRP$￨O￨- arguments￨L￨NNS￨O￨- caution￨L￨VBP￨O￨- against￨L￨IN￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- preference￨L￨NN￨O￨- for￨L￨IN￨O￨- MSMs￨U￨NNS￨O￨- over￨L￨IN￨O￨- ASMs￨U￨NNS￨O￨- for￨L￨IN￨O￨- policy￨L￨NN￨O￨- decision￨L￨NN￨O￨- purposes￨L￨NNS￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- problems￨L￨NNS￨O￨- in￨L￨IN￨O￨- particular.KeywordsEvidence-based￨L￨JJ￨O￨- policy￨L￨NN￨O￨- Epidemiology￨U￨NNP￨O￨- Modeling￨U￨NNP￨O￨- Macro￨U￨NNP￨O￨- versus￨L￨CC￨O￨- micro￨L￨JJ￨O￨- Microsimulations￨U￨NNPS￨MISC￨- Agent-based￨U￨JJ￨MISC￨- modeling￨L￨NN￨O￨- Robustness￨U￨NNP￨O￨- Isolation￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionEpidemic￨U￨JJ￨O￨- prevention￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- of￨L￨IN￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- authorities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Synthese￨U￨JJ￨O￨- pp￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asChoosing￨L￨VBG￨O￨- the￨L￨DT￨O￨- right￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- policy￨L￨NN￨O￨- decision-making￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A epidemiologyAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsTill￨L￨NN￨O￨- Grüne-YanoffOpen￨U￨NN￨O￨- AccessS.I.￨U￨NNP￨O￨- :￨L￨:￨O￨- Philosophy￨U￨NN￨O￨- of￨L￨IN￨O￨- EpidemiologyFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 204￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨O￨- AbstractPolicymakers￨U￨NNPS￨O￨- increasingly￨L￨RB￨O￨- draw￨L￨VB￨O￨- on￨L￨IN￨O￨- scientific￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- simulation￨L￨NN￨O￨- modeling￨L￨NN￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- justify￨L￨VB￨O￨- their￨L￨PRP$￨O￨- decisions￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- dimensions￨L￨NNS￨O￨- include￨L￨VBP￨O￨- the￨L￨DT￨O￨- representation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨A target￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- accurate￨L￨JJ￨O￨- measurement￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- included￨L￨VBD￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mechanisms￨L￨NNS￨O￨- modeled￨L￨VBD￨O￨- simultaneously￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- ways￨L￨NNS￨O￨- of￨L￨IN￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- structural￨L￨JJ￨O￨- uncertainty￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- analyzing￨L￨VBG￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- proposed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- last￨L￨JJ￨DATE￨- 20￨L￨CD￨DATE￨- years￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- discusses￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- justify￨L￨VB￨O￨- strategy￨L￨NN￨O￨- choice￨L￨NN￨O￨- with￨L￨IN￨O￨- reference￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- core￨L￨NN￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- respective￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Discussing￨U￨VBG￨O￨- the￨L￨DT￨O￨- example￨L￨NN￨O￨- of￨L￨IN￨O￨- smallpox￨L￨NN￨CAUSE_OF_DEATH￨A epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- distinguishes￨L￨VBZ￨O￨- three￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- strategies￨L￨NNS￨O￨- :￨L￨:￨O￨- Massive￨U￨JJ￨O￨- Simulation￨U￨NN￨O￨- Models￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- MSMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Abstract￨U￨NNP￨O￨- Simulation￨U￨NNP￨O￨- Models￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- ASMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Macro￨U￨NNP￨MISC￨- Equation￨U￨NNP￨MISC￨- Models￨U￨NNS￨MISC￨- (￨L￨-LRB-￨O￨- MEMs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- perform￨L￨VBP￨O￨- simulations￨L￨NNS￨O￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- messages￨L￨NNS￨O￨- originating￨L￨VBG￨O￨- from￨L￨IN￨O￨- different￨L￨JJ￨O￨- organizations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨- aid￨L￨NN￨O￨A community￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- different￨L￨JJ￨O￨- reach.KeywordsWeb￨L￨NN￨O￨- crawlingGlobal￨L￨NN￨O￨- health￨L￨NN￨O￨- architectureComplex￨L￨NN￨O￨- networks￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionInternational￨U￨JJ￨O￨- aid￨L￨NN￨O￨- —￨L￨:￨O￨- or￨L￨CC￨O￨- “￨L￨``￨O￨- Global￨U￨NNP￨O￨- Health￨U￨NNP￨O￨- Architecture￨U￨NNP￨O￨- ”￨L￨''￨O￨- NumericCitation￨U￨NNP￨O￨- when￨L￨WRB￨O￨- focusing￨L￨VBG￨O￨- on￨L￨IN￨O￨- health￨L￨NN￨O￨- topics￨L￨NNS￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- —￨L￨:￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- system￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- web￨L￨NN￨O￨- crawling￨L￨VBG￨O￨- to￨L￨TO￨O￨- collect￨L￨VB￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- activities￨L￨NNS￨O￨- of￨L￨IN￨O￨- international￨L￨JJ￨O￨- aid￨L￨NN￨O￨A organizations￨L￨NNS￨O￨- on￨L￨IN￨O￨- different￨L￨JJ￨O￨- health-related￨L￨JJ￨O￨- topics￨L￨NNS￨O￨- and￨L￨CC￨O￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- depict￨L￨VB￨O￨- this￨L￨DT￨O￨- complex￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- relationships￨L￨NNS￨O￨- among￨L￨IN￨O￨- organizations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Mapping￨U￨NN￨MISC￨- the￨L￨DT￨O￨- international￨L￨JJ￨O￨- health￨L￨NN￨O￨- aid￨L￨NN￨O￨A community￨L￨NN￨O￨- using￨L￨VBG￨O￨- web￨L￨NN￨O￨- dataMichele￨L￨NN￨O￨- Coscia1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Katsumasa￨U￨NNP￨O￨- Hamaguchi3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Maria￨U￨NNP￨PERSON￨- Elena￨U￨NNP￨PERSON￨- Pinglo3￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Antonio￨U￨NNP￨O￨- Giuffrida3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:12￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractInternational￨U￨NNP￨O￨- aid￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complex￨L￨JJ￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- it￨L￨PRP￨O￨- involves￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- issues￨L￨NNS￨O￨- ,￨L￨,￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- donors￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- systematically￨L￨RB￨O￨- collecting￨L￨VBG￨O￨- co-occurrences￨L￨NNS￨O￨- of￨L￨IN￨O￨- issues￨L￨NNS￨O￨- ,￨L￨,￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- organization￨L￨NN￨O￨- names￨L￨NNS￨O￨- from￨L￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- hundred￨L￨CD￨NUMBER￨- websites￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- construct￨L￨VB￨O￨- multilayer￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- describing￨L￨VBG￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- issues￨L￨NNS￨O￨- are￨L￨VBP￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- which￨L￨WDT￨O￨- organizations￨L￨NNS￨O￨A .￨L￨.￨O￨- +Following￨U￨VBG￨O￨- previous￨L￨JJ￨O￨- work￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- decide￨L￨VBP￨O￨- to￨L￨TO￨O￨- use￨L￨VB￨O￨- the￨L￨DT￨O￨- speech￨L￨NN￨O￨- each￨L￨DT￨O￨- aid￨L￨NN￨O￨A organization￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- public￨L￨JJ￨O￨- communications￨L￨NNS￨O￨- ,￨L￨,￨O￨- specifically￨L￨RB￨O￨- their￨L￨PRP$￨O￨- websites￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- further￨L￨RB￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- fractional￨L￨JJ￨O￨- order￨L￨NN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- D￨U￨NN￨O￨- alpha￨L￨NN￨O￨A S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Lambda￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- Equality￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- D￨U￨NN￨O￨- alpha￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- r￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- D￨U￨NN￨O￨- alpha￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- r￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- mu￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Pow￨U￨NN￨O￨- D￨U￨NN￨O￨- alpha￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Caputo￨U￨NNP￨PERSON￨- fractional￨L￨JJ￨O￨- derivative￨L￨NN￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- LessThan￨U￨NN￨O￨- StrictLessThan￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- defined￨L￨VBN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- arbitrary￨L￨JJ￨O￨- function￨L￨NN￨O￨- f￨L￨FW￨O￨- t￨L￨NN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- In￨U￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- first￨L￨JJ￨ORDINAL￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equivalent￨L￨JJ￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- D￨U￨NN￨O￨- alpha￨L￨NN￨O￨A S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Lambda￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Also￨U￨RB￨O￨- ,￨L￨,￨O￨- another￨L￨DT￨O￨- advantage￨L￨NN￨O￨- for￨L￨IN￨O￨- using￨L￨VBG￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- derivative￨L￨NN￨O￨- is￨L￨VBZ￨O￨- enlarging￨L￨VBG￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- systems.In￨L￨NN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- works￨L￨NNS￨O￨- involving￨L￨VBG￨O￨- fractional￨L￨JJ￨O￨- order￨L￨NN￨O￨- derivative￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- done￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- are￨L￨VBP￨O￨- mainly￨L￨RB￨O￨- concerned￨L￨VBN￨O￨- with￨L￨IN￨O￨- SIR-type￨U￨JJ￨MISC￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- linear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨NN￨O￨A and￨L￨CC￨O￨- c￨L￨NN￨O￨- satisfy￨L￨VBP￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- xi￨L￨NN￨O￨- F￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- prime￨L￨JJ￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- textstyle￨L￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- xi￨L￨NNP￨O￨- Mul￨U￨NNP￨O￨- J￨U￨NNP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- ast￨L￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- xi￨L￨NN￨O￨- F￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- prime￨L￨JJ￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨NN￨O￨- Mul￨U￨NN￨O￨- J￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- ast￨L￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- and￨L￨CC￨O￨- Similar￨U￨JJ￨O￨- to￨L￨TO￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- shall￨L￨MD￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- phi￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- satisfying￨L￨VBG￨O￨- Equality￨U￨NNP￨O￨- Limit￨U￨NNP￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- xi￨L￨NN￨O￨- xi￨L￨NN￨O￨- Mul￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- k￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- spatial￨L￨JJ￨O￨- homogeneous￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Equality￨U￨NN￨O￨- k￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- -1￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- c￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- provided￨L￨VBN￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- When￨U￨WRB￨O￨- the￨L￨DT￨O￨- scalar￨L￨JJ￨O￨- equation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- concerned￨L￨VBN￨O￨- ,￨L￨,￨O￨- Jin￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Zhao￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- with￨L￨IN￨O￨- dispersal￨L￨NN￨O￨- .￨L￨.￨O￨- +Since￨U￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Dunbar￨U￨NNP￨PERSON￨- [￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- much￨L￨JJ￨O￨- attention￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- paid￨L￨VBN￨O￨- to￨L￨TO￨O￨- traveling￨L￨VBG￨O￨- wave￨L￨NN￨O￨A solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- reaction￨L￨NN￨O￨- –￨L￨:￨O￨- diffusion￨L￨NN￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- predator￨L￨NN￨O￨- –￨L￨:￨O￨- prey￨L￨NN￨O￨- nonlinearities￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- energy￨L￨NN￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- Equality￨U￨NNP￨O￨- bigl￨L￨NN￨O￨- u￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- u￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- bigl￨L￨NN￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨NN￨O￨A Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- phi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- xi￨L￨RB￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- traveling￨L￨VBG￨O￨- wave￨L￨NN￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- functions￨L￨NNS￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- represent￨L￨VBP￨O￨- saturated￨L￨JJ￨O￨A growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- microorganism￨L￨NN￨O￨- population￨L￨NN￨O￨- under￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- nutrients.It￨L￨NN￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- in￨L￨IN￨O￨- reality￨L￨NN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- inevitably￨L￨RB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- random￨L￨JJ￨O￨- disturbances￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 48￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 54￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨A stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- try￨L￨VB￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- criteria￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- mean￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- microorganism￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- memristive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- recast￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- tractable￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- defining￨L￨VBG￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- state-dependent￨L￨JJ￨O￨- switched￨L￨VBN￨O￨- signals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- calculation￨L￨NN￨O￨- cost￨L￨NN￨O￨- is￨L￨VBZ￨O￨- reduced￨L￨VBN￨O￨- effectively￨L￨RB￨O￨- when￨L￨WRB￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- connection￨L￨NN￨O￨- weights￨L￨NNS￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- robust￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- method.On￨L￨NN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- complex-valued￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- undergone￨L￨VBN￨O￨- a￨L￨DT￨O￨- research￨L￨NN￨O￨- upsurge￨L￨NN￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- more￨L￨RBR￨O￨- extensive￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- radar￨L￨NN￨O￨- imaging￨L￨NN￨O￨- ,￨L￨,￨O￨- electromagnetic￨L￨JJ￨O￨- waves￨L￨NNS￨O￨- ,￨L￨,￨O￨- remote￨L￨JJ￨O￨- sensing￨L￨VBG￨O￨- ,￨L￨,￨O￨- quantum￨L￨NN￨O￨- devices￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- situation￨L￨NN￨O￨- prompts￨L￨VBZ￨O￨- our￨L￨PRP$￨O￨- current￨L￨JJ￨DATE￨- research.Considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- inevitability￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- practical￨L￨JJ￨O￨- projects￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 50￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 57￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- discussions￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- estimation￨L￨NN￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- complex-valued￨L￨JJ￨O￨- memristive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- delays￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- State￨U￨NN￨O￨- estimation￨L￨NN￨O￨- for￨L￨IN￨O￨- complex-valued￨L￨JJ￨O￨- memristive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- delaysRunan￨L￨NN￨O￨- Guo1￨U￨NN￨O￨- ,￨L￨,￨O￨- Ziye￨U￨NN￨O￨- Zhang1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Ming￨U￨VBG￨O￨- Gao2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:118￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- estimation￨L￨NN￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- complex-valued￨L￨JJ￨O￨- memristive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- delays￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- mainly￨L￨RB￨O￨- embodied￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- respects￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- state￨L￨NN￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- complex-valued￨L￨JJ￨O￨- memristive￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- time-varying￨L￨JJ￨O￨- delays￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- no￨L￨DT￨O￨- information￨L￨NN￨O￨- published￨L￨VBN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- estimation￨L￨NN￨O￨- problem￨L￨NN￨O￨- for￨L￨IN￨O￨- memristor-based￨L￨JJ￨O￨- complex-valued￨L￨JJ￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- logistic￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- y￨L￨NNP￨O￨- Tuple￨U￨NNP￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- y￨L￨RB￨O￨- ,￨L￨,￨O￨- here￨L￨RB￨O￨- C￨U￨NN￨O￨- is￨L￨VBZ￨O￨- environment￨L￨NN￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- proportional￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨A abundance￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NN￨O￨- C￨U￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NN￨O￨- alpha￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- conversion￨L￨NN￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- prey￨L￨NN￨O￨- into￨L￨IN￨O￨- predator￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- situation￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- taken￨L￨VBN￨O￨- over￨L￨RP￨O￨- by￨L￨IN￨O￨- adding￨L￨VBG￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- denominator￨L￨NN￨O￨- ;￨L￨:￨O￨- this￨L￨DT￨O￨- modification￨L￨NN￨O￨- prevents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- predator￨L￨NN￨O￨- population￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- prey￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- equation￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- y￨L￨NNP￨O￨- Tuple￨U￨NNP￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- y￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨NNP￨ORGANIZATION￨- y￨L￨NNP￨ORGANIZATION￨- Tuple￨U￨NNP￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +All￨U￨PDT￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- defined￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- A￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- half￨L￨NN￨O￨- saturation￨L￨NN￨O￨A constant￨L￨JJ￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- transfer￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- node￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- is￨L￨VBZ￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- nodes￨L￨NNS￨O￨- lose￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- join￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximal￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- crashing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- all￨L￨DT￨O￨- classes￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- half￨L￨NN￨O￨- saturation￨L￨NN￨O￨- constant￨L￨JJ￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- I￨U￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- rate￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- induced￨L￨VBD￨O￨- crashing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- Dénes￨U￨NNPS￨PERSON￨- and￨L￨CC￨O￨- Röst￨U￨NNP￨MISC￨- NumericCitation￨U￨NNP￨MISC￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- Tuple￨U￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- f￨L￨LS￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- f￨L￨LS￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- -1￨L￨CD￨NUMBER￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- Equality￨U￨VBP￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- constant￨L￨JJ￨O￨- size￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- compartments￨L￨NNS￨O￨- :￨L￨:￨O￨- susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- denoted￨L￨VBN￨O￨A by￨L￨IN￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- I￨U￨PRP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- e-epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- Tuple￨U￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- V￨U￨NN￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- alpha￨L￨NN￨O￨A Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- E￨U￨NN￨ORGANIZATION￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- delta￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- a￨L￨DT￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- :￨L￨:￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- E￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- I￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- GreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- V￨U￨NNP￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- V￨U￨NNP￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- Lyapunov￨U￨NN￨PERSON￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨JJ￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- treatment￨L￨NN￨O￨A functions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- several￨L￨JJ￨O￨- authors￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- some￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 14￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 27￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 31￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 35￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 38￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- incidences￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- particles￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨A ,￨L￨,￨O￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- forms￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- f￨L￨FW￨O￨- V￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- f￨L￨FW￨O￨- and￨L￨CC￨O￨- g￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- forces￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- virus￨L￨NN￨O￨- particles￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- and￨L￨CC￨O￨- satisfy￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- properties￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- false￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- It￨U￨PRP￨O￨- then￨L￨RB￨O￨- follows￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨JJ￨O￨- value￨L￨NN￨O￨- theorem￨L￨NN￨O￨- that￨L￨WDT￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Epidemiologically￨U￨RB￨O￨- ,￨L￨,￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- spread￨L￨VB￨O￨- if￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- incidences￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- f￨L￨FW￨O￨- V￨U￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- become￨L￨VBP￨O￨- faster￨L￨RBR￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- particles￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- increase￨L￨VBP￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- iii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- per￨L￨FW￨O￨- capita￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- by￨L￨IN￨O￨- virus￨L￨NN￨O￨- particles￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- will￨L￨MD￨O￨- slow￨L￨VB￨O￨- down￨L￨RP￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- certain￨L￨JJ￨O￨- inhibition￨L￨NN￨O￨- effect￨L￨NN￨O￨- since￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- implies￨L￨VBZ￨O￨- that￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- V￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- f￨L￨LS￨O￨- V￨U￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- taking￨L￨VBG￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- viruses￨L￨NNS￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- T￨U￨NN￨O￨- partial￨L￨JJ￨O￨A Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dT￨L￨NNP￨O￨- lambda￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- I￨U￨PRP￨O￨- partial￨L￨JJ￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- V￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- V￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- V￨U￨NN￨O￨- x￨L￨CC￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- D￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Delta￨U￨NN￨O￨- V￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- uninfected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- free￨L￨JJ￨O￨- virus￨L￨NN￨O￨- at￨L￨IN￨O￨- position￨L￨NN￨O￨- x￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- D￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- diffusion￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Δ￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Laplacian￨U￨JJ￨MISC￨- operator.Notice￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- studies￨L￨NNS￨O￨- mentioned￨L￨VBD￨O￨- only￨L￨RB￨O￨- focus￨L￨VB￨O￨- on￨L￨IN￨O￨- virus-to-cell￨L￨JJ￨O￨- spread￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- bloodstream￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- cells￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- state￨L￨NN￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- cells￨L￨NNS￨O￨- W￨U￨NNP￨O￨- t￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- introduced￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- reads￨L￨VBZ￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- T￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- W￨U￨NNP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- uninfected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- productively￨L￨RB￨O￨- infected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- free￨L￨JJ￨O￨- virus￨L￨NN￨O￨- particles￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- uninfected￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- virus-to-cell￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Hence￨U￨RB￨O￨- ,￨L￨,￨O￨- inspired￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- aforementioned￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- T￨U￨NN￨O￨- partial￨L￨JJ￨O￨A Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dT￨L￨NNP￨O￨- lambda￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- W￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- gamma￨L￨NN￨O￨- W￨U￨NN￨O￨- x￨L￨CC￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- f￨L￨FW￨O￨- V￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- T￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- I￨U￨PRP￨O￨- partial￨L￨JJ￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- partial￨L￨JJ￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- W￨U￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- I￨U￨PRP￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- cell-to-cell￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- means￨L￨NNS￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- hypothesis￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- problem￨L￨NN￨O￨A of￨L￨IN￨O￨- ISFC￨U￨NN￨O￨- is￨L￨VBZ￨O￨- transformed￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- unspecified￨L￨JJ￨O￨- time￨L￨NN￨O￨- with￨L￨IN￨O￨- inequality￨L￨NN￨O￨- constraints￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- constraint￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- arrival￨L￨NN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Problem￨U￨NNP￨O￨- statement￨L￨NN￨O￨- and￨L￨CC￨O￨- translationConsider￨L￨NN￨O￨- the￨L￨DT￨O￨- ISFC￨U￨NN￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨PERSON￨- t￨L￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathbb￨L￨NN￨O￨A ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- hat￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- boldsymbol￨L￨NN￨O￨- y￨L￨NN￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨PERSON￨- boldsymbol￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- f￨L￨FW￨ORGANIZATION￨- Mul￨U￨FW￨ORGANIZATION￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- parameter￨L￨NN￨O￨- vectors.Denote￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- satisfying￨L￨VBG￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- Mul￨U￨NN￨O￨- hat￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bigl￨L￨NN￨O￨- Mul￨U￨NN￨O￨- boldsymbol￨L￨NN￨O￨- y￨L￨NN￨O￨- For￨U￨IN￨O￨- convenience￨L￨NN￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- abbreviated￨L￨JJ￨O￨- to￨L￨TO￨O￨- Mul￨U￨NN￨O￨- hat￨L￨NN￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- boldsymbol￨L￨NN￨O￨- y￨L￨NN￨O￨- or￨L￨CC￨O￨- Mul￨U￨NN￨O￨- hat￨L￨NN￨O￨- Mul￨U￨NN￨O￨- boldsymbol￨L￨NN￨O￨- y￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- problem￨L￨NN￨O￨A of￨L￨IN￨O￨- state￨L￨NN￨O￨- impulse￨L￨NN￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- transformed￨L￨VBN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- optimization￨L￨NN￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- unspecified￨L￨JJ￨O￨- time￨L￨NN￨O￨- with￨L￨IN￨O￨- inequality￨L￨NN￨O￨- constraint￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- together￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- constraint￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- arrival￨L￨NN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- much￨L￨JJ￨O￨- literature￨L￨NN￨O￨- considered￨L￨VBN￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- regime￨L￨NN￨O￨- switching￨L￨NN￨O￨A ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- System￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- false￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- considered￨L￨VBN￨O￨- by￨L￨IN￨O￨- Liu￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- author￨L￨NN￨TITLE￨- ignored￨L￨VBD￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- degenerate￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- matrix￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- ensure￨L￨VB￨O￨- uniform￨L￨JJ￨O￨- ellipticity.Throughout￨L￨NN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vector￨L￨NN￨O￨- or￨L￨CC￨O￨- matrix￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- to￨L￨TO￨O￨- denote￨L￨VB￨O￨- its￨L￨PRP$￨O￨- transpose￨L￨NN￨O￨- ;￨L￨:￨O￨- set￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- vector￨L￨NN￨O￨- ;￨L￨:￨O￨- set￨L￨VBN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨JJ￨O￨- where￨L￨WRB￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- linear￨L￨JJ￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Remark￨U￨NN￨O￨- 1.1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Lemma￨U￨NN￨PERSON￨- 2.1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Incorporating￨U￨VBG￨O￨- color￨L￨NN￨O￨- noise￨L￨NN￨O￨A into￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- get￨L￨VBP￨O￨- a￨L￨DT￨O￨- regime-switching￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Lambda￨U￨NNP￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- mu￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- varepsilon￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- gamma￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- alpha￨L￨NN￨O￨- i￨L￨FW￨O￨- and￨L￨CC￨O￨- sigma￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constants.In￨L￨NN￨O￨- the￨L￨DT￨O￨- earlier￨L￨JJR￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- regime￨L￨NN￨O￨- switching￨L￨NN￨O￨- was￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- into￨L￨IN￨O￨- population￨L￨NN￨O￨- models￨L￨NNS￨O￨- ;￨L￨:￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- important￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- color￨L￨NN￨O￨- noise￨L￨NN￨O￨- on￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- author￨L￨NN￨TITLE￨- considered￨L￨VBN￨O￨- deterministic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Markovian￨U￨JJ￨O￨- switching￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- Pow￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- s￨L￨VBZ￨O￨- mathcal￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- becomes￨L￨VBZ￨O￨- extinct￨L￨JJ￨O￨- exponentially￨L￨RB￨O￨- ;￨L￨:￨O￨- whereas￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- s￨L￨VBZ￨O￨- mathcal￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- beta￨L￨NN￨O￨- i￨L￨FW￨O￨- alpha￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- can￨L￨MD￨O￨- converge￨L￨VB￨O￨- in￨L￨IN￨O￨- Pow￨U￨NNP￨O￨- L￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- invariant￨L￨JJ￨O￨- density.KeywordsStationary￨L￨JJ￨O￨- distributionMarkov￨L￨NN￨O￨- semigroupsAsymptotic￨L￨JJ￨O￨- stabilityMSC47D0760J6060H1092D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionInfectious￨U￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- influenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- noise￨L￨NN￨O￨A ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- typical￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- long-time￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- can￨L￨MD￨O￨- converge￨L￨VB￨O￨- in￨L￨IN￨O￨- Pow￨U￨NNP￨O￨- L￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- invariant￨L￨JJ￨O￨- density.In￨L￨NN￨O￨- reality￨L￨NN￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- for￨L￨IN￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨A there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- another￨L￨DT￨O￨- important￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- noise￨L￨NN￨O￨- :￨L￨:￨O￨- color￨L￨NN￨O￨- noise￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- cause￨L￨VB￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- switch￨L￨VB￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- environmental￨L￨JJ￨O￨- regime￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- stationary￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- r￨L￨NN￨O￨- t￨L￨NN￨O￨- which￨L￨WDT￨O￨- satisfies￨L￨VBZ￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- Gamma￨U￨NNP￨ORGANIZATION￨- pi￨L￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- Sum￨U￨NNP￨O￨- pi￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- Tuple￨U￨NNP￨ORGANIZATION￨- i￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- pi￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- forall￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- mathbb￨L￨NN￨O￨A .￨L￨.￨O￨- +RIPK3-deficient￨U￨JJ￨O￨- mice￨L￨NNS￨O￨A have￨L￨VBP￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- demonstrated￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- protected￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- direct￨L￨JJ￨O￨- evidence￨L￨NN￨O￨- for￨L￨IN￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- necroptosis￨L￨NN￨O￨- in￨L￨FW￨O￨- vivo￨L￨FW￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- limited￨L￨VBN￨O￨- .￨L￨.￨O￨- +Green4￨U￨NN￨O￨- ,￨L￨,￨O￨- Christian￨U￨NNP￨RELIGION￨- Hugo1￨U￨NNP￨O￨- &￨L￨CC￨O￨- Andreas￨U￨NNP￨PERSON￨- Linkermann￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- Cell￨U￨NN￨O￨- Death￨U￨NNP￨O￨- &￨L￨CC￨O￨- Diseasevolume￨U￨NNP￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 359￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2018￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- A￨U￨DT￨O￨- Correction￨U￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨A was￨L￨VBD￨O￨- published￨L￨VBN￨O￨- on￨L￨IN￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- This￨U￨DT￨O￨- article￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- updated￨L￨VBN￨O￨- AbstractReceptor-interacting￨U￨JJ￨O￨- protein￨L￨NN￨O￨- kinases￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 3￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- RIPK1/3￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- best￨L￨RB￨O￨- been￨L￨VBN￨O￨- described￨L￨VBN￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- mediating￨L￨VBG￨O￨- a￨L￨DT￨O￨- regulated￨L￨JJ￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- necrosis￨L￨NN￨O￨- ,￨L￨,￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- necroptosis￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- both￨L￨DT￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- MLKL-ko￨U￨JJ￨O￨- mice￨L￨NNS￨O￨A were￨L￨VBD￨O￨- significantly￨L￨RB￨O￨- protected￨L￨VBN￨O￨- from￨L￨IN￨O￨- injury￨L￨NN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- degree￨L￨NN￨O￨- that￨L￨WDT￨O￨- was￨L￨VBD￨O￨- slightly￨L￨RB￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- statistically￨L￨RB￨O￨- significantly￨L￨RB￨O￨- exceeding￨L￨VBG￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- RIPK3-deficient￨U￨JJ￨O￨- mice￨L￨NNS￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- sought￨L￨VBD￨O￨- to￨L￨TO￨O￨- further￨L￨RB￨O￨- examine￨L￨VB￨O￨- the￨L￨DT￨O￨- activation￨L￨NN￨O￨A of￨L￨IN￨O￨- necroptosis￨L￨NN￨O￨- in￨L￨IN￨O￨- kidney￨L￨NN￨O￨- ischemia-reperfusion￨L￨NN￨O￨- injury￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IRI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- TNFα-induced￨U￨JJ￨MISC￨- severe￨L￨JJ￨O￨- inflammatory￨L￨JJ￨O￨- response￨L￨NN￨O￨- syndrome￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- RIPK3-dependent￨U￨JJ￨O￨- injury￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- further￨L￨RBR￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- mode￨L￨NN￨O￨- of￨L￨IN￨O￨- regulation￨L￨NN￨O￨- of￨L￨IN￨O￨- cell￨L￨NN￨O￨A death￨L￨NN￨O￨- by￨L￨IN￨O￨- MLKL￨U￨NN￨ORGANIZATION￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- screened￨L￨VBD￨O￨- a￨L￨DT￨O￨- panel￨L￨NN￨O￨- of￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- plasma￨L￨NN￨O￨- membrane￨L￨NN￨O￨- channel￨L￨NN￨O￨- blockers￨L￨NNS￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- found￨L￨VBD￨O￨- phenytoin￨L￨NN￨O￨- to￨L￨TO￨O￨- inhibit￨L￨VB￨O￨- necroptosis￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- b￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- c￨L￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨A Add￨U￨VB￨O￨- E￨U￨NN￨O￨- I￨U￨PRP￨O￨- h￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- c￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- without￨L￨IN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- population￨L￨NN￨O￨- becoming￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- again￨L￨RB￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- recovery￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- Qi￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Cui￨U￨NNP￨PERSON￨- established￨L￨VBD￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- SEIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- forming￨L￨VBG￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨A Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- h￨L￨NN￨O￨- S￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- also￨L￨RB￨O￨- satisfied￨L￨VBD￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- characteristics.In￨L￨NN￨O￨- real￨L￨JJ￨O￨- life￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- transmitted￨L￨VBN￨O￨- through￨L￨IN￨O￨- both￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- HBV￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stability￨U￨NN￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resistance￨L￨NN￨O￨- SEIRS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rateJianwen￨L￨NN￨O￨- Jia1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- and￨L￨CC￨O￨- Jing￨U￨NN￨O￨- Xiao1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2018:75￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- SEIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- general￨L￨JJ￨TITLE￨- form￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resistance￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Add￨U￨VB￨O￨- E￨U￨NN￨O￨- I￨U￨PRP￨O￨- h￨L￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- h￨L￨NN￨O￨- satisfies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- for￨L￨IN￨O￨- GreaterThan￨U￨NNP￨O￨- x￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨PERSON￨- h￨L￨NN￨O￨- x￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- equality￨L￨NN￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- only￨L￨RB￨O￨- if￨L￨IN￨O￨- Equality￨U￨NN￨O￨- x￨L￨CC￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- where￨L￨WRB￨O￨- ′￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- differentiation￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- x￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- Re￨U￨NNP￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Re￨U￨NNP￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- geometric￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- some￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- knowledge￨L￨NN￨O￨- ,￨L￨,￨O￨- projective￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A of￨L￨IN￨O￨- fractional-order￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- was￨L￨VBD￨O￨- previously￨L￨RB￨DATE￨- investigated￨L￨VBN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- Laplace￨U￨NNP￨CITY￨- transform￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- special￨L￨JJ￨O￨- Lyapunov￨U￨NNP￨PERSON￨- functions￨L￨NNS￨O￨- were￨L￨VBD￨O￨- derived￨L￨VBN￨O￨- for￨L￨IN￨O￨- synchronization￨L￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Projective￨U￨JJ￨MISC￨- synchronization￨L￨NN￨O￨A of￨L￨IN￨O￨- fractional-order￨L￨NN￨O￨- delayed￨L￨VBN￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- comparison￨L￨NN￨O￨- principleWeiwei￨L￨NN￨O￨- Zhang1Email￨U￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Jinde￨U￨NNP￨PERSON￨- Cao2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ranchao￨U￨NNP￨O￨- Wu4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Ahmed￨U￨NNP￨PERSON￨- Alsaedi5￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Fuad￨U￨NNP￨PERSON￨- E.￨U￨NNP￨O￨- Alsaadi6￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:73￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- considers￨L￨VBZ￨O￨- projective￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨- of￨L￨IN￨O￨- fractional-order￨L￨NN￨O￨- delayed￨L￨VBN￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- results￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- projective￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A of￨L￨IN￨O￨- fractional-order￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- were￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- [￨L￨-LRB-￨O￨- 30￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 32￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- LMI-based￨U￨JJ￨MISC￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- Mittag￨U￨NNP￨O￨- –￨L￨:￨O￨- Leffler￨U￨NNP￨PERSON￨- projective￨L￨JJ￨O￨- synchronization￨L￨NN￨O￨A for￨L￨IN￨O￨- fractional-order￨L￨JJ￨O￨- neural￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- was￨L￨VBD￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- unavoidable￨L￨JJ￨O￨- in￨L￨IN￨O￨- biological￨L￨JJ￨O￨- ,￨L￨,￨O￨- engineering￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- neural￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- not￨L￨RB￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- in￨L￨IN￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- previous￨L￨JJ￨O￨- works￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- constructed￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- followed￨L￨VBD￨O￨- the￨L￨DT￨O￨- Logistic￨U￨JJ￨O￨- growth￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- γ￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- ε￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-induced￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- beta￨L￨NN￨O￨A I￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NN￨O￨- beta￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- textstyle￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Pow￨U￨NNP￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- All￨U￨PDT￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- nonnegative￨L￨JJ￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- The￨U￨DT￨MISC￨- persistence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Logistic￨U￨JJ￨O￨- growthJiamin￨L￨NN￨O￨- Liu1￨U￨NN￨O￨- ,￨L￨,￨O￨- Lijuan￨U￨NNP￨PERSON￨- Chen1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Fengying￨U￨NNP￨O￨- Wei1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:68￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Logistic￨U￨JJ￨O￨- growth￨L￨NN￨O￨A are￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- always￨L￨RB￨O￨- exists￨L￨VBZ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- LessThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- a￨L￨DT￨O￨- beta￨L￨NN￨O￨A Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- shall￨L￨MD￨O￨A consider￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- deterministic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- endemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NNP￨O￨- b￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- a￨L￨DT￨O￨- -1￨L￨CD￨NUMBER￨- r￨L￨NN￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- N.Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- periodic￨L￨JJ￨O￨A coefficients￨L￨NNS￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- main￨L￨JJ￨O￨- concerns￨L￨NNS￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- are￨L￨VBP￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- What￨U￨WP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- and￨L￨CC￨O￨- positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ?￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Random￨U￨NNP￨MISC￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- population￨L￨NN￨O￨- sizeDianli￨L￨NNS￨O￨- Zhao1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Sanling￨U￨VBG￨O￨- Yuan1￨U￨NN￨O￨- and￨L￨CC￨O￨- Haidong￨U￨NNP￨O￨- Liu2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2018:64￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- coefficients￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- this￨L￨DT￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- perturbations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- like￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- For￨U￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Lin￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Jiang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- solution￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- they￨L￨PRP￨O￨- showed￨L￨VBD￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- survival￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- understand￨L￨VBP￨O￨- the￨L￨DT￨O￨- instant￨L￨JJ￨O￨- situation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- contacting￨L￨VBG￨O￨- with￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- Zhang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Sun￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- feedback￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- :￨L￨:￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- given￨L￨VBN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- Theta￨U￨NNP￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- any￨L￨DT￨O￨- given￨L￨VBN￨O￨- link￨L￨NN￨O￨- pointing￨L￨VBG￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Theta￨U￨NNP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- langle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- rangle￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Sum￨U￨NN￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- P￨U￨NN￨O￨- k￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- P￨U￨NN￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- has￨L￨VBZ￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- with￨L￨IN￨O￨- Equality￨U￨NN￨O￨- Mul￨U￨NN￨O￨- langle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- rangle￨L￨NN￨O￨- Sum￨U￨NN￨O￨- Mul￨U￨NN￨O￨- P￨U￨NN￨O￨- k￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- StrictGreaterThan￨U￨NN￨O￨- alpha￨L￨NN￨O￨A 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- the￨L￨DT￨O￨- “￨L￨``￨O￨- fear￨L￨NN￨O￨- factor￨L￨NN￨O￨- .￨L￨.￨O￨- ”￨L￨''￨O￨- +This￨U￨DT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- written￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- They￨U￨PRP￨O￨- obtained￨L￨VBD￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- lambda￨L￨NN￨ORGANIZATION￨A Mul￨U￨NN￨ORGANIZATION￨- langle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- k￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- rangle￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- langle￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- rangle￨L￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- gamma￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- langle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- k￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- rangle￨L￨NN￨O￨- Sum￨U￨NN￨O￨- Mul￨U￨NN￨O￨- P￨U￨NN￨O￨- Pow￨U￨NN￨O￨- k￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Tuple￨U￨NN￨ORGANIZATION￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨DATE￨- 1￨L￨CD￨DATE￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- E￨U￨NN￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- Mul￨U￨NN￨PERSON￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- I￨U￨PRP￨PERSON￨- Mul￨U￨VBP￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Theta￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equation￨L￨NN￨O￨- f￨L￨FW￨O￨- Theta￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 1.6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Application￨U￨NN￨MISC￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- inequalities￨L￨NNS￨O￨- to￨L￨TO￨O￨- global￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNS￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨A treatment￨L￨NN￨O￨- functionShengqiang￨L￨NN￨O￨- Zhang1￨U￨NN￨O￨- ,￨L￨,￨O￨- Xinzhu￨U￨FW￨O￨- Meng1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- and￨L￨CC￨O￨- Xinzeng￨U￨NN￨O￨- Wang1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2018:50￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNS￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- standard￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- saturated￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- nu￨L￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- lambda￨L￨NN￨O￨A I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- dN￨L￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dS￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- d￨L￨NN￨O￨- r￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- d￨L￨NN￨O￨- nu￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- λ￨L￨VBP￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- ν￨L￨NN￨O￨- and￨L￨CC￨O￨- r￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- Mul￨U￨JJ￨O￨- lambda￨L￨NN￨O￨A Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- SIRS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- Mul￨U￨NNP￨O￨- lambda￨L￨NN￨O￨A Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- p￨L￨NN￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- q￨L￨VBP￨O￨- alpha￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- mean￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNS￨O￨- epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- techniques￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- inequalities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Review￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- A￨U￨DT￨O￨- review￨L￨NN￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A detection￨L￨NN￨O￨- and￨L￨CC￨O￨- prediction￨L￨NN￨O￨- through￨L￨IN￨O￨- social￨L￨JJ￨O￨- networking￨L￨NN￨O￨- sitesAli￨L￨NN￨O￨- Alessa1￨U￨NN￨O￨- and￨L￨CC￨O￨- Miad￨U￨NN￨O￨- Faezipour1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 15:2￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractEarly￨U￨NNP￨O￨- prediction￨L￨NN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- may￨L￨MD￨O￨- reduce￨L￨VB￨O￨- their￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- in￨L￨IN￨O￨- daily￨L￨JJ￨SET￨- lives￨L￨NNS￨O￨- .￨L￨.￨O￨- +Search￨U￨VB￨O￨- engines￨L￨NNS￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- networking￨L￨NN￨O￨- sites￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- track￨L￨VB￨O￨A trends￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- seven￨L￨CD￨DURATION￨- to￨L￨TO￨DURATION￨- ten￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- faster￨L￨RBR￨O￨- than￨L￨IN￨O￨- government￨L￨NN￨O￨- agencies￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Center￨U￨NNP￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Disease￨U￨NNP￨ORGANIZATION￨- Control￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Prevention￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- CDC￨U￨NNP￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +CDC￨U￨NNP￨ORGANIZATION￨- uses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- Illness-Like￨U￨NNP￨ORGANIZATION￨- Influenza￨U￨NNP￨ORGANIZATION￨- Surveillance￨U￨NNP￨ORGANIZATION￨- Network￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- ILINet￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- program￨L￨NN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- monitor￨L￨VB￨O￨- Influenza-Like￨U￨NNP￨O￨- Illness￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- ILI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- sent￨L￨VBN￨O￨- by￨L￨IN￨O￨- thousands￨L￨NNS￨O￨- of￨L￨IN￨O￨- health￨L￨NN￨O￨- care￨L￨NN￨O￨- providers￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- that￨L￨DT￨O￨- reason￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- aim￨L￨VBP￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- do￨L￨VBP￨O￨- real￨L￨JJ￨O￨- time￨L￨NN￨O￨- analysis￨L￨NN￨O￨- to￨L￨TO￨O￨- track￨L￨VB￨O￨A ILI￨U￨NNP￨O￨- using￨L￨VBG￨O￨- social￨L￨JJ￨O￨- networking￨L￨NN￨O￨- sites￨L￨NNS￨O￨- .￨L￨.￨O￨- +Social￨U￨NNP￨O￨- media￨L￨NNS￨O￨- data￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Twitter￨U￨NNP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- flu￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- help￨L￨VB￨O￨- in￨L￨IN￨O￨- getting￨L￨VBG￨O￨A early￨L￨JJ￨O￨- warnings￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- Pow￨U￨NN￨ORGANIZATION￨- D￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- alpha￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- g￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- h￨L￨NN￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- e￨L￨SYM￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Lambda￨U￨NNP￨ORGANIZATION￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- mu￨L￨NN￨O￨A Equality￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- D￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- alpha￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 3.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- reduces￨L￨VBZ￨O￨- to￨L￨TO￨O￨- false￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 3.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Second￨U￨NNP￨ORDINAL￨- ,￨L￨,￨O￨- let￨L￨VBD￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- makes￨L￨VBZ￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- h￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- leqslant￨L￨NN￨O￨- t￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- FDE￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelLet￨L￨NN￨O￨- us￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- IDE￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- g￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- r￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- d￨L￨NN￨ORGANIZATION￨- e￨L￨SYM￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Add￨U￨VB￨O￨- Lambda￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- mu￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- constructed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Iwami￨U￨NNP￨LOCATION￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Section￨U￨NN￨O￨- 4￨L￨CD￨NUMBER￨- discusses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- fixed￨L￨VBN￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- discretized-time￨L￨JJ￨O￨- SI￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- the￨L￨DT￨O￨- state-dependent￨L￨JJ￨O￨- impulse￨L￨NN￨O￨- fishing￨L￨NN￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- predators￨L￨NNS￨O￨- are￨L￨VBP￨O￨- produced￨L￨VBN￨O￨- by￨L￨IN￨O￨- supplementing￨L￨VBG￨O￨- preys￨L￨NNS￨O￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- Equality￨U￨NNP￨O￨- f￨L￨LS￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- y￨L￨NN￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- a￨L￨DT￨O￨- Add￨U￨VB￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NN￨O￨- f￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- y￨L￨NN￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- impulsive￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨PERSON￨- textstyle￨L￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨A fish￨L￨NN￨O￨- and￨L￨CC￨O￨- predator￨L￨NN￨O￨- fish￨L￨NN￨O￨- densities￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Periodic￨U￨JJ￨MISC￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- prey-predator￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- harvestingJianmei￨L￨NN￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- Huidong￨U￨NNP￨O￨- Cheng1Email￨U￨NNP￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Hongxia￨U￨NNP￨O￨- Liu1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Yanhui￨U￨NNP￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2018:41￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2018Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- prey-predator￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- state-dependent￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨- harvesting￨L￨NN￨O￨- and￨L￨CC￨O￨- constant￨L￨JJ￨O￨- rate￨L￨NN￨O￨- harvesting￨L￨NN￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- replenishment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- prey￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- harvesting￨L￨VBG￨O￨- rate￨L￨NN￨O￨- are￨L￨VBP￨O￨- linearly￨L￨RB￨O￨- related￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- selected￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨A fish￨L￨NN￨O￨- density￨L￨NN￨O￨- decreases￨L￨VBZ￨O￨- to￨L￨TO￨O￨- h￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- x￨L￨CC￨O￨- h￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ecological￨L￨JJ￨O￨- balance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fishery￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- in￨L￨IN￨O￨- disorder￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- must￨L￨MD￨O￨- replenish￨L￨VB￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨- fish￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- replenishment￨L￨NN￨O￨- rate￨L￨NN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- tau￨L￨VBD￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- harvest￨L￨NN￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨- fish￨L￨NN￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- Mul￨U￨NN￨O￨- q￨L￨NN￨O￨- in￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- harvest￨L￨VBP￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨- fish￨L￨NN￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- in￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- while￨L￨IN￨O￨- harvesting￨L￨VBG￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨- fish￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Preliminaries￨U￨NNPS￨O￨- Definition￨U￨NNP￨O￨- 2.1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Consider￨U￨VB￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- differential￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- state-dependent￨L￨JJ￨O￨- impulse￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- triangle￨L￨NN￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- beta￨L￨NN￨O￨- x￨L￨CC￨O￨- y￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- dynamic￨L￨JJ￨O￨- system￨L￨NN￨O￨- constituted￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨A mappings￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- a￨L￨DT￨O￨- semi-continuous￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- denoted￨L￨VBN￨O￨- as￨L￨IN￨O￨- Omega￨U￨NNP￨O￨- .￨L￨.￨O￨- +Inspired￨U￨VBN￨O￨- by￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- 39￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 43￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- unilateral￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- Gompertz￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- indicate￨L￨VBP￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- densities￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- patches￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- K￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨JJ￨O￨- environmental￨L￨JJ￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- within￨L￨IN￨O￨- patch￨L￨NN￨O￨A two￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- migration￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- from￨L￨IN￨O￨- patch￨L￨NN￨O￨- one￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- patch￨L￨NN￨O￨- two￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- K￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Preliminaries￨U￨NNPS￨O￨- Definition￨U￨NNP￨O￨- 2.1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Consider￨U￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- state-dependent￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- dynamic￨L￨JJ￨O￨- system￨L￨NN￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- solution￨L￨NN￨O￨A mapping￨L￨NN￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- a￨L￨DT￨O￨- semicontinuous￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- Omega￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- function￨L￨NN￨O￨- φ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- mapping￨L￨NN￨O￨- that￨L￨WDT￨O￨- meets￨L￨VBZ￨O￨- Equality￨U￨NN￨O￨- varphi￨L￨NN￨O￨- M￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- }￨L￨-RRB-￨O￨- M￨U￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- order-one￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨A of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- geometry￨L￨NN￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- monotonicity￨L￨NN￨O￨- of￨L￨IN￨O￨- successor￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- order-one￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨A solution￨L￨NN￨O￨A by￨L￨IN￨O￨- the￨L￨DT￨O￨- geometry￨L￨NN￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- successor￨L￨NN￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- tools￨L￨NNS￨O￨A implement￨L￨VBP￨O￨- numerical￨L￨JJ￨O￨- algorithms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- compute￨L￨VBP￨O￨- probabilities￨L￨NNS￨O￨- up￨L￨IN￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- precision￨L￨NN￨O￨- ,￨L￨,￨O￨- suffering￨L￨VBG￨O￨- though￨L￨IN￨O￨- from￨L￨IN￨O￨- state￨L￨NN￨O￨- space￨L￨NN￨O￨- explosion￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- simulation￨L￨NN￨O￨- engines￨L￨NNS￨O￨- that￨L￨WDT￨O￨- allow￨L￨VBP￨O￨- statistical￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- when￨L￨WRB￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- too￨L￨RB￨O￨- large.All￨L￨JJ￨O￨- classic￨L￨JJ￨O￨- quantitative￨L￨JJ￨O￨- verification￨L￨NN￨O￨- tools￨L￨NNS￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- fully￨L￨RB￨O￨- specified￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- application￨L￨NN￨O￨- domains￨L￨NNS￨O￨- like￨L￨IN￨O￨- system￨L￨NN￨O￨- biology￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- many￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- estimated￨L￨VBN￨O￨- from￨L￨IN￨O￨- data￨L￨NNS￨O￨- or￨L￨CC￨O￨- are￨L￨VBP￨O￨- only￨L￨RB￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- belong￨L￨VB￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- range￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- Tools￨U￨NNS￨O￨- and￨L￨CC￨O￨- Algorithms￨U￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Construction￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Analysis￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Systems￨U￨NNPS￨ORGANIZATION￨- pp￨L￨NN￨O￨- 396-413￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asBayesian￨L￨JJ￨O￨- Statistical￨U￨JJ￨O￨- Parameter￨U￨NN￨O￨- Synthesis￨U￨NN￨O￨- for￨L￨IN￨O￨- Linear￨U￨NNP￨O￨- Temporal￨U￨JJ￨O￨- Properties￨U￨NNPS￨O￨- of￨L￨IN￨O￨- Stochastic￨U￨NNP￨O￨- ModelsAuthorsAuthors￨U￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsLuca￨L￨NNP￨O￨- BortolussiSimone￨U￨NNP￨MISC￨- SilvettiOpen￨U￨NNP￨MISC￨- AccessConference￨U￨NNP￨MISC￨- paperFirst￨L￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- 3￨L￨CD￨NUMBER￨- Readers￨U￨NNS￨O￨- 1.2￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- Part￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Lecture￨U￨NNP￨O￨- Notes￨U￨NNP￨O￨- in￨L￨IN￨O￨- Computer￨U￨NNP￨O￨- Science￨U￨NNP￨O￨- book￨L￨NN￨O￨- series￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LNCS￨U￨NN￨O￨- ,￨L￨,￨O￨- volume￨L￨NN￨O￨- 10806￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- AbstractParameterized￨U￨NNP￨O￨- verification￨L￨NN￨O￨- of￨L￨IN￨O￨- temporal￨L￨JJ￨O￨- properties￨L￨NNS￨O￨A is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- research￨L￨NN￨O￨- area￨L￨NN￨O￨- ,￨L￨,￨O￨- being￨L￨VBG￨O￨- extremely￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- model-based￨L￨JJ￨O￨- design￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- focus￨L￨VBP￨O￨- on￨L￨IN￨O￨- parameter￨L￨NN￨O￨- synthesis￨L￨NN￨O￨- for￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- looking￨L￨VBG￨O￨- for￨L￨IN￨O￨- regions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- satisfies￨L￨VBZ￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- time￨L￨NN￨O￨- specification￨L￨NN￨O￨- with￨L￨IN￨O￨- probability￨L￨NN￨O￨- greater￨L￨JJR￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- less￨L￨JJR￨O￨- )￨L￨-RRB-￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- applicable￨L￨JJ￨O￨- to￨L￨TO￨O￨- linear￨L￨JJ￨O￨- time￨L￨NN￨O￨- specifications￨L￨NNS￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- constraints￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨A models￨L￨NNS￨O￨A than￨L￨IN￨O￨- Markov￨U￨NNP￨PERSON￨- Chains.KeywordsParameter￨U￨NNP￨O￨- synthesis￨L￨NN￨O￨- Parametric￨U￨NNP￨ORGANIZATION￨- verification￨L￨NN￨O￨- Smoothed￨U￨VBN￨O￨- model￨L￨NN￨TITLE￨- checking￨L￨VBG￨O￨- Gaussian￨U￨NNP￨O￨- Processes￨U￨NNP￨O￨- Download￨U￨VB￨O￨- conference￨L￨NN￨O￨- paper￨L￨NN￨O￨- PDF1￨U￨NN￨O￨- IntroductionOverview￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- approach￨L￨NN￨O￨- relying￨L￨VBG￨O￨- on￨L￨IN￨O￨- simulation￨L￨NN￨O￨- and￨L￨CC￨O￨- leveraging￨L￨VBG￨O￨- a￨L￨DT￨O￨- machine￨L￨NN￨O￨- learning￨L￨NN￨O￨- method￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Gaussian￨U￨NNP￨O￨- Processes￨U￨NNP￨O￨- for￨L￨IN￨O￨- statistical￨L￨JJ￨O￨- parametric￨L￨JJ￨O￨A verification￨L￨NN￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- Smoothed￨U￨VBN￨O￨- Model￨U￨NNP￨TITLE￨- Checking￨U￨NNP￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Holling￨U￨JJ￨PERSON￨- type￨L￨NN￨O￨- II￨U￨CD￨NUMBER￨- functional￨L￨JJ￨O￨- response￨L￨NN￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨- and￨L￨CC￨O￨- obtained￨L￨VBN￨O￨- sufficient￨L￨JJ￨O￨A conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- principle￨L￨NN￨O￨- of￨L￨IN￨O￨- competitive￨L￨JJ￨O￨- exclusion￨L￨NN￨O￨- ;￨L￨:￨O￨- they￨L￨PRP￨O￨- also￨L￨RB￨O￨- provided￨L￨VBD￨O￨- numerical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- to￨L￨TO￨O￨- verify￨L￨VB￨O￨- their￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- Milstein￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- higher￨L￨JJR￨O￨- order￨L￨NN￨O￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +Zhao￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Yuan￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- formulated￨L￨VBD￨O￨- a￨L￨DT￨O￨- single-species￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- periodic￨L￨JJ￨O￨A coefficients￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- seasonal￨L￨JJ￨O￨- fluctuation￨L￨NN￨O￨- ;￨L￨:￨O￨- they￨L￨PRP￨O￨- obtained￨L￨VBD￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- condition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- random￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- .￨L￨.￨O￨- +Standard￨U￨NNP￨O￨- Brownian￨U￨NNP￨O￨- motion￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- tool￨L￨NN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- system.Scholars￨L￨NNS￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- by￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- obtained￨L￨VBN￨O￨A many￨L￨JJ￨O￨- important￨L￨JJ￨O￨- results￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- periodic￨L￨JJ￨O￨A wash-out￨L￨JJ￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- established￨L￨JJ￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- nontrivial￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Li￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- competition￨L￨NN￨O￨- turbidostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- inconstant￨L￨JJ￨O￨- dilution￨L￨NN￨O￨- rate￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨ORGANIZATION￨- d￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- k￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- dynamic￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- deterministic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- expressed￨L￨VBN￨O￨- by￨L￨IN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- mu￨L￨NN￨O￨A p￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- A￨U￨DT￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- alpha￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- mu￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- V￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- A￨U￨DT￨O￨- q￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- input￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- members￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- q￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- LessThan￨U￨NN￨ORGANIZATION￨- LessThan￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- for￨L￨IN￨O￨- newborns￨L￨NNS￨O￨- ;￨L￨:￨O￨- β￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- per￨L￨IN￨O￨- capita￨L￨NN￨O￨- ,￨L￨,￨O￨- p￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- proportional￨L￨JJ￨O￨- coefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- losing￨L￨VBG￨O￨- immunity￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-caused￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- regime￨L￨NN￨O￨- switching￨L￨NN￨O￨A SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- Lévy￨U￨NNP￨O￨- noise.Keywordsstochastic￨L￨NNP￨O￨- SIS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- modelvaccinationLévy￨L￨NN￨O￨- noiseMarkov￨L￨NN￨O￨- switchingglobal￨L￨NN￨O￨- positive￨L￨JJ￨O￨- solutionasymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionIt￨U￨NN￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- that￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- SARS￨U￨NNP￨O￨- ,￨L￨,￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- etc.￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- always￨L￨RB￨O￨- bring￨L￨VB￨O￨- great￨L￨JJ￨O￨- harm￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- and￨L￨CC￨O￨- threat￨L￨NN￨O￨- individual￨L￨JJ￨O￨- health￨L￨NN￨O￨- ,￨L￨,￨O￨- Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- society￨L￨NN￨O￨- and￨L￨CC￨O￨- frequent￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- among￨L￨IN￨O￨- people￨L￨NNS￨O￨- can￨L￨MD￨O￨- accelerate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Zhao￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Jiang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- stochastically￨L￨RB￨O￨- perturbed￨L￨VBN￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- B￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Equality￨U￨NN￨O￨- i￨L￨FW￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- independent￨L￨JJ￨RELIGION￨- Brownian￨U￨JJ￨MISC￨- motions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sigma￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- their￨L￨PRP$￨O￨- intensities￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- application￨L￨NN￨O￨- to￨L￨TO￨O￨- perturbed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- discussed.KeywordsSemi-Markov￨L￨JJ￨O￨- process￨L￨NN￨O￨- Perturbation￨U￨NN￨O￨- Asymptotic￨U￨JJ￨O￨- expansion￨L￨NN￨O￨- Regenerative￨U￨JJ￨O￨- process￨L￨NN￨O￨- Renewal￨U￨NN￨O￨- equation￨L￨NN￨O￨- Solidarity￨U￨NNP￨ORGANIZATION￨- property￨L￨NN￨O￨- First￨U￨NNP￨ORDINAL￨- hitting￨L￨VBG￨O￨- time￨L￨NN￨O￨- Mathematics￨U￨NNS￨O￨- Subject￨U￨NNP￨O￨- Classifications￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- 60K15￨L￨NNP￨O￨- 41A60￨L￨CD￨NUMBER￨- 60K05￨L￨NNP￨O￨- Download￨U￨VB￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- article￨L￨NN￨O￨- textReferencesAllen￨L￨NN￨O￨- LJS￨U￨NN￨O￨- ,￨L￨,￨O￨- Burgin￨U￨NNP￨PERSON￨- AM￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Comparison￨U￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- and￨L￨CC￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Linear￨U￨JJ￨O￨- Algebra￨U￨NNP￨O￨- Appl￨U￨NN￨O￨- 386:243￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 259MathSciNetCrossRefzbMATHGoogle￨L￨JJ￨O￨- ScholarBlanchet￨U￨NN￨O￨- J￨U￨NN￨O￨- ,￨L￨,￨O￨- Zwart￨U￨NN￨PERSON￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- Asymptotic￨U￨JJ￨O￨- expansions￨L￨NNS￨O￨- of￨L￨IN￨O￨- defective￨L￨JJ￨O￨- renewal￨L￨NN￨O￨- equations￨L￨NNS￨O￨- with￨L￨IN￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- perturbed￨L￨VBN￨O￨- risk￨L￨NN￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- processor￨L￨NN￨TITLE￨- sharing￨L￨NN￨O￨- queues￨L￨NNS￨O￨- .￨L￨.￨O￨- +Math￨U￨NNP￨O￨- Biosci￨U￨NNP￨O￨- 163:1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 33MathSciNetCrossRefzbMATHGoogle￨L￨NN￨O￨- ScholarAltman￨U￨NN￨O￨- E￨U￨NN￨O￨- ,￨L￨,￨O￨- Avrachenkov￨U￨NNP￨PERSON￨- KE￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Núñez-Queija￨U￨NNP￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2004￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Perturbation￨U￨NN￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- denumerable￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- chains￨L￨NNS￨O￨- with￨L￨IN￨O￨- application￨L￨NN￨O￨A to￨L￨TO￨O￨- queueing￨L￨VBG￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Pow￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- D￨U￨NNP￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- serves￨L￨VBZ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- parameter￨L￨NN￨O￨- that￨L￨WDT￨O￨- predicts￨L￨VBZ￨O￨- whether￨L￨IN￨O￨- the￨L￨DT￨O￨- coexistence￨L￨NN￨O￨A will￨L￨MD￨O￨- exist￨L￨VB￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- operator￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- related￨L￨JJ￨O￨- eigenvalue￨L￨NN￨O￨- problems￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- first-order￨L￨JJ￨O￨- differential￨L￨JJ￨O￨A equations￨L￨NNS￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- ,￨L￨,￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ith￨L￨NN￨O￨- species￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- widehat￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ith￨L￨NN￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- K￨U￨NN￨O￨- widehat￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- widehat￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- harvesting￨L￨VBG￨O￨- effort￨L￨NN￨O￨- upon￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- species￨L￨NNS￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨LS￨NUMBER￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- provide￨L￨VBP￨O￨- illustrated￨L￨JJ￨O￨- numerical￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- to￨L￨TO￨O￨- verify￨L￨VB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- results￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- study.Keywordsfractional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equationsstability￨L￨NN￨O￨- analysismutualism￨L￨NN￨O￨- modelCaputo￨L￨NN￨O￨- fractional￨L￨JJ￨O￨A derivativeLyapunov￨L￨NN￨O￨- function￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionA￨U￨NN￨O￨- population￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- many￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- concerning￨L￨VBG￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- delay￨L￨NN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- fractional￨L￨JJ￨O￨A differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 31￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 35￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- linearization￨L￨NN￨O￨- and￨L￨CC￨O￨- Lyapunov￨U￨NN￨PERSON￨- methods￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- popular￨L￨JJ￨O￨- technique￨L￨NN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- without￨L￨IN￨O￨- visibly￨L￨RB￨O￨- solving￨L￨VBG￨O￨- the￨L￨DT￨O￨- equations￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 36￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 38￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨PERSON￨- StrictLessThan￨U￨NNP￨PERSON￨- 1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- and￨L￨CC￨O￨- LessThan￨U￨NNP￨O￨- LessThan￨U￨NNP￨O￨- LessThan￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- q￨L￨VB￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- q￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Let￨U￨VB￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- q￨L￨NN￨O￨- and￨L￨CC￨O￨- GreaterThan￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- Pow￨U￨NN￨O￨- p￨L￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- N￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- q￨L￨VB￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- 2.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- are￨L￨VBP￨O￨- interested￨L￨JJ￨O￨- in￨L￨IN￨O￨- mild￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- u￨L￨NN￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2.5￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2.5￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2.5￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- (￨L￨-LRB-￨O￨- 2.6￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2.6￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2.6￨L￨CD￨NUMBER￨- c￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- zeta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- alpha￨L￨NN￨O￨A }￨L￨-RRB-￨O￨- theta￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- probability￨L￨NN￨O￨- density￨L￨NN￨O￨- function￨L￨NN￨O￨- defined￨L￨VBN￨O￨- on￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Γ￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- contour￨L￨NN￨O￨- starting￨L￨VBG￨O￨- and￨L￨CC￨O￨- ending￨L￨VBG￨O￨- at￨L￨IN￨O￨- −￨L￨CD￨NUMBER￨- ∞￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- the￨L￨DT￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- semigroups￨L￨NNS￨O￨- G￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- for￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- operators￨L￨NNS￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- T￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- alpha￨L￨NN￨O￨A }￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- alpha￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- i￨L￨FW￨O￨- t￨L￨NN￨O￨- for￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- ones.Consider￨L￨NN￨O￨- the￨L￨DT￨O￨- fractional￨L￨JJ￨O￨- system￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- d￨L￨NN￨O￨- alpha￨L￨NN￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- dt￨L￨NN￨O￨- alpha￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- A￨U￨DT￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- f￨L￨FW￨O￨- x￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- 2.7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- in￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mul￨U￨NN￨PERSON￨- A￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NN￨O￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- f￨L￨FW￨O￨- Mul￨U￨FW￨O￨- Pow￨U￨NN￨O￨- C￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- D￨U￨NN￨ORGANIZATION￨- f￨L￨FW￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- solution￨L￨NN￨O￨- in￨L￨IN￨O￨- Besov￨U￨NNP￨LOCATION￨- spaces￨L￨NNS￨O￨A for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- d￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- regularity￨L￨NN￨O￨- initial￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- matter￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- solution￨L￨NN￨O￨- ,￨L￨,￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- spatial￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- discrete￨L￨JJ￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- given￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- global￨L￨JJ￨O￨A asymptotic￨L￨JJ￨O￨A stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibria￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- Lyapunov￨U￨NNP￨PERSON￨- functionals￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Different￨U￨JJ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- schemes￨L￨NNS￨O￨- ,￨L￨,￨O￨- Mickens￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- efficient￨L￨JJ￨O￨- in￨L￨IN￨O￨- preserving￨L￨VBG￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A asymptotic￨L￨JJ￨O￨A stability￨L￨NN￨O￨- for￨L￨IN￨O￨- equilibria￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- models￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- [￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- PreliminariesRearranging￨U￨VBG￨O￨- the￨L￨DT￨O￨- equations￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- gives￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- It￨U￨PRP￨O￨- follows￨L￨VBZ￨O￨- from￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- initial￨L￨JJ￨O￨A condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- remain￨L￨VBP￨O￨- nonnegative￨L￨JJ￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- Mul￨U￨NN￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stationary￨U￨JJ￨MISC￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- information￨L￨NN￨O￨- interventionKangbo￨L￨NN￨O￨- Bao1￨U￨NN￨O￨- and￨L￨CC￨O￨- Qimin￨U￨NNP￨O￨- Zhang1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:352￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- considers￨L￨VBZ￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- intervention￨L￨NN￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- noise￨L￨NN￨O￨A is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- noise￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathscr￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- stationary￨L￨JJ￨O￨A distribution￨L￨NN￨O￨A is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- prevalent￨L￨JJ￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- production￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathscr￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- threshold￨L￨NN￨O￨- which￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨A or￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- SIR￨U￨NN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- information￨L￨NN￨O￨A intervention￨L￨NN￨O￨- and￨L￨CC￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- information￨L￨NN￨O￨- could￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- noise￨L￨NN￨O￨A is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathscr￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- die￨L￨VB￨O￨- out￨L￨RP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A problems￨L￨NNS￨O￨- are￨L￨VBP￨O￨- procured￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- Pontryagin￨U￨NNP￨LOCATION￨- ’s￨L￨POS￨O￨- maximum￨L￨NN￨O￨- principle￨L￨NN￨O￨- and￨L￨CC￨O￨- determined￨L￨VBD￨O￨- numerically￨L￨RB￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- progressive-regressive￨L￨JJ￨O￨- discrete￨L￨JJ￨O￨- schema￨L￨NN￨O￨- that￨L￨WDT￨O￨- converges￨L￨VBZ￨O￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- convenient￨L￨JJ￨O￨- test￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Forward-Backward￨U￨NNP￨MISC￨- Sweep￨U￨NNP￨MISC￨- Method￨U￨NNP￨MISC￨- (￨L￨-LRB-￨O￨- FBSM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control.Keywordsdiscrete￨L￨NN￨O￨- marital￨L￨JJ￨O￨- status￨L￨NN￨O￨- modelmonogamous￨L￨JJ￨O￨- marriagePontryagin￨L￨NN￨O￨- ’s￨L￨POS￨O￨- maximum￨L￨NN￨O￨- principleoptimal￨L￨NN￨O￨- control￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionThere￨U￨NNP￨O￨- are￨L￨VBP￨O￨- different￨L￨JJ￨O￨- categories￨L￨NNS￨O￨- of￨L￨IN￨O￨- marriage￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Discrete￨U￨NNP￨MISC￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- marital￨L￨JJ￨O￨- status￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- monogamous￨L￨JJ￨O￨- marriage￨L￨NN￨O￨- caseMustapha￨L￨NN￨O￨- Lhous1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Mostafa￨U￨NNP￨PERSON￨- Rachik2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Hassan￨U￨NNP￨PERSON￨- Laarabi2￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Ahmed￨U￨NNP￨PERSON￨- Abdelhak3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:339￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- marital￨L￨JJ￨O￨- status￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- family￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨A of￨L￨IN￨O￨- an￨L￨DT￨O￨- awareness￨L￨NN￨O￨- campaign￨L￨NN￨O￨- to￨L￨TO￨O￨- educate￨L￨VB￨O￨- virgin￨L￨JJ￨O￨- men￨L￨NNS￨O￨- and￨L￨CC￨O￨- women￨L￨NNS￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- benefits￨L￨NNS￨O￨- of￨L￨IN￨O￨- marriage￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- society￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- control￨L￨NN￨O￨- characterizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- legal￨L￨JJ￨O￨- procedures￨L￨NNS￨O￨- ,￨L￨,￨O￨- administrative￨L￨JJ￨O￨- complications￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- heavy￨L￨JJ￨O￨- financial￨L￨JJ￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- divorces￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- treat￨L￨VB￨O￨- the￨L￨DT￨O￨- modeling￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- that￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- monogamous￨L￨JJ￨O￨- marriage.Mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- functioning￨L￨NN￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- evolution￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- Pow￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- s￨L￨VBZ￨O￨- mathcal￨L￨JJ￨O￨A 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- becomes￨L￨VBZ￨O￨- extinct￨L￨JJ￨O￨- exponentially￨L￨RB￨O￨- ;￨L￨:￨O￨- whereas￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- s￨L￨VBZ￨O￨- mathcal￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- beta￨L￨NN￨O￨- i￨L￨FW￨O￨- alpha￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- can￨L￨MD￨O￨- converge￨L￨VB￨O￨- in￨L￨IN￨O￨- Pow￨U￨NNP￨O￨- L￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- invariant￨L￨JJ￨O￨- density.Keywordsstationary￨L￨JJ￨O￨- distributionMarkov￨L￨NN￨O￨- semigroupsasymptotic￨L￨JJ￨O￨- stabilityMSC47D0760J6060H1092D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionA￨U￨NN￨O￨- deterministic￨L￨JJ￨O￨- Susceptible-Infective￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- standard￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Lambda￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Here￨U￨RB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- Λ￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- influx￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptibles￨L￨NNS￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-related￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate.Because￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- noises￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- appearing￨L￨VBG￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- emphatically￨L￨RB￨O￨- not￨L￨RB￨O￨- constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +Incorporating￨U￨VBG￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- noises￨L￨NNS￨O￨- into￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- get￨L￨VBP￨O￨- a￨L￨DT￨O￨- regime-switching￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- Lambda￨U￨NNP￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- sigma￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constants.Recently￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- long-time￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- regime￨L￨NN￨O￨- switching￨L￨NN￨O￨A was￨L￨VBD￨O￨- considered￨L￨VBN￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- ellipticity￨L￨NN￨O￨- condition￨L￨NN￨O￨- was￨L￨VBD￨O￨- needed￨L￨VBN￨O￨- when￨L￨WRB￨O￨- proving￨L￨VBG￨O￨- the￨L￨DT￨O￨- ergodicity￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- suitable￨L￨JJ￨O￨- Lyapunov￨U￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- attractiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system.Keywordsepidemic￨L￨JJ￨O￨- spreadingscale-free￨L￨JJ￨O￨- networkbasic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- numberglobal￨L￨JJ￨O￨- attractivenesstime￨L￨NN￨O￨- delay￨L￨NN￨O￨A 1￨L￨CD￨NUMBER￨- IntroductionFollowing￨U￨NNP￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- seminal￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- small-world￨L￨JJ￨O￨- network￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- by￨L￨IN￨O￨- Watts￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Strogatz￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- p￨L￨NN￨O￨- k￨L￨NN￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- node￨L￨NN￨O￨- with￨L￨IN￨O￨- k￨L￨NN￨O￨- links￨L￨NNS￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- distributed￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- power￨L￨NN￨O￨- law￨L￨NN￨O￨- Equality￨U￨NN￨O￨- p￨L￨NN￨O￨- k￨L￨NN￨O￨- Mul￨U￨NN￨O￨- C￨U￨NN￨O￨- Pow￨U￨NN￨O￨- k￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- StrictLessThan￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- le￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- suggested￨L￨VBN￨O￨- by￨L￨IN￨O￨- Barabási￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Albert￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- by￨L￨IN￨O￨- many￨L￨JJ￨O￨- researchers￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Chen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- present￨L￨VB￨DATE￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- functional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- SIRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨A represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨- vector￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- network.Assuming￨L￨VBG￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- N￨U￨NN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- suppose￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- time-invariant￨L￨JJ￨O￨- and￨L￨CC￨O￨- p￨L￨NN￨O￨- k￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Kang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Fu￨U￨NNP￨PERSON￨- also￨L￨RB￨O￨- established￨L￨VBD￨O￨- a￨L￨DT￨O￨- functional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- infective￨L￨JJ￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on.Considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- individual￨L￨NN￨O￨- may￨L￨MD￨O￨- become￨L￨VB￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- Chen￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Sun￨U￨NNP￨PERSON￨- discussed￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- without￨L￨IN￨O￨- delay￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- give￨L￨VBP￨O￨- an￨L￨DT￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- prove￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dies￨L￨VBZ￨O￨- out￨L￨RP￨O￨- when￨L￨WRB￨O￨- StrictLessThan￨U￨NNP￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- uniformly￨L￨RB￨O￨- persistent￨L￨JJ￨O￨- when￨L￨WRB￨O￨- StrictGreaterThan￨U￨NNP￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- nonlinear￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- competition￨L￨NN￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A effectXuejin￨L￨NN￨O￨- Lv1￨U￨NN￨O￨- ,￨L￨,￨O￨- Lu￨U￨NNP￨PERSON￨- Wang2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Xinzhu￨U￨NNP￨O￨- Meng1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2017:296￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- competition￨L￨NN￨O￨- chemostat￨L￨NN￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- impulsive￨L￨JJ￨O￨- toxicant￨L￨NN￨O￨- input￨L￨NN￨O￨- .￨L￨.￨O￨- +Second￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- qualitative￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A stochastic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- in￨L￨IN￨O￨- mean￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- microorganisms￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- main￨L￨JJ￨O￨- purpose￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- high-dimensional￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- find￨L￨VB￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- between￨L￨IN￨O￨- persistence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- chemostat￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- between￨L￨IN￨O￨- persistence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A toxicant￨L￨NN￨O￨- input￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- microorganisms￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- polluted￨L￨JJ￨O￨- environment￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 18￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Mathematical￨U￨JJ￨MISC￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- macroalgaeArtorn￨L￨NN￨O￨- Nokkaew1￨U￨NN￨O￨- ,￨L￨,￨O￨- Charin￨U￨NNP￨O￨- Modchang2￨U￨NNP￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Somkid￨U￨NNP￨O￨- Amornsamankul3￨U￨NNP￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yongwimon￨U￨NNP￨O￨- Lenbury3￨U￨NNP￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Busayamas￨U￨NNP￨O￨- Pimpunchat5￨U￨NNP￨O￨- and￨L￨CC￨O￨- Wannapong￨U￨NNP￨O￨- Triampo2￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2017:288￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractUnderstanding￨U￨VBG￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- algae￨L￨NN￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- significant￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨A for￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- intervention￨L￨NN￨O￨- and/or￨L￨CC￨O￨- prevention￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- this￨L￨DT￨O￨- reason￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- computationally￨L￨RB￨O￨- model￨L￨VBP￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- algae￨L￨NN￨O￨- reservoir￨L￨NN￨O￨- or￨L￨CC￨O￨- container￨L￨NN￨O￨- systems￨L￨NNS￨O￨- consisting￨L￨VBG￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- patches￨L￨NNS￨O￨A or￨L￨CC￨O￨- clusters￨L￨NNS￨O￨- of￨L￨IN￨O￨- algae￨L￨NN￨O￨- being￨L￨VBG￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- contagious￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SEIR￨U￨NN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- dividing￨L￨VBG￨O￨- the￨L￨DT￨O￨- whole￨L￨JJ￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- groups￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- never￨L￨RB￨O￨- contacted￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- S￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- infected￨L￨VBN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- hesitate￨L￨VB￨O￨- state￨L￨NN￨O￨- not￨L￨RB￨O￨- spreading￨L￨VBG￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- E￨U￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- accepted￨L￨VBN￨O￨- and￨L￨CC￨O￨- spread￨L￨VBN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- I￨U￨PRP￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- ,￨L￨,￨O￨- referring￨L￨VBG￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- know￨L￨VBP￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- but￨L￨CC￨O￨- have￨L￨VBP￨O￨- ceased￨L￨VBN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- it￨L￨PRP￨O￨- ,￨L￨,￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- R.￨U￨NNP￨O￨- Based￨U￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- hypotheses￨L￨NNS￨O￨- and￨L￨CC￨O￨- notation￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- mean-field￨L￨JJ￨O￨- reaction￨L￨NN￨O￨- rate￨L￨NN￨O￨- equations￨L￨NNS￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- StrictGreaterThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- k￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- acceptability￨L￨NN￨O￨- of￨L￨IN￨O￨- k￨L￨NN￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- Theta￨U￨NNP￨O￨- t￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- link￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infected￨L￨JJ￨O￨- individual￨L￨NN￨O￨- ,￨L￨,￨O￨- satisfying￨L￨VBG￨O￨- Equality￨U￨NNP￨O￨- Theta￨U￨NNP￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- langle￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- k￨L￨NN￨O￨- rangle￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- Pow￨U￨NNP￨O￨- i￨L￨FW￨O￨- -1￨L￨CD￨NUMBER￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- i￨L￨FW￨O￨- ,￨L￨,￨O￨- will￨L￨MD￨O￨- contact￨L￨VB￨O￨- this￨L￨DT￨O￨- individual￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- time￨L￨NN￨O￨- step￨L￨NN￨O￨- ;￨L￨:￨O￨- P￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨NN￨O￨- of￨L￨IN￨O￨- degree￨L￨NN￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- with￨L￨IN￨O￨- degree￨L￨NN￨O￨- i.￨L￨NN￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- immigration￨L￨NN￨O￨- and￨L￨CC￨O￨- emigration￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- and￨L￨CC￨O￨- analyze￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- hesitating￨L￨VBG￨O￨- mechanism￨L￨NN￨O￨- on￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- and￨L￨CC￨O￨- comprehensively￨L￨RB￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- globally￨L￨RB￨O￨- asymptotical￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A in￨L￨IN￨O￨- detail.The￨L￨NNP￨O￨- rest￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- rumor￨L￨NN￨O￨A spreading￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- demographics￨L￨NNS￨O￨- on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networksChen￨L￨NN￨O￨- Wan1￨U￨NN￨O￨- ,￨L￨,￨O￨- Tao￨U￨NNP￨O￨- Li1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Zhicheng￨U￨NNP￨O￨- Sun1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:253￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-exposed-infected-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- demographics￨L￨NNS￨O￨- on￨L￨IN￨O￨- scale-free￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Although￨U￨IN￨O￨- references￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- hesitating￨L￨VBG￨O￨- mechanism￨L￨NN￨O￨- ,￨L￨,￨O￨- neither￨L￨CC￨O￨- could￨L￨MD￨O￨- serve￨L￨VB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- strict￨L￨JJ￨O￨- proof￨L￨NN￨O￨- of￨L￨IN￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Geometrical￨U￨JJ￨MISC￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- optimization￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- predator-prey￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- multi￨L￨NNS￨O￨- state-dependent￨L￨JJ￨O￨- impulseJianmei￨L￨NN￨O￨- Wang1￨U￨NN￨O￨- ,￨L￨,￨O￨- Huidong￨U￨NNP￨O￨- Cheng1Email￨U￨NNP￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Xinzhu￨U￨FW￨O￨- Meng1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- BG￨U￨NNP￨ORGANIZATION￨- Sampath￨U￨NNP￨ORGANIZATION￨- Aruna￨U￨NNP￨ORGANIZATION￨- Pradeep3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:252￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- predator-prey￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Holling￨U￨NNP￨PERSON￨- type-I￨L￨NN￨O￨- functional￨L￨JJ￨O￨- response￨L￨NN￨O￨- and￨L￨CC￨O￨- multi￨L￨JJ￨O￨- state￨L￨NN￨O￨- impulsive￨L￨JJ￨O￨A feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- is￨L￨VBZ￨O￨- established￨L￨VBN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- pesticide￨L￨NN￨O￨- spraying￨L￨VBG￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- release￨L￨NN￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- enemies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- linearly￨L￨RB￨O￨- dependent￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- given￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- impulse￨L￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- pest￨L￨NN￨O￨- management￨L￨NN￨O￨- control￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- time￨L￨NN￨O￨- impulse￨L￨NN￨O￨- was￨L￨VBD￨O￨- presented￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- were￨L￨VBD￨O￨- studied￨L￨VBN￨O￨- by￨L￨IN￨O￨- Zhang￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- established￨L￨VBN￨O￨- a￨L￨DT￨O￨- pest￨L￨NN￨O￨- control￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- Holling￨U￨NNP￨PERSON￨- type-I￨L￨NN￨O￨- functional￨L￨JJ￨O￨A response￨L￨NN￨O￨- and￨L￨CC￨O￨- studied￨L￨VBD￨O￨- its￨L￨PRP$￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- attractiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- order-1￨L￨NN￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- worthy￨L￨JJ￨O￨- to￨L￨TO￨O￨- note￨L￨VB￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- scholars￨L￨NNS￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- single￨L￨JJ￨O￨- state￨L￨NN￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- on￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- only￨L￨RB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- reaches￨L￨VBZ￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- threshold￨L￨NN￨O￨- .￨L￨.￨O￨- +considered￨L￨VBN￨O￨- a￨L￨DT￨O￨- pest￨L￨NN￨O￨- management￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- state￨L￨NN￨O￨- impulsive￨L￨JJ￨O￨A control￨L￨NN￨O￨- and￨L￨CC￨O￨- Holling￨U￨NN￨PERSON￨- type-II￨L￨JJ￨O￨- functional￨L￨JJ￨O￨- response￨L￨NN￨O￨- and￨L￨CC￨O￨- focused￨L￨VBD￨O￨- their￨L￨PRP$￨O￨- attention￨L￨NN￨O￨- on￨L￨IN￨O￨- geometric￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- further￨L￨JJ￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- readers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- directed￨L￨VBN￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨A the￨L￨DT￨O￨- references￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 35￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 37￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Parameters￨U￨NNPS￨O￨- Description￨U￨NN￨O￨- A￨U￨DT￨O￨- The￨U￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- by￨L￨IN￨O￨- birth￨L￨NN￨O￨- or￨L￨CC￨O￨- immigration￨L￨NN￨O￨- μ￨L￨NN￨O￨- Per￨U￨IN￨O￨- capita￨L￨NN￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- θ￨L￨NN￨O￨- The￨U￨DT￨O￨- duration￨L￨NN￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- compartment￨L￨NN￨O￨A a￨L￨DT￨O￨- Age￨U￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- lapsed￨L￨VBN￨O￨- since￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- became￨L￨VBD￨O￨- infectious￨L￨JJ￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- removed￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- a￨L￨DT￨O￨- γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- that￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- with￨L￨IN￨O￨- age￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- a￨L￨DT￨O￨- recovers￨L￨VBZ￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ν￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- θ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- compartment￨L￨NN￨O￨- for￨L￨IN￨O￨- duration￨L￨NN￨O￨- θ￨L￨NN￨O￨- ,￨L￨,￨O￨- progress￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- δ￨L￨NN￨O￨- The￨U￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- treated￨L￨VBN￨O￨- individual￨L￨JJ￨O￨- leaves￨L￨VBZ￨O￨- the￨L￨DT￨O￨- treated￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- p￨L￨NN￨O￨- The￨U￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨- infected￨L￨VBN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- directly1￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- The￨U￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- newly￨L￨RB￨O￨- infected￨L￨VBN￨O￨- to￨L￨TO￨O￨- enter￨L￨VB￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- class￨L￨NN￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- treated￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- In￨U￨IN￨O￨- the￨L￨DT￨O￨- sequel￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- further￨L￨RB￨O￨- make￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- means￨L￨NNS￨O￨- of￨L￨IN￨O￨- suitable￨L￨JJ￨O￨- Lyapunov￨U￨NNP￨PERSON￨- functionals￨L￨NNS￨O￨- and￨L￨CC￨O￨- LaSalle￨U￨NNP￨ORGANIZATION￨- ’s￨L￨POS￨O￨- invariance￨L￨NN￨O￨- principle￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- proven￨L￨VBN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- steady￨L￨JJ￨O￨- state￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable.Keywordstuberculosisage￨L￨JJ￨O￨- structurestabilityLyapunov￨L￨NN￨O￨- functionalLaSalle￨L￨NN￨O￨- ’s￨L￨POS￨O￨- invariance￨L￨NN￨O￨- principleMSC37N2592B0537B25￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionTuberculosis￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- bacterial￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- Mycobacterium￨U￨NN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- usually￨L￨RB￨O￨- acquired￨L￨VBN￨O￨- through￨L￨IN￨O￨- airborne￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- active￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Active￨U￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- developing￨L￨VBG￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- 2-5￨L￨CD￨NUMBER￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- most￨L￨JJS￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- remain￨L￨VBP￨O￨- latent￨L￨JJ￨O￨A for￨L￨IN￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- until￨L￨IN￨O￨- immune￨L￨JJ￨O￨- compromise￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- aging￨L￨VBG￨O￨- or￨L￨CC￨O￨- co-infection￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- illnesses￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- [￨L￨-LRB-￨O￨- 26￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- boundary￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- initial￨L￨JJ￨O￨- condition￨L￨NN￨O￨- X￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1.6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- X￨U￨NN￨O￨- mathscr￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathbb￨L￨NN￨O￨A ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- integrable￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- from￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- into￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- analysis￨L￨NN￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- simultaneously￨L￨RB￨O￨- releasing￨L￨VBG￨O￨- Wolbachia-harboring￨U￨JJ￨MISC￨- female￨L￨NN￨O￨- and￨L￨CC￨O￨- male￨L￨JJ￨O￨A mosquitoes￨L￨NNS￨O￨- will￨L￨MD￨O￨- achieve￨L￨VB￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- replacement￨L￨NN￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- releasing￨L￨VBG￨O￨- only￨L￨RB￨O￨- Wolbachia-harboring￨U￨JJ￨MISC￨- male￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- will￨L￨MD￨O￨- suppress￨L￨VB￨O￨- or￨L￨CC￨O￨- even￨L￨RB￨O￨- eradicate￨L￨VB￨O￨- wild￨L￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- eventually￨L￨RB￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- only￨L￨RB￨O￨- releasing￨L￨VBG￨O￨- male￨L￨JJ￨O￨A Wolbachia￨U￨JJ￨O￨- mosquitoes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- better￨L￨JJR￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- control￨L￨NN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NN￨O￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- formulate￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- control￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- releasing￨L￨VBG￨O￨- transgenosis￨L￨NN￨O￨- mosquitoes￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- introducing￨L￨VBG￨O￨- bacterium￨L￨NN￨O￨- Wolbachia￨U￨NNP￨O￨- into￨L￨IN￨O￨- Aedes￨U￨NNP￨O￨- aegypti￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NN￨PERSON￨- virus￨L￨NN￨O￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨A and￨L￨CC￨O￨- assessment￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- limited￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- reported￨L￨VBN￨O￨- suspected￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨- a￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 2.5020￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Modeling￨U￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- Zika￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- Brazil￨U￨NNP￨COUNTRY￨- Liping￨U￨NNP￨O￨- Wang1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Hongyong￨U￨NNP￨PERSON￨- Zhao1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Sergio￨U￨NNP￨PERSON￨- Muniz￨U￨NNP￨PERSON￨- Oliva2￨U￨NNP￨O￨- &￨L￨CC￨O￨- Huaiping￨U￨NNP￨O￨- Zhu3￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 7721￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNP￨O￨- Applied￨U￨NNP￨O￨- mathematicsEpidemiology￨L￨NNP￨O￨- AbstractZika￨U￨NNP￨O￨- virus￨L￨NN￨O￨A ,￨L￨,￨O￨- a￨L￨DT￨O￨- reemerging￨L￨VBG￨O￨- mosquito-borne￨L￨JJ￨O￨- flavivirus￨L￨NN￨O￨- ,￨L￨,￨O￨- started￨L￨VBD￨O￨- spread￨L￨NN￨O￨- across￨L￨IN￨O￨- Central￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨ORGANIZATION￨- Southern￨U￨NNP￨ORGANIZATION￨- America￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- more￨L￨RBR￨O￨- recently￨L￨RB￨DATE￨- to￨L￨TO￨O￨- North￨U￨NNP￨LOCATION￨- America￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- the￨L￨DT￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infected-removed￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- mathematically￨L￨RB￨O￨- expressed￨L￨VBN￨O￨- as￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- p.￨L￨NN￨O￨- 47￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨A Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- bilinear￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- system￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- p.￨L￨NN￨O￨- 62￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨A I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- dS￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- d￨L￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Dynamical￨U￨JJ￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- double￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- hypothesisAnqi￨L￨NN￨O￨- Miao1￨U￨NN￨O￨- ,￨L￨,￨O￨- Xinyang￨U￨NNP￨CITY￨- Wang1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Tongqian￨U￨NNP￨O￨- Zhang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Wei￨U￨NNP￨PERSON￨- Wang3￨U￨NNP￨O￨- and￨L￨CC￨O￨- BG￨U￨NNP￨ORGANIZATION￨- Sampath￨U￨NNP￨ORGANIZATION￨- Aruna￨U￨NNP￨ORGANIZATION￨- Pradeep4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:226￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- double￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- hypothesis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- analysed￨L￨VBN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- this￨L￨DT￨O￨- end￨L￨NN￨O￨- ,￨L￨,￨O￨- firstly￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- neglecting￨L￨VBG￨O￨- stochastic￨L￨JJ￨O￨A disturbance￨L￨NN￨O￨- and￨L￨CC￨O￨- obtained￨L￨VBD￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- kinds￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibria￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +Recently￨U￨RB￨DATE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨A ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨- semi-dynamic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- hot￨L￨JJ￨O￨- topic￨L￨NN￨O￨- and￨L￨CC￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- applied￨L￨VBN￨O￨- in￨L￨IN￨O￨- other￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- and￨L￨CC￨O￨- science￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- suggests￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- tactics￨L￨NNS￨O￨- should￨L￨MD￨O￨- only￨L￨RB￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- once￨L￨RB￨DATE￨- the￨L￨DT￨COUNTRY￨- states￨L￨NNS￨COUNTRY￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- reach￨L￨VBP￨O￨- a￨L￨DT￨O￨- prescribed￨L￨VBN￨O￨- given￨L￨VBN￨O￨- threshold.Following￨L￨VBG￨O￨- this￨L￨DT￨O￨- idea￨L￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- PVS￨U￨NNS￨O￨- and￨L￨CC￨O￨- pulse￨L￨NN￨O￨- treatment￨L￨NN￨O￨- strategy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- PTS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- authors￨L￨NNS￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Nonlinear￨U￨JJ￨MISC￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨A strategy￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- resource￨L￨NN￨O￨- limitationZhi￨L￨NNP￨O￨- Long￨U￨NNP￨O￨- He1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Ji￨U￨NN￨O￨- Gang￨U￨NN￨O￨- Li1￨U￨NN￨O￨- ,￨L￨,￨O￨- Lin￨U￨NNP￨PERSON￨- Fei￨U￨NNP￨PERSON￨- Nie2￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Zhen￨U￨NNP￨O￨- Zhao3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2017:209￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- present￨L￨JJ￨DATE￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- avoid￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- impulse￨L￨NN￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- implemented￨L￨VBN￨O￨- to￨L￨TO￨O￨- keep￨L￨VB￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- low￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- first￨L￨RB￨ORDINAL￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- PVS￨U￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- periodical￨L￨JJ￨O￨- repetitions￨L￨NNS￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A vaccinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- age￨L￨NN￨O￨- cohorts￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- confirmed￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- and￨L￨CC￨O￨- effective￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases.In￨L￨NN￨O￨- a￨L￨DT￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- application￨L￨NN￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- eradication￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- sometimes￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- both￨L￨CC￨O￨- practically￨L￨RB￨O￨- and￨L￨CC￨O￨- economically￨L￨RB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- short￨L￨JJ￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- resource￨L￨NN￨O￨- limitation￨L￨NN￨O￨- including￨L￨VBG￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨- function￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨A scheme￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- many￨L￨JJ￨O￨- practical￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- ,￨L￨,￨O￨- impulse￨L￨NN￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- often￨L￨RB￨O￨- occurs￨L￨VBZ￨O￨- at￨L￨IN￨O￨- state-dependent￨L￨JJ￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- more￨L￨RBR￨O￨- reasonable￨L￨JJ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- a￨L￨DT￨O￨- strategy￨L￨NN￨O￨- of￨L￨IN￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨A to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- issues￨L￨NNS￨O￨- of￨L￨IN￨O￨- real￨L￨JJ￨O￨- world￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- combination￨L￨NN￨O￨- of￨L￨IN￨O￨- methods￨L￨NNS￨O￨- –￨L￨:￨O￨- wavelet￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- economic￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- statistical￨L￨JJ￨O￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- modelling￨L￨NN￨O￨- –￨L￨:￨O￨- we￨L￨PRP￨O￨- aimed￨L￨VBD￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- climatic￨L￨JJ￨O￨A and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- Highly￨U￨RB￨O￨- Pathogenic￨U￨JJ￨O￨- Avian￨U￨JJ￨O￨- Influenza￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- domestic￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- Vietnam￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Economic￨U￨NNP￨O￨- factors￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- zoonotic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- demand￨L￨NN￨O￨- for￨L￨IN￨O￨- poultry￨L￨NN￨O￨- meat￨L￨NN￨O￨- and￨L￨CC￨O￨- seasonal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Vietnam￨U￨NNP￨COUNTRY￨- Alexis￨U￨NNP￨PERSON￨- Delabouglise￨U￨NNP￨PERSON￨- ORCID￨U￨NNP￨O￨- :￨L￨:￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Marc￨U￨NNP￨PERSON￨- Choisy3￨U￨NNP￨O￨- ,4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Thang￨U￨NNP￨O￨- D.￨U￨NNP￨O￨- Pfeiffer1￨U￨NNP￨O￨- ,7￨L￨NNP￨O￨- &￨L￨CC￨O￨- Guillaume￨U￨NNP￨O￨- Fournié1￨U￨NNP￨O￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 5905￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- Influenza￨U￨NNP￨CAUSE_OF_DEATH￨- virusStatistical￨L￨JJ￨O￨- methods￨L￨NNS￨O￨- AbstractWhile￨U￨NNP￨O￨- climate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- presented￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- key￨L￨JJ￨O￨- factor￨L￨NN￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- seasonality￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- anthropogenic￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- less￨L￨RBR￨O￨- commonly￨L￨RB￨O￨- evaluated￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- temporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- H5N1￨U￨NN￨O￨- incidence￨L￨NN￨O￨- are￨L￨VBP￨O￨- similar￨L￨JJ￨O￨- across￨L￨IN￨O￨- these￨L￨DT￨O￨- 3￨L￨CD￨NUMBER￨- regions￨L￨NNS￨O￨- :￨L￨:￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- high￨L￨JJ￨O￨- H5N1￨U￨NN￨O￨- incidence￨L￨NN￨O￨- coincide￨L￨VBP￨O￨- with￨L￨IN￨O￨- Lunar￨U￨JJ￨MISC￨- New￨U￨JJ￨DATE￨- Year￨U￨NN￨DATE￨- festival￨L￨NN￨O￨- ,￨L￨,￨O￨- occurring￨L￨VBG￨O￨- in￨L￨IN￨O￨- January-February￨U￨NNP￨DATE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- 3￨L￨CD￨NUMBER￨- climatic￨L￨JJ￨O￨A regions￨L￨NNS￨O￨- for￨L￨IN￨O￨- 5￨L￨CD￨NUMBER￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- 8￨L￨CD￨NUMBER￨- study￨L￨NN￨O￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- while￨L￨IN￨O￨- climatic￨L￨JJ￨O￨A variables￨L￨NNS￨O￨- are￨L￨VBP￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- North￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Centre￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- South￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- a￨L￨DT￨O￨- setting￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- want￨L￨VBP￨O￨- to￨L￨TO￨O￨- localize￨L￨VB￨O￨- the￨L￨DT￨O￨- source￨L￨NN￨O￨- based￨L￨VBN￨O￨- exclusively￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- provided￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- observers￨L￨NNS￨O￨- –￨L￨:￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- reveal￨L￨VB￨O￨- if￨L￨IN￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- –￨L￨:￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- where￨L￨WRB￨O￨- such￨L￨JJ￨O￨- observers￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- placed.We￨L￨JJ￨O￨- show￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- observer￨L￨NN￨O￨- placement￨L￨NN￨O￨- depends￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- topology￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- variance￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- node-to-node￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- delays￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- intricate￨L￨JJ￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- CSTCS￨U￨NNP￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- Lyapunov￨U￨NN￨O￨- function￨L￨NN￨O￨- and￨L￨CC￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- symbol￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- derivative￨L￨NN￨O￨- are￨L￨VBP￨O￨- complex￨L￨JJ￨O￨- and￨L￨CC￨O￨- technical￨L￨JJ￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- circumstances￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- coupling￨L￨NN￨O￨A structure.Motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- discussions￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- time-varying￨L￨JJ￨O￨- coupling￨L￨NN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- CSs￨U￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- CSTCS￨U￨NNP￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- general￨L￨JJ￨TITLE￨- CSs￨U￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- described￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- f￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- bigl￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- t￨L￨NN￨O￨- Sum￨U￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- bigl￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- h￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- l￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- f￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- continuous￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- h￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- coupling￨L￨NN￨O￨A strength￨L￨NN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- Xu￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ren￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIR￨U￨NN￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- spreading￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- with￨L￨IN￨O￨- limited￨L￨JJ￨O￨- anti-virus￨L￨JJ￨O￨- ability￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- varrho￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- E￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- where￨L￨WRB￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- latent￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- where￨L￨WRB￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- breaking￨L￨VBG￨O￨- out￨L￨RP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- equipped￨L￨VBN￨O￨- with￨L￨IN￨O￨- anti-virus￨L￨JJ￨O￨- software￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- above￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- delays￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- E￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- E￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varepsilon￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- E￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- p￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- varrho￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- computers￨L￨NNS￨O￨A and￨L￨CC￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- that￨L￨WDT￨O￨- anti-virus￨L￨JJ￨O￨- software￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Xu￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Ren￨U￨NN￨PERSON￨- NumericCitation￨U￨NN￨PERSON￨- studied￨L￨VBN￨O￨- stabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- virus-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- virus￨L￨NN￨O￨- equilibrium.However￨L￨NNP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- pointed￨L￨VBN￨O￨- out￨L￨RP￨O￨- that￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- neglects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- exposed￨L￨VBN￨O￨- computers￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- that￨L￨WDT￨O￨- anti-virus￨L￨JJ￨O￨- software￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Dynamical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- extensively￨L￨RB￨O￨- by￨L￨IN￨O￨- scholars￨L￨NNS￨O￨- at￨L￨IN￨O￨- home￨L￨NN￨O￨- and￨L￨CC￨O￨- abroad￨L￨RB￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- predator-prey￨L￨JJ￨O￨- models￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 27￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- computer￨L￨NN￨O￨A virus￨L￨NN￨O￨A models￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 31￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- measures￨L￨NNS￨O￨- for￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- still￨L￨RB￨O￨- lack￨L￨VBP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- needs￨L￨VBZ￨O￨- more￨L￨JJR￨O￨- attention￨L￨NN￨O￨- by￨L￨IN￨O￨- medical￨L￨JJ￨O￨- staff￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemiologists￨L￨NNS￨O￨A ,￨L￨,￨O￨- mathematicians￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- stakeholders.Mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- is￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- in￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- some￨L￨DT￨O￨- useful￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Modeling￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- quarantine￨L￨NN￨O￨- and￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- on￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- diseaseThomas￨L￨NNP￨MISC￨- Wetere￨U￨NNP￨MISC￨- Tulu1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Boping￨U￨VBG￨O￨- Tian1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Zunyou￨U￨NN￨O￨- Wu2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2017:178￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractEbola￨U￨NNP￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- severe￨L￨JJ￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- case￨L￨NN￨O￨A fatality￨L￨NN￨O￨A rate￨L￨NN￨O￨A which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- treat￨L￨NN￨O￨- now￨L￨RB￨DATE￨- .￨L￨.￨O￨- +Last￨U￨JJ￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- least￨L￨JJS￨O￨- ,￨L￨,￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨NN￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨O￨- epidemic.Keywordsmathematical￨L￨JJ￨O￨- modelingCaputo￨L￨NN￨O￨- derivativestabilityepidemic￨L￨JJ￨O￨- modelnumerical￨L￨JJ￨O￨- simulationMSC37N2592D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionEbola￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- severe￨L￨JJ￨O￨- and￨L￨CC￨O￨- often￨L￨RB￨O￨- deadly￨L￨JJ￨O￨- illness￨L￨NN￨CAUSE_OF_DEATH￨- killing￨L￨NN￨O￨- between￨L￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- and￨L￨CC￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- those￨L￨DT￨O￨- infected￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- named￨L￨VBN￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- river￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- Democratic￨U￨JJ￨IDEOLOGY￨- Republic￨U￨NN￨LOCATION￨- of￨L￨IN￨LOCATION￨- Congo￨U￨NNP￨COUNTRY￨- (￨L￨-LRB-￨O￨- formerly￨L￨RB￨O￨- Zaire￨U￨NNP￨COUNTRY￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- case￨L￨NN￨O￨A fatality￨L￨NN￨O￨A rate￨L￨NN￨O￨A .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- both￨L￨CC￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- quarantine￨L￨NN￨O￨A to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- developed￨L￨VBN￨O￨- and￨L￨CC￨O￨- comprehensively￨L￨RB￨O￨- analyzed￨L￨VBN￨O￨- using￨L￨VBG￨O￨- fractional￨L￨JJ￨O￨- derivative￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Caputo￨U￨NNP￨O￨- derivative￨L￨NN￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- our￨L￨PRP$￨O￨- study￨L￨NN￨O￨- it￨L￨PRP￨O￨- was￨L￨VBD￨O￨- also￨L￨RB￨O￨- seen￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- for￨L￨IN￨O￨- getting￨L￨VBG￨O￨- Ebola￨U￨NN￨MISC￨- virus￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- time￨L￨NN￨O￨- if￨L￨IN￨O￨- they￨L￨PRP￨O￨- survived￨L￨VBD￨O￨- his/her￨L￨JJR￨O￨- first￨L￨JJ￨ORDINAL￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Individual￨U￨JJ￨MISC￨- position￨L￨NN￨O￨- diversity￨L￨NN￨O￨- in￨L￨IN￨O￨- dependence￨L￨NN￨O￨A socioeconomic￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- increases￨L￨VBZ￨O￨- economic￨L￨JJ￨O￨- outputWen-Jie￨L￨NN￨O￨- Xie1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yan-Hong￨U￨NNP￨PERSON￨- Yang1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Ming-Xia￨U￨NNP￨O￨- Li2￨U￨NNP￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Zhi-Qiang￨U￨NNP￨PERSON￨- Jiang1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Wei-Xing￨U￨JJ￨O￨- Zhou1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 6:10￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- availability￨L￨NN￨O￨- of￨L￨IN￨O￨- big￨L￨JJ￨O￨- data￨L￨NNS￨O￨- recorded￨L￨VBN￨O￨- from￨L￨IN￨O￨- massively￨L￨RB￨O￨- multiplayer￨L￨JJ￨O￨- online￨L￨NN￨O￨- role-playing￨L￨NN￨O￨- games￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- MMORPGs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- allows￨L￨VBZ￨O￨- us￨L￨PRP￨O￨- to￨L￨TO￨O￨- gain￨L￨VB￨O￨- a￨L￨DT￨O￨- deeper￨L￨JJR￨O￨- understanding￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- connection￨L￨NN￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- ’￨L￨POS￨O￨- network￨L￨NN￨O￨- positions￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- economic￨L￨JJ￨O￨- outputs￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- classical￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vital￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- Tuple￨U￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- mu￨L￨NN￨O￨A Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- N￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- N￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- above￨L￨IN￨O￨- ,￨L￨,￨O￨- except￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- inflow￨L￨NN￨O￨- of￨L￨IN￨O￨- newborns￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- at￨L￨IN￨O￨- rate￨L￨NN￨O￨- μN￨L￨NN￨O￨- and￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- classes￨L￨NNS￨O￨- at￨L￨IN￨O￨- rates￨L￨NNS￨O￨- μN￨L￨NN￨O￨- ,￨L￨,￨O￨- μI￨L￨NN￨O￨- and￨L￨CC￨O￨- μR￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- N￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- denoting￨L￨VBG￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- Tuple￨U￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨A Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- removed￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- presented￨L￨VBD￨O￨- four￨L￨CD￨NUMBER￨- discrete￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- forward￨L￨JJ￨O￨- Euler￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- backward￨L￨RB￨O￨- Euler￨U￨NNP￨PERSON￨- methods￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- discussed￨L￨VBD￨O￨A the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- discretizations￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Robinson￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Holmes￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- discussed￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Schrödingerean￨U￨JJ￨MISC￨- predator-prey￨L￨NN￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- undergoes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- flip￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨A and￨L￨CC￨O￨- Hopf￨U￨NN￨PERSON￨- bifurcation￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- center￨L￨NN￨O￨- manifold￨L￨NN￨O￨- theorem￨L￨NN￨O￨- and￨L￨CC￨O￨- bifurcation￨L￨NN￨O￨- theory￨L￨NN￨O￨- .￨L￨.￨O￨- +Guckenheimer￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Holmes￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- examined￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- non-monotonic￨L￨JJ￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- also￨L￨RB￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- derived￨L￨VBD￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- calculation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- equilibriums￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- grouped￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- three￨L￨CD￨NUMBER￨- cases￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- StrictGreaterThan￨U￨NNP￨PERSON￨- c￨L￨NN￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NNP￨O￨- a￨L￨DT￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- b￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- c￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- trivial￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- semi-trivial￨L￨JJ￨O￨- equilibria￨L￨NNS￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +Levins￨U￨NNP￨PERSON￨- posed￨L￨VBD￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- general￨L￨JJ￨TITLE￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- site￨L￨NN￨O￨- occupancy￨L￨NN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- dp￨L￨NNP￨O￨- Pow￨U￨NNP￨O￨- dt￨L￨NNP￨O￨A -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- p￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- c￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- colonization￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- m￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- morality￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- local￨L￨JJ￨O￨- extinction￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asHellRank￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- Hellinger-based￨U￨JJ￨MISC￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨- for￨L￨IN￨O￨- bipartite￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networksAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsSeyed￨L￨NNP￨O￨- Mohammad￨U￨NNP￨PERSON￨- TaheriHamidreza￨U￨NNP￨PERSON￨- MahyarMohammad￨U￨NNP￨PERSON￨- FirouziElahe￨U￨NNP￨O￨- Ghalebi￨U￨NNP￨MISC￨- K.Radu￨U￨NNP￨MISC￨- GrosuAli￨U￨NNP￨MISC￨- MovagharOpen￨U￨NNP￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- ArticleFirst￨U￨NNP￨MISC￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1.5￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractMeasuring￨U￨VBG￨O￨- centrality￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- in￨L￨IN￨O￨- bipartite￨L￨JJ￨O￨- mode￨L￨NN￨O￨- ,￨L￨,￨O￨- poses￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- challenges￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- requirement￨L￨NN￨O￨- of￨L￨IN￨O￨- full￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- properly￨L￨RB￨O￨- detecting￨L￨VBG￨O￨- top-k￨L￨JJ￨O￨- behavioral￨L￨JJ￨O￨- representative￨L￨JJ￨TITLE￨- users￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- partial￨L￨JJ￨O￨- ranking￨L￨JJ￨O￨- similarity￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- HellRank￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- conventional￨L￨JJ￨O￨- metrics￨L￨NNS￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Kendall￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Spearman￨U￨NNP￨PERSON￨- rank￨L￨NN￨O￨- correlation￨L￨NN￨O￨- coefficient.KeywordsBipartite￨L￨NN￨O￨- social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- Top-k￨U￨JJ￨MISC￨- central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- Hellinger￨U￨NNP￨O￨- distance￨L￨NN￨O￨- Recommender￨U￨NN￨MISC￨- systems￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSocial￨U￨NNP￨O￨- networking￨L￨VBG￨O￨- sites￨L￨NNS￨O￨- have￨L￨VBP￨O￨- become￨L￨VBN￨O￨- a￨L￨DT￨O￨- very￨L￨RB￨O￨- important￨L￨JJ￨O￨- social￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- modern￨L￨JJ￨O￨- society￨L￨NN￨O￨- with￨L￨IN￨O￨- hundreds￨L￨NNS￨O￨- of￨L￨IN￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- users￨L￨NNS￨O￨- nowadays￨L￨RB￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- overcome￨L￨VB￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- mentioned￨L￨VBN￨O￨- challenges￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- HellRank￨U￨NNP￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- accurate￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measure￨L￨NN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- central￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- bipartite￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- experimentally￨L￨RB￨O￨- evaluate￨L￨VBP￨O￨- the￨L￨DT￨O￨- performance￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HellRank￨U￨NNP￨O￨- measure￨L￨NN￨O￨- in￨L￨IN￨O￨- correlation￨L￨NN￨O￨- with￨L￨IN￨O￨- other￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- on￨L￨IN￨O￨- real-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +HellRank￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Hellinger￨U￨NNP￨O￨- distance￨L￨NN￨O￨A between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- nodes￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- side￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- bipartite￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- describe￨L￨VBP￨O￨- the￨L￨DT￨O￨- various￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- features￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Epi-features￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- included￨L￨VBD￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- output￨L￨NN￨O￨- of￨L￨IN￨O￨- forecasting￨L￨NN￨O￨- methods￨L￨NNS￨O￨- and￨L￨CC￨O￨- provide￨L￨VBP￨O￨- suitable￨L￨JJ￨O￨- error￨L￨NN￨O￨A measures￨L￨VBZ￨O￨- that￨L￨DT￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- methods￨L￨NNS￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- Epi-features￨U￨NNS￨MISC￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- framework￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- for￨L￨IN￨O￨- combining￨L￨VBG￨O￨- different￨L￨JJ￨O￨- features￨L￨NNS￨O￨- ,￨L￨,￨O￨- error￨L￨NN￨O￨A measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ranking￨L￨JJ￨O￨- schema￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- forecasts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Further￨U￨RB￨O￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- experimental￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- no￨L￨DT￨O￨- single￨L￨JJ￨O￨- method￨L￨NN￨O￨- dominates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rest￨L￨NN￨O￨- in￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- all￨L￨DT￨O￨- Epi-features￨U￨NNS￨MISC￨- when￨L￨WRB￨O￨- evaluated￨L￨VBN￨O￨- across￨L￨IN￨O￨- error￨L￨NN￨O￨A measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- demonstrate￨L￨VBP￨O￨- that￨L￨IN￨O￨- different￨L￨JJ￨O￨- error￨L￨NN￨O￨A measures￨L￨VBZ￨O￨- lead￨L￨NN￨O￨- to￨L￨TO￨O￨- different￨L￨JJ￨O￨- rankings￨L￨NNS￨O￨- even￨L￨RB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- Epi-feature￨U￨NN￨MISC￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- geometric￨L￨JJ￨O￨- method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- to￨L￨TO￨O￨- resolve￨L￨VB￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- asymptotical￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- with￨L￨IN￨O￨- bilinear￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rates.Motivated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- HIV/AIDS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stability￨U￨NN￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A and￨L￨CC￨O￨- treatmentJianwen￨L￨NN￨O￨- Jia1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Gailing￨U￨NN￨O￨- Qin1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2017:136￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractAn￨U￨NNP￨O￨- HIV/AIDS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- is￨L￨VBZ￨O￨- formulated￨L￨VBN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- treatment￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HIV/AIDS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model.In￨L￨NN￨O￨- mathematical￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨A plays￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- carrying￨L￨VBG￨O￨- out￨L￨RP￨O￨- an￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- geometric￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Anderson￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- R.M.￨U￨NNP￨PERSON￨- May￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- Infectious￨U￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- humans￨L￨NNS￨O￨A :￨L￨:￨O￨- Dynamics￨U￨NNP￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Scholar2.H.W￨U￨NNP￨O￨- .￨L￨.￨O￨- +KeywordsComputational￨U￨NNP￨O￨- Methods￨U￨NNS￨O￨- Download￨U￨VBP￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨A the￨L￨DT￨O￨- full￨L￨JJ￨O￨- article￨L￨NN￨O￨- textReferences1.R.M￨L￨NN￨O￨- .￨L￨.￨O￨- +Hethcote￨U￨NNP￨O￨- ,￨L￨,￨O￨- SIAM￨U￨NNP￨COUNTRY￨- Rev.￨U￨NNP￨TITLE￨- 42￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 599￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- MathSciNetCrossRefADSGoogle￨U￨NNP￨O￨- Scholar3.T￨U￨NNP￨O￨- .￨L￨.￨O￨- +1.2￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- new￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vicinity￨L￨NN￨O￨- travel-blocking￨L￨NN￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- We￨U￨PRP￨O￨- suggest￨L￨VBP￨O￨- here￨L￨RB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approach￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- multi-regions￨L￨JJ￨O￨- discrete-time￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spatial-temporal￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- which￨L￨WDT￨O￨- emerges￨L￨VBZ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- global￨L￨JJ￨O￨- domain￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- Ω￨U￨NN￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- grid￨L￨NN￨O￨- of￨L￨IN￨O￨- colored￨L￨VBN￨O￨- cells￨L￨NNS￨O￨A which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- uniform￨L￨JJ￨O￨- in￨L￨IN￨O￨- size￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- some￨L￨DT￨O￨- regions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- suggest￨L￨VBP￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- control￨L￨NN￨O￨- approach￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- travel-blocking￨L￨JJ￨O￨- vicinity￨L￨NN￨O￨- strategy￨L￨NN￨O￨- which￨L￨WDT￨O￨- aims￨L￨VBZ￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- a￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- cells￨L￨NNS￨O￨A ,￨L￨,￨O￨- or￨L￨CC￨O￨- a￨L￨DT￨O￨- patch￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- restricting￨L￨VBG￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- people￨L￨NNS￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- its￨L￨PRP$￨O￨- neighboring￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- .￨L￨.￨O￨- +Explicitly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- seek￨L￨VBP￨O￨- to￨L￨TO￨O￨- minimize￨L￨VB￨O￨- an￨L￨DT￨O￨- objective￨L￨JJ￨O￨- function￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- group￨L￨NN￨O￨- of￨L￨IN￨O￨- cells￨L￨NNS￨O￨A or￨L￨CC￨O￨- patch￨L￨NN￨O￨- with￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- m￨L￨NN￨O￨- M￨U￨NN￨O￨- ,￨L￨,￨O￨- subject￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- system￨L￨NN￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- C￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- *￨L￨SYM￨O￨- q￨L￨SYM￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- optimal￨L￨JJ￨O￨- controls￨L￨NNS￨O￨- functions￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- as￨L￨IN￨O￨- effectiveness￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- travel-blocking￨L￨JJ￨O￨- operations￨L￨NNS￨O￨- followed￨L￨VBD￨O￨- between￨L￨IN￨O￨- P￨U￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- neighbors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- harvest￨L￨NN￨O￨- by￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A flocculant￨L￨NN￨O￨- inputTongqian￨L￨NN￨O￨- Zhang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Wanbiao￨U￨NNP￨O￨- Ma1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Xinzhu￨U￨NN￨O￨- Meng2￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2017:115￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractA￨U￨NNP￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- describing￨L￨VBG￨O￨- continuous￨L￨JJ￨O￨- microbial￨L￨JJ￨O￨- culture￨L￨NN￨O￨- and￨L￨CC￨O￨- harvest￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- chemostat￨L￨NN￨O￨- ,￨L￨,￨O￨- incorporating￨L￨VBG￨O￨- a￨L￨DT￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- and￨L￨CC￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- and￨L￨CC￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- proposed￨L￨VBN￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- DDEs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- microbial￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- culture￨L￨NN￨O￨A and￨L￨CC￨O￨- harvest￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨O￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- F￨U￨NN￨O￨- t￨L￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- concentration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- substrate￨L￨NN￨O￨- ,￨L￨,￨O￨- microbia￨L￨NN￨O￨- and￨L￨CC￨O￨- flocculating￨L￨VBG￨O￨- agent￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- culture￨L￨NN￨O￨- chemostat￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- and￨L￨CC￨O￨- impulsive￨L￨JJ￨O￨A harvest￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- x￨L￨CC￨O￨- F￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- T￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨- effect￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- F￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- gamma￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- input￨L￨NN￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- flocculant￨L￨NN￨O￨- at￨L￨IN￨O￨- every￨L￨DT￨O￨- impulsive￨L￨JJ￨O￨- period￨L￨NN￨O￨- T.￨U￨FW￨O￨- +Analysis￨U￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- microbial￨L￨JJ￨O￨- culture￨L￨NN￨O￨- and￨L￨CC￨O￨- harvest￨L￨NN￨O￨- process￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- implemented￨L￨VBN￨O￨- by￨L￨IN￨O￨- adjusting￨L￨VBG￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- ,￨L￨,￨O￨- impulsive￨L￨JJ￨O￨A period￨L￨NN￨O￨- or￨L￨CC￨O￨- input￨L￨NN￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- flocculant￨L￨NN￨O￨- .￨L￨.￨O￨- +Theoretical￨U￨JJ￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- microbe-extinction￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- permanent￨L￨JJ￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- greater￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨- .￨L￨.￨O￨- +Biologically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- result￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- significance￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- an￨L￨DT￨O￨- incubation￨L￨NN￨O￨- phase￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- small￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- perturbation￨L￨NN￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- via￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- phase￨L￨NN￨O￨- will￨L￨MD￨O￨- enhance￨L￨VB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- state￨L￨NN￨O￨- if￨L￨IN￨O￨- both￨L￨DT￨O￨- components￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- are￨L￨VBP￨O￨- non-trivial￨L￨JJ￨O￨- ;￨L￨:￨O￨- otherwise￨L￨RB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- will￨L￨MD￨O￨- not￨L￨RB￨O￨- be￨L￨VB￨O￨- disturbed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Simulations￨U￨NNS￨O￨- illustrate￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- stability￨L￨NN￨O￨A theorem.KeywordsSEIRS￨L￨NN￨O￨- modelstochastic￨L￨JJ￨O￨- transmissionalmost￨L￨NN￨O￨- sure￨L￨JJ￨O￨- exponential￨L￨JJ￨O￨- stability￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionIn￨U￨NN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- articles￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- published￨L￨VBN￨O￨- on￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- sufficiently￨L￨RB￨O￨- small￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨A parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- exponential￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- whenever￨L￨WRB￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- invariant￨L￨JJ￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- below￨L￨IN￨O￨- unity￨L￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- latter￨L￨JJ￨O￨- being￨L￨VBG￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Article￨U￨NNP￨O￨- |￨L￨NNP￨O￨- Open￨U￨NNP￨O￨- |￨L￨SYM￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- A￨U￨NNP￨O￨- Novel￨U￨JJ￨O￨- Method￨U￨NN￨O￨- of￨L￨IN￨O￨- Evaluating￨U￨VBG￨O￨- Knee￨U￨NN￨O￨- Joint￨U￨NNP￨O￨- Stability￨U￨NN￨O￨- of￨L￨IN￨O￨- Patients￨U￨NNS￨O￨- with￨L￨IN￨O￨- Knee￨U￨NN￨O￨- Osteoarthritis￨U￨NN￨O￨- :￨L￨:￨O￨- Multiscale￨U￨NNP￨ORGANIZATION￨- Entropy￨U￨NNP￨ORGANIZATION￨- Analysis￨U￨NN￨ORGANIZATION￨- with￨L￨IN￨O￨- A￨U￨DT￨O￨- Knee-Aiming￨U￨JJ￨O￨- Task￨U￨NNP￨O￨- Diange￨U￨NNP￨O￨- Zhou1￨U￨NN￨O￨- ,2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Shijie￨U￨NNP￨PERSON￨- Zhang2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Hui￨U￨NNP￨O￨- Zhang2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Long￨U￨NNP￨O￨- Jiang1￨U￨NN￨O￨- ,￨L￨,￨O￨- Jue￨U￨NN￨O￨- Zhang2￨U￨NN￨O￨- ,3￨L￨NN￨O￨- &￨L￨CC￨O￨- Jing￨U￨NNP￨O￨- Fang2￨U￨NNP￨O￨- ,3￨L￨CD￨NUMBER￨- Scientific￨U￨NNP￨O￨- Reportsvolume￨U￨NNP￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Article￨U￨NNP￨O￨- number￨L￨NN￨O￨- :￨L￨:￨O￨- 354￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2017￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- |￨L￨SYM￨O￨- Download￨U￨VB￨O￨- Citation￨U￨NNP￨O￨- Subjects￨U￨NNPS￨O￨- OsteoarthritisQuality￨U￨NNP￨O￨- of￨L￨IN￨O￨- lifeStatistics￨L￨NNPS￨O￨- AbstractDeteriorating￨U￨NNP￨O￨- knee￨L￨NN￨O￨- stability￨L￨NN￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- risk￨L￨NN￨O￨- factor￨L￨NN￨O￨- that￨L￨WDT￨O￨- reflects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- aggregative￨L￨NN￨O￨- of￨L￨IN￨O￨- osteoarthritis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- OA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- attempt￨L￨VBP￨O￨- to￨L￨TO￨O￨- depict￨L￨VB￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- knee￨L￨NN￨O￨- joint￨L￨NN￨O￨A from￨L￨IN￨O￨- a￨L￨DT￨O￨- holistic￨L￨JJ￨O￨- viewpoint￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- index￨L￨NN￨O￨- of￨L￨IN￨O￨- knee￨L￨NN￨O￨- joint￨L￨JJ￨O￨- stability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IKJS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- thus￨L￨RB￨O￨- extracted￨L￨VBN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- compared￨L￨VBD￨O￨- the￨L￨DT￨O￨- differences￨L￨NNS￨O￨- of￨L￨IN￨O￨- IKJS￨U￨NN￨O￨- in￨L￨IN￨O￨- 57￨L￨CD￨NUMBER￨- healthy￨L￨JJ￨O￨- volunteers￨L￨NNS￨O￨- and￨L￨CC￨O￨- 55￨L￨CD￨NUMBER￨- patients￨L￨NNS￨O￨A with￨L￨IN￨O￨- OA￨U￨NN￨O￨- before￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- total￨L￨JJ￨O￨- knee￨L￨NN￨O￨- replacement￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- TKR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- conclusion￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- IKJS￨U￨NNS￨ORGANIZATION￨- that￨L￨WDT￨O￨- employs￨L￨VBZ￨O￨- the￨L￨DT￨O￨- knee-aiming￨L￨JJ￨O￨- task￨L￨NN￨O￨- is￨L￨VBZ￨O￨- feasible￨L￨JJ￨O￨- for￨L￨IN￨O￨- quantitatively￨L￨RB￨O￨- determining￨L￨VBG￨O￨- knee￨L￨NN￨O￨- stability￨L￨NN￨O￨A .￨L￨.￨O￨- +Also￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- IKJS￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- operated￨L￨VBN￨O￨- leg￨L￨NN￨O￨- in￨L￨IN￨O￨- patients￨L￨NNS￨O￨A with￨L￨IN￨O￨- knee￨L￨NN￨O￨- OA￨U￨NN￨O￨- increased￨L￨VBD￨O￨- remarkably￨L￨RB￨O￨- after￨L￨IN￨O￨- TKR￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- p￨L￨NN￨O￨- <￨L￨JJR￨O￨- 0.0001￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- numeric￨L￨JJ￨O￨- replications￨L￨NNS￨O￨- for￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- are￨L￨VBP￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- data￨L￨NNS￨O￨- attained￨L￨VBN￨O￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- good￨L￨JJ￨O￨- agreement￨L￨NN￨O￨- with￨L￨IN￨O￨- theoretical￨L￨JJ￨O￨- outcomes￨L￨NNS￨O￨- ,￨L￨,￨O￨- displaying￨L￨VBG￨O￨- a￨L￨DT￨O￨- vital￨L￨JJ￨O￨- perception￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A coupled￨L￨VBN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- babesiosis￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- tick￨L￨VB￨O￨- populations.Keywordsbovine￨L￨NN￨O￨- babesiosisstabilitypredictor-corrector￨L￨NN￨O￨- techniquereproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionBovine￨U￨NNP￨O￨- babesiosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BB￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- communicated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- bite￨L￨NN￨O￨- of￨L￨IN￨O￨- ticks￨L￨NNS￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- important￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- bovine￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- in￨L￨IN￨O￨- humid￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Fractional-order￨U￨NN￨MISC￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- babesiosis￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- tick￨L￨VB￨O￨- populationsZain￨L￨NNP￨O￨- Ul￨U￨NNP￨O￨- Abadin￨U￨NNP￨O￨- Zafar1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Kashif￨U￨NNP￨PERSON￨- Rehan3￨U￨NN￨O￨- and￨L￨CC￨O￨- M￨U￨NN￨O￨- Mushtaq1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2017:86￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- article￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- earlier￨L￨JJR￨O￨- suggested￨L￨VBN￨O￨- in￨L￨IN￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- philosophy￨L￨NN￨O￨- ,￨L￨,￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- extended￨L￨VBN￨O￨- to￨L￨TO￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- reliable￨L￨JJ￨O￨- agenda￨L￨NN￨O￨- of￨L￨IN￨O￨- biological￨L￨JJ￨O￨- comportment￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- worldwide￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- point￨L￨NN￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- StrictLessThan￨U￨NNP￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- verified￨L￨VBN￨O￨- by￨L￨IN￨O￨- comparison￨L￨NN￨O￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- parameter￨L￨NN￨O￨- StrictLessThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- LaSalle-Lyapunov￨U￨NNP￨O￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨A free￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- DFE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- point￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- introduced￨L￨VBD￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- bovine￨L￨JJ￨O￨- babesiosis￨L￨NN￨O￨- and￨L￨CC￨O￨- tick￨L￨VB￨O￨- populations￨L￨NNS￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- frequently￨L￨RB￨O￨- been￨L￨VBN￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- modeling￨L￨NN￨O￨- memory-dependent￨L￨JJ￨O￨- processes￨L￨NNS￨O￨- of￨L￨IN￨O￨- physical￨L￨JJ￨O￨- and￨L￨CC￨O￨- life￨L￨NN￨O￨- sciences￨L￨NNS￨O￨- that￨L￨WDT￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨A derivatives￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- better￨L￨JJR￨O￨- agreement￨L￨NN￨O￨- between￨L￨IN￨O￨- solutions￨L￨NNS￨O￨- and￨L￨CC￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- both￨L￨DT￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- integer￨L￨NN￨O￨- order￨L￨NN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨A population￨L￨NN￨O￨A size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- constant.The￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- constant￨L￨JJ￨O￨- are￨L￨VBP￨O￨- classical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- given￨L￨VBN￨O￨- for￨L￨IN￨O￨- short-term￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +What￨U￨WP￨O￨- is￨L￨VBZ￨O￨- more￨L￨JJR￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- choice￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- function￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- gives￨L￨VBZ￨O￨- a￨L￨DT￨O￨- classical￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- population.We￨L￨NN￨O￨- also￨L￨RB￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- memory￨L￨NN￨O￨A dependence￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- obesity￨L￨NN￨O￨- contagion￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- A￨U￨DT￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨A model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- obesity￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- non-constant￨L￨JJ￨O￨- populationElif￨L￨NN￨O￨- Demirci1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2017:79￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- fractional￨L￨JJ￨O￨- order￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- obesity￨L￨NN￨O￨- contagion￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- also￨L￨RB￨O￨- considered￨L￨VBD￨O￨- obesity￨L￨NN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨A and￨L￨CC￨O￨- gave￨L￨VBD￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- explain￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- obesity￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 10￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 129￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 141￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asA￨L￨NN￨O￨- slow-fast￨L￨JJ￨O￨- dynamic￨L￨JJ￨O￨- decomposition￨L￨NN￨O￨- links￨L￨NNS￨O￨- neutral￨L￨JJ￨IDEOLOGY￨A and￨L￨CC￨O￨- non-neutral￨L￨JJ￨O￨- coexistence￨L￨NN￨O￨- in￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- multi-strain￨L￨JJ￨O￨- pathogensAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsErida￨L￨NN￨MISC￨- GjiniSten￨U￨NN￨MISC￨- MadecOpen￨U￨NN￨MISC￨- AccessORIGINAL￨U￨NN￨MISC￨- PAPERFirst￨U￨NN￨MISC￨- Online￨U￨NN￨MISC￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 858￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- AbstractUnderstanding￨U￨VBG￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- multi-type￨L￨JJ￨O￨- microbial￨L￨JJ￨O￨- ecosystems￨L￨NNS￨O￨- remains￨L￨VBZ￨O￨- a￨L￨DT￨O￨- challenge￨L￨NN￨O￨- ,￨L￨,￨O￨- despite￨L￨IN￨O￨- advancing￨L￨VBG￨O￨- molecular￨L￨JJ￨O￨- technologies￨L￨NNS￨O￨- for￨L￨IN￨O￨- diversity￨L￨NN￨O￨- resolution￨L￨NN￨O￨- within￨L￨IN￨O￨- and￨L￨CC￨O￨- between￨L￨IN￨O￨- hosts￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- slow-fast￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- approach￨L￨VBP￨O￨- interpolates￨L￨VBZ￨O￨- between￨L￨IN￨O￨- a￨L￨DT￨O￨- neutral￨L￨JJ￨IDEOLOGY￨A and￨L￨CC￨O￨- non-neutral￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- multi-strain￨L￨JJ￨O￨- coexistence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- quantifies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- asymmetries￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- maintenance￨L￨NN￨O￨- and￨L￨CC￨O￨- stabilisation￨L￨NN￨O￨- of￨L￨IN￨O￨- diversity.KeywordsNeutrality￨L￨NN￨O￨- Diversity￨U￨NN￨O￨- Slow￨U￨JJ￨O￨- manifold￨L￨NN￨O￨- Epidemiological￨U￨JJ￨O￨- model￨L￨NN￨TITLE￨- Coinfection￨U￨NNP￨O￨- Competition￨U￨NNP￨O￨- Cooperation￨U￨NNP￨O￨- The￨U￨NNP￨O￨- original￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- was￨L￨VBD￨O￨- revised￨L￨VBN￨O￨- :￨L￨:￨O￨- Mistakes￨U￨NNS￨O￨- were￨L￨VBD￨O￨- introduced￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- publishing￨L￨NN￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- apply￨L￨VBP￨O￨- Goldstone￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- idea￨L￨NN￨O￨- of￨L￨IN￨O￨- slow￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- resulting￨L￨VBG￨O￨- from￨L￨IN￨O￨- spontaneously￨L￨RB￨O￨- broken￨L￨VBN￨O￨- symmetries￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- direct￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- in￨L￨IN￨O￨- co-colonization￨L￨NN￨O￨- ,￨L￨,￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- competition￨L￨NN￨O￨- to￨L￨TO￨O￨- facilitation￨L￨NN￨O￨- between￨L￨IN￨O￨- strains￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- provide￨L￨VB￨O￨- the￨L￨DT￨O￨- reader￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- user￨L￨NN￨O￨- friendly￨L￨JJ￨O￨- introduction￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- techniques￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- dealing￨L￨VBG￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- datasets￨L￨NNS￨O￨- that￨L￨WDT￨O￨- exists￨L￨VBZ￨O￨- in￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- ecological￨L￨JJ￨O￨- science￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- common￨L￨JJ￨O￨- pitfalls￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- avoided￨L￨VBN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- introduction￨L￨NN￨O￨- to￨L￨TO￨O￨- inference￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- from￨L￨IN￨O￨- spatiotemporal￨L￨JJ￨O￨A datasets.KeywordsEpidemiology￨L￨NNP￨O￨- Modelling￨U￨NNP￨O￨- Bayesian￨U￨NNP￨O￨- Inference￨U￨NNP￨O￨- Simulation￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- Spatio-temporal￨U￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionSpatiotemporal￨U￨NNP￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- those￨L￨DT￨O￨- that￨L￨WDT￨O￨- contain￨L￨VBP￨O￨- both￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- location￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- temporal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- properties￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- review￨L￨VB￨O￨- some￨L￨DT￨O￨- useful￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- pertinent￨L￨JJ￨O￨- information￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- spatiotemporal￨L￨JJ￨O￨A dataset￨L￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- generated￨L￨VBN￨O￨- datasets￨L￨NNS￨O￨- ,￨L￨,￨O￨- provide￨L￨VBP￨O￨- examples￨L￨NNS￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- techniques￨L￨NNS￨O￨- .2￨L￨NN￨NUMBER￨- Network￨U￨NNP￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- spatiotemporal￨L￨JJ￨O￨- dataPurely￨L￨NNP￨O￨- spatial￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- confounded￨L￨VBN￨O￨- in￨L￨IN￨O￨- modelling￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- occasional￨L￨JJ￨O￨- long-distance￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Martínez-Ló￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- often￨L￨RB￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- “￨L￨``￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- analysis￨L￨NN￨O￨- ”￨L￨''￨O￨- .￨L￨.￨O￨- +Traditionally￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- common￨L￨JJ￨O￨A to￨L￨TO￨O￨- ignore￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- contact￨L￨NN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- instead￨L￨RB￨O￨- process￨L￨NN￨O￨- known￨L￨JJ￨O￨- or￨L￨CC￨O￨- modelled￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨- network￨L￨NN￨O￨- prior￨L￨RB￨O￨- to￨L￨TO￨O￨- analysis￨L￨NN￨O￨- :￨L￨:￨O￨- common￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- included￨L￨VBN￨O￨- aggregation￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- over￨L￨IN￨O￨- some￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- time￨L￨NN￨O￨- frame￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- “￨L￨``￨O￨- snapshot￨L￨NN￨O￨- ”￨L￨''￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- taking￨L￨VBG￨O￨- an￨L￨DT￨O￨- average￨L￨JJ￨O￨- network￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- longer￨L￨JJR￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- a￨L￨DT￨O￨- phenomenological￨L￨JJ￨O￨- perspective￨L￨NN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- write￨L￨VB￨O￨- simple￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- solve￨L￨VB￨O￨- them￨L￨PRP￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- farms￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- spatially￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- temporally￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- incorporating￨L￨VBG￨O￨- the￨L￨DT￨O￨- movements￨L￨NNS￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- potentially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- animals￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- veterinary￨L￨JJ￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨DATE￨- may￨L￨MD￨DATE￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- records￨L￨NNS￨O￨- of￨L￨IN￨O￨- tests￨L￨NNS￨O￨- carried￨L￨VBD￨O￨- out￨L￨RP￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- location￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- a￨L￨DT￨O￨- farm￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- or￨L￨CC￨O￨- simply￨L￨RB￨O￨- the￨L￨DT￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- animals￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- recording￨L￨NN￨O￨- of￨L￨IN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- mandated￨L￨VBN￨O￨- by￨L￨IN￨O￨- governments￨L￨NNS￨O￨- and￨L￨CC￨O￨- provides￨L￨VBZ￨O￨- researchers￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- wealth￨L￨NN￨O￨- of￨L￨IN￨O￨- data￨L￨NNS￨O￨- with￨L￨IN￨O￨- which￨L￨WDT￨O￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- algorithm￨L￨NN￨O￨- is￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- by￨L￨IN￨O￨- exploiting￨L￨VBG￨O￨- the￨L￨DT￨O￨- special￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model.Consider￨L￨NN￨O￨- a￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- system￨L￨NN￨O￨- representing￨L￨VBG￨O￨- an￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- x￨L￨CC￨O￨- Add￨U￨VB￨O￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- f￨L￨FW￨O￨- bigl￨L￨FW￨O￨- x￨L￨CC￨O￨- k￨L￨NN￨O￨- Mul￨U￨NN￨O￨- mathbf￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- p￨L￨NN￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨A x￨L￨CC￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- vector￨L￨NN￨O￨- ,￨L￨,￨O￨- Mul￨U￨NN￨O￨- mathbf￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- p￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- l￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- parameter￨L￨NN￨O￨- vector￨L￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- R￨U￨NN￨O￨- l￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- Mul￨U￨NN￨O￨- f￨L￨FW￨O￨- Pow￨U￨FW￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NN￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- mathbb￨L￨VBG￨O￨- -1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- continuously￨L￨RB￨O￨- differentiable￨L￨JJ￨O￨- function￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- execute￨L￨VB￨O￨- a￨L￨DT￨O￨- parameter￨L￨NN￨O￨- estimation￨L￨NN￨O￨- task￨L￨NN￨O￨- ,￨L￨,￨O￨- first￨L￨RB￨ORDINAL￨- one￨L￨CD￨NUMBER￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- the￨L￨DT￨O￨- identifiability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- unknown￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- very￨L￨RB￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- impossible￨L￨JJ￨O￨- to￨L￨TO￨O￨- find￨L￨VB￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- problem.Identification￨L￨NN￨O￨- of￨L￨IN￨O￨- systems￨L￨NNS￨O￨- deals￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨A of￨L￨IN￨O￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- previous￨L￨JJ￨O￨- information￨L￨NN￨O￨- available￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- a￨L￨DT￨O￨- parameterized￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- uniquely￨L￨RB￨O￨- identify￨L￨VB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- since￨L￨IN￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- do￨L￨VB￨O￨- experimental￨L￨JJ￨O￨- design￨L￨NN￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- unknown￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- using￨L￨VBG￨O￨- experimental￨L￨JJ￨O￨- data.The￨L￨NN￨O￨- identifiability￨L￨NN￨O￨- problem￨L￨NN￨O￨A is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- determination￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- parameter￨L￨NN￨O￨- sets￨L￨NNS￨O￨- which￨L￨WDT￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- input-output￨L￨JJ￨O￨- response￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- our￨L￨PRP$￨O￨- problem￨L￨NN￨O￨- this￨L￨DT￨O￨- linear￨L￨JJ￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- type￨L￨NN￨O￨- Equality￨U￨NN￨O￨- x￨L￨CC￨O￨- Add￨U￨VB￨O￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- A￨U￨NN￨O￨- Mul￨U￨NN￨O￨- mathbf￨L￨NN￨O￨- p￨L￨NN￨O￨- x￨L￨CC￨O￨- k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NN￨O￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨A A￨U￨NN￨O￨- Mul￨U￨NN￨O￨- mathbf￨L￨NN￨O￨- p￨L￨NN￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨PERSON￨- in￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NNP￨O￨- n￨L￨NN￨O￨- mathbb￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Add￨U￨VB￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- mu￨L￨NN￨O￨- Equality￨U￨NN￨O￨- Derivative￨U￨JJ￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Add￨U￨VB￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- alpha￨L￨NN￨O￨- mu￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- sigma￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- sigma￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨JJ￨O￨- eta￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- mu￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- percentages￨L￨NNS￨O￨- of￨L￨IN￨O￨- uninfected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- no￨L￨DT￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- latent￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- breaking￨L￨VBG￨O￨- out￨L￨RP￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- quarantined￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- computers￨L￨NNS￨O￨- that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ;￨L￨:￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- external￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- connected￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- Internet￨U￨NN￨MISC￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- internal￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- disconnected￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- Internet￨U￨NN￨MISC￨- ;￨L￨:￨O￨- σ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- crashing￨L￨VBG￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- computers￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- ,￨L￨,￨O￨- η￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- δ￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- state￨L￨NN￨O￨- transition￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Stability￨U￨NN￨O￨- of￨L￨IN￨O￨- viral￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcationAccording￨L￨NNP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- obtain￨L￨VB￨O￨- that￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Add￨U￨VB￨O￨- alpha￨L￨NN￨O￨- mu￨L￨NN￨O￨A Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨MISC￨- mu￨L￨NN￨MISC￨- Add￨U￨VB￨MISC￨- alpha￨L￨NN￨O￨- gamma￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- The￨U￨DT￨O￨- linearized￨L￨VBN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- viral￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- L￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- L￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 32￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 33￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 43￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 44￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 54￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- B￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 55￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- b￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 53￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- The￨U￨DT￨O￨- characteristic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- obtained￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Add￨U￨VB￨O￨- p￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- p￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 5￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- tau￨L￨VBD￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- q￨L￨VB￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- q￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- When￨U￨WRB￨O￨- Equality￨U￨NNP￨O￨- tau￨L￨VBD￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Suppose￨U￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- inequalities￨L￨NNS￨O￨- are￨L￨VBP￨O￨- satisfied￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- condition￨L￨NN￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Then￨U￨RB￨O￨- is￨L￨VBZ￨O￨- locally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable.For￨L￨JJ￨O￨- StrictGreaterThan￨U￨NNP￨O￨- tau￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- Equality￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- omega￨L￨FW￨O￨- StrictGreaterThan￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- this￨L￨DT￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- delayed￨L￨VBN￨O￨- system￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨A S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Add￨U￨VB￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- mu￨L￨NN￨O￨- Equality￨U￨NN￨O￨- Derivative￨U￨JJ￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Add￨U￨VB￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- alpha￨L￨NN￨O￨- mu￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- L￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- sigma￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- B￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- delta￨L￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- sigma￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨JJ￨O￨- eta￨L￨NN￨O￨- B￨U￨NN￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- tau￨L￨FW￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- mu￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- needs￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Qualitative￨U￨JJ￨O￨- analysis￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- latent￨L￨JJ￨O￨- and￨L￨CC￨O￨- breaking-out￨L￨NN￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- InternetZizhen￨U￨NNP￨O￨- Zhang1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Yougang￨U￨NN￨O￨- Wang1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2017:31￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2017Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- generalize￨L￨VB￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- known￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- SLBQRS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- computer￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- period￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- uses￨L￨VBZ￨O￨- to￨L￨TO￨O￨- clean￨L￨JJ￨O￨- viruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- breaking￨L￨VBG￨O￨- out￨L￨RP￨O￨- computers￨L￨NNS￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- quarantined￨L￨VBN￨O￨- computers￨L￨NNS￨O￨- .￨L￨.￨O￨- +DAVA￨U￨NNP￨PERSON￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- that￨L￨WDT￨O￨- treats￨L￨VBZ￨O￨- infected￨L￨JJ￨O￨- sub-graphs￨L￨NNS￨O￨- as￨L￨IN￨O￨- super￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- and￨L￨CC￨O￨- all￨L￨DT￨O￨- its￨L￨PRP$￨O￨- infected￨L￨JJ￨O￨- node￨L￨NN￨O￨- neighbors￨L￨NNS￨O￨- as￨L￨IN￨O￨- rooted￨L￨JJ￨O￨- bidirectional￨L￨JJ￨O￨- sub-trees￨L￨NNS￨O￨- that￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- representational￨L￨JJ￨O￨- optimal￨L￨JJ￨O￨- solution￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- adjacent￨L￨JJ￨O￨A neighbors￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- root￨L￨NN￨O￨- super￨L￨JJ￨O￨- node￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- node￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- solution￨L￨NN￨O￨A that￨L￨WDT￨O￨- seeks￨L￨VBZ￨O￨- to￨L￨TO￨O￨- take￨L￨VB￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- local￨L￨JJ￨O￨- recalculations.KeywordsDynamic￨L￨JJ￨O￨- networksImmunizationDominance￨L￨NN￨O￨- tree￨L￨NN￨O￨- BackgroundEvent￨U￨NN￨O￨- propagation￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- complex￨L￨NN￨O￨- and￨L￨CC￨O￨- frequently￨L￨RB￨O￨- studied￨L￨VBN￨O￨- human￨L￨JJ￨O￨- phenomena￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Another￨U￨DT￨O￨- trivial￨L￨JJ￨O￨- situation￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- active￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- available￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- much￨L￨RB￨O￨- larger￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- non-infected￨L￨JJ￨O￨- adjacent￨L￨JJ￨O￨A nodes￨L￨NNS￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +An￨U￨DT￨O￨- effective￨L￨JJ￨O￨- solution￨L￨NN￨O￨A for￨L￨IN￨O￨- arbitrary￨L￨JJ￨O￨- static￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- with￨L￨IN￨O￨- sparse￨L￨JJ￨O￨- connectivity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- called￨L￨VBN￨O￨- Data-Aware￨U￨NNP￨O￨- Vaccine￨U￨NNP￨O￨- Allocation￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- or￨L￨CC￨O￨- DAVA￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2095￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asAgent-based￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- of￨L￨IN￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A diffusionAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsEllen-Wien￨L￨JJ￨O￨- AugustijnTom￨U￨NN￨MISC￨- DoldersumJuliana￨U￨NNP￨MISC￨- UseyaDenie￨U￨NNP￨MISC￨- AugustijnOpen￨U￨NNP￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- PaperFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 05￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1.5￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- introduces￨L￨VBZ￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- agent-based￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- micro-scale￨L￨JJ￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- diffusion￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 8,500￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- resulting￨L￨VBG￨O￨- cumulative￨L￨JJ￨O￨- case￨L￨NN￨O￨- fatality￨L￨NN￨O￨- rate￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 1.2￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- unusually￨L￨RB￨O￨- high￨L￨JJ￨O￨- figure￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- likely￨L￨JJ￨O￨- attributable￨L￨JJ￨O￨- ,￨L￨,￨O￨- among￨L￨IN￨O￨- other￨L￨JJ￨O￨- causes￨L￨NNS￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- unpreparedness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Haitian￨U￨JJ￨NATIONALITY￨- health￨L￨NN￨O￨- infrastructure￨L￨NN￨O￨- to￨L￨TO￨O￨- deal￨L￨VB￨O￨- with￨L￨IN￨O￨- such￨L￨PDT￨O￨- an￨L￨DT￨O￨- emergency￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- earthquake￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- low￨L￨JJ￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- extinction￨L￨NN￨O￨- highlights￨L￨VBZ￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- for￨L￨IN￨O￨- more￨L￨JJR￨O￨- targeted￨L￨VBN￨O￨- and￨L￨CC￨O￨- effective￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- to￨L￨TO￨O￨- possibly￨L￨RB￨O￨- stop￨L￨VB￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Haiti.KeywordsHaiti￨U￨NNP￨O￨- Cholera￨U￨NNP￨CAUSE_OF_DEATH￨- Extinction￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- Stochastic￨U￨NNP￨O￨- simulator￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionThe￨U￨NNP￨O￨- largest￨L￨JJS￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- ever￨L￨RB￨O￨- recorded￨L￨VBN￨O￨- during￨L￨IN￨O￨- the￨L￨DT￨O￨- current￨L￨JJ￨DATE￨- pandemic￨L￨JJ￨O￨- wave￨L￨NN￨O￨- is￨L￨VBZ￨O￨- striking￨L￨JJ￨O￨- Haiti￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 30￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 8￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2055￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asOn￨L￨NN￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Haiti￨U￨NNP￨COUNTRY￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨A epidemicAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsEnrico￨L￨NNP￨O￨- BertuzzoFlavio￨U￨NNP￨MISC￨- FingerLorenzo￨U￨NNP￨MISC￨- MariMarino￨U￨NNP￨MISC￨- GattoAndrea￨U￨NNP￨MISC￨- RinaldoOpen￨U￨NNP￨MISC￨- AccessArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2.3￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 10￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractMore￨U￨NN￨O￨- than￨L￨IN￨O￨- three￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- its￨L￨PRP$￨O￨- appearance￨L￨NN￨O￨- in￨L￨IN￨O￨- Haiti￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- cholera￨L￨NN￨CAUSE_OF_DEATH￨- has￨L￨VBZ￨O￨- already￨L￨RB￨O￨- caused￨L￨VBN￨O￨- more￨L￨JJR￨O￨- than￨L￨IN￨O￨- 8,500￨L￨CD￨NUMBER￨- deaths￨L￨NNS￨O￨- and￨L￨CC￨O￨- 695,000￨L￨CD￨NUMBER￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- feared￨L￨VBN￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- endemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Cholera￨U￨NN￨CAUSE_OF_DEATH￨- spreading￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- spatially-explicit￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- hosted￨L￨VBN￨O￨- in￨L￨IN￨O￨- different￨L￨JJ￨O￨- local￨L￨JJ￨O￨- communities￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- through￨L￨IN￨O￨- hydrologic￨L￨JJ￨O￨- and￨L￨CC￨O￨- human￨L￨JJ￨O￨A mobility￨L￨NN￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- general￨L￨JJ￨TITLE￨- ,￨L￨,￨O￨- SParSE￨U￨JJ￨O￨- outputs￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- hypersurface￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- filtered￨L￨VBN￨O￨- using￨L￨VBG￨O￨- user-defined￨L￨JJ￨O￨- cost￨L￨NN￨O￨- functions￨L￨NNS￨O￨- or￨L￨CC￨O￨- constraints￨L￨NNS￨O￨- to￨L￨TO￨O￨- further￨L￨JJ￨O￨- refine￨L￨VB￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨A characterization.SParSE￨L￨NN￨O￨- is￨L￨VBZ￨O￨- comprised￨L￨VBN￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- components￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- multi-level￨L￨JJ￨O￨- cross-entropy￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- exponential￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- interpolation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- inverse￨L￨JJ￨O￨- biasing￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- below￨L￨IN￨O￨- for￨L￨IN￨O￨- details￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- systems￨L￨NNS￨O￨- with￨L￨IN￨O￨- low￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- intrinsic￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- even￨L￨RB￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- subset￨L￨NN￨O￨- of￨L￨IN￨O￨- reactions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- multi-level￨L￨JJ￨O￨- CE￨U￨NN￨O￨- method￨L￨NN￨O￨- can￨L￨MD￨O￨- exhibit￨L￨VB￨O￨- slow￨L￨JJ￨O￨- convergence￨L￨NN￨O￨A properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- when￨L￨WRB￨O￨- initial￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- are￨L￨VBP￨O￨- far￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- hypersurface￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- Stochastic￨U￨NNP￨O￨- Parameter￨U￨NNP￨O￨- Search￨U￨VB￨O￨- for￨L￨IN￨O￨- Events￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- SParSE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- was￨L￨VBD￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- efficiently￨L￨RB￨O￨- sample￨L￨NN￨O￨- biochemical￨L￨JJ￨O￨- reaction￨L￨NN￨O￨- rate￨L￨NN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- a￨L￨DT￨O￨- user-specified￨L￨JJ￨O￨- target￨L￨NN￨O￨- event￨L￨NN￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- probability￨L￨NN￨O￨- and￨L￨CC￨O￨- error￨L￨NN￨O￨- tolerance￨L￨NN￨O￨- .￨L￨.￨O￨- +SParSE￨U￨VB￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- main￨L￨JJ￨O￨- components￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- multi-level￨L￨JJ￨O￨- cross-entropy￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- identifies￨L￨VBZ￨O￨- biasing￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- to￨L￨TO￨O￨- push￨L￨VB￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- toward￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨A of￨L￨IN￨O￨- interest￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- related￨L￨JJ￨O￨- inverse￨L￨JJ￨O￨- biasing￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- an￨L￨DT￨O￨- optional￨L￨JJ￨O￨- interpolation￨L￨NN￨O￨- of￨L￨IN￨O￨- identified￨L￨VBN￨O￨- parameters￨L￨NNS￨O￨- .￨L￨.￨O￨- +SParSE￨U￨VB￨O￨- +￨L￨CC￨O￨- +￨L￨CC￨O￨- makes￨L￨VBZ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- novel￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- leaping￨L￨VBG￨O￨- methods￨L￨NNS￨O￨- that￨L￨WDT￨O￨- accelerate￨L￨VBP￨O￨- the￨L￨DT￨O￨- convergence￨L￨NN￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- target￨L￨NN￨O￨- event￨L￨NN￨O￨A ,￨L￨,￨O￨- particularly￨L￨RB￨O￨- in￨L￨IN￨O￨- low￨L￨JJ￨O￨- stochasticity￨L￨NN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- employed￨L￨VBN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨A to￨L￨TO￨O￨- this￨L￨DT￨O￨- problem￨L￨NN￨O￨- is￨L￨VBZ￨O￨- robust￨L￨JJ￨O￨- ,￨L￨,￨O￨- easy￨L￨JJ￨O￨- ,￨L￨,￨O￨- reliable￨L￨JJ￨O￨- and￨L￨CC￨O￨- quick￨L￨JJ￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- time.KeywordsCryptosporidiosisHomotopyGastrointestinalDecompositionNoninteger￨L￨NN￨O￨- BackgroundHuman￨U￨NN￨O￨- cryptosporidiosis￨L￨NN￨O￨- is￨L￨VBZ￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- cryptosporidium￨L￨NN￨O￨- protozoan￨L￨NN￨O￨- and￨L￨CC￨O￨- constitutes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- gastrointestinal￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- usually￨L￨RB￨O￨- connected￨L￨VBN￨O￨- with￨L￨IN￨O￨- recreational￨L￨JJ￨O￨- water￨L￨NN￨O￨- use￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- in￨L￨IN￨O￨- Australia￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- other￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- e.g.￨L￨FW￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Approximate￨U￨JJ￨MISC￨- solution￨L￨NN￨O￨A of￨L￨IN￨O￨- cryptosporidiosis￨L￨NN￨O￨- modelEbenezer￨L￨NN￨O￨- Bonyah1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Abdon￨U￨NNP￨PERSON￨- Atangana2￨U￨NNP￨O￨- ,￨L￨,￨O￨- Kazeem￨U￨NNP￨PERSON￨- Okosun3￨U￨NN￨O￨- and￨L￨CC￨O￨- Muhammad￨U￨NNP￨PERSON￨- Altaf￨U￨NNP￨PERSON￨- Khan4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 3:2￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- 2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractCryptosporidium￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- waterborne￨L￨NN￨O￨- transmission￨L￨NN￨O￨- mechanism￨L￨NN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- faecal￨L￨JJ￨O￨- –￨L￨:￨O￨- oral￨L￨JJ￨O￨- path￨L￨NN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- recreational￨L￨JJ￨O￨- water￨L￨NN￨O￨- facilities￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- numerical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- approximate￨L￨JJ￨O￨A solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- function￨L￨NN￨O￨- form￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- noninteger-order￨L￨JJ￨O￨- derivative￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- probable￨L￨JJ￨O￨- approximate￨L￨JJ￨O￨A solution￨L￨NN￨O￨- of￨L￨IN￨O￨- integer￨L￨NN￨O￨- and￨L￨CC￨O￨- noninteger￨L￨NN￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- representing￨L￨VBG￨O￨- cryptosporidiosis￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approximate￨L￨JJ￨O￨A or￨L￨CC￨O￨- estimate￨L￨NN￨O￨- solution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- through￨L￨IN￨O￨- recent￨L￨JJ￨O￨- developed￨L￨JJ￨O￨- analytic￨L￨JJ￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- homotopy￨L￨JJ￨O￨- decomposition￨L￨NN￨O￨- method￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HDM￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- conclude￨L￨VBP￨O￨- that￨L￨IN￨O￨- when￨L￨WRB￨O￨- studying￨L￨VBG￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- constrained￨L￨VBN￨O￨A control￨L￨NN￨O￨- ,￨L￨,￨O￨- special￨L￨JJ￨O￨- care￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- given￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- interplay￨L￨NN￨O￨- with￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- effects.KeywordsDisease￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- modelling￨L￨VBG￨O￨- Control￨U￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- Bifurcations￨U￨NNS￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionThere￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- increasing￨L￨VBG￨O￨- interest￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- integration￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- control￨L￨NN￨O￨- with￨L￨IN￨O￨- economic￨L￨JJ￨O￨- considerations￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- by￨L￨IN￨O￨- constrained￨L￨VBN￨O￨A control￨L￨NN￨O￨- we￨L￨PRP￨O￨- refer￨L￨VBP￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- necessarily￨L￨RB￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- limited￨L￨JJ￨O￨- resources.In￨L￨NN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- select￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- widely￨L￨RB￨O￨- used￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- constrained￨L￨VBN￨O￨- control￨L￨NN￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- its￨L￨PRP$￨O￨- deterministic￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- its￨L￨PRP$￨O￨- simplicity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- mathematically￨L￨RB￨O￨- rich￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- multiple￨L￨JJ￨O￨- stable￨L￨JJ￨O￨- fixed￨L￨JJ￨O￨- points￨L￨NNS￨O￨- and￨L￨CC￨O￨- stable￨L￨JJ￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨A arising￨L￨VBG￨O￨- from￨L￨IN￨O￨- global￨L￨JJ￨O￨- bifurcations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- despite￨L￨IN￨O￨- its￨L￨PRP$￨O￨- simplicity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- mathematically￨L￨RB￨O￨- rich￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- including￨L￨VBG￨O￨- stable￨L￨JJ￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨A and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- global￨L￨JJ￨O￨- bifurcations￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- important￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- in￨L￨IN￨O￨- modelling￨L￨VBG￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- potential￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- the￨L￨DT￨O￨- control￨L￨NN￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- mathop￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- any￨L￨DT￨O￨- constant￨L￨JJ￨O￨- StrictGreaterThan￨U￨NNP￨O￨- xi￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- mathop￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Proof￨U￨NNP￨O￨- By￨U￨IN￨O￨- choosing￨L￨VBG￨O￨- Equality￨U￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- k￨L￨NN￨O￨- Rational￨U￨JJ￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- upsilon￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Equality￨U￨NNP￨O￨- theta￨L￨NN￨O￨A 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- Lemma￨U￨NNP￨LOCATION￨- 2.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- sufficiently￨L￨RB￨O￨- large￨L￨JJ￨O￨- k￨L￨NN￨O￨- and￨L￨CC￨O￨- LessThan￨U￨NN￨MISC￨- StrictLessThan￨U￨NNP￨MISC￨- Add￨U￨VB￨MISC￨- k￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- By￨U￨IN￨O￨- applying￨L￨VBG￨O￨- Lemma￨U￨NNP￨PERSON￨- 2.2￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- Then￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- follows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- Noting￨U￨VBG￨O￨- that￨L￨IN￨O￨- LessThan￨U￨NNP￨MISC￨- StrictLessThan￨U￨NNP￨MISC￨- Add￨U￨VB￨MISC￨- k￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- yields￨L￨NNS￨O￨- that￨L￨WDT￨O￨- Mul￨U￨VBP￨O￨- mathop￨L￨NN￨O￨- sup￨L￨NN￨O￨- This￨U￨DT￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- mathop￨L￨VB￨O￨- To￨U￨TO￨O￨- prove￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- choose￨L￨VBP￨O￨- Equality￨U￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- xi￨L￨NN￨O￨- Add￨U￨VB￨O￨- k￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- k￨L￨NN￨O￨- Rational￨U￨JJ￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- upsilon￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Equality￨U￨NNP￨O￨- theta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- Lemma￨U￨NNP￨O￨- 2.2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- persistent￨L￨JJ￨O￨- in￨L￨IN￨O￨- mean￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- mathop￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Equality￨U￨NN￨O￨- D￨U￨NN￨O￨- Add￨U￨VB￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- sigma￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- mu￨L￨NN￨O￨A phi￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- eta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- phi￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- eta￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- mu￨L￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- phi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- phi￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- eta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 2￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- mu￨L￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- phi￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨- phi￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- eta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- mu￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- mu￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- sigma￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- verified￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- is￨L￨VBZ￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- exponentially￨L￨RB￨O￨- stable￨L￨JJ￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- mu￨L￨NN￨O￨A -1￨L￨CD￨NUMBER￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- improves￨L￨VBZ￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- permits￨L￨VBZ￨O￨- solutions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- positive￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- theorem￨L￨NN￨O￨- on￨L￨IN￨O￨- exponential￨L￨JJ￨O￨- stability￨L￨NN￨O￨- in￨L￨IN￨O￨- mean￨L￨JJ￨O￨- square￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Subsequently￨U￨NNP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Witbooi￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- integral￨L￨JJ￨O￨A equation￨L￨NN￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- avoid￨L￨VB￨O￨- considering￨L￨VBG￨O￨- various￨L￨JJ￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ad￨L￨NN￨O￨- hoc.The￨L￨NN￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- approach￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- cover￨L￨VB￨O￨- various￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- for￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- on￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- interval￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- or￨L￨CC￨O￨- fractional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- unified￨L￨JJ￨O￨- way￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- avoids￨L￨VBZ￨O￨- treating￨L￨VBG￨O￨- these￨L￨DT￨O￨- problems￨L￨NNS￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- case-by-case￨L￨JJ￨O￨- basis￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Positive￨U￨JJ￨MISC￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- integral￨L￨JJ￨O￨A equations￨L￨NNS￨O￨- with￨L￨IN￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equationsChunfang￨L￨NN￨O￨- Shen1￨U￨NN￨O￨- ,￨L￨,￨O￨- Hui￨U￨NNP￨O￨- Zhou1￨U￨NNP￨O￨- and￨L￨CC￨O￨- Liu￨U￨NNP￨PERSON￨- Yang1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2016:260￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- Guo-Krasnoselskii￨U￨NNP￨LOCATION￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- nonexistence￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- integral￨L￨JJ￨O￨- equation￨L￨NN￨O￨- with￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- generalization￨L￨NN￨O￨- of￨L￨IN￨O￨- various￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- for￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- on￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- interval￨L￨NN￨O￨- and￨L￨CC￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- or￨L￨CC￨O￨- fractional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- giving￨L￨VBG￨O￨- some￨L￨DT￨O￨- examples￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- will￨L￨MD￨O￨- show￨L￨VB￨O￨- how￨L￨WRB￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- consider￨L￨VB￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- variety￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- of￨L￨IN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- ,￨L￨,￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- on￨L￨IN￨O￨- time￨L￨NN￨O￨- scales￨L￨NNS￨O￨- or￨L￨CC￨O￨- fractional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations.Keywordspositive￨L￨JJ￨O￨- solutionboundary￨L￨JJ￨O￨- value￨L￨NN￨O￨- problemintegral￨L￨JJ￨O￨- equationfixed￨L￨JJ￨O￨- pointconeMSC45C0534B18￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionWe￨U￨NN￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- eigenvalues￨L￨NNS￨O￨- yielding￨L￨VBG￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- integral￨L￨JJ￨O￨A equations￨L￨NNS￨O￨- where￨L￨WRB￨O￨- lambda￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- H1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- f￨L￨LS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- Song￨U￨NN￨O￨- and￨L￨CC￨O￨- Chen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- predator-prey￨L￨JJ￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- structure￨L￨NN￨O￨- :￨L￨:￨O￨- where￨L￨WRB￨O￨- u￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- immature￨L￨JJ￨O￨- and￨L￨CC￨O￨- mature￨L￨JJ￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- v￨L￨LS￨O￨- t￨L￨NN￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- predator.Positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- n-dimensional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- system￨L￨NN￨O￨- or￨L￨CC￨O￨- fractional￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- some￨L￨DT￨O￨- boundary￨L￨NN￨O￨A conditions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- received￨L￨VBN￨O￨- wide￨L￨JJ￨O￨- attention￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- its￨L￨PRP$￨O￨- distinguished￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- in￨L￨IN￨O￨- engineering￨L￨NN￨O￨- ,￨L￨,￨O￨- science￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- biology￨L￨NN￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- fields￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- nonexistence￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- integral￨L￨JJ￨O￨A equation￨L￨NN￨O￨- system￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- H1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- H2￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- so￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- may￨L￨MD￨O￨- include￨L￨VB￨O￨- some￨L￨DT￨O￨- known￨L￨JJ￨O￨- results￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- special￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- and￨L￨CC￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- unconsidered￨L￨JJ￨O￨- boundary￨L￨NN￨O￨- value￨L￨NN￨O￨- problems￨L￨NNS￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- formulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- integral￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- like￨L￨IN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- Quebec￨U￨NNP￨STATE_OR_PROVINCE￨- City￨U￨NNP￨LOCATION￨- presents￨L￨VBZ￨O￨- an￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- location￨L￨NN￨O￨- for￨L￨IN￨O￨- expansion￨L￨NN￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- as￨L￨RB￨O￨- ,￨L￨,￨O￨- Las￨U￨NNP￨CITY￨- Vegas￨U￨NNP￨CITY￨- is￨L￨VBZ￨O￨- suboptimal.KeywordsLocational￨L￨JJ￨O￨- QualityGreat￨U￨NNP￨ORGANIZATION￨- Toronto￨U￨NNP￨ORGANIZATION￨- AreaNational￨U￨NNP￨ORGANIZATION￨- Hockey￨U￨NN￨ORGANIZATION￨- LeagueSeason￨U￨NN￨O￨- TicketBasic￨U￨NNP￨O￨- Reproductive￨U￨NNP￨O￨- Ratio￨U￨NNP￨O￨- IntroductionExpansion￨U￨NNP￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- National￨U￨NNP￨ORGANIZATION￨- Hockey￨U￨NN￨ORGANIZATION￨- League￨U￨NN￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- NHL￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- a￨L￨DT￨O￨- major￨L￨JJ￨O￨- conversation￨L￨NN￨O￨- topic￨L￨NN￨O￨- of￨L￨IN￨O￨- team￨L￨NN￨O￨- owners￨L￨NNS￨O￨- ,￨L￨,￨O￨- players￨L￨NNS￨O￨- and￨L￨CC￨O￨- fans￨L￨NNS￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨DATE￨- past￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Success￨U￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- NHL￨U￨NN￨ORGANIZATION￨- team￨L￨NN￨O￨- will￨L￨MD￨O￨- depend￨L￨VB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- locational￨L￨JJ￨O￨- quality￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- city￨L￨NN￨O￨A or￨L￨CC￨O￨- geographic￨L￨JJ￨O￨- region￨L￨NN￨O￨- that￨L￨WDT￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- support￨L￨VB￨O￨- a￨L￨DT￨O￨- team￨L￨NN￨O￨- through￨L￨IN￨O￨- thick￨L￨JJ￨O￨- and￨L￨CC￨O￨- thin￨L￨JJ￨O￨- .￨L￨.￨O￨- +Success￨U￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- expansion￨L￨NN￨O￨A team￨L￨NN￨O￨- will￨L￨MD￨O￨- rely￨L￨VB￨O￨- on￨L￨IN￨O￨- approved￨L￨VBN￨O￨- geographic￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- most￨L￨RBS￨O￨- importantly￨L￨RB￨O￨- fan￨L￨NN￨O￨- support￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- relocation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Atlanta￨U￨NNP￨ORGANIZATION￨- Thrashers￨U￨NNPS￨ORGANIZATION￨- to￨L￨TO￨O￨- Winnipeg￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- team￨L￨NN￨O￨- was￨L￨VBD￨O￨- renamed￨L￨VBN￨O￨- the￨L￨DT￨O￨- Winnipeg￨U￨NNP￨ORGANIZATION￨- Jets￨U￨NNS￨ORGANIZATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- to￨L￨TO￨O￨- become￨L￨VB￨O￨- the￨L￨DT￨O￨- Phoenix￨U￨NNP￨ORGANIZATION￨- Coyotes￨U￨NNPS￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- led￨L￨VBN￨O￨- to￨L￨TO￨O￨- speculation￨L￨NN￨O￨- that￨L￨IN￨O￨- Quebec￨U￨NNP￨STATE_OR_PROVINCE￨- City￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- Quebec￨U￨NNP￨ORGANIZATION￨- Nordiques￨U￨NNPS￨ORGANIZATION￨- were￨L￨VBD￨O￨- moved￨L￨VBN￨O￨- to￨L￨TO￨O￨- form￨L￨VB￨O￨- the￨L￨DT￨O￨- Colorado￨U￨NNP￨ORGANIZATION￨- Avalanche￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- could￨L￨MD￨O￨- provide￨L￨VB￨O￨- an￨L￨DT￨O￨- ideal￨L￨JJ￨O￨- location￨L￨NN￨O￨- for￨L￨IN￨O￨- relocation￨L￨NN￨O￨- or￨L￨CC￨O￨- expansion￨L￨NN￨O￨A NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- this￨L￨DT￨O￨- sensitivity￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨A structure￨L￨NN￨O￨A is￨L￨VBZ￨O￨- assessed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- ways￨L￨NNS￨O￨- :￨L￨:￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- predictions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- routine￨L￨JJ￨O￨- drug￨L￨NN￨O￨- therapy￨L￨NN￨O￨- ,￨L￨,￨O￨- general￨L￨JJ￨TITLE￨- vector￨L￨NN￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- VC￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- mass￨L￨NN￨O￨- drug￨L￨NN￨O￨- administration￨L￨NN￨O￨- and￨L￨CC￨O￨- whether￨L￨IN￨O￨- these￨L￨DT￨O￨- predictions￨L￨NNS￨O￨- differ￨L￨VBP￨O￨- between￨L￨IN￨O￨- models￨L￨NNS￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- data￨L￨NNS￨O￨- or￨L￨CC￨O￨- not￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- epidemiology￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨A models￨L￨NNS￨O￨A ,￨L￨,￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- among￨L￨IN￨O￨- other￨L￨JJ￨O￨- things￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- emergence￨L￨NN￨O￨- and￨L￨CC￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- and￨L￨CC￨O￨- efficacy￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- drug￨L￨NN￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- vaccine￨L￨NN￨O￨- introduction￨L￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- control￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- Murray￨U￨NNP￨O￨- JD￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 2003￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Mathematical￨U￨JJ￨O￨- Biology￨U￨NN￨O￨- II￨U￨CD￨NUMBER￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 18￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- but￨L￨CC￨O￨- different￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- structures￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- ranging￨L￨VBG￨O￨- from￨L￨IN￨O￨- simple￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- to￨L￨TO￨O￨- complex￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- were￨L￨VBD￨O￨- compared￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- absence￨L￨NN￨O￨- and￨L￨CC￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- several￨L￨JJ￨O￨- policy￨L￨NN￨O￨- interventions￨L￨NNS￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- sensitivity￨L￨NN￨O￨- to￨L￨TO￨O￨- model￨L￨NN￨TITLE￨A structure￨L￨NN￨O￨A .￨L￨.￨O￨- +Yet￨U￨CC￨O￨- there￨L￨EX￨O￨- may￨L￨MD￨O￨- still￨L￨RB￨O￨- be￨L￨VB￨O￨- differences￨L￨NNS￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- predictions￨L￨NNS￨O￨- between￨L￨IN￨O￨- compartmental￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- equivalent￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- but￨L￨CC￨O￨- different￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨A structure￨L￨NN￨O￨A .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- single￨L￨JJ￨O￨- compartmental￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨A structure￨L￨NN￨O￨A that￨L￨WDT￨O￨- fits￨L￨VBZ￨O￨- all￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- many￨L￨JJ￨O￨- different￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- that￨L￨WDT￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Ruan￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨A Mul￨U￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- Pow￨U￨NNP￨MISC￨- Add￨U￨VB￨MISC￨- Pow￨U￨NN￨MISC￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- corresponds￨L￨VBZ￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- saturated￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- obtained￨L￨VBN￨O￨- rich￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NN￨O￨- model.Wang￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- considered￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- form￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- d￨L￨NN￨O￨- Mul￨U￨NN￨PERSON￨- S￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- I￨U￨PRP￨O￨- a￨L￨DT￨O￨- Pow￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- d￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- removed￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- who￨L￨WP￨O￨- lose￨L￨VBP￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- return￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- Pow￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- intervention￨L￨NN￨O￨- policies￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- valid￨L￨JJ￨O￨- contact￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- a￨L￨DT￨O￨- Pow￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- .￨L￨.￨O￨- +He￨U￨PRP￨O￨- assumed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- Equality￨U￨NN￨O￨- N￨U￨NN￨O￨- Add￨U￨VB￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- to￨L￨TO￨O￨- ensure￨L￨VB￨O￨- a￨L￨DT￨O￨- nonmonotonic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- force￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- StrictGreaterThan￨U￨NN￨O￨- f￨L￨FW￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- I￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- ii￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- StrictGreaterThan￨U￨NNP￨O￨- xi￨L￨NN￨O￨A 0￨L￨CD￨NUMBER￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- Pow￨U￨VBP￨O￨- f￨L￨SYM￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- xi￨L￨VBP￨O￨- and￨L￨CC￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- Pow￨U￨VBP￨O￨- f￨L￨SYM￨O￨- I￨U￨PRP￨O￨- -1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- I￨U￨PRP￨O￨- xi￨L￨VBP￨O￨- .￨L￨.￨O￨- +Capasso￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Serio￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- introduced￨L￨VBD￨O￨- a￨L￨DT￨O￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- S￨U￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- delta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- StrictGreaterThan￨U￨NN￨O￨- delta￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +At￨U￨IN￨O￨- present￨L￨JJ￨DATE￨- ,￨L￨,￨O￨- lots￨L￨NNS￨O￨- of￨L￨IN￨O￨- scholars￨L￨NNS￨O￨- have￨L￨VBP￨O￨- studied￨L￨VBN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- spatial￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- traveling￨L￨VBG￨O￨- wave￨L￨NN￨O￨- solutions￨L￨NNS￨O￨- play￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- the￨L￨DT￨O￨- long-time￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- reaction-diffusion￨L￨NN￨O￨- models￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 24￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +van￨L￨NN￨O￨- den￨L￨NN￨O￨- Driessche￨U￨NNP￨O￨- and￨L￨CC￨O￨- Watmough￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- also￨L￨RB￨O￨- studied￨L￨VBD￨O￨- an￨L￨DT￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- k￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- StrictGreaterThan￨U￨NNP￨O￨- b￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- GreaterThan￨U￨NNP￨PERSON￨- m￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- k￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +According￨U￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- can￨L￨MD￨O￨- see￨L￨VB￨O￨- that￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NN￨PERSON￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Lambda￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- mu￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- when￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- Mul￨U￨NN￨PERSON￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- S￨U￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- approach￨L￨NN￨O￨- has￨L￨VBZ￨O￨- some￨L￨DT￨O￨- limitations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- specifically￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- almost￨L￨RB￨O￨- surely￨L￨RB￨O￨- exponential￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- Pow￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- stochastic￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stochastic￨U￨NNP￨MISC￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- modelBo￨L￨NN￨O￨- Yang1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2016:226￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- latent￨L￨JJ￨O￨- patients￨L￨NNS￨O￨A and￨L￨CC￨O￨- active￨L￨JJ￨O￨- patients￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- Mul￨U￨JJ￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A which￨L￨WDT￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- parameters￨L￨NNS￨O￨- Pow￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- s￨L￨NNS￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨A dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- exchange￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- layer￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A network￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- analyzes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- node￨L￨NN￨O￨- properties￨L￨NNS￨O￨- and￨L￨CC￨O￨- correlation￨L￨NN￨O￨- among￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- energy￨L￨NN￨O￨- field￨L￨NN￨O￨- and￨L￨CC￨O￨- graph￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Node￨U￨NN￨MISC￨- importance￨L￨NN￨O￨- evaluation￨L￨NN￨O￨- method￨L￨NN￨O￨- in￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A network￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- energy￨L￨NN￨O￨- field￨L￨NN￨O￨- modelQindong￨L￨NN￨O￨- Sun1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yimin￨U￨NNP￨O￨- Qiao1￨U￨NNP￨O￨- ,￨L￨,￨O￨- Jiamin￨U￨NNP￨O￨- Wang3￨U￨NNP￨O￨- and￨L￨CC￨O￨- Si￨U￨NNP￨O￨- Shen1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2016:199￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- The￨U￨DT￨O￨- Author￨U￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- s￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- puts￨L￨VBZ￨O￨- forward￨L￨RB￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- importance￨L￨NN￨O￨- evaluation￨L￨NN￨O￨- method￨L￨NN￨O￨- in￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A network￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- energy￨L￨NN￨O￨- field￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- stability￨L￨NN￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- indicator￨L￨NN￨O￨- of￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A network￨L￨NN￨O￨- performance￨L￨NN￨O￨- .￨L￨.￨O￨- +Appropriate￨U￨JJ￨O￨- node￨L￨NN￨O￨- importance￨L￨NN￨O￨- evaluation￨L￨NN￨O￨A method￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- precondition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- identification￨L￨NN￨O￨- of￨L￨IN￨O￨- key￨L￨JJ￨O￨- node￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- stability￨L￨NN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- large￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- numerical￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- percentage￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- internal￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- )￨L￨-RRB-￨O￨- to￨L￨TO￨O￨- denote￨L￨VB￨O￨- the￨L￨DT￨O￨- saturation￨L￨NN￨O￨A effect￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- ,￨L￨,￨O￨- use￨L￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- to￨L￨TO￨O￨- replace￨L￨VB￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Impact￨U￨NN￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A detoxication￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- computer￨L￨NN￨O￨- virusXianxiu￨L￨NN￨O￨- Zhang1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- authorView￨L￨NN￨O￨- ORCID￨U￨NN￨O￨- ID￨U￨NN￨STATE_OR_PROVINCE￨- profile￨L￨NN￨O￨- ,￨L￨,￨O￨- Chuandong￨U￨NNP￨LOCATION￨- Li1￨U￨NN￨O￨- and￨L￨CC￨O￨- Tingwen￨U￨NN￨MISC￨- Huang3￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2016:218￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- SIRS￨U￨NNP￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- detoxication￨L￨NN￨O￨- and￨L￨CC￨O￨- saturation￨L￨NN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- how￨L￨WRB￨O￨- impulsive￨L￨JJ￨O￨A detoxication￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- saturation￨L￨NN￨O￨- effects￨L￨NNS￨O￨- prohibit￨L￨VBP￨O￨- virus￨L￨NN￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- established￨L￨VBN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theoretical￨L￨JJ￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- a￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- virus-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- BRR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- unity￨L￨NN￨O￨A ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- b￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- uniformly￨L￨RB￨O￨- permanent￨L￨JJ￨O￨- when￨L￨WRB￨O￨- BRR￨U￨NN￨ORGANIZATION￨- exceeds￨L￨VBZ￨O￨- unity￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- (￨L￨-LRB-￨O￨- c￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- a￨L￨DT￨O￨- supercritical￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- when￨L￨WRB￨O￨- BRR￨U￨NN￨O￨- equals￨L￨VBZ￨O￨- unity￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- A￨U￨NN￨O￨- coupled￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- government￨L￨NN￨O￨- communication￨L￨NN￨O￨- and￨L￨CC￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- emergenciesJiuping￨L￨VBG￨O￨- Xu1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Mengxiang￨U￨NN￨O￨- Zhang1￨U￨NN￨O￨- and￨L￨CC￨O￨- Jingneng￨U￨NN￨MISC￨- Ni1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2016:208￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- dissemination￨L￨NN￨O￨- of￨L￨IN￨O￨- official￨L￨JJ￨O￨A messages￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- rumors￨L￨NNS￨O￨- are￨L￨VBP￨O￨- both￨L￨DT￨O￨- key￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- in￨L￨IN￨O￨- emergency￨L￨NN￨O￨- situations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Official￨U￨NNP￨O￨- dissemination￨L￨NN￨O￨- of￨L￨IN￨O￨- emergency￨L￨NN￨O￨- event￨L￨NN￨O￨- information￨L￨NN￨O￨- through￨L￨IN￨O￨- official￨L￨NN￨O￨A and￨L￨CC￨O￨- sanctioned￨L￨VBN￨O￨- channels￨L￨NNS￨O￨- can￨L￨MD￨O￨- have￨L￨VB￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- public￨L￨NN￨O￨- ’s￨L￨POS￨O￨- behavior￨L￨NN￨O￨- since￨L￨IN￨O￨- false￨L￨JJ￨O￨- rumors￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- quashed￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- true￨L￨JJ￨O￨- information￨L￨NN￨O￨- confirmed￨L￨VBD￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- rapid￨L￨JJ￨O￨- dissemination￨L￨NN￨O￨- of￨L￨IN￨O￨- government￨L￨NN￨O￨- information￨L￨NN￨O￨- ,￨L￨,￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- effective￨L￨JJ￨O￨- and￨L￨CC￨O￨- essential￨L￨JJ￨O￨- measure￨L￨NN￨O￨- to￨L￨TO￨O￨- combat￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- false￨L￨JJ￨O￨- rumors￨L￨NNS￨O￨A and￨L￨CC￨O￨- to￨L￨TO￨O￨- guide￨L￨VB￨O￨- public￨L￨JJ￨O￨- opinion￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- coupled￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- established￨L￨VBN￨O￨- to￨L￨TO￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- official￨L￨JJ￨O￨A government￨L￨NN￨O￨- communiques￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- rumors￨L￨NNS￨O￨- during￨L￨IN￨O￨- emergencies￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- mathematical￨L￨JJ￨O￨- property￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- discussed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- official￨L￨JJ￨O￨A message￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- has￨L￨VBZ￨O￨- positive￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- thwarting￨L￨VBG￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Influence￨U￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- mobility￨L￨NN￨O￨- on￨L￨IN￨O￨- virus￨L￨NN￨O￨- spreading￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨A in￨L￨IN￨O￨- multi-hop￨L￨JJ￨O￨- networkPeng￨L￨NN￨O￨- Li1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Siyu￨U￨NN￨O￨- Liu1￨U￨NN￨O￨- ,￨L￨,￨O￨- Jiyu￨U￨NNP￨PERSON￨- Jin1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Zhisen￨U￨NN￨MISC￨- Wang1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2016:172￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractMulti-hop￨U￨NNP￨O￨- network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- received￨L￨VBN￨O￨- growing￨L￨VBG￨O￨- attention￨L￨NN￨O￨- recently￨L￨RB￨DATE￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- widely￨L￨RB￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- network￨L￨NN￨O￨- communication￨L￨NN￨O￨- technology￨L￨NN￨O￨- .￨L￨.￨O￨- +Virus￨U￨NN￨O￨- spreading￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨A are￨L￨VBP￨O￨- examined￨L￨VBN￨O￨- through￨L￨IN￨O￨- contact￨L￨NN￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- ,￨L￨,￨O￨- communication￨L￨NN￨O￨- radius￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- distribution￨L￨NN￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- initial￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- node￨L￨NN￨O￨- mobility￨L￨NN￨O￨- has￨L￨VBZ￨O￨- significant￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- virus￨L￨NN￨O￨- spreading￨L￨NN￨O￨- behaviors￨L￨NNS￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stability￨U￨NN￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fractional-order￨L￨NN￨O￨- epidemics￨L￨NNS￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- equilibriumsDavood￨L￨NN￨O￨- Rostamy1￨U￨NN￨O￨- and￨L￨CC￨O￨- Ehsan￨U￨NN￨MISC￨- Mottaghi1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2016:170￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- fractional-order￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A ordinary￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Caputo￨U￨NNP￨O￨- derivative￨L￨NN￨O￨- of￨L￨IN￨O￨- order￨L￨NN￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- region￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨VBZ￨O￨- increases￨L￨NNS￨O￨- by￨L￨IN￨O￨- choosing￨L￨VBG￨O￨- an￨L￨DT￨O￨- appropriate￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- α￨L￨NN￨O￨- .￨L￨.￨O￨- +Mathematically￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- containing￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- lead￨L￨NN￨O￨- to￨L￨TO￨O￨- multiple￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A points￨L￨NNS￨O￨A and￨L￨CC￨O￨- show￨L￨VBP￨O￨- bifurcation￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- applying￨L￨VBG￨O￨- fractional￨L￨JJ￨O￨A calculus￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- reason￨L￨NN￨O￨- that￨L￨WDT￨O￨- intra-domains￨L￨VBZ￨O￨- interventions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- always￨L￨RB￨O￨- sufficient￨L￨JJ￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- people￨L￨NNS￨O￨- belonging￨L￨VBG￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- domain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- neighborhood￨L￨NN￨O￨- ,￨L￨,￨O￨- town￨L￨NN￨O￨- or￨L￨CC￨O￨- city￨L￨NN￨O￨- for￨L￨IN￨O￨- example￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- rapid￨L￨JJ￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- travel-blocking￨L￨NN￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨DURATION￨- second￨L￨JJ￨DURATION￨- approach￨L￨NN￨O￨- presenting￨L￨VBG￨O￨- inter-domains￨L￨NNS￨O￨- interventions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- health-policy￨L￨NN￨O￨- makers￨L￨NNS￨O￨- could￨L￨MD￨O￨- follow￨L￨VB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- restricting￨L￨VBG￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- suspicious￨L￨JJ￨O￨- people￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- participate￨L￨VB￨O￨- in￨L￨IN￨O￨- spreading￨L￨VBG￨O￨- HIV/AIDS￨U￨NN￨O￨- via￨L￨IN￨O￨- travel￨L￨NN￨O￨- ,￨L￨,￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- domains￨L￨NNS￨O￨A at￨L￨IN￨O￨- high-risk￨L￨JJ￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- enter￨L￨VB￨O￨- domains￨L￨NNS￨O￨- with￨L￨IN￨O￨- lower￨L￨JJR￨O￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +Sometimes￨U￨RB￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- most-deadly￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- fact￨L￨NN￨O￨- believed￨L￨VBD￨O￨- that￨L￨IN￨O￨- awareness￨L￨NN￨O￨A may￨L￨MD￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- social￨L￨JJ￨O￨- vaccine￨L￨NN￨O￨- for￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- this￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- that￨L￨IN￨O￨- it￨L￨PRP￨O￨- could￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- consciousness￨L￨NN￨O￨- amongst￨L￨IN￨O￨- children￨L￨NNS￨O￨- and￨L￨CC￨O￨- adults￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Song￨U￨NN￨O￨- and￨L￨CC￨O￨- Pang￨U￨NN￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIQR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible-infective-quarantined-recovered￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- input￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dS￨L￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- sigma￨L￨NN￨O￨A Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- sigma￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- p￨L￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- d￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dR￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- ,￨L￨,￨O￨- quarantined￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- system￨L￨NN￨O￨- with￨L￨IN￨O￨- delays￨L￨NNS￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dS￨L￨NN￨O￨- Add￨U￨VB￨O￨- A￨U￨DT￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- I￨U￨PRP￨O￨- 2￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨A Add￨U￨VB￨O￨- a￨L￨DT￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- p￨L￨NN￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- sigma￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- b￨L￨NN￨O￨- d￨L￨NN￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dR￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- p￨L￨NN￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- delay￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- f￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- f￨L￨SYM￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Derivative￨U￨JJ￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- The￨U￨DT￨O￨- linear￨L￨JJ￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Case￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- false￨L￨JJ￨O￨- ,￨L￨,￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- reduces￨L￨VBZ￨O￨- to￨L￨TO￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨A m￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Obviously￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- H￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 8￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- -￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 11￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- holds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- all￨L￨PDT￨O￨- the￨L￨DT￨O￨- roots￨L￨NNS￨O￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 7￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- must￨L￨MD￨O￨- have￨L￨VB￨O￨- negative￨L￨JJ￨O￨- real￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- Equality￨U￨NNP￨O￨- tau￨L￨FW￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Add￨U￨VB￨O￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨A m￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- lambda￨L￨NN￨ORGANIZATION￨- 3￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- bigl￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- bigr￨L￨NN￨O￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- lambda￨L￨NN￨O￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- Pow￨U￨NNP￨ORGANIZATION￨- lambda￨L￨NN￨ORGANIZATION￨- 3￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Let￨U￨VB￨O￨- Equality￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- omega￨L￨FW￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- StrictGreaterThan￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- sin￨L￨NN￨O￨- Mul￨U￨NN￨O￨- omega￨L￨JJ￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Add￨U￨VB￨O￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- _￨L￨VBG￨O￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- cos￨L￨NNS￨O￨- Mul￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- m￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 4￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- get￨L￨VB￨O￨- Equality￨U￨NNP￨O￨- Add￨U￨VB￨O￨- c￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 20￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- 21￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 22￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 4￨L￨CD￨NUMBER￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨O￨- _￨L￨VBD￨O￨- {￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 6￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 8￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- Let￨U￨VB￨O￨- Equality￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 2￨L￨CD￨NUMBER￨- v￨L￨LS￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 14￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Define￨U￨VB￨O￨- The￨U￨DT￨O￨- discussion￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- roots￨L￨NNS￨O￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 15￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Existence￨U￨NN￨O￨- of￨L￨IN￨O￨- Hopf￨U￨NNP￨PERSON￨- bifurcationAccording￨L￨NNP￨O￨- to￨L￨TO￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- computation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨PERSON￨- Pow￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- 4￨L￨CD￨NUMBER￨- Pow￨U￨NNP￨O￨- d￨L￨NN￨O￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨A Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- d￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NNP￨MISC￨- Pow￨U￨NNP￨MISC￨- A￨U￨NNP￨MISC￨- 2￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- equilibriums￨L￨NNS￨O￨- where￨L￨WRB￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- Add￨U￨VB￨O￨- sigma￨L￨NN￨O￨- Add￨U￨VB￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- a￨L￨DT￨O￨- d￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Let￨U￨VB￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- general￨L￨JJ￨TITLE￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- formulated￨L￨VBN￨O￨- as￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨PRP￨O￨- Tuple￨U￨VBP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- gamma￨L￨NN￨O￨A Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- g￨L￨NN￨O￨- I￨U￨PRP￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- R￨U￨NNP￨O￨- Tuple￨U￨NNP￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- mu￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Lambda￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NNP￨O￨- mu￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- gamma￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Asymptotic￨U￨JJ￨MISC￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- global￨L￨JJ￨O￨- positive￨L￨JJ￨O￨A solution￨L￨NN￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- media￨L￨NNS￨O￨- coverageMiaochan￨L￨NN￨O￨- Zhao1￨U￨NN￨O￨- and￨L￨CC￨O￨- Huitao￨U￨NN￨O￨- Zhao1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2016:149￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- features￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- incorporating￨L￨VBG￨O￨- media￨L￨NNS￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- the￨L￨DT￨O￨- positivity￨L￨NN￨O￨- and￨L￨CC￨O￨- boundedness￨L￨NN￨O￨- of￨L￨IN￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- within￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- environment￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- asymptotical￨L￨JJ￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibria￨L￨NNS￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A .￨L￨.￨O￨- +Secondly￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- global￨L￨JJ￨O￨- positive￨L￨JJ￨O￨A solution￨L￨NN￨O￨A and￨L￨CC￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- solution￨L￨NN￨O￨- oscillates￨L￨VBZ￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibria￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- certain￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- and￨L￨CC￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stage-structured￨L￨JJ￨O￨- predator-prey￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- prey￨L￨NN￨O￨A impulsively￨L￨RB￨O￨- diffusing￨L￨VBG￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- patches￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- triangle￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- triangle￨L￨NN￨O￨- y￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- triangle￨L￨NN￨O￨- y￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- suppose￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- is￨L￨VBZ￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- patches￨L￨NNS￨O￨- connected￨L￨VBN￨O￨- by￨L￨IN￨O￨- diffusion￨L￨NN￨O￨- and￨L￨CC￨O￨- occupied￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- single￨L￨JJ￨O￨- species￨L￨NNS￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- Equality￨U￨NNP￨O￨- i￨L￨FW￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- density￨L￨NN￨O￨- of￨L￨IN￨O￨- species￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- ith￨L￨NN￨O￨- patch￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- biological￨L￨JJ￨O￨- pest￨L￨NN￨O￨- control￨L￨NN￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- a￨L￨DT￨O￨- pest￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- program￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- releases￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨VBN￨O￨- yield￨L￨NN￨O￨- of￨L￨IN￨O￨- predators￨L￨NNS￨O￨- that￨L￨WDT￨O￨- prey￨L￨VBP￨O￨A on￨L￨IN￨O￨- the￨L￨DT￨O￨- pest￨L￨JJ￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +Illustrative￨U￨JJ￨O￨- example￨L￨NN￨O￨- is￨L￨VBZ￨O￨- included￨L￨VBN￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- the￨L￨DT￨O￨- validity￨L￨NN￨O￨- and￨L￨CC￨O￨- applicability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- operational￨L￨JJ￨O￨- matrices.Mathematics￨L￨NNS￨O￨- Subject￨U￨JJ￨O￨- Classification65C30￨U￨NN￨O￨- 60H35￨L￨NN￨O￨- 65C20￨L￨NN￨O￨- 60H20￨L￨NN￨O￨- 37N25￨L￨CD￨NUMBER￨- Open￨U￨NNP￨MISC￨- image￨L￨NN￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- window￨L￨NN￨O￨- Download￨U￨VB￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- article￨L￨NN￨O￨- textReferences1.Babolian￨L￨NN￨MISC￨- E.￨U￨NNP￨MISC￨- ,￨L￨,￨O￨- Mokhtari￨U￨NNP￨PERSON￨- R.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Salmani￨U￨NNP￨PERSON￨- M.￨U￨NNP￨O￨- :￨L￨:￨O￨- Using￨U￨VBG￨O￨- direct￨L￨JJ￨O￨- method￨L￨NN￨O￨- for￨L￨IN￨O￨- solving￨L￨VBG￨O￨- variational￨L￨JJ￨O￨- problems￨L￨NNS￨O￨- via￨L￨IN￨O￨- triangular￨L￨JJ￨O￨- orthogonal￨L￨JJ￨O￨- functions￨L￨NNS￨O￨A .￨L￨.￨O￨- +201￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 452￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 456￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- MathSciNetzbMATHGoogle￨U￨NNP￨O￨- Scholar3.Babolian￨U￨NNP￨O￨- E.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Masouri￨U￨NNP￨O￨- Z.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Hatamzadeh-Varmazyarb￨U￨NNP￨O￨- S.￨U￨NNP￨O￨- :￨L￨:￨O￨- Numerical￨U￨JJ￨O￨- solution￨L￨NN￨O￨- of￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- Volterra￨U￨NNP￨CITY￨- –￨L￨:￨O￨- Fredholm￨U￨NNP￨PERSON￨- integro-differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- via￨L￨IN￨O￨- direct￨L￨JJ￨O￨- method￨L￨NN￨O￨- using￨L￨VBG￨O￨- triangular￨L￨JJ￨O￨- functions￨L￨NNS￨O￨A .￨L￨.￨O￨- +58￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 239￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 247￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2009￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- MathSciNetCrossRefzbMATHGoogle￨U￨NNP￨O￨- Scholar4.Babolian￨U￨NNP￨O￨- E.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Maleknejad￨U￨NNP￨PERSON￨- K.￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Roodaki￨U￨NNP￨O￨- M.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Almasieh￨U￨NNP￨O￨- H.￨U￨NNP￨O￨- :￨L￨:￨O￨- Two-dimensional￨U￨JJ￨O￨- triangular￨L￨JJ￨O￨- functions￨L￨NNS￨O￨A and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- nonlinear￨L￨JJ￨O￨- 2D￨L￨NN￨O￨- Volterra￨U￨NNP￨CITY￨- –￨L￨:￨O￨- Fredholm￨U￨NNP￨PERSON￨- integral￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +191￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 206￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 217￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2007￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- MathSciNetzbMATHGoogle￨U￨NNP￨O￨- Scholar2.Babolian￨U￨NNP￨O￨- E.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Marzban￨U￨NNP￨PERSON￨- H.R.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Salmani￨U￨NNP￨PERSON￨- M.￨U￨NNP￨O￨- :￨L￨:￨O￨- Using￨U￨VBG￨O￨- triangular￨L￨JJ￨O￨- orthogonal￨L￨JJ￨O￨- functions￨L￨NNS￨O￨A for￨L￨IN￨O￨- solving￨L￨VBG￨O￨- Fredholm￨U￨NNP￨PERSON￨- integral￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- kind￨L￨NN￨O￨- .￨L￨.￨O￨- +60￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1711￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1722￨L￨CD￨DATE￨- (￨L￨-LRB-￨O￨- 2010￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- MathSciNetCrossRefzbMATHGoogle￨U￨NNP￨O￨- Scholar5.Deb￨U￨NNP￨O￨- A.￨U￨NN￨O￨- ,￨L￨,￨O￨- Dasgupta￨U￨NNP￨PERSON￨- A.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Sarkar￨U￨NNP￨PERSON￨- G.￨U￨NNP￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- new￨L￨JJ￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- orthogonal￨L￨JJ￨O￨- functions￨L￨NNS￨O￨A and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- application￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- .￨L￨.￨O￨- +Meng￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Chen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- both￨L￨CC￨O￨- vertical￨L￨JJ￨O￨- and￨L￨CC￨O￨- horizontal￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- analyzed￨L￨VBD￨O￨- some￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- infection-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- permanence￨L￨NN￨O￨- ,￨L￨,￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- one￨L￨CD￨NUMBER￨- obtained￨L￨VBN￨O￨- some￨L￨DT￨O￨- important￨L￨JJ￨O￨- qualitative￨L￨JJ￨O￨- properties.Recently￨L￨NN￨O￨- ,￨L￨,￨O￨- pulse￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- against￨L￨IN￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Hethcote￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- considered￨L￨VBD￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- value￨L￨NN￨O￨- problem￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- IVP￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- vital￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- S￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- GreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- 0￨L￨CD￨NUMBER￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- Equality￨U￨NNP￨ORGANIZATION￨- Add￨U￨VB￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- N￨U￨NN￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- N￨U￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- λ￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- removal￨L￨NN￨O￨- rate￨L￨NN￨O￨- constant￨L￨JJ￨O￨- γ￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- constant￨L￨JJ￨O￨- μ￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨A constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Dynamics￨U￨NNP￨MISC￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- pulse￨L￨NN￨O￨A vaccinationAiren￨L￨NN￨O￨- Zhou1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Pairote￨U￨NNP￨O￨- Sattayatham1￨U￨NNP￨O￨- and￨L￨CC￨O￨- Jianjun￨U￨NNP￨PERSON￨- Jiao2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2016:140￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractPulse￨U￨NNP￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- pulse￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- pulse￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +More￨U￨RBR￨O￨- related￨L￨JJ￨O￨- research￨L￨NN￨O￨- works￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- pulse￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- also￨L￨RB￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- references￨L￨NNS￨O￨- therein.Looking￨L￨VBG￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- of￨L￨IN￨O￨- existing￨L￨VBG￨O￨- researches￨L￨VBZ￨O￨- on￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- using￨L￨VBG￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- vector-borne￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- with￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Of￨U￨IN￨O￨- course￨L￨NN￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- also￨L￨RB￨O￨- used￨L￨VBD￨O￨- to￨L￨TO￨O￨- discuss￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rules￨L￨NNS￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- vector-borne￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- [￨L￨-LRB-￨O￨- 13￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- references￨L￨NNS￨O￨A therein.Recently￨L￨RB￨O￨- ,￨L￨,￨O￨- vaccines￨L￨NNS￨O￨- are￨L￨VBP￨O￨- generally￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- protect￨L￨VB￨O￨- animals￨L￨NNS￨O￨- from￨L￨IN￨O￨- Rift￨U￨NNP￨O￨- Valley￨U￨NNP￨O￨- Fever￨U￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- regions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Modelling￨U￨VBG￨MISC￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- Rift￨U￨NNP￨O￨- Valley￨U￨NNP￨O￨- Fever￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- transmissionChen-Xia￨L￨JJ￨O￨- Yang1￨U￨NN￨O￨- and￨L￨CC￨O￨- Lin-Fei￨U￨JJ￨MISC￨- Nie1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2016:134￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- vector-bone￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Rift￨U￨NNP￨O￨- Valley￨U￨NNP￨O￨- Fever￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- RVF￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- ruminants￨L￨NNS￨O￨- and￨L￨CC￨O￨- mosquitoes￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- impulsive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- for￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ruminants￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- introduced￨L￨VBN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨A behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- RVFV￨U￨NN￨O￨- with￨L￨IN￨O￨- human￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- computed￨L￨VBD￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- threshold￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- for￨L￨IN￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibria￨L￨NNS￨O￨- .￨L￨.￨O￨- +d’Onofrio￨L￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- pulse￨L￨NN￨O￨A vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- periodic￨L￨JJ￨O￨- eradication￨L￨NN￨O￨- solution￨L￨NN￨O￨- are￨L￨VBP￨O￨- analyzed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- Lyapunov￨U￨NN￨PERSON￨- function￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- LessThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- exists￨L￨VBZ￨O￨- and￨L￨CC￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable.Consider￨L￨NN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- continuous￨L￨JJ￨O￨- SEIRS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- Some￨U￨DT￨O￨- particular￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- is￨L￨VBZ￨O￨- calculated￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- established￨L￨VBN￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- examples￨L￨NNS￨O￨- verify￨L￨VBP￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- open￨L￨JJ￨O￨- problem￨L￨NN￨O￨- that￨L￨WDT￨O￨- when￨L￨WRB￨O￨- Mul￨U￨NN￨PERSON￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- SEIRS￨U￨NN￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- globally￨L￨RB￨O￨- attractive.Keywordsdiscrete￨L￨JJ￨O￨- SEIRS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelnonlinear￨L￨NN￨O￨- incidencebasic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numberglobal￨L￨JJ￨O￨- attractivitypermanenceMSC37M9939A1192D30￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionAs￨U￨NNPS￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- known￨L￨VBN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- possess￨L￨VBP￨O￨- a￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- Hepatitis￨U￨NNP￨O￨- ,￨L￨,￨O￨- HIV￨U￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- SARS￨U￨NNP￨O￨- ,￨L￨,￨O￨- Ebola￨U￨NNP￨O￨- ,￨L￨,￨O￨- MERS￨U￨NNP￨O￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- and￨L￨CC￨O￨- important￨L￨JJ￨O￨- research￨L￨NN￨O￨- subjects￨L￨NNS￨O￨- for￨L￨IN￨O￨- these￨L￨DT￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- computing￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- thresholds￨L￨NNS￨O￨- values￨L￨NNS￨O￨- and￨L￨CC￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- numbers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- and￨L￨CC￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- ,￨L￨,￨O￨- permanence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- extinction￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- bifurcations￨L￨NNS￨O￨- and￨L￨CC￨O￨- chaos￨L￨NN￨O￨- phenomena￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- when￨L￨WRB￨O￨- some￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- models￨L￨NNS￨O￨- vary￨L￨VBP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- if￨L￨IN￨O￨- Mul￨U￨NN￨PERSON￨- R￨U￨NN￨PERSON￨- mathcal￨L￨NN￨PERSON￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- permanent￨L￨JJ￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- degenerates￨L￨VBZ￨O￨- into￨L￨IN￨O￨- SEIR￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- Mul￨U￨NN￨PERSON￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- To￨U￨TO￨O￨- demonstrate￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- structural￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- among￨L￨IN￨O￨- people￨L￨NNS￨O￨- influences￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- multi-strain￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- investigate￨L￨VBP￨O￨- a￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- strain￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- where￨L￨WRB￨O￨- every￨L￨DT￨O￨- individual￨L￨JJ￨O￨- randomly￨L￨RB￨O￨- contacts￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +2016Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- One￨U￨CD￨NUMBER￨- common￨L￨JJ￨O￨- observation￨L￨NN￨O￨- in￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- multi-strain￨L￨JJ￨O￨- pathogens￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- all￨L￨DT￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- each￨L￨DT￨O￨- strain￨L￨NN￨O￨A oscillate￨L￨VBP￨O￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- so-called￨L￨JJ￨O￨- Epidemic￨U￨JJ￨O￨- cycling￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Compared￨U￨VBN￨O￨- to￨L￨TO￨O￨- one￨L￨CD￨NUMBER￨- strain￨L￨NN￨O￨A epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- strain￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- presented￨L￨VBN￨O￨- here￨L￨RB￨O￨- can￨L￨MD￨O￨- generate￨L￨VB￨O￨- epidemic￨L￨JJ￨O￨- cycling￨L￨NN￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- much￨L￨JJ￨O￨- wider￨L￨JJR￨O￨- parameter￨L￨NN￨O￨- range￨L￨NN￨O￨- that￨L￨WDT￨O￨- covers￨L￨VBZ￨O￨- many￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Zhang￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Yang￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIRS￨U￨NN￨O￨- worm￨L￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨PRP￨O￨- Derivative￨U￨JJ￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- zeta￨L￨NN￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dS￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- q￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- b￨L￨NN￨O￨- p￨L￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Add￨U￨VB￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dE￨L￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- varepsilon￨L￨NN￨O￨A E￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- q￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- eta￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dI￨L￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- zeta￨L￨NN￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- dR￨L￨NN￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- in￨L￨IN￨O￨- states￨L￨NNS￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Local￨U￨JJ￨O￨- stability￨L￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- Hopf￨U￨NNP￨O￨- bifurcationAccording￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- analysis￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- Equality￨U￨NNP￨ORGANIZATION￨- R￨U￨NN￨ORGANIZATION￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨PERSON￨- Pow￨U￨NNP￨PERSON￨- Mul￨U￨NNP￨PERSON￨- Add￨U￨VB￨PERSON￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- gamma￨L￨NN￨O￨- d￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨A -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- dp￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- dq￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- p￨L￨NN￨O￨- b￨L￨NN￨O￨- Add￨U￨VB￨O￨- eta￨L￨NN￨O￨- Add￨U￨VB￨O￨- d￨L￨NN￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- q￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- The￨U￨DT￨O￨- Jacobian￨U￨JJ￨MISC￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- is￨L￨VBZ￨O￨- J￨U￨NNP￨O￨- where￨L￨WRB￨O￨- Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Case￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- false￨L￨JJ￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- H21￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- holds￨L￨VBZ￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- root￨L￨NN￨O￨- StrictGreaterThan￨U￨NNP￨ORGANIZATION￨- v￨L￨LS￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 12￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- such￨L￨JJ￨O￨- that￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- pair￨L￨NN￨O￨- of￨L￨IN￨O￨- purely￨L￨RB￨O￨- imaginary￨L￨JJ￨O￨- roots￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- pm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- omega￨L￨FW￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨ORGANIZATION￨- pm￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- i￨L￨FW￨ORGANIZATION￨- Pow￨U￨FW￨ORGANIZATION￨- v￨L￨LS￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Rational￨U￨NNP￨O￨- .￨L￨.￨O￨- +Equation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Multiplying￨U￨VBG￨O￨- by￨L￨IN￨O￨- Pow￨U￨NN￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- tau￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- equation￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Let￨U￨VB￨O￨- Equality￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- omega￨L￨FW￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- StrictGreaterThan￨U￨NNP￨O￨- omega￨L￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- root￨L￨NN￨O￨- of￨L￨IN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 10￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Let￨U￨VB￨O￨- us￨L￨PRP￨O￨- denote￨L￨VB￨O￨- by￨L￨IN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A against￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- antibiotics￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- population￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- A￨U￨DT￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- concentration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- i-th￨L￨JJ￨O￨- antibiotic￨L￨JJ￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t.￨L￨NN￨O￨- Also￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- interacts￨L￨VBZ￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- expressed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- generalised￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- local￨L￨JJ￨O￨- bacterial￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- urinary￨L￨JJ￨O￨- tract￨L￨NN￨O￨- ,￨L￨,￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- or￨L￨CC￨O￨- wound￨L￨NN￨O￨- infection.During￨L￨VBG￨O￨- the￨L￨DT￨O￨- administration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- i￨L￨FW￨O￨- th￨L￨DT￨O￨- antibiotic￨L￨JJ￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- to￨L￨TO￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- showed￨L￨VBN￨O￨- up￨L￨IN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- mutations￨L￨NNS￨O￨- of￨L￨IN￨O￨- exposed￨L￨VBN￨O￨- sensitive￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- to￨L￨TO￨O￨- such￨L￨JJ￨O￨- antibiotic￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- model￨L￨VBP￨O￨- this￨L￨DT￨O￨- situation￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- term￨L￨NN￨O￨- Mul￨U￨NN￨O￨- overline￨L￨NN￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- A￨U￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- where￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- }￨L￨-RRB-￨O￨- overline￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- mutation￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- i￨L￨FW￨O￨- th￨L￨DT￨O￨- antibiotic￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- reactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- different￨L￨JJ￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- response￨L￨NN￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- host.In￨L￨NN￨O￨- light￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- ,￨L￨,￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- relations￨L￨NNS￨O￨- among￨L￨IN￨O￨- antibiotics￨L￨NNS￨O￨- ,￨L￨,￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- cells￨L￨NNS￨O￨- and￨L￨CC￨O￨- bacteria￨L￨NNS￨O￨A are￨L￨VBP￨O￨- important￨L￨JJ￨O￨- to￨L￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection.Mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- significant￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- used￨L￨VBN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- analyzing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- timing￨L￨NN￨O￨- and￨L￨CC￨O￨- expansion￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- possible￨L￨JJ￨O￨- reinfection￨L￨NN￨O￨- processes￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- context￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- defining￨L￨VBG￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- specific￨L￨JJ￨O￨- immune￨L￨JJ￨O￨- cells￨L￨NNS￨O￨- produced￨L￨VBD￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- bacteria￨L￨NNS￨O￨A by￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- bacteria￨L￨NNS￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- multiple￨L￨JJ￨O￨- antibiotics￨L￨NNS￨O￨- synchronically￨L￨RB￨O￨- ,￨L￨,￨O￨- presuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- resistance￨L￨NN￨O￨- is￨L￨VBZ￨O￨- gained￨L￨VBN￨O￨- through￨L￨IN￨O￨- mutations￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- antibiotic￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- respect￨L￨NN￨O￨- ,￨L￨,￨O￨- understanding￨L￨NN￨O￨- and￨L￨CC￨O￨- anticipating￨L￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- of￨L￨IN￨O￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- load￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- bacteria￨L￨NNS￨O￨A and￨L￨CC￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- cells￨L￨NNS￨O￨- by￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- crucial￨L￨JJ￨O￨- in￨L￨IN￨O￨- selecting￨L￨VBG￨O￨- effective￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- results￨L￨VBZ￨O￨- on￨L￨IN￨O￨- reproduction￨L￨NN￨O￨- of￨L￨IN￨O￨- sensitive￨L￨JJ￨O￨- and￨L￨CC￨O￨- resistant￨L￨JJ￨O￨- bacteria￨L￨NNS￨O￨A to￨L￨TO￨O￨- antibiotics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- obtained￨L￨VBN￨O￨- in￨L￨IN￨O￨- Austin￨U￨NNP￨CITY￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- point￨L￨NN￨O￨- solutions￨L￨NNS￨O￨- ,￨L￨,￨O￨- periodic￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- were￨L￨VBD￨O￨- also￨L￨RB￨O￨- identified￨L￨VBN￨O￨- and￨L￨CC￨O￨- conditions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- were￨L￨VBD￨O￨- derived￨L￨VBN￨O￨- analytically.KeywordsSchelling￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- Agent￨U￨NNP￨O￨- based￨L￨VBN￨O￨- State￨U￨NNP￨ORGANIZATION￨- equation￨L￨NN￨O￨- Discrete￨U￨NNP￨O￨- map￨L￨NN￨O￨- IntroductionWe￨U￨NN￨O￨- frequently￨L￨RB￨O￨- find￨L￨VBP￨O￨- social￨L￨JJ￨O￨- or￨L￨CC￨O￨- natural￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- composed￨L￨VBN￨O￨A of￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- or￨L￨CC￨O￨- more￨L￨JJR￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- interacting￨L￨VBG￨O￨- groups￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- :￨L￨:￨O￨- cities￨L￨NNS￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- races￨L￨NNS￨O￨- ,￨L￨,￨O￨- ecological￨L￨JJ￨O￨- system￨L￨NN￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- species￨L￨NNS￨O￨- ,￨L￨,￨O￨- social￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- composed￨L￨VBN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- opinions￨L￨NNS￨O￨- ,￨L￨,￨O￨- cultures￨L￨NNS￨O￨- ,￨L￨,￨O￨- etc￨L￨FW￨O￨- .￨L￨.￨O￨- +Open￨U￨VB￨O￨- image￨L￨NN￨O￨- in￨L￨IN￨O￨- new￨L￨JJ￨O￨- window￨L￨NN￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Two-room￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- aspatial￨L￨JJ￨O￨- version￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- Schelling￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- NumericCitation￨U￨NNP￨O￨- To￨U￨TO￨O￨- understand￨L￨VB￨O￨- these￨L￨DT￨O￨- phenomena￨L￨NNS￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- different￨L￨JJ￨O￨- approaches￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- in￨L￨IN￨O￨- use￨L￨NN￨O￨- :￨L￨:￨O￨- state￨L￨NN￨O￨- equation-based￨L￨JJ￨O￨- approach￨L￨NN￨O￨- and￨L￨CC￨O￨- agent-based￨L￨JJ￨O￨- one￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 35￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 43￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asA￨L￨NN￨O￨- state￨L￨NN￨O￨- equation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Schelling￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- segregation￨L￨NN￨O￨- modelAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsJae￨L￨NNP￨O￨- Kyun￨U￨NNP￨PERSON￨- ShinHiroki￨U￨NNP￨PERSON￨- SayamaSeung￨U￨NNP￨PERSON￨- Ryul￨U￨NNP￨PERSON￨- ChoiOpen￨U￨NNP￨PERSON￨- AccessOriginal￨U￨NNP￨O￨- ArticleFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractAn￨U￨NN￨O￨- aspatial￨L￨JJ￨O￨- version￨L￨NN￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- famous￨L￨JJ￨O￨- Schelling￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- segregation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- recently￨L￨RB￨DATE￨- been￨L￨VBN￨O￨- proposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- agent-based￨L￨JJ￨O￨- format￨L￨NN￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- original￨L￨JJ￨O￨- Schelling￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- ,￨L￨,￨O￨- state￨L￨NN￨O￨- equation￨L￨NN￨O￨- version￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- Schelling￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- indirect￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- where￨L￨WRB￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- exposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- infectious￨L￨JJ￨O￨- organisms￨L￨NNS￨O￨- present￨L￨JJ￨DATE￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- well-mixed￨L￨JJ￨O￨- environment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- individual￨L￨JJ￨O￨- scales￨L￨NNS￨O￨- linearly￨L￨RB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogen￨L￨NN￨O￨- shed￨L￨NN￨O￨- ,￨L￨,￨O￨- individuals￨L￨NNS￨O￨- shedding￨L￨VBG￨O￨A pathogens￨L￨NNS￨O￨- several￨L￨JJ￨O￨- orders￨L￨NNS￨O￨- of￨L￨IN￨O￨- magnitude￨L￨NN￨O￨- higher￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- would￨L￨MD￨O￨- drive￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- by￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- order￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- precise￨L￨JJ￨O￨- contribution￨L￨NN￨O￨A of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- producing￨L￨VBG￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- concentration￨L￨NN￨O￨- of￨L￨IN￨O￨- pathogens￨L￨NNS￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- remains￨L￨VBZ￨O￨- poorly￨L￨RB￨O￨- understood.If￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- direct￨L￨JJ￨O￨- host-to-host￨L￨JJ￨O￨- contact￨L￨NN￨O￨- process￨L￨NN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- with￨L￨IN￨O￨- all￨L￨DT￨O￨- contacts￨L￨NNS￨O￨- being￨L￨VBG￨O￨- effective￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- every￨L￨DT￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- results￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- contribution￨L￨NN￨O￨- of￨L￨IN￨O￨- each￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individual￨L￨NN￨O￨- is￨L￨VBZ￨O￨- capped￨L￨VBN￨O￨- by￨L￨IN￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨O￨- Impact￨U￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- shedding￨L￨VBG￨O￨A level￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- persistent￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- Mycobacterium￨U￨NN￨O￨- avium￨L￨NN￨O￨- subspecies￨L￨NNS￨O￨- paratuberculosis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MAP￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- Noa￨U￨NN￨O￨- Slater1￨U￨NN￨O￨- ,￨L￨,￨O￨- Rebecca￨U￨NNP￨PERSON￨- Mans￨U￨NNP￨PERSON￨- Mitchell2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Robert￨U￨NNP￨PERSON￨- H.￨U￨NNP￨PERSON￨- Using￨U￨VBG￨PERSON￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- likelihood￨L￨NN￨O￨- approach￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- estimate￨L￨VBP￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- multiple￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- routes￨L￨NNS￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- direct￨L￨JJ￨O￨- contact￨L￨NN￨O￨- ,￨L￨,￨O￨- indirect￨L￨JJ￨O￨- contact￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- background￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- linear￨L￨JJ￨O￨- mass-action￨L￨NN￨O￨- functional￨L￨JJ￨O￨- response￨L￨NN￨O￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- ecoepidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- takes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- t￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- prey￨L￨NN￨O￨A ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- predator￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- K￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- λ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- θ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- conversion￨L￨NN￨O￨- efficiency￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rates￨L￨NNS￨O￨- on￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- and￨L￨CC￨O￨- δ￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- and￨L￨CC￨O￨- predators￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively.The￨L￨NN￨O￨- authors￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- detail￨L￨NN￨O￨- that￨L￨WDT￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equilibria￨L￨NNS￨O￨- :￨L￨:￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- System￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- around￨L￨IN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- parametric￨L￨JJ￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- around￨L￨IN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- StrictLessThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictLessThan￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- K￨U￨NNP￨O￨- theta￨L￨IN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- around￨L￨IN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictLessThan￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mu￨L￨NN￨O￨- theta￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- theta￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- K￨U￨NN￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- K￨U￨NN￨O￨- lambda￨L￨NN￨O￨- r￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- around￨L￨IN￨O￨- E￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- K￨U￨NNP￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NN￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- lambda￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mu￨L￨NN￨O￨- theta￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- unstable￨L￨JJ￨O￨- around￨L￨IN￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- parametric￨L￨JJ￨O￨- values.However￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- case￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- effects￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- environmental￨L￨JJ￨O￨- noise￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- neglected￨L￨VBN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- basis￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NN￨O￨- studied￨L￨VBN￨O￨- and￨L￨CC￨O￨- compared￨L￨VBN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- proposed￨L￨VBN￨O￨- ecoepidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- explore￨L￨VB￨O￨- the￨L￨DT￨O￨- crucial￨L￨JJ￨O￨- system￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- ranges￨L￨NNS￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- different￨L￨JJ￨O￨- theoretical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- predicted￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- prey￨L￨NN￨O￨A ,￨L￨,￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- predators￨L￨NNS￨O￨- .￨L￨.￨O￨- +Keeping￨U￨VBG￨O￨- this￨L￨DT￨O￨- in￨L￨IN￨O￨- mind￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- have￨L￨VBP￨O￨- modified￨L￨VBN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- proposed￨L￨VBN￨O￨- by￨L￨IN￨O￨- NumericCitation￨U￨NN￨ORGANIZATION￨- and￨L￨CC￨O￨- taken￨L￨VBN￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- randomly￨L￨RB￨O￨- fluctuating￨L￨VBG￨O￨- and￨L￨CC￨O￨- stochastically￨L￨RB￨O￨- perturbed￨L￨VBD￨O￨- force￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- λ￨L￨NN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- :￨L￨:￨O￨- lambda￨L￨NN￨O￨A Consequently￨U￨RB￨O￨- ,￨L￨,￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- B￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- standard￨L￨JJ￨O￨- Brownian￨U￨JJ￨MISC￨- motion￨L￨NN￨O￨- ,￨L￨,￨O￨- StrictGreaterThan￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- sigma￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- author￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- studied￨L￨VBD￨O￨- an￨L￨DT￨O￨- SI￨U￨NNP￨O￨- or￨L￨CC￨O￨- SIS￨U￨NNP￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- spread￨L￨NN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- prey￨L￨NN￨O￨A when￨L￨WRB￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- predator￨L￨NN￨O￨- and￨L￨CC￨O￨- prey￨L￨NN￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- predators￨L￨NNS￨O￨- eat￨L￨VBP￨O￨- infected￨L￨JJ￨O￨- prey￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +Further￨U￨RB￨O￨- ,￨L￨,￨O￨- interpreting￨L￨VBG￨O￨- the￨L￨DT￨O￨- edge￨L￨NN￨O￨- weights￨L￨NNS￨O￨- as￨L￨IN￨O￨- time￨L￨NN￨O￨- or￨L￨CC￨O￨- cost￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- vertices￨L￨NNS￨O￨A can￨L￨MD￨O￨- also￨L￨RB￨O￨- correspond￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- it￨L￨PRP￨O￨- takes￨L￨VBZ￨O￨- for￨L￨IN￨O￨- information￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- vertex￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- cost￨L￨NN￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- vertices.We￨L￨NNP￨O￨- say￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- sequence￨L￨NN￨O￨- of￨L￨IN￨O￨- events￨L￨NNS￨O￨- happens￨L￨VBZ￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- probability￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- w.h.p.￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- if￨L￨IN￨O￨- Limit￨U￨NN￨O￨- Mul￨U￨NN￨O￨- P￨U￨NN￨O￨- mathbb￨L￨NN￨O￨- n￨L￨NN￨O￨- -￨L￨:￨O￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- probability￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- event￨L￨NN￨O￨- holds￨L￨VBZ￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- 1￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- graph￨L￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- weight￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- weight￨L￨NN￨O￨- path￨L￨NN￨O￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- by￨L￨IN￨O￨- Mul￨U￨NN￨O￨- P￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Theorem￨U￨NNP￨O￨- 1.1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- Typical￨U￨JJ￨O￨- distances￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- Let￨U￨VB￨O￨- U￨U￨NNP￨O￨- ,￨L￨,￨O￨- V￨U￨NNP￨O￨- be￨L￨VB￨O￨- two￨L￨CD￨NUMBER￨- uniformly￨L￨RB￨O￨- chosen￨L￨VBN￨O￨- vertices￨L￨NNS￨O￨A in￨L￨IN￨O￨- [￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- write￨L￨VBP￨O￨- Mul￨U￨JJ￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- W￨U￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- realization￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- weighted￨L￨JJ￨O￨- random￨L￨JJ￨O￨- graph.We￨L￨NN￨O￨- define￨L￨VB￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- vertices￨L￨NNS￨O￨A in￨L￨IN￨O￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- W￨U￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- sum￨L￨NN￨O￨- of￨L￨IN￨O￨- weights￨L￨NNS￨O￨- along￨L￨IN￨O￨- the￨L￨DT￨O￨- shortest￨L￨JJS￨O￨- weight￨L￨NN￨O￨- path￨L￨NN￨O￨- connecting￨L￨VBG￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- vertices￨L￨NNS￨O￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- circle￨L￨NN￨O￨- with￨L￨IN￨O￨- circumference￨L￨NN￨O￨- n￨L￨NN￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- cycle￨L￨NN￨O￨- on￨L￨IN￨O￨- n￨L￨NN￨O￨- many￨L￨JJ￨O￨- vertices￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- added￨L￨VBD￨O￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- 2￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- rho￨L￨VBG￨O￨- Mul￨U￨NN￨O￨- P￨U￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- o￨L￨NN￨O￨- many￨L￨JJ￨O￨- 0-length￨L￨JJ￨O￨- shortcuts￨L￨NNS￨O￨- at￨L￨IN￨O￨- locations￨L￨NNS￨O￨- chosen￨L￨VBN￨O￨- according￨L￨VBG￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- uniform￨L￨JJ￨O￨- measure￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- circle￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- worm￨L￨NN￨O￨- repeatedly￨L￨RB￨O￨- infected￨L￨VBN￨O￨- the￨L￨DT￨O￨- internal￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- Norwegian￨U￨JJ￨NATIONALITY￨- bank￨L￨NN￨O￨- ,￨L￨,￨O￨- illustrates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- reinfections￨L￨NNS￨O￨- can￨L￨MD￨O￨- occur￨L￨VB￨O￨- in￨L￨IN￨O￨- real￨L￨JJ￨O￨- networks.The￨L￨NN￨O￨- stochastic￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- first￨L￨RB￨ORDINAL￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- immunize￨L￨VB￨O￨- unknown￨L￨JJ￨O￨- hubs￨L￨NNS￨O￨- on￨L￨IN￨O￨- diverse￨L￨JJ￨O￨- inhomogeneous￨L￨JJ￨O￨- spreading￨L￨NN￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spreading￨L￨NN￨O￨A process￨L￨NN￨O￨- was￨L￨VBD￨O￨- completely￨L￨RB￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- spreading￨L￨NN￨O￨- network￨L￨NN￨O￨- ’s￨L￨POS￨O￨- topology￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- configuration￨L￨NN￨O￨- of￨L￨IN￨O￨- node￨L￨NN￨O￨- types￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- selection￨L￨NN￨O￨- of￨L￨IN￨O￨- initially￨L￨RB￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- or￨L￨CC￨O￨- seeds￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- malware￨L￨NN￨O￨- ’s￨L￨POS￨O￨- spreading￨L￨NN￨O￨A network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- modeled￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- undirected￨L￨JJ￨O￨- graph￨L￨NN￨O￨- with￨L￨IN￨O￨- M￨U￨NN￨O￨- edges￨L￨NNS￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- nodes￨L￨NNS￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- types￨L￨NNS￨O￨- .￨L￨.￨O￨- +Any￨U￨DT￨O￨- spreading￨L￨VBG￨O￨A network￨L￨NN￨O￨- has￨L￨VBZ￨O￨- L￨U￨NN￨O￨- different￨L￨JJ￨O￨- node￨L￨NN￨O￨- types￨L￨NNS￨O￨- Equality￨U￨NNP￨O￨- l￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- for￨L￨IN￨O￨- Mul￨U￨NNP￨O￨- le￨L￨DT￨O￨- Mul￨U￨NN￨O￨- L￨U￨NN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- ll￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- applications￨L￨NNS￨O￨- are￨L￨VBP￨O￨- taken￨L￨VBN￨O￨- from￨L￨IN￨O￨- biology￨L￨NN￨O￨- ,￨L￨,￨O￨- finance￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- physics￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- cover￨L￨VB￨O￨- population￨L￨NN￨O￨- growth￨L￨NN￨O￨- or￨L￨CC￨O￨- decay￨L￨NN￨O￨A ,￨L￨,￨O￨- interacting￨L￨VBG￨O￨- predator-prey￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- compound￨L￨NN￨O￨- interest￨L￨NN￨O￨- and￨L￨CC￨O￨- inflation￨L￨NN￨O￨- ,￨L￨,￨O￨- radioactive￨L￨JJ￨O￨- decay￨L￨NN￨O￨- ,￨L￨,￨O￨- chemical￨L￨NN￨O￨- and￨L￨CC￨O￨- biochemical￨L￨JJ￨O￨- reaction￨L￨NN￨O￨- ,￨L￨,￨O￨- spreading￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- cooling￨L￨NN￨O￨- of￨L￨IN￨O￨- objects￨L￨NNS￨O￨- ,￨L￨,￨O￨- compaction￨L￨NN￨O￨- of￨L￨IN￨O￨- geological￨L￨JJ￨O￨- media￨L￨NNS￨O￨- ,￨L￨,￨O￨- pressure￨L￨NN￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- atmosphere￨L￨NN￨O￨- ,￨L￨,￨O￨- viscoelastic￨L￨JJ￨O￨- response￨L￨NN￨O￨- in￨L￨IN￨O￨- materials￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- air￨L￨NN￨O￨- resistance￨L￨NN￨O￨- on￨L￨IN￨O￨- falling￨L￨VBG￨O￨- or￨L￨CC￨O￨- rising￨L￨VBG￨O￨- bodies.Before￨L￨NN￨O￨- we￨L￨PRP￨O￨- turn￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- applications￨L￨NNS￨O￨- ,￨L￨,￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- take￨L￨VBP￨O￨- a￨L￨DT￨O￨- brief￨L￨JJ￨O￨- look￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- technique￨L￨NN￨O￨- of￨L￨IN￨O￨- scaling￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- so￨L￨RB￨O￨- useful￨L￨JJ￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- applications￨L￨NNS￨O￨- .4.1￨L￨CD￨NUMBER￨- ScalingReal￨U￨NNP￨O￨- applications￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- Equality￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- u￨L￨NN￨O￨- prime￨L￨JJ￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- u￨L￨NN￨O￨- b￨L￨NN￨O￨- will￨L￨MD￨O￨- often￨L￨RB￨O￨- involve￨L￨VB￨O￨- a￨L￨DT￨O￨- lot￨L￨NN￨O￨- of￨L￨IN￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- expressions￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- .￨L￨.￨O￨- +4.1.1￨L￨CD￨NUMBER￨- Dimensionless￨U￨JJ￨O￨- VariablesScaling￨U￨NN￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- we￨L￨PRP￨O￨- introduce￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- function￨L￨NN￨O￨- Mul￨U￨NN￨O￨- bar￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- u￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- bar￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- Equality￨U￨NNP￨ORGANIZATION￨- Mul￨U￨NNP￨ORGANIZATION￨- bar￨L￨NN￨ORGANIZATION￨- u￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- Pow￨U￨NN￨ORGANIZATION￨- u￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VB￨O￨- u￨L￨FW￨O￨- Mul￨U￨FW￨O￨- -1￨L￨CD￨NUMBER￨- u￨L￨NN￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- m￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- um￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨A value￨L￨NN￨O￨- of￨L￨IN￨O￨- u￨L￨NN￨O￨- ,￨L￨,￨O￨- uc￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- u￨L￨NN￨O￨- values￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- tc￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- characteristic￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- t￨L￨NN￨O￨- where￨L￨WRB￨O￨- u￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- significant￨L￨JJ￨O￨- variation￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- shown￨L￨VBN￨O￨- that￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- data￨L￨NNS￨O￨- on￨L￨IN￨O￨- structural￨L￨JJ￨O￨- interdependencies￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- examined￨L￨VBN￨O￨- with￨L￨IN￨O￨- measures￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- science.KeywordsComplex￨L￨NN￨O￨- network￨L￨NN￨O￨- Supply￨U￨NN￨O￨- Manufacturing￨U￨NNP￨O￨- Robustness￨U￨NNP￨O￨- This￨U￨DT￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- focus￨L￨NN￨O￨- collection￨L￨NN￨O￨- on￨L￨IN￨O￨- “￨L￨``￨O￨- Robust￨U￨JJ￨O￨- Manufacturing￨U￨NNP￨O￨- Control￨U￨NNP￨O￨- :￨L￨:￨O￨- Robustness￨U￨NNP￨O￨- and￨L￨CC￨O￨- Resilience￨U￨NNP￨O￨- in￨L￨IN￨O￨- Global￨U￨NNP￨O￨- Manufacturing￨U￨NNP￨O￨- Networks￨U￨NNP￨O￨- ”￨L￨''￨O￨- .1￨L￨CD￨NUMBER￨- Introduction￨U￨NN￨O￨- and￨L￨CC￨O￨- backgroundA￨L￨NN￨O￨- supply￨L￨NN￨O￨A network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- created￨L￨VBN￨O￨- when￨L￨WRB￨O￨- companies￨L￨NNS￨O￨- buy￨L￨VBP￨O￨- and￨L￨CC￨O￨- sell￨L￨VBP￨O￨- goods￨L￨NNS￨O￨- to￨L￨TO￨O￨- each￨L￨DT￨O￨- other￨L￨JJ￨O￨- ,￨L￨,￨O￨- transferring￨L￨VBG￨O￨- necessary￨L￨JJ￨O￨- parts￨L￨NNS￨O￨- downstream￨L￨JJ￨O￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨- a￨L￨DT￨O￨- final￨L￨JJ￨O￨- product￨L￨NN￨O￨- .￨L￨.￨O￨- +These￨U￨DT￨O￨- studies￨L￨NNS￨O￨- examined￨L￨VBD￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- supply￨L￨NN￨O￨- networks￨L￨NNS￨O￨- are￨L￨VBP￨O￨- complex￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- their￨L￨PRP$￨O￨- robustness￨L￨NN￨O￨A properties￨L￨NNS￨O￨- would￨L￨MD￨O￨- be￨L￨VB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- structure￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- find￨L￨VB￨O￨- empirical￨L￨JJ￨O￨- consensus￨L￨NN￨O￨- on￨L￨IN￨O￨- universal￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Brintrup￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Nair￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Vidal￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- examined￨L￨VBD￨O￨- robustness￨L￨NN￨O￨A against￨L￨IN￨O￨- disruptions￨L￨NNS￨O￨- under￨L￨IN￨O￨- random￨L￨JJ￨O￨- ,￨L￨,￨O￨- small-world￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- scale-free￨L￨JJ￨O￨- network￨L￨NN￨O￨- topologies￨L￨NNS￨O￨- using￨L￨VBG￨O￨- multi-agent￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- model￨L￨VB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- rumor￨L￨NN￨O￨A throughout￨L￨IN￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- assumptions￨L￨NNS￨O￨- are￨L￨VBP￨O￨- imposed￨L￨VBN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- i￨L￨LS￨O￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- ignorant￨L￨JJ￨O￨- users￨L￨NNS￨O￨- and￨L￨CC￨O￨- stifle￨L￨VBP￨O￨- users￨L￨NNS￨O￨- usually￨L￨RB￨O￨- to￨L￨TO￨O￨- have￨L￨VB￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- these￨L￨DT￨O￨- spatial-temporal￨L￨JJ￨O￨- models￨L￨NNS￨O￨- will￨L￨MD￨O￨- provide￨L￨VB￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- insight￨L￨NN￨O￨- to￨L￨TO￨O￨- research￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A propagation￨L￨NN￨O￨- in￨L￨IN￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- networks.It￨L￨NN￨O￨- is￨L￨VBZ￨O￨- worth￨L￨JJ￨O￨- noting￨L￨VBG￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- works￨L￨NNS￨O￨- mentioned￨L￨VBN￨O￨- above￨L￨IN￨O￨- on￨L￨IN￨O￨- rumor￨L￨NN￨O￨- propagation￨L￨NN￨O￨- modeling￨L￨NN￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- no￨L￨DT￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- over￨L￨IN￨O￨- rumor￨L￨NN￨O￨- spreading￨L￨NN￨O￨- .￨L￨.￨O￨- +Based￨U￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- users￨L￨NNS￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- online￨L￨JJ￨O￨- social￨L￨JJ￨O￨- network￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- divided￨L￨VBN￨O￨- into￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- classes￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- different￨L￨JJ￨O￨- states￨L￨NNS￨O￨- :￨L￨:￨O￨- ignorants￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- those￨L￨DT￨O￨- not￨L￨RB￨O￨- aware￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- spreaders￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- spreading￨L￨VBG￨O￨- it￨L￨PRP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- stiflers￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- those￨L￨DT￨O￨- who￨L￨WP￨O￨- know￨L￨VBP￨O￨- the￨L￨DT￨O￨- rumor￨L￨NN￨O￨- but￨L￨CC￨O￨- have￨L￨VBP￨O￨- ceased￨L￨VBN￨O￨- communicating￨L￨VBG￨O￨- it￨L￨PRP￨O￨- after￨L￨IN￨O￨- meeting￨L￨VBG￨O￨- somebody￨L￨NN￨O￨- already￨L￨RB￨O￨- informed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Dynamic￨U￨NNP￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- rumor￨L￨NN￨O￨A propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- delayChunru￨L￨NN￨O￨- Li1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Zujun￨U￨NN￨O￨- Ma3￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2015:364￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- reaction-diffusion￨L￨NN￨O￨- rumor￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- government￨L￨NN￨O￨- control￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- diffusive￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- DL￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- spatial-temporal￨L￨JJ￨O￨- diffusion￨L￨NN￨O￨- terms￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- propagation￨L￨NN￨O￨- process￨L￨NN￨O￨- in￨L￨IN￨O￨- online￨L￨JJ￨O￨A social￨L￨JJ￨O￨A networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +Consider￨U￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- discontinuous￨L￨JJ￨O￨A treatment￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- E￨U￨NN￨O￨- Add￨U￨VB￨O￨- mu￨L￨NN￨O￨- Mul￨U￨NN￨O￨- beta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- Equality￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- E￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- gamma￨L￨NN￨O￨- Add￨U￨VB￨O￨- alpha￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- h￨L￨NN￨O￨- I￨U￨PRP￨O￨- Equality￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- d￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- mathrm￨L￨NN￨O￨- Mul￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- gamma￨L￨NN￨O￨- h￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Λ￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- contact￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- induced￨L￨VBN￨O￨- by￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- naturally￨L￨RB￨O￨- leaving￨L￨VBG￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- stage￨L￨NN￨O￨- and￨L￨CC￨O￨- infected￨L￨JJ￨O￨- stage￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- Lyapunov￨U￨NNP￨PERSON￨- theory￨L￨NN￨O￨- for￨L￨IN￨O￨- discontinuous￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- and￨L￨CC￨O￨- other￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- on￨L￨IN￨O￨- non-smooth￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- sharp￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- which￨L￨WDT￨O￨- completely￨L￨RB￨O￨- determines￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- becomes￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A ,￨L￨,￨O￨- then￨L￨RB￨O￨- there￨L￨EX￨O￨- only￨L￨RB￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- function￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- h￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- I￨U￨PRP￨O￨- phi￨L￨NN￨O￨- I￨U￨PRP￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨A rate￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- investigated￨L￨VBD￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨- potential￨L￨NN￨O￨- of￨L￨IN￨O￨- four￨L￨CD￨NUMBER￨- wild￨L￨JJ￨O￨- animals￨L￨NNS￨O￨- in￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨A ZVL￨U￨NNP￨O￨- ,￨L￨,￨O￨- using￨L￨VBG￨O￨- prevalence￨L￨NN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- Latin￨U￨JJ￨MISC￨- American￨U￨JJ￨NATIONALITY￨- countries￨L￨NNS￨O￨- in￨L￨IN￨O￨- Amazons￨U￨NNP￨O￨- and￨L￨CC￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- crab-eating￨L￨JJ￨O￨- fox￨L￨NN￨O￨- ,￨L￨,￨O￨- spiny￨L￨JJ￨O￨- rat￨L￨NN￨O￨- ,￨L￨,￨O￨- common￨L￨JJ￨O￨- opossum￨L￨NN￨O￨- and￨L￨CC￨O￨- black￨L￨JJ￨O￨- rat￨L￨NN￨O￨- in￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 32￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 661￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 673￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asExamining￨L￨VBG￨O￨- the￨L￨DT￨O￨- reservoir￨L￨NN￨O￨A potential￨L￨NN￨O￨- of￨L￨IN￨O￨- animal￨L￨NN￨O￨- species￨L￨NNS￨O￨- for￨L￨IN￨O￨- Mul￨U￨NN￨O￨- varvec￨L￨NN￨O￨- Mul￨U￨NN￨O￨- textit￨L￨NN￨O￨- Mul￨U￨NN￨O￨- L￨U￨NN￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- s￨L￨NNS￨O￨- Mul￨U￨NN￨O￨- h￨L￨NN￨O￨- Mul￨U￨NN￨O￨- m￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- i￨L￨FW￨O￨- Mul￨U￨FW￨ORGANIZATION￨- n￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- f￨L￨FW￨O￨- Mul￨U￨FW￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- n￨L￨NN￨O￨- Mul￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- m￨L￨NN￨O￨- u￨L￨NN￨O￨- infectionAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsRyutaro￨L￨NN￨O￨- FukamiHiroshi￨U￨NN￨MISC￨- NishiuraOpen￨U￨NN￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- Paper￨U￨NNP￨MISC￨- Area￨U￨NNP￨MISC￨- 3First￨L￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractLeishamaniasis￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- parasitic￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmitted￨L￨VBN￨O￨- by￨L￨IN￨O￨- sandfly￨L￨NN￨O￨- Phlebotomus￨U￨NN￨O￨- spp￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- present￨L￨JJ￨DATE￨- study￨L￨NN￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- animal￨L￨NN￨O￨- species￨L￨NNS￨O￨- other￨L￨JJ￨O￨- than￨L￨IN￨O￨- canine￨L￨JJ￨O￨- play￨L￨NN￨O￨- important￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨A transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Leishmania￨U￨NN￨LOCATION￨- infantum￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- conventional￨L￨JJ￨O￨- wisdom￨L￨NN￨O￨- that￨L￨WDT￨O￨- centered￨L￨VBD￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- canine￨L￨NN￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 1￨L￨CD￨NUMBER￨- Summary￨U￨NNP￨O￨- of￨L￨IN￨O￨- notation￨L￨NN￨O￨- Notation￨U￨NN￨O￨- Explanation￨U￨NN￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Rate￨U￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- S￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Pow￨U￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- Pow￨U￨NN￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- ,￨L￨,￨O￨- Pow￨U￨NN￨O￨- d￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- Nature￨U￨NN￨O￨- mortality￨L￨NN￨O￨- of￨L￨IN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- compartments￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨A ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- Lambda￨U￨NNP￨O￨- _￨L￨NNP￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Recruitment￨U￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- varepsilon￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Fatality￨U￨NN￨O￨- rate￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Recovery￨U￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- delta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Removed￨U￨VBN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- recovered￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Positive￨U￨JJ￨O￨- parameter￨L￨NN￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- all￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- throughout￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- their￨L￨PRP$￨O￨- paper￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Gao￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Hethcote￨U￨NNP￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- logistic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- N￨U￨NNP￨O￨- Tuple￨U￨NNP￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- biggl￨L￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- N￨U￨NN￨O￨- N￨U￨NN￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- biggl￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- biggr￨L￨NN￨O￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- N￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- StrictLessThan￨U￨NNP￨O￨- StrictLessThan￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- convex￨L￨NN￨O￨- combination￨L￨NN￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- and￨L￨CC￨O￨- μ￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NN￨O￨- r￨L￨NN￨O￨- Add￨U￨VB￨O￨- b￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- mu￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- intrinsic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- K￨U￨NNP￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +mention￨L￨VB￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- logistic￨L￨JJ￨O￨- birth￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- Here￨U￨RB￨O￨- Equality￨U￨NN￨O￨- N￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- R￨U￨NN￨O￨- Add￨U￨VB￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NN￨O￨- beta￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨MISC￨- delta￨L￨NN￨MISC￨- Add￨U￨VB￨MISC￨- mu￨L￨NN￨MISC￨A Add￨U￨VB￨MISC￨- alpha￨L￨NN￨O￨- gamma￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- non-negative￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- represents￨L￨VBZ￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- consider￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- prevail￨L￨VB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- is￨L￨VBZ￨O￨- small￨L￨JJ￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨A rate￨L￨NN￨O￨A due￨L￨JJ￨O￨- to￨L￨TO￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- limited.Keywordsstochastic￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- modellogistic￨L￨JJ￨O￨- birthdisease-free￨L￨JJ￨O￨- equilibriumendemic￨L￨JJ￨O￨- equilibriumstochastic￨L￨JJ￨O￨- Lyapunov￨U￨NN￨O￨- functionasymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionFrom￨U￨NNP￨O￨- the￨L￨DT￨O￨- pioneering￨L￨JJ￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Kermack￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Mckendrick￨U￨NNP￨PERSON￨- on￨L￨IN￨O￨- SIR￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- many￨L￨JJ￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- have￨L￨VBP￨O￨- descended￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- [￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- carry￨L￨VBP￨O￨- out￨L￨RP￨O￨- the￨L￨DT￨O￨- globally￨L￨RB￨O￨- asymptotical￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨A through￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- Lyapunov￨U￨NNP￨PERSON￨- functional￨L￨JJ￨O￨- method￨L￨NN￨O￨- if￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- le￨L￨DT￨O￨- .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- StrictGreaterThan￨U￨NNP￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- system￨L￨NN￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- will￨L￨MD￨O￨- oscillate￨L￨VB￨O￨- around￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- summarized￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- list￨L￨NN￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- input￨L￨NN￨O￨- of￨L￨IN￨O￨- new￨L￨JJ￨O￨- members￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- per￨L￨IN￨O￨- unit￨L￨NN￨O￨- time￨L￨NN￨O￨- ;￨L￨:￨O￨- q￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- new-borns￨L￨NNS￨O￨- ;￨L￨:￨O￨- β￨L￨NN￨O￨- :￨L￨:￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- ;￨L￨:￨O￨- μ￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨A rate￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- V￨U￨NNP￨O￨- compartments￨L￨NNS￨O￨- ;￨L￨:￨O￨- p￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- proportionality￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ;￨L￨:￨O￨- γ￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- ε￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- losing￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- immunity￨L￨NN￨O￨- for￨L￨IN￨O￨- vaccinated￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- α￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- disease-caused￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals.All￨L￨NN￨O￨- parameter￨L￨NN￨O￨- values￨L￨NNS￨O￨- are￨L￨VBP￨O￨- assumed￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- nonnegative￨L￨JJ￨O￨- and￨L￨CC￨O￨- mu￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- system￨L￨NN￨O￨- has￨L￨VBZ￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Mul￨U￨NNP￨O￨- textstyle￨L￨NN￨O￨- Mul￨U￨NN￨O￨- begin￨L￨VB￨O￨- Mul￨U￨NN￨PERSON￨- Mul￨U￨NN￨PERSON￨- c￨L￨NN￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- Mul￨U￨NN￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- e￨L￨SYM￨O￨- s￨L￨VBZ￨O￨- Mul￨U￨NN￨O￨- dot￨L￨NN￨O￨- Mul￨U￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- varepsilon￨L￨NN￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- I￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- mu￨L￨NN￨O￨- p￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- A￨U￨DT￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- beta￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Here￨U￨RB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨A the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- t￨L￨NN￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- members￨L￨NNS￨O￨- who￨L￨WP￨O￨- are￨L￨VBP￨O￨- immune￨L￨JJ￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disease-related￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- are￨L￨VBP￨O￨- small￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- derive￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- persist￨L￨VB￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- measured￨L￨VBN￨O￨- through￨L￨IN￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- LessThan￨U￨JJ￨O￨- R￨U￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- type￨L￨NN￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- also￨L￨RB￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- the￨L￨DT￨O￨- perturbation￨L￨NN￨O￨- is￨L￨VBZ￨O￨- large￨L￨JJ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- decays￨L￨NNS￨O￨- exponentially￨L￨RB￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- converges￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A regardless￨L￨RB￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- magnitude￨L￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- A￨U￨DT￨O￨- delayed￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rateLuju￨L￨NN￨O￨- Liu1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2015:329￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractAn￨U￨NNP￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- incorporating￨L￨VBG￨O￨- an￨L￨DT￨O￨- incubation￨L￨NN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A and￨L￨CC￨O￨- a￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- growth￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- governed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- logistic￨L￨JJ￨O￨- equation￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- analyzed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIR￨U￨NN￨O￨- vector￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- incubation￨L￨NN￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A and￨L￨CC￨O￨- logistic￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- with￨L￨IN￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- K￨U￨NN￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- host￨L￨NN￨TITLE￨- individuals￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- delayed￨L￨VBN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- bilinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- vector￨L￨NN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- McCluskey￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- discussed￨L￨VBD￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibria￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- extended￨L￨VBD￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- vector￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨A :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- ,￨L￨,￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- mu￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- meanings￨L￨NNS￨O￨- as￨L￨IN￨O￨- that￨L￨DT￨O￨- defined￨L￨VBN￨O￨- in￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- GreaterThan￨U￨NNP￨O￨- alpha￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- the￨L￨DT￨O￨- saturation￨L￨NN￨O￨- effect￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- applying￨L￨VBG￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨A delay￨L￨NN￨O￨A as￨L￨IN￨O￨- a￨L￨DT￨O￨- bifurcation￨L￨NN￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- condition￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- absolutely￨L￨RB￨O￨- stable￨L￨JJ￨O￨- or￨L￨CC￨O￨- conditionally￨L￨RB￨O￨- stable￨L￨JJ￨O￨- is￨L￨VBZ￨O￨- established￨L￨VBN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- unclear￨L￨JJ￨O￨- if￨L￨IN￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨O￨- HAT￨U￨NN￨O￨- elimination￨L￨NN￨O￨- goal￨L￨NN￨O￨- is￨L￨VBZ￨O￨- feasible￨L￨JJ￨O￨- under￨L￨IN￨O￨- current￨L￨JJ￨DATE￨- interventions￨L￨NNS￨O￨- or￨L￨CC￨O￨- if￨L￨IN￨O￨- complementary￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- considered.We￨L￨NN￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- HAT￨U￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- likelihood￨L￨NN￨O￨- that￨L￨WDT￨O￨- ongoing￨L￨JJ￨O￨- vector￨L￨NN￨O￨A control￨L￨NN￨O￨A ,￨L￨,￨O￨- active￨L￨JJ￨O￨- screening￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- could￨L￨MD￨O￨- eliminate￨L￨VB￨O￨- Gambian￨U￨JJ￨NATIONALITY￨- HAT￨U￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- HAT￨U￨NN￨O￨- elimination￨L￨NN￨O￨- goal￨L￨NN￨O￨- seeks￨L￨VBZ￨O￨- to￨L￨TO￨O￨- eliminate￨L￨VB￨O￨A Gambian￨U￨JJ￨NATIONALITY￨- HAT￨U￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- problem￨L￨NN￨O￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- annual￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- to￨L￨TO￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 1￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- 10,000￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- in￨L￨IN￨O￨- 90￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- foci￨L￨NNS￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- target￨L￨NN￨O￨- in￨L￨IN￨O￨- Boffa￨U￨NNP￨CITY￨- prefecture￨L￨NN￨O￨- in￨L￨IN￨O￨- Guinea￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- one￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- prevalences￨L￨NNS￨O￨- for￨L￨IN￨O￨- HAT￨U￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- country￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- where￨L￨WRB￨O￨- vector￨L￨NN￨O￨A control￨L￨NN￨O￨A measures￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- implemented￨L￨VBN￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- screen￨L￨NN￨O￨- and￨L￨CC￨O￨- treat￨L￨VB￨O￨- strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- renewed￨L￨VBN￨O￨- control￨L￨NN￨O￨- activities￨L￨NNS￨O￨- that￨L￨WDT￨O￨- centered￨L￨VBD￨O￨- around￨L￨IN￨O￨- case￨L￨NN￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- reported￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- Gambian￨U￨JJ￨NATIONALITY￨- HAT￨U￨NN￨O￨- fell￨L￨VBD￨O￨- by￨L￨IN￨O￨- 75￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Citation￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- 27,862￨L￨CD￨NUMBER￨- to￨L￨TO￨NUMBER￨- 6,984￨L￨CD￨NUMBER￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- multi-state￨L￨JJ￨O￨- Markov￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- visceral￨L￨JJ￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- was￨L￨VBD￨O￨- fitted￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- going￨L￨VBG￨O￨- on￨L￨IN￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- clinical￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- still￨L￨RB￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- uncertainty￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- particular￨L￨JJ￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatically￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- that￨L￨WDT￨O￨- develop￨L￨VBP￨O￨- clinical￨L￨JJ￨O￨- visceral￨L￨JJ￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- estimated￨L￨VBN￨O￨- average￨L￨JJ￨O￨- durations￨L￨NNS￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- symptomatic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- are￨L￨VBP￨O￨- 147￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- 130￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 166￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- 140￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- CI￨U￨NN￨O￨- 123￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 160￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- are￨L￨VBP￨O￨- significantly￨L￨RB￨O￨- longer￨L￨JJR￨O￨- than￨L￨IN￨O￨- previously￨L￨RB￨DATE￨- reported￨L￨VBN￨O￨- estimates￨L￨NNS￨O￨- .￨L￨.￨O￨- +Clinical￨U￨JJ￨O￨- and￨L￨CC￨O￨- laboratory￨L￨JJ￨O￨- diagnostics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- imprecise￨L￨JJ￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- partly￨L￨RB￨O￨- because￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- develop￨L￨VBP￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- alone￨L￨RB￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- diagnostic￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- partly￨L￨RB￨O￨- because￨L￨IN￨O￨- the￨L￨DT￨O￨- clinical￨L￨JJ￨O￨A features￨L￨NNS￨O￨- of￨L￨IN￨O￨- VL￨U￨NN￨O￨- overlap￨L￨VBP￨O￨- with￨L￨IN￨O￨- those￨L￨DT￨O￨- of￨L￨IN￨O￨- other￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- hyperreactive￨L￨JJ￨O￨- malarial￨L￨JJ￨O￨- splenomegaly￨L￨NN￨O￨- ,￨L￨,￨O￨- typhoid￨L￨JJ￨CAUSE_OF_DEATH￨- fever￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- disseminated￨L￨VBN￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- that￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- presentation￨L￨NN￨O￨- alone￨L￨RB￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- diagnostic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- Extended￨U￨JJ￨O￨- periods￨L￨NNS￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- important￨L￨JJ￨O￨- for￨L￨IN￨O￨- visceral￨L￨JJ￨O￨- leishmaniasis￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- this￨L￨DT￨O￨- depends￨L￨VBZ￨O￨- critically￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- infectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- symptomatic￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- to￨L￨TO￨O￨- sandflies￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- address￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- issues￨L￨NNS￨O￨- and￨L￨CC￨O￨- explore￨L￨VB￨O￨- their￨L￨PRP$￨O￨- biological￨L￨JJ￨O￨- implications￨L￨NNS￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- precise￨L￨JJ￨O￨- information￨L￨NN￨O￨- as￨L￨IN￨O￨- regards￨L￨VBZ￨O￨- the￨L￨DT￨O￨- domains￨L￨NNS￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- sets￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- phase￨L￨NN￨O￨- sets￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- domains￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- Poincaré￨U￨NNP￨O￨- map￨L￨NN￨O￨- of￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- point￨L￨NN￨O￨- series￨L￨NN￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- order-1￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- boundary￨L￨NN￨O￨- order-1￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- order-2￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- and￨L￨CC￨O￨- non-existence￨L￨NN￨O￨- of￨L￨IN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- with￨L￨IN￨O￨- order￨L￨NN￨O￨- no￨L￨RB￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- problem￨L￨NN￨O￨- listed￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- necessary￨L￨JJ￨O￨- condition￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- order-2￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- order-2￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- and￨L￨CC￨O￨- order-1￨L￨NN￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- precise￨L￨JJ￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- parameter￨L￨NN￨O￨- space￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- finite￨L￨JJ￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- actions￨L￨NNS￨O￨- ,￨L￨,￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- designing￨L￨VBG￨O￨- threshold￨L￨NN￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- ;￨L￨:￨O￨- the￨L￨DT￨O￨- description￨L￨NN￨O￨- of￨L￨IN￨O￨- smaller￨L￨JJR￨O￨- attractors￨L￨NNS￨O￨- ,￨L￨,￨O￨- their￨L￨PRP$￨O￨- basins￨L￨NNS￨O￨- of￨L￨IN￨O￨- attraction￨L￨NN￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- phase￨L￨NN￨O￨- sets￨L￨NNS￨O￨- and￨L￨CC￨O￨- interior￨L￨JJ￨O￨- structures￨L￨NNS￨O￨- of￨L￨IN￨O￨- horseshoe-like￨L￨JJ￨O￨- attractors￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- derive￨L￨VBP￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- under￨L￨IN￨O￨- which￨L￨WDT￨O￨- any￨L￨DT￨O￨- trajectory￨L￨NN￨O￨- initiating￨L￨VBG￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- phase￨L￨NN￨O￨- set￨L￨NN￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- free￨L￨JJ￨O￨- from￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- after￨L￨IN￨O￨- finite￨L￨JJ￨O￨- state-dependent￨L￨JJ￨O￨- feedback￨L￨NN￨O￨- control￨L￨NN￨O￨- actions￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- order-k￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GreaterThan￨U￨NN￨O￨- k￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- limit￨L￨NN￨O￨- cycles￨L￨NNS￨O￨A do￨L￨VBP￨O￨- not￨L￨RB￨O￨- exist￨L￨VB￨O￨- ,￨L￨,￨O￨- providing￨L￨VBG￨O￨- a￨L￨DT￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- open￨L￨JJ￨O￨- problem￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- integrated￨L￨VBN￨O￨- pest￨L￨NN￨O￨- management￨L￨NN￨O￨- community￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- control￨L￨VB￨O￨- the￨L￨DT￨O￨- pest￨L￨NN￨O￨- we￨L￨PRP￨O￨- assume￨L￨VBP￨O￨- ,￨L￨,￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- that￨L￨WDT￨O￨- GreaterThan￨U￨NNP￨O￨- tau￨L￨NN￨O￨- Mul￨U￨NN￨O￨- b￨L￨NN￨O￨- Pow￨U￨NN￨O￨- p￨L￨NN￨O￨- -1￨L￨CD￨NUMBER￨- if￨L￨IN￨O￨- Equality￨U￨NNP￨O￨- theta￨L￨IN￨O￨A 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- biological￨L￨JJ￨O￨- point￨L￨NN￨O￨- of￨L￨IN￨O￨- view￨L￨NN￨O￨- ,￨L￨,￨O￨- sufficient￨L￨JJ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- enemies￨L￨NNS￨O￨- must￨L￨MD￨O￨- be￨L￨VB￨O￨- released￨L￨VBN￨O￨- to￨L￨TO￨O￨- prevent￨L￨VB￨O￨- the￨L￨DT￨O￨- pest￨L￨JJS￨O￨- population￨L￨NN￨O￨- exceeding￨L￨VBG￨O￨- V￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- L￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- by￨L￨IN￨O￨- maintaining￨L￨VBG￨O￨- StrictLessThan￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- for￨L￨IN￨O￨- some￨L￨DT￨O￨- time￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- StrictGreaterThan￨U￨NNP￨O￨- theta￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- if￨L￨IN￨O￨- Equality￨U￨NN￨O￨- tau￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Denoting￨U￨VBG￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- level￨L￨NN￨O￨- as￨L￨IN￨O￨- V￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- L￨U￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- state-dependent￨L￨JJ￨O￨- impulsive￨L￨JJ￨O￨A differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- are￨L￨VBP￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- y￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- omega￨L￨JJ￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- x￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- pests￨L￨NNS￨O￨- and￨L￨CC￨O￨- natural￨L￨JJ￨O￨- enemies￨L￨NNS￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- applied￨L￨VBD￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- x￨L￨NN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- initial￨L￨JJ￨O￨- densities￨L￨NNS￨O￨- of￨L￨IN￨O￨- pest￨L￨NN￨O￨- and￨L￨CC￨O￨- natural￨L￨JJ￨O￨- enemy￨L￨NN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- reasonable￨L￨JJ￨O￨- to￨L￨TO￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- x￨L￨NN￨O￨- could￨L￨MD￨O￨- grow￨L￨VB￨O￨- exponentially￨L￨RB￨O￨- before￨L￨IN￨O￨- reaching￨L￨VBG￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- level￨L￨NN￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- value￨L￨NN￨O￨- is￨L￨VBZ￨O￨- relatively￨L￨RB￨O￨- small￨L￨JJ￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- carrying￨L￨VBG￨O￨- capacity￨L￨NN￨O￨- ,￨L￨,￨O￨- i.e.￨L￨FW￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- let￨L￨VB￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- becomes￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨A y￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- q￨L￨NN￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨ORGANIZATION￨- c￨L￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- Mul￨U￨NN￨ORGANIZATION￨- x￨L￨CC￨O￨- t￨L￨NN￨O￨- y￨L￨NN￨O￨- t￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- omega￨L￨JJ￨O￨- x￨L￨NN￨O￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- -1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- Equality￨U￨NN￨O￨- b￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- a￨L￨DT￨O￨- r￨L￨NN￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- stated￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- may￨L￨MD￨O￨- purposely￨L￨RB￨O￨- lay￨L￨VB￨O￨- dormant￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- prior￨L￨JJ￨O￨- to￨L￨TO￨O￨- infecting￨L￨VBG￨O￨- other￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A for￨L￨IN￨O￨- stealth￨L￨NN￨O￨- reasons￨L￨NNS￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- more￨L￨RBR￨O￨- realistic￨L￨JJ￨O￨- to￨L￨TO￨O￨- assume￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infected￨L￨VBN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- these￨L￨DT￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- have￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ability￨L￨NN￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t.￨L￨NN￨O￨- Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- incorporate￨L￨VBP￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- delay￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- into￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- eta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- S￨U￨NN￨O￨- Add￨U￨VB￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- tau￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨ORGANIZATION￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- varepsilon￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- delta￨L￨NN￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- gamma￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- E￨U￨NNP￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- delay￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- external￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 2￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- delta￨L￨NN￨O￨- I￨U￨PRP￨O￨- Mul￨U￨VBP￨O￨- eta￨L￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨CD￨NUMBER￨- t￨L￨NN￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- t￨L￨NN￨O￨- and￨L￨CC￨O￨- E￨U￨NN￨O￨- t￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- and￨L￨CC￨O￨- external￨L￨JJ￨O￨- computers￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +[￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR￨U￨NNP￨O￨- computer￨L￨NN￨O￨- virus￨L￨NN￨O￨- propagation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- viruses￨L￨NNS￨O￨- may￨L￨MD￨O￨- purposely￨L￨RB￨O￨- lay￨L￨VB￨O￨- dormant￨L￨JJ￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- time￨L￨NN￨O￨- prior￨L￨JJ￨O￨- to￨L￨TO￨O￨- infecting￨L￨VBG￨O￨- other￨L￨JJ￨O￨- computers￨L￨NNS￨O￨A for￨L￨IN￨O￨- stealth￨L￨NN￨O￨- reasons￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- paper￨L￨NN￨O￨- deals￨L￨VBZ￨O￨- both￨L￨CC￨O￨- with￨L￨IN￨O￨- classical￨L￨JJ￨O￨- and￨L￨CC￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- SEIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- removed￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- real￨L￨JJ￨O￨- data￨L￨NNS￨O￨- extracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- reports￨L￨NNS￨O￨- periodically￨L￨RB￨O￨- published￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- WHO￨U￨WP￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- starting￨L￨VBG￨O￨- from￨L￨IN￨O￨- March￨U￨NNP￨DATE￨- 27￨L￨CD￨DATE￨- Citation￨U￨NNP￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- shown￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- physical￨L￨JJ￨O￨- meaning￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- in￨L￨IN￨O￨- fractional￨L￨JJ￨O￨- derivatives￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- index￨L￨NN￨O￨- of￨L￨IN￨O￨- memory￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- therefore￨L￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- seems￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- exist￨L￨VBP￨O￨- different￨L￨JJ￨O￨- models￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨A to￨L￨TO￨O￨- predict￨L￨VB￨O￨- its￨L￨PRP$￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- most￨L￨JJS￨O￨- of￨L￨IN￨O￨- them￨L￨PRP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- data￨L￨NNS￨O￨- coming￨L￨VBG￨O￨- from￨L￨IN￨O￨- previous￨L￨JJ￨O￨- outbreaks￨L￨NNS￨O￨- or￨L￨CC￨O￨- using￨L￨VBG￨O￨- restricted￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- persons￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- variable￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- On￨U￨IN￨O￨- a￨L￨DT￨O￨- fractional￨L￨JJ￨O￨A order￨L￨NN￨O￨- Ebola￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- modelIvan￨L￨NN￨O￨- Area1￨U￨NN￨O￨- ,￨L￨,￨O￨- Hanan￨U￨NNP￨PERSON￨- Batarfi2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jorge￨U￨NNP￨PERSON￨- Losada3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Juan￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Nieto2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Wafa￨U￨NNP￨ORGANIZATION￨- Shammakh2￨U￨NNP￨O￨- and￨L￨CC￨O￨- Ángela￨U￨NNP￨MISC￨- Torres4￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 2015:278￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractEbola￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- world￨L￨NN￨O￨- health￨L￨NN￨O￨- problem￨L￨NN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- recent￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- confirmed￨L￨VBN￨O￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- WHO￨U￨WP￨ORGANIZATION￨- in￨L￨IN￨O￨- its￨L￨PRP$￨O￨- reports￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- our￨L￨PRP$￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- classical￨L￨JJ￨O￨- and￨L￨CC￨O￨- fractional￨L￨JJ￨O￨A SEIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- latency￨L￨NN￨O￨A :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- varphi￨L￨FW￨O￨- _￨L￨FW￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- net￨L￨JJ￨O￨- growth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- immature￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- class￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- kth￨L￨NN￨O￨- group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- a￨L￨DT￨O￨- typical￨L￨JJ￨O￨- form￨L￨NN￨O￨- of￨L￨IN￨O￨- varphi￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- Equality￨U￨NNP￨O￨- varphi￨L￨FW￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Pow￨U￨NN￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- b￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- with￨L￨IN￨O￨- b￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- constant￨L￨JJ￨O￨- and￨L￨CC￨O￨- Pow￨U￨NN￨O￨- d￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rates￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- populationBaodan￨L￨NN￨O￨- Tian1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yunguo￨U￨NNP￨O￨- Jin2￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Shouming￨U￨VBG￨O￨- Zhong2￨U￨NN￨O￨- and￨L￨CC￨O￨- Ning￨U￨NN￨MISC￨- Chen1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2015:260￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 6￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- stage￨L￨NN￨O￨- structure￨L￨NN￨O￨- and￨L￨CC￨O￨- latency￨L￨NN￨O￨A spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- call￨L￨NN￨O￨- data￨L￨NN￨O￨- records￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- CDRs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- needed￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- mobile￨L￨JJ￨TITLE￨A phone￨L￨NN￨O￨- operators￨L￨NNS￨O￨- for￨L￨IN￨O￨- billing￨L￨NN￨O￨- purposes￨L￨NNS￨O￨- ,￨L￨,￨O￨- contain￨L￨VBP￨O￨- an￨L￨DT￨O￨- enormous￨L￨JJ￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- how￨L￨WRB￨O￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- whom￨L￨WP￨O￨- we￨L￨PRP￨O￨- communicate.In￨L￨VBP￨O￨- the￨L￨DT￨DATE￨- past￨L￨NN￨DATE￨- ,￨L￨,￨O￨- research￨L￨NN￨O￨- on￨L￨IN￨O￨- social￨L￨JJ￨O￨- interactions￨L￨NNS￨O￨- between￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- were￨L￨VBD￨O￨- mostly￨L￨RB￨O￨- done￨L￨VBN￨O￨- by￨L￨IN￨O￨- surveys￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- participants￨L￨NNS￨O￨- ranges￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- around￨L￨RB￨O￨- 1,000￨L￨CD￨NUMBER￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- results￨L￨NNS￨O￨- were￨L￨VBD￨O￨- biased￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- subjectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- participants￨L￨NNS￨O￨- ’￨L￨POS￨O￨- answers￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- survey￨L￨VBP￨O￨- the￨L￨DT￨O￨- contributions￨L￨NNS￨O￨- made￨L￨VBN￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- social￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- constructed￨L￨VBN￨O￨- with￨L￨IN￨O￨- such￨L￨JJ￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- personal￨L￨JJ￨O￨- mobility￨L￨NN￨O￨- ,￨L￨,￨O￨- geographical￨L￨JJ￨O￨- partitioning￨L￨NN￨O￨- ,￨L￨,￨O￨- urban￨L￨JJ￨O￨- planning￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- help￨L￨VB￨O￨- towards￨L￨IN￨O￨- development￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- security￨L￨NN￨O￨- and￨L￨CC￨O￨- privacy￨L￨NN￨O￨- issues.Keywordsmobile￨L￨NN￨O￨- phone￨L￨NN￨O￨- datasetsbig￨L￨NN￨O￨- data￨L￨NNS￨O￨- analysisdata￨L￨NN￨O￨- miningsocial￨L￨JJ￨O￨- networkstemporal￨L￨JJ￨O￨- networksgeographical￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionAs￨U￨NNPS￨O￨- the￨L￨DT￨O￨- Internet￨U￨NN￨MISC￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- the￨L￨DT￨O￨- technological￨L￨JJ￨O￨- breakthrough￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨DATE￨- ’90s￨L￨NNS￨DATE￨- ,￨L￨,￨O￨- mobile￨L￨JJ￨TITLE￨A phones￨L￨NNS￨O￨- have￨L￨VBP￨O￨- changed￨L￨VBN￨O￨- our￨L￨PRP$￨O￨- communication￨L￨NN￨O￨- habits￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨DATE￨- first￨L￨JJ￨DATE￨- decade￨L￨NN￨DATE￨- of￨L￨IN￨DATE￨- the￨L￨DT￨DATE￨- twenty-first￨L￨JJ￨DATE￨- century￨L￨NN￨DATE￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- example￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- simple￨L￨JJ￨O￨- logistic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NN￨O￨- r￨L￨NN￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Ricker￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- Equality￨U￨NNP￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- Pow￨U￨NNP￨O￨- e￨L￨SYM￨O￨- Add￨U￨VB￨O￨- r￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- Pow￨U￨NN￨O￨- K￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 11￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- Hassell￨U￨NNP￨PERSON￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Equality￨U￨NNP￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- Mul￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- Pow￨U￨NNP￨O￨- x￨L￨CC￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- Add￨U￨VB￨O￨- Mul￨U￨NN￨O￨- a￨L￨DT￨O￨- x￨L￨NN￨O￨- _￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- b￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- exhibit￨L￨VBP￨O￨- a￨L￨DT￨O￨- rich￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behavior.There￨L￨NN￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- increasing￨L￨VBG￨O￨- interest￨L￨NN￨O￨- and￨L￨CC￨O￨- more￨L￨JJR￨O￨- studies￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- discrete￨L￨JJ￨O￨A time￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- recently￨L￨RB￨DATE￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- theoretical￨L￨JJ￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- discrete￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- focuses￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- computation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 19￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 14￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 16￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- papers￨L￨NNS￨O￨- using￨L￨VBG￨O￨- discrete￨L￨JJ￨O￨A mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- latent￨L￨JJ￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- TB￨U￨NN￨CAUSE_OF_DEATH￨- control￨L￨NN￨O￨- strategy￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- The￨U￨DT￨O￨- discrete￨L￨JJ￨O￨A tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- transmission￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individualsHui￨L￨NN￨O￨- Cao1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Hongwu￨U￨NN￨O￨- Tan1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2015:165￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractA￨U￨NNP￨O￨- discrete￨L￨JJ￨O￨- tuberculosis￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- direct￨L￨JJ￨O￨- progression￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- latently￨L￨RB￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- presented￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- with￨L￨IN￨O￨- different￨L￨JJ￨O￨- control￨L￨NN￨O￨- measures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- determined￨L￨VBN￨O￨- and￨L￨CC￨O￨- analyzed￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- give￨L￨VBP￨O￨- the￨L￨DT￨O￨- critical￨L￨JJ￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- probability￨L￨NN￨O￨- of￨L￨IN￨O￨- successful￨L￨JJ￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨A of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- .￨L￨.￨O￨- +171￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 143￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 154￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 2001￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Scholar4.Brauer￨U￨NNP￨O￨- ,￨L￨,￨O￨- F.￨U￨NNP￨O￨- ;￨L￨:￨O￨- van￨L￨NNP￨O￨- den￨L￨NN￨O￨A Driessche￨U￨NNP￨O￨- ,￨L￨,￨O￨- P.￨U￨NNP￨O￨- ;￨L￨:￨O￨- Wu￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- J.￨U￨NNP￨O￨- :￨L￨:￨O￨- Mathematical￨U￨JJ￨O￨- Epidemiology￨U￨NNP￨O￨- ,￨L￨,￨O￨- Springer￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Berlin￨U￨NNP￨CITY￨- (￨L￨-LRB-￨O￨- 2008￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Google￨U￨NNP￨ORGANIZATION￨- Scholar5.Capasso￨U￨NNP￨O￨- V.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Serio￨U￨NNP￨O￨- G.￨U￨NNP￨O￨- :￨L￨:￨O￨- A￨U￨NNP￨O￨- generalization￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Kermack￨U￨NNP￨O￨- –￨L￨:￨O￨- McKendrick￨U￨NNP￨PERSON￨- deterministic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +42￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 41￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 61￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1978￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- CrossRefMathSciNetGoogle￨U￨NNP￨O￨- Scholar6.Carletti￨U￨NNP￨O￨- M.￨U￨NNP￨O￨- :￨L￨:￨O￨- Mean-square￨U￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- bacteriophage￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- delays￨L￨NNS￨O￨- .￨L￨.￨O￨- +33￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 250￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 260￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1995￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- CrossRefzbMATHMathSciNetGoogle￨U￨NNP￨O￨- Scholar2.Beretta￨U￨NNP￨O￨- E.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Kolmanovskii￨U￨NNP￨PERSON￨- V.￨U￨NNP￨O￨- ,￨L￨,￨O￨- Shaikhet￨U￨NNP￨O￨- L.￨U￨NNP￨O￨- :￨L￨:￨O￨- Stability￨U￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨A with￨L￨IN￨O￨- time￨L￨NN￨O￨- delay￨L￨NN￨O￨- ifluenced￨L￨VBN￨O￨- by￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- perturbations￨L￨NNS￨O￨- .￨L￨.￨O￨- +45￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 269￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 277￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- 1998￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- CrossRefzbMATHMathSciNetGoogle￨U￨NNP￨O￨- Scholar3.Brauer￨U￨NNP￨O￨- ,￨L￨,￨O￨- F.￨U￨NNP￨O￨- ;￨L￨:￨O￨- van￨L￨NNP￨O￨- den￨L￨NN￨O￨A Driessche￨U￨NNP￨O￨- ,￨L￨,￨O￨- P.￨U￨NNP￨O￨- :￨L￨:￨O￨- Models￨U￨NNS￨O￨- for￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- immigration￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- periodic￨L￨JJ￨O￨- forced￨L￨JJ￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨NNP￨O￨- I￨U￨NNP￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- Add￨U￨VBP￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- Mul￨U￨NN￨O￨- I￨U￨PRP￨O￨- S￨U￨NN￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- beta￨L￨NN￨O￨- t￨L￨NN￨O￨- Equality￨U￨NNP￨O￨- Derivative￨U￨JJ￨O￨- R￨U￨NN￨O￨- t￨L￨NN￨O￨- Tuple￨U￨NN￨PERSON￨- t￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Add￨U￨VBP￨O￨- Mul￨U￨NN￨O￨- I￨U￨NN￨O￨- gamma￨L￨NN￨O￨- Mul￨U￨NN￨O￨- -1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- mu￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- fractions￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- denote￨L￨VBP￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- death￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- t￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- seasonally-dependent￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- T-periodic￨U￨JJ￨MISC￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- decreasing￨L￨VBG￨O￨- piecewise￨L￨NN￨O￨- smooth￨L￨JJ￨O￨- factor￨L￨NN￨O￨- which￨L￨WDT￨O￨- can￨L￨MD￨O￨- describe￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- coverage￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- by￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- factor￨L￨NN￨O￨- of￨L￨IN￨O￨- influences￨L￨NNS￨O￨- ,￨L￨,￨O￨- σ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- small￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- _￨L￨SYM￨O￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- critical￨L￨JJ￨O￨- level￨L￨NN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- Leray-Schauder￨U￨JJ￨O￨- degree￨L￨NN￨O￨- theory￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- establish￨L￨VBP￨O￨- new￨L￨JJ￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- one￨L￨CD￨NUMBER￨- positive￨L￨JJ￨O￨- periodic￨L￨JJ￨O￨- solution￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- seasonally￨L￨RB￨O￨- forced￨L￨VBN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +When￨U￨WRB￨O￨- Mul￨U￨NN￨O￨- equiv￨L￨FW￨O￨- f￨L￨FW￨O￨- I￨U￨PRP￨O￨- in￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Katriel￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- got￨L￨VBD￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- periodic￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- periodically￨L￨RB￨O￨- forced￨L￨VBN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- Leray-Schauder￨U￨NNP￨O￨- degree￨L￨NN￨O￨- theory￨L￨NN￨O￨- provided￨L￨VBN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- .￨L￨.￨O￨- +2015Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- periodic￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- seasonally￨L￨RB￨O￨- forced￨L￨VBN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- coverage￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Periodic￨U￨JJ￨MISC￨- solutions￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- seasonally￨L￨RB￨O￨- forced￨L￨VBN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- media￨L￨NNS￨O￨- coverageJian￨L￨NN￨O￨- Zu1￨U￨NN￨O￨- and￨L￨CC￨O￨- Lin￨U￨NNP￨O￨- Wang2￨U￨NNP￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2015:136￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Zu￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Wang￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- experimental￨L￨JJ￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- among￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- features￨L￨NNS￨O￨- that￨L￨WDT￨O￨- include￨L￨VBP￨O￨- degree￨L￨NN￨O￨- and￨L￨CC￨O￨- different￨L￨JJ￨O￨- centrality￨L￨NN￨O￨A measures￨L￨NNS￨O￨- ,￨L￨,￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- effective￨L￨JJ￨O￨- feature￨L￨NN￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- latent￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- nodes.KeywordsEpidemicsInformation￨L￨NN￨O￨- cascadesInformation￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- IntroductionNetworks￨U￨NNS￨O￨- are￨L￨VBP￨O￨- underlying￨L￨VBG￨O￨- mediums￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- rumors￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- computer￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- evaluate￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- state￨L￨NN￨O￨- classifiers￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Naive￨U￨JJ￨LOCATION￨- Bayes￨U￨NNS￨LOCATION￨- ,￨L￨,￨O￨- Naive￨U￨JJ￨O￨- Bayes￨U￨NNS￨PERSON￨- with￨L￨IN￨O￨- kernel￨L￨NN￨O￨- density￨L￨NN￨O￨- estimation￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- decision￨L￨NN￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- combination￨L￨NN￨O￨- with￨L￨IN￨O￨- features￨L￨NNS￨O￨- including￨L￨VBG￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- betweenness￨L￨NN￨O￨- centrality￨L￨NN￨O￨A and￨L￨CC￨O￨- different￨L￨JJ￨O￨- centrality￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +2015Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractAlgorithms￨U￨NNP￨O￨- for￨L￨IN￨O￨- identifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- are￨L￨VBP￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- understanding￨L￨VBG￨O￨- and￨L￨CC￨O￨- containing￨L￨VBG￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- cascades￨L￨NNS￨O￨A .￨L￨.￨O￨- +Determining￨U￨VBG￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- states￨L￨NNS￨O￨A of￨L￨IN￨O￨- network￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- to￨L￨TO￨O￨- taking￨L￨VBG￨O￨- corrective￨L￨JJ￨O￨- or￨L￨CC￨O￨- preventive￨L￨JJ￨O￨- action￨L￨NN￨O￨- to￨L￨TO￨O￨- stop￨L￨VB￨O￨- or￨L￨CC￨O￨- slow￨L￨VB￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Stability￨U￨NN￨MISC￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- observer￨L￨NN￨O￨- design￨L￨NN￨O￨A for￨L￨IN￨O￨- discrete-time￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelsAsier￨L￨NN￨O￨- Ibeas1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Manuel￨U￨NNP￨O￨- de￨L￨FW￨O￨- la￨L￨FW￨O￨- Sen2￨U￨NN￨O￨- ,￨L￨,￨O￨- Santiago￨U￨NNP￨CITY￨- Alonso-Quesada2￨U￨NN￨O￨- and￨L￨CC￨O￨- Iman￨U￨NN￨O￨- Zamani3￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2015:122￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Ibeas￨U￨NNPS￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- along￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- observer￨L￨NN￨O￨- design￨L￨NN￨O￨A is￨L￨VBZ￨O￨- faced￨L￨VBN￨O￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- implicit￨L￨JJ￨O￨- way￨L￨NN￨O￨- instead￨L￨RB￨O￨- of￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨- first￨L￨RB￨ORDINAL￨- an￨L￨DT￨O￨- explicit￨L￨JJ￨O￨- formulation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- novelty￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- presented￨L￨VBN￨O￨- approach￨L￨NN￨O￨- .￨L￨.￨O￨- +Afterwards￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- design￨L￨NN￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- state￨L￨NN￨O￨- observer￨L￨NN￨O￨- for￨L￨IN￨O￨- this￨L￨DT￨O￨- discrete-time￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- tackled￨L￨VBN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- theoretical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- lambda￨L￨NN￨O￨A _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- StrictLessThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- lambda￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NNP￨O￨- lambda￨L￨NN￨O￨- lambda￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- exists￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- .￨L￨.￨O￨- +Classical￨U￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- revealed￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- threshold￨L￨NN￨O￨- lambda￨L￨NN￨O￨A _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- c￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- on￨L￨IN￨O￨- homogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- below￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- die￨L￨VB￨O￨- out￨L￨RP￨O￨- ;￨L￨:￨O￨- otherwise￨L￨RB￨O￨- there￨L￨EX￨O￨- will￨L￨MD￨O￨- exist￨L￨VB￨O￨- a￨L￨DT￨O￨- persistence￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- apart￨L￨RB￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- external￨L￨JJ￨O￨- environment￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- vector￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- mosquitoes￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- may￨L￨MD￨O￨- also￨L￨RB￨O￨- play￨L￨VB￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- role￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +2015Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIRS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- not￨L￨RB￨O￨- containing￨L￨VBG￨O￨- the￨L￨DT￨O￨- permanent￨L￨JJ￨O￨- acquired￨L￨VBN￨O￨- immunity￨L￨NN￨O￨- with￨L￨IN￨O￨- non-linear￨L￨JJ￨O￨- generalized￨L￨VBN￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- preventive￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stable￨L￨JJ￨O￨- locally￨L￨RB￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- globally￨L￨RB￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨JJ￨O￨A and￨L￨CC￨O￨- an￨L￨DT￨O￨- unstable￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- occurs￨L￨VBZ￨O￨- for￨L￨IN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- SEIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- non-linear￨L￨JJ￨O￨- generalized￨L￨VBN￨O￨- incidences￨L￨NNS￨O￨- and￨L￨CC￨O￨- preventive￨L￨JJ￨O￨A vaccinationMuhammad￨L￨NNP￨O￨- Altaf￨U￨NNP￨PERSON￨- Khan1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Qaisar￨U￨NNP￨PERSON￨- Badshah1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Saeed￨U￨NNP￨PERSON￨- Islam1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ilyas￨U￨NNP￨PERSON￨- Khan2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Sharidan￨U￨NNP￨O￨- Shafie3Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Sher￨U￨NNP￨O￨- Afzal￨U￨NNP￨O￨- Khan4￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2015:88￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Khan￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stable￨L￨JJ￨O￨- both￨L￨CC￨O￨- locally￨L￨RB￨O￨- and￨L￨CC￨O￨- globally￨L￨RB￨O￨- when￨L￨WRB￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- global￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- completely￨L￨RB￨O￨- described￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- Mul￨U￨NN￨O￨- R￨U￨NN￨O￨- mathcal￨L￨NN￨O￨A .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- a￨L￨DT￨O￨- vaccine-induced￨L￨JJ￨O￨- protection￨L￨NN￨O￨- equivalent￨L￨NN￨O￨- to￨L￨TO￨O￨- that￨L￨DT￨O￨- of￨L￨IN￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- our￨L￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- annual￨L￨JJ￨SET￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- students￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- alternative￨L￨NN￨O￨- strategy￨L￨NN￨O￨- to￨L￨TO￨O￨- routine￨L￨JJ￨O￨- immunization￨L￨NN￨O￨- of￨L￨IN￨O￨- infants￨L￨NNS￨O￨A able￨L￨JJ￨O￨- to￨L￨TO￨O￨- trigger￨L￨VB￨O￨- a￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- and￨L￨CC￨O￨- persistent￨L￨JJ￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- infant￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- on￨L￨IN￨O￨- average￨L￨NN￨O￨- ,￨L￨,￨O￨- of￨L￨IN￨O￨- 35.6￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- versus￨L￨CC￨O￨- 41.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- 10￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- In￨U￨IN￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- explicitly￨L￨RB￨O￨- accounts￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- socio-demographic￨L￨JJ￨O￨- population￨L￨NN￨O￨- structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- developed￨L￨VBN￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- RSV￨U￨NN￨O￨- transmission￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- rural￨L￨JJ￨O￨- setting￨L￨NN￨O￨- of￨L￨IN￨O￨- Kenya￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- alternative￨L￨JJ￨O￨A population￨L￨NN￨O￨- targets￨L￨NNS￨O￨- in￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- RSV￨U￨NN￨O￨- infant￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Evaluating￨U￨VBG￨MISC￨- vaccination￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- for￨L￨IN￨O￨- reducing￨L￨VBG￨O￨A infant￨L￨NN￨O￨- respiratory￨L￨JJ￨O￨- syncytial￨L￨NN￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- low-income￨L￨JJ￨O￨- settingsPiero￨L￨NN￨O￨- Poletti1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Stefano￨U￨NNP￨PERSON￨- Merler2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Marco￨U￨NNP￨PERSON￨- Ajelli2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Piero￨U￨NNP￨O￨- Manfredi3￨U￨NNP￨O￨- ,￨L￨,￨O￨- Patrick￨U￨NNP￨PERSON￨- K￨U￨NNP￨PERSON￨- Munywoki4￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- D￨U￨NN￨O￨- James￨U￨NNP￨PERSON￨- Nokes4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Alessia￨U￨NNP￨PERSON￨- Melegaro1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 13:49￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Poletti￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨O￨- Central￨U￨NNP￨O￨- .￨L￨.￨O￨- +Interestingly￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- pregnant￨L￨JJ￨O￨- women￨L￨NNS￨O￨- boosts￨L￨VBZ￨O￨- maternal￨L￨JJ￨O￨- antibody￨L￨NN￨O￨- protection￨L￨NN￨O￨- in￨L￨IN￨O￨- infants￨L￨NNS￨O￨A by￨L￨IN￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- 4￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- RSV￨U￨NN￨O￨- infant￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- reduced￨L￨VBN￨O￨- by￨L￨IN￨O￨- 31.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- household￨L￨NN￨O￨A transmission￨L￨NN￨O￨- is￨L￨VBZ￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- 39￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- infant￨L￨NN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- school-age￨L￨JJ￨O￨- children￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- household￨L￨NN￨O￨- ,￨L￨,￨O￨- causing￨L￨VBG￨O￨- around￨L￨IN￨O￨- 55￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- stationary￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- ergodic.Throughout￨L￨JJ￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- let￨L￨VB￨O￨- (￨L￨-LRB-￨O￨- Ω￨U￨NNP￨O￨- ,￨L￨,￨O￨- F￨U￨NN￨O￨- ,￨L￨,￨O￨- {￨L￨-LRB-￨O￨- F￨U￨NN￨O￨- t￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- P￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- be￨L￨VB￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- probability￨L￨NN￨O￨- space￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- filtration￨L￨NN￨O￨- {￨L￨-LRB-￨O￨- F￨U￨NN￨O￨- t￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- t￨L￨NN￨O￨- ≥￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- satisfying￨L￨VBG￨O￨- the￨L￨DT￨O￨- usual￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- right￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- and￨L￨CC￨O￨- F￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- contains￨L￨VBZ￨O￨- all￨L￨DT￨O￨- P-null￨U￨JJ￨MISC￨- sets￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- takes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- dI￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- Ideally￨U￨RB￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- coefficients￨L￨NNS￨O￨A beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- should￨L￨MD￨O￨- suffer￨L￨VB￨O￨- from￨L￨IN￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- proved￨L￨VBD￨O￨- that￨L￨IN￨O￨- this￨L￨DT￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- unique￨L￨JJ￨O￨- global￨L￨JJ￨O￨- positive￨L￨JJ￨O￨A solution￨L￨NN￨O￨- and￨L￨CC￨O￨- establish￨L￨VB￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- extinction￨L￨NN￨O￨- and￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- alpha￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- beta￨L￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- j￨L￨NN￨O￨- *￨L￨SYM￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- N￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants.Since￨L￨NN￨O￨- gonorrhea￨L￨NN￨O￨- is￨L￨VBZ￨O￨- in￨L￨IN￨O￨- essence￨L￨NN￨O￨- a￨L￨DT￨O￨- nonseasonal￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- less￨L￨JJR￨O￨- than￨L￨IN￨O￨- a￨L￨DT￨O￨- 10￨L￨CD￨PERCENT￨- percent￨L￨NN￨PERCENT￨- seasonal￨L￨JJ￨O￨- component￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- variation￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- give￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- time-independent￨L￨JJ￨O￨- coefficients￨L￨NNS￨O￨A .￨L￨.￨O￨- +The￨U￨DT￨O￨- work￨L￨NN￨O￨- is￨L￨VBZ￨O￨- interdisciplinary￨L￨JJ￨O￨- ,￨L￨,￨O￨- combining￨L￨VBG￨O￨- anthropological￨L￨JJ￨O￨- concepts￨L￨NNS￨O￨- with￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- with￨L￨IN￨O￨- archaeological￨L￨JJ￨O￨- parallels￨L￨NNS￨O￨- in￨L￨IN￨O￨- regards￨L￨VBZ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- findings.KeywordsSIRS￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- Periodic￨U￨JJ￨O￨- forcing￨L￨VBG￨O￨- Social￨U￨NNP￨O￨- dynamics￨L￨NNS￨O￨- Nonlinear￨U￨JJ￨O￨- dynamics￨L￨NNS￨O￨- Sabbath￨U￨NNP￨O￨- Cultural￨U￨NNP￨O￨- anthropology￨L￨NNP￨O￨- Electronic￨U￨NNP￨O￨- supplementary￨L￨JJ￨O￨A materialThe￨L￨NN￨O￨- online￨L￨NN￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- doi￨L￨FW￨O￨- :￨L￨:￨O￨- 10.1007￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- s10867-014-9373-9￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- contains￨L￨VBZ￨O￨- supplementary￨L￨JJ￨O￨- material￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- available￨L￨JJ￨O￨- to￨L￨TO￨O￨- authorized￨L￨VBN￨O￨- users￨L￨NNS￨O￨- .1￨L￨VBP￨NUMBER￨- IntroductionEspecially￨U￨RB￨O￨- in￨L￨IN￨O￨- recent￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- proven￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- important￨L￨JJ￨O￨- tools￨L￨NNS￨O￨- for￨L￨IN￨O￨- shedding￨L￨VBG￨O￨- light￨L￨NN￨O￨- on￨L￨IN￨O￨- complex￨L￨JJ￨O￨- aspects￨L￨NNS￨O￨- of￨L￨IN￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- ,￨L￨,￨O￨- culture￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- communications￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- investigating￨L￨VBG￨O￨- topical￨L￨JJ￨O￨- anthropological￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- approach￨L￨NN￨O￨- takes￨L￨VBZ￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- analogy￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- populations￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- transgression￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- define￨L￨VBP￨O￨- here￨L￨RB￨O￨- as￨L￨IN￨O￨- violation￨L￨NN￨O￨- of￨L￨IN￨O￨- social￨L￨JJ￨O￨A norms￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- human￨L￨JJ￨O￨- society.Interestingly￨L￨NN￨O￨- ,￨L￨,￨O￨- similar￨L￨JJ￨O￨- contagion￨L￨NN￨O￨- models￨L￨NNS￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- formulated￨L￨VBN￨O￨- to￨L￨TO￨O￨- express￨L￨VB￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- any￨L￨DT￨O￨- human￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- acquired￨L￨VBN￨O￨- by￨L￨IN￨O￨- learning￨L￨VBG￨O￨- from￨L￨IN￨O￨- others￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- vein￨L￨NN￨O￨- ,￨L￨,￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- demonstrates￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- mathematical￨L￨JJ￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- may￨L￨MD￨O￨- help￨L￨VB￨O￨- understand￨L￨VB￨O￨- justice￨L￨NN￨O￨- administration￨L￨NN￨O￨- systems￨L￨NNS￨O￨- of￨L￨IN￨O￨- societies￨L￨NNS￨O￨- and￨L￨CC￨O￨- their￨L￨PRP$￨O￨- social￨L￨JJ￨O￨A organization￨L￨NN￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- specific￨L￨JJ￨O￨- focus￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- institution￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Sabbath￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- appearance￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- early￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- Israel￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- work￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- how￨L￨WRB￨O￨- a￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- Sabbath￨U￨NNP￨O￨- could￨L￨MD￨O￨- in￨L￨IN￨O￨- theory￨L￨NN￨O￨- enhance￨L￨VBP￨O￨- social￨L￨JJ￨O￨A resilience￨L￨NN￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- similar￨L￨JJ￨O￨- assembly￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- more￨L￨RBR￨O￨- natural￨L￨JJ￨O￨- and￨L￨CC￨O￨- longer￨L￨JJR￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- say￨L￨VBP￨O￨- between￨L￨IN￨O￨- New￨U￨NNP￨LOCATION￨- Moon￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- Full￨U￨JJ￨O￨- Moon￨U￨NN￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- mathematical￨L￨JJ￨O￨- examination￨L￨NN￨O￨- points￨L￨NNS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- cultural￨L￨JJ￨O￨A ,￨L￨,￨O￨- civic￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- weekly￨L￨JJ￨SET￨- Sabbath￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- that￨L￨DT￨O￨- is￨L￨VBZ￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- Sabbath￨U￨NNP￨MISC￨- institution￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- deviation￨L￨NN￨O￨- from￨L￨IN￨O￨- social￨L￨JJ￨O￨- norms￨L￨NNS￨O￨- .￨L￨.￨O￨- +NumericCitation￨U￨NNP￨O￨- proposed￨L￨VBD￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- immunity￨L￨NN￨O￨- and￨L￨CC￨O￨- latency￨L￨NN￨O￨- spreading￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- was￨L￨VBD￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- case￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- backward￨L￨RB￨O￨A Euler￨U￨NNP￨PERSON￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- obtained￨L￨VBD￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- plentiful￨L￨JJ￨O￨- and￨L￨CC￨O￨- complex￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- including￨L￨VBG￨O￨- bifurcations.In￨L￨NN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- backward￨L￨RB￨O￨A Euler￨U￨NNP￨PERSON￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- discretize￨L￨VB￨O￨- a￨L￨DT￨O￨- continuous-time￨L￨JJ￨O￨- plant￨L￨NN￨O￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- roguing￨L￨NN￨O￨- and￨L￨CC￨O￨- replanting￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- A￨U￨DT￨O￨- discrete￨L￨JJ￨O￨- plant￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- roguing￨L￨NN￨O￨- and￨L￨CC￨O￨- replantingYueli￨L￨NN￨O￨- Luo1￨U￨NN￨O￨- ,￨L￨,￨O￨- Shujing￨U￨VBG￨O￨- Gao1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Dehui￨U￨NNP￨O￨- Xie1￨U￨NN￨O￨- and￨L￨CC￨O￨- Yanfei￨U￨NN￨MISC￨- Dai1￨U￨NN￨MISC￨- Citation￨U￨NNP￨MISC￨- 2015:12￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Luo￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- plant￨L￨NN￨O￨- virus￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- roguing￨L￨NN￨O￨- and￨L￨CC￨O￨- replanting￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- derived￨L￨VBN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- continuous￨L￨JJ￨O￨- case￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- well-known￨L￨JJ￨O￨- backward￨L￨RB￨O￨A Euler￨U￨NNP￨PERSON￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- applying￨L￨VBG￨O￨- analytic￨L￨JJ￨O￨- techniques￨L￨NNS￨O￨- and￨L￨CC￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨A Lyapunov￨U￨NN￨PERSON￨- function￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- result￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- attractive￨L￨JJ￨O￨- if￨L￨IN￨O￨- LessThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- permanent￨L￨JJ￨O￨- if￨L￨IN￨O￨- StrictGreaterThan￨U￨NN￨O￨- R￨U￨NN￨O￨- _￨L￨CD￨NUMBER￨- {￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- }￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +NumericCitation￨U￨NN￨O￨- constructed￨L￨VBD￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨A SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- they￨L￨PRP￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- principles￨L￨NNS￨O￨- discussed￨L￨VBN￨O￨- herein￨L￨RB￨O￨- will￨L￨MD￨O￨- help￨L￨VB￨O￨- organizations￨L￨NNS￨O￨A and￨L￨CC￨O￨- investigators￨L￨NNS￨O￨- document￨L￨VBP￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- ranaviruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- identify￨L￨VBP￨O￨- hotspots￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- determine￨L￨VB￨O￨- factors￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- emergence￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- collect￨L￨VB￨O￨- data￨L￨NNS￨O￨- necessary￨L￨JJ￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- practical￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies.KeywordsDetection￨L￨NN￨O￨- Probability￨U￨NN￨O￨- Infection￨U￨NN￨CAUSE_OF_DEATH￨- Prevalence￨U￨NN￨O￨- Require￨U￨VB￨O￨- Sample￨U￨NNP￨O￨- Size￨U￨NN￨O￨- Captive￨U￨NNP￨O￨- Population￨U￨NNP￨O￨- Wood￨U￨NNP￨O￨- Frog￨U￨NNP￨O￨- These￨U￨DT￨O￨- keywords￨L￨NNS￨O￨- were￨L￨VBD￨O￨- added￨L￨VBN￨O￨- by￨L￨IN￨O￨- machine￨L￨NN￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- chapter￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- discuss￨L￨VBP￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- design￨L￨VB￨O￨- surveillance￨L￨NN￨O￨- studies￨L￨NNS￨O￨- for￨L￨IN￨O￨- ranavirus￨L￨NN￨O￨- ,￨L￨,￨O￨- required￨L￨VBN￨O￨- sample￨L￨NN￨O￨A sizes￨L￨NNS￨O￨- ,￨L￨,￨O￨- statistical￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- data￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- modeling￨L￨NN￨O￨- approaches￨L￨NNS￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outcomes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Considering￨U￨VBG￨O￨- that￨L￨DT￨O￨- adequate￨L￨JJ￨O￨- sample￨L￨NN￨O￨- sizes￨L￨NNS￨O￨- to￨L￨TO￨O￨- detect￨L￨VB￨O￨- ranavirus￨L￨NN￨O￨- and￨L￨CC￨O￨- obtain￨L￨VB￨O￨- precise￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨A prevalence￨L￨NN￨O￨A can￨L￨MD￨O￨- be￨L￨VB￨O￨- high￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- >￨L￨JJR￨O￨- 60￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- laboratory￨L￨NN￨O￨- expenses￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- ranavirus￨L￨NN￨O￨- testing￨L￨NN￨O￨- are￨L￨VBP￨O￨- substantial￨L￨JJ￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- organizations￨L￨NNS￨O￨A that￨L￨WDT￨O￨- have￨L￨VBP￨O￨- limited￨L￨VBN￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- ranaviruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- region￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- take￨L￨VB￨O￨- several￨L￨JJ￨DURATION￨- years￨L￨NNS￨DURATION￨- to￨L￨TO￨O￨- document￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- ranaviruses￨L￨NNS￨O￨- ,￨L￨,￨O￨- identify￨L￨VBP￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- hotspots￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- implement￨L￨VB￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- thwart￨L￨VBP￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- ranavirus￨L￨NN￨O￨- or￨L￨CC￨O￨- reduce￨L￨VB￨O￨- its￨L￨PRP$￨O￨- prevalence￨L￨NN￨O￨- .￨L￨.￨O￨- +Studies￨U￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- designed￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- the￨L￨DT￨O￨- distribution￨L￨NN￨O￨- and￨L￨CC￨O￨- prevalence￨L￨NN￨O￨A of￨L￨IN￨O￨- ranavirus￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- pathogen￨L￨NN￨O￨- into￨L￨IN￨O￨- an￨L￨DT￨O￨- uninfected￨L￨JJ￨O￨- area￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- possible￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- modified￨L￨VBN￨O￨- metapopulation￨L￨NN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- produce￨L￨VBP￨O￨- a￨L￨DT￨O￨- discontinuous￨L￨JJ￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- jump￨L￨NN￨O￨- at￨L￨IN￨O￨- R0￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- two￨L￨CD￨NUMBER￨- infectious￨L￨JJ￨O￨- stages￨L￨NNS￨O￨- in￨L￨IN￨O￨- our￨L￨PRP$￨O￨- modified￨L￨VBN￨O￨- metapopulation￨L￨NN￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- produce￨L￨VBP￨O￨- a￨L￨DT￨O￨- discontinuous￨L￨JJ￨O￨- final￨L￨JJ￨O￨- size￨L￨NN￨O￨- distribution￨L￨NN￨O￨- .￨L￨.￨O￨- +Given￨U￨VBN￨O￨- their￨L￨PRP$￨O￨- broad￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- ranges￨L￨NNS￨O￨- ,￨L￨,￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- high￨L￨JJ￨O￨- virulence￨L￨NN￨O￨- ,￨L￨,￨O￨- multiple￨L￨JJ￨O￨- routes￨L￨NNS￨O￨- of￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- frequent￨L￨JJ￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- amphibians￨L￨NNS￨O￨- ,￨L￨,￨O￨- fish￨L￨NN￨O￨- and￨L￨CC￨O￨- reptiles￨L￨NNS￨O￨- in￨L￨IN￨O￨- global￨L￨JJ￨O￨- trade￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- appears￨L￨VBZ￨O￨- that￨L￨IN￨O￨- some￨L￨DT￨O￨- ranaviruses￨L￨NNS￨O￨- have￨L￨VBP￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- to￨L￨TO￨O￨- significantly￨L￨RB￨O￨- impact￨L￨VB￨O￨- host￨L￨NN￨TITLE￨A populations￨L￨NNS￨O￨A and￨L￨CC￨O￨- even￨L￨RB￨O￨- cause￨L￨VB￨O￨- extinctions￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- wild.KeywordsLargemouth￨L￨NNP￨O￨- Bass￨U￨NNP￨O￨- Wood￨U￨NNP￨O￨- Frog￨U￨NNP￨O￨- Tiger￨U￨NNP￨O￨- Salamander￨U￨NNP￨O￨- Ectothermic￨U￨NNP￨O￨- Vertebrate￨U￨NNP￨O￨- Pallid￨U￨NNP￨O￨- Sturgeon￨U￨NNP￨O￨- These￨U￨DT￨O￨- keywords￨L￨NNS￨O￨- were￨L￨VBD￨O￨- added￨L￨VBN￨O￨- by￨L￨IN￨O￨- machine￨L￨NN￨O￨- and￨L￨CC￨O￨- not￨L￨RB￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- .￨L￨.￨O￨- +Generally￨U￨RB￨O￨- ,￨L￨,￨O￨- ranaviruses￨L￨NNS￨O￨- are￨L￨VBP￨O￨- locally￨L￨RB￨O￨- adapted￨L￨VBN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨A populations￨L￨NNS￨O￨A ,￨L￨,￨O￨- but￨L￨CC￨O￨- movement￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- over￨L￨IN￨O￨- long￨L￨JJ￨O￨- distances￨L￨NNS￨O￨- can￨L￨MD￨O￨- disrupt￨L￨VB￨O￨- these￨L￨DT￨O￨- associations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Ranavirus￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- their￨L￨PRP$￨O￨- host￨L￨NN￨TITLE￨A populations￨L￨NNS￨O￨A ,￨L￨,￨O￨- from￨L￨IN￨O￨- apparently￨L￨RB￨O￨- benign￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- to￨L￨TO￨O￨- mass￨L￨NN￨O￨- mortality￨L￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- extirpation￨L￨NN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- view￨L￨NN￨O￨- changed￨L￨VBD￨O￨- with￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- evidence￨L￨NN￨O￨A that￨L￨IN￨O￨- ranaviruses￨L￨NNS￨O￨- were￨L￨VBD￨O￨- responsible￨L￨JJ￨O￨- for￨L￨IN￨O￨- widespread￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- and￨L￨CC￨O￨- mortality￨L￨NN￨O￨- in￨L￨IN￨O￨- several￨L￨JJ￨O￨- fishes￨L￨NNS￨O￨- and￨L￨CC￨O￨- later￨L￨RB￨O￨- amphibians￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- evidence￨L￨NN￨O￨- of￨L￨IN￨O￨- increased￨L￨VBN￨O￨- virulence￨L￨NN￨O￨A of￨L￨IN￨O￨- ranaviruses￨L￨NNS￨O￨- in￨L￨IN￨O￨- captive￨L￨JJ￨O￨- fish￨L￨NN￨O￨- and￨L￨CC￨O￨- amphibian￨L￨NN￨O￨- populations￨L￨NNS￨O￨- raised￨L￨VBD￨O￨- for￨L￨IN￨O￨- production￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- parameters￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- summarized￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- list￨L￨NN￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptibles￨L￨NNS￨O￨- corresponding￨L￨VBG￨O￨- to￨L￨TO￨O￨- births￨L￨NNS￨O￨- and￨L￨CC￨O￨- immigration￨L￨NN￨O￨- ;￨L￨:￨O￨- β￨L￨NN￨O￨- :￨L￨:￨O￨- transmission￨L￨NN￨O￨- coefficient￨L￨NN￨O￨- between￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- I￨U￨PRP￨O￨- ;￨L￨:￨O￨- μ￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- per￨L￨FW￨O￨- capita￨L￨NN￨O￨- natural￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- δ￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- for￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- leaving￨L￨VBG￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- compartment￨L￨NN￨O￨A I￨U￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- quarantine￨L￨NN￨O￨- compartment￨L￨NN￨O￨- Q￨U￨NNP￨O￨- ;￨L￨:￨O￨- γ￨L￨NN￨O￨- :￨L￨:￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- ;￨L￨:￨O￨- ε￨L￨NN￨O￨- :￨L￨:￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- individuals￨L￨NNS￨O￨- return￨L￨VBP￨O￨- to￨L￨TO￨O￨- susceptible￨L￨JJ￨O￨- compartment￨L￨NN￨O￨- S￨U￨NN￨O￨- from￨L￨IN￨O￨- compartments￨L￨NNS￨O￨- Q￨U￨NNP￨O￨- ;￨L￨:￨O￨- α￨L￨NN￨O￨- :￨L￨:￨O￨- disease-caused￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals.In￨L￨NN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- generally￨L￨RB￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- P￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- unstable￨L￨JJ￨O￨- and￨L￨CC￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- P￨U￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- ∗￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨A under￨L￨IN￨O￨- a￨L￨DT￨O￨- sufficient￨L￨JJ￨O￨- condition￨L￨NN￨O￨- in￨L￨IN￨O￨- invariant￨L￨JJ￨O￨- set￨L￨NN￨O￨- Γ.In￨U￨NN￨O￨- fact￨L￨NN￨O￨- ,￨L￨,￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- inevitably￨L￨RB￨O￨- affected￨L￨VBN￨O￨- by￨L￨IN￨O￨- environmental￨L￨JJ￨O￨- white￨L￨JJ￨O￨- noise￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- an￨L￨DT￨O￨- important￨L￨JJ￨O￨- component￨L￨NN￨O￨- in￨L￨IN￨O￨- realism￨L￨NN￨O￨- ,￨L￨,￨O￨- because￨L￨IN￨O￨- it￨L￨PRP￨O￨- can￨L￨MD￨O￨- provide￨L￨VB￨O￨- an￨L￨DT￨O￨- additional￨L￨JJ￨O￨- degree￨L￨NN￨O￨- of￨L￨IN￨O￨- realism￨L￨NN￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- to￨L￨TO￨O￨- their￨L￨PRP$￨O￨- deterministic￨L￨JJ￨O￨- counterparts￨L￨NNS￨O￨- .￨L￨.￨O￨- +They￨U￨PRP￨O￨- obtain￨L￨VB￨O￨- if￨L￨IN￨O￨- β￨L￨NN￨O￨- <￨L￨JJR￨O￨- γ￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- μ￨L￨NN￨O￨- −￨L￨NN￨O￨- σ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- /￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- stochastically￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- large￨L￨JJ￨O￨- and￨L￨CC￨O￨- exponentially￨L￨RB￨O￨- mean-square￨L￨JJ￨O￨- stable￨L￨JJ￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- stochastic￨L￨JJ￨O￨- version￨L￨NN￨O￨- corresponding￨L￨VBG￨O￨A to￨L￨TO￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- takes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- μ￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- σ￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- β￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- σ￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- B￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- δ￨L￨JJ￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- This￨U￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- organized￨L￨VBN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- .￨L￨.￨O￨- +in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- discuss￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIQS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ˙￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- μ￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ˙￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- Q￨U￨NNP￨O￨- ˙￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- δ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- parameters￨L￨NNS￨O￨- A￨U￨DT￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- constants￨L￨NNS￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- δ￨L￨NN￨O￨- are￨L￨VBP￨O￨- non-negative￨L￨JJ￨O￨- constants￨L￨NNS￨O￨- .￨L￨.￨O￨- +Previous￨U￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- complemented￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- optimal￨L￨JJ￨O￨- selection￨L￨NN￨O￨- algorithm￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨A networks￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- Value￨U￨NN￨ORGANIZATION￨- of￨L￨IN￨ORGANIZATION￨- Information￨U￨NN￨ORGANIZATION￨- (￨L￨-LRB-￨O￨- VoI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- reporting￨L￨VBG￨O￨- nodes￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- subnetworks￨L￨NNS￨O￨- of￨L￨IN￨O￨- mobility￨L￨NN￨O￨- networks￨L￨NNS￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- people￨L￨NNS￨O￨- ,￨L￨,￨O￨- food￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- species￨L￨NNS￨O￨- move￨L￨VBP￨O￨- .￨L￨.￨O￨- +Surveillance￨U￨NN￨O￨- network￨L￨NN￨O￨- topologies￨L￨NNS￨O￨- are￨L￨VBP￨O￨- selected￨L￨VBN￨O￨- by￨L￨IN￨O￨- considering￨L￨VBG￨O￨- their￨L￨PRP$￨O￨- integrated￨L￨VBN￨O￨- network￨L￨NN￨O￨- resilience￨L￨NN￨O￨- expressing￨L￨VBG￨O￨- the￨L￨DT￨O￨- rewiring￨L￨NN￨O￨- probability￨L￨NN￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- report￨L￨VB￨O￨- outbreak￨L￨NN￨O￨- information￨L￨NN￨O￨A even￨L￨RB￨O￨- in￨L￨IN￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- network￨L￨NN￨O￨- destruction￨L￨NN￨O￨- or￨L￨CC￨O￨- missing￨L￨VBG￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +Thus￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- functioning￨L￨NN￨O￨- of￨L￨IN￨O￨- surveillance￨L￨NN￨O￨A networks￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- crucial￨L￨JJ￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨- detection￨L￨NN￨O￨- and￨L￨CC￨O￨- rapid￨L￨JJ￨O￨- response￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- possibly￨L￨RB￨O￨- the￨L￨DT￨O￨- only￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- respond￨L￨VB￨O￨- to￨L￨TO￨O￨- emerging/re-emerging￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- for￨L￨IN￨O￨- which￨L￨WDT￨O￨- we￨L￨PRP￨O￨- are￨L￨VBP￨O￨- unprepared￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- surveillance￨L￨NN￨O￨A network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- the￨L￨DT￨O￨- response￨L￨NN￨O￨- variable￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- in￨L￨IN￨O￨- maximizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- accuracy￨L￨NN￨O￨- of￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- source￨L￨NN￨O￨- detections￨L￨NNS￨O￨- while￨L￨IN￨O￨- minimizing￨L￨VBG￨O￨- detection￨L￨NN￨O￨- error￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Optimal￨U￨JJ￨MISC￨- surveillance￨L￨NN￨O￨A network￨L￨NN￨O￨- design￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- modelMatteo￨L￨NN￨O￨- Convertino1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yang￨U￨NNP￨PERSON￨- Liu1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Haejin￨U￨NN￨O￨- Hwang1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2:6￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Convertino￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- attacking￨L￨VBG￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- possible￨L￨JJ￨O￨- worms￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨A network￨L￨NN￨O￨- and￨L￨CC￨O￨- considering￨L￨VBG￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- basic￨L￨JJ￨O￨- similarity￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- software￨L￨NN￨O￨- viruses￨L￨NNS￨O￨- spread￨L￨VBN￨O￨- among￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- devices￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- Mishra￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Keshri￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SEIRS-V￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- p￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- sensor￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- in￨L￨IN￨O￨- states￨L￨NNS￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- exposed￨L￨VBN￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- recovered￨L￨VBD￨O￨- and￨L￨CC￨O￨- vaccinated￨L￨VBD￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Motivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- above￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- considering￨L￨VBG￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- sensor￨L￨NN￨O￨A nodes￨L￨NNS￨O￨- need￨L￨VBP￨O￨- some￨L￨DT￨O￨- time￨L￨NN￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- worms￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨- network￨L￨NN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- sensor￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- have￨L￨VBP￨O￨- a￨L￨DT￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- period￨L￨NN￨O￨- after￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- again￨L￨RB￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- incorporate￨L￨VBP￨O￨- two￨L￨CD￨NUMBER￨- delays￨L￨NNS￨O￨- into￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- get￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- delayed￨L￨VBN￨O￨- SEIRS-V￨U￨NN￨O￨- system￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- worms￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- wireless￨L￨JJ￨O￨- sensor￨L￨NN￨O￨- network￨L￨NN￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- E￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- −￨L￨SYM￨O￨- μ￨L￨SYM￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- δ￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- p￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- μ￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- η￨L￨NN￨O￨- V￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- τ￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- time￨L￨NN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- sensor￨L￨NN￨O￨- nodes￨L￨NNS￨O￨- need￨L￨VBP￨O￨- to￨L￨TO￨O￨- clean￨L￨VB￨O￨- the￨L￨DT￨O￨- worms￨L￨NNS￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- and￨L￨CC￨O￨- τ￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- temporary￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- period￨L￨NN￨O￨- after￨L￨IN￨O￨- which￨L￨WDT￨O￨- they￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- again￨L￨RB￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- antivirus￨L￨NN￨O￨- software￨L￨NN￨O￨- .￨L￨.￨O￨- +2￨L￨CD￨NUMBER￨- Local￨U￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- positive￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨A and￨L￨CC￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- Hopf￨U￨NNP￨O￨- bifurcationIt￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- verify￨L￨VB￨O￨- that￨L￨IN￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- η￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- unique￨L￨JJ￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- D￨U￨NN￨O￨- ∗￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- R￨U￨NNP￨O￨- ∗￨L￨NNP￨O￨- ,￨L￨,￨O￨- V￨U￨NNP￨O￨- ∗￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- E￨U￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- α￨L￨NN￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- V￨U￨NN￨O￨- =￨L￨JJ￨O￨- p￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- η￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- α￨L￨NN￨O￨- β￨L￨NN￨O￨- δ￨L￨NN￨O￨- γ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- η￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- Jacobian￨U￨JJ￨MISC￨- matrix￨L￨NN￨O￨- of￨L￨IN￨O￨- system￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 3￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- positive￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- D￨U￨NN￨O￨- ∗￨L￨NN￨O￨- is￨L￨VBZ￨O￨- J￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- D￨U￨NN￨O￨- ∗￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- λ￨L￨JJ￨O￨- −￨L￨NN￨O￨- a￨L￨DT￨O￨- 11￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- a￨L￨DT￨O￨- 13￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- b￨L￨NN￨O￨- 14￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨FW￨O￨- τ￨L￨FW￨O￨- −￨L￨FW￨O￨- b￨L￨NN￨O￨- 15￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨FW￨O￨- τ￨L￨FW￨O￨- −￨L￨FW￨O￨- a￨L￨DT￨O￨- 21￨L￨CD￨NUMBER￨- λ￨L￨NN￨O￨- −￨L￨VBD￨O￨- a￨L￨DT￨O￨- 22￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- a￨L￨DT￨O￨- 23￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- a￨L￨DT￨O￨- 32￨L￨CD￨NUMBER￨- λ￨L￨NN￨O￨- −￨L￨VBD￨O￨- a￨L￨DT￨O￨- 33￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- b￨L￨NN￨O￨- 33￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨SYM￨O￨- τ￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- b￨L￨NN￨O￨- 43￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨FW￨O￨- τ￨L￨FW￨O￨- λ￨L￨FW￨O￨- −￨L￨FW￨O￨- a￨L￨DT￨O￨- 44￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- b￨L￨NN￨O￨- 44￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨NN￨O￨- τ￨L￨NN￨O￨- 0￨L￨CD￨NUMBER￨- −￨L￨SYM￨O￨- a￨L￨DT￨O￨- 51￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- 0￨L￨CD￨NUMBER￨- λ￨L￨NN￨O￨- −￨L￨VBD￨O￨- a￨L￨DT￨O￨- 55￨L￨CD￨NUMBER￨A −￨L￨NN￨O￨- b￨L￨NN￨O￨- 55￨L￨CD￨NUMBER￨- e￨L￨SYM￨O￨- −￨L￨SYM￨O￨- λ￨L￨FW￨O￨- τ￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- 11￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- ∗￨L￨NN￨O￨- +￨L￨CC￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 13￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 21￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 22￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 23￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- ∗￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 32￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 33￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 44￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 51￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- p￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 55￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 14￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- δ￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 15￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- η￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 33￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 43￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 44￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- δ￨L￨NN￨O￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 55￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- −￨L￨NN￨O￨- η￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- SParSE￨U￨VBP￨O￨- provides￨L￨VBZ￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- ,￨L￨,￨O￨- efficient￨L￨JJ￨O￨- ,￨L￨,￨O￨- event-oriented￨L￨JJ￨O￨- parameter￨L￨NN￨O￨A estimation￨L￨NN￨O￨A method￨L￨NN￨O￨- for￨L￨IN￨O￨- computing￨L￨VBG￨O￨- parametric￨L￨JJ￨O￨- configurations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- readily￨L￨RB￨O￨- applied￨L￨VBN￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- obeying￨L￨VBG￨O￨- chemical￨L￨JJ￨O￨- master￨L￨NN￨O￨- equation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- CME￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- have￨L￨VBP￨O￨- developed￨L￨VBN￨O￨- a￨L￨DT￨O￨- novel￨L￨JJ￨O￨- parameter￨L￨NN￨O￨A estimation￨L￨NN￨O￨A algorithm￨L￨NN￨O￨- —￨L￨:￨O￨- Stochastic￨U￨NNP￨O￨- Parameter￨U￨NNP￨O￨- Search￨U￨VB￨O￨- for￨L￨IN￨O￨- Events￨U￨NNS￨O￨- (￨L￨-LRB-￨O￨- SParSE￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- —￨L￨:￨O￨- that￨L￨IN￨O￨- automatically￨L￨RB￨O￨- computes￨L￨VBZ￨O￨- parameter￨L￨NN￨O￨- configurations￨L￨NNS￨O￨- for￨L￨IN￨O￨- propagating￨L￨VBG￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- to￨L￨TO￨O￨- produce￨L￨VB￨O￨- an￨L￨DT￨O￨- event￨L￨NN￨O￨- of￨L￨IN￨O￨- interest￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- user-specified￨L￨JJ￨O￨- success￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- error￨L￨NN￨O￨- tolerance￨L￨NN￨O￨- .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- parameter￨L￨NN￨O￨A estimation￨L￨NN￨O￨A algorithms￨L￨NNS￨O￨- in￨L￨IN￨O￨- stochastic￨L￨JJ￨O￨- chemical￨L￨NN￨O￨- kinetics￨L￨NNS￨O￨- setting￨L￨VBG￨O￨- take￨L￨VB￨O￨- time-series￨L￨JJ￨O￨- data￨L￨NNS￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- input￨L￨NN￨O￨- and￨L￨CC￨O￨- compute￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- reaction￨L￨NN￨O￨- rate￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- that￨L￨IN￨O￨- most￨L￨JJS￨O￨- closely￨L￨RB￨O￨- reproduce￨L￨VB￨O￨- the￨L￨DT￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- also￨L￨RB￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- novel￨L￨JJ￨O￨- heuristic￨L￨NN￨O￨- for￨L￨IN￨O￨- handling￨L￨VBG￨O￨- over-perturbing￨L￨JJ￨O￨- parameter￨L￨NN￨O￨A sets￨L￨NNS￨O￨- enables￨L￨VBZ￨O￨- SParSE￨U￨NNP￨O￨- to￨L￨TO￨O￨- compute￨L￨VB￨O￨- biasing￨L￨VBG￨O￨- parameters￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- class￨L￨NN￨O￨- of￨L￨IN￨O￨- rare￨L￨JJ￨O￨- events￨L￨NNS￨O￨- that￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- amenable￨L￨JJ￨O￨- to￨L￨TO￨O￨- current￨L￨JJ￨DATE￨- algorithms￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- importance￨L￨NN￨O￨- sampling￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- obtained￨L￨VBN￨O￨- may￨L￨MD￨O￨- help￨L￨VB￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- more￨L￨RBR￨O￨- complex￨L￨JJ￨O￨- fractional￨L￨JJ￨O￨A epidemic￨L￨JJ￨O￨- models.Keywordsfractional￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- modelKermack-McKendrick￨L￨NN￨O￨- modelnonlinear￨L￨NN￨O￨- incidenceexistence￨L￨NN￨O￨- of￨L￨IN￨O￨- solutionswellposedness￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- pioneering￨L￨JJ￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Kermack￨U￨NNP￨O￨- and￨L￨CC￨O￨- McKendrick￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- interesting￨L￨JJ￨O￨- and￨L￨CC￨O￨- useful￨L￨JJ￨O￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Kermack-McKendrick￨U￨NNP￨LOCATION￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- and￨L￨CC￨O￨- fractional￨L￨JJ￨O￨A derivative￨L￨JJ￨O￨- order￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- sense￨L￨NN￨O￨- of￨L￨IN￨O￨- Caputo￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Kermack-McKendrick￨U￨NN￨LOCATION￨- with￨L￨IN￨O￨- zero￨L￨CD￨NUMBER￨- immunity￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- investigated￨L￨VBN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A function￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Some￨U￨DT￨MISC￨- properties￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- Kermack-McKendrick￨U￨NNP￨LOCATION￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- fractional￨L￨JJ￨O￨A derivative￨L￨NN￨O￨- and￨L￨CC￨O￨- nonlinear￨L￨JJ￨O￨- incidenceEmile￨L￨NNP￨O￨- Franc￨U￨NNP￨O￨- Doungmo￨U￨NNP￨O￨- Goufo1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Riëtte￨U￨NNP￨O￨- Maritz1￨U￨NN￨O￨- and￨L￨CC￨O￨- Justin￨U￨NNP￨PERSON￨- Munganga1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2014:278￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Doungmo￨U￨NNP￨O￨- Goufo￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- numerical￨L￨JJ￨O￨- simulations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- monotonic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- for￨L￨IN￨O￨- different￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- fractional￨L￨JJ￨O￨A derivative￨L￨JJ￨O￨- order￨L￨NN￨O￨- α￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- α￨L￨NN￨O￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- saw￨L￨VBD￨O￨- a￨L￨DT￨O￨- weak￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- hospital￨L￨NN￨O￨- system￨L￨NN￨O￨- ’s￨L￨POS￨O￨- response￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- testing￨L￨NN￨O￨- positive￨L￨JJ￨O￨- -￨L￨:￨O￨- after￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- test￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- moved￨L￨VBD￨O￨- to￨L￨TO￨O￨- units￨L￨NNS￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- lower￨L￨JJR￨O￨- centrality￨L￨NN￨O￨- measured￨L￨VBN￨O￨- as￨L￨IN￨O￨- degree￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- links￨L￨NNS￨O￨- to￨L￨TO￨O￨- other￨L￨JJ￨O￨- units￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- care￨L￨NN￨O￨- episodes￨L￨NNS￨O￨- became￨L￨VBD￨O￨- longer￨L￨RBR￨O￨- .￨L￨.￨O￨- +Regular￨U￨JJ￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨O￨- Access￨U￨NN￨O￨- The￨U￨DT￨O￨- network￨L￨NN￨O￨- positions￨L￨NNS￨O￨- of￨L￨IN￨O￨- methicillin￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- Staphylococcus￨U￨FW￨O￨- aureus￨L￨FW￨O￨- affected￨L￨VBN￨O￨- units￨L￨NNS￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- regional￨L￨JJ￨O￨- healthcare￨L￨NN￨O￨- systemJan￨L￨NN￨O￨- Ohst1￨U￨NN￨O￨- ,￨L￨,￨O￨- Fredrik￨U￨NNP￨PERSON￨- Liljeros2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Mikael￨U￨NNP￨PERSON￨- Stenhem4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Petter￨U￨NNP￨PERSON￨- Holme3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 3:29￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Ohst￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- studied￨L￨VBD￨O￨- a￨L￨DT￨O￨- dataset￨L￨NN￨O￨- of￨L￨IN￨O￨- care￨L￨NN￨O￨- episodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- regional￨L￨JJ￨O￨- Swedish￨U￨JJ￨NATIONALITY￨- hospital￨L￨NN￨O￨- system￨L￨NN￨O￨- .￨L￨.￨O￨- +From￨U￨IN￨O￨- this￨L￨DT￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- characterized￨L￨VBD￨O￨- the￨L￨DT￨O￨- typical￨L￨JJ￨O￨- network￨L￨NN￨O￨- position￨L￨NN￨O￨- of￨L￨IN￨O￨- units￨L￨NNS￨O￨A with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- methicillin￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- Staphylococcus￨U￨FW￨MISC￨- aureus￨L￨FW￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- patient￨L￨NN￨O￨- ’s￨L￨POS￨O￨- location￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- changed￨L￨VBN￨O￨- upon￨L￨IN￨O￨- testing￨L￨NN￨O￨- positive￨L￨JJ￨O￨- .￨L￨.￨O￨- +To￨U￨TO￨O￨- simplify￨L￨VB￨O￨- the￨L￨DT￨O￨- complex￨L￨NN￨O￨- flow￨L￨NN￨O￨- of￨L￨IN￨O￨- patients￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- represented￨L￨VBD￨O￨- it￨L￨PRP￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- units￨L￨NNS￨O￨A ,￨L￨,￨O￨- where￨L￨WRB￨O￨- two￨L￨CD￨NUMBER￨- units￨L￨NNS￨O￨- were￨L￨VBD￨O￨- connected￨L￨VBN￨O￨- if￨L￨IN￨O￨- a￨L￨DT￨O￨- patient￨L￨NN￨O￨- moved￨L￨VBD￨O￨- from￨L￨IN￨O￨- one￨L￨CD￨NUMBER￨- unit￨L￨NN￨O￨- to￨L￨TO￨O￨- another￨L￨DT￨O￨- ,￨L￨,￨O￨- without￨L￨IN￨O￨- visiting￨L￨VBG￨O￨- a￨L￨DT￨O￨- third￨L￨JJ￨ORDINAL￨- unit￨L￨NN￨O￨- in￨L￨IN￨O￨- between￨L￨IN￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- for￨L￨IN￨O￨- e.g.￨L￨FW￨O￨- sexually￨L￨RB￨O￨- transmitted￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- -￨L￨:￨O￨- the￨L￨DT￨O￨- topic￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- -￨L￨:￨O￨- healthcare￨L￨NN￨O￨A associated￨L￨VBN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- HAI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- version￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- perform￨L￨VBP￨O￨- a￨L￨DT￨O￨- detailed￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- also￨L￨RB￨O￨- depends￨L￨VBZ￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- when￨L￨WRB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨A equilibrium￨L￨NN￨O￨A by￨L￨IN￨O￨- measuring￨L￨VBG￨O￨- the￨L￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- solution￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- deterministic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- time-averaged￨L￨JJ￨O￨- data￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- problem￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- studied￨L￨VBN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- -￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- susceptible-infected￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- homogeneous￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- information￨L￨NN￨O￨- diffusion￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- snapshot￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- given.While￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- -￨L￨:￨O￨- NumericCitation￨U￨NN￨O￨- answered￨L￨VBD￨O￨- some￨L￨DT￨O￨- basic￨L￨JJ￨O￨- questions￨L￨NNS￨O￨- about￨L￨IN￨O￨- information￨L￨NN￨O￨- source￨L￨NN￨O￨- detection￨L￨NN￨O￨- in￨L￨IN￨O￨- large-scale￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- complete￨L￨JJ￨O￨- snapshot￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- real-world￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- may￨L￨MD￨O￨- have￨L￨VB￨O￨- hundreds￨L￨NNS￨O￨- of￨L￨IN￨O￨- millions￨L￨NNS￨O￨- of￨L￨IN￨O￨- nodes￨L￨NNS￨O￨- ,￨L￨,￨O￨- is￨L￨VBZ￨O￨- expensive￨L￨JJ￨O￨- to￨L￨TO￨O￨- obtain￨L￨VB￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- adopt￨L￨VBP￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- path-based￨L￨JJ￨O￨- estimator￨L￨NN￨O￨A developed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- work￨L￨NN￨O￨- of￨L￨IN￨O￨- Zhu￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Ying￨U￨NNP￨PERSON￨- (￨L￨-LRB-￨O￨- arXiv￨L￨NNP￨O￨- :￨L￨:￨O￨- 1206.5421￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2012￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- prove￨L￨VB￨O￨- that￨L￨DT￨O￨- on￨L￨IN￨O￨- infinite￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- path-based￨L￨JJ￨O￨- estimator￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- Jordan￨U￨NNP￨CITY￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- center￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- observed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- further￨L￨RB￨O￨- prove￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- distance￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- estimator￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- actual￨L￨JJ￨O￨- source￨L￨NN￨O￨- is￨L￨VBZ￨O￨- upper￨L￨JJ￨O￨- bounded￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- constant￨L￨JJ￨O￨- independent￨L￨JJ￨RELIGION￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- probability￨L￨NN￨O￨- on￨L￨IN￨O￨- infinite￨L￨JJ￨O￨- trees￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- other￨L￨JJ￨O￨- words￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- sample￨L￨NN￨O￨- path-based￨L￨JJ￨O￨- estimator￨L￨NN￨O￨A minimizes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- maximum￨L￨NN￨O￨- distance￨L￨NN￨O￨- to￨L￨TO￨O￨- observed￨L￨VBN￨O￨- infected￨L￨JJ￨O￨- nodes￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- assume￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- piece￨L￨NN￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨A spreads￨L￨NNS￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- following￨L￨VBG￨O￨- a￨L￨DT￨O￨- heterogeneous￨L￨JJ￨O￨- susceptible-infected-recovered￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIR￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- a￨L￨DT￨O￨- node￨L￨NN￨O￨- is￨L￨VBZ￨O￨- said￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- infected￨L￨VBN￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- receives￨L￨VBZ￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- and￨L￨CC￨O￨- recovered￨L￨VBD￨O￨- when￨L￨WRB￨O￨- it￨L￨PRP￨O￨- removes￨L￨VBZ￨O￨- or￨L￨CC￨O￨- hides￨L￨VBZ￨O￨- the￨L￨DT￨O￨- information￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Using￨U￨VBG￨O￨- a￨L￨DT￨O￨- range￨L￨NN￨O￨- of￨L￨IN￨O￨- historical￨L￨JJ￨O￨- ,￨L￨,￨O￨- experimental￨L￨JJ￨O￨- mosquito-transmitted￨L￨JJ￨O￨- human￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- Bayesian￨U￨JJ￨O￨- estimation￨L￨NN￨O￨- with￨L￨IN￨O￨- non-informative￨L￨JJ￨O￨- priors￨L￨NNS￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- parametric￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- readily￨L￨RB￨O￨- implemented￨L￨VBN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- incubation￨L￨NN￨O￨A period￨L￨NN￨O￨- and￨L￨CC￨O￨- time-to-first￨L￨JJ￨O￨- relapse￨L￨NN￨O￨- in￨L￨IN￨O￨- P.￨U￨NNP￨O￨- Results￨U￨NNS￨O￨- Using￨U￨VBG￨O￨- the￨L￨DT￨O￨- Deviance￨U￨NNP￨O￨- Information￨U￨NNP￨O￨- Criteria￨U￨NNP￨O￨- to￨L￨TO￨O￨- compare￨L￨VB￨O￨- parameterizations￨L￨NNS￨O￨- ,￨L￨,￨O￨- experimental￨L￨JJ￨O￨- incubation￨L￨NN￨O￨- periods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- most￨L￨RBS￨O￨- closely￨L￨RB￨O￨- modeled￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- shifted￨L￨VBN￨O￨- log-logistic￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- ;￨L￨:￨O￨- a￨L￨DT￨O￨- log-logistic￨L￨JJ￨O￨- mixture￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- best￨L￨JJS￨O￨- fit￨L￨NN￨O￨- for￨L￨IN￨O￨- incubations￨L￨NNS￨O￨- in￨L￨IN￨O￨- observational￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- distribution￨L￨NN￨O￨- of￨L￨IN￨O￨- incubation￨L￨NN￨O￨A and￨L￨CC￨O￨- relapse￨L￨NN￨O￨- times￨L￨NNS￨O￨- in￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- human￨L￨JJ￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasite￨L￨NN￨O￨- Plasmodium￨U￨NN￨O￨- vivax￨L￨NN￨O￨- Andrew￨U￨NNP￨O￨- A￨U￨NNP￨O￨- Lover1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Xiahong￨U￨NNP￨O￨- Zhao1￨U￨NN￨O￨- ,￨L￨,￨O￨- Zheng￨U￨NNP￨PERSON￨- Gao2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Richard￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Coker1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Alex￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- Cook1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 14:539￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Lover￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2014Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- incubation￨L￨NN￨O￨- and￨L￨CC￨O￨- relapse￨L￨NN￨O￨- periods￨L￨NNS￨O￨- are￨L￨VBP￨O￨- key￨L￨JJ￨O￨- components￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasite￨L￨NN￨O￨- Plasmodium￨U￨NN￨O￨- vivax￨L￨NN￨O￨- ;￨L￨:￨O￨- however￨L￨RB￨O￨- ,￨L￨,￨O￨- detailed￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- based￨L￨VBN￨O￨- upon￨L￨IN￨O￨- experimental￨L￨JJ￨O￨- data￨L￨NNS￨O￨- are￨L￨VBP￨O￨- lacking￨L￨VBG￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- future￨L￨JJ￨DATE￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- log-logistic￨L￨JJ￨O￨- and￨L￨CC￨O￨- Gompertz￨U￨NNP￨PERSON￨- distributions￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- utilized￨L￨VBN￨O￨- for￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- incubation￨L￨NN￨O￨A periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- relapse￨L￨NN￨O￨- times￨L￨NNS￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- region-specific￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- considered￨L￨VBN￨O￨- to￨L￨TO￨O￨- accurately￨L￨RB￨O￨- model￨L￨VB￨O￨- and￨L￨CC￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- important￨L￨JJ￨O￨- human￨L￨JJ￨O￨- pathogen￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- These￨U￨DT￨O￨- results￨L￨NNS￨O￨- suggest￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- exponential￨L￨JJ￨O￨- and￨L￨CC￨O￨- gamma￨L￨NN￨O￨- distributions￨L￨NNS￨O￨- commonly￨L￨RB￨O￨- used￨L￨VBN￨O￨- for￨L￨IN￨O￨- modeling￨L￨NN￨O￨- incubation￨L￨NN￨O￨A periods￨L￨NNS￨O￨- and￨L￨CC￨O￨- relapse￨L￨NN￨O￨- times￨L￨NNS￨O￨- inadequately￨L￨RB￨O￨- capture￨L￨VBP￨O￨- the￨L￨DT￨O￨- complexity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- distributions￨L￨NNS￨O￨- of￨L￨IN￨O￨- event￨L￨NN￨O￨- times￨L￨NNS￨O￨- in￨L￨IN￨O￨- P￨U￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- semi-automated￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- quality￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- language￨L￨NN￨O￨A of￨L￨IN￨O￨- influence￨L￨NN￨O￨- using￨L￨VBG￨O￨- semantic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- singular￨L￨JJ￨O￨- value￨L￨NN￨O￨- decomposition￨L￨NN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- middle￨L￨JJ￨O￨- ground￨L￨NN￨O￨- between￨L￨IN￨O￨- high-level￨L￨JJ￨O￨- abstract￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- and￨L￨CC￨O￨- simple￨L￨JJ￨O￨- word￨L￨NN￨O￨- counting.We￨L￨NN￨O￨- then￨L￨RB￨O￨- apply￨L￨VB￨O￨- this￨L￨DT￨O￨- approach￨L￨NN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- intelligence￨L￨NN￨O￨- application￨L￨NN￨O￨- :￨L￨:￨O￨- examining￨L￨VBG￨O￨- the￨L￨DT￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- language￨L￨NN￨O￨- of￨L￨IN￨O￨- influence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- jihadist￨L￨NN￨O￨- magazines￨L￨NNS￨O￨- Inspire￨U￨NNP￨O￨- and￨L￨CC￨O￨- Azan￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- enables￨L￨VBZ￨O￨- model￨L￨NN￨TITLE￨- intensity￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- documents￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- compared￨L￨VBN￨O￨- ,￨L￨,￨O￨- especially￨L￨RB￨O￨- for￨L￨IN￨O￨- each￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- magazines￨L￨NNS￨O￨- across￨L￨IN￨O￨- time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hypotheses￨L￨NNS￨O￨- about￨L￨IN￨O￨- expected￨L￨VBN￨O￨- language￨L￨NN￨O￨A use￨L￨NN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- validated￨L￨VBN￨O￨- or￨L￨CC￨O￨- falsified￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- textual￨L￨JJ￨O￨- content￨L￨NN￨O￨- of￨L￨IN￨O￨- issues￨L￨NNS￨O￨A of￨L￨IN￨O￨- Azan￨U￨NNP￨PERSON￨- is￨L￨VBZ￨O￨- typically￨L￨RB￨O￨- between￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- and￨L￨CC￨NUMBER￨- four￨L￨CD￨NUMBER￨- times￨L￨NNS￨O￨- longer￨L￨JJR￨O￨- than￨L￨IN￨O￨- the￨L￨DT￨O￨- textual￨L￨JJ￨O￨- content￨L￨NN￨O￨- of￨L￨IN￨O￨- issues￨L￨NNS￨O￨- of￨L￨IN￨O￨- Inspire￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- issues￨L￨NNS￨O￨- are￨L￨VBP￨O￨- appearing￨L￨VBG￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- often￨L￨RB￨O￨- so￨L￨IN￨O￨- their￨L￨PRP$￨O￨- author/editor￨L￨NN￨O￨- is￨L￨VBZ￨O￨- noticeably￨L￨RB￨O￨- more￨L￨RBR￨O￨- productive.The￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- magazines￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- difficult￨L￨JJ￨O￨- to￨L￨TO￨O￨- judge￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Issues￨U￨NNS￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- product￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- far￨L￨RB￨O￨- unknown￨L￨JJ￨O￨- ,￨L￨,￨O￨- editors.The￨L￨JJ￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- Inspire￨U￨NNP￨O￨- appears￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- to￨L￨TO￨O￨- motivate￨L￨VB￨O￨- lone-wolf￨L￨JJ￨O￨- attacks￨L￨NNS￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- Western￨U￨JJ￨MISC￨- countries￨L￨NNS￨O￨- by￨L￨IN￨O￨- diaspora￨L￨NN￨O￨- jihadists￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Language￨U￨NN￨MISC￨- use￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- Jihadist￨U￨NNP￨MISC￨- magazines￨L￨NNS￨O￨- inspire￨L￨VB￨O￨- and￨L￨CC￨O￨- AzanDavid￨U￨NN￨O￨- B￨U￨NN￨O￨- Skillicorn1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Edna￨U￨NNP￨PERSON￨- F￨U￨NN￨O￨- Reid2￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 3:9￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Skillicorn￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Reid￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨MISC￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A rate￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- and￨L￨CC￨O￨- treatment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- we￨L￨PRP￨O￨- extend￨L￨VBP￨O￨- some￨L￨DT￨O￨- recent￨L￨JJ￨O￨- results.By￨L￨NN￨O￨- a￨L￨DT￨O￨- saturated￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- consists￨L￨VBZ￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- population￨L￨NN￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- at￨L￨IN￨O￨- time￨L￨NN￨O￨- t￨L￨NN￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- δ￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- ≤￨L￨VBP￨O￨- I￨U￨PRP￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- I￨U￨PRP￨O￨- ≥￨L￨VBP￨O￨- I￨U￨PRP￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- k￨L￨NN￨O￨- =￨L￨JJ￨O￨- δ￨L￨NN￨O￨- I￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- treated￨L￨VBN￨O￨- ;￨L￨:￨O￨- A￨U￨DT￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- newborns￨L￨NNS￨O￨- and￨L￨CC￨O￨- immigrants￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- population￨L￨NN￨O￨- ;￨L￨:￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ;￨L￨:￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- recovered￨L￨VBN￨O￨- ;￨L￨:￨O￨- ε￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-related￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- A￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- ,￨L￨,￨O￨- ε￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- positive￨L￨JJ￨O￨- numbers.Thus￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨CD￨NUMBER￨- I￨U￨PRP￨O￨- ≤￨L￨VBP￨O￨- I￨U￨PRP￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- implies￨L￨VBZ￨O￨- {￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- I￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- δ￨L￨NN￨O￨- I￨U￨PRP￨O￨- .￨L￨.￨O￨- +Steady￨U￨JJ￨O￨- states￨L￨NNS￨O￨- of￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- satisfy￨L￨VBP￨O￨A the￨L￨DT￨O￨- following￨L￨VBG￨O￨- equations￨L￨NNS￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- T￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- We￨U￨PRP￨O￨- easily￨L￨RB￨O￨- see￨L￨VBP￨O￨- that￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- a￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A P￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- A￨U￨DT￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +(￨L￨-LRB-￨O￨- 1.2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- If￨U￨IN￨O￨- I￨U￨PRP￨O￨- >￨L￨JJR￨O￨- I￨U￨PRP￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- implies￨L￨VBZ￨O￨A {￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- +￨L￨CC￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- S￨U￨NN￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- ε￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- k￨L￨NN￨O￨- .￨L￨.￨O￨- +2014Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 9￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractTo￨U￨NNP￨O￨- facilitate￨L￨VB￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- heterogeneous￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- control￨L￨NN￨O￨- plane￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- C-plane￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- user￨L￨NN￨O￨- plane￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- U-plane￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- decoupled￨L￨JJ￨O￨- architecture￨L￨NN￨O￨A is￨L￨VBZ￨O￨- being￨L￨VBG￨O￨- considered￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- fifth￨L￨JJ￨ORDINAL￨- generation￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 5G￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- wireless￨L￨JJ￨O￨- communication￨L￨NN￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- which￨L￨WDT￨O￨- relatively￨L￨RB￨O￨- crucial￨L￨JJ￨O￨- C-plane￨U￨NN￨MISC￨- is￨L￨VBZ￨O￨- expanded￨L￨VBN￨O￨- and￨L￨CC￨O￨- kept￨L￨VBN￨O￨- at￨L￨IN￨O￨- dependable￨L￨JJ￨O￨- lower￨L￨JJR￨O￨- frequency￨L￨NN￨O￨- bands￨L￨NNS￨O￨- to￨L￨TO￨O￨- guarantee￨L￨VB￨O￨- transmission￨L￨NN￨O￨- reliability￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- corresponding￨L￨JJ￨O￨- U-plane￨U￨NN￨MISC￨- is￨L￨VBZ￨O￨- moved￨L￨VBN￨O￨- to￨L￨TO￨O￨- available￨L￨JJ￨O￨- higher￨L￨JJR￨O￨- frequency￨L￨NN￨O￨- bands￨L￨NNS￨O￨- to￨L￨TO￨O￨- boost￨L￨VB￨O￨- capacity￨L￨NN￨O￨- .￨L￨.￨O￨- +Due￨U￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- lack￨L￨NN￨O￨- of￨L￨IN￨O￨- ability￨L￨NN￨O￨- to￨L￨TO￨O￨- reflect￨L￨VB￨O￨- the￨L￨DT￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- C-plane￨U￨NN￨O￨- ,￨L￨,￨O￨- conventional￨L￨JJ￨O￨- outage￨L￨NN￨O￨- probability￨L￨NN￨O￨- can￨L￨MD￨O￨- not￨L￨RB￨O￨- properly￨L￨RB￨O￨- indicate￨L￨VBP￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- reliability￨L￨NN￨O￨- of￨L￨IN￨O￨- C/U-plane￨U￨NN￨O￨- decoupled￨L￨VBN￨O￨- architecture￨L￨NN￨O￨A whose￨L￨WP$￨O￨- primary￨L￨JJ￨O￨- design￨L￨NN￨O￨- consideration￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- C-plane￨U￨NN￨MISC￨- more￨L￨RBR￨O￨- heavily￨L￨RB￨O￨- affects￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- reliability￨L￨NN￨O￨- thereby￨L￨RB￨O￨- being￨L￨VBG￨O￨- kept￨L￨VBN￨O￨- at￨L￨IN￨O￨- dependable￨L￨JJ￨O￨- lower￨L￨JJR￨O￨- frequency￨L￨NN￨O￨- bands￨L￨NNS￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- article￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- problem￨L￨NN￨O￨- of￨L￨IN￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- appropriately￨L￨RB￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- reliability￨L￨NN￨O￨- of￨L￨IN￨O￨- C/U-plane￨U￨NN￨O￨- decoupled￨L￨VBN￨O￨- architecture￨L￨NN￨O￨A is￨L￨VBZ￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Reliability￨U￨NN￨MISC￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- 5G￨L￨NN￨O￨- C/U-plane￨U￨NN￨O￨- decoupled￨L￨VBN￨O￨- architecture￨L￨NN￨O￨A for￨L￨IN￨O￨- high-speed￨L￨JJ￨O￨- railwayLi￨L￨NNP￨O￨- Yan￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Xuming￨U￨NN￨O￨- Fang￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1￨L￨CD￨NUMBER￨- †￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 2014:127￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Yan￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Fang￨U￨NNP￨PERSON￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +Under￨U￨IN￨O￨- some￨L￨DT￨O￨- assumptions￨L￨NNS￨O￨- ,￨L￨,￨O￨- they￨L￨PRP￨O￨- proposed￨L￨VBD￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- realize￨L￨VB￨O￨- the￨L￨DT￨O￨- genetic￨L￨JJ￨O￨- switching￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- GATA-PU.1￨U￨NN￨O￨- regulatory￨L￨JJ￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- following￨L￨JJ￨O￨- form￨L￨NN￨O￨- :￨L￨:￨O￨- d￨L￨NN￨O￨- x￨L￨CC￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- a￨L￨DT￨O￨- 3￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- 4￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- 5￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- 6￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- +￨L￨CC￨O￨- a￨L￨DT￨O￨- 7￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- z￨L￨SYM￨O￨- −￨L￨SYM￨O￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- y￨L￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- b￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- b￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- b￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- b￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- +￨L￨CC￨O￨- b￨L￨NN￨O￨- 5￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- +￨L￨CC￨O￨- b￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- z￨L￨SYM￨O￨- −￨L￨SYM￨O￨- k￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- z￨L￨SYM￨O￨- d￨L￨FW￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- c￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- c￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- x￨L￨NN￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- 4￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- 5￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- 6￨L￨CD￨NUMBER￨- x￨L￨CC￨O￨- z￨L￨SYM￨O￨- +￨L￨CC￨O￨- c￨L￨NN￨O￨- 7￨L￨CD￨NUMBER￨- y￨L￨NN￨O￨- z￨L￨SYM￨O￨- −￨L￨SYM￨O￨- k￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- z￨L￨SYM￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- x￨L￨NN￨O￨- ,￨L￨,￨O￨- y￨L￨NN￨O￨- and￨L￨CC￨O￨- z￨L￨SYM￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- concentrations￨L￨NNS￨O￨- of￨L￨IN￨O￨- TFs￨U￨NNS￨MISC￨- GATA-1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- GATA-2￨U￨NN￨O￨- and￨L￨CC￨O￨- PU￨U￨NN￨O￨- .1￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- b￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- c￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- represent￨L￨VBP￨O￨- the￨L￨DT￨O￨- expression￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨- GATA-1￨U￨NN￨O￨- ,￨L￨,￨O￨- GATA-2￨U￨NN￨O￨- and￨L￨CC￨O￨- PU￨U￨NN￨O￨- .1￨L￨CD￨NUMBER￨- auto-regulated￨L￨JJ￨O￨- by￨L￨IN￨O￨- itself￨L￨PRP￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- 2￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- expression￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- gene￨L￨NN￨O￨- GATA-1￨U￨NN￨O￨- regulated￨L￨VBN￨O￨- by￨L￨IN￨O￨- TF￨U￨NN￨O￨- GATA-2￨U￨NN￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- k￨L￨NN￨O￨- 3￨L￨CD￨NUMBER￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- degradation￨L￨NN￨O￨- rates￨L￨NNS￨O￨- of￨L￨IN￨O￨- TFs￨U￨NNS￨MISC￨- GATA-1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- GATA-2￨U￨NN￨O￨- and￨L￨CC￨O￨- PU￨U￨NN￨O￨- .1￨L￨NN￨NUMBER￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- An￨U￨DT￨O￨- NSFD￨U￨NN￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategyQianqian￨L￨NN￨O￨- Cui1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jiabo￨U￨NNP￨O￨- Xu3￨U￨NN￨O￨- ,￨L￨,￨O￨- Qiang￨U￨NNP￨PERSON￨- Zhang2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Kai￨U￨NNP￨MISC￨- Wang4￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 2014:172￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Cui￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- construct￨L￨VBP￨O￨- a￨L￨DT￨O￨- nonstandard￨L￨JJ￨O￨- finite￨L￨JJ￨O￨- difference￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- NSFD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- scheme￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- SIR￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- NumericCitation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- childhood￨L￨NN￨CAUSE_OF_DEATH￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- constant￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- are￨L￨VBP￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- p￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- μ￨L￨NN￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- R￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- p￨L￨NN￨O￨- A￨U￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- −￨L￨VBP￨O￨- μ￨L￨NN￨O￨- R￨U￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- noted￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- system￨L￨NN￨O￨- of￨L￨IN￨O￨- continuous￨L￨JJ￨O￨- equations￨L￨NNS￨O￨A ,￨L￨,￨O￨- if￨L￨IN￨O￨- added￨L￨VBN￨O￨- together￨L￨RB￨O￨- ,￨L￨,￨O￨- satisfies￨L￨VBZ￨O￨- the￨L￨DT￨O￨- conservation￨L￨NN￨O￨- law￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- d￨L￨NN￨O￨- N￨U￨NN￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- A￨U￨DT￨O￨- −￨L￨NN￨O￨- μ￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Moreover￨U￨RB￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- easy￨L￨JJ￨O￨- to￨L￨TO￨O￨- verify￨L￨VB￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- domain￨L￨NN￨O￨- D￨U￨NN￨O￨- =￨L￨JJ￨O￨- {￨L￨-LRB-￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ∈￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- +￨L￨CC￨O￨- 3￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- S￨U￨NN￨O￨- +￨L￨CC￨O￨- I￨U￨PRP￨O￨- +￨L￨CC￨O￨- R￨U￨NN￨O￨- ≤￨L￨NN￨O￨- A￨U￨NN￨O￨- /￨L￨:￨O￨- μ￨L￨NN￨O￨- }￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- compact￨L￨JJ￨O￨- ,￨L￨,￨O￨- positively￨L￨RB￨O￨A invariant￨L￨JJ￨O￨- set￨L￨NN￨O￨- for￨L￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1.1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +For￨U￨IN￨O￨- illustrating￨L￨VBG￨O￨- our￨L￨PRP$￨O￨- theoretical￨L￨JJ￨O￨- conclusions￨L￨NNS￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- give￨L￨VBP￨O￨- some￨L￨DT￨O￨- numerical￨L￨JJ￨O￨- simulation￨L￨NN￨O￨- examples.For￨L￨NN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- and￨L￨CC￨O￨- more￨L￨JJR￨O￨- information￨L￨NN￨O￨- on￨L￨IN￨O￨- bifurcation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A of￨L￨IN￨O￨- map￨L￨NN￨O￨- ,￨L￨,￨O￨- one￨L￨CD￨NUMBER￨- should￨L￨MD￨O￨- refer￨L￨VB￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- references￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 17￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- those￨L￨DT￨O￨- cited￨L￨VBN￨O￨- therein.We￨L￨NN￨O￨- consider￨L￨VB￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- deterministic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- studied￨L￨VBN￨O￨- by￨L￨IN￨O￨- Allen￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨O￨- :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- α￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- N￨U￨NN￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- β￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- N￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- N￨U￨NN￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- represent￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- infective￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- removed￨L￨VBN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- isolated￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- subgroups￨L￨NNS￨O￨- ,￨L￨,￨O￨- respectively￨L￨RB￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- represents￨L￨VBZ￨O￨- n￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- Δt￨U￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- time￨L￨NN￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨DURATION￨- hour￨L￨NN￨DURATION￨- or￨L￨CC￨O￨- 1￨L￨CD￨DURATION￨- day￨L￨NN￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- no￨L￨DT￨O￨- deaths￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- no￨L￨DT￨O￨- recruitment￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- no￨L￨DT￨O￨- vertical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- all￨L￨DT￨O￨- new-born￨L￨JJ￨O￨- members￨L￨NNS￨O￨- are￨L￨VBP￨O￨- susceptible￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨NN￨O￨- ’s￨L￨POS￨O￨- recovery￨L￨NN￨O￨- leads￨L￨VBZ￨O￨- to￨L￨TO￨O￨- immunity.In￨L￨NN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- discuss￨L￨VB￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- easily￨L￨RB￨O￨- ,￨L￨,￨O￨- some￨L￨DT￨O￨- preliminary￨L￨JJ￨O￨- transformations￨L￨NNS￨O￨- will￨L￨MD￨O￨- be￨L￨VB￨O￨- made￨L￨VBN￨O￨- hereafter.Dividing￨L￨VBG￨O￨- both￨L￨DT￨O￨- sides￨L￨NNS￨O￨- of￨L￨IN￨O￨- every￨L￨DT￨O￨- equation￨L￨NN￨O￨- of￨L￨IN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- N￨U￨NN￨O￨- and￨L￨CC￨O￨- performing￨L￨VBG￨O￨- a￨L￨DT￨O￨- scaling￨L￨NN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- n￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- →￨L￨NN￨O￨- α￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- →￨L￨NN￨O￨- β￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- →￨L￨NN￨O￨- γ￨L￨NN￨O￨- Δ￨U￨NN￨O￨- t￨L￨NN￨O￨- ,￨L￨,￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- →￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- n￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- →￨L￨CD￨NUMBER￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- N￨U￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- write￨L￨VBP￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- form￨L￨NN￨O￨A {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- α￨L￨NN￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- β￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨CD￨NUMBER￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- −￨L￨NN￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- n￨L￨NN￨O￨- S￨U￨NN￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- −￨L￨NN￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨PRP￨O￨- n￨L￨NN￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- α￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- β￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- pay￨L￨VBP￨O￨- attention￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- theoretical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- structural￨L￨JJ￨O￨- stabilities￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- under￨L￨IN￨O￨- certain￨L￨JJ￨O￨- restrictive￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- of￨L￨IN￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- <￨L￨JJR￨O￨- s￨L￨NNS￨O￨- ≤￨L￨VBP￨O￨- 0￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- map￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 4￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- has￨L￨VBZ￨O￨- only￨L￨RB￨O￨- one￨L￨CD￨NUMBER￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- s￨L￨NNS￨O￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- two￨L￨CD￨NUMBER￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- P￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 0￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- Q￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- ∗￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- I￨U￨PRP￨O￨- ∗￨L￨VBP￨O￨- =￨L￨JJ￨O￨- s￨L￨NNS￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- ∗￨L￨NN￨O￨- =￨L￨JJ￨O￨- γ￨L￨NN￨O￨- s￨L￨NNS￨O￨- α￨L￨VBP￨O￨- β￨L￨NN￨O￨- .￨L￨.￨O￨- +Then￨U￨RB￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- SIRI￨U￨NNP￨ORGANIZATION￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨A :￨L￨:￨O￨- {￨L￨-LRB-￨O￨- d￨L￨LS￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- b￨L￨NN￨O￨- −￨L￨NN￨O￨- d￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- k￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- μ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- d￨L￨NN￨O￨- t￨L￨NN￨O￨- =￨L￨JJ￨O￨- μ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- d￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- b￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- birth￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- proportionality￨L￨NN￨O￨- constant￨L￨JJ￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infected￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- become￨L￨VBP￨O￨- temporarily￨L￨RB￨O￨- immune￨L￨JJ￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- recovered￨L￨VBN￨O￨- class￨L￨NN￨O￨- revert￨L￨VBP￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- infective￨L￨JJ￨O￨- class￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- saturated￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- b￨L￨NN￨O￨- ,￨L￨,￨O￨- d￨L￨NN￨O￨- ,￨L￨,￨O￨- k￨L￨NN￨O￨- ,￨L￨,￨O￨- α￨L￨NN￨O￨- ,￨L￨,￨O￨- γ￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- ,￨L￨,￨O￨- h￨L￨NN￨O￨- are￨L￨VBP￨O￨- positive￨L￨JJ￨O￨- parameters.For￨L￨NN￨O￨- convenience￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- first￨L￨RB￨ORDINAL￨- transform￨L￨VB￨O￨- the￨L￨DT￨O￨- three-dimensional￨L￨JJ￨O￨- Eq￨U￨NN￨O￨- .￨L￨.￨O￨- +Moreira￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Wang￨U￨NNP￨PERSON￨- NumericCitation￨U￨NNP￨PERSON￨- studied￨L￨VBD￨O￨- an￨L￨DT￨O￨- SIRI￨U￨NNP￨MISC￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- saturated￨L￨JJ￨O￨A incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- φ￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨PRP￨O￨- and￨L￨CC￨O￨- derived￨L￨VBN￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- asymptotic￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibria￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- an￨L￨DT￨O￨- elementary￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- Lienard￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- equation￨L￨NN￨O￨- and￨L￨CC￨O￨- Lyapunov￨U￨NNP￨PERSON￨- ’s￨L￨POS￨O￨- direct￨L￨JJ￨O￨- method￨L￨NN￨O￨- .￨L￨.￨O￨- +2014Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 27￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- study￨L￨VBP￨O￨- an￨L￨DT￨O￨- SIRI￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- incidence￨L￨NN￨O￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨A ,￨L￨,￨O￨- namely￨L￨RB￨O￨- k￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- describes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- psychological￨L￨JJ￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- certain￨L￨JJ￨O￨- serious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- when￨L￨WRB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- infective￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- getting￨L￨VBG￨O￨- larger￨L￨JJR￨O￨- .￨L￨.￨O￨- +Therefore￨U￨RB￨O￨- ,￨L￨,￨O￨- delay￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- incorporated￨L￨VBN￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- nonlinear￨L￨JJ￨O￨A incidence￨L￨NN￨O￨A function￨L￨NN￨O￨- as￨L￨IN￨O￨- follows￨L￨VBZ￨O￨- :￨L￨:￨O￨- g￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- =￨L￨JJ￨O￨- k￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- S￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- +￨L￨CC￨O￨- α￨L￨NN￨O￨- I￨U￨CD￨NUMBER￨- h￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- −￨L￨CD￨NUMBER￨- τ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- obtain￨L￨VBP￨O￨- the￨L￨DT￨O￨- threshold￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- on￨L￨IN￨O￨- stability￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- without￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨A period￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- ,￨L￨,￨O￨- τ￨L￨NN￨O￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 28￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 611￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 625￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asStochastic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- hepatitis￨L￨NN￨CAUSE_OF_DEATH￨- B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- through￨L￨IN￨O￨- maternal￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- vertical￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- environmental￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- horizontal￨L￨JJ￨O￨A )￨L￨-RRB-￨O￨- transmission￨L￨NN￨O￨- with￨L￨IN￨O￨- applications￨L￨NNS￨O￨- to￨L￨TO￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- estimation￨L￨NN￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- appraisal￨L￨NN￨O￨- of￨L￨IN￨O￨- preventive￨L￨JJ￨O￨- strategiesAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsHui-Fang￨L￨JJ￨O￨- HungYa-Chuan￨U￨JJ￨MISC￨- WangAmy￨U￨NNP￨MISC￨- Ming-Fang￨U￨NNP￨MISC￨- YenHsiu-Hsi￨U￨NNP￨MISC￨- ChenOpen￨U￨NNP￨MISC￨- AccessOriginal￨U￨NNP￨MISC￨- PaperFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 1.5￨L￨CD￨NUMBER￨- k￨L￨NN￨O￨- Downloads￨U￨NNS￨O￨- 5￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractElucidating￨U￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- Hepatitis￨U￨NNP￨CAUSE_OF_DEATH￨- B￨U￨NN￨CAUSE_OF_DEATH￨- virus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- HBV￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- provides￨L￨VBZ￨O￨- not￨L￨RB￨O￨- only￨L￨RB￨O￨- useful￨L￨JJ￨O￨- information￨L￨NN￨O￨- for￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- but￨L￨CC￨O￨- also￨L￨RB￨O￨- a￨L￨DT￨O￨- bedrock￨L￨NN￨O￨- for￨L￨IN￨O￨- economic￨L￨JJ￨O￨- appraisal￨L￨NN￨O￨- of￨L￨IN￨O￨- population-based￨L￨JJ￨O￨- preventive￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- universal￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- linking￨L￨VBG￨O￨- the￨L￨DT￨O￨- temporal￨L￨JJ￨O￨- natural￨L￨JJ￨O￨- history￨L￨NN￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- previously￨L￨RB￨DATE￨- established￨L￨VBN￨O￨- Markov￨U￨NNP￨PERSON￨- process￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- sequelae￨L￨NN￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- chronic￨L￨JJ￨O￨- hepatitis￨L￨NN￨O￨A infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- liver￨L￨NN￨O￨- cirrhosis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- hepatocelluar￨L￨JJ￨O￨- carcinoma￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- Markov￨U￨NNP￨PERSON￨- cycle￨L￨NN￨O￨- decision￨L￨NN￨O￨- tree￨L￨NN￨O￨- to￨L￨TO￨O￨- evaluate￨L￨VB￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- population-based￨L￨JJ￨O￨- preventive￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- related￨L￨VBN￨O￨- to￨L￨TO￨O￨- vaccination￨L￨NN￨O￨- and￨L￨CC￨O￨- maternal￨L￨JJ￨O￨- lamivudine￨L￨NN￨O￨- use￨L￨NN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- analysis￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- began￨L￨VBD￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- two-state￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- further￨L￨JJ￨O￨- developed￨L￨VBD￨O￨- a￨L￨DT￨O￨- five-state￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- including￨L￨VBG￨O￨- susceptible￨L￨JJ￨O￨- ,￨L￨,￨O￨- latent￨L￨JJ￨O￨- phase￨L￨NN￨O￨- ,￨L￨,￨O￨- active￨L￨JJ￨O￨- viral￨L￨JJ￨O￨- replication￨L￨NN￨O￨- ,￨L￨,￨O￨- carrier￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- recovery￨L￨NN￨O￨- states￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- stochastic￨L￨JJ￨O￨- process￨L￨NN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- making￨L￨VBG￨O￨- allowances￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- mixed￨L￨JJ￨O￨- proportion￨L￨NN￨O￨- of￨L￨IN￨O￨- vertical￨L￨JJ￨O￨- and￨L￨CC￨O￨- horizontal￨L￨JJ￨O￨A transmissions￨L￨NNS￨O￨- .￨L￨.￨O￨- +As￨U￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- process￨L￨NN￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- to￨L￨TO￨O￨- active￨L￨JJ￨O￨- virus￨L￨NN￨O￨- replication￨L￨NN￨O￨A and￨L￨CC￨O￨- finally￨L￨RB￨O￨- to￨L￨TO￨O￨- recovery￨L￨NN￨O￨- state￨L￨NN￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- carrier￨L￨NN￨O￨- state￨L￨NN￨O￨- through￨L￨IN￨O￨- both￨L￨DT￨O￨- routes￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- directly￨L￨RB￨O￨- observable￨L￨JJ￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- were￨L￨VBD￨O￨- therefore￨L￨RB￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- quantitatively￨L￨RB￨O￨- elucidate￨L￨VB￨O￨- the￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- process￨L￨NN￨O￨- of￨L￨IN￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- with￨L￨IN￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- the￨L￨DT￨O￨- five-state￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- horizontal￨L￨JJ￨O￨A transmission￨L￨NN￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- to￨L￨TO￨O￨- contribute￨L￨VB￨O￨- more￨L￨JJR￨O￨- to￨L￨TO￨O￨- HBV￨U￨NN￨ORGANIZATION￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- than￨L￨IN￨O￨- vertical￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- northern￨L￨JJ￨O￨- area￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 59￨L￨CD￨NUMBER￨- vs.￨L￨CC￨O￨- +In￨U￨IN￨O￨- Section￨U￨NN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- consider￨L￨VBP￨O￨- the￨L￨DT￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- equilibria￨L￨NN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- Jacobian￨U￨JJ￨MISC￨- matrix￨L￨NN￨O￨- method￨L￨NN￨O￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- of￨L￨IN￨O￨- constructing￨L￨VBG￨O￨- a￨L￨DT￨O￨- Lyapunov￨U￨NN￨MISC￨- function￨L￨NN￨O￨- and￨L￨CC￨O￨- employing￨L￨VBG￨O￨- the￨L￨DT￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- competitive￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- are￨L￨VBP￨O￨- investigated￨L￨VBN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- authors￨L￨NNS￨O￨- considered￨L￨VBN￨O￨- plant￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- impulsive￨L￨JJ￨O￨- effects.Although￨L￨NN￨O￨- early￨L￨JJ￨O￨- investigations￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- plant￨L￨NN￨O￨- pathogens￨L￨NNS￨O￨- seldom￨L￨RB￨O￨- included￨L￨VBD￨O￨- the￨L￨DT￨O￨- demographics￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- replenishment￨L￨NN￨O￨- of￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- common￨L￨JJ￨O￨- in￨L￨IN￨O￨- those￨L￨DT￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +If￨U￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- ≤￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- means￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- plant￨L￨NN￨O￨A disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- disappear￨L￨VB￨O￨- eventually￨L￨RB￨O￨- ;￨L￨:￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- indicates￨L￨VBZ￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- plant￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- will￨L￨MD￨O￨- persist￨L￨VB￨O￨- for￨L￨IN￨O￨- all￨L￨DT￨O￨- time￨L￨NN￨O￨- .￨L￨.￨O￨- +Firstly￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- analytical￨L￨JJ￨O￨- formula￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- by￨L￨IN￨O￨- using￨L￨VBG￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- generation￨L￨NN￨O￨- matrix￨L￨NN￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- is￨L￨VBZ￨O￨- discussed￨L￨VBN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Invasion￨U￨NNP￨MISC￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- Salmonella￨U￨FW￨LOCATION￨- Kentucky￨U￨NNP￨STATE_OR_PROVINCE￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- adult￨L￨JJ￨O￨- dairy￨L￨NN￨O￨- herd￨L￨NN￨O￨- using￨L￨VBG￨O￨- approximate￨L￨JJ￨O￨- Bayesian￨U￨JJ￨O￨- computationZhao￨L￨NN￨O￨- Lu1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Rebecca￨U￨NNP￨PERSON￨- M￨U￨NNP￨O￨- Mitchell1￨U￨NN￨O￨- ,￨L￨,￨O￨- Rebecca￨U￨NNP￨PERSON￨- L￨U￨NNP￨PERSON￨- Smith1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Jeffrey￨U￨NNP￨PERSON￨- S￨U￨NN￨PERSON￨- Karns2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Jo￨U￨NNP￨PERSON￨- Ann￨U￨NNP￨PERSON￨- S￨U￨NN￨PERSON￨- van￨L￨NN￨PERSON￨- Kessel2￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- R￨U￨NNP￨PERSON￨- Wolfgang3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Ynte￨U￨NNP￨PERSON￨- H￨U￨NNP￨PERSON￨- Schukken1￨U￨NN￨PERSON￨- and￨L￨CC￨O￨- Yrjo￨U￨NN￨PERSON￨- T￨U￨NN￨O￨- Grohn1￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 9:245￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Lu￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- An￨U￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- Salmonella￨U￨FW￨LOCATION￨- Kentucky￨U￨NNP￨STATE_OR_PROVINCE￨- followed￨L￨VBN￨O￨- by￨L￨IN￨O￨- a￨L￨DT￨O￨- high￨L￨JJ￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- sustained￨L￨JJ￨O￨- endemic￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- was￨L￨VBD￨O￨- recently￨L￨RB￨DATE￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- US￨U￨NNP￨COUNTRY￨- adult￨L￨JJ￨O￨- dairy￨L￨NN￨O￨- herd￨L￨NN￨O￨- enrolled￨L￨VBN￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- longitudinal￨L￨JJ￨O￨A study￨L￨NN￨O￨- involving￨L￨VBG￨O￨- intensive￨L￨JJ￨O￨- fecal￨L￨JJ￨O￨- sampling￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- approximate￨L￨JJ￨O￨- Bayesian￨U￨JJ￨MISC￨- computation￨L￨NN￨O￨- technique￨L￨NN￨O￨- was￨L￨VBD￨O￨- applied￨L￨VBN￨O￨- for￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- shape￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- parameters￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- gamma￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- shedding￨L￨VBG￨O￨- )￨L￨-RRB-￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- given￨L￨VBN￨O￨- a￨L￨DT￨O￨- susceptible-infectious-recovered-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIRS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- compartment￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- gamma￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨A period￨L￨NN￨O￨A .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- results￨L￨NNS￨O￨- report￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- β￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- 0.417￨L￨CD￨NUMBER￨- month-1￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- median￨L￨NN￨O￨- :￨L￨:￨O￨- 0.417￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨A %￨L￨NN￨PERCENT￨- credible￨L￨JJ￨O￨- interval￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 0.406￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 0.429￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- γ-1￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- 7.95￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- (￨L￨-LRB-￨O￨- median￨L￨NN￨O￨- :￨L￨:￨O￨- 7.95￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- credible￨L￨JJ￨O￨- interval￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 7.70￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 8.22￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- shape￨L￨NN￨O￨- parameter￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- gamma￨L￨NN￨O￨- distribution￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- is￨L￨VBZ￨O￨- 242￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- median￨L￨NN￨O￨- :￨L￨:￨O￨- 182￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- credible￨L￨JJ￨O￨- interval￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mean￨L￨NN￨O￨- basic￨L￨JJ￨O￨- reproduction￨L￨NN￨O￨- ratio￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- 2.91￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- median￨L￨NN￨O￨- :￨L￨:￨O￨- 2.91￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 95￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- credible￨L￨JJ￨O￨- interval￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 2.83￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3.00￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Conclusions￨U￨NNS￨O￨- This￨U￨DT￨O￨- study￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- Salmonella￨U￨FW￨LOCATION￨- Kentucky￨U￨NNP￨STATE_OR_PROVINCE￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- herd￨L￨NN￨O￨- was￨L￨VBD￨O￨- of￨L￨IN￨O￨- mild￨L￨JJ￨O￨- infectiousness￨L￨NN￨O￨- and￨L￨CC￨O￨- had￨L￨VBD￨O￨- a￨L￨DT￨O￨- long￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- together￨L￨RB￨O￨- provide￨L￨VBP￨O￨- an￨L￨DT￨O￨- explanation￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- observed￨L￨VBN￨O￨- prevalence￨L￨NN￨O￨- pattern￨L￨NN￨O￨- after￨L￨IN￨O￨- invasion￨L￨NN￨O￨A .￨L￨.￨O￨- +To￨U￨TO￨O￨- understand￨L￨VB￨O￨- the￨L￨DT￨O￨- invasion￨L￨NN￨O￨A ability￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- Salmonella￨U￨FW￨LOCATION￨- Kentucky￨U￨NNP￨STATE_OR_PROVINCE￨- in￨L￨IN￨O￨- dairy￨L￨NN￨O￨- cattle￨L￨NNS￨O￨- ,￨L￨,￨O￨- accurate￨L￨JJ￨O￨- estimation￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- epidemiological￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- from￨L￨IN￨O￨- longitudinal￨L￨JJ￨O￨- field￨L￨NN￨O￨- data￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- necessary￨L￨JJ￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- study￨L￨NN￨O￨- offers￨L￨VBZ￨O￨- a￨L￨DT￨O￨- feasible￨L￨JJ￨O￨- approach￨L￨NN￨O￨- for￨L￨IN￨O￨- quantifying￨L￨VBG￨O￨- the￨L￨DT￨O￨- risk￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- community￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- valuable￨L￨JJ￨O￨- for￨L￨IN￨O￨- designing￨L￨VBG￨O￨- and￨L￨CC￨O￨- optimizing￨L￨VBG￨O￨- the￨L￨DT￨O￨- virus￨L￨NN￨O￨- defense￨L￨NN￨O￨- systems.KeywordsDynamic￨L￨JJ￨O￨- networkPropagation￨L￨NN￨O￨- powerVirus￨L￨NN￨O￨- restraintBasic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨A structure￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Three￨U￨CD￨NUMBER￨- basic￨L￨JJ￨O￨- propagation￨L￨NN￨O￨- structures￨L￨NNS￨O￨- are￨L￨VBP￨O￨- presented￨L￨VBN￨O￨- through￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- risk￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- quantified￨L￨VBN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- framework￨L￨NN￨O￨- is￨L￨VBZ￨O￨- proposed￨L￨VBN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A in￨L￨IN￨O￨- different￨L￨JJ￨O￨- network￨L￨NN￨O￨- structures￨L￨NNS￨O￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- the￨L￨DT￨O￨- mobility￨L￨NN￨O￨- of￨L￨IN￨O￨- smart￨L￨JJ￨O￨- devices￨L￨NNS￨O￨- can￨L￨MD￨O￨- greatly￨L￨RB￨O￨- increase￨L￨VB￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A even￨L￨RB￨O￨- if￨L￨IN￨O￨- most￨L￨JJS￨O￨- nodes￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- remain￨L￨VBP￨O￨- still￨L￨RB￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- present￨L￨VBP￨DATE￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- way￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- and￨L￨CC￨O￨- restrain￨L￨VB￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A by￨L￨IN￨O￨- proposing￨L￨VBG￨O￨- the￨L￨DT￨O￨- concepts￨L￨NNS￨O￨- of￨L￨IN￨O￨- propagation￨L￨NN￨O￨- power￨L￨NN￨O￨- and￨L￨CC￨O￨- propagation￨L￨NN￨O￨- structure￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- relationship￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- speed￨L￨NN￨O￨- of￨L￨IN￨O￨- virus￨L￨NN￨O￨A propagation￨L￨NN￨O￨A and￨L￨CC￨O￨- network￨L￨NN￨O￨- structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- explored￨L￨VBN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 58￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NNP￨O￨- 15￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 1818￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1831￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asExploring￨L￨VBG￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- SARS￨U￨NNP￨O￨- in-out￨L￨JJ￨O￨- flow￨L￨NN￨O￨- in￨L￨IN￨O￨- mainland￨L￨NN￨O￨- ChinaAuthorsAuthors￨U￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsBiSong￨L￨NNP￨O￨- HuJianHua￨U￨NNP￨MISC￨- GongJun￨U￨NNP￨MISC￨- SunJiePing￨U￨NNP￨MISC￨- ZhouOpen￨U￨NNP￨MISC￨- AccessArticle￨U￨NNP￨MISC￨- GeographyFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 612￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- 2￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractThe￨U￨NNP￨O￨- changing￨L￨VBG￨O￨- spatiotemporal￨L￨JJ￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- individual￨L￨JJ￨O￨- susceptible-infected-symptomatic-treated-recovered￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- interactions￨L￨NNS￨O￨- of￨L￨IN￨O￨- information￨L￨NN￨O￨- /￨L￨:￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2003￨L￨CD￨DATE￨A Severe￨U￨JJ￨O￨- Acute￨U￨JJ￨O￨- Respiratory￨U￨JJ￨O￨- Syndrome￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- SARS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- epidemiological￨L￨JJ￨O￨- investigation￨L￨NN￨O￨- data￨L￨NNS￨O￨- in￨L￨IN￨O￨- mainland￨L￨NN￨O￨- China￨U￨NNP￨COUNTRY￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- three￨L￨CD￨NUMBER￨- typical￨L￨JJ￨O￨- locations￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- working￨L￨VBG￨O￨- unit/home￨L￨NN￨O￨- address￨L￨NN￨O￨- ,￨L￨,￨O￨- onset￨L￨NN￨O￨- location￨L￨NN￨O￨- and￨L￨CC￨O￨- reporting￨L￨VBG￨O￨- unit￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- define￨L￨VB￨O￨- the￨L￨DT￨O￨- in-out￨L￨JJ￨O￨- flow￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SARS￨U￨NNP￨MISC￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- .￨L￨.￨O￨- +Epidemiology￨U￨NNP￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- and￨L￨CC￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- SARS￨U￨NNP￨O￨- :￨L￨:￨O￨- Citation￨U￨NNP￨O￨- –￨L￨:￨O￨- 2003￨L￨CD￨DATE￨A epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 3215￨L￨CD￨DATE￨- –￨L￨:￨O￨- 3221CrossRefGoogle￨L￨NN￨O￨- Scholar7.Cao￨U￨NN￨O￨- Z￨U￨NN￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- Zeng￨U￨NN￨PERSON￨- D￨U￨NN￨PERSON￨- J￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Zheng￨U￨NN￨PERSON￨- X￨U￨NN￨O￨- L￨U￨NN￨O￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 1017￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1028CrossRefGoogle￨L￨JJ￨O￨- Scholar8.Fang￨U￨NN￨O￨- L￨U￨NN￨O￨- Q￨U￨NNP￨O￨- ,￨L￨,￨O￨- de￨L￨FW￨PERSON￨- Vlas￨U￨FW￨PERSON￨- S￨U￨NN￨PERSON￨- J￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Feng￨U￨NN￨O￨- D￨U￨NN￨O￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +Remark￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- For￨U￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- can￨L￨MD￨O￨- easily￨L￨RB￨O￨- see￨L￨VB￨O￨- that￨L￨DT￨O￨- when￨L￨WRB￨O￨- β￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 0￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- describes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- SIRS￨U￨NNP￨O￨- type￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- courses￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- y￨L￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- i￨L￨FW￨O￨- th￨L￨DT￨O￨A course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ;￨L￨:￨O￨- and￨L￨CC￨O￨- when￨L￨WRB￨O￨- β￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- =￨L￨JJ￨O￨- 0￨L￨CD￨NUMBER￨- then￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- describes￨L￨VBZ￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- SEIRS￨U￨NN￨O￨- type￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- courses￨L￨NNS￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- y￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- exposed￨L￨VBN￨O￨- and￨L￨CC￨O￨- y￨L￨NN￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- (￨L￨-LRB-￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- …￨L￨:￨O￨- ,￨L￨,￨O￨- m￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- denotes￨L￨VBZ￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- i￨L￨FW￨O￨- th￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease.Remark￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- In￨U￨IN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- assumption￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- know￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- term￨L￨NN￨O￨- is￨L￨VBZ￨O￨- denoted￨L￨VBN￨O￨- by￨L￨IN￨O￨- ∑￨L￨NN￨O￨- i￨L￨FW￨O￨- =￨L￨JJ￨O￨- 1￨L￨CD￨NUMBER￨- m￨L￨NN￨O￨- β￨L￨NN￨O￨- i￨L￨FW￨O￨- y￨L￨FW￨O￨- i￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- x￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- n￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 58￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 741￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 749￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asInfluence￨L￨NN￨O￨- of￨L￨IN￨O￨- extreme￨L￨JJ￨O￨- weather￨L￨NN￨O￨- and￨L￨CC￨O￨- meteorological￨L￨JJ￨O￨- anomalies￨L￨NNS￨O￨- on￨L￨IN￨O￨- outbreaks￨L￨NNS￨O￨- of￨L￨IN￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- A￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- H1N1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- AuthorsAuthors￨U￨NNPS￨ORGANIZATION￨- and￨L￨CC￨O￨- affiliationsHong￨L￨NNP￨O￨- XiaoHuaiYu￨U￨NNP￨O￨- TianXiaoLing￨U￨NNP￨O￨- LinLiDong￨U￨NNP￨O￨- GaoXiangYu￨U￨NNP￨O￨- DaiXiXing￨U￨NNP￨O￨- ZhangBiYun￨U￨NNP￨MISC￨- ChenJian￨U￨NNP￨MISC￨- ZhaoJingZhe￨U￨NNP￨MISC￨- XuOpen￨U￨NNP￨MISC￨- AccessArticle￨U￨NNP￨MISC￨- Preventive￨U￨NNP￨MISC￨- Medicine￨U￨NNP￨MISC￨- &￨L￨CC￨O￨- HygienicsFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 834￨L￨CD￨NUMBER￨- Downloads￨U￨NNPS￨O￨- 10￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractBiological￨U￨JJ￨O￨- experiments￨L￨NNS￨O￨- and￨L￨CC￨O￨- epidemiological￨L￨JJ￨O￨- evidence￨L￨NN￨O￨A indicate￨L￨VBP￨O￨- that￨L￨IN￨O￨- variations￨L￨NNS￨O￨- in￨L￨IN￨O￨- environment￨L￨NN￨O￨- have￨L￨VBP￨O￨- important￨L￨JJ￨O￨- effect￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- occurrence￨L￨NN￨O￨- and￨L￨CC￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 2211￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2218CrossRefGoogle￨L￨JJ￨O￨- Scholar7.Barry￨U￨NN￨O￨- J￨U￨NN￨O￨- M￨U￨NN￨O￨- ,￨L￨,￨O￨- Viboud￨U￨NN￨O￨- C￨U￨NN￨O￨- ,￨L￨,￨O￨- Simonsen￨U￨NNP￨ORGANIZATION￨- L.￨U￨NNP￨ORGANIZATION￨- Citation￨U￨NNP￨ORGANIZATION￨- –￨L￨:￨O￨- 1919￨L￨CD￨DATE￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- :￨L￨:￨O￨- Epidemiological￨U￨JJ￨O￨- evidence￨L￨NN￨O￨A from￨L￨IN￨O￨- US￨U￨NNP￨ORGANIZATION￨- Army￨U￨NNP￨ORGANIZATION￨- camps￨L￨NNS￨O￨- and￨L￨CC￨O￨- from￨L￨IN￨O￨- Britain￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 7313￨L￨CD￨DATE￨- –￨L￨:￨O￨- 7314CrossRefGoogle￨L￨JJ￨O￨- Scholar3.Webster￨U￨NN￨O￨- R￨U￨NN￨O￨- G￨U￨NN￨O￨- ,￨L￨,￨O￨- Bean￨U￨NNP￨O￨- W￨U￨NNP￨O￨- J￨U￨NNP￨O￨- ,￨L￨,￨O￨- Gorman￨U￨NNP￨PERSON￨- O￨U￨NNP￨O￨- T￨U￨NN￨O￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 22CrossRefGoogle￨L￨JJ￨O￨- Scholar6.Murray￨U￨NN￨O￨- C￨U￨NN￨O￨- J￨U￨NN￨O￨- L￨U￨NN￨O￨- ,￨L￨,￨O￨- Lopez￨U￨NNP￨PERSON￨- A￨U￨NNP￨O￨- D￨U￨NNP￨O￨- ,￨L￨,￨O￨- Chin￨U￨NNP￨PERSON￨- B￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +Most￨U￨JJS￨O￨- research￨L￨NN￨O￨- works￨L￨VBZ￨O￨- on￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- concern￨L￨NN￨O￨- the￨L￨DT￨O￨- definition￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- and￨L￨CC￨O￨- local￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- endemic￨L￨JJ￨O￨- equilibria￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- flip￨L￨JJ￨O￨- bifurcation￨L￨NN￨O￨- and￨L￨CC￨O￨- Hopf￨U￨NN￨PERSON￨- bifurcation￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨A stability￨L￨NN￨O￨A of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- are￨L￨VBP￨O￨- quite￨L￨RB￨O￨- few￨L￨JJ￨O￨- for￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- two￨L￨CD￨NUMBER￨- factors￨L￨NNS￨O￨- :￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- There￨U￨EX￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- enough￨L￨JJ￨O￨- effective￨L￨JJ￨O￨- theory￨L￨NN￨O￨- and￨L￨CC￨O￨- methods￨L￨NNS￨O￨- for￨L￨IN￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- discrete￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- systems￨L￨NNS￨O￨- ;￨L￨:￨O￨- (￨L￨-LRB-￨O￨- 2￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- The￨U￨DT￨O￨- discrete￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- exhibits￨L￨VBZ￨O￨- much￨L￨RB￨O￨- more￨L￨RBR￨O￨- complicated￨L￨JJ￨O￨- dynamical￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- than￨L￨IN￨O￨- its￨L￨PRP$￨O￨- corresponding￨L￨JJ￨O￨- continuous￨L￨JJ￨O￨- model.We￨L￨NN￨O￨- will￨L￨MD￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- global￨L￨JJ￨O￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- get￨L￨VB￨O￨- sufficient￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Global￨U￨JJ￨MISC￨- stability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨A SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelXia￨L￨NN￨O￨- Ma1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Yicang￨U￨NNP￨O￨- Zhou1￨U￨NN￨O￨- and￨L￨CC￨O￨- Hui￨U￨NNP￨O￨- Cao2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2013:42￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Ma￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 10￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- discrete￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- defined￨L￨VBN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- behavior￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- discrete￨L￨JJ￨O￨A SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- {￨L￨-LRB-￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- Λ￨U￨NN￨O￨- −￨L￨CD￨NUMBER￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- μ￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- I￨U￨CD￨NUMBER￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- β￨L￨NN￨O￨- S￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- N￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- μ￨L￨NN￨O￨- +￨L￨CC￨O￨- δ￨L￨NN￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- +￨L￨CC￨O￨- γ￨L￨NN￨O￨- I￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- −￨L￨CD￨NUMBER￨- μ￨L￨NN￨O￨- R￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- t￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- (￨L￨-LRB-￨O￨- 1￨L￨LS￨NUMBER￨- )￨L￨-RRB-￨O￨- where￨L￨WRB￨O￨- Λ￨U￨NNP￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- constant￨L￨JJ￨O￨- recruitment￨L￨NN￨O￨- rate￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- β￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- μ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- ,￨L￨,￨O￨- δ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- death￨L￨NN￨O￨- rate￨L￨NN￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- γ￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- recovery￨L￨NN￨O￨- rate￨L￨NN￨O￨- .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- proved￨L￨VBN￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A is￨L￨VBZ￨O￨- globally￨L￨RB￨O￨- asymptotically￨L￨RB￨O￨- stable￨L￨JJ￨O￨- if￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- <￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- obtained￨L￨VBN￨O￨- when￨L￨WRB￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- >￨L￨JJR￨O￨- 1￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- A￨U￨NNP￨O￨- low-cost￨L￨JJ￨O￨- method￨L￨NN￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- importance￨L￨NN￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- controlling￨L￨VBG￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaksTimo￨L￨NN￨O￨- Smieszek1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Marcel￨U￨NNP￨O￨- Salathé1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 11:35￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Smieszek￨U￨NNP￨O￨- and￨L￨CC￨O￨- Salathé￨U￨NNP￨LOCATION￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2013Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨MISC￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Infectious￨U￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- in￨L￨IN￨O￨- communities￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- early￨L￨JJ￨O￨A detection￨L￨NN￨O￨A and￨L￨CC￨O￨- effective￨L￨JJ￨O￨- prevention￨L￨NN￨O￨- measures￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- describe￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- ,￨L￨,￨O￨- low-cost￨L￨JJ￨O￨- method￨L￨NN￨O￨- -￨L￨:￨O￨- called￨L￨VBN￨O￨- collocation￨L￨NN￨O￨- ranking￨L￨NN￨O￨- -￨L￨:￨O￨- to￨L￨TO￨O￨- assess￨L￨VB￨O￨- individual￨L￨JJ￨O￨- importance￨L￨NN￨O￨- for￨L￨IN￨O￨- early￨L￨JJ￨O￨A detection￨L￨NN￨O￨A and￨L￨CC￨O￨- targeted￨L￨VBN￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- that￨L￨WDT￨O￨- are￨L￨VBP￨O￨- easily￨L￨RB￨O￨- implementable￨L￨JJ￨O￨- in￨L￨IN￨O￨- practice￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- computationally￨L￨RB￨O￨- validate￨L￨VBP￨O￨- our￨L￨PRP$￨O￨- method￨L￨NN￨O￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- school￨L￨NN￨O￨- setting￨L￨NN￨O￨- by￨L￨IN￨O￨- comparing￨L￨VBG￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- method￨L￨NN￨O￨- against￨L￨IN￨O￨- computational￨L￨JJ￨O￨- predictions￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- outbreak￨L￨NN￨O￨- simulations￨L￨NNS￨O￨- on￨L￨IN￨O￨- an￨L￨DT￨O￨- empirical￨L￨JJ￨O￨- high-resolution￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Assessing￨U￨VBG￨O￨- the￨L￨DT￨O￨- relative￨L￨JJ￨O￨- importance￨L￨NN￨O￨A of￨L￨IN￨O￨- each￨L￨DT￨O￨- individual￨L￨JJ￨O￨- community￨L￨NN￨O￨- member￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- these￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- processes￨L￨NNS￨O￨- requires￨L￨VBZ￨O￨- detailed￨L￨JJ￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- the￨L￨DT￨O￨- underlying￨L￨VBG￨O￨- social￨L￨JJ￨O￨- contact￨L￨NN￨O￨- network￨L￨NN￨O￨- on￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- can￨L￨MD￨O￨- spread￨L￨VB￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨A is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- knowledge￨L￨NN￨O￨- about￨L￨IN￨O￨- individual￨L￨JJ￨O￨- collocation￨L￨NN￨O￨- which￨L￨WDT￨O￨- is￨L￨VBZ￨O￨- readily￨L￨RB￨O￨- available￨L￨JJ￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- community￨L￨NN￨O￨- settings￨L￨NNS￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- schools￨L￨NNS￨O￨- ,￨L￨,￨O￨- offices￨L￨NNS￨O￨- ,￨L￨,￨O￨- hospitals￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- on￨L￨IN￨O￨- .￨L￨.￨O￨- +Analysis￨U￨NN￨O￨- shows￨L￨VBZ￨O￨- that￨L￨IN￨O￨- shared￨L￨JJ￨O￨- access￨L￨NN￨O￨- achieves￨L￨VBZ￨O￨- at￨L￨IN￨O￨- least￨L￨JJS￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- throughput￨L￨NN￨O￨- of￨L￨IN￨O￨- open￨L￨JJ￨O￨- access￨L￨NN￨O￨- while￨L￨IN￨O￨- also￨L￨RB￨O￨- satisfying￨L￨VBG￨O￨- rate￨L￨NN￨O￨- requirements￨L￨NNS￨O￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- closed￨L￨JJ￨O￨- access￨L￨NN￨O￨- fails￨L￨VBZ￨O￨- for￨L￨IN￨O￨- cellular￨L￨JJ￨O￨- users￨L￨NNS￨O￨- and￨L￨CC￨O￨- open￨L￨JJ￨O￨- access￨L￨NN￨O￨- fails￨L￨VBZ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- home￨L￨NN￨O￨A user.KeywordsNetwork￨L￨NN￨MISC￨- ThroughputComplementary￨U￨NNP￨MISC￨- Cumulative￨U￨NNP￨MISC￨- Distribution￨U￨NN￨MISC￨- FunctionMacrocell￨U￨NNP￨MISC￨- Base￨U￨NNP￨MISC￨- StationCellular￨U￨NNP￨MISC￨- UserHome￨U￨NNP￨MISC￨- User￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionFemtocells￨U￨NNS￨O￨- are￨L￨VBP￨O￨- small￨L￨JJ￨O￨- form-factor￨L￨JJ￨O￨- base￨L￨NN￨O￨- stations￨L￨NNS￨O￨- that￨L￨WDT￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- installed￨L￨VBN￨O￨- within￨L￨IN￨O￨- an￨L￨DT￨O￨- existing￨L￨VBG￨O￨- cellular￨L￨JJ￨O￨- network￨L￨NN￨O￨- .￨L￨.￨O￨- +Closed￨U￨JJ￨O￨- access￨L￨NN￨O￨- ,￨L￨,￨O￨- where￨L￨WRB￨O￨- only￨L￨RB￨O￨- specified￨L￨VBN￨O￨- registered￨L￨VBN￨O￨- home￨L￨NN￨O￨A users￨L￨NNS￨O￨- can￨L￨MD￨O￨- communicate￨L￨VB￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- femtocell￨L￨NN￨O￨- access￨L￨NN￨O￨- point￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- FAP￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- appears￨L￨VBZ￨O￨- attractive￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- home￨L￨NN￨O￨- user￨L￨NN￨O￨- but￨L￨CC￨O￨- can￨L￨MD￨O￨- result￨L￨VB￨O￨- in￨L￨IN￨O￨- severe￨L￨JJ￨O￨- cross-tier￨L￨JJ￨O￨- interference￨L￨NN￨O￨- from￨L￨IN￨O￨- nearby￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- users￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- uplink￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Figure1￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- to￨L￨TO￨O￨- nearby￨L￨JJ￨O￨- cellular￨L￨JJ￨O￨- users￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- downlink￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- average￨L￨JJ￨O￨- sum￨L￨NN￨O￨- throughput￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- any￨L￨DT￨O￨- other￨L￨JJ￨O￨- SINR-based￨U￨JJ￨MISC￨- metric￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- home￨L￨NN￨O￨A users￨L￨NNS￨O￨- and￨L￨CC￨O￨- cellular￨L￨JJ￨O￨- users￨L￨NNS￨O￨- under￨L￨IN￨O￨- open￨L￨JJ￨O￨- and￨L￨CC￨O￨- closed￨L￨JJ￨O￨- access￨L￨NN￨O￨- can￨L￨MD￨O￨- readily￨L￨RB￨O￨- be￨L￨VB￨O￨- determined￨L￨VBN￨O￨- from￨L￨IN￨O￨- these￨L￨DT￨O￨- expressions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Such￨U￨PDT￨O￨- a￨L￨DT￨O￨- random￨L￨JJ￨O￨- BS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- appears￨L￨VBZ￨O￨- useful￨L￨JJ￨O￨- for￨L￨IN￨O￨- obtaining￨L￨VBG￨O￨- outage/throughput￨L￨JJ￨O￨- averaged￨L￨VBD￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- entire￨L￨JJ￨O￨- network￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- may￨L￨MD￨O￨- not￨L￨RB￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- throughput￨L￨NN￨O￨- of￨L￨IN￨O￨- open￨L￨JJ￨O￨- ,￨L￨,￨O￨- closed￨L￨VBD￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- shared￨L￨VBD￨O￨A access￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- particular￨L￨JJ￨O￨- femtocell￨L￨NN￨O￨- at￨L￨IN￨O￨- a￨L￨DT￨O￨- given￨L￨VBN￨O￨- distance￨L￨NN￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- MBS￨U￨NNP￨O￨- .￨L￨.￨O￨- +With￨U￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- uplink￨L￨NN￨O￨- throughput￨L￨NN￨O￨- of￨L￨IN￨O￨- registered￨L￨VBN￨O￨- home￨L￨NN￨O￨A users￨L￨NNS￨O￨- ,￨L￨,￨O￨- open￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- shared￨L￨VBN￨O￨- )￨L￨-RRB-￨O￨- access￨L￨NN￨O￨- reduces￨L￨VBZ￨O￨- interference￨L￨NN￨O￨- by￨L￨IN￨O￨- handing￨L￨VBG￨O￨- over￨L￨IN￨O￨- the￨L￨DT￨O￨- loud￨L￨JJ￨O￨- neighbor￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- expense￨L￨NN￨O￨- of￨L￨IN￨O￨- FAP￨U￨NN￨ORGANIZATION￨- resource￨L￨NN￨O￨- sharing￨L￨NN￨O￨- .￨L￨.￨O￨- +On￨U￨IN￨O￨- the￨L￨DT￨O￨- other￨L￨JJ￨O￨- hand￨L￨NN￨O￨- ,￨L￨,￨O￨- an￨L￨DT￨O￨- advantage￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- discrete-time￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- easier￨L￨JJR￨O￨- to￨L￨TO￨O￨- analyse￨L￨VB￨O￨- than￨L￨IN￨O￨- continuous-time￨L￨JJ￨O￨- ones￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- then￨L￨RB￨O￨- the￨L￨DT￨O￨- effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- potential￨L￨JJ￨O￨- treatment￨L￨NN￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- easier￨L￨JJR￨O￨- to￨L￨TO￨O￨- derive.The￨L￨NN￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨- of￨L￨IN￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- ,￨L￨,￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- either￨L￨CC￨O￨- the￨L￨DT￨O￨- persistence￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A point￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- or￨L￨CC￨O￨- extinction￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- disease-free￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- point￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 9￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 11￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- constraints￨L￨NNS￨O￨- for￨L￨IN￨O￨- guaranteeing￨L￨VBG￨O￨- the￨L￨DT￨O￨- positivity￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- boundedness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- solutions￨L￨NNS￨O￨- of￨L￨IN￨O￨- such￨L￨JJ￨O￨- models￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- conditions￨L￨NNS￨O￨- that￨L￨WDT￨O￨- generate￨L￨VBP￨O￨- an￨L￨DT￨O￨- oscillatory￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- in￨L￨IN￨O￨- such￨L￨JJ￨O￨- solutions￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- have￨L￨VBP￨O￨- been￨L￨VBN￨O￨- some￨L￨DT￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- objectives￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- literature￨L￨NN￨O￨- about￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- positivity￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- eradication￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- under￨L￨IN￨O￨- feedback￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- laws￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- stability￨L￨NN￨O￨- properties￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- asymptotic￨L￨JJ￨O￨- convergence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- estimation￨L￨NN￨O￨- errors￨L￨NNS￨O￨- to￨L￨TO￨O￨- zero￨L￨CD￨NUMBER￨- as￨L￨IN￨O￨- time￨L￨NN￨O￨- tends￨L￨VBZ￨O￨- to￨L￨TO￨O￨- infinity￨L￨NN￨O￨- are￨L￨VBP￨O￨- investigated.KeywordsSEIR￨L￨NN￨O￨- epidemic￨L￨JJ￨O￨- modelsvaccinationnonlinear￨L￨NN￨O￨- controlstabilitypositivitynonlinear￨L￨NN￨O￨- observers￨L￨NNS￨O￨- design￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionA￨U￨NN￨O￨- relevant￨L￨JJ￨O￨- area￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- theory￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- development￨L￨NN￨O￨- of￨L￨IN￨O￨- models￨L￨NNS￨O￨- for￨L￨IN￨O￨- studying￨L￨VBG￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- a￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 20￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Concretely￨U￨RB￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- research￨L￨NN￨O￨- in￨L￨IN￨O￨- NumericCitation￨U￨NNP￨O￨- exhaustively￨L￨RB￨O￨- analyses￨L￨NNS￨O￨- the￨L￨DT￨O￨- equilibrium￨L￨NN￨O￨- points￨L￨NNS￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- under￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- state￨L￨NN￨O￨- feedback￨L￨NN￨O￨A control￨L￨NN￨O￨- law￨L￨NN￨O￨- with￨L￨IN￨O￨- respect￨L￨NN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- parameters￨L￨NNS￨O￨- and/or￨L￨CC￨O￨- the￨L￨DT￨O￨- controller￨L￨NN￨TITLE￨- gains￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- An￨U￨DT￨O￨- observer-based￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- control￨L￨NN￨O￨- law￨L￨NN￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- SEIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- feedback￨L￨NN￨O￨- linearization￨L￨NN￨O￨- techniques￨L￨NNS￨O￨- for￨L￨IN￨O￨- nonlinear￨L￨JJ￨O￨- systemsS￨L￨NN￨O￨- Alonso-Quesada1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- M￨U￨NN￨O￨- De￨U￨NNP￨O￨- la￨L￨NNP￨O￨- Sen1￨U￨NN￨O￨- ,￨L￨,￨O￨- RP￨U￨NN￨MISC￨- Agarwal2￨U￨NN￨MISC￨- and￨L￨CC￨O￨- A￨U￨DT￨O￨- Ibeas3￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- 2012:161￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Alonso-Quesada￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- presents￨L￨VBZ￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- strategy￨L￨NN￨O￨- for￨L￨IN￨O￨- fighting￨L￨VBG￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- propagation￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨A diseases￨L￨NNS￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +Furthermore￨U￨RB￨O￨- ,￨L￨,￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- higher￨L￨JJR￨O￨- in￨L￨IN￨O￨- pre-weaning￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨A compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- post-weaning￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- which￨L￨WDT￨O￨- might￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- an￨L￨DT￨O￨- age-related￨L￨JJ￨O￨- susceptibility￨L￨NN￨O￨- or￨L￨CC￨O￨- the￨L￨DT￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- sow￨L￨VB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- primary￨L￨JJ￨O￨- source￨L￨NN￨O￨- of￨L￨IN￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NN￨O￨- .￨L￨.￨O￨- +Data￨U￨NNS￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- large-scale￨L￨JJ￨O￨- longitudinal￨L￨JJ￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- Danish￨U￨JJ￨NATIONALITY￨- and￨L￨CC￨O￨- four￨L￨CD￨NUMBER￨- Dutch￨U￨JJ￨NATIONALITY￨- pig￨L￨NN￨O￨- herds￨L￨NNS￨O￨- were￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NN￨O￨- transmission￨L￨NN￨O￨- rates￨L￨NNS￨O￨- within￨L￨IN￨O￨- pig￨L￨NN￨O￨- herds￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- identify￨L￨VB￨O￨- factors￨L￨NNS￨O￨- affecting￨L￨VBG￨O￨- transmission￨L￨NN￨O￨- between￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Longitudinal￨U￨JJ￨MISC￨- study￨L￨NN￨O￨- on￨L￨IN￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NN￨O￨- within￨L￨IN￨O￨- pig￨L￨NN￨O￨A herdsEls￨L￨NNS￨O￨- M￨U￨NN￨O￨- Broens1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Carmen￨U￨NNP￨PERSON￨- Espinosa-Gongora3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Elisabeth￨U￨NNP￨PERSON￨- AM￨U￨NNP￨PERSON￨- Graat1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Nadia￨U￨NNP￨PERSON￨- Vendrig1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Peter￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- Der￨U￨NNP￨PERSON￨- Wolf4￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Luca￨U￨NNP￨PERSON￨- Guardabassi3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Patrick￨U￨NNP￨PERSON￨- Butaye5￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Jens￨U￨NNP￨PERSON￨- Peter￨U￨NNP￨PERSON￨- Nielsen7￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Mart￨U￨NNP￨O￨- CM￨U￨NN￨O￨- De￨U￨NNP￨O￨- Jong1￨U￨NNP￨O￨- and￨L￨CC￨O￨- Arjen￨U￨NNP￨PERSON￨- W￨U￨NNP￨PERSON￨- Van￨U￨NNP￨PERSON￨- De￨U￨NNP￨PERSON￨- Giessen2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 8:58￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- 2012￨L￨CD￨DATE￨- Broens￨U￨NNP￨O￨- et￨L￨FW￨O￨- al.￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2012Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 19￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Since￨U￨IN￨O￨- the￨L￨DT￨O￨- detection￨L￨NN￨O￨- of￨L￨IN￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- has￨L￨VBZ￨O￨- emerged￨L￨VBN￨O￨- in￨L￨IN￨O￨- livestock￨L￨NN￨O￨- worldwide￨L￨RB￨O￨- .￨L￨.￨O￨- +Transmission￨U￨NNP￨O￨- rates￨L￨NNS￨O￨- were￨L￨VBD￨O￨- higher￨L￨JJR￨O￨- in￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A treated￨L￨VBN￨O￨- with￨L￨IN￨O￨- tetracyclins￨L￨NNS￨O￨- and￨L￨CC￨O￨- β-lactams￨L￨NNS￨O￨- compared￨L￨VBN￨O￨- to￨L￨TO￨O￨- untreated￨L￨JJ￨O￨- pigs￨L￨NNS￨O￨- implying￨L￨VBG￨O￨- a￨L￨DT￨O￨- selective￨L￨JJ￨O￨- advantage￨L￨NN￨O￨- of￨L￨IN￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NN￨O￨- when￨L￨WRB￨O￨- these￨L￨DT￨O￨- antimicrobials￨L￨NNS￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- distinct￨L￨JJ￨O￨- clone￨L￨NN￨O￨- of￨L￨IN￨O￨- methicillin￨L￨NN￨O￨- resistant￨L￨JJ￨O￨- Staphylococcus￨U￨FW￨O￨- aureus￨L￨FW￨O￨- (￨L￨-LRB-￨O￨- MRSA￨U￨NNP￨O￨- CC398￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- referred￨L￨VBN￨O￨- to￨L￨TO￨O￨- as￨L￨IN￨O￨- livestock-associated￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- LA￨U￨NNP￨CITY￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- found￨L￨VBN￨O￨- in￨L￨IN￨O￨- pigs￨L￨NNS￨O￨A and￨L￨CC￨O￨- in￨L￨IN￨O￨- people￨L￨NNS￨O￨- in￨L￨IN￨O￨- contact￨L￨NN￨O￨- with￨L￨IN￨O￨- pigs￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Simulation￨U￨NN￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- compared￨L￨VBN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- Spray￨U￨NN￨O￨- and￨L￨CC￨O￨- Wait￨U￨VB￨O￨- protocols￨L￨NNS￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- H￨U￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- hop￨L￨NN￨O￨- forwarding￨L￨NN￨O￨- mode￨L￨NN￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- better￨L￨JJR￨O￨- performance￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- delivery￨L￨NN￨O￨A delay￨L￨NN￨O￨- and￨L￨CC￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- copies.Keywordsintermittently￨L￨NN￨O￨- connectedmobile￨L￨NN￨O￨- ad￨L￨NN￨O￨- hoc￨L￨FW￨O￨- and￨L￨CC￨O￨- sensor￨L￨NN￨O￨- networksepidemic￨L￨JJ￨O￨- theoryforwardingMarkov￨L￨NN￨O￨- chain￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- IntroductionThanks￨U￨NNPS￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- increasing￨L￨VBG￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- mobile￨L￨JJ￨TITLE￨- devices￨L￨NNS￨O￨- with￨L￨IN￨O￨- wireless￨L￨JJ￨O￨- capabilities￨L￨NNS￨O￨- [￨L￨-LRB-￨O￨- 1￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- communication￨L￨NN￨O￨- without￨L￨IN￨O￨- network￨L￨NN￨O￨- infrastructure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- becoming￨L￨VBG￨O￨- a￨L￨DT￨O￨- reality￨L￨NN￨O￨- .￨L￨.￨O￨- +2012Received￨L￨VBN￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractIn￨U￨NNP￨O￨- intermittently￨L￨RB￨O￨- connected￨L￨JJ￨O￨- mobile￨L￨JJ￨TITLE￨- ad￨L￨NN￨O￨- hoc￨L￨FW￨O￨- networks￨L￨NNS￨O￨- ,￨L￨,￨O￨- how￨L￨WRB￨O￨- to￨L￨TO￨O￨- guarantee￨L￨VB￨O￨- the￨L￨DT￨O￨- packet￨L￨NN￨O￨- delivery￨L￨NN￨O￨A ratio￨L￨NN￨O￨- and￨L￨CC￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- delay￨L￨NN￨O￨- has￨L￨VBZ￨O￨- become￨L￨VBN￨O￨- the￨L￨DT￨O￨- new￨L￨JJ￨O￨- challenge￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- researchers￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Epidemic￨U￨JJ￨MISC￨- theory￨L￨NN￨O￨- based￨L￨VBN￨O￨- H￨U￨NN￨O￨- +￨L￨CC￨O￨- 1￨L￨CD￨NUMBER￨- hop￨L￨NN￨O￨- forwarding￨L￨NN￨O￨- for￨L￨IN￨O￨- intermittently￨L￨RB￨O￨- connected￨L￨VBN￨O￨- mobile￨L￨JJ￨TITLE￨- ad￨L￨NN￨O￨A hoc￨L￨FW￨O￨A networksXin￨L￨FW￨O￨- Guan1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Min￨U￨NN￨DURATION￨- Chen2￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Tomoaki￨U￨NNP￨PERSON￨- Ohtsuki1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 2012:76￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Guan￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- Springer￨U￨NNP￨PERSON￨- .￨L￨.￨O￨- +First￨U￨RB￨ORDINAL￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- utilize￨L￨VBP￨O￨- the￨L￨DT￨O￨- susceptible￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- recovered￨L￨VBN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- theory￨L￨NN￨O￨- to￨L￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- amount￨L￨NN￨O￨- of￨L￨IN￨O￨- relay￨L￨NN￨O￨- node￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- epidemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- delivery￨L￨NN￨O￨A delay￨L￨NN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- process￨L￨NN￨O￨- .￨L￨.￨O￨- +Finally￨U￨RB￨O￨- ,￨L￨,￨O￨- large-scale￨L￨JJ￨O￨- Monte￨U￨NNP￨ORGANIZATION￨- Carlo￨U￨NNP￨ORGANIZATION￨- simulations￨L￨NNS￨O￨- were￨L￨VBD￨O￨- carried￨L￨VBN￨O￨- out￨L￨RP￨O￨- to￨L￨TO￨O￨- visualize￨L￨VB￨O￨- and￨L￨CC￨O￨- interpret￨L￨VB￨O￨- these￨L￨DT￨O￨- phenomena￨L￨NNS￨O￨- explicitly.Keywordsprisoner￨L￨NNP￨O￨- ’s￨L￨POS￨O￨- dilemma￨L￨NN￨O￨- game￨L￨NN￨O￨- emergence￨L￨NN￨O￨- of￨L￨IN￨O￨- cooperation￨L￨NN￨O￨A size￨L￨NN￨O￨- of￨L￨IN￨O￨- interaction￨L￨NN￨O￨- neighborhood￨L￨NN￨O￨- This￨U￨DT￨O￨- article￨L￨NN￨O￨- is￨L￨VBZ￨O￨- published￨L￨VBN￨O￨- with￨L￨IN￨O￨- open￨L￨JJ￨O￨- access￨L￨NN￨O￨- at￨L￨IN￨O￨- Download￨U￨VB￨O￨- to￨L￨TO￨O￨- read￨L￨VB￨O￨- the￨L￨DT￨O￨- full￨L￨JJ￨O￨- article￨L￨NN￨O￨- textReferences1.Hamilton￨L￨NN￨O￨- W￨U￨NN￨O￨- D.￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 1390￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1396CrossRefGoogle￨L￨NN￨O￨- Scholar4.Wang￨U￨NN￨O￨- Z￨U￨NN￨O￨- ,￨L￨,￨O￨- Du￨U￨NNP￨O￨- W￨U￨NNP￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- Cao￨U￨NNP￨PERSON￨- X￨U￨NN￨O￨- B￨U￨NN￨O￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 57￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 724￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 728￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asSpatial￨L￨JJ￨O￨- prisoner￨L￨NN￨O￨- ’s￨L￨POS￨O￨- dilemma￨L￨NN￨O￨- games￨L￨NNS￨O￨- with￨L￨IN￨O￨- increasing￨L￨VBG￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- neighborhood￨L￨NN￨O￨- on￨L￨IN￨O￨- regular￨L￨JJ￨O￨- latticesAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsJuan￨L￨JJ￨MISC￨- WangChengYi￨U￨NN￨MISC￨- XiaYiLing￨U￨NN￨MISC￨- WangShuai￨U￨NNP￨MISC￨- DingJunQing￨U￨NNP￨MISC￨- SunOpen￨U￨NNP￨MISC￨- AccessArticle￨U￨NNP￨MISC￨- Statistical￨U￨NNP￨MISC￨- PhysicsFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractWe￨U￨NNP￨O￨- studied￨L￨VBD￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- cooperation￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- prisoner￨L￨NN￨O￨- ’s￨L￨POS￨O￨- dilemma￨L￨NN￨O￨- game￨L￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- square￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- where￨L￨WRB￨O￨- the￨L￨DT￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- interaction￨L￨NN￨O￨- neighborhood￨L￨NN￨O￨- is￨L￨VBZ￨O￨- considered￨L￨VBN￨O￨- .￨L￨.￨O￨- +Integrating￨U￨VBG￨O￨- neighborhoods￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- evaluation￨L￨NN￨O￨- of￨L￨IN￨O￨- fitness￨L￨NN￨O￨- promotes￨L￨VBZ￨O￨- cooperation￨L￨NN￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- spatial￨L￨JJ￨O￨- prisoner￨L￨NN￨O￨- ’s￨L￨POS￨O￨- dilemma￨L￨NN￨O￨- game￨L￨NN￨O￨- .￨L￨.￨O￨- +Volunteering￨U￨VBG￨O￨- as￨L￨IN￨O￨- red￨L￨JJ￨O￨- queen￨L￨NN￨TITLE￨- mechanism￨L￨NN￨O￨- for￨L￨IN￨O￨- cooperation￨L￨NN￨O￨A in￨L￨IN￨O￨- public￨L￨JJ￨O￨- goods￨L￨NNS￨O￨- game￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 23￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 35￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asGetting￨L￨NN￨O￨- a￨L￨DT￨O￨- free￨L￨JJ￨O￨- ride￨L￨NN￨O￨- on￨L￨IN￨O￨- poultry￨L￨NN￨O￨- farms￨L￨NNS￨O￨- :￨L￨:￨O￨- how￨L￨WRB￨O￨- highly￨L￨RB￨O￨- pathogenic￨L￨JJ￨O￨- avian￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A may￨L￨MD￨O￨- persist￨L￨VB￨O￨- in￨L￨IN￨O￨- spite￨L￨NN￨O￨- of￨L￨IN￨O￨- its￨L￨PRP$￨O￨- virulenceAuthorsAuthors￨L￨NNP￨O￨- and￨L￨CC￨O￨- affiliationsGiulio￨L￨NNP￨O￨- Alessandro￨U￨NNP￨PERSON￨- De￨U￨NNP￨PERSON￨- LeoLuca￨U￨NNP￨PERSON￨- BolzoniOpen￨U￨NNP￨PERSON￨- AccessOriginal￨U￨NNP￨O￨- paperFirst￨L￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 864￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- 3￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractIt￨U￨NN￨O￨- is￨L￨VBZ￨O￨- well-known￨L￨JJ￨O￨- that￨L￨IN￨O￨- highly￨L￨RB￨O￨- pathogenic￨L￨JJ￨O￨- avian￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- HPAI￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- strains￨L￨NNS￨O￨- can￨L￨MD￨O￨- arise￨L￨VB￨O￨- from￨L￨IN￨O￨- low￨L￨JJ￨O￨- pathogenic￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- LPAI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- during￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- in￨L￨IN￨O￨- poultry￨L￨NN￨O￨- farms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- this￨L￨DT￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- that￨L￨IN￨O￨- partial￨L￨JJ￨O￨- cross-immunity￨L￨NN￨O￨- triggered￨L￨VBN￨O￨- by￨L￨IN￨O￨- previous￨L￨JJ￨O￨- exposure￨L￨NN￨O￨- to￨L￨TO￨O￨- LPAI￨U￨NN￨O￨- viruses￨L￨NNS￨O￨- may￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- pathogenicity￨L￨NN￨O￨- of￨L￨IN￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- thus￨L￨RB￨O￨- enhance￨L￨VBP￨O￨- its￨L￨PRP$￨O￨- persistence￨L￨NN￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- generally￨L￨RB￨O￨- overlooked￨L￨VBN￨O￨- in￨L￨IN￨O￨- both￨L￨CC￨O￨- empirical￨L￨JJ￨O￨- and￨L￨CC￨O￨- theoretical￨L￨JJ￨O￨- work￨L￨NN￨O￨- on￨L￨IN￨O￨- avian￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A .￨L￨.￨O￨- +We￨U￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- simple￨L￨JJ￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- the￨L￨DT￨O￨- interacting￨L￨VBG￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- and￨L￨CC￨O￨- LPAI￨U￨NNP￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- avian￨L￨JJ￨O￨A influenza￨L￨NN￨CAUSE_OF_DEATH￨A in￨L￨IN￨O￨- small-scale￨L￨JJ￨O￨- poultry￨L￨NN￨O￨- farms￨L￨NNS￨O￨- .￨L￨.￨O￨- +Because￨U￨IN￨O￨- simulations￨L￨NNS￨O￨- showed￨L￨VBD￨O￨- that￨L￨IN￨O￨- troughs￨L￨NNS￨O￨- between￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- deep￨L￨RB￨O￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- only￨L￨RB￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- existing￨L￨VBG￨O￨- flocks￨L￨NNS￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- strain￨L￨NN￨O￨A ,￨L￨,￨O￨- we￨L￨PRP￨O￨- also￨L￨RB￨O￨- ran￨L￨VBD￨O￨- an￨L￨DT￨O￨- individual-based￨L￨JJ￨O￨- stochastic￨L￨JJ￨O￨- version￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- potential￨L￨NN￨O￨- for￨L￨IN￨O￨- natural￨L￨JJ￨O￨- fade-out￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- HPAI￨U￨NNP￨ORGANIZATION￨- strain￨L￨NN￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- ,￨L￨,￨O￨- Volume￨U￨NN￨O￨- 56￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Issue￨U￨NNP￨O￨- 34￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- pp￨L￨NN￨O￨- 3683￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3688￨L￨CD￨DATE￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asModeling￨L￨NN￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- with￨L￨IN￨O￨- white￨L￨JJ￨O￨A Gaussian￨U￨JJ￨MISC￨- noiseAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsJiao￨L￨NNP￨O￨- GuZongMao￨U￨NNP￨MISC￨- GaoWei￨U￨NNP￨MISC￨- LiOpen￨U￨NNP￨MISC￨- AccessArticle￨U￨NNP￨O￨- Statistical￨U￨NNP￨O￨- Physics￨U￨NN￨O￨- and￨L￨CC￨O￨- Mathematics￨U￨NN￨O￨- for￨L￨IN￨O￨- Complex￨U￨NN￨O￨- SystemsFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 02￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 605￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- 3￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractMotivated￨U￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- need￨L￨NN￨O￨- to￨L￨TO￨O￨- include￨L￨VB￨O￨- the￨L￨DT￨O￨- different￨L￨JJ￨O￨- characteristics￨L￨NNS￨O￨- of￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- damping￨L￨VBG￨O￨- effect￨L￨NN￨O￨- in￨L￨IN￨O￨- predictions￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spreading￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- build￨L￨VBP￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- variant￨L￨JJ￨O￨- coefficients￨L￨NNS￨O￨- and￨L￨CC￨O￨- white￨L￨JJ￨O￨- Gaussian￨U￨JJ￨MISC￨- noise￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- traditional￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Spreading￨U￨VBG￨O￨- speed￨L￨NN￨O￨- and￨L￨CC￨O￨- traveling￨L￨VBG￨O￨A waves￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- multi-type￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +J￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 270￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 296CrossRefGoogle￨L￨JJ￨O￨- Scholar4.Han￨U￨NN￨O￨- X￨U￨NN￨O￨- P.￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 2168￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2170CrossRefGoogle￨L￨JJ￨O￨- Scholar8.Chen￨U￨NN￨O￨- H￨U￨NN￨O￨- L.￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 2677￨L￨CD￨DATE￨- –￨L￨:￨O￨- 2683CrossRefGoogle￨L￨JJ￨O￨- Scholar10.Cao￨U￨NN￨O￨- C￨U￨NN￨O￨- X￨U￨NN￨O￨- ,￨L￨,￨O￨- Xu￨U￨NN￨O￨- M￨U￨NN￨O￨- ,￨L￨,￨O￨- Chang￨U￨NNP￨PERSON￨- C￨U￨NNP￨O￨- Y￨U￨NN￨O￨- ,￨L￨,￨O￨- et￨L￨FW￨O￨A al￨L￨FW￨O￨A .￨L￨.￨O￨- +For￨U￨IN￨O￨- both￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- and￨L￨CC￨O￨- static￨L￨JJ￨O￨A small￨L￨JJ￨O￨- worlds￨L￨NNS￨O￨- we￨L￨PRP￨O￨- observe￨L￨VBP￨O￨- suppression￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- epidemic￨L￨JJ￨O￨- size￨L￨NN￨O￨- dependence￨L￨NN￨O￨- on￨L￨IN￨O￨- network￨L￨NN￨O￨- size￨L￨NN￨O￨- in￨L￨IN￨O￨- comparison￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- finite-size￨L￨JJ￨O￨- scaling￨L￨NN￨O￨- known￨L￨VBN￨O￨- for￨L￨IN￨O￨- regular￨L￨JJ￨O￨- lattice￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- result￨L￨NN￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- behaviour￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- on￨L￨IN￨O￨- dynamic￨L￨JJ￨O￨- network￨L￨NN￨O￨- is￨L￨VBZ￨O￨- that￨L￨IN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- static￨L￨JJ￨O￨A small￨L￨JJ￨O￨- world￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- shortcuts￨L￨NNS￨O￨- increased￨L￨VBN￨O￨- by￨L￨IN￨O￨- 20.7￨L￨CD￨PERCENT￨- ±￨L￨CD￨PERCENT￨- 1.4￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- ,￨L￨,￨O￨- while￨L￨IN￨O￨- the￨L￨DT￨O￨- overall￨L￨JJ￨O￨- qualitative￨L￨JJ￨O￨- behaviour￨L￨NN￨O￨- stays￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- :￨L￨:￨O￨- 373￨L￨CD￨NUMBER￨- |￨L￨SYM￨O￨- Cite￨U￨VB￨O￨- asShift￨L￨NN￨O￨- of￨L￨IN￨O￨- percolation￨L￨NN￨O￨- thresholds￨L￨NNS￨O￨- for￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- between￨L￨IN￨O￨- static￨L￨JJ￨O￨A and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- small-world￨L￨JJ￨O￨- networksAuthorsAuthors￨L￨NNS￨O￨- and￨L￨CC￨O￨- affiliationsJ￨L￨NN￨O￨- .￨L￨.￨O￨- +F.￨U￨NNP￨O￨- GóraOpen￨U￨NNP￨O￨- AccessInterdisciplinary￨U￨NNP￨O￨- PhysicsFirst￨U￨NNP￨O￨- Online￨U￨NNP￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 269￨L￨CD￨NUMBER￨- Downloads￨U￨NNS￨O￨- 4￨L￨CD￨NUMBER￨- Citations￨U￨NNS￨O￨- AbstractThe￨U￨NNP￨O￨- study￨L￨NN￨O￨- compares￨L￨VBZ￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- spread￨L￨NN￨O￨- on￨L￨IN￨O￨- static￨L￨JJ￨O￨A and￨L￨CC￨O￨- dynamic￨L￨JJ￨O￨- small-world￨L￨JJ￨O￨- networks￨L￨NNS￨O￨- .￨L￨.￨O￨- +There￨U￨EX￨O￨- are￨L￨VBP￨O￨- other￨L￨JJ￨O￨- many￨L￨JJ￨O￨- variants￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- above￨L￨JJ￨O￨- models￨L￨NNS￨O￨- ,￨L￨,￨O￨- for￨L￨IN￨O￨- instance￨L￨NN￨O￨- ,￨L￨,￨O￨- including￨L￨VBG￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- kinds￨L￨NNS￨O￨- :￨L￨:￨O￨- constant￨L￨JJ￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- impulsive￨L￨JJ￨O￨A NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- discrete-time￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- forth￨L￨RB￨O￨- ,￨L￨,￨O￨- incorporating￨L￨VBG￨O￨- point￨L￨NN￨O￨- or￨L￨CC￨O￨- distributed￨L￨VBN￨O￨- delays￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- oscillatory￨L￨JJ￨O￨- behaviors￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- so￨L￨RB￨O￨- forth￨L￨RB￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- well-known￨L￨JJ￨O￨- types￨L￨NNS￨O￨- of￨L￨IN￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- are￨L￨VBP￨O￨- the￨L￨DT￨O￨- so-called￨L￨JJ￨O￨- SVEIRS￨U￨NNP￨O￨- epidemic￨L￨JJ￨O￨- models￨L￨NNS￨O￨- which￨L￨WDT￨O￨- incorporate￨L￨VBP￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- vaccinated￨L￨VBN￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- "￨L￨``￨O￨- infected￨L￨JJ￨O￨- "￨L￨''￨O￨- population￨L￨NN￨O￨- without￨L￨IN￨O￨- external￨L￨JJ￨O￨- symptoms￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- SEIR-type￨U￨JJ￨O￨- models￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- replaced￨L￨VBN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- "￨L￨``￨O￨- exposed￨L￨VBN￨O￨- "￨L￨''￨O￨- population￨L￨NN￨O￨- subject￨L￨JJ￨O￨A to￨L￨TO￨O￨- a￨L￨DT￨O￨- certain￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- ,￨L￨,￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- discusses￨L￨VBZ￨O￨- the￨L￨DT￨O￨- disease-free￨L￨JJ￨O￨- and￨L￨CC￨O￨- endemic￨L￨JJ￨O￨- equilibrium￨L￨NN￨O￨A points￨L￨NNS￨O￨A of￨L￨IN￨O￨- a￨L￨DT￨O￨- SVEIRS￨U￨NN￨O￨- propagation￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- which￨L￨WDT￨O￨- potentially￨L￨RB￨O￨- involves￨L￨VBZ￨O￨- a￨L￨DT￨O￨- regular￨L￨JJ￨O￨- constant￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- provide￨L￨VBP￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A policies￨L￨NNS￨O￨- for￨L￨IN￨O￨- an￨L￨DT￨O￨- isolation￨L￨NN￨O￨- only￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- vaccination￨L￨NN￨O￨- only￨L￨RB￨O￨- model￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- combined￨L￨JJ￨O￨- isolation￨L￨NN￨O￨- –￨L￨:￨O￨- vaccination￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- (￨L￨-LRB-￨O￨- or￨L￨CC￨O￨- mixed￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Oxford￨U￨NNP￨ORGANIZATION￨- Science￨U￨NNP￨ORGANIZATION￨- Publications￨U￨NNP￨ORGANIZATION￨- ,￨L￨,￨O￨- OxfordGoogle￨U￨NNP￨O￨- ScholarBehncke￨U￨NNP￨O￨- H￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- 2000￨L￨CD￨DATE￨A )￨L￨-RRB-￨O￨- Optimal￨U￨JJ￨O￨- control￨L￨NN￨O￨- of￨L￨IN￨O￨- deterministic￨L￨JJ￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Springer-Verlag￨U￨NNP￨O￨- ,￨L￨,￨O￨- New￨U￨NNP￨O￨- YorkGoogle￨U￨NNP￨O￨- ScholarGreenhalgh￨U￨NNP￨O￨- D￨U￨NNP￨O￨- (￨L￨-LRB-￨O￨- 1988￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Some￨U￨DT￨O￨- results￨L￨NNS￨O￨- on￨L￨IN￨O￨- optimal￨L￨JJ￨O￨A control￨L￨NN￨O￨A applied￨L￨VBD￨O￨- to￨L￨TO￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +J￨U￨NNP￨PERSON￨- Appl￨U￨NNP￨PERSON￨- Probab￨U￨NNP￨PERSON￨- 10￨L￨CD￨NUMBER￨- :￨L￨:￨O￨- 247￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 262zbMATHCrossRefMathSciNetGoogle￨L￨JJ￨O￨- ScholarAbakuks￨U￨NNPS￨O￨- A￨U￨DT￨O￨- (￨L￨-LRB-￨O￨- 1974￨L￨CD￨DATE￨- )￨L￨-RRB-￨O￨- Optimal￨U￨JJ￨O￨- immunization￨L￨NN￨O￨- policies￨L￨NNS￨O￨A for￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- Received￨U￨NNP￨O￨- :￨L￨:￨O￨- 17￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 14￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThis￨U￨NNP￨O￨- paper￨L￨NN￨O￨- discusses￨L￨VBZ￨O￨- a￨L￨DT￨O￨- generalized￨L￨VBN￨O￨- time-varying￨L￨JJ￨O￨- SEIR￨U￨NN￨O￨- propagation￨L￨NN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- model￨L￨NN￨TITLE￨- subject￨L￨NN￨O￨- to￨L￨TO￨O￨- delays￨L￨NNS￨O￨A which￨L￨WDT￨O￨- potentially￨L￨RB￨O￨- involves￨L￨VBZ￨O￨- mixed￨L￨JJ￨O￨- regular￨L￨JJ￨O￨- and￨L￨CC￨O￨- impulsive￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- rules￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- takes￨L￨VBZ￨O￨- also￨L￨RB￨O￨- into￨L￨IN￨O￨- account￨L￨NN￨O￨- the￨L￨DT￨O￨- natural￨L￨JJ￨O￨- population￨L￨NN￨O￨- growing￨L￨VBG￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- mortality￨L￨NN￨O￨- associated￨L￨VBN￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- presence￨L￨NN￨O￨- of￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- endemic￨L￨JJ￨O￨- thresholds￨L￨NNS￨O￨- for￨L￨IN￨O￨- both￨L￨CC￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- population￨L￨NN￨O￨- dynamics￨L￨NNS￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- lost￨L￨VBN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- of￨L￨IN￨O￨- newborns￨L￨NNS￨O￨A .￨L￨.￨O￨- +It￨U￨PRP￨O￨- is￨L￨VBZ￨O￨- also￨L￨RB￨O￨- assumed￨L￨VBN￨O￨- that￨L￨IN￨O￨- there￨L￨EX￨O￨- are￨L￨VBP￨O￨- time-varying￨L￨JJ￨O￨- point￨L￨NN￨O￨- delays￨L￨NNS￨O￨A for￨L￨IN￨O￨- the￨L￨DT￨O￨- susceptible-infected￨L￨JJ￨O￨- coupled￨L￨VBN￨O￨- dynamics￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infected￨L￨JJ￨O￨- ,￨L￨,￨O￨- infectious￨L￨JJ￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- removed-by-immunity￨L￨NN￨O￨- differential￨L￨JJ￨O￨- equations￨L￨NNS￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- proposed￨L￨VBN￨O￨- regular￨L￨JJ￨O￨A vaccination￨L￨NN￨O￨- control￨L￨NN￨O￨- objective￨L￨NN￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- tracking￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- prescribed￨L￨VBN￨O￨- suited￨L￨VBN￨O￨- infectious￨L￨JJ￨O￨- trajectory￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- given￨L￨VBN￨O￨- initial￨L￨JJ￨O￨- conditions￨L￨NNS￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- cutting-plane￨L￨JJ￨O￨- approach￨L￨NN￨O￨- to￨L￨TO￨O￨- mixed￨L￨JJ￨O￨- 0-1￨L￨CD￨NUMBER￨- stochastic￨L￨JJ￨O￨- integer￨L￨NN￨O￨A programs￨L￨NNS￨O￨- .￨L￨.￨O￨- +CrossRefGoogle￨U￨NNP￨O￨- Scholar￨U￨NNP￨TITLE￨- Dyer￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- M.￨U￨NNP￨O￨- ,￨L￨,￨O￨- &￨L￨CC￨O￨- Stougie￨U￨NNP￨O￨- ,￨L￨,￨O￨- L.￨U￨NNP￨O￨- Integer￨U￨NNP￨O￨- programming￨L￨NN￨O￨- and￨L￨CC￨O￨- combinatorial￨L￨JJ￨O￨- optimization￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- pp￨L￨NN￨O￨A .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Article￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Existence￨U￨NN￨MISC￨- of￨L￨IN￨MISC￨- a￨L￨DT￨MISC￨- Nonautonomous￨U￨JJ￨MISC￨- SIR￨U￨NN￨MISC￨- Epidemic￨U￨JJ￨MISC￨- Model￨U￨NNP￨TITLE￨- with￨L￨IN￨O￨- Age￨U￨NNP￨MISC￨- StructureJunyuan￨U￨NNP￨MISC￨- Yang1￨U￨NN￨MISC￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- Xiaoyan￨U￨NNP￨MISC￨- Wang2￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 2010:212858￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- J.￨U￨NNP￨O￨- 2010Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractA￨U￨NN￨O￨- nonautonomous￨L￨JJ￨O￨- SIR￨U￨NN￨O￨- epidemic￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- with￨L￨IN￨O￨- age￨L￨NN￨O￨A structure￨L￨NN￨O￨- is￨L￨VBZ￨O￨- studied￨L￨VBN￨O￨- .￨L￨.￨O￨- +Using￨U￨VBG￨O￨- integro-differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- fixed￨L￨JJ￨O￨- point￨L￨NN￨O￨- theorem￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- prove￨L￨VBP￨O￨- the￨L￨DT￨O￨- existence￨L￨NN￨O￨A and￨L￨CC￨O￨- uniqueness￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- positive￨L￨JJ￨O￨- solution￨L￨NN￨O￨- to￨L￨TO￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨O￨- Access￨U￨NN￨O￨- Identification￨U￨NN￨O￨- of￨L￨IN￨O￨- expressed￨L￨VBN￨O￨- genes￨L￨NNS￨O￨A during￨L￨IN￨O￨- compatible￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- between￨L￨IN￨O￨- stripe￨L￨NN￨O￨- rust￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Puccinia￨U￨NN￨O￨- striiformis￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- wheat￨L￨NN￨O￨- using￨L￨VBG￨O￨- a￨L￨DT￨O￨- cDNA￨L￨NN￨O￨- libraryJinbiao￨L￨NN￨O￨- Ma1￨U￨NN￨O￨- ,￨L￨,￨O￨- Xueling￨U￨VBG￨O￨- Huang2￨U￨NN￨O￨- ,￨L￨,￨O￨- Xiaojie￨U￨NN￨O￨- Wang2￨U￨NN￨O￨- ,￨L￨,￨O￨- Xianming￨U￨VBG￨O￨- Chen3￨U￨NN￨O￨- ,￨L￨,￨O￨- Zhipeng￨U￨NN￨O￨- Qu2￨U￨NN￨O￨- ,￨L￨,￨O￨- Lili￨U￨NNP￨PERSON￨- Huang2￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Zhensheng￨U￨NNP￨PERSON￨- Kang1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 10:586￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Ma￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2009Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 1￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 8￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Wheat￨U￨NNP￨O￨- stripe￨L￨NN￨O￨- rust￨L￨NN￨O￨- ,￨L￨,￨O￨- caused￨L￨VBN￨O￨- by￨L￨IN￨O￨- Puccinia￨U￨NN￨O￨- striiformis￨L￨NN￨O￨- f.￨L￨NN￨O￨- To￨U￨TO￨O￨- establish￨L￨VB￨O￨- compatibility￨L￨NN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- host￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Pst￨U￨NN￨O￨- forms￨L￨NNS￨O￨- special￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- structures￨L￨NNS￨O￨- to￨L￨TO￨O￨- invade￨L￨VB￨O￨- the￨L￨DT￨O￨- plant￨L￨NN￨O￨- with￨L￨IN￨O￨- minimal￨L￨JJ￨O￨- damage￨L￨NN￨O￨- to￨L￨TO￨O￨- host￨L￨NN￨TITLE￨- cells￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Total￨U￨JJ￨O￨- RNA￨U￨NN￨O￨- ,￨L￨,￨O￨- extracted￨L￨VBN￨O￨- from￨L￨IN￨O￨- susceptible￨L￨JJ￨O￨- infected￨L￨JJ￨O￨- wheat￨L￨NN￨O￨- leaves￨L￨VBZ￨O￨- harvested￨L￨VBN￨O￨- at￨L￨IN￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 8￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- post￨L￨JJ￨O￨- inoculation￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- dpi￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- create￨L￨VB￨O￨- a￨L￨DT￨O￨- cDNA￨L￨NN￨O￨- library￨L￨NN￨O￨- ,￨L￨,￨O￨- from￨L￨IN￨O￨- which￨L￨WDT￨O￨- 5,793￨L￨CD￨NUMBER￨- ESTs￨U￨NNS￨O￨- with￨L￨IN￨O￨- high￨L￨JJ￨O￨- quality￨L￨NN￨O￨- were￨L￨VBD￨O￨- obtained￨L￨VBN￨O￨- and￨L￨CC￨O￨- clustered￨L￨VBN￨O￨- into￨L￨IN￨O￨- 583￨L￨CD￨NUMBER￨- contigs￨L￨NNS￨O￨- and￨L￨CC￨O￨- 2,160￨L￨CD￨NUMBER￨- singletons￨L￨NNS￨O￨- to￨L￨TO￨O￨- give￨L￨VB￨O￨- a￨L￨DT￨O￨- set￨L￨NN￨O￨- of￨L￨IN￨O￨- 2,743￨L￨CD￨NUMBER￨- unisequences￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- GenBank￨U￨NN￨ORGANIZATION￨- accessions￨L￨NNS￨O￨- :￨L￨:￨O￨- GR302385￨U￨NN￨O￨- to￨L￨TO￨O￨- GR305127￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +About￨U￨IN￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- ESTs￨U￨NNS￨O￨- were￨L￨VBD￨O￨- significantly￨L￨RB￨O￨- homologous￨L￨JJ￨O￨- to￨L￨TO￨O￨- genes￨L￨NNS￨O￨A encoding￨L￨VBG￨O￨- proteins￨L￨NNS￨O￨- with￨L￨IN￨O￨- known￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- ;￨L￨:￨O￨- 20￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- were￨L￨VBD￨O￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- genes￨L￨NNS￨O￨- encoding￨L￨VBG￨O￨- proteins￨L￨NNS￨O￨- with￨L￨IN￨O￨- unknown￨L￨JJ￨O￨- functions￨L￨NNS￨O￨- and￨L￨CC￨O￨- 30￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- did￨L￨VBD￨O￨- not￨L￨RB￨O￨- have￨L￨VB￨O￨- significant￨L￨JJ￨O￨- homology￨L￨NN￨O￨- to￨L￨TO￨O￨- any￨L￨DT￨O￨- sequence￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- database￨L￨NN￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- aim￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- study￨L￨NN￨O￨- was￨L￨VBD￨O￨- to￨L￨TO￨O￨- develop￨L￨VB￨O￨- an￨L￨DT￨O￨- EST￨U￨NN￨MISC￨- database￨L￨NN￨O￨- of￨L￨IN￨O￨- wheat￨L￨NN￨O￨- infected￨L￨VBN￨O￨- by￨L￨IN￨O￨- Pst￨U￨NN￨O￨- in￨L￨IN￨O￨- order￨L￨NN￨O￨- to￨L￨TO￨O￨- determine￨L￨VB￨O￨- transcription￨L￨NN￨O￨- profiles￨L￨NNS￨O￨- of￨L￨IN￨O￨- genes￨L￨NNS￨O￨A involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- compatible￨L￨JJ￨O￨- wheat-Pst￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- .￨L￨.￨O￨- +Dividing￨U￨VBG￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- into￨L￨IN￨O￨- regions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- continents￨L￨NNS￨O￨- ,￨L￨,￨O￨- countries￨L￨NNS￨O￨- etc￨L￨FW￨O￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- linear￨L￨JJ￨O￨- differential￨L￨JJ￨O￨- equation￨L￨NN￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨- which￨L￨WDT￨O￨- has￨L￨VBZ￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- eradication￨L￨NN￨O￨A properties￨L￨NNS￨O￨- as￨L￨IN￨O￨- more￨L￨JJR￨O￨- complex￨L￨NN￨O￨- models￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- develop￨L￨VBP￨O￨- a￨L￨DT￨O￨- mathematical￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- that￨L￨WDT￨O￨- predicts￨L￨VBZ￨O￨- eradication￨L￨NN￨O￨A or￨L￨CC￨O￨- persistence￨L￨NN￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- on￨L￨IN￨O￨- a￨L￨DT￨O￨- world￨L￨NN￨O￨- scale￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- ,￨L￨,￨O￨- even￨L￨RB￨O￨- if￨L￨IN￨O￨- HIV/AIDS￨U￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- eradicated￨L￨VBN￨O￨- in￨L￨IN￨O￨- each￨L￨DT￨O￨- region￨L￨NN￨O￨- independently￨L￨RB￨O￨- ,￨L￨,￨O￨- travel/immigration￨L￨NN￨O￨- of￨L￨IN￨O￨- infectives￨L￨NNS￨O￨A could￨L￨MD￨O￨- still￨L￨RB￨O￨- sustain￨L￨VB￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- .￨L￨.￨O￨- +Volume￨U￨NN￨O￨- 9￨L￨CD￨NUMBER￨- Supplement￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- OptAIDS￨U￨NN￨O￨- project￨L￨NN￨O￨A :￨L￨:￨O￨- towards￨L￨IN￨O￨- global￨L￨JJ￨O￨- halting￨L￨VBG￨O￨- of￨L￨IN￨O￨- HIV/AIDS￨U￨NNP￨MISC￨- Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Can￨U￨MD￨MISC￨- we￨L￨PRP￨O￨- spend￨L￨VB￨O￨- our￨L￨PRP$￨O￨- way￨L￨NN￨O￨- out￨L￨IN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- AIDS￨U￨NNP￨CAUSE_OF_DEATH￨- epidemic￨L￨JJ￨O￨- ?￨L￨.￨O￨- +By￨U￨IN￨O￨- using￨L￨VBG￨O￨- Latin￨U￨JJ￨O￨- hypercube￨L￨NN￨O￨- sampling￨L￨NN￨O￨- scheme￨L￨NN￨O￨- ,￨L￨,￨O￨- parameters￨L￨NNS￨O￨- governing￨L￨VBG￨O￨- killing￨L￨NN￨O￨A ,￨L￨,￨O￨- diverting￨L￨VBG￨O￨- and￨L￨CC￨O￨- personal￨L￨JJ￨O￨- protection￨L￨NN￨O￨- of￨L￨IN￨O￨- net￨L￨JJ￨O￨- users￨L￨NNS￨O￨- were￨L￨VBD￨O￨- evaluated￨L￨VBN￨O￨- for￨L￨IN￨O￨- their￨L￨PRP$￨O￨- relative￨L￨JJ￨O￨- roles￨L￨NNS￨O￨- in￨L￨IN￨O￨- containing￨L￨VBG￨O￨- mosquito￨L￨NN￨O￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- entomological￨L￨JJ￨O￨- inoculation￨L￨NN￨O￨- rates￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- EIRs￨U￨NNS￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- incidence￨L￨NN￨O￨- .￨L￨.￨O￨- +Consistent￨U￨JJ￨O￨- with￨L￨IN￨O￨- early￨L￨JJ￨O￨- estimates￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- from￨L￨IN￨O￨- data￨L￨NNS￨O￨- from￨L￨IN￨O￨- the￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- in￨L￨IN￨O￨- Mexico￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- two￨L￨CD￨NUMBER￨- plausible￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- profiles￨L￨NNS￨O￨- were￨L￨VBD￨O￨- tested￨L￨VBN￨O￨- :￨L￨:￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- the￨L￨DT￨O￨- value￨L￨NN￨O￨- at￨L￨IN￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- transmissibility￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- max￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- 1.5￨L￨CD￨NUMBER￨- was￨L￨VBD￨O￨- assumed￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- whereas￨L￨IN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- second￨L￨JJ￨ORDINAL￨- a￨L￨DT￨O￨- higher￨L￨JJR￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- max￨L￨NN￨O￨- ,￨L￨,￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- 2.2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- was￨L￨VBD￨O￨- chosen￨L￨VBN￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- a￨L￨DT￨O￨- two-wave￨L￨JJ￨O￨- pandemic￨L￨JJ￨O￨- dynamic￨L￨NN￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- Southern￨U￨NNP￨MISC￨- hemisphere￨L￨NN￨O￨- because￨L￨IN￨O￨- of￨L￨IN￨O￨- seasonal￨L￨JJ￨O￨- constraints￨L￨NNS￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- maximum￨L￨NN￨O￨- value￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- basic￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- max￨L￨NN￨O￨A )￨L￨-RRB-￨O￨- within￨L￨IN￨O￨- a￨L￨DT￨O￨- city￨L￨NN￨O￨- equal￨L￨JJ￨O￨- to￨L￨TO￨O￨- 1.5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- mean￨L￨NN￨O￨- generation￨L￨NN￨O￨- interval￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- GI￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- 2￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +By￨U￨IN￨O￨- extrapolation￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- find￨L￨VBP￨O￨- that￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- all￨L￨DT￨O￨- countries￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- i.e.￨L￨FW￨O￨- up￨L￨RP￨O￨- to￨L￨TO￨O￨- 50￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- implemented￨L￨VBD￨O￨- 6￨L￨CD￨DURATION￨- months￨L￨NNS￨DURATION￨- after￨L￨IN￨O￨- the￨L￨DT￨O￨- start￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨NN￨O￨- may￨L￨MD￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- cumulative￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- by￨L￨IN￨O￨- 91￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- case￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- low￨L￨JJ￨O￨- transmissible￨L￨JJ￨O￨- strain￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- max￨L￨NN￨O￨A =￨L￨JJ￨O￨- 1.5￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- aim￨L￨VBP￨O￨- at￨L￨IN￨O￨- predicting￨L￨VBG￨O￨- the￨L￨DT￨O￨- pattern￨L￨NN￨O￨- of￨L￨IN￨O￨- global￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- potential￨L￨JJ￨O￨- S-OIV￨U￨NN￨O￨- pandemic￨L￨JJ￨O￨A flu￨L￨NN￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- at￨L￨IN￨O￨- estimating￨L￨VBG￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- campaigns￨L￨NNS￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- attempted￨L￨VBD￨O￨- to￨L￨TO￨O￨- quantify￨L￨VB￨O￨- the￨L￨DT￨O￨- possible￨L￨JJ￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨A across￨L￨IN￨O￨- a￨L￨DT￨O￨- network￨L￨NN￨O￨- of￨L￨IN￨O￨- 52￨L￨CD￨NUMBER￨- major￨L￨JJ￨O￨- cities￨L￨NNS￨O￨- and￨L￨CC￨O￨- to￨L￨TO￨O￨- predict￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccination￨L￨NN￨O￨- against￨L￨IN￨O￨- the￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- strain￨L￨NN￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- available￨L￨JJ￨O￨- .￨L￨.￨O￨- +No￨U￨DT￨O￨- suboptimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- ,￨L￨,￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- treatment￨L￨NN￨O￨- provided￨L￨VBN￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- age-dependent￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- were￨L￨VBD￨O￨- found￨L￨VBN￨O￨- able￨L￨JJ￨O￨- to￨L￨TO￨O￨- remarkably￨L￨RB￨O￨- reduce￨L￨VB￨O￨- both￨L￨DT￨O￨- clinical￨L￨JJ￨O￨- attack￨L￨NN￨CAUSE_OF_DEATH￨- rate￨L￨NN￨O￨- and￨L￨CC￨O￨- antiviral￨L￨JJ￨O￨A drugs￨L￨NNS￨CRIMINAL_CHARGE￨- needs￨L￨VBZ￨O￨- ,￨L￨,￨O￨- though￨L￨IN￨O￨- they￨L￨PRP￨O￨- can￨L￨MD￨O￨- contribute￨L￨VB￨O￨- to￨L￨TO￨O￨- largely￨L￨RB￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- excess￨L￨JJ￨O￨- mortality￨L￨NN￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Age-prioritized￨U￨JJ￨MISC￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- antivirals￨L￨NNS￨O￨- during￨L￨IN￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemicStefano￨L￨NN￨O￨- Merler1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Marco￨U￨NNP￨PERSON￨- Ajelli1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Caterina￨U￨NNP￨MISC￨- Rizzo3￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 9:117￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Merler￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2009Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- WHO￨U￨WP￨ORGANIZATION￨- suggested￨L￨VBD￨O￨- that￨L￨IN￨O￨- governments￨L￨NNS￨O￨- stockpile￨L￨VBP￨O￨- ,￨L￨,￨O￨- as￨L￨IN￨O￨- part￨L￨NN￨O￨- of￨L￨IN￨O￨- preparations￨L￨NNS￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- next￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨- ,￨L￨,￨O￨- sufficient￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- antiviral￨L￨JJ￨O￨A drugs￨L￨NNS￨CRIMINAL_CHARGE￨- to￨L￨TO￨O￨- treat￨L￨VB￨O￨- approximately￨L￨RB￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- their￨L￨PRP$￨O￨- populations￨L￨NNS￨O￨- .￨L￨.￨O￨- +Our￨U￨PRP$￨O￨- aim￨L￨NN￨O￨- is￨L￨VBZ￨O￨- two-fold￨L￨JJ￨O￨- :￨L￨:￨O￨- first￨L￨RB￨ORDINAL￨- ,￨L￨,￨O￨- since￨L￨IN￨O￨- in￨L￨IN￨O￨- many￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- the￨L￨DT￨O￨- antiviral￨L￨JJ￨O￨A stockpile￨L￨NN￨O￨- is￨L￨VBZ￨O￨- well￨L￨RB￨O￨- below￨L￨IN￨O￨- this￨L￨DT￨O￨- level￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- search￨L￨VBP￨O￨- for￨L￨IN￨O￨- suboptimal￨L￨JJ￨O￨- strategies￨L￨NNS￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- treatment￨L￨NN￨O￨- provided￨L￨VBD￨O￨- only￨L￨RB￨O￨- to￨L￨TO￨O￨- an￨L￨DT￨O￨- age-dependent￨L￨JJ￨O￨- fraction￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Our￨U￨PRP$￨O￨- results￨L￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- antiviral￨L￨JJ￨O￨A stockpile￨L￨NN￨O￨- required￨L￨VBN￨O￨- for￨L￨IN￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- ranges￨L￨VBZ￨O￨- from￨L￨IN￨O￨- 10￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- to￨L￨TO￨O￨- 35￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- population￨L￨NN￨O￨- for￨L￨IN￨O￨- R￨U￨NN￨O￨- 0￨L￨CD￨NUMBER￨- in￨L￨IN￨O￨- 1.4￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3￨L￨CD￨NUMBER￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- systematically￨L￨RB￨O￨- test￨L￨NN￨O￨- and￨L￨CC￨O￨- compare￨L￨VB￨O￨- how￨L￨WRB￨O￨- the￨L￨DT￨O￨- total￨L￨JJ￨O￨- size￨L￨NN￨O￨- of￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- differs￨L￨VBZ￨O￨- between￨L￨IN￨O￨- these￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- types￨L￨NNS￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- parameters￨L￨NNS￨O￨- transmission￨L￨NN￨O￨- probability￨L￨NN￨O￨- ,￨L￨,￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨A ,￨L￨,￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- different￨L￨JJ￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- clustering￨L￨NN￨O￨- and￨L￨CC￨O￨- varying￨L￨VBG￨O￨- proportions￨L￨NNS￨O￨- of￨L￨IN￨O￨- repetitive￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨O￨- Open￨U￨NNP￨O￨- Access￨U￨NN￨O￨- Models￨U￨NNS￨O￨- of￨L￨IN￨O￨- epidemics￨L￨NNS￨O￨- :￨L￨:￨O￨- when￨L￨WRB￨O￨- contact￨L￨NN￨O￨- repetition￨L￨NN￨O￨- and￨L￨CC￨O￨- clustering￨L￨NN￨O￨- should￨L￨MD￨O￨- be￨L￨VB￨O￨- includedTimo￨L￨JJ￨O￨- Smieszek1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Lena￨U￨NNP￨PERSON￨- Fiebig2￨U￨NNP￨O￨- and￨L￨CC￨O￨- Roland￨U￨NNP￨O￨- W￨U￨NNP￨O￨- Scholz1￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 6:11￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Smieszek￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2009Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 05￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 29￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- spread￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- determined￨L￨VBN￨O￨- by￨L￨IN￨O￨- biological￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- social￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- ,￨L￨,￨O￨- e.g.￨L￨FW￨O￨- the￨L￨DT￨O￨- arrangement￨L￨NN￨O￨- of￨L￨IN￨O￨- potentially￨L￨RB￨O￨- contagious￨L￨JJ￨O￨- contacts￨L￨NNS￨O￨A .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- The￨U￨DT￨O￨- simulation￨L￨NN￨O￨- runs￨L￨VBZ￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- parameter￨L￨NN￨O￨- constellations￨L￨NNS￨O￨- provide￨L￨VBP￨O￨- the￨L￨DT￨O￨- following￨L￨VBG￨O￨- results￨L￨NNS￨O￨- :￨L￨:￨O￨- The￨U￨DT￨O￨- difference￨L￨NN￨O￨- between￨L￨IN￨O￨- both￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- types￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- highest￨L￨JJS￨O￨- for￨L￨IN￨O￨- low￨L￨JJ￨O￨- numbers￨L￨NNS￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- per￨L￨IN￨O￨- day￨L￨NN￨DURATION￨A and￨L￨CC￨O￨- low￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- probabilities￨L￨NNS￨O￨- .￨L￨.￨O￨- +Repetitiveness￨U￨NNP￨O￨- and￨L￨CC￨O￨- clustering￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨A are￨L￨VBP￨O￨- known￨L￨VBN￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- relevant￨L￨JJ￨O￨- factors￨L￨NNS￨O￨- influencing￨L￨VBG￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- droplet￨L￨NN￨O￨- or￨L￨CC￨O￨- contact￨L￨NN￨O￨- transmitted￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Rotavirus￨U￨NNP￨O￨- vaccination￨L￨NN￨O￨- would￨L￨MD￨O￨- not￨L￨RB￨O￨- completely￨L￨RB￨O￨- protect￨L￨VB￨O￨- young￨L￨JJ￨O￨A children￨L￨NNS￨O￨- against￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- partial￨L￨JJ￨O￨- nature￨L￨NN￨O￨- of￨L￨IN￨O￨- vaccine￨L￨NN￨O￨- immunity￨L￨NN￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- would￨L￨MD￨O￨- effectively￨L￨RB￨O￨- reduce￨L￨VB￨O￨- severe￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- gastroenteritis￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- outpatient￨L￨NN￨O￨- visits￨L￨NNS￨O￨- ,￨L￨,￨O￨- hospitalizations￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- deaths￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- by￨L￨IN￨O￨- about￨L￨IN￨O￨- 67￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- over￨L￨IN￨O￨- the￨L￨DT￨DURATION￨- first￨L￨JJ￨DURATION￨- 5￨L￨CD￨DURATION￨- years￨L￨NNS￨DURATION￨- of￨L￨IN￨O￨- life￨L￨NN￨O￨- .￨L￨.￨O￨- +Some￨U￨DT￨O￨- previous￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- have￨L￨VBP￨O￨- provided￨L￨VBN￨O￨- broad￨L￨JJ￨O￨- qualitative￨L￨JJ￨O￨- insights￨L￨NNS￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- health￨L￨NN￨O￨- and￨L￨CC￨O￨- economic￨L￨JJ￨O￨- consequences￨L￨NNS￨O￨- of￨L￨IN￨O￨- introducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- vaccines￨L￨NNS￨O￨- into￨L￨IN￨O￨- low-income￨L￨JJ￨O￨- countries￨L￨NNS￨O￨- ,￨L￨,￨O￨- representing￨L￨VBG￨O￨- several￨L￨JJ￨O￨- features￨L￨NNS￨O￨A of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- such￨L￨JJ￨O￨- as￨L￨IN￨O￨- varying￨L￨VBG￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- severity￨L￨NN￨O￨- and￨L￨CC￨O￨- age-dependency￨L￨NN￨O￨- of￨L￨IN￨O￨- clinical￨L￨JJ￨O￨- manifestation￨L￨NN￨O￨- ,￨L￨,￨O￨- in￨L￨IN￨O￨- their￨L￨PRP$￨O￨- model-based￨L￨JJ￨O￨- analyses￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- Cost-effectiveness￨U￨NN￨MISC￨- of￨L￨IN￨MISC￨- Rotavirus￨U￨NNP￨MISC￨- vaccination￨L￨NN￨O￨- in￨L￨IN￨O￨- VietnamSun-Young￨U￨NNP￨O￨- Kim1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Sue￨U￨NNP￨PERSON￨- J￨U￨NNP￨PERSON￨- Goldie1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Joshua￨U￨NNP￨PERSON￨- A￨U￨NNP￨PERSON￨- Salomon1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 9:29￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Kim￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2009Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 18￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 21￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨ORGANIZATION￨- Open￨U￨NNP￨ORGANIZATION￨- Peer￨U￨NNP￨ORGANIZATION￨- Review￨U￨NNP￨ORGANIZATION￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨MISC￨- Background￨U￨NNP￨MISC￨- Rotavirus￨U￨NNP￨MISC￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- most￨L￨RBS￨O￨- common￨L￨JJ￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- severe￨L￨JJ￨O￨- diarrhea￨L￨NN￨O￨- leading￨L￨VBG￨O￨- to￨L￨TO￨O￨- hospitalization￨L￨NN￨O￨- or￨L￨CC￨O￨- disease-specific￨L￨JJ￨O￨- death￨L￨NN￨O￨- among￨L￨IN￨O￨- young￨L￨JJ￨O￨A children￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- extend￨L￨VBP￨O￨- this￨L￨DT￨O￨- work￨L￨NN￨O￨- to￨L￨TO￨O￨- reflect￨L￨VB￨O￨- additional￨L￨JJ￨O￨- features￨L￨NNS￨O￨A of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- e.g.￨L￨FW￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- possibility￨L￨NN￨O￨- of￨L￨IN￨O￨- reinfection￨L￨NN￨O￨- and￨L￨CC￨O￨- varying￨L￨VBG￨O￨- degrees￨L￨NNS￨O￨- of￨L￨IN￨O￨- partial￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- conferred￨L￨VBD￨O￨- by￨L￨IN￨O￨- natural￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- )￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- assess￨L￨VB￨O￨- the￨L￨DT￨O￨- influence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- features￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- cost-effectiveness￨L￨NN￨O￨- of￨L￨IN￨O￨- rotavirus￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- .￨L￨.￨O￨- +Software￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Multi-agent￨U￨JJ￨MISC￨- systems￨L￨NNS￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- :￨L￨:￨O￨- a￨L￨DT￨O￨- first￨L￨JJ￨ORDINAL￨- step￨L￨NN￨O￨- for￨L￨IN￨O￨- computational￨L￨JJ￨O￨A biology￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- vector-borne￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- transmissionBenjamin￨L￨NN￨O￨- Roche1Email￨U￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Jean-François￨U￨NNP￨O￨- Guégan1￨U￨NNP￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- François￨U￨NNP￨O￨- Bousquet3￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 9:435￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Roche￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2008Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 15￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Computational￨U￨NNP￨O￨- biology￨L￨NN￨O￨- is￨L￨VBZ￨O￨- often￨L￨RB￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- or￨L￨CC￨O￨- genomic￨L￨JJ￨O￨- studies￨L￨NNS￨O￨- only￨L￨RB￨O￨- .￨L￨.￨O￨- +So￨U￨RB￨O￨- far￨L￨RB￨O￨- ,￨L￨,￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- remain￨L￨VBP￨O￨- the￨L￨DT￨O￨- main￨L￨JJ￨O￨- tool￨L￨NN￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiological￨L￨JJ￨O￨- and￨L￨CC￨O￨- ecological￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- with￨L￨IN￨O￨- SIR￨U￨NN￨O￨- models￨L￨NNS￨O￨- could￨L￨MD￨O￨- be￨L￨VB￨O￨- seen￨L￨VBN￨O￨- as￨L￨IN￨O￨- an￨L￨DT￨O￨- implicit￨L￨JJ￨O￨- standard￨L￨NN￨O￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨A .￨L￨.￨O￨- +Such￨U￨JJ￨O￨- modeling￨L￨NN￨O￨- systems￨L￨NNS￨O￨- are￨L￨VBP￨O￨- particularly￨L￨RB￨O￨- relevant￨L￨JJ￨O￨- for￨L￨IN￨O￨- the￨L￨DT￨O￨- study￨L￨NN￨O￨- of￨L￨IN￨O￨- complex￨L￨NN￨O￨- systems￨L￨NNS￨O￨- ,￨L￨,￨O￨- like￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemiology￨L￨NN￨O￨A of￨L￨IN￨O￨- emerging￨L￨VBG￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- propose￨L￨VBP￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- computational￨L￨JJ￨O￨A model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- study￨L￨VB￨O￨- the￨L￨DT￨O￨- transmission￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- spatially￨L￨RB￨O￨- explicit￨L￨JJ￨O￨- context￨L￨NN￨O￨- .￨L￨.￨O￨- +Statistical￨U￨JJ￨O￨- models￨L￨NNS￨O￨- based￨L￨VBN￨O￨- only￨L￨RB￨O￨- on￨L￨IN￨O￨- climate￨L￨NN￨O￨A indexes￨L￨NNS￨O￨- work￨L￨VBP￨O￨- well￨L￨RB￨O￨- in￨L￨IN￨O￨- Niger￨U￨NNP￨COUNTRY￨- showing￨L￨VBG￨O￨- that￨L￨IN￨O￨- 25￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- variance￨L￨NN￨O￨- from￨L￨IN￨O￨- year-to-year￨L￨JJ￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- country￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- explained￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- winter￨L￨NN￨DATE￨- climate￨L￨NN￨O￨- but￨L￨CC￨O￨- fail￨L￨VBP￨O￨- to￨L￨TO￨O￨- represent￨L￨VB￨O￨- accurately￨L￨RB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- in￨L￨IN￨O￨- Burkina￨U￨NNP￨COUNTRY￨- Faso￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- A￨U￨DT￨O￨- statistical￨L￨JJ￨O￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- annual￨L￨JJ￨SET￨- incidence￨L￨NN￨O￨- of￨L￨IN￨O￨- MCM￨U￨NN￨O￨- and￨L￨CC￨O￨- climatic￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- has￨L￨VBZ￨O￨- been￨L￨VBN￨O￨- performed￨L￨VBN￨O￨- to￨L￨TO￨O￨- highlight￨L￨VB￨O￨- the￨L￨DT￨O￨- relationships￨L￨NNS￨O￨- between￨L￨IN￨O￨- climate￨L￨NN￨O￨A and￨L￨CC￨O￨- MCM￨U￨NN￨O￨- for￨L￨IN￨O￨- two￨L￨CD￨NUMBER￨- highly￨L￨RB￨O￨- afflicted￨L￨VBD￨O￨- countries￨L￨NNS￨O￨- :￨L￨:￨O￨- Niger￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- Burkina￨U￨NNP￨COUNTRY￨- Faso￨U￨NNP￨COUNTRY￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Relationships￨U￨NNPS￨MISC￨- between￨L￨IN￨O￨- climate￨L￨NN￨O￨A and￨L￨CC￨O￨- year-to-year￨L￨JJ￨O￨- variability￨L￨NN￨O￨- in￨L￨IN￨O￨- meningitis￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- case￨L￨NN￨O￨- study￨L￨NN￨O￨- in￨L￨IN￨O￨- Burkina￨U￨NNP￨COUNTRY￨- Faso￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- NigerPascal￨U￨NNP￨O￨- Yaka1￨U￨NN￨O￨- ,￨L￨,￨O￨- Benjamin￨U￨NNP￨PERSON￨- Sultan2Email￨U￨NNP￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Hélène￨U￨NN￨O￨- Broutin3￨U￨NN￨O￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Serge￨U￨NNP￨PERSON￨- Janicot2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Solenne￨U￨NNP￨O￨- Philippon1￨U￨NN￨O￨- and￨L￨CC￨O￨- Nicole￨U￨NNP￨MISC￨- Fourquet1￨U￨NNP￨MISC￨- Citation￨U￨NNP￨MISC￨- 7:34￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Yaka￨U￨FW￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2008Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 24￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 02￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 02￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Every￨U￨DT￨SET￨- year￨L￨NN￨SET￨- ,￨L￨,￨O￨- West￨U￨NNP￨LOCATION￨- Africa￨U￨NNP￨LOCATION￨- is￨L￨VBZ￨O￨- afflicted￨L￨VBN￨O￨- with￨L￨IN￨O￨- Meningococcal￨U￨JJ￨O￨- Meningitis￨U￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- MCM￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- outbreaks￨L￨NNS￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- resurgence￨L￨NN￨O￨- in￨L￨IN￨O￨- Niger￨U￨NNP￨COUNTRY￨- and￨L￨CC￨O￨- in￨L￨IN￨O￨- Burkina￨U￨NNP￨COUNTRY￨- Faso￨U￨NNP￨COUNTRY￨- is￨L￨VBZ￨O￨- likely￨L￨JJ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- partly￨L￨RB￨O￨- controlled￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- winter￨L￨NN￨DATE￨- climate￨L￨NN￨O￨A through￨L￨IN￨O￨- enhanced￨L￨VBN￨O￨- Harmattan￨U￨NNP￨MISC￨- winds￨L￨NNS￨O￨- .￨L￨.￨O￨- +MCM￨U￨NN￨O￨- epidemics￨L￨NNS￨O￨- occur￨L￨VBP￨O￨- worldwide￨L￨JJ￨O￨- but￨L￨CC￨O￨- the￨L￨DT￨O￨- highest￨L￨JJS￨O￨- incidence￨L￨NN￨O￨A is￨L￨VBZ￨O￨- observed￨L￨VBN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- "￨L￨``￨O￨- meningitis￨L￨NN￨CAUSE_OF_DEATH￨- belt￨L￨NN￨O￨- "￨L￨''￨O￨- (￨L￨-LRB-￨O￨- Fig.￨U￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- of￨L￨IN￨O￨- sub-Saharan￨L￨NNP￨O￨- Africa￨U￨NNP￨LOCATION￨- ,￨L￨,￨O￨- stretching￨L￨VBG￨O￨- from￨L￨IN￨O￨- Senegal￨U￨NNP￨COUNTRY￨- to￨L￨TO￨O￨- Ethiopia￨U￨NNP￨COUNTRY￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +Research￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Clinically￨U￨RB￨MISC￨- immune￨L￨JJ￨O￨- hosts￨L￨NNS￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- refuge￨L￨NN￨O￨- for￨L￨IN￨O￨- drug-sensitive￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨- parasitesEili￨L￨NN￨O￨- Y￨U￨NN￨O￨- Klein1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- L￨U￨NNP￨PERSON￨- Smith3￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Maciej￨U￨NNP￨PERSON￨- F￨U￨NN￨PERSON￨- Boni1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Ramanan￨U￨NNP￨PERSON￨- Laxminarayan1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 4￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 7:67￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Klein￨U￨NNP￨PERSON￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2008Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 28￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 25￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Mutations￨U￨NNS￨O￨- in￨L￨IN￨O￨- Plasmodium￨U￨NN￨LOCATION￨- falciparum￨L￨NN￨O￨- that￨L￨WDT￨O￨- confer￨L￨VBP￨O￨- resistance￨L￨NN￨O￨- to￨L￨TO￨O￨- first-line￨L￨JJ￨O￨- antimalarial￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- have￨L￨VBP￨O￨- spread￨L￨VBN￨O￨- throughout￨L￨IN￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- from￨L￨IN￨O￨- a￨L￨DT￨O￨- few￨L￨JJ￨O￨- independent￨L￨JJ￨RELIGION￨- foci￨L￨NNS￨O￨- ,￨L￨,￨O￨- all￨L￨DT￨O￨- located￨L￨JJ￨O￨- in￨L￨IN￨O￨- areas￨L￨NNS￨O￨- that￨L￨WDT￨O￨- were￨L￨VBD￨O￨- likely￨L￨JJ￨O￨- characterized￨L￨VBN￨O￨- by￨L￨IN￨O￨- low￨L￨JJ￨O￨- or￨L￨CC￨O￨- unstable￨L￨JJ￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Simulations￨U￨NNS￨O￨- found￨L￨VBD￨O￨- that￨L￨IN￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- introduction￨L￨NN￨O￨- of￨L￨IN￨O￨- resistance￨L￨NN￨O￨- into￨L￨IN￨O￨- a￨L￨DT￨O￨- population￨L￨NN￨O￨- ,￨L￨,￨O￨- clinical￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- can￨L￨MD￨O￨- significantly￨L￨RB￨O￨- alter￨L￨VB￨O￨- the￨L￨DT￨O￨- fitness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- parasite￨L￨NN￨O￨A ,￨L￨,￨O￨- and￨L￨CC￨O￨- thereby￨L￨RB￨O￨- impact￨L￨NN￨O￨- the￨L￨DT￨O￨- ability￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- parasite￨L￨NN￨O￨- to￨L￨TO￨O￨- spread￨L￨VB￨O￨- from￨L￨IN￨O￨- an￨L￨DT￨O￨- initial￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- the￨L￨DT￨O￨- effective￨L￨JJ￨O￨- reproductive￨L￨JJ￨O￨- number￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- resistant￨L￨JJ￨O￨- parasite￨L￨NN￨O￨- as￨L￨IN￨O￨- transmission￨L￨NN￨O￨- intensity￨L￨NN￨O￨- increases￨L￨NNS￨O￨- .￨L￨.￨O￨- +This￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- reconsiders￨L￨VBZ￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- immunity￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A and￨L￨CC￨O￨- its￨L￨PRP$￨O￨- impact￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- antimalarial￨L￨JJ￨O￨- drug￨L￨NN￨O￨- resistance￨L￨NN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- assumption￨L￨NN￨O￨- that￨L￨IN￨O￨- immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- are￨L￨VBP￨O￨- infectious￨L￨JJ￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- epidemiological￨L￨JJ￨O￨- models￨L￨NNS￨O￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A have￨L￨VBP￨O￨- generally￨L￨RB￨O￨- ignored￨L￨VBN￨O￨- the￨L￨DT￨O￨- role￨L￨NN￨O￨- of￨L￨IN￨O￨- immune￨L￨JJ￨O￨- individuals￨L￨NNS￨O￨- in￨L￨IN￨O￨- transmission￨L￨NN￨O￨- ,￨L￨,￨O￨- assuming￨L￨VBG￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- do￨L￨VBP￨O￨- not￨L￨RB￨O￨- affect￨L￨VB￨O￨- the￨L￨DT￨O￨- fitness￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- parasite￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- The￨U￨DT￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- constructed￨L￨VBN￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- two-stage￨L￨JJ￨O￨- susceptible-infected-susceptible￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- SIS￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- model￨L￨NN￨TITLE￨- of￨L￨IN￨O￨- malaria￨L￨NN￨CAUSE_OF_DEATH￨A transmission￨L￨NN￨O￨A that￨L￨WDT￨O￨- assumes￨L￨VBZ￨O￨- that￨L￨IN￨O￨- individuals￨L￨NNS￨O￨- build￨L￨VBP￨O￨- up￨L￨RP￨O￨- clinical￨L￨JJ￨O￨- immunity￨L￨NN￨O￨- over￨L￨IN￨O￨- a￨L￨DT￨O￨- period￨L￨NN￨O￨- of￨L￨IN￨O￨- years￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- In￨U￨IN￨O￨- WT￨U￨JJ￨O￨- mice￨L￨NNS￨O￨A ,￨L￨,￨O￨- CpG-ODN￨U￨NN￨O￨- induced￨L￨VBD￨O￨- a￨L￨DT￨O￨- strong￨L￨JJ￨O￨- activation￨L￨NN￨O￨- of￨L￨IN￨O￨- pulmonary￨L￨JJ￨O￨- NFκB￨U￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- a￨L￨DT￨O￨- significant￨L￨JJ￨O￨- increase￨L￨NN￨O￨- in￨L￨IN￨O￨- pulmonary￨L￨JJ￨O￨- TNF-α￨U￨NN￨O￨- and￨L￨CC￨O￨- IL-1β￨U￨NN￨O￨- mRNA/protein￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Clinical￨U￨JJ￨O￨- manifestation￨L￨NN￨O￨- of￨L￨IN￨O￨- inflammation￨L￨NN￨O￨- Clinical￨U￨JJ￨O￨- symptoms￨L￨NNS￨O￨- of￨L￨IN￨O￨- inflammation￨L￨NN￨O￨- were￨L￨VBD￨O￨- monitored￨L￨VBN￨O￨- after￨L￨IN￨O￨- CpG-ODN￨U￨NN￨O￨- application￨L￨NN￨O￨- in￨L￨IN￨O￨- WT￨U￨NNP￨O￨- and￨L￨CC￨O￨- TLR9-D￨U￨NN￨O￨- mice￨L￨NNS￨O￨A .￨L￨.￨O￨- +Increased￨U￨VBN￨O￨- pulmonary￨L￨JJ￨O￨- content￨L￨NN￨O￨- of￨L￨IN￨O￨- lung￨L￨NN￨O￨- myeloperoxidase￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- MPO￨U￨NN￨ORGANIZATION￨- )￨L￨-RRB-￨O￨- was￨L￨VBD￨O￨- documented￨L￨VBN￨O￨- in￨L￨IN￨O￨- WT￨U￨NNP￨O￨- mice￨L￨NNS￨O￨A following￨L￨VBG￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- CpG-ODN￨U￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- contrast￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- CpG-ODN-induced￨U￨JJ￨O￨- inflammatory￨L￨JJ￨O￨- response￨L￨NN￨O￨- was￨L￨VBD￨O￨- abolished￨L￨VBN￨O￨- in￨L￨IN￨O￨- TLR9-D￨U￨NN￨O￨- mice￨L￨NNS￨O￨A .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- Wild-type￨U￨JJ￨O￨- (￨L￨-LRB-￨O￨- WT￨U￨JJ￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- TLR9-deficient￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- TLR9-D￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- mice￨L￨NNS￨O￨A received￨L￨VBD￨O￨- CpG-ODN￨U￨NN￨O￨- intraperitoneally￨L￨RB￨O￨- (￨L￨-LRB-￨O￨- 1668-Thioat￨L￨NN￨O￨- ,￨L￨,￨O￨- 1￨L￨CD￨NUMBER￨- nmol/g￨L￨NN￨O￨- BW￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- and￨L￨CC￨O￨- were￨L￨VBD￨O￨- observed￨L￨VBN￨O￨- for￨L￨IN￨O￨- up￨L￨RB￨DURATION￨- to￨L￨TO￨DURATION￨- 6￨L￨CD￨DURATION￨- hrs￨L￨NNS￨DURATION￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- A￨U￨NNP￨O￨- rationale￨L￨NN￨O￨- for￨L￨IN￨O￨- continuing￨L￨VBG￨O￨- mass￨L￨NN￨O￨- antibiotic￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- for￨L￨IN￨O￨- trachomaKathryn￨L￨NN￨O￨- J￨U￨NN￨O￨- Ray1￨U￨NN￨O￨- ,￨L￨,￨O￨- 2Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Travis￨U￨NNP￨O￨- C￨U￨NNP￨O￨- Porco1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Kevin￨U￨NNP￨PERSON￨- C￨U￨NNP￨O￨- Hong1￨U￨NN￨O￨- ,￨L￨,￨O￨- David￨U￨NNP￨PERSON￨- C￨U￨NNP￨PERSON￨- Lee1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- Wondu￨U￨NNP￨PERSON￨- Alemayehu4￨U￨NNP￨O￨- ,￨L￨,￨O￨- Muluken￨U￨JJ￨O￨- Melese4￨U￨NN￨O￨- ,￨L￨,￨O￨- Takele￨U￨NNP￨O￨- Lakew4￨U￨NN￨O￨- ,￨L￨,￨O￨- Elizabeth￨U￨NNP￨PERSON￨- Yi1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Jenafir￨U￨NNP￨O￨- House1￨U￨NN￨O￨- ,￨L￨,￨O￨- Jaya￨U￨NNP￨PERSON￨- D￨U￨NNP￨O￨- Chidambaram1￨U￨NN￨O￨- ,￨L￨,￨O￨- John￨U￨NNP￨PERSON￨- P￨U￨NN￨PERSON￨- Whitcher1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Bruce￨U￨NNP￨PERSON￨- D￨U￨NNP￨PERSON￨- Gaynor1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- Thomas￨U￨NNP￨PERSON￨- M￨U￨NN￨PERSON￨- Lietman1￨U￨NN￨PERSON￨- ,￨L￨,￨O￨- 5￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 6￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 7￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- 7:91￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Ray￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2007Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨A Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 07￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- World￨U￨NNP￨ORGANIZATION￨- Health￨U￨NNP￨ORGANIZATION￨- Organization￨U￨NNP￨ORGANIZATION￨- recommends￨L￨VBZ￨O￨- periodic￨L￨JJ￨O￨- mass￨L￨NN￨O￨- antibiotic￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- to￨L￨TO￨O￨- reduce￨L￨VB￨O￨- the￨L￨DT￨O￨- ocular￨L￨JJ￨O￨- strains￨L￨NNS￨O￨- of￨L￨IN￨O￨- chlamydia￨L￨NN￨O￨- that￨L￨WDT￨O￨- cause￨L￨VBP￨O￨- trachoma￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- world￨L￨NN￨O￨- 's￨L￨POS￨O￨- leading￨L￨VBG￨O￨- cause￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- blindness￨L￨NN￨O￨- .￨L￨.￨O￨- +However￨U￨RB￨O￨- ,￨L￨,￨O￨- if￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- eliminated￨L￨VBN￨O￨- in￨L￨IN￨O￨- every￨L￨DT￨O￨- individual￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- gradually￨L￨RB￨O￨- return￨L￨VB￨O￨- back￨L￨RB￨O￨- into￨L￨IN￨O￨- the￨L￨DT￨O￨- community￨L￨NN￨O￨- ,￨L￨,￨O￨- so￨L￨RB￨O￨- often￨L￨RB￨O￨- repeated￨L￨VBN￨O￨A treatments￨L￨NNS￨O￨- are￨L￨VBP￨O￨- necessary￨L￨JJ￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- to￨L￨TO￨O￨- simulate￨L￨VB￨O￨- the￨L￨DT￨O￨- effect￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- treatment￨L￨NN￨O￨A programs￨L￨NNS￨O￨- in￨L￨IN￨O￨- terms￨L￨NNS￨O￨- of￨L￨IN￨O￨- local￨L￨JJ￨O￨- elimination￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- use￨L￨VBP￨O￨- mathematical￨L￨JJ￨O￨- models￨L￨NNS￨O￨- to￨L￨TO￨O￨- demonstrate￨L￨VB￨O￨- that￨L￨IN￨O￨- repeated￨L￨VBN￨O￨A antibiotic￨L￨JJ￨O￨- distributions￨L￨NNS￨O￨- can￨L￨MD￨O￨- eliminate￨L￨VB￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- reasonable￨L￨JJ￨O￨- time￨L￨NN￨O￨- period￨L￨NN￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- Simulations￨U￨NNS￨O￨- show￨L￨VBP￨O￨- that￨L￨IN￨O￨- the￨L￨DT￨O￨- average￨L￨JJ￨O￨- prevalence￨L￨NN￨O￨- of￨L￨IN￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- across￨L￨IN￨O￨- all￨L￨DT￨O￨- villages￨L￨NNS￨O￨- progressively￨L￨RB￨O￨- decreases￨L￨VBZ￨O￨- after￨L￨IN￨O￨- each￨L￨DT￨O￨- treatment￨L￨NN￨O￨A ,￨L￨,￨O￨- as￨L￨RB￨O￨- long￨L￨RB￨O￨- as￨L￨IN￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- and￨L￨CC￨O￨- coverage￨L￨NN￨O￨- of￨L￨IN￨O￨- antibiotics￨L￨NNS￨O￨- are￨L￨VBP￨O￨- high￨L￨JJ￨O￨- enough￨L￨RB￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- We￨U￨PRP￨O￨- show￨L￨VBP￨O￨- how￨L￨WRB￨O￨- our￨L￨PRP$￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- closely￨L￨RB￨O￨- related￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- classical￨L￨JJ￨O￨- SIS￨U￨NN￨O￨- model￨L￨NN￨TITLE￨- in￨L￨IN￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- find￨L￨VB￨O￨- that￨L￨DT￨O￨- :￨L￨:￨O￨- depending￨L￨VBG￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- relation￨L￨NN￨O￨- between￨L￨IN￨O￨- the￨L￨DT￨O￨- rate￨L￨NN￨O￨- at￨L￨IN￨O￨- which￨L￨WDT￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- are￨L￨VBP￨O￨- eliminated￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- immune￨L￨JJ￨O￨- system￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- within￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- effective￨L￨JJ￨O￨- population￨L￨NN￨O￨- size￨L￨NN￨O￨- ,￨L￨,￨O￨- genetic￨L￨JJ￨O￨A diversity￨L￨NN￨O￨A increases￨L￨VBZ￨O￨- with￨L￨IN￨O￨- R0￨U￨NN￨O￨- or￨L￨CC￨O￨- peaks￨L￨VBZ￨O￨- at￨L￨IN￨O￨- intermediate￨L￨JJ￨O￨- R0￨U￨NN￨O￨- levels￨L￨NNS￨O￨- ;￨L￨:￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- diversity￨L￨NN￨O￨- in￨L￨IN￨O￨- this￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- are￨L￨VBP￨O￨- in￨L￨IN￨O￨- general￨L￨JJ￨TITLE￨- similar￨L￨JJ￨O￨- to￨L￨TO￨O￨- those￨L￨DT￨O￨- expected￨L￨VBN￨O￨- under￨L￨IN￨O￨- the￨L￨DT￨O￨- standard￨L￨JJ￨O￨- neutral￨L￨JJ￨IDEOLOGY￨- model￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- in￨L￨IN￨O￨- a￨L￨DT￨O￨- scale￨L￨NN￨O￨- free￨L￨JJ￨O￨- network￨L￨NN￨O￨- and￨L￨CC￨O￨- for￨L￨IN￨O￨- low￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- a￨L￨DT￨O￨- distortion￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- neutral￨L￨JJ￨IDEOLOGY￨- mutation￨L￨NN￨O￨- frequency￨L￨NN￨O￨- spectrum￨L￨NN￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- observed￨L￨VBN￨O￨- ;￨L￨:￨O￨- highly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- hosts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- hubs￨L￨NNS￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- network￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- show￨L￨VBP￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- diversity￨L￨NN￨O￨- different￨L￨JJ￨O￨- from￨L￨IN￨O￨- poorly￨L￨RB￨O￨- connected￨L￨VBN￨O￨- individuals￨L￨NNS￨O￨- ,￨L￨,￨O￨- namely￨L￨RB￨O￨- higher￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- ,￨L￨,￨O￨- lower￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨- differentiation￨L￨NN￨O￨- and￨L￨CC￨O￨- larger￨L￨JJR￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- Tajima￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- D.￨U￨NNP￨O￨- Furthermore￨U￨RB￨O￨- for￨L￨IN￨O￨- low￨L￨JJ￨O￨- values￨L￨NNS￨O￨- of￨L￨IN￨O￨- R0￨U￨NN￨O￨- ,￨L￨,￨O￨- very￨L￨RB￨O￨- heterogeneous￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- contact￨L￨NN￨O￨- structures￨L￨NNS￨O￨- lead￨L￨VBP￨O￨- to￨L￨TO￨O￨- lower￨L￨JJR￨O￨- levels￨L￨NNS￨O￨- of￨L￨IN￨O￨- diversity￨L￨NN￨O￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- addition￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- agent￨L￨NN￨O￨- variation￨L￨NN￨O￨- can￨L￨MD￨O￨- ,￨L￨,￨O￨- under￨L￨IN￨O￨- certain￨L￨JJ￨O￨- circumstances￨L￨NNS￨O￨- ,￨L￨,￨O￨- be￨L￨VB￨O￨- used￨L￨VBN￨O￨- to￨L￨TO￨O￨- infer￨L￨VB￨O￨- host￨L￨NN￨TITLE￨- population￨L￨NN￨O￨- history￨L￨NN￨O￨- NumericCitation￨U￨NNP￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- level￨L￨NN￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- agent￨L￨NN￨O￨- genetic￨L￨JJ￨O￨A structure￨L￨NN￨O￨- may￨L￨MD￨O￨- reflect￨L￨VB￨O￨- its￨L￨PRP$￨O￨- evolutionary￨L￨JJ￨O￨- potential￨L￨JJ￨O￨- NumericCitation￨U￨NN￨O￨- .￨L￨.￨O￨- +Here￨U￨RB￨O￨- we￨L￨PRP￨O￨- study￨L￨VB￨O￨- a￨L￨DT￨O￨- model￨L￨NN￨TITLE￨- for￨L￨IN￨O￨- assessing￨L￨VBG￨O￨- the￨L￨DT￨O￨- levels￨L￨NNS￨O￨- and￨L￨CC￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A diversity￨L￨NN￨O￨A in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- .￨L￨.￨O￨- +KeywordsInfectious￨U￨NNP￨MISC￨- AgentInfected￨U￨NNP￨MISC￨- HostContact￨U￨NNP￨MISC￨- StructureScale￨U￨NNP￨MISC￨- Free￨U￨NNP￨MISC￨- NetworkContact￨U￨NNP￨MISC￨- Network￨U￨NNP￨MISC￨- BackgroundPatterns￨U￨NNP￨MISC￨- of￨L￨IN￨O￨- genetic￨L￨JJ￨O￨A diversity￨L￨NN￨O￨A in￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨O￨- agents￨L￨NNS￨O￨- contain￨L￨VBP￨O￨- important￨L￨JJ￨O￨- information￨L￨NN￨O￨- about￨L￨IN￨O￨- their￨L￨PRP$￨O￨- epidemiology￨L￨NN￨O￨- and￨L￨CC￨O￨- evolution￨L￨NN￨O￨- .￨L￨.￨O￨- +Other￨U￨JJ￨O￨- control￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- like￨L￨IN￨O￨- pharmaceutical￨L￨JJ￨O￨- (￨L￨-LRB-￨O￨- antiviral￨L￨JJ￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- non-pharmaceutical￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- reduction￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- rates￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- NumericCitation￨U￨NNP￨O￨- will￨L￨MD￨O￨- have￨L￨VB￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- implemented.The￨L￨JJ￨O￨- use￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨A during￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- seems￨L￨VBZ￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- the￨L￨DT￨O￨- treatment￨L￨NN￨O￨- of￨L￨IN￨O￨- choice￨L￨NN￨O￨- at￨L￨IN￨O￨- present￨L￨JJ￨DATE￨- [￨L￨-LRB-￨O￨- 9￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 12￨L￨CD￨NUMBER￨- ]￨L￨-RRB-￨O￨- ,￨L￨,￨O￨- but￨L￨CC￨O￨- not￨L￨RB￨O￨- all￨L￨DT￨O￨- countries￨L￨NNS￨O￨- can￨L￨MD￨O￨- afford￨L￨VB￨O￨- stockpiling￨L￨NN￨O￨- enough￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨- .￨L￨.￨O￨- +In￨U￨IN￨O￨- particular￨L￨JJ￨O￨- ,￨L￨,￨O￨- we￨L￨PRP￨O￨- examine￨L￨VBP￨O￨- how￨L￨WRB￨O￨- intervention￨L￨NN￨O￨- schedules￨L￨NNS￨O￨- ,￨L￨,￨O￨- restricted￨L￨JJ￨O￨- stockpiles￨L￨NNS￨O￨- and￨L￨CC￨O￨- contact￨L￨NN￨O￨- reduction￨L￨NN￨O￨A (￨L￨-LRB-￨O￨- social￨L￨JJ￨O￨- distancing￨L￨VBG￨O￨- measures￨L￨NNS￨O￨- and￨L￨CC￨O￨- isolation￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- determine￨L￨VBP￨O￨- the￨L￨DT￨O￨- course￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- wave￨L￨NN￨O￨- and￨L￨CC￨O￨- the￨L￨DT￨O￨- success￨L￨NN￨O￨- of￨L￨IN￨O￨- interventions￨L￨NNS￨O￨- .￨L￨.￨O￨- +Results￨U￨NNS￨O￨- A￨U￨DT￨O￨- timely￨L￨JJ￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- antiviral￨L￨JJ￨O￨- drugs￨L￨NNS￨CRIMINAL_CHARGE￨A combined￨L￨VBN￨O￨- with￨L￨IN￨O￨- a￨L￨DT￨O￨- quick￨L￨JJ￨O￨- implementation￨L￨NN￨O￨- of￨L￨IN￨O￨- contact￨L￨NN￨O￨- reduction￨L￨NN￨O￨- measures￨L￨NNS￨O￨- is￨L￨VBZ￨O￨- required￨L￨VBN￨O￨- to￨L￨TO￨O￨- substantially￨L￨RB￨O￨- protract￨L￨VB￨O￨- the￨L￨DT￨O￨- peak￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- and￨L￨CC￨O￨- reduce￨L￨VB￨O￨- its￨L￨PRP$￨O￨- height￨L￨NN￨O￨- .￨L￨.￨O￨- +Methods￨U￨NNS￨O￨- We￨U￨PRP￨O￨- use￨L￨VBP￨O￨- the￨L￨DT￨O￨- freely￨L￨RB￨O￨- available￨L￨JJ￨O￨- planning￨L￨NN￨O￨- tool￨L￨NN￨O￨- InfluSim￨U￨NNP￨O￨- to￨L￨TO￨O￨- investigate￨L￨VB￨O￨- how￨L￨WRB￨O￨- pharmaceutical￨L￨JJ￨O￨- and￨L￨CC￨O￨- non-pharmaceutical￨L￨JJ￨O￨- interventions￨L￨NNS￨O￨- can￨L￨MD￨O￨- mitigate￨L￨VB￨O￨- an￨L￨DT￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨NN￨O￨A .￨L￨.￨O￨- +An￨U￨DT￨O￨- epidemic￨L￨JJ￨O￨- can￨L￨NN￨O￨- also￨L￨RB￨O￨- be￨L￨VB￨O￨- mitigated￨L￨VBN￨O￨- by￨L￨IN￨O￨- reducing￨L￨VBG￨O￨- contact￨L￨NN￨O￨A rates￨L￨NNS￨O￨A in￨L￨IN￨O￨- the￨L￨DT￨O￨- general￨L￨JJ￨TITLE￨- population￨L￨NN￨O￨- and￨L￨CC￨O￨- by￨L￨IN￨O￨- decreasing￨L￨VBG￨O￨- the￨L￨DT￨O￨- infectivity￨L￨NN￨O￨- of￨L￨IN￨O￨- cases￨L￨NNS￨O￨- NumericCitation￨U￨NNP￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- initiated￨L￨VBD￨O￨- replicate￨L￨VB￨O￨- longitudinal￨L￨JJ￨O￨- host-schistosome￨L￨JJ￨O￨- co-selection￨L￨NN￨O￨- trials￨L￨NNS￨O￨- under￨L￨IN￨O￨- different￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- genotype￨L￨NN￨O￨- combinations￨L￨NNS￨O￨- :￨L￨:￨O￨- Schistosoma￨U￨NN￨O￨- mansoni￨L￨NN￨O￨- parasite￨L￨NN￨O￨- lines￨L￨NNS￨O￨A were￨L￨VBD￨O￨- co-selected￨L￨VBN￨O￨- with￨L￨IN￨O￨- populations￨L￨NNS￨O￨- of￨L￨IN￨O￨- either￨L￨CC￨O￨- previously￨L￨RB￨DATE￨- resistant-selected￨L￨JJ￨O￨- Biomphalaria￨U￨NN￨O￨- glabrata￨L￨NN￨O￨- host￨L￨NN￨TITLE￨- genotypes￨L￨NNS￨O￨- ,￨L￨,￨O￨- or￨L￨CC￨O￨- unselected￨L￨JJ￨O￨- susceptible￨L￨JJ￨O￨- B.￨U￨NNP￨O￨- KeywordsParasite￨U￨NNP￨O￨- InfectivityIntermediate￨U￨NNP￨O￨- HostSimian￨U￨NNP￨O￨- Immunodeficiency￨U￨NN￨O￨- VirusDefinitive￨U￨JJ￨O￨- HostUnweighted￨U￨NNP￨O￨- Pair￨U￨NNP￨O￨- Group￨U￨NNP￨O￨- Method￨U￨NNP￨O￨- With￨U￨IN￨O￨- Arithmetic￨U￨NNP￨O￨- BackgroundHost-parasite￨U￨NNP￨O￨- coevolution￨L￨NN￨O￨- is￨L￨VBZ￨O￨- driven￨L￨VBN￨O￨- by￨L￨IN￨O￨- the￨L￨DT￨O￨- reciprocal￨L￨JJ￨O￨- evolution￨L￨NN￨O￨- of￨L￨IN￨O￨- host￨L￨NN￨TITLE￨- resistance￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- infectivity￨L￨NN￨O￨- and/or￨L￨CC￨O￨- virulence￨L￨NN￨O￨- NumericCitation￨U￨NN￨O￨- (￨L￨-LRB-￨O￨- see￨L￨VB￨O￨- Appendix￨U￨NNP￨O￨- for￨L￨IN￨O￨- definitions￨L￨NNS￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Host-parasite￨U￨JJ￨O￨- coevolution￨L￨NN￨O￨A requires￨L￨VBZ￨O￨- additive￨L￨JJ￨O￨- genetic￨L￨JJ￨O￨- variation￨L￨NN￨O￨- in￨L￨IN￨O￨- the￨L￨DT￨O￨- relevant￨L￨JJ￨O￨- host￨L￨NN￨TITLE￨- and￨L￨CC￨O￨- parasite￨L￨NN￨O￨- traits￨L￨NNS￨O￨- ,￨L￨,￨O￨- reciprocal￨L￨JJ￨O￨- effects￨L￨NNS￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- fitness￨L￨NN￨O￨- traits￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- two￨L￨CD￨NUMBER￨- populations￨L￨NNS￨O￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- a￨L￨DT￨O￨- dependence￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- outcome￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- host-parasite￨L￨JJ￨O￨- interaction￨L￨NN￨O￨- on￨L￨IN￨O￨- the￨L￨DT￨O￨- combinations￨L￨NNS￨O￨- of￨L￨IN￨O￨- genotypes￨L￨NNS￨O￨- involved￨L￨VBN￨O￨- .￨L￨.￨O￨- +Sources￨U￨NNS￨O￨- :￨L￨:￨O￨- A￨U￨DT￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- B￨U￨NN￨O￨- NumericCitation￨U￨NN￨O￨- ,￨L￨,￨O￨- C￨U￨NN￨O￨- assumed￨L￨VBD￨O￨- ,￨L￨,￨O￨- D￨U￨NNP￨O￨- NumericCitation￨U￨NNP￨O￨- Table￨U￨NNP￨O￨- 5￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- to￨L￨TO￨O￨- 5960￨L￨CD￨DATE￨- and￨L￨CC￨O￨- olderHospitalized￨L￨VBN￨O￨- fraction￨L￨NN￨O￨- h￨L￨NN￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- of￨L￨IN￨O￨- untreated￨L￨JJ￨O￨- severe￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- low￨L￨JJ￨O￨- risk￨L￨NN￨O￨- group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- r￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 0.187￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 2.339￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 3.560￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- high￨L￨JJ￨O￨- risk￨L￨NN￨O￨- group￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- r￨L￨NN￨O￨- =￨L￨JJ￨O￨- r￨L￨NN￨O￨- 2￨L￨CD￨NUMBER￨- )￨L￨-RRB-￨O￨- 1.333￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 2.762￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- 7.768￨L￨CD￨NUMBER￨- se￨L￨FW￨O￨- fatality￨L￨NN￨O￨- d￨L￨NN￨O￨- a￨L￨DT￨O￨- of￨L￨IN￨O￨- hospitalized￨L￨VBN￨O￨- cases5￨L￨NN￨O￨- .541￨L￨CD￨PERCENT￨- .5319.505￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- Independent￨U￨NNP￨RELIGION￨- of￨L￨IN￨O￨- age￨L￨NN￨O￨- a￨L￨DT￨O￨- and￨L￨CC￨O￨- risk￨L￨VB￨O￨- group￨L￨NN￨O￨- r￨L￨NN￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- c￨L￨NN￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- A￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 33￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- of￨L￨IN￨O￨- infections￨L￨NNS￨CAUSE_OF_DEATH￨- result￨L￨VBP￨O￨- in￨L￨IN￨O￨- asymptomatic￨L￨JJ￨O￨- cases￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- fraction￨L￨NN￨O￨- c￨L￨NN￨O￨- a￨L￨DT￨O￨- ,￨L￨,￨O￨- r￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- M￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- =￨L￨JJ￨O￨- 33.5￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- become￨L￨VBN￨O￨- moderately￨L￨RB￨O￨- sick￨L￨JJ￨O￨A and￨L￨CC￨O￨- the￨L￨DT￨O￨- remaining￨L￨VBG￨O￨- fraction￨L￨NN￨O￨- develops￨L￨VBZ￨O￨- severe￨L￨JJ￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Software￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Access￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- The￨U￨NNP￨MISC￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- pandemic￨L￨JJ￨O￨- preparedness￨L￨NN￨O￨- planning￨L￨NN￨O￨A tool￨L￨NN￨O￨- InfluSim￨U￨NNP￨O￨- Martin￨U￨NNP￨O￨- Eichner1￨U￨NN￨O￨- ,￨L￨,￨O￨- Markus￨U￨NNP￨PERSON￨- Schwehm1Email￨U￨NNP￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Hans-Peter￨U￨NNP￨PERSON￨- Duerr1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Stefan￨U￨NNP￨PERSON￨- O￨U￨NNP￨O￨- Brockmann2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:17￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Eichner￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2007Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 31￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 13￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨MISC￨- Open￨U￨NNP￨MISC￨- Peer￨U￨NNP￨MISC￨- Review￨U￨NNP￨MISC￨- reports￨L￨VBZ￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- Planning￨U￨NNP￨O￨- public￨L￨JJ￨O￨- health￨L￨NN￨O￨- responses￨L￨NNS￨O￨- against￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- relies￨L￨VBZ￨O￨- on￨L￨IN￨O￨- predictive￨L￨JJ￨O￨- models￨L￨NNS￨O￨- by￨L￨IN￨O￨- which￨L￨WDT￨O￨- the￨L￨DT￨O￨- impact￨L￨NN￨O￨- of￨L￨IN￨O￨- different￨L￨JJ￨O￨- intervention￨L￨NN￨O￨- strategies￨L￨NNS￨O￨- can￨L￨MD￨O￨- be￨L￨VB￨O￨- evaluated￨L￨VBN￨O￨- .￨L￨.￨O￨- +A￨U￨DT￨O￨- minimum￨L￨NN￨O￨- requirement￨L￨NN￨O￨- for￨L￨IN￨O￨- a￨L￨DT￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- planning￨L￨NN￨O￨A tool￨L￨NN￨O￨- is￨L￨VBZ￨O￨- a￨L￨DT￨O￨- dynamic￨L￨JJ￨O￨- modelling￨L￨NN￨O￨- structure￨L￨NN￨O￨- which￨L￨WDT￨O￨- allows￨L￨VBZ￨O￨- investigation￨L￨NN￨O￨- of￨L￨IN￨O￨- time-dependent￨L￨JJ￨O￨- variables￨L￨NNS￨O￨- like￨L￨IN￨O￨- incidence￨L￨NN￨O￨- ,￨L￨,￨O￨- height￨L￨NN￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- epidemic￨L￨JJ￨O￨- peak￨L￨NN￨O￨- ,￨L￨,￨O￨- antiviral￨L￨JJ￨O￨- availability￨L￨NN￨O￨- etc￨L￨NN￨O￨- .￨L￨.￨O￨- +Table￨U￨NNP￨O￨- 4￨L￨CD￨NUMBER￨- Sojourn￨U￨NNP￨O￨- times￨L￨NNS￨O￨- Periodaverage￨U￨JJ￨O￨- durationstagescoefficient￨L￨NN￨O￨- of￨L￨IN￨O￨- variationLatent￨L￨JJ￨O￨- period￨L￨NN￨O￨- D￨U￨NN￨O￨- E￨U￨NN￨O￨- =￨L￨JJ￨O￨- 1.9￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨A A￨U￨DT￨O￨- n￨L￨NN￨O￨- =￨L￨JJ￨O￨- 737.8￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- A￨U￨NN￨O￨- Fully￨U￨RB￨O￨- contagious￨L￨JJ￨O￨- period￨L￨NN￨O￨- asymptomatic￨L￨JJ￨O￨- and￨L￨CC￨O￨- moderately￨L￨RB￨O￨- sick￨L￨JJ￨O￨- adults4￨L￨NN￨O￨- .1￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- A￨U￨DT￨O￨- m￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1922.9￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- A￨U￨NN￨O￨- others7￨L￨NN￨O￨- .0￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- B￨U￨NN￨O￨- m￨L￨NN￨O￨- =￨L￨JJ￨O￨- 1922.9￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- C￨U￨NN￨O￨- Period￨U￨NN￨O￨- of￨L￨IN￨O￨- convalescence￨L￨NN￨O￨- D￨U￨NN￨O￨- R￨U￨NN￨O￨- =￨L￨JJ￨O￨- 5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- D￨U￨NN￨O￨- j￨L￨NN￨O￨- =￨L￨JJ￨O￨- 933.3￨L￨CD￨PERCENT￨- %￨L￨NN￨PERCENT￨- C￨U￨NN￨O￨- Distribution￨U￨NN￨O￨- of￨L￨IN￨O￨- sojourn￨L￨NN￨O￨- times￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- the￨L￨DT￨O￨- last￨L￨JJ￨O￨- two￨L￨CD￨NUMBER￨- stages￨L￨NNS￨O￨- of￨L￨IN￨O￨- the￨L￨DT￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- are￨L￨VBP￨O￨- used￨L￨VBN￨O￨- as￨L￨IN￨O￨- early￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- average￨L￨JJ￨O￨- duration￨L￨NN￨O￨- of￨L￨IN￨O￨- D￨U￨NN￨O￨- L￨U￨NN￨O￨- =￨L￨JJ￨O￨- 0.5￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Source￨U￨NN￨O￨- :￨L￨:￨O￨- NumericCitation￨U￨NNP￨ORGANIZATION￨- Table￨U￨NNP￨ORGANIZATION￨- 3￨L￨CD￨NUMBER￨- WAIFW￨U￨NN￨ORGANIZATION￨- matrix￨L￨NN￨O￨A 0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 56￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 1213￨L￨CD￨DATE￨- –￨L￨:￨O￨- 1920￨L￨CD￨DATE￨- –￨L￨:￨O￨- 3940￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5960￨L￨CD￨NUMBER￨- +0￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5169.1431.4717.7634.5015.8311.476￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 1231.47274.5132.3134.8620.6111.5013￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 1917.7632.31224.2550.7537.5214.9620￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 3934.5034.8650.7575.6649.4525.0840￨L￨CD￨NUMBER￨- –￨L￨:￨O￨- 5915.8320.6137.5249.4561.2632.9960￨L￨CD￨NUMBER￨- +11.4711.5014.9625.0832.9954.23￨L￨CD￨NUMBER￨- The￨U￨DT￨O￨- who-acquires-infection-from-whom￨L￨NN￨O￨- matrix￨L￨NN￨O￨- K￨U￨NN￨O￨- a￨L￨DT￨O￨- s￨L￨NNS￨O￨- ,￨L￨,￨O￨- a￨L￨DT￨O￨- i￨L￨FW￨O￨- @￨L￨SYM￨O￨- @￨L￨SYM￨O￨- +￨L￨CC￨O￨- =￨L￨JJ￨O￨- feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY￨L￨NN￨O￨- =￨L￨JJ￨O￨- wiFfYdH8Gipec8Eeeu0xXdbba9frFj0￨L￨NN￨O￨- =￨L￨JJ￨O￨- OqFfea0dXdd9vqai￨U￨NN￨O￨- =￨L￨JJ￨O￨- hGuQ8kuc9pgc9s8qqaq￨L￨NN￨O￨- =￨L￨JJ￨O￨- dirpe0xb9q8qiLsFr0￨L￨NN￨O￨- =￨L￨JJ￨O￨- vr0￨L￨NN￨O￨- =￨L￨JJ￨O￨- @￨L￨SYM￨O￨- shows￨L￨VBZ￨O￨- the￨L￨DT￨O￨- frequency￨L￨NN￨O￨- of￨L￨IN￨O￨- contacts￨L￨NNS￨O￨- (￨L￨-LRB-￨O￨- per￨L￨IN￨O￨- week￨L￨NN￨DURATION￨- per￨L￨IN￨O￨- person￨L￨NN￨O￨- )￨L￨-RRB-￨O￨- between￨L￨IN￨O￨- different￨L￨JJ￨O￨- age￨L￨NN￨O￨- classes￨L￨NNS￨O￨- .￨L￨.￨O￨- +Research￨U￨NN￨O￨- article￨L￨NN￨O￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Comparative￨U￨JJ￨MISC￨- analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- ESTs￨U￨NNS￨O￨- involved￨L￨VBN￨O￨- in￨L￨IN￨O￨- grape￨L￨NN￨O￨- responses￨L￨NNS￨O￨- to￨L￨TO￨O￨- Xylella￨U￨NNP￨LOCATION￨- fastidiosa￨L￨FW￨O￨- infectionHong￨L￨NNP￨O￨- Lin￨U￨NNP￨O￨- †￨L￨SYM￨O￨- 1Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Harshavardhan￨U￨NNP￨O￨- Doddapaneni￨U￨NNP￨O￨- †￨L￨NN￨O￨- 1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- 2￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- Yuri￨U￨NNP￨PERSON￨- Takahashi2￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- 3￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- M￨U￨NN￨O￨- Andrew￨U￨NNP￨O￨- Walker2￨U￨NNP￨O￨- †￨L￨NNP￨O￨- Citation￨U￨NNP￨O￨- 7:8￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Lin￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2007Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 23￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨A Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 22￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Background￨U￨NNP￨O￨- The￨U￨NNP￨O￨- gram-negative￨L￨JJ￨O￨- bacterium￨L￨NN￨O￨- Xylella￨U￨NNP￨O￨- fastidiosa￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Xf￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- is￨L￨VBZ￨O￨- the￨L￨DT￨O￨- causal￨L￨JJ￨O￨- agent￨L￨NN￨O￨- of￨L￨IN￨O￨- Pierce￨U￨NNP￨PERSON￨- 's￨L￨POS￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- (￨L￨-LRB-￨O￨- PD￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- in￨L￨IN￨O￨- grape￨L￨NN￨O￨- as￨L￨RB￨O￨- well￨L￨RB￨O￨- as￨L￨IN￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- of￨L￨IN￨O￨- many￨L￨JJ￨O￨- fruit￨L￨NN￨O￨- and￨L￨CC￨O￨- ornamental￨L￨JJ￨O￨- plants￨L￨NNS￨O￨- .￨L￨.￨O￨- +Once￨U￨RB￨DATE￨- resistance￨L￨NN￨O￨A genes￨L￨NNS￨O￨- are￨L￨VBP￨O￨- identified￨L￨VBN￨O￨- it￨L￨PRP￨O￨- may￨L￨MD￨O￨- be￨L￨VB￨O￨- possible￨L￨JJ￨O￨- to￨L￨TO￨O￨- directly￨L￨RB￨O￨- introduce￨L￨VB￨O￨- resistance￨L￨NN￨O￨- into￨L￨IN￨O￨- elite￨L￨JJ￨O￨- wine￨L￨NN￨O￨- grape￨L￨NN￨O￨- cultivars￨L￨NNS￨O￨- by￨L￨IN￨O￨- transgenic￨L￨JJ￨O￨- technologies.Systemic￨L￨JJ￨O￨- infection￨L￨NN￨CAUSE_OF_DEATH￨- studies￨L￨NNS￨O￨- under￨L￨IN￨O￨- greenhouse￨L￨NN￨O￨- conditions￨L￨NNS￨O￨- have￨L￨VBP￨O￨- shown￨L￨VBN￨O￨- differential￨L￨JJ￨O￨- distribution￨L￨NN￨O￨- patterns￨L￨NNS￨O￨- of￨L￨IN￨O￨- X.￨U￨NNP￨O￨- +Results￨U￨NNS￨O￨- Basic￨U￨JJ￨O￨- reproduction￨L￨NN￨O￨- number￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- R0￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- values￨L￨NNS￨O￨- for￨L￨IN￨O￨- three￨L￨CD￨NUMBER￨- possible￨L￨JJ￨O￨- scenarios￨L￨NNS￨O￨- ranged￨L￨VBD￨O￨A between￨L￨IN￨O￨- 1.3￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 3.1￨L￨CD￨NUMBER￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- corresponding￨L￨JJ￨O￨- average￨L￨JJ￨O￨- latent￨L￨JJ￨O￨- period￨L￨NN￨O￨- and￨L￨CC￨O￨- infectious￨L￨JJ￨O￨- period￨L￨NN￨O￨- estimates￨L￨NNS￨O￨- ranged￨L￨VBD￨O￨- between￨L￨IN￨O￨- 0.7￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 1.3￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- ,￨L￨,￨O￨- and￨L￨CC￨O￨- 0.2￨L￨CD￨NUMBER￨- and￨L￨CC￨O￨- 0.3￨L￨CD￨DURATION￨- days￨L￨NNS￨DURATION￨- respectively￨L￨RB￨O￨- .￨L￨.￨O￨- +Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A pandemic￨L￨JJ￨O￨A estimated￨L￨VBN￨O￨- by￨L￨IN￨O￨- mathematical￨L￨JJ￨O￨- modellingGabriel￨L￨NN￨O￨- Sertsou1￨U￨NN￨O￨- ,￨L￨,￨O￨- Nick￨U￨NNP￨PERSON￨- Wilson1Email￨U￨NN￨PERSON￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Michael￨U￨NNP￨PERSON￨- Baker1￨U￨NNP￨PERSON￨- ,￨L￨,￨O￨- Peter￨U￨NNP￨PERSON￨- Nelson1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Mick￨U￨NNP￨PERSON￨- G￨U￨NNP￨O￨- Roberts2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 3:38￨L￨CD￨TIME￨- ©￨L￨SYM￨O￨- Sertsou￨U￨FW￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2006Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 26￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 30￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Abstract￨U￨NNP￨O￨- Aim￨U￨NNP￨O￨- To￨U￨TO￨O￨- estimate￨L￨VB￨O￨- the￨L￨DT￨O￨- key￨L￨JJ￨O￨- transmission￨L￨NN￨O￨- parameters￨L￨NNS￨O￨- associated￨L￨VBN￨O￨- with￨L￨IN￨O￨- an￨L￨DT￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- pandemic￨L￨JJ￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨- in￨L￨IN￨O￨- an￨L￨DT￨O￨- institutional￨L￨JJ￨O￨- setting￨L￨NN￨O￨- (￨L￨-LRB-￨O￨- Citation￨U￨NNP￨O￨- )￨L￨-RRB-￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- These￨U￨DT￨O￨- R0￨U￨NN￨O￨- Citation￨U￨NNP￨O￨- influenza￨L￨NN￨CAUSE_OF_DEATH￨A pandemic￨L￨NN￨O￨A and￨L￨CC￨O￨- are￨L￨VBP￨O￨- not￨L￨RB￨O￨- particularly￨L￨RB￨O￨- large￨L￨JJ￨O￨- relative￨L￨JJ￨O￨- to￨L￨TO￨O￨- some￨L￨DT￨O￨- other￨L￨JJ￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +Methodology￨U￨NN￨MISC￨- Open￨U￨VB￨MISC￨- Access￨U￨NN￨MISC￨- Stochastic￨U￨JJ￨MISC￨- modeling￨L￨NN￨O￨- of￨L￨IN￨O￨- empirical￨L￨JJ￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A of￨L￨IN￨O￨- childhood￨L￨NN￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- data￨L￨NNS￨O￨- before￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccinationHelen￨L￨NN￨O￨- Trottier1￨U￨NN￨O￨- ,￨L￨,￨O￨- 3Email￨L￨NN￨O￨- author￨L￨NN￨TITLE￨- ,￨L￨,￨O￨- Pierre￨U￨NNP￨PERSON￨- Philippe1￨U￨NNP￨PERSON￨- and￨L￨CC￨O￨- Roch￨U￨NNP￨O￨- Roy2￨U￨NNP￨O￨- Citation￨U￨NNP￨O￨- 3:9￨L￨CD￨NUMBER￨- ©￨L￨SYM￨O￨- Trottier￨U￨NNP￨O￨- et￨L￨FW￨O￨- al￨L￨FW￨O￨- ;￨L￨:￨O￨- licensee￨L￨NN￨O￨- BioMed￨U￨NNP￨ORGANIZATION￨- Central￨U￨NNP￨ORGANIZATION￨- Ltd.￨U￨NNP￨ORGANIZATION￨- 2006Received￨L￨NNP￨O￨- :￨L￨:￨O￨- 06￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Accepted￨U￨NNP￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- Published￨U￨VBN￨O￨- :￨L￨:￨O￨- 08￨L￨CD￨NUMBER￨- Citation￨U￨NNP￨O￨- AbstractThe￨U￨NNP￨O￨- goal￨L￨NN￨O￨- of￨L￨IN￨O￨- this￨L￨DT￨O￨- paper￨L￨NN￨O￨- is￨L￨VBZ￨O￨- to￨L￨TO￨O￨- analyze￨L￨VB￨O￨- the￨L￨DT￨O￨- stochastic￨L￨JJ￨O￨- dynamics￨L￨NNS￨O￨- of￨L￨IN￨O￨- childhood￨L￨NN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- time￨L￨NN￨O￨- series￨L￨NN￨O￨- .￨L￨.￨O￨- +Canadian￨U￨JJ￨NATIONALITY￨- chronological￨L￨JJ￨O￨- series￨L￨NN￨O￨- of￨L￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- mumps￨L￨NNS￨O￨- ,￨L￨,￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- rubella￨L￨NN￨O￨A ,￨L￨,￨O￨- before￨L￨IN￨O￨- and￨L￨CC￨O￨- after￨L￨IN￨O￨- mass￨L￨NN￨O￨- vaccination￨L￨NN￨O￨- ,￨L￨,￨O￨- are￨L￨VBP￨O￨- analyzed￨L￨VBN￨O￨- to￨L￨TO￨O￨- characterize￨L￨VB￨O￨- the￨L￨DT￨O￨- statistical￨L￨JJ￨O￨- structure￨L￨NN￨O￨- of￨L￨IN￨O￨- these￨L￨DT￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- method￨L￨NN￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- enables￨L￨VBZ￨O￨- the￨L￨DT￨O￨- dependency￨L￨NN￨O￨- structure￨L￨NN￨O￨- embedded￨L￨VBN￨O￨- in￨L￨IN￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A data￨L￨NNS￨O￨- to￨L￨TO￨O￨- be￨L￨VB￨O￨- modeled￨L￨VBN￨O￨- ,￨L￨,￨O￨- has￨L￨VBZ￨O￨- potential￨L￨JJ￨O￨- research￨L￨NN￨O￨- applications￨L￨NNS￨O￨- in￨L￨IN￨O￨- studies￨L￨NNS￨O￨- of￨L￨IN￨O￨- infectious￨L￨JJ￨CAUSE_OF_DEATH￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- dynamics￨L￨NNS￨O￨- .￨L￨.￨O￨- +Despite￨U￨IN￨O￨- the￨L￨DT￨O￨- fact￨L￨NN￨O￨- that￨L￨IN￨O￨- these￨L￨DT￨O￨- infectious￨L￨JJ￨O￨- diseases￨L￨NNS￨CAUSE_OF_DEATH￨- are￨L￨VBP￨O￨- biologically￨L￨RB￨O￨- different￨L￨JJ￨O￨- ,￨L￨,￨O￨- it￨L￨PRP￨O￨- is￨L￨VBZ￨O￨- found￨L￨VBN￨O￨- that￨L￨IN￨O￨- they￨L￨PRP￨O￨- are￨L￨VBP￨O￨- all￨L￨DT￨O￨- represented￨L￨VBN￨O￨- by￨L￨IN￨O￨- simple￨L￨JJ￨O￨- models￨L￨NNS￨O￨- with￨L￨IN￨O￨- the￨L￨DT￨O￨- same￨L￨JJ￨O￨- basic￨L￨JJ￨O￨- statistical￨L￨JJ￨O￨A structure￨L￨NN￨O￨- .￨L￨.￨O￨- +We￨U￨PRP￨O￨- present￨L￨VBP￨DATE￨- an￨L￨DT￨O￨- univariate￨L￨JJ￨O￨- time￨L￨NN￨O￨A series￨L￨NN￨O￨A analysis￨L￨NN￨O￨- of￨L￨IN￨O￨- pertussis￨L￨NN￨CAUSE_OF_DEATH￨- ,￨L￨,￨O￨- mumps￨L￨NNS￨O￨- ,￨L￨,￨O￨- measles￨L￨NNS￨CAUSE_OF_DEATH￨- and￨L￨CC￨O￨- rubella￨L￨NN￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- Box-Jenkins￨U￨NNS￨MISC￨- or￨L￨CC￨MISC￨- AutoRegressive￨U￨NNP￨MISC￨- Integrated￨U￨NNP￨MISC￨- Moving￨U￨VBG￨MISC￨- Average￨U￨JJ￨MISC￨- (￨L￨-LRB-￨O￨- ARIMA￨U￨NN￨O￨- )￨L￨-RRB-￨O￨- modeling￨L￨NN￨O￨- .￨L￨.￨O￨- +Conclusion￨U￨NN￨O￨- For￨U￨IN￨O￨- practical￨L￨JJ￨O￨- emergency￨L￨NN￨O￨- management￨L￨NN￨O￨- of￨L￨IN￨O￨- a￨L￨DT￨O￨- new￨L￨JJ￨O￨- outbreak￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A ,￨L￨,￨O￨- the￨L￨DT￨O￨- ring-like￨L￨JJ￨O￨- application￨L￨NN￨O￨- of￨L￨IN￨O￨- oral￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- is￨L￨VBZ￨O￨- not￨L￨RB￨O￨- a￨L￨DT￨O￨- favourable￨L￨JJ￨O￨- strategy￨L￨NN￨O￨- at￨L￨IN￨O￨- all￨L￨DT￨O￨- .￨L￨.￨O￨- +The￨U￨DT￨O￨- spatial-explicit￨L￨JJ￨O￨- model￨L￨NN￨TITLE￨- is￨L￨VBZ￨O￨- based￨L￨VBN￨O￨- on￨L￨IN￨O￨- fox￨L￨NN￨O￨- group￨L￨NN￨O￨- home-ranges￨L￨NNS￨O￨- ,￨L￨,￨O￨- which￨L￨WDT￨O￨- facilitates￨L￨VBZ￨O￨- the￨L￨DT￨O￨- simulation￨L￨NN￨O￨- of￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A spread￨L￨VBD￨O￨- to￨L￨TO￨O￨- larger￨L￨JJR￨O￨- areas￨L￨NNS￨O￨- relevant￨L￨JJ￨O￨- to￨L￨TO￨O￨- management￨L￨NN￨O￨- .￨L￨.￨O￨- +Worldwide￨U￨NNP￨O￨- efforts￨L￨NNS￨O￨- to￨L￨TO￨O￨- combat￨L￨VB￨O￨- the￨L￨DT￨O￨- disease￨L￨NN￨CAUSE_OF_DEATH￨- by￨L￨IN￨O￨- oral￨L￨JJ￨O￨- vaccination￨L￨NN￨O￨- of￨L￨IN￨O￨- reservoirs￨L￨NNS￨O￨- have￨L￨VBP￨O￨- managed￨L￨VBN￨O￨- to￨L￨TO￨O￨- eradicate￨L￨VB￨O￨- wildlife￨L￨NN￨O￨- rabies￨L￨NNP￨O￨A in￨L￨IN￨O￨- large￨L￨JJ￨O￨- areas￨L￨NNS￨O￨- of￨L￨IN￨O￨- central￨L￨JJ￨O￨- Europe￨U￨NNP￨LOCATION￨- and￨L￨CC￨O￨- North-America￨U￨NNP￨LOCATION￨- .￨L￨.￨O￨- +But￨U￨CC￨O￨- then￨L￨RB￨O￨- as￨L￨IN￨O￨- rabies￨L￨NNP￨O￨A is￨L￨VBZ￨O￨- eliminated￨L￨VBN￨O￨- within￨L￨IN￨O￨- the￨L￨DT￨O￨- circle￨L￨NN￨O￨- area￨L￨NN￨O￨- ,￨L￨,￨O￨- the￨L￨DT￨O￨- respective￨L￨JJ￨O￨- ring￨L￨NN￨O￨- area￨L￨NN￨O￨- fails￨L￨VBZ￨O￨- ,￨L￨,￨O￨- due￨L￨JJ￨O￨- to￨L￨TO￨O￨- the￨L￨DT￨O￨- non-controlled￨L￨JJ￨O￨- inner￨L￨JJ￨O￨- part￨L￨NN￨O￨- .￨L￨.￨O￨- diff --git a/test/key_sentence_extraction_summa_taylor.ipynb b/test/key_sentence_extraction_summa_taylor.ipynb new file mode 100644 index 0000000..c3e4c32 --- /dev/null +++ b/test/key_sentence_extraction_summa_taylor.ipynb @@ -0,0 +1,109 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import os \n", + "import summa\n", + "import json\n", + "\n", + "os.chdir('/Users/taylor_bolt/PycharmProjects/multivac/multivac/data')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Parse Article Json file" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "article_json = json.load(open('cleanedArticles-03042019.json'))\n", + "all_article_text = [ article['text'] for article in article_json.values() ]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Extract Key Sentences w/ TextRank" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from summa.summarizer import summarize\n", + "key_sentences = []\n", + "for count,article in enumerate(all_article_text):\n", + " print('{} out of {} articles'.format(count,len(all_article_text)))\n", + " try:\n", + " summary = summarize(article, split=True)\n", + " key_sentences.append(summary[0:10])\n", + " except ValueError: \n", + " key_sentences.append('No text found for article')\n", + " " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/test/preprocess_First_submitted.py b/test/preprocess_First_submitted.py new file mode 100644 index 0000000..99e8ca9 --- /dev/null +++ b/test/preprocess_First_submitted.py @@ -0,0 +1,181 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Tue Jul 30 15:27:25 2019 + +@author: domonique_hodge +""" + +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Thu Mar 28 17:31:50 2019 + +@author: domonique_hodge +""" + +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Wed Jan 2 11:21:36 2019 +@author: domonique_hodge +""" + +""" +This code preprocess pdfs for the QG-Net (Query Generation) algorithm +""" + +import os +os.environ["CORENLP_HOME"] = r'Users/domonique_hodge/Downloads/stanford-corenlp-full-2018-10-05' + +import corenlp +import warnings +import logging +import os +import json +from sklearn.feature_extraction.text import TfidfVectorizer +from sortedcontainers import SortedDict + + +import logging +import os +import json +from sklearn.feature_extraction.text import TfidfVectorizer +from sortedcontainers import SortedDict + + +def preprocess_pdf(abstract, features, tfidf, num_sentences=5): + ''' + Chooses top `num_sentences` based on the sum of their terms' TF-IDF scores, + and then picks the word/term in each sentence with the top TF-IDF score as + the "answer." + ''' + document = nlp.annotate(abstract) + term_scores = [(w,s) for w, s in zip(tfidf.get_feature_names(), features.reshape(-1)) if s > 0] + sent_scores = SortedDict() + + for i, sentence in enumerate(document['sentences']): + score = sum([s for w, s in term_scores if w in str(sentence)]) + sent_scores[score] = i + + warnings.filterwarnings('ignore', category=UserWarning, append=True) + + for i in reversed(sent_scores.values()): + out_str = '' + if i >= num_sentences: + break + + sentence = document['sentences'][i] + str_sent = ' '.join([t['originalText'] for t in sentence['tokens']]) + top_term = sorted([(w,s) for w, s in term_scores if w in str_sent], + key=lambda x: x[1], reverse=True)[0][0] + top_term = top_term.split() + + for i, token in enumerate(sentence['tokens']): + tok_text = token['originalText'] + + if tok_text[0].isupper(): + low = 'U' + else: + low = 'L' + + if len(top_term) > 0: + ans = 'A' + else: + ans = '-' + + for j, t in enumerate(top_term): + if sentence['tokens'][i+j]['originalText'] != top_term[j]: + ans = '-' + break + + if ans =='A' and len(top_term) > 0: + del top_term[0] + #updated here + out_str += "{}￨{}￨{}￨{}￨{} ".format(tok_text,low,token['pos'],token['ner'],ans) + + if '￨A' in out_str: + print(out_str) + + + + + +def load_data(jsonPath, picklePath = None): + """Load data - if picklePath is specified, load the pickle. Else, try json file. + This returns the JSON file as well as a list of document texts + """ + if picklePath is not None: + l_docs = pickle.load(open(picklePath, "rb" )) + else: + + ## Read JSON data into the datastore variable - this comes from Peter and Domonique's effort. Don + with open(jsonPath, 'r') as f: + datastore = json.load(f) + + ## These were some bad files - nothing substantive in them, or they were retrieved in bad format + for e in ['1805.10677v1', '0911.5378v1']: + if e in datastore: + del datastore[e] + + ## Extract texts + l_docs = [value['text'] for key,value in list(datastore.items())[0:] if value['text'] ] + + print('# of documents: ', len(l_docs)) + + return datastore, l_docs + + +def create_tf_idf(docs, writeFile=True, pathToFolders=''): + """ Creates a TF-IDF matrix of terms in the corpus and saves this to disk + as a sparse matrix in the data/processed folder when writeFile=True and + pathToFolders is provided. + """ + + tfidf = TfidfVectorizer(sublinear_tf=True, + min_df=10, + norm=None, + ngram_range=(1, 3), + stop_words='english', + use_idf=True, + smooth_idf=True) + + features = tfidf.fit_transform(docs) + + if writeFile: + if len(pathToFolders) == 0: + pathToFolders = settings.processed_dir + + with open(pathToFolders / 'multivac_tfidf.pkl', 'wb') as f: + pickle.dump({'features': features, 'tfidf': tfidf}, f) + + return True + else: + return features, tfidf + + +# #################### +# +# Substitute this hard-coded path for a path passed during the automated +# pre-processing. +# +# #################### + +jsonObj, allDocs = load_data("/Users/domonique_hodge/Documents/External Clients/DARPA/cleanedArticles-03042019.json") +abstracts = [] + +for value in jsonObj.values(): + if "summary" in value['metadata']: + abstracts.append(value['metadata']["summary"]) + elif "abstract" in value['metadata']: + abstracts.append(value['metadata']["abstract"]) + +nlp = corenlp.CoreNLPClient(output_format='json', properties={ + 'timeout': '50000'}) + +# Once we've determined the proper filepath to output, we can change +# this call to write the files out to disk +features, tfidf = create_tf_idf(abstracts, False) + +for i, abstract in enumerate(abstracts): + preprocess_pdf(abstract, features[i,:].toarray(), tfidf) \ No newline at end of file diff --git a/test/preprocess_keysentences.py b/test/preprocess_keysentences.py new file mode 100644 index 0000000..fce28ab --- /dev/null +++ b/test/preprocess_keysentences.py @@ -0,0 +1,189 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Tue Jul 30 15:27:25 2019 + +@author: domonique_hodge +""" + +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Thu Mar 28 17:31:50 2019 + +@author: domonique_hodge +""" + +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Wed Jan 2 11:21:36 2019 +@author: domonique_hodge +""" + +""" +This code preprocess pdfs for the QG-Net (Query Generation) algorithm +""" + +import os +os.environ["CORENLP_HOME"] = r'Users/domonique_hodge/Downloads/stanford-corenlp-full-2018-10-05' + +import corenlp +import warnings +import logging +import os +import json +from sklearn.feature_extraction.text import TfidfVectorizer +from sortedcontainers import SortedDict +import pickle + + +import logging +import os +import json +from sklearn.feature_extraction.text import TfidfVectorizer +from sortedcontainers import SortedDict + + +def preprocess_pdf(abstract, features, tfidf, num_sentences=5): + ''' + Chooses top `num_sentences` based on the sum of their terms' TF-IDF scores, + and then picks the word/term in each sentence with the top TF-IDF score as + the "answer." + ''' + document = nlp.annotate(abstract) + term_scores = [(w,s) for w, s in zip(tfidf.get_feature_names(), features.reshape(-1)) if s > 0] + sent_scores = SortedDict() + + for i, sentence in enumerate(document['sentences']): + score = sum([s for w, s in term_scores if w in str(sentence)]) + sent_scores[score] = i + + warnings.filterwarnings('ignore', category=UserWarning, append=True) + + try: + for i in reversed(sent_scores.values()): + out_str = '' + if i >= num_sentences: + break + + sentence = document['sentences'][i] + str_sent = ' '.join([t['originalText'] for t in sentence['tokens']]) + + + + top_term = sorted([(w,s) for w, s in term_scores if w in str_sent], + key=lambda x: x[1], reverse=True)[0][0] + top_term = top_term.split() + + for i, token in enumerate(sentence['tokens']): + tok_text = token['originalText'] + + if tok_text[0].isupper(): + low = 'U' + + else: + low = 'L' + + if len(top_term) > 0: + ans = 'A' + + else: + ans = '-' + + for j, t in enumerate(top_term): + + if sentence['tokens'][i+j]['originalText'] != top_term[j]: + ans = '-' + break + + if ans =='A' and len(top_term) > 0: + del top_term[0] + #updated here + out_str += "{}￨{}￨{}￨{}￨{} ".format(tok_text,low,token['pos'],token['ner'],ans) + + if '￨A' in out_str: + print(out_str) + except: + pass + + + + + +def load_data(jsonPath, picklePath = None): + """Load data - if picklePath is specified, load the pickle. Else, try json file. + This returns the JSON file as well as a list of document texts + """ + if picklePath is not None: + l_docs = pickle.load(open(picklePath, "rb" )) + else: + + ## Read JSON data into the datastore variable - this comes from Peter and Domonique's effort. Don + with open(jsonPath, 'r') as f: + datastore = json.load(f) + + ## These were some bad files - nothing substantive in them, or they were retrieved in bad format + for e in ['1805.10677v1', '0911.5378v1']: + if e in datastore: + del datastore[e] + + ## Extract texts + l_docs = [value['text'] for key,value in list(datastore.items())[0:] if value['text'] ] + + print('# of documents: ', len(l_docs)) + + return datastore, l_docs + + +def create_tf_idf(docs, writeFile=True, pathToFolders=''): + """ Creates a TF-IDF matrix of terms in the corpus and saves this to disk + as a sparse matrix in the data/processed folder when writeFile=True and + pathToFolders is provided. + """ + + tfidf = TfidfVectorizer(sublinear_tf=True, + min_df=10, + norm=None, + ngram_range=(1, 3), + stop_words='english', + use_idf=True, + smooth_idf=True) + + features = tfidf.fit_transform(docs) + + if writeFile: + if len(pathToFolders) == 0: + pathToFolders = settings.processed_dir + + with open(pathToFolders / 'multivac_tfidf.pkl', 'wb') as f: + pickle.dump({'features': features, 'tfidf': tfidf}, f) + + return True + else: + return features, tfidf + + +# #################### +# +# Substitute this hard-coded path for a path passed during the automated +# pre-processing. +# +# #################### +keysent = pickle.load( open( "/Users/domonique_hodge/Documents/External Clients/DARPA/QG Net update/key_sentences.pickle", "rb" ) ) + +topsent = [] + +for k in range(0,len(keysent)): + topsent.append(' '.join(keysent[k])) + + +nlp = corenlp.CoreNLPClient(output_format='json', properties={ + 'timeout': '50000'}) + +# Once we've determined the proper filepath to output, we can change +# this call to write the files out to disk +features, tfidf = create_tf_idf(topsent, False) + +for i, abstract in enumerate(topsent): + preprocess_pdf(abstract, features[i,:].toarray(), tfidf) \ No newline at end of file diff --git a/test/preprocessing_pdf.py b/test/preprocessing_pdf.py new file mode 100644 index 0000000..da0cbc8 --- /dev/null +++ b/test/preprocessing_pdf.py @@ -0,0 +1,111 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Tue Jul 23 13:27:52 2019 + +@author: domonique_hodge +""" + +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +import pickle +import warnings + +from sklearn.feature_extraction.text import TfidfVectorizer +from sortedcontainers import SortedDict + +from multivac import settings + + +def create_tf_idf(docs, writeFile=True, pathToFolders=''): + """ Creates a TF-IDF matrix of terms in the corpus and saves this to disk + as a sparse matrix in the data/processed folder when writeFile=True and + pathToFolders is provided. + """ + + tfidf = TfidfVectorizer(sublinear_tf=True, + min_df=10, + norm=None, + ngram_range=(1, 3), + stop_words='english', + use_idf=True, + smooth_idf=True) + + features = tfidf.fit_transform(docs) + + if writeFile: + if len(pathToFolders) == 0: + pathToFolders = settings.processed_dir + + with open(pathToFolders / 'multivac_tfidf.pkl', 'wb') as f: + pickle.dump({'features': features, 'tfidf': tfidf}, f) + + return True + else: + return features, tfidf + + +def preprocess_pdf(abstract, features, tfidf, nlp, num_sentences=5): + ''' + Chooses top `num_sentences` based on the sum of their terms' TF-IDF scores, + and then picks the word/term in each sentence with the top TF-IDF score as + the "answer." + ''' + + + document = nlp.annotate(abstract) + term_scores = [(w,s) for w, s in zip(tfidf.get_feature_names(), + features.reshape(-1)) if s > 0] + sent_scores = SortedDict() + + for i, sentence in enumerate(document['sentences']): + score = sum([s for w, s in term_scores if w in str(sentence)]) + sent_scores[score] = i + + warnings.filterwarnings('ignore', category=UserWarning, append=True) + + output_vec = [] + for i in reversed(sent_scores.values()): + out_str = '' + if i >= num_sentences: + break + + sentence = document['sentences'][i] + str_sent = ' '.join([t['originalText'] for t in sentence['tokens']]) + top_term = sorted([(w,s) for w, s in term_scores if w in str_sent], + key=lambda x: x[1], reverse=True)[0][0] + top_term = top_term.split() + + for i, token in enumerate(sentence['tokens']): + tok_text = token['originalText'] + + if tok_text[0].isupper(): + low = 'U' + else: + low = 'L' + + if len(top_term) > 0: + ans = 'A' + else: + ans = '-' + + for j, t in enumerate(top_term): + if sentence['tokens'][i+j]['originalText'] != top_term[j]: + ans = '-' + break + + if ans =='A' and len(top_term) > 0: + del top_term[0] + + out_str += "{}￨{}￨{}￨{}￨{} ".format(tok_text, low, token['pos'], + token['ner'], ans) + + if '￨A' in out_str: + output_vec.append(out_str[:-1]) + + with open('{}/test/testinput/input.txt'.format(settings.qgnet_dir), + 'w') as f: + f.write('\n'.join(output_vec)) + + return None +